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Boston Public Library
PURCHASED FROM THE
James Lyman Whitney
MEMORIAL FUND ESTABLISHED BY
James Lyman Whitney
BIBLIOGRAPHER AND SOMETIME LIBRARIAN
LETTERS
OF
EULER
ON DIFFERENT SUBJECTS
IN
PHYSICS AND PHILOSOPHY.
ADDRESSED TO
A GERMAN PRINCESS.
TRANSLATED FROM THE TRENCH BY
HENRY HUNTER, D.D.
WITH
ORIGINAL NOTES,
And a Glojfary of Foreign and Scientific Terms:
4beconD €irition.
IN TWO VOLUMES. VOL. II.
EonDon :
PRINTED FOR MURRAY AND HIGHLEY ; J. CUTHELL ; VERNOR AND HOOD; LONGMAN AND REES ; WYNN AND SCHOLEY ; G. CAWTHORNJ J. HARDING; AND J. MAWMAN,
1802.
..y- x
Salisburj'-S'jiiwe.
CONTENTS
OF THE
SECOND VOLUME.
Letter Page
I. • /CONTINUATION of the Subjea, and of
V.^ Miftakes in the Knowledge of Truth I
II. Firfr Clafs of known Truths. Conviction that
Things exift externally correfponding to the Ideas reprefented by the Senfes. Objection of the Pyrrhonifts. Reply.' - 5
III. Another Objection of the Fyrrhonifts againft the
Certainty of Truths perceived by the Senfes. Reply ; and Precautions for attaining Affur- ance of fenfible Truths 8
IV. Of demonstrative, phyfical, and particularly of
/ moral Certainty - - 12
V. Remarks that the Senfes contribute to the Increafe
of Knowledge ; and Precautions for acquiring the Certainty of Hiftorical Truths - 16
VI. Whether the Effence of Bodies be known by us 20
VII. The true Notion of Extenfion - 24
VIII. Divisibility of Extenfion in infinitum - 27
IX. Whether this Divisibility in infinitum takes Place
in exifting Bodies r - - 31
X. Of Monads - - 35
XI. Reflections on Divisibility in infinitum, and on
Monads • - "39
Vol, II. A XII. Reply
v. CONTENTS.
Letter , j
XII. Reply to the Objections of the Monadifls to
Divifibility in infinitum <-
XIII. Principle of xhzfatisfyingReafon, the ftrongeft
Support of the Monadifts
XIV. Another Argument of the Monadifts, derived
from the Principle of the fufficient Reafon. Absurdities refulting from it
XV. Reflections on the Syftem of Monads XVT. Continuation
XVII. Conclufion of Reflections on this Syftem
XVIII. Elucidation refpecYing the Nature of Colours
XIX. Reflections on the Analogy between Colours
and Sounds
XX. Continuation
XXI. How opaque Bodies are rendered vifible
XXII. The Wonders of the Human Voice
XXIII. A Summary of the principal Phenomena of
Electricity
XXIV. The true Principle of Nature, on which are
founded all the Phenomena of Electricity
XXV. Continuation. Different Nature of Bodies
relatively to Electricity
XXVI. On the fame Subject
XXVII. Of pofijive and negative Electricity. Expla-
nation of the Phenomenon of Attraction
XXVIII. On the fame Subjeft
XXIX. On the electric Atmofphere
XXX. Communication of Electricity to a Bar of
Iron, by Means of a Globe of Glafs XXXL Ele&rifation of Men and Animals
XXXII. Diftin&ive Character of the two Species of
Electricity - . -
XXXIII. How the fame Globe of Glafs may furnifh,
at once, the two Species of Electricity
XXXIV. The
'age
43
46
5°
53
57 61
65
69
73
76
79
83
87
91 95
99
103 106
in "5
119 122
CONTENTS. Vii
Letter Page
XXX IV. The Leyden Experiment - 125
XXXV. Reflections on the Caufe and Nature of
Eledtricity, and on other Means proper to produce it - - - 129
XXXVI. Nature of Thunder : Explanations of the
ancient Philofophers, and of D ef cartes : Refemblance of the Phenomena of Thun- der, and thofe of Electricity - 133
XXXVII. Explanation of the Phenomena of Lightning
and Thunder - - 136
XXXVIII. Continuation - - 140
XXXIX. The Poffi'uility of preventing, and of avert-
ing the Effects of Thunder - 143
XL. On the celebrated Problem of the Longi-
tude : General Defcription of the Earth, of it's Axis, it's two Poles, and the Equa- tor 150
XLI. Of the Magnitude of the Earth; of Men-?
dians, and the fhorteft Road from Place to Place - - 154
XLII. Of Latitude, and it's Influence on the Sea-
fons, and the Length of the Day 159
XLIII. . Of Parallels, of the Firft Meridian, and of
Longitude - - 163
XLIV. Choice of the Firft Meridian - 167
XLV. Method of determining the Latitude, or the
Elevation of the Pole - 171
XLVI. Knowledge of the Longitude, from a Calcu- lation of the Direction, and of the Space pafled through ■ •■■«. - 176
XLVII. Continuation. Defects of this Method 180
XLVIII. Second Method of determining the Longi- tude, by means of an exacl: Time-Piece 184
XLIX. Continuation, and farther Elucidations 188
K% L. Eclipfes
V1U
Letter L.
LI.
LTI. LIII.
LIV.
LV.
LVI,
LVII.
LVIIL
CONTENTS.
Page
lix?
LX.
Lxi.
LXII. LXIII. LXIV. J.XV.
Eclipfes of the Moon, a third Method of find..
ing the Longitude Obfervation of the Eclipfes of the Satellites of Jupiter, a fourth Method of finding the Longitude - -
The Motion of the Moon, a fifth Method Advantages of this laft Method ; it's Degree of Precifion - r
On the Mariner's Compafs, and the Proper- ties of the Magnetic Needle -
Declination of the Compafs, and Manner of obferving it -
Difference in the Declination of the Com- pafs at the fame Place
Chart of Declinations ; Method of employ- ing it for the Difcovery of the Longitude
Why does the Magnetic Needle affect, in every Place of the Earth, a certain Direct tion, differing in different Places ; and for what Reafon does it change, with Time, at the fame Place ?
Elucidations refpedYing the Caufe and Varia- tion of the Declination, of Magnetic Nee- dles -
Inclination of Magnetic Needles
True Magnetic Direction ; fubtile Matter which produces the Magnetic Power
Nature of the Magnetic Matter, and of it's rapid Current. Magnetic Canals
Magnetic Vortex. Adtion of Magnets upon each other .«
Nature of Iron and Steel. Manner of com- municating ro them the Magnetic Force Action of Lqadftpnes on Iron. Phenomenon
pbfervable
"93
197
201
205 209. 214 217 222
226
230 234
239
243
247
25*
CONTENTS.
Letter
LXVI.
Lxvir.
LXVIII.
Page
255
260 264.
268
LXIX. LXX,
LXXL JLXXII,
iXXIII.
LXXIV. LXXV.
LXXVI.
LXXVII.
LXXVIII
LXXIX.
LXXX.
LXXXI.
obfervable on placing pieces of Iron near a Loadftone Arming of Loadftones Action and Force of armed Loadffones The Manner of communicating to Steel the Magnetic Force, and of magnetizing Needles for the Compafs: the Simple Touch, it's Defeats ; means of remedying thefe -
On the Double Touch. Means of preferving
the Magnetic Matter in magnetized Bars 273 The Method of communicating to Bars of Steel a very great Magnetic Force, by means of other Bars which have it in a very inferior degree ConftrucYion of artificial Magnets in form
of a Horfe-fhoe •»
On Dioptricks ; Inftruments which that Science fupplies : ofTelefcopes and Mi- crofcopes. , Different Figures given to Glaffes or Lenfes Difference of Lenfes with refpecr. to the curve of their furfaces. Distribution of Lenfes into three claffes ■*• 290
Effe6l of Convex Lenfes - 204
The fame Subject : Difiance of the Focus
of Convex Lenfes Difiance of the Image of Objects Magnitude of Images , Burning Glaffes The Camera Obfcura' Reflections on the Reprefentation in the
27S 2S2
286
298
302 306 310
3l3
Camera Obfcura
;iS
Of the Magic Lantern, and Solar Microfcope 322 6 LXXXII. Ufe
Letter
LXXXII.
lxxxiii.
LXXXIV.
LXXXV.
LXXXVI.
LXXXVII.
LXXXVIII LXXXIX. XC. XCI,
XCII.
XCIII.
XCIV.
xcv.
342
345 350
353
XCVI. XCVII.
XCVIII.
CONTENTS.
• Page Ufe and Effect; of a fimple Convex Lens 326 Ufe and/Effect of a Concave Lens 330
Of apparent Magnitude, of the Vifual
Angle, and of Microfcopes in general 334 Eflimation of the Magnitude of Objects
viewed through the Microfcope 338
Fundamental Proportion for the conftruc- tion of fimple Microfcopes. Plan of fome fimple Microfcopes Bounds and Defects of the fimple Micro
fcope On Telefcopes and their Effect: Of Pocket-Glaffes On the magnifying power of Pocket Glaffes 357 Defects of Pocket- Glaffes. Of the appa- rent Field - - 362 Determination of the apparent Field for
Pocket-Glaffes •» 367
Aftronomical Telefcopes, and their magni- fying Powers - " - 371 Of the apparent Field, and the Place of
the Eye - - 37.4
Determination of the magnifying Power of Aftronomical Telefcopes, and the con- ftruction of, a Telefcope which fhall magnify Objects a given Number of Times - - 379
Degree of Clearnefs - 383
Aperture of Objective Lenfes 387
On Diftinctnefs in the Expreffion : On the Space of Diffufion occafioned by the Aperture of Objective Lenfes, and con-. Jidered as the fir ft Source of want of Dif- tinctnefs in the Reprefentation
XCJX. Dimi
39?
CONTENTS. xi
Letter Pag<
XCIX. Diminution of the Aperture of Lenfes, and
other Means of leffening the Space of Diffu- fion, till it is reduced to nothing 396
C. Of Compound Objective Lenfes • 401
CI. Formation of Simple Objective Lenfes 405
CII. Second Source of Defect, as to Diftinctnefs of Reprefentation by the Telefcope. Different Refrangibility of Rays - 410
CIII. Means of remedying this Defect by compound
Objectives - - 414
CIV. Other Means more practicable - 418
CV. Recapitulation of the Qualities of a good Tele- fcope - . - - 422 CVI. Terreftrial Telefcopes with four Lenfes 426 CVII. Arrangement of Lenfes in Terreftrial Telefcopes 430 CVIII. Precautions to be obferved in the conftruction of Telefcopes. Neceffity of blackening the infide of Tubes. Diaphragms - 433 CIX. In what maimer Telefcopes reprefent the Moon, the Planets, the Sun, and the fixed , Stars. Why thefe la ft appear (mailer through the Telefcope than to the naked Eye. Calcula- tion of the Diftance of the fixed Stars, from a Comparifon of their apparent Magnitude with that of the Sun - - 437 CX. Why do the Moon and the Sun appear greater at rifing and fetting, than at a certain eleva- tion? Difficulties attending the Solution of this Phenomenon - - 441 CXI. Reflections on the Queftion reflecting the Moon's apparent Magnitude: Progrefs to- ward a Solution of the Difficulty. Abfurd Explanations - - aa± CXII. An Attempt toward the true Explanation of the
Pheno-
XII
Letter
CXIII. CXIV.
cxv.
CXVI. CXVII.
CXVIII CXIX.
CONTENTS;
Page
Phenomenon : the Moon appears more dis- tant when in the Horizon, than when at a great Elevation - - 448
The Heavens appear under the Form of an Arch flattened toward the Zenith 452
Reafon affigned for the Faintnefs of the Light of Heavenly Bodies in the Horizon 456
Illufion refpefting the Diftance of Objects, and the Diminution of Luftre - 463
On the Azure Colour of the Heavens 463
What the Appearance would be, were the Air perfectly tranfparen-t - - 467
Refra£bon of Rays of Light in the Atmofphere, aod it's Effects. Of the Twilight. Of the apparent riling and fetting of the Heavenly Bodies - - - ■ - 471
The Stars appear at a greater Elevation than they are. Table of Refraction -. 475
LETTERS
letters
ON
DIFFERENT SUBJECTS
IN
PHYSICS AND PHILOSOPHY.
LETTER I;
Continuation of the Subjecl, and of Mi/lakes in the Knowledge of Truth. Madam,
THE three claffes of truths which I have how un- folded, are the only fources of all our know- ledge ; all being derived from our own experiences from reafoning, or from the report of others.
It is not eafy to determine which of thefe three fources contributes moil to the increafe of know- ledge. Adam and Eve mull have derived theirs chiefly from the two firft j God, however, revealed many things to them, the knowledge of which is to be referred to the third fource, as neither their own experience, nor their powers of reafoning, could have conducted them fo far.
Without recurring to a period fo remote, we are fumciently convinced, that if we were determined to believe nothing of what we hear from others, or read
Vol. II. B in
2 MISTAKES IN THE
in their writings, we fhould be in a ftate of almofl total ignorance. It is very far, however, from being our duty to believe every thing that is faid, or that we read. We ought conftantly to employ Our dis- cerning faculties, not only with refpect to truths of the third ciafs, but like wife of the two others.
We are fo liable to fuffer ourfelves to be dazzled by the fenfes, and to nliftake in our reafonings, that the very fources laid open by the Creator for the difcovery of truth, very frequently plunge us into error. Notions of the third clafs, therefore, ought not," in reafon, to fall under fufpicion, any more than fuch as belong to the other two. We ought, there- fore, to be equally on our guard againft deception, whatever be the clafs to which the notion belongs ; for we find as many inftances of error in the firft and fecond clafTes as in the third. The fame thing holds with regard to the certainty of the particular articles of knowledge which thefe three fources fup- ply ; and it cannot be affirmed that the truths of any one order have a furer foundation than thofe of another. Each clafs is liable to errors, by which we may be milled ; but there are likewife precautions which, carefully obferved, furniih us with nearly the fame degree of conviction. I do not know whether you are more thoroughly convinced of this truth, that two triangles which have the fame bafe, and the fame height, are equal to one another, than of this, that the Ruffians have been at Berlin ; though the former is founded on a chain of accurate
rea foiling,
KNOWLEDGE OF TRUTH. g
)reafoning, whereas the latter depends entirely on the Veracity of your informer*
Refpe&ing the truths, therefore, of each of thefe clafles, we muft reft fatisfied with fuch proofs as correfpond to their nature j and it would be ridicu- lous to infift upon a geometrical demonftration of the truths of experience, or of hiftory. This is ufu- ally the fault of thofe who make a bad ufe of their penetration in intellectual truths, to require mathe- matical demonftration, in proof of all the truths of religion, a great part of which belongs to the third clafs.
There are perfons determined to believe and ad- mit nothing but what they fee and touch 5 what- ever you would prove to them by reafoning, be it ever fo folid, they are difpofed to fufpeft, unlefs you place it before their eyes. Chymifts, anatomifts, v and natural philofophers, who employ themfelves wholly in making experiments, are moft chargeable with this fault. Every thing that the one cannot melt in his crucible, or the other dkTect with his fcalpel, they reject as unfounded. To no purpofe you would fpeak to them of the qualities and nature of the foul j they admit nothing but what ftrikes the fenfes.
Thus, the particular kind of ftudy to which every one is addicted, has fuch a powerful influence on his manner of thinking, that the natural philofopher and chymift will have nothing but experiments, and the geometrician and logician nothing but argu=> ments j which conftitute, however, proofs entirely
B 2 different,
4 MISTAKES, &C.
different, the one attached to the firft clafs, the other to the fecond, which ought always to be carefully diilinguiihed, according to the nature of the objects.
But can it be pofiible that perfons fhould exift, who, wholly abforbed in purfuits pertaining to the third clafs, call only for proofs derived from that fource ? I have known fome of this defcription, who, totally devoted to the fludy of hiftory and antiquity, would admit nothing as true, but what you could prove by hiftory, or the authority of fome ancient author. They perfectly agree with you, refpecting the truth of the proportions of Euclid, but merely on the authority of that author, without paying any attention to the demonftrations by which he fup- ports them ; they even imagine that the contrary of thefe proportions might be true, if the ancient geometricians had thought proper to maintain it.
This is a fource of error which retards many in the purfuit of truth j but we find it rather among the learned, than among thofe who are beginning to apply themfelves to the ftudy of the fciences. We ought to have no _ predilection in favour of any one of the three fpecies of proofs which each clafs re- quires ; and provided they are fufficient, in their kind, we are bound to admit them.
/ have fcen or felt, is the proof of the firft clafs. I can demonftrate it, is that of the fecond ; we like- wife fay, / know it is fo. Finally, / receive it on the tejiimony of perfons worthy of credit, or / believe it on folid grounds, is the proof of the third clafs.
Aftb April, 1761,
LETTER
OBJECTION OF THE PYRRHONISTS. $
LETTER II.
Firji Clafs of known Truths, Convicllon that Things exifi externally correfponding to the Ideas rcprefented by the Senfes. Objection of the Pyrrhoriifis. Reply.
TI7E include in the firft clafs of known truths, * * thofe which we acquire immediately by means of the fenfes. I have already remarked, that they not only fupply the foul with certain reprefentations relative to the changes produced in a part of the brain ; but that they excite there a conviction of the real exiftence of things external, correfponding to the ideas which the fenfes prefent to us.
The foul is frequently compared to a man {hut up in a dark room, in which the images of external ob- jects are reprefented on the wall by means of a glafs. This comparifon is tolerably juft, as far as it refpecfcs the man looking at the images on the wall : for this act is fuhicientiy iimilar to that of the foul, contem- plating the impreffions made in the brain ; but the comparifon appears to me extremely defective, as far as it refpects the conviction, that the objects, which occafton thefe images, really exift.
The man in the dark room will immediately fuf* peel the exiftence of thefe objects j and, if he has no doubt about the matter, it is becaufe he has been out of doors, and has feen them ; befides this, knowing the nature of his glafs, he is allured, that nothing can be reprefented on the wall but the images of the ob- jects which are without the chamber before the glafs.
B 3 But
6 OBJECTION OF THE PYRRHONISTS.
But this is not the cafe with the foul ; it has never quitted its place of relidence to contemplate the ob- jects themfelves : and it knows ftill lefs the conftruc- tion of the fenfitive organs, and the nerves which terminate in the brain. It is, neverthelefs, much more powerfully convinced of the real exiftence of objects, than our man in the dark room poffibly can be. I am apprehenfive of no objection on the fubject, the thing being too clear of itfelf to admit any, though we do not know the true foundation of it. No one ever entertained any doubt about it, except certain viiionaries, who have bewildered themfelves in their, own reveries. Though they fay, that they doubt the exiftence of external objects, they entertain no fuch doubt in fact. ; for why would they have affirmed it, unlefs they had believed the exiftence of other men, to whom they wifhed to communicate their extrava- gant opinions ?
This conviction, refpecting the exiftence of the, things whofe images the fenfes reprefent, appears not only in men of every age and condition, but likewife in all animals. The dog which barks at me has no doubt of my exiftence, though his foul perceives but a flight image of my perfon. Hence I conclude, that this conviction is eiTentially connected with our fen- fationsa and that the truths which the fenfes, convey to us 3 are as well founded as the moil undoubted truths of geometry.
Without this conviction no human fociety could fubfift, for we.fhould be continually falling into the greateft ahfurclities, and the groffeft contradictions.
Were
OBJECTION OF THE PYRRHONISTS. 7
Were the peafantry to dream of doubting about the exiftence of their bailiff, or foldiers about that of their officers, into what confufion mould we be plunged! fuch abfurdities are entertained only by philofophers ; any other giving himfelf up to them, would be confidered as having loft his reafon. Let us, then, acknowledge this convictiorf as one of the principal laws of nature, and that it is complete, though we are abfolutely ignorant of its true reafons, and very far from being able to explain them in an intelligible manner.
However important this reflection may be, it is by no means, however, exempted from difficulties ; but were they ever fo great, and though it might be impoffible for us to folve them, they do no$ in the fmalleft degree affect, the truth which I have juft eftablifhed, and- which we ought to confider as the molt folid foundation of human knowledge.
It muft be allowed, that our fenfes fometimes de- ceive us ; and hence it is that thofe fubtile philofo- phers, who value themfelves on doubting o£ every thing, deduce the confequence, that we ought never to depend on Our fenfes. I have perhaps often er than once met an unknown perfon in the flreet, whom I miftook for an acquaintance : as I was de- ceived in that inftance, nothing prevents my being always deceived ; and I am, therefore, never allured, that the perfon to whom I fpeak is in reality the one I imagine.
Were I to go to Magdeburg, and to prefent my- ■ felf to your Highiiefs, I ought always to be appre-
B 4 heniive
8 ANOTHER OBJECTION OF
henfive of grofsly miitaking : nay, perhaps, I mould not be at Magdeburg, for there are initances of a man's fometimes taking one city for another. It is even poffible I may never have had the happinefs of feeing you, but was always under the power of de- lufion, when I thought myfelf to be enjoying that felicity.
Such are the natural confequences refulting from the fentiments of certain philofophers ; and you muft be abundantly fenfible, that ^hey not only lead to manifeft abfurdity, but have a tendency to diffolve all the bands of fociety,
7 th April, 1 76 1,
LETTER III.
Another Objection of the Pyrrhonifts againjl the Certainty of Truths perceived by the Senfes. Reply ; and Pre- cautions for attaining Ajfurance of fenfible Truths.
fT^HQUGrH the objection raifed againft the cer- -"- tainty of truths perceived by the fenfes, of which I have been fpe'aking, may appear mfficiently powerful, attempts have been made to give it addi- tional fupport from the well-known maxim, that we ought never to truft him who has once deceived us. A fingle example, therefore, of miftake in the. fenfes, is fufficient to deftroy all their credit. If this objection is well-founded, it muft be admitted, that human fociety is, of courfe, completely fubverted. By way of reply, I remark, that the two other
fources
THE PYRRHONISTS. 9
iburces of knowledge are fubject to difficulties of a fimilar nature, nay perhaps ftill more formidable. How often are our reafonings erroneous ? I venture to affirm, that we are much more frequently de- ceived by thefe, than by our fenfes. But does it follow, that our reafonings are always fallacious, and that we can have no dependance on any truth difco- vered to us by the underilanding? It muil be a mat- ter of doubt, then, whether two and two make four, or whether the three angles of a triangle be equal to two right angles j it would even be ridiculous to pre- tend that this mould pafs for truth. Though, there- fore, men may have frequently reafoned inconclu- lively, it would be moil abfurd to infer, that there are not many intellectual truths, of which we have the moil complete conviction.
The fame remark applies to the third fource of human knowledge, which is unqueilionably the moil fubject to error. How often have we been deceived by a groundlefs , rumour, or falfe report reflecting certain events ? And who would be fo weak as to believe all that gazetteers and hiftorians have writ- ten ? At the fame time, whoever ihould think of maintaining that every thing related or written by others is falfe, would undoubtedly fall into greater abfurditiesjthan the perfon who believed every thing. Accordingly, notwithstanding fo many groundlefs reports and falfe teftimonies, we are perfectly allured of the truth of numberlefs facts, of which we have no evidence but teflimony.
There are certain characters which enable us to
diflinguiih
SO ANOTHER OBJECTION OF
diftinguifh truth, and each of the three fources has characters peculiar to itfelf. When my eyes have deceived me, in miftaking one man for another, I prefently difcovered my error ; it is evident, there- fore, that precautions may be ufed for the preven- tion of error. If there were not, it would be im- pollible ever to perceive that we had been deceived. Thofe, then, who maintain that we fo often deceive ourfelves, are obliged to admit, that it is poffible for us to perceive we have been deceived, or they muft acknowledge that they themfelves are deceived when they charge us with error.
It is remarkable, that truth is fo we'll eftablifhed, that the moft violent propenfity to doubt of every thing, muft come to this, in fpite of itfelf. There- fore, as logick prefcribes rules for juft reafoning, the obfervance of which will feture us from error, where intellectual truth is concerned; there are likewife certain rules, as well for the iirft fource, that of our fenfes, as for the third, that of belief.
The rules of the firfl are fo natural to us, that all men, the moft ftupid not excepted, underftand and practife them much better than the greateft fcholars are able to defcribe them. Though it may be eafy fometimes to confound a clown, yet when the hail deftroys his crop, or the thunder breaks upon his cottage, the moft ingenious phiiofopher will never perfuade him that it was a mere illufion ; and every man of fenfe muft admit that the country-fellow is in the right, and that he is not always the dupe of the fallaciouftiefs of his fenfes. The phiiofopher may i be
THE PYRRHONISTS. II
be able, perhaps, to perplex him to fuch a degree that he fhall be unable to reply, but he will inwardly treat all the line reafonings, which attempted to con- found him, with the utmoil fcorn. The argument, that the fenfes fometimes deceive us, will make but a very flight impreflion on his mind ; and when he is told, with the greatest eloquence, that every thing the fenfes reprefent to us has no more reality than the vifions of the night, it will only provoke laughter.
But if the clown mould pretend to play the phi- lofopher, in his turn, and maintain thai the bailiff is a mere phantom, and that all who confider him as fomething real, and fubmit to his authority, are fools ; this fublime philofophy would be in a mo- ment overturned, and the leader of the feci foon made to feel, to his coft, the force of the proofs which the bailiff could give him of the reality of his ex- igence.
You muft: be perfectly fatisfied, then, that there are certain characters which deftroy every ihadow of doubt refpecting the reality and truth of what we know by the fenfes ; and thefe fame characters are fo Weil known, and fo ftrongly imprefled on our minds, that we are never deceived when we employ the precautions neceffary to that effect. But it is ex- tremely difficult to make an exact enumeration of thefe characters, and to explain their nature. We commonly lay, that the fenfitive organs ought to be in a good natural ilate; that the air ought not to, be obfeured by a fog; finally, that we muft employ a fufScient degree of attention, and endeavour, above
all
12 DEMONSTRATIVE, PHYSICAL,
all things, to examine the fame object by two or more of our fenfes at once. But I am firmly per- fuaded, that every one knows, and puts in practice, rules much more folid than any which could be pre-* fcribed to him.
I lib April, 1 76 1.
LETTER IV.
Of demonjlrative, phyfical, and particularly of moral, Certainty.
k 1 *HERE are, therefore, three fpecies of know-
-*■ ledge, which we muft confider as equally cer- tain, provided we employ the precautions necefTary to fecure us againft error. And hence, likewife, re- fult three fpecies of certainty.
The firft is called phyfical certainty. When I am convinced of the truth of any thing, becaufe I my- felf have feen it, I have a phyfical certainty of it ; and, if I am afked the reafon, I anfwer, that my own fenfes give me full affurance of it, and that I am, or have been, an eye-witnefs of it. It is thus I know, that Auftrians have been at Berlin, and that fome of them committed great irregularities there. I know, in the fame manner, that fire confumes all combuflible fubftances; for I myfelf have feen it, and I have a phyfical certainty of its truth.
The certainty which we acquire by a procefs of reafoning, is called logical or demonfirative certainty, becaufe we are convinced of its truth by demonfrra-
tion.
AND MORAL CERTAINTY. 1 3
t:on. The truths of geometry may here be produced as examples, and it is logical certainty which gives us the affurance of them.
Finally, the certainty which we have of the truth of what we know only by the report of others, is called moral certainty, becaufe it is founded on the credibility of the perfons who make the report. Thus, you have only a moral certainty that the Ruffians have been at Berlin, and the fame thing applies to all hiftorical facts. We know with a moral certainty, that there was formerly at Rome a Julius Caefar, an Auguftus, a Nero, &c. and the teftimonies refpecting thefe are fo authentic, that we are as fully convinced of them, as of the truths which we difcover by our fenfes, or by a chain of fair reafoning.
We mult take care, however, not to confound thefe three fpecies of certainty, phyfiqal, logical, and moral, each of which is of a nature totally different from the others. I propofe to treat of each fepa- rately ; and mall begin with a more particular expla- nation of moral certainty, which is the third fpecies.
It is to be attentively remarked, that this third fource divides into two branches, according as others fimply relate what they themfelves have feen, or made full proof of by their fenfes, or as they communicate to us, together with thefe, their reflections and rea- fonings upon them. We might add ftill a third branch, when they relate what they have heard from others.
As to this third branch, it is generally allowed to be very liable to error, and that a witnefs is to be
believed
14 DEMONSTRATIVE, PHYSICAL,
believed only reflecting what he himfelf has feen o£ experienced. Accordingly, in courts of juftice, when witnefies are examined, great care is taken to dif- tinguiih, in their declarations, what they themfelves have feen and experienced, from what they fre- quently add of their reflections and reafonings upon it. Strefs is laid only on what they themfelves have feen or experienced; but their reflections, and the conclulions which they draw, however well founded they may otherwife be, are entirely fet alide. The fame maxim is obferved with refpect to hiftorians, and we wifh them to relate only what they them- felves have witnefTed, without purfuing the ^reflec- tions which they fo frequently annex, though thefe may be a great ornament to hiftory. Thus we have a greater dependance on the truth of what others have experienced by their own fenfes, than on what they have difcovered by purfuing their meditations. Every one wifhes to be mafter of his own judgment, and tinlefs he himfelf feels the foundation and the demonftration, he is not perfuaded.
Euclid would in vain have announced to us the molt important truths of geometry; we fhould ne- ver have believed him on his word, but have infiftec^ on profecuting the demonftration ftep by ftep our- felves. If I were to tell you, that I had feen fuch or fuch a thing, fuppofing my report faithful, you would without hefitation give credit to it ; nay I mould be very much mortified if you were to fuf- pect me of falfhood. But when I inform you, that in a right-angled triangle, the fquares dcfcribcd on
the
AMD MORAL CERTAINTY. 1$
the two fmaller fides are together equal to the fquare of the greater fide, I do not wifh to be believed on my word, though I am as much convinced of it, as it is poffible to be of any thing ; and though I could allege, to the fame purpofe, the authority of the greateft geniufes who have had the fame conviction, I mould rather wifh you to difcredit my alfertion, and to withhold your affent, till you yourfelf com- prehended the folidity of the reafonings on which the demonftration is founded.
It does not follow, however, that phyfical cer- tainty, or that which the fenfes fupply, is greater than logical certainty, founded on reafoning; but, whenever a truth of this fpecies prefents itfelf, it is proper that the mind fhould give clofe application to it, and become mafter of the demonftration. This is the bell method of cultivating the fciences, and of carrying them to the higheft degree of perfection.
The truths ©f the fenfes, and of hiftory, greatly multiply the particulars of human knowledge; but the faculties of the mind are put in action only by reflection or reafoning.
We never flop at the fimple evidence of the fenfes, or the fads related by others; but always follow them up and blend them with reflections of our own : we infenfibly fupply what feems deficient, by the addition of caufes and motives, and the deduc- tion of confequences. It is extremely difficult, for this reafon, in courts of juftice, to procure fimple, unblended teftimony, fuch as contains what the wit- nefs actually faw and felt, and no more; for witnefles
ever
l6 THE SENSES CONTRIBUTE TO
ever will be mingling their own reflections, without perceiving that they are doing fo*
l^tb April, 1 76 1.
LETTER V.
Remarks that the Senfes contribute to the Increafe of Knowledge ; and Precautions for acquiring the Cer~ . tainty of Hijiorical Truths,
'"TPHE knowledge fupplied by our fenfes is un- -** doubtedly the earlieft which we acquire, and upon this the foul founds the thoughts and reflec- tions which difcover to it a great variety of intel* tactual truths. In order the better to comprehend how the fenfes contribute to the advancement of knowledge, I begin with remarking, that the fenfes act only on individual things, which actually exifl: under circumftances determined or limited on all fides.
Let us fuppofe a man fuddenly placed in the world, poiTelfed of all his faculties, but entirely deftitute of experience; let a Hone be put in his hand, let him then open that hand, and obferve that the ftone falls. This is an experiment limited on all fides, which gives him no information, except that this ftone be- ing in the left hand, for example, and dropped, falls to the ground ; he is by no means abfolutely certain that the fame effect would enfue, were he to take another ftone, or the fame ftone with his right hand.
It
THE INCREASE OF KNOWLEDGE. 1J
Xt is ftill uncertain whether this ftone, under the fame circumftances, would again fall, or whether it would have fallen, had it been taken up an. hour fooner. This experiment alone gives him no light refpecting thefe particulars.
The man in queftion takes another ftone, and ob- serves that it falls likewife, whether dropped from the right hand or from the left ; he repeats the ex- periment with a third and a fourth ftone, and uni- formly obferves the fame effect. He hence concludes that ftones have the property of falling when drop- ped, or when that which fupports them is with- drawn.
Here then is an article of knowledge which the . man has derived from the experiments which he has made. He is very far from having made trial of every ftone, or, fuppofing him to have done fo, what certainty has he that the fame thing would happen \ at all times? He knows nothing as to this, except what concerns the particular moments when he made the experiments ; and what afliirance has he that the fame effect would take place in the hands of another . man ? Might he not think, that this quality of making ftones fall was attached to his hands exclu- sively? A thoufand other doubts might ftill be formed on the fubjecl. ,
I have never, for example, made trial of the ftones which compofe the cathedral church of Magdeburg, and yet I have not the leaft doubt, that all of them without exception are heavy, and that each of them would fall as foon as detached from the building.
Vol. II. C I even
l3 THE SENSES GONTRIBUtfi tO
I even imagine that experience has fupplied me with this knowledge, though I have never tried any one of thofe (tones*
This example is fufficient to fhew, how experi- ments made on individual obje&s . only, have led mankind to the knowledge of univerfal proportions ; but it mull be admitted, that the underftanding and the other faculties of the foul interfere in a manner which it would be extremely difficult dearly to un- fold j and if we were determined to be over fcrupu- lous about every circumftance, no progrefs in fcience could be made, for we fhould be Hopped fhort at every ftep.
It mull: be allowed, that the vulgar difcover, in this refpecl, much more good fenfe than thofe fcru- pulous philofophers, who are obftinately determined to doubt of every thing. It is neceffary, at the fame time, to be on our guard againft falling into the op- polite extreme, by negle&ing to employ the neceffary precautions.
The three fources from which our knowledge is , derived, require all of them certain precautions, which muft be carefully obferved, in order to ac- quire afhirance of the truth \ but it is poflible, in each, to carry matters too far, and it is always pro- per to fleer a middle courfe.
The third fource clearly proves this. It would undoubtedly be extreme folly to believe every thing that is told us ; but exceflive diftruft would be no lefs blame-worthy. He who is determined to doubt of every thing, will never want a pretence : when a
man
THE INCREASE OF KNOWLEDGE. jg
man fays, or writes, that he has feen fuch or fuch an action, we may fay at once, that is not true, and that the man takes amufement in relating things which may excite furprize; and if his veracity is beyond fufpicion, it might be faid, that he did not fee clearly, that his eyes were dazzled; and examples are to be found in abundance of perfons deceiving themfelves, falfely imagining they faw what they did not. The rules prefcribed, in this refpect, lofe all their weight when you have to do with a wrangler.
Ufually, in order to be afcertained of the truth of a recital or hiftory, it is required, that the author fhould have been himfelf a witnefs of what he relates, and that he mould have no intereft in relating it diffe- rently from the truth. If afterwards two or more perfons relate the fame thing, with the fame circum- ftances, k is juftly coniidered as a ftrong confirma- tion. Sometimes, however, a coincidence carried to extreme minutenefs becomes fufpicious. For two perfons obferving the fame incident, fee it in diffe- rent points of view, and the one will always difcern certain little circumftances which the other muit have overlooked. A flight difference in two feveral ac- counts of the fame event, rather eflablifhes than in- validates the truth of it.
But it is always extremely difficult to reafon on the firft principles of our knowledge, and to attempt an explanation of the mechanifm and of the moving powers which the foul employs. It would be glo- rious to fucceed in fuch an attempt, as it would elu- cidate a great variety of important points refpecting the nature of the foul and its operations. But- we
C 2 . feem
20 WHE < HE& THE ESSENCE. OF
feerri deftined rather to make ufe of our faculties, than to trace their nature through all its, depths.
iStb Apr'ily 1 76 1.
-~j»»-;c"?;
LETTER VL
Whether the Effence of Bodies be known by us*
X FTER fo many reflections on the nature and -*- -*■ faculties of the foul, you will not, perhaps, be difpleafed to return to the confideration of body, the principal properties of which I have already endea- voured to explain.
I have remarked that the nature of body necef- farily contains three things, extenjion, impenetrability ', and inertia ; fo that a being, in which thefe three properties do not meet at once, cannot be admitted into the clafs of bodies j and reciprocally, when they are united in any one being, no one will hefitate to acknowledge it for a body.
In thefe three things, then, we are warranted to ■conftitute the effence of body, though there are many philofophers who pretend that the effence of bodies is wholly unknown to us. This is not only the • opinion of the Pyrrhonifts, who doubt of every thing ; but there are other feels likewife, who main- tain, that the effence of all things is abfolutely un- known : and no doubt, in certain refpecls they have truth on their fide : this is but too certain as to all the individual beings which exift.
You will eafily comprehend, that it would be the height of abfurdity were I to pretend fo much as to
know
BODIES BE KNOWN BY US. 21
know the effence of the pen which I employ in writ- ing this letter. If I knew the effence of this pen, (I fpeak not of pens in general, but of that one only now between my fingers, which is an individual beings as it is called in metaphyfics, and which is diilin- guifhed from all the other pens in the world ;) if I knew, then, the effence of this individual pen, 1 mould be in a condition to diftinguiih it' from every other, and it would be impoffible to change it with- out my perceiving the change ; I muff know its na- ture thoroughly, the number and the arrangement of all the parts whereof it is compofed. But how far am I from having iuch a knowledge ! Were I to rife but for a moment, one of my children might eafily change it, leaving another in its room, without my perceiving the difference ; and were I even to put a mark upon it, how eafily might that mark be coun- terfeited on another pen ? And fuppoling this im- poffible for my children, it muft always be admitted as poffible for God ■ to make another pen fo limilar to this, that I fhould be unable to difcern any difference. It would be, however, another pen, really diftin- guifhable from mine, and God would undoubtedly know the difference of them ; in other words, God perfectly knows the effence of both the one and the other of thefe two pens : but as to me, who difcern no difference, it is certain that the effence is altogether beyond my knowledge.
The fame obfervation is applicable to all other in- dividual things ; and it may be confidently main- tained, that God alone can know the effence or na- ture of each. It were impoffible to fix on any one
C 3 thing
22 WHETHER THE ESSENCE OP
thing really exifting, of which we could have a know- ledge fo perfect, as to put us beyond the reach of miftake : this is, if I may ufe the expreulon, the im- prefs of the Creator on all created things, the nature of which will ever remain a myftery to us.
It is undoubtedly certain, then, that we do not - know the effence of individual things, or all the cha- racters whereby each is diftinguiftied from every other ; but the cafe is different with refpect to genera •md /pedes: thefe are general notions which include at once an infinite number of individual things. They are not beings actually exifting, but notions which we ourfelves form in our minds, when we arrange a great many individual things in the fame clafs, which we denominate a fpecies or genus, ac- cording as the number of individual things which it comprehends is greater or lefs.
And to return to the example of the pen, as there. are an infinite number of things to each of which I give the fame name, though they all differ one from another ; the notion of pen is a general idea of which we ourfelves are the creators, and which exifts only in our own minds. This notion contains but the common characters which conftitute the effence of the general notion of a pen ; and this effence muff be well known to us, as we are in a condition to diftinguifh. ail the things which we call pens from thofe which we do not comprehend under that ap- pellation.
As foon as we remark in any thing certain cha- racters, or certain qualities, we fay it is a pen ; and we are in a condition to cliixinguifli it from ail other
things
BODIES BE KNOWN BY US. 23
things which are not pens, though we are very far from being able to diftinguilh it from other pens.
The more general a notion is, the fewer it con- tains of the characters which conftitute its effence, and it is accordingly eafier alfo to difcover this effence. We comprehend more eafily what is meant by a tree, in general, than by the term cherry-tree, pear-tree, or apple-tree ; that is, when we defcend to the fpecies. When I fay, fuch an object, which I fee in the garden is a tree, I run little rifK of being mif- taken ; but it is extremely poiTible I might be wrong, if 1 affirmed it was a cherry-tree. It follows then, that I know much better the effence of tree, in ge- neral, than of the fpecies : I mould not fo eafily con- found a tree with a {tone, as a cherry-tree with a plum-tree..
Now a notion, in general, extends infinitely far- ther ; its effence accordingly comprehends only the characters which are common to all beings bearing the name of bodies. It is reduced, therefore, to a very few particulars, as we muft exclude from it all the characters which diftinguifh one body from another.
It is ridiculous then to pretend, with certain phi- lofophers, that the effence of bodies, in general, is unknown to us. If it were fo, we mould never be in a condition to affirm with affurance, that fuch a thing is a body, or it is not : and as it is impoffiblfe we fhould be miftaken in this refpect, it necefiarily follows, that we know fufficiently the nature or ef- fence of body in general; Now this knowledge is reduced to three articles, extenfion, impenetrability, and inertia.
ai/4>,v75i76i. LETTER
24 THE TRUE NOTION OF EXTENSION,
LETTER VII.
The true Notion of Extenjion.
T HAVE already demonftrated, that the genera^ ■*■ notion of body neceffarily comprehends thefe three qualities, extenfion, impenetrability, and inertia, without which no being can be ranked in the clafs of bodies. Even the moil fcrupulous muft allow the necefiity of thefe three qualities, in order to confti- tute a body ; but the doubt with fonie is, Are thefe three . characters fufiicient ? Perhaps, fay they, there may be feveral other characters, which are equally neceffary to the effence of body.
But I alk : were God to create a being divefted of thefe other unknown characters, and that it polfeffed only the three above mentioned, Would they hefi- tate to give the name of body to fuch a being ? No, affuredly ; for if they had the leatt doubt on the fubjecl, they could not fay with certainty, that the , ft ones in the ftreet are bodies, becaufe they are not fure whether the pretended unknown characters are. to be found in them or no.
Some imagine, that gravity is an effential property of all bodies, as all thofe which we know are heavy; but were God to divcft them of gravity, would they therefore ceafe to be bodies ? Let them confider the fyeavenly bodies, which do not fall downward ; as muft be the cafe, if they were heavy as the bodies which we touch, yet they give them the fame name.
And
THE TRUE NOTION OF EXTENSION. 25
And even on the fuppofition that all bodies were heavy, it would not follow that gravity is a property elfential to them, for a body would {till remain a body, though its gravity were to.be deflroyed by a miracle.
But this reafoning does not apply to the three ef- fential properties above mentioned. Were God to annihilate the extenfion of a body, it would certainly be no longer a body ; and a body divefted of impe- netrability would no longer be body ; it would be a fpectre, a phantom : the fame holds as to inertia.
You know that extenfion is the proper object of geometry, which confiders bodies only in fo far as they are extended, abftractedly from impenetrability and inertia ; the object of geometry, therefore, is a notion much more general than that of body, as it comprehends not only bodies, but all beings limply extended without impenetrability, if any fuch there be. Hence it follows, that ail the properties deduced in geometry from the notion of extenfion mult like- wife take place in bodies, in as much as they are ex- tended ; for whatever is applicable to a more general notion, to that of a tree, for example, mult likewife be applicable to the notion of an oak, an afh, an elm, &c. and this principle is even the foundation of all the reafpnings in virtue of which we always affirm and deny of the fpecies, and of individuals, every , thing that we affirm and deny of the genus.
There are however philofophers,particularlyamong our contemporaries, who boldly deny, that the pro- perties applicable to extenfion, in general, that is,
according
Z6 THE TltOS NOTION OF EXTENSION.
according as we confider them in geometry, take place in bodies really exifting. They allege that geo- metrical extenfion is an abftract. being, from the pro- per ties of which it is impoffible to draw any conclu- fion, with refped to real objects : thus, when I have demonftrated that the three angles of a triangle are together equal to two right angles, this is a property belonging only to an abftract. triangle, and not at all to one really exifting.
But thefe philofophers are not aware of the per- plexing confequences which naturally refult from the difference which they eftablifh between objects formed by abitraction, and real objects ; and if it were not permitted to conclude from the firft to the laft, no conclusion, and no reafoning whatever could fubfift, as we always conclude from general notions to particular.
Now all general notions are as much abftract beings as geometrical extenfion ; and a tree, in general, or the general notion of trees, is formed only by ab- ftraction, and no more exifts out of our mind than geometrical extenfion does. The notion of man in general is of the fame kind, and man in general no where exifts : all men who exift are individual beings, and correfpond to individual notions. The general idea which comprehends all, is formed only by ab- ftraciion.
The fault which thefe philofophers are ever find- ing with geometricians, for employing themfelves about abstractions merely, is therefore groundlefs, as all other fciences principally turn on general notions, 2 which
DIVISIBILITY, &C. 27
which are no more real than the objects of geometry. The patient, in general, whom the phyfician has in view, and the idea of whom contains all patients really exifting, is only an abftract idea ; nay the very merit of each fcience is fo much the greater, as it ex- tends to notions more general, that is to fay, more abftract.
I fhall endeavour, by next poft, to point out the tendency of the cenfures pronounced by thefe phi- lofophers upon geometricians ; and the reafons why they are unwilling that we Ihould afcribe to real, extended beings, that is, to exifting bodies, the pro- perties applicable to extenlion in general, or to ab- ft rafted extenfion. They are afraid left their meta* phyfical principles ihould fuffer in the caufe.
2 5/6 April t 1 761.
LETTER VIII.
Dlvifibility of Exterfwn in infinitum.
THE controverfy between modern philofophers and geometricians to which I have alluded, turns on the dlvifibility of body. This property is undoubtedly founded on extenlion, and it is only in fo far as bodies are extended that they are divilible, and capable of being reduced to parts.
You will recollect that in geometry it is always poffible to divide a line, however fmall, into two equal parts. We are likewife, by that fcience, in-
ftructed
28 DIVISIBILITY OF
ftracted in the method of dividing a fmall line, as a i, into any number of equal parts at pleafure, and the conftruc&on of this diviiion is there demonftrated beyond the poiTibility of doubting its accuracy.
You have only to draw (plate II. Jig. 2-5.) a line A I parallel to a /of any length, and at any diftance you pleafe, and to divide it into as many equal parts AB, BC, CD, DE, &c. as the fmall line given is to have divisions, fay eight. Draw afterwards,through the extremities A, a, and I, i, the ftraight lines A a O, I i O, till they meet in the point O ; and from O draw toward the points of divifion B, C, D, E, &c. the ftraight lines OB, QC, OD, OE, &c. which mail likewife cut the fmall line ai into eight equal parts.
This operation may be performed, however fmall the given line ai, and however great the number of parts into which you propofe to divide it. True it is, that in execution we are not permitted to go too far ; the lines which we draw always have fome breadth, whereby they are at length confounded, as. may be feen in the figure near the point O ; but the queftion is not what may be poiiible for us to execute, but what is poiiible in itfelf. Now in geometry lines have no breadth, and confequently can never be con- founded. Hence it follows that fuch divifion is il- limitable.
, If it is once admitted that a line may be divided into a thoufand parts, by dividing each part into two it will be divifible into two thoufand parts, and for the 'fame reafon into four thoufand, and into eight thoufand, without ever arriving at parts in divifible.
However
EXTENSION IN INFINITUM. 29
However fmall a line may be fuppofed, it is ftill di- vifible into halves, and each half again into two, and each of thefe again in like manner, and fo on to in* finity.
What I have faid of a line is eafily applicable to a furface, and, with greater ffcrength of reafoning, to a folid endowed with three dimenfions, length, breadth, and thicknefs. Hence it is affirmed that all exten- fion is divifible to infinity, and this property is deno- minated divifibility in infinitum.
Whoever is difpofed to deny this property of ex- tenfion, is under the necefiity of maintaining, that it is poillble to arrive at laft at parts fo minute as to be unfufceptible of any farther divifion, becaufe they ceafed to have any extenfion. Neverthelefs all thefe particles taken together muft reproduce the whole, by the divifion of which you acquired them ; and as the quantity of each would be a nothing or cypher o, a combination of cyphers would produce quantity, which is manifeftly abfurd. For you know perfectly well, that in arithmetic, two or more cyphers joined never produce any thing.
This opinion that in the divifion of extenfion, or of any quantity whatever, we may come at laft to particles fo minute as to be no longer divifible, be- caufe they are fo fmall, or becaufe quantity no longer exifts, is, therefore, a pofition abfolutely untenable.
In order to render the abfurdity of it more fen- fible, let us fuppofe a line of an inch long, divided into a thoufand parts, and that thefe parts are fo fmall as
to
$0 DIVISIBILITY, &C.
to admit of no farther divifion ; each part, then, would no longer have any length, for if it had any, it would be ftill divifible. Each particle, then, would of confequence be a nothing. But if thefe thouiand particles together conftituted the length, of an inch, the thoufandth part of an inch would, ofconfequence, be a nothing ; which is equally abfurd with main- taining, that the half of t any quantity whatever is nothing. And if it be abfurd to affirm, that the half of any quantity is nothing, it is equally fo to affirm, that the half of a half, or that the fourth part of the fame quantity, is nothing ; and what mufl be granted as to the fourth, muft likewife be granted with re- fpecl to the thoufandth, and the millionth part. Fi- nally, however far you may have already carried, in imagination, the divifion of an inch, it is always poffible to carry it ftill farther ; and never will you be able to carry on your fubdivifion fo far, as that the laft parts mall be abfolutely indivifible. Thefe parts will undoubtedly always become fmaller, and their magnitude will approach nearer and nearer to o, but can never reach it.
The geometrician, therefore, is warranted in affirm- ing, that every magnitude is divifible to infinity ; and that you cannot proceed fo far in your divifion, as that all farther divifion fhall be impoiTible. But it is always neceffary to diftinguifh between what is poffible in itfelf, and what we are in a condition to perform. Our execution is indeed extremely limited. After having, for example, divided an inch into a
thoufand
WHETHES. TtllS DIVISIBILITY, &C. $t
thoufand parts, thefe parts are fo fmall as to efcape our fenfes, and a farther divifion would to us, no doubt, be impofiible.
But you have only to look at this thoufandth part of an inch through a good microfcope, which mag- nifies, for example, a thoufand times, and each par- ticle, will appear as large as an inch to the naked eye; and you will be convinced of the poflibility of di- viding each of thefe particles again into a thoufand parts : the fame reafoning may always be carried for- ward, without limit and without end.
It is therefore an indubitable truth, that all mag- nitude is divifible in infinitum, and that this takes place not only with refpect to extenfion, which is the object of geometry, but like wife with refpecl to every other fpecies of quantity, fuch as time and number.
%%th Aprily 1761.
LETTER IX.
Whether this Dlvifibllity in infinitum takes place in exifting Bodies?
IT is, then, a completely eftablifhed truth, that ex- tenfion is divifible to infinity, and that it is inv poilible to conceive parts fo fmall as to be unfufcep- tible of farther divifion. Philofophers accordingly do not impugn this truth itfelf, but deny that it takes place in exifting bodies. They allege, that ex- tenfion, the divisibility of which to infinity has been
demon-
32 WHETHER THIS DIVISIBILITY TAKES
dernonftrated, is merely a chimerical object, formed by abftraction ; and that fimple extenfion, as confi* dered in geometry, can have no real exiftence.
Here they are in the right ; and extenfion is un- doubtedly a general idea, formed in the fame man- ner as that of man, or of tree in general, by abftrac- tion; and as man or tree in general exifts not, no more does extenfion in general exiit. You are per- fectly feniible, that individual beings alone exift, and that general notions are to be found only in the mind; but it cannot therefore be maintained that thefe general notions are chimerical; they contain, on the contrary, -the foundation of all our know- ledge.
Whatever applies to a general notion, and all the properties attached to it, of neceflity take place in all the individuals comprehended under that general notion. When it is affirmed that the general notion of man contains an underftanding and a will, it is undoubtedly meant, that every individual man is endowed with thofe faculties. And how many pro- perties do thefe very philofophers boaft of having dernonftrated as belonging to fubftance in general, which is furely an idea as abftracT: as that of exten- fion; and yet they maintain, that all thefe properties apply to all individual fubftances, which are all ex- tended. If, in effect, fuch a fubftance had not thefe properties, it would be falfe that they belonged to fubftance in general.
If then bodies, which infallibly are extended be- ings, or endowed with extenfion, were not divifible
to
PLACE IN EXISTING BODIES f 33
to infinity, it would be likewife falfe, that divifibi- lity in infinitum is a property of extenfion. Now thofe philofophers readily admit that this property belongs to extenfion, but they infill that it cannot take place in extended beings. This is the fame thing with affirming, that the underfcanding and will are indeed attributes of the notion of man in gene- ral ; but that they can have no place in individual men actually exifting.
Hence you will readily draw this conclusion ■: if diviiibility in infinitum is a property of extenfion in general, it muft of neceffity likewife belong to all individual extended beings; or if real extended be- ings are not divifible to infinity, it is falfe that divi- fibility in infinitum can be a property of extenfion in general.
It is impoffible to deny the one or the other of thefe confequences without fubverting the moft fo- lid principles of all knowledge ; and the philofophers who refufe to admit divifibiiity in infinitum in real
' extended beings, ought as little to admit it with refpecl: to extenfion in general; but as they grant this laft, they fall into a glaring contradiction.
You need not to be furprized at this; it is a failing from which the greateft men are not exempt. But what is rather furprizing, thefe philofophers, in order to get rid of their embarraffment, have thought pro-
. per to deny that body is extended. They fay, that it is only an appearance of extenfion which is per- ceived in bodies, but that real extenfion by no means belongs to them.
Vol. II. D You
34 WHETHER THIS DIVISIBILITY, &C.
You fee clearly that this is merely a wretched cavil, by which the principal, and the moft evident pro- perty of body is denied. It is an extravagance nmi- lar to that formerly imputed to the Epicurean phi- lofophers, who maintained that every thing which exifts in the univerfe is material, without even ex- cepting the gods whofe exiftence they admitted. But as they faw that thefe corporeal gods would be fub- jected to the greateft difficulties, they invented a fubterfuge fimilar to that of our modern philofo- phers, alleging, That the gods had not bodies, but as it were bodies, (auaft corpara,J and that -they had not fenfes, but fenfes as it were; and fo of all the members. The other philofophical feels of antiquity made themfelves abundantly merry with thefe quafi- corpora and quaji-fenfus ; and they would have equal reafon, in modern times, to laugh at the quaji-exten- fion which our philofophers afcribe to body; this term quafi-extenfion feems perfectly well to exprefs that appearance of extenfion, without being fo in reality.
Geometricians, if they meant to confound them, have only to fay, that the objects whofe divifibility in infinitum they have demonftrated, were likewife only as it were extended, and that accordingly ail bodies extended as it were, were neceffarily divifible in infinitum. But nothing is to be gained with them ; they are refolute to maintain the greateft abfurdities rather than acknowledge a miftake. You muft have remarked, that this is the character of almoft all fcholars.
id May, 1 761,
LETTER
OF MONADS. 2S
LETTER X.
Of Monads.
TT7HEN we talk, in company, on philofophical * * fubjects, the converfation ufually turns on fuch articles as have excited violent difputes among philofophers.
The diviiibility of body is one of them, refpe-fting which the fentiments of the learned are greatly di- vided. Some maintain, that this diviiibility goes on to infinity, without the poffibility of ever arriving at particles fo fmall as to be fufceptible of no farther divifion. But others infill, that this divifion ex- tends only to a certain point, and that you may come at length to particles fo minute, that, having no magnitude, they are no longer divisible. Thefe ul- timate particles, which enter into the compofition of bodies, they denominated^/? beings ', and monads.
There was a time when the difpute refpefting mo- nads employed fuch general attention, and was con- ducted with fo much warmth, that it forced its way into company of every defcription, that of the guard- room not excepted. There was fcarce a lady at court who did not take a decided part in favour of mo- nads or againft them. In a word, all converfation was engroffed by monads, no other fubjecl: could find admiflion.
• The Royal Academy of Berlin took up the con- ttoverfy, and being accuftomed annually to propofe
Da a queflion
3^ OF MONADS.
a queftion for difcuflion, and to beftow a gold medal of the value of fifty ducats on the perfon who in the judgment of the Academy has given the moft inge- nious folution, the queftion refpecting monads was ■ felected for the year 1748. A great variety of effays on the fubject were accordingly produced. The preiident, Mr. de Maupertuis, named a committee to examine them, under the direction of the late Count Dohna, great chamberlain to the queen ; who, being an impartial judge, examined, with all imagi- nable attention, the arguments adduced both for and againft the exiftence of monads. Upon the whole, it was found that thofe which went to the eftablilh- ment of their exiftence were fo feeble, and fo chi- merical, that they tended to the fubverfion of all the principles of human knowledge. The queftion was, therefore, determined in favour of the oppofite opi- nion, and the prize adjudged to Mr. Jufti, whofe piece was deemed the moft complete refutation of the monadifts.
You may eafily imagine how violently this deci- fion of the Academy muft irritate the partifans of monads, at the head of whom ftood the celebrated Mr. Wolff. His followers, who were then much more numerous, and more formidable than at pre- fent, exclaimed in high terms againft the partiality and injuftice of the Academy; and their chief had well nigh proceeded to launch the thunder of a phi- lofophical anathema againft it. I do not now recol- lect to whom we are indebted for the care of avert-
ing this difafter.
As
OF MONADS. 37
As this controverfy has made a great deal of noife, you will not be difpleafed, undoubtedly, if 1 dwell a little upon it. The whole is reduced to this fimple queftion, Is body divifible to infinity? or, in other words, Has the divifibility of bodies any bound, or has it not? I have already remarked as to this, that extenfion, geometrically conlidered, is on all hands allowed to be divifible in infinitum; becaufe, how- ever fin all a magnitude may be, it is poffible to con- ceive the half of it, and aeain the half of that half, and fo on to infinity.
This notion of exteniion is very abftract, as are thofe of all genera, fuch as that of man, of horfe, of tree, &c. as far as they are not applied to an indivi- dual and determinate bein°\ Aerain, it is the,mofl certain principle of all our knowledge, that whatever can be truly affirmed of the genus, muft be true of all the individuals comprehended under it. If there- fore all bodies are extended, all the properties be- longing to extenfion muft belong to each body iri particular. Now all bodies are extended ; and ex- tenfion is divifible to infinity; therefore everybody muft be fo likewife. This is a fyllogifm of the beft form; and as the firft propofition is indubitable, all that remains, is to be allured that the fecond is true, that is, whether it be true or not, that bodies are extended.
The partifans of monads, iri maintaining their opinion, are obliged to affirm, that bodies are not extended, but have only an appearance of extenfion. They imagine that by this they have fubverted the
D 3 argument
$8 OF MONADS.
argument adduced in fupport of the divifibility in in- finitum. But if body is not extended, I fliould be glad to know, from whence we derived the idea of extenfion ; for, if body is not extended, nothing in the world is, as fpirits are ftill lefs fo. Our idea of exteniion, therefore, would be altogether imaginary and chimerical.
Geometry would accordingly be a fpeculation en- tirely ufelefs and illufory, and never could admit of any application to things really exifting. In effect, if no one thing is extended, to what purpofe inves- tigate the properties of extenfion ? But as geometry is, beyond contradiction, one of the moft ufeful of fciences, its object cannot poffibly be a mere chi- mera.
There is a neceffity,then,of admitting, that the ob- ject of geometry is at leaft the fame apparent exten^ fion which thofe philofophers allow to body; but this very object is divifible to infinity : therefore ex* ifting beings, endowed with this apparent extenfion, muft neceffarily be extended.
Finally, let thofe philofophers turn themfelves which way foever they will in fupport of their mo- nads, or thofe ultimate and minute particles, divefted of all magnitude, of which, according to them, all bodies are compofed, they ftill plunge into' difficul- ties, out of which they cannot extricate themfelves. They are right in faying, that it is a proof of dulnefs to be incapable of relifhing their fublime doctrine ; it may however be remarked, that here the greatefl ftupidity is the moft fuccelsful.
stbMay, i76i. BETTER
REFLECTIONS ON DIVISIBILITY, &C. 39
LETTER XL
Reflettions on Div'ifibUity in infinitum, and on Monads.
TN fpeaking of the divifibility of body, we muft -*- carefully distinguish what is in our power, from what is poffible in itfelf. In the Sirft fenfe, it cannot be denied, that fuch a division of body as we are capable of, muft be very limited.
By pounding a ftone we can eafily reduce it to powder; and if it were poSiible to reckon all the little grains which form that powder, their number would undoubtedly be fo great, that it would be matter of furprize, to have divided the ftone into fo many parts. But thefe very grains will be almoft indivisible with refpecl: to us, as no inftrument we could employ will be able to lay hold of them. But it cannot with truth be affirmed that they are indi- vifible in themfelves. You have only to view them with a good microfcope, and each will appear itfelf a coniiderable ftone, on which are distinguishable a great many points and inequalities j which demon- strates the poffibility of a farther divifion, though we are not in a condition to execute it. For where- ever we can diftinguifh feveral points in any object, it muft be divisible into fo many parts.
We fpeak not? therefore, of a division practicable by our Strength and Skill, but of that which is pof- fible in itfelf, and which the Divine Omnipotence is able to accomplish.
D 4 It
40 REFLECTIONS ON DIVISIBILITY,
It is in this fenfe, accordingly, that philofophers life the word ' divisibility;' fo that if there were a ilone fo hard that no force could break it, it might be without hefitation affirmed as divifible in its own nature, as the moft brittle, of the fame magnitude. And how many bodies are there on which we can- not lay any hold, and of whofe divilibility we can entertain not the frnalleft doubt? No one efcabts that the moon is a divifible body, though he is in- capable of detaching the frnalleft particle fror, and the fimpie reafon for its divifibility, is its being extended.
Wherever we remark extenfion, we are under the neceffity of acknowledging divilibility, fo that divili- bility is an infeparable property of extenfion. But experience likewife demon Urates that the divifion of bodies extends very far. I mail not infill at great length on the inftance ufually produced of a ducat : the artifan can beat it out into a leaf fo fine, as to cover a very large furface, and the ducat may be di- vided into as many parts as that furface is capable of being divided. Our own body furnifhes an example much more furprizing. Only confider the delicate veins and nerves with which it is filled, and the fluids which circulate through them. The fubtilty there difcoverable far furpaffes imagination.
The frnalleft infects, fuch as are fcarcely vifible to the naked eye, have all their members, and legs on which they walk with amazing velocity. Hence we fee that each limb has its mufcies compofed of a great number of fibres \ that they have veins, and nerves,
and
AND ON MONADS. /f«
and a fluid flail much more fubtile which flows through their whole extent.
On viewing with a good microfcope a fingle drop of water, it has the appearance of a, fea ; we fee thoufands of living creatures fwimming in it, each of which is neceffarily compofed of an infinite number of mufcular and nervous fibres, whofe marvellous ftru&ure ought to excite our admiration. And though thefe creatures may perhaps be the fmalleft which we are capable of dilcovering by the help of the microfcope, undoubtedly they are not the finalleft which the Creator has produced. Animalcules pro- bably exift as fmah relatively to them, as they are relatively to us. And thefe after all are not yet the finalleft, but may be followed by an infinity of new claries, each of which contains creatures incomparably fmaller than thole of the preceding clafs.
We ought in this to acknowledge the omnipotence and infinite wifdom of the Creator, as in objects of the greateft magnitude. It appears to me, that the eonfideration of thefe minute fpecies, each of which is followed by another inconceivably: more minute, ought to make the livelieft impreflion on our minds, and infpire us with the moil fublime ideas of the works of the Almighty, whofe power knows no bounds, whether as to great objects or fmall.
To imagine that after having divided a body into a great number of parts, we arrive, at length, at particles fo fmall as to defy all farther divifion, is therefore the indication of a very contracted mind. But fuppofing it poffible to defcend to particles fo
minute
42 REFLECTIONS ON DIVISIBILITY, &C.
minute as to be, in their own nature; no longer di- vifible, as in the cafe of the fuppofed monads ; be- fore coming to this point, we fhall have a particle compofed of only two monads, and this particle will be of a certain magnitude or extenfion, other-, wife it could not have been divifible into thefe two monads. Let us farther fuppofe, that this particle, as it has fome extenfion, may be the thoufandth part of an inch, or ftill fmaller if you will ; for it is of no importance, what I fay of the thoufandth part of an inch may be faid with equal truth of every fmaller part. This thoufandth part of an inch, then, is com* pofed of two monads, and confequently two monads together would be the thoufandth part of an inch, and two thoufand times nothing, a whole inch ; the abfurdity ftrikes at firft fight.
The partifans of the fyftem of monads accordingly ftnink from the force of this argument, and are re- duced to a terrible nonplus when afked how many monads are requifite to conftitute an extenfion. Two, they apprehend, would appear infufEcient, they there- fore allow that more muft be neceftary. But, if two monads cannot ^conftitute extenfion, as each of the two has none j neither three, nor four, nor any number whatever will produce it ; and this com- pletely fubverts the fyftem of monads.
yb May, 176 1. ♦
LETTER
REPLY TO THE OBJECTIONS, fee, 43
LETTER XII,
Reply to the QbjccTwns of the Monadifts to Divifibiiity in infinitum.
T
HE partifans of monads are far from fubmitting to the arguments adduced to eftablifh the di- vifibility of body to infinity. Without attacking them directly, they allege that divifibiiity in infinitum is a chimera of geometricians, and that it is involved in contradiction. For, if each body is divifible to infinity, it would contain an infinite number of parts, the fmalleft bodies as well as the greateft : the number of thefe particles to which divifibiiity in infinitum would lead, that is to fay, the moft minute of which bodies are compofed, will then be as great in the fmalleft body as in the largeft, this number being in- finite in both ; and hence the partifans of monads triumph in their reafoning as invincible. For, if the number of ultimate particles of which two bodies are compofed is the fame in both, it muft follow, fay they, that the bodies are perfectly equal to each other. Now this goes on the fuppofition, that the ulti- mate particles are all perfectly equal to each other ; for if fome were greater than others, it would not be furprizing that one of the two bodies fhould be much greater than the other. But it is abfolutely neceffary, lay they, that the ultimate particles of all bodies mould be equal to each other, as they no longer have any extenfion, and their magnitude abfolutely va.
nifties^
44 RFPLY TO THE OBJECTIONS
nifhes, or becomes nothing. They even form a new objection, by alleging that all bodies would be com- pofed of an infinite number of nothings, which is a ftill greater abfurdity,
I readily admit this ; but I remark at the fame time, that it ill becomes them to raife fuch an ob- jection, feeing they maintain, that all bodies are compofed of a certain number of monads, though, relatively to magnitude, they are abfolute nothings : fo that by their own confeilion, feveral nothings are capable of producing a body. They are right in faying their monads are not nothings, but beings en- dowed with an excellent quality, on which the na- ture of the bodies which they compofe is founded. Now, the only queftion here is refpecling exteniion ; and as they arc under the neceffity of admitting that their monads have none, feveral nothings, according to them, would always be fomething. ■ But I mall pufh this argument againft the fyftem of monads no farther ; my object being to make a direct reply to the objection founded on the ultimate particles of bodies, raifed by the monadifts in'fupport of their fyftem, by which they flatter themfelves in the confidence of a complete victory over the parti- fans of divisibility in infinitum.
I fhould be glad to know, in the firft place, what they mean by the ultimate particles of bodies. In their fyftem, according to which every body is com- pofed of a certain number of monads, I clearly com- prehend that the ultimate particles of a body, are the monads themfelves which conftitute it j but in the
fyftem
OF THE MONADISTS. 45
fyftem of divisibility in infinitum, the term ultimate particle is abfolutely unintelligible.
They are right in faying, that thefe are the par* tides at which we arrive from the divifion of bodies, after having continued it to infinity. But this is juft the fame thing with faying, after having finifncd a divifion which never comes to an end. For divi- fibility in infinitum means nothing elfe but the pof- fibility of always carrying on the divifion, without ever arriving at the point where it would be neceffary to ftop. He who maintains divifibility in infinitum, boldly denies, therefore, the exiftence of the ultimate particles of body ; and it is a manifeft contradiction, *o fuppofe at once ultimate particles and divifibility in infinitum.
I reply, then, to the partifans of the fyftem of monads, that their objection to the divifibility of body to infinity would be a very folid one, did that fyftem admit of ultimate particles; but being ex- prefsly excluded from it, all this reafoning, of courfe, falls to the ground.
It is falfe, therefore, that in the fyftem of divifibi- lity in infinitum, bodies are compofed of an infinity of particles. However clofely connected thefe two propofitions may appear to the partifans of monads, they manifestly contradict each other ; for whoever maintains that body is divifible in infinitum, or with- out end, abfolutely denies the exiftence of ultimate particles, and confequently has no concern in the queftion. The term can only mean fuch particles as are no longer divifible, an idea totally inconfiftent
with
46 STRONGEST SUPPORT
with the iyfbm of diviiibility in infinitum. This formidable attack, then, is completely repelled.
1 2 lb Iday, 1 761.
LETTER .XIII.
Principle of the fatisfying Reafon, the firongefi Support of the Monadijis.
"OU muft be perfectly fenftble that one of the two fyftem s, which have undergone fuch ample difcufiion, is necelfarily true, and the other falfe, fee- ing they are contradictory.
It is admitted on both fides, that bodies are divi- sible : the only queflion is, Whether this diviiibility is limited ? or Whether it may always be carried farther, without the poftibility of ever arriving at indivifible particles ?
The fyftem of monads is eftablifhed in the former cafe, fince after having divided a body into indivifible particles, thefe very particles are monads, and there would be reafon for faying that all bodies are com- pofed of them, and each of a certain determinate number. Whoever denies the fyftem of monads, muft likewife, then, deny that the diviiibility of bo- dies is limited. He is under the neceflity of main- taining, that it is always poiiible to carry this diviii- bility farther, without ever being obliged to ftop; and this is the cafe of diviiibility in infinitum, on which fyftem we abfolutely deny the exiftence of ul- timate particles : confequently the difficulties refult-
ing
OF THE MONADISTS. 47
ing from their infinite number fall to the ground of themfelves. In denying monads, it is impoffible to talk any longer of ultimate particles^ and Hill lefs of the number of them which enters into the compo- fition of each body. ,
You muft have remarked, that what I have hitherto produced in fupport of the fyftem of monads is defti- tute of folidity. I now proceed to inform you that its fupporters reft their caufe chiefly on the great principle of the fufficient reafon, which they know how to employ fo dexteroufly, that by means of it they are in a condition to demonftrate whatever fuits their purpofe, and to demolifh whatever makes againft them. The blelTed diicovery made, then, is this, That nothing can be without a fufficient reafon; and to modern phiiofophers we Hand indebted for it.
In order to give you an idea of this principle, you have only to confider, that in every thing prefented to you, it may always be alked, Why it is fuch ? And the anfwer is what they call the fufficie?it reafon, fup- pofing it really to correfpond with the queftion pro- pofed. Wherever the why can take place, the pof- fibility of a fatisfactory anfwer is taken for granted, which {hall, of courfe, contain the fufEcient reafon of the thing.
This is very far, however, from being a myftery of modern difcovery. Men in every age have alked why ; an inconteftable proof of their conviction that every thing muft have a fatisfying reafon of its exift- ence. This principle, that nothing is without a caufe, was very well known to ancient phiiofophers ; but
unhappily
48 STRONGEST SUPPORT
unhappily tliis caufe is for the mod part concealed from us. To little purpofe do we afk why : no one is qualified to affign the reafon. It is not a matter of doubt j that every thing has its caufe ; but a progrefs thus far hardly deferves the name ; and fo long as it remains concealed, we have not advanced a {ingle Hep in real knowledge.
You may perhaps imagine, that modern philofo- phers, who make fuch a boaft of the principle of a fatisfying reafon, have actually difcovered that of all things, and are in a condition to anfwer every why that can be propofed to them; which would un- doubtedly be the very fummit of human knowledge; but, in this refpect, they are juft as ignorant as their neighbours : their whole merit amounts to no more than a pretenfion to have demonflrated, that where- ever it is poffible to afk the queftion why, there muft be a fatisfying anfwer to it, though concealed from us.
They readily admit, that the ancients had a know- ledge of this principle, but a knowledge very obfcure ; whereas they pretend to have placed it in its cleareft light, and to have demonftrated the truth of it : and therefore it is that they know how to turn it moft to their account, and that this principle puts them in a condition to prove, that bodies are compofed of monads.
Bodies, fay they, muft have their fufEcient reafon fomewhere ; but if they were divifible to infinity, fuch reafon could not take place : and hence they conclude, with an air altogether philofophic, that, as every thing mujl have its fujjicient reafon, it is abfolutely 6 necejfary
OF THE MONADISTS. 49
rteceffary that all bodies Jhould be compofed of monads: which was to be demonftrated. This, I muft admit, is a demonftration not to be refilled.
It were greatly to be wifhed that a reafoning fo flight could elucidate to us queftions of this import- ance ; but I frankly confefs, I comprehend nothing of the matter. They talk of the fufticient reafon of bodies, by which they mean to reply to a certain wherefore, which remains unexplained. But it would be proper, undoubtedly, clearly to underftand, and carefully to examine a queftion, before a reply is at- tempted -> in the prefent cafe, the anfwer is given before the queftion is formed.
Is it afked, Why do bodies exift ? It would be ri- diculous, in my opinion, to reply, Becaufe they are compofed of monads ; as if they contained the caufe of that exiftence. Monads have not created bodies : and when I ail?:, Why fuch a being exifts ? I fee no other reafon that can be given but this, Becaufe the Creator has given it exiftence ; and as to the manner in which creation is performed, philofophers, I think, would do' well honeftly to acknowledge their igno- rance.
But they maintain, that God could not have pro- duced bodies, without having created monads, which were neceffary to form the compofition of them. This manifeftly fuppofes, that bodies are compofed pf monads, the point which they meant to prove by this reafoning. And you are abundantly fenfible, that it is not fair reafoning to take for granted the truth of a proportion which you are bound to prove
Vol. II. E by
$0 ANOTHER ARGUMENT
by reafoning. It is a fophifm known in logic by the name of a petitio principii, or, begging the queftion*
ibtbMay, 1761.
LETTER XIV.
Another Argument of the Monadi/is, derived from the Principle of the fufficient Reafon. Abfurdities re- fusing from it,
HPHE partifans of .monads likewife derive their grand argument from the principle of the fa- tisfying reafon, by alleging that they could not even comprehend the poffibility of bodies, if they were divifible to infinity, as there would be nothing in them capable of checking imagination : they mult have ultimate particles or elements, the compolition of which muft ferve to explain the compolition of bodies.
But do they pretend to underftand the poffibility of all the things which exift ? This would favour too much of pride ; nothing is more common among philofophers than this kind of reafoning : I cannot comprehend the poffibility of this, unlefs it is fuch as I imagine it to be : therefore it neceffarily muft be fuch.
You clearly comprehend the frivoloufnefs of fuch reafoning j and that in order to arrive at truth, re- fear'ch much more profound muft be employed. Ig- norance can never become an argument to conduct us to the knowledge of truth, and the one in queftion
is
OF THE MONADISTS* 5 1
is evidently founded on ignorance of the different manners which may render the thing; poflible.
But on the fuppoiition that nothing exifts but that whofe poiTIbility they are able to comprehend, is it poffible for them to explain how bodies would be compofed of monads ? Monads, having no exten- fion, mull be confidered as points in geometry, or as we reprefent to ourfelves fpirits and fouls* Now it is well known that many geometrical points, let the number be fuppofed ever fo great, never can pro- duce a line, and confequently ftill lefs a furface, or a body. If a thoufand points were fufficient to con- ftitute the thoufandth part of an inch, each of thefe muft neceffarily have an extenfion, which, taken a thoufand times, would become equal to the thou- fandth part of an inch. Finally, it is an incontestable truth, that take any number of points you will, they never can produce extension. I fpeak here of points fuch as we conceive in geometry, without any length, breadth or thicknefs, and which in that refpecl, are abfolutely nothing.
Our philofophers accordingly admit that no eX- tenfion can be produced by geometrical points, and they folemnly protefl that their monads ought not to be confounded with thefe points. They have no more extenfion than points, fay they ; but they are invefted with admirable qualities > fuch as reprefent- ing to them the whole univerfe by ideas, though ex- tremely obfeure ; and thefe qualities render them proper to produce the phenomenon of extenfion, or rather that apparent extenfion which I formerly
E 2 mentioned.
£2 ANOTHER ARGUMENT
mentioned. The fame idea, then , ought to be formed of monads as of fpirits and fouls, with this difference, that the faculties of monads are much more imper-
feft.
The difficulty appears to me by this greatly in- creafed, and I flatter myfelf you will be of my opi- nion, that two or more fpirits cannot poffibly be joined fo as to form extenfion. Several fpirits may very well form an affernbly, or a council, but never an extenfion ; abftraction made of the body of each counfellor, which contributes nothing to the delibe- ration going forward, for this is the production of fpirits only ; a council is nothing elfe but an affernbly of fpirits or fouls : but could fuch an affernbly re- prefentan extenfion? Hence it follows, that monads are flill lefs proper to produce extenfion than geo- metrical points are.
The partifans of the fyflem, accordingly, are not agreed as to this point. Some allege, that monads are actual parts of bodies ; and that after having di- vided a body as far as poffiple, you then arrive at the monads which conftitute it.
Others abfolutely deny that monads can be con- fidered as conftituent parts of bodies ; according to them, they contain only the fufficient reafon : while the body is in motion, the monads flir not, but they contain the fufficient reafon of motion. Finally, they cannot touch each other ; thus, when my hand touches a body, no one monad of my hand touches a monad of the body.
What is it then, you will afk, that touches in this
cafe,,
OF THE MONADISTS. $$
cafe, if it is not the monads which compofe the hand and the body ? The anfwer muil be, that two no- things touch each other, or rather it muft be denied that there is a real contact. It is a mere iilufion defti- tute of all foundation. They are under the neceifity of affirming the fame thing of all bodies, which ac- cording to thefe philofophers are only phantoms formed by the imagination, reprefenting to itfelf very confufedly the monads which contain the fuf- ficient reafon.of all that we denominate body.
In this philofophy every thing is fpirit, phantom and iilufion ; and when we cannot comprehend thefe myfteries, it is our ftupidity that keeps up an attach- ment to the grofs notions of the vulgar.
The greateft fingularity in the cafe is, that thefe philofophers, with a defign to inveftigate and explain the nature of bodies and of exteniion, are at laft re- duced to deny their exiftence. This is undoubtedly the fureft way to fucceed in explaining the pheno- mena of nature ; you have only to deny them, and to allege, in proof, the principle of the fuffieient reafon. Into fuch extravagancies will philofophers run, rather than acknowledge their ignorance.
19/16 Mny, I 761.
LETTER XV.
Refctlions on the Svjiem of Monads.
rT would be a great pity, however, that this inge- A nious fyftem of monads fhould crumble into ruins. It has made too much noife, it has coft its partifans
E 3 too
54 REFLECTIONS ON THE
too many fublime and profound fpeculations, to be permitted to fink into total oblivion. It will ever remain a finking monument of the extravagance into which the fpirit of philofophizing may run. It is well worth while, then, to prefent you with a more particular account of it.
It is necefiary, firft of all, to banifli from the mind every thing corporeal, all extenfion, all motion, all time and fpace, for all thefe are mere illufion. No- thing exifls in the world but monads, the number of which undoubtedly is prodigious. No one monad is to be found in connection with others ; and it is demonstrated by the principle of the fuflicient rea- fon, that monads can in no manner whatever act upon each other. They are indeed invefted with powers, but thefe exerted only within themfelves, without having the leaft influence externally.
Thefe powers, with which each monad is endowed, have a tendency only to be continually changing their own ftate, and confift in the reprefentation of all other monads. My foul, for example, ■ is a mo- nad, and contains in itfelf ideas of the ftate of all other monads. Thefe ideas are for the moft part very obfcure; but the powers of my foul are conti- nually employed in their farther elucidation, and in carrying them to a higher degree of clearnefs. Other monads have, in this refpect, a fuflicient re- femblance to my foul ; each is replete with a prodi- gious quantity of obfcure ideas of all other monads, and of their ftate j and they are continually exert- ing themfelves with more or lefs fuccefs in unfolding
thefe
SYSTEM OF MONADS. $$
thefe ideas, and in carrying them to a higher degree of clearnefs.
Such monads as have fucceeded better than I have done are fpirits more perfect ; but the greater part flili remain in a ftate of ftagnation, in the greateft obfeurity of their ideas; and when they are the ob- ject of the ideas of my foul, they produce in it the illufory and chimerical idea' of extenfion, and of body. As often as my foul thinks of bodies and of motion, this proves that a great quantity of other monads are ftill buried in their obfeurity; it is like- wife when I think of them, that my foul forms with- in itfelf the idea of fome extenfion, which is confe- quently nothing but mere illufion.
The more monads there are plunged in the abyfs of the obfeurity of their ideas, the more is my foul dazzled with the idea of extenfion ; but when they come to clear up their obfeure ideas, exteniion feems to me to diminifh, and this produces in my foul the illufory idea of motion.
You will afk, no doubt, How my foul perceives that other monads fucceed in developing their ob- feure ideas, feeing there is no connection between them and me? The partifans of the fyftem of mo- nads are^ ready with this reply, that it takes place conformably to the perfect harmony which the Cre- ator (who is himfelf only a monad,) has eftabliilied between monads, by which each perceives in itfelf, as in a mirror, every developement produced in 'others, without any manner of connection between them.
E 4 It
$6 REFLECTIONS ON THE
It is to be hoped, then, that all monads may at length become fo happy as to clear up their obfcure ideas, and then we mould lofe all ideas of body and of motion; and the illufion, arifmg- merely from the obfcurity of ideas, would entirely ceafe.
But there is little appearance of the arrival of this bleffed ftate; moll monads, after having acquired the capacity of clearing up their obfcure ideas, fud- denly relapfe. When fhut up in my chamber, I per- ceive myfelf but of fin all extenfion, becaufe feveral monads have then unfolded their ideas: but as fpon as I walk abroad, and contemplate the vaft expanfe of heaven, they niuft all have relapfed into their ftate of dulnefs.
There is no change of place or of motion; all that is illufion merely : my foul remains almoft al- ways in the fame place, juft as all other monads. But, when it begins to unfold fome ideas, which be< fore were but very obfcure, it appears to me then that I am approaching the object which they repre- fent to me, or rather that which the monads of fuch idea excite in me : and this is the real explanation of the phenomenon, when it appears to us that we are approaching to certain objects.
It happens but too frequently that the elucidations we had acquired are again loft ; then it appears to us that we are removing from, the fame object. And here we muft look for the true folution of our jour- neyings. My idea, for example, of the city of Mag- deburg is produced by certain monads, of which at prefent I have but very obfcure ideas ; and this is
the
SYSTEM OF MONADS. 57
the reafon why I confider myfelf as at a diftance from Magdeburg. Laft year, thefe fame ideas fuddenly became clear, and then I imagined I was travelling to Magdeburg, and that I remained there feveral days. This journey, however, was an illufion merely, for my foul never ftirs from its place. It is likewife an illufion when you imagine yourfelf abfent from Berlin, becaufe the confufed representation of certain monads excites an obfcure idea of Berlin, which you have only to clear up, and that inftant you are at Berlin. Nothing more is neceffary. What we call journeys, and on which we expend fo much money, is mere illulion. Such is the real plan of the fyitem of monads.
You will aik, Is it poffible there ever fhould have been perfons of good fenfe, who ferioufly maintained thefe extravagances ? I reply, there have been but too many, that I know feveral of them, that there are fome at Berlin, nay perhaps at Magdeburg. 23d Miy, 1761.
LETTER XVI.
Continuation,
HPHE fyftem of monads, fuch as I have been de- fcribing it, is a neceffary confequence from the principle, that bodies are compounded of iimple be- ings. The moment this principle is admitted, you are obliged to acknowledge the juftnefs of all the other confequences, which refult from it fo naturally,
that
5 & REFLECTIONS ON THE
that it is impoffibie to reject, any one, however ab- fm'd and contradictory.
Firft, thefe fimple beings, which mull enter into the compofition of bodies, being monads which have no exteniion, neither can their compounds, that is bodies, have any; and all thefe exteniion s become iliufion, chimera, it being certain, that parts defd- tute of exteniion are incapable of producing a real exteniion ; it can be, at moll, an appearance, or a phantom which dazzles by a fallacious idea of ex- teniion. In a word, every thing becomes illulion, and upon this is founded the fyftem of pre-eitablilhed harmony, the difficulties of which I have already pointed out.
It is neceffary then to take care that we be not en- tangled in this labyrinth of abfurdities. If you make a fingle falfe Hep over the threlhold, you are in- volved beyond the power of efcaping. Every thing depends on the firil ideas formed of exteniion ; and the manner in which the partifans of the fyltern of monads endeavour to eftablilh it, is extremely re- ductive.
Thefe philofophers love not to fpeak of the ex- teniion of bodies, becaufe they clearly forefee, that it lTmft become fatal to them in the fequel j but in- ftead of faying, that bodies are extended, they de- nominate them compound beings, /which no one can deny, as exteniion neceffarily fuppofes divisibility, and confequently a combination of parts which con- ftitute bodies. But they prefently make a wrong ufe of this notion of a compound being, for, fay
they,
SYSTEM OF MONADS. 59
tliey, a being can be compounded only fo far as it is made up of fimple beings ; and hence they conclude, that every body is compounded of fimple beings. As foon as you grant them this conclufion, you are caught, beyond the power of retreating; for you are under the neceffity of admitting, that thefe fimple beings, not being compounded, are not extended.
This captious argument is exceedingly feductive. If you permit yourfelf to be dazzled with it, they have gained their point. Only admit this propofl- tion, bodies are compounded of fimple beings, that is, of parts which have no extenfion, and you are • entangled. With all your might, then, refift this affertion : every compound being is made up of fimple beings ; and though you may not be able directly to prove the fallacy, the abmrd confequences which immediately remit, would be fufEcient to over- throw it.
In effect, they admit that bodies are extended ; from this point the partifans of the fyftem of mo- nads fet out, to eftablifh the proportion that they are compound beings; and having hence deduced, that bodies are compounded of fimple beings, they are obliged to allow, that fimple beings are incapable of producing real extenfion, and confequently, that the extenfion of bodies is mere illufion.
An argument whofe conclufion is a direct contra- diction of the premifes is Angularly jxrange : this reafoninsj fets out with advancing that bodies are ex- tended; for, if they were not, how could it be known that they are compound beings, and then
comes
6o REFLECTIONS ON THE
comes the conclusion, that they are not fo. Never was a fallacious argument, in my opinion, more com- pletely refuted than this has been. The queftion was, Why are bodies extended? And, after a little turning and winding, it is anfwered, Becaufe they are notfo. Were I to be afked, Why has a triangle three fides ? and I mould reply, that it is a mere S- lufion, would fuch a reply be deemed fatisfaciory ?
It is therefore certain, that this proportion, ' Every compound being is neceffarily made up of fimple be- ings,' leads to a falfe conclufion, however well-founded it may appear to the partifans of monads, who even pretend to rank it among the axioms, or firft prin- ciples of human knowledge. The abfurdity in which it immediately iffues, is fuflicient to overturn it, were there no other reafons for calling it in queftion.
But as a compound being here means the fame thing as an extended being, it is juft as if it were affirmed, ' Every extended being is compounded of beings which are not fo.' And this is precifely the queftion. It is afked, Whether, on dividing a body, you arrive at length at parts uniufceptible of any farther divifion, for want of extenfion ; or, Whether you never arrive at particles fuch as that the divifi- bility mould be unbounded ?
In order to determine this important queftion, for the fake of argument let it be fuppofed, that every body is compounded of parts without exten- fion. Certain fpecious reafonings may eafilybe em- ployed, drawn from the noted principle of the fuf- ficient rcafon; and it will be faid, that a compound 2 beings
SYSTEM OF MONADS. 6 1
being can have its fufficient reafon only in the fimple beings which compofe it ; which might be true, if the Compound being were in fact made up of fimple beings, the very point in queftion; and whenever this composition is denied, the fufficient reafon be- comes totally inapplicable.
But it is dangerous to enter the lifts with perfons who believe in monads ; for, befides that there is nothing to be gained, they loudly exclaim that you are attacking the principle of the fufficient reafon, which is the bafis of all certainty, even of the exig- ence of God. According to them, whoever refufes to admit monads, and rejects the magnificent fabric, in which every thing is illufion, is an infidel and an atheift. Sure I am that fuch a frivolous imputation will not make the flighted: impreffion on your mind, but that you will perceive the wild extravagancies into which men are driven, when they embrace the fyftem of monads, a fyftem too abfurd to need a refutation in detail ; their foundation being abfo- lutely reduced to a wretched abufe of the principle of the fufficient reafon.
ibth May, 1 76 1.
>»•?:-«<
LETTER XVII.
Conclufion of Reflections on this Syflem.
TX7"E are under the neceffity of acknowledging the divifibility of bodies in infinitum, or of admitting the fyftem of monads with all the extrava- gancies
62 REFLECTIONS ON THE
gancies refulting from it ; there is no other choice ! an alternative which fupplies the partifans of that fyftem with another formidable argument in fupport of it.
They pretend that, by divifibility in infinitum, we are obliged to afcribe to bodies an infinite quality, whereas it is certain that God alone is infinite.
The partifans of the fyftem of monads are very dangerous perfons ; they accufed us of atheifm, and now they charge us with polytheifm, alleging that we afcribe to all bodies infinite perfections. Thus we mould be much worfe than pagans, who only worfhip certain idols, whereas we are accufed of pay- ing homage to all bodies as fo many divinities. A . dreadful imputation, no doubt, were it well founded; and I mould certainly prefer embracing the fyftem of monads, with all the chimeras and illufions which flow from it, to a declaration in favour of divifibility in infinitum, if it involved a conclufion fo impious.
You will allow that to reproach one's adverfaries with atheifm or idolatry is a very ftrange mode of arguing j but where do they find us afcribing to bo- dies this divine infinity ? Are they infinitely power- ful, wife, good, or happy ? By no means : we only affirm, that on dividing bodies, though the divifion be carried on ever fo far, it will always be pofiible to continue it farther, and that you never can arrive I at indivifible particles. It may accordingly be af- i firmed that the divifibility of bodies is without limits ; and it is improper to ufe the term infinity which is f applicable to God alone.
I muft.
SYSTEM OF MONADS; - 63
I muft remark at the fame time, that the word 1 infinity' is not fo dangerous as thefe philofophers infinuate. In faying, for example, infinitely wicked, nothing is more remote from the perfections of God.
They admit that our fouls will never have an end, and thus acknowledge an infinity in the duration of the foul, without marking the leaft difrefpect to the infinite perfections of God. Again, when you afk them if the extent of the univerfe is bounded, are they very indecilive in their anfwer ? Some of them frankly allow, that the extent of the univerfe may very probably be infinite, without our being able, however far our ideas are carried, ^tq. determine its limits. Here then is one infinity more, which they do not deem heretical.
For a ftill ftronger reafon divifibility in infinitum oii9'ht not to give them the leaft offence. To be di- vifible to infinity is not furcly an attribute which any one could ever think of afcribing to the Supreme Being, and confers not on bodies a degree of perfec- tion which would not be far from that which thefe philofophers allow them, in compounding them of monads, which, on their fyftem, are beings endowed with qualities fo eminent, that they hefitate not to give to God himfelf the denomination of monad.
In truth, the idea of a divifion which may be con- tinued without any bounds, contains fo little of the character of the Deity, that it rather places bodies in a rank far inferior to that which fpirits and our fouls occupy ; for it may well be affirmed, that a foul, in its effence, is infinitely more valuable than all the
bodies
64 REFLECTIONS ON THE
bodies in the world. But, on the fyftem of monads, every body, even the vileft, is compounded of a vaft number of monads, whofe nature has a great refem- blance to that of our fouls. Each monad reprefents to itfelf the whole world as eafily as our fouls j but, fay they, their ideas of it are very obfcure, though we have already clear, and fometimes alfo diftinci, ideas of it. ♦.
But what affurance have they of this difference ? Is it not to be apprehended that the monads which compofe the pen wherewith I am writing, may have ideas of the univerfe much clearer than thofe of my foul ? How can I be affured of the contrary ? I ought to be aihamed to employ a pen in conveying my feeble conceptions, while the monads of which it conlifts poffibly conceive much more fublimely ; and you might have greater reafon to be fatisfied, fliould the pen commit its own thoughts to paper, inftead of mine.
In the fyftem of monads, that is not neceffary ; the foul reprefents to itfelf, beforehand, by its inherent- powers, all the ideas of my pen, but in a very obfcure manner. What I am now taking the liberty to fug- geft, contributes abfolutely nothing to your informa- tion. The partifans of this fyftem have demonftrated that fimple beings cannot exercife the flighteft influ- ence on each other ; and your own foul derives from itfelf what I have been endeavouring to convey, with- out my having any concern in the matter.
Converfation," reading and writing, therefore, are merely chimerical and deceptive formalities, which
illufion
NATURE OF COLOURS. 65
illufion would impofe upon us as the means of ac- quiring and extending knowledge. But I have al- ready had the honour of pointing out to you the wonderful confequences refulting from the fyftem of the pre-eftablifhed harmony ; and I am apprehenfive that thefe reveries may have become too fevere a trial of your patience, though many perfons of fupe- rior illumination confider this fyftem as the moft fublime production of human underftanding, and are incapable of mentioning it but with the moft pro- found refpect.
I flatter myfelf that I have guarded you fufEciently againfl fuch chimeras, however feductive their ap- pearance -> I mould be forry, at the fame time, to have injured in your good opinion a conliderable part of our modern philofophers. They are, for the mofl part, extremely innocent, but remain obftinately at- tached to the fyftem which at firft impofed on them, without greatly troubling themfelves about the ab- furd confequences which flow from it.
$Qtb May, ij6l.
LETTER XVIII.
Elucidation refpecling the Nature of Colours.
[" AM under the neeeility of acknowledging, that
-*- the ideas refpecling colour, which I have already
taken the liberty to fuggeft,* come far fhort of that
* Vol. I. Letters XXVII. XXVIII. and XXXI.
Vol. II, F degree
66 ELUCIDATION RESPECTING
degree of evidence to which I could have wifhed to carry them. This fubject has hitherto proved a ftumbling-block to philofophers, and I muft not flat- ter myfelf with the belief that I am able to clear it of every difficulty. I hope, at the fame time, that the elucidations which I am going to fubmit to your ex- amination, may go far toward removing a confider- able part of them'.
The ancient philofophers ranked colours among the bodies of which we know only the names. When they were alked, for example, why fuch a body was red, they anfwered, it was in virtue of a quality which made it appear red. You muft be fenfible that fuch an anfwer conveys no information, and that it would have been quite as much to the purpofe to confefs ignorance.
Defcartes, who firft had the courage to plunge into the myfteries of nature, afcribes colours to a certain mixture of light and fhade, which laft being nothing elfe but a want of light, as it is always found where the light does not penetrate, muft be incapable of producing the different colours we obferve.
Having remarked that the fenfations of the organ of fight are produced by the rays which ftrike that organ, it neceffarily follows, that thofe which excite in it the fenfation of red, muft be of quite a different nature from thofe which produce the fenfation of the other colours ; hence it is Cafily comprehended that each colour is attached to a certain quality of the rays which ftrike the organ of vifton. A body ap- pears
THE NATURE OF COLOURS. 6f
pears to us red, when the rays which it emits are of a nature to excite in our eyes the fenfation of that colour*
The whole, then, refults in an enquiry into the difference of the rays which variety of colours pro- duces. This difference muft be great, to produce fo many particular fenfations in our eyes. But wherein can it confift ? This is the great queftion, toward the fblution of which our prefent refearch is directed.
The firft difference between rays which prefents itfelf is, that fome are ftronger than others. It can- not be doubted that thofe of the fun, or of any other body very brilliant, or very powerfully illuminated, muft be much ftronger than thofe of a body feebly illuminated, or endowed with a flender degree of light j our eyes are affuredly ftruck in a very different manner by the one and by the other.
Hence it might be inferred, that different colours refult from the force of the rays of light ; fo that the moft powerful rays mould produce, for example, red ; thofe which are lefs fo, yellow ; and in progreffion, green, and blue.
But there is nothing more eafy than to overturn this fyftem, as we know from experience that the fame body always appears to be of the fame colour, be it lefs or more illuminated, or whether its rays be ftrong or feeble. A red body, for example, appears equally red, expofed to the brighteft luftre of the fun, and in the ftiade, where the rays are extremely faint. We muft not then look for the caufe of the difference of colour in the different degrees of the force of rays
F2 of
68 NATURE OF COLOURS.
of light, it being poffible to reprefent the fame colour as well by very forcible as by very faint rays. The feebleft glimmering ferves equally well to difcover to us difference of colours, as the brighteft effulgence.
It is abfolutely neceffary, therefore, that there mould be another difference of rays difcovered, which may characterize their nature relatively to the dif- ferent colours. You will undoubtedly conclude, that in order to difcover this difference, we muft be better acquainted with the nature of luminous rays ; in other words, we muft know what it is that, reaching cur eyes, renders bodies vifible : this definition of a ray muft be the jufteft, as in effect it is nothing elfe but that which enters into the eye by the pupil, and excites the fenfation in it.
I have already informed you, that there are only two fyftems or theories which pretend to explain the origin and nature of rays of light. The one is that of Newton, who confiders them as emanations pro- ceeding from the fun and other luminous bodies \ and the other, that which I have endeavoured to de- monftrate, and of which I have the reputation of bein^ the author, though others have had nearly the fame ideas of it. Perhaps I may have fucceeded better than they, in carrying it to a higher degree of evidence. It will be of importance, then, to fliew, in both fyftems, on what principle the difference of colours may be eftablifhed.
In that of emanation, which fuppofes the rays to
iftue from luminous bodies, in the form of rivers, or
rather of fountains, fpouting out a fluid in all direc-
. ; tions,
THE ANALOGY, &C. 69
tions, it is alleged that the particles of light differ in fize or in fubftance, as a fountain might emit wine, oil, and other liquids j fo that the different colours are occafioned by the diverfity of the fubtile matter which emanates from luminous bodies. Red would be, accordingly, a fubtile matter iffuing from the lu- minous body, and fo of yellow and the other colours. This explication would exhibit clearly enough . the origin of the different colours, if the fyftem itfelf had a folid foundation. I fhall enter into the fubject more at large in my next letter.
zd June, 1 761.
LETTER XIX. Reflexions on the Analogy between Colours and Sounds,
YOU will be pleafed to recollect the objections I offered to the fyftem of the emanation of light.* They appear to me fo powerful, as completely to overturn that fyftem. I have accordingly fucceeded in my endeavours to convince certain natural philo- fophers of diftinction, and they have embraced my fentiments of the fubje& with expreilions of lingular fatisfaction,
Rays of light, then, are not an emanation from the fun and other luminous bodies, and confift not of a fubtile matter emitted forcibly by the fun, and transmitted to us with a rapidity which may well
* Vol. I. Letters XVII. and XVIII.
F3 fill
JO THE ANALOGY BETWEEN
fill you with aftonifhment. If the rays employed only eight minutes in their courfe from the fun to us, the torrent would be terrible, and the mafs of that luminary, however vaft, muft fpeedily be ex- hausted.
According to my fyftem, the rays of the fun, of which we have a fenfible perception, do not proceed immediately from that luminary ; they are only par- ticles of ether floating around us, to which the fun communicates nearer and nearer a motion of vibra- tion, and confequently they do not greatly change their place in this motion.
This propagation of light is performed in a manner fimilar to that of found. A bell, whofe found you hear, by no means emits the particles which enter your ears. You have only to touch it when ftruck, to be affured that all its parts are in a very fenfible agitation. This agitation immediately communicates itfelf to the more remote particles of air, fo that all receive from it fucceflively a fimilar motion of vibra- tion, which, reaching the ear, excite in it the fenfation of found. The firings of a Vnufical inftrurnent put the matter beyond all doubt ; you fee them tremble, go and come. It is even poflible to determine by calculation how often in a fecond each firing vibrates ; and this agitation, being communicated to the par- ticles of air adjacent to the organ of hearing, the ear is ftruck by it precifely as often in a fecond. It is the perception of this tremulous agitation which con- ftitutes the nature of found. The greater the num- ber
COLOURS AND SOUNDS. Jl
ber of vibrations, produced by the firing in a fecond, the higher or ftiarper is the found. Vibrations lefs frequent produce lower notes.
We find the circumftances, which accompany the fenfation of hearing, in a manner perfectly analogous, in that of fight.
The medium only, and the rapidity of the vibra- tions differ. In found, it is the air through which the vibrations of fonorous bodies are tranfmitted. But with refpect to light, it is the ether, or that me- dium incomparably more fubtile and more elaftic than air, which is univerfally diffufed wherever the air and groffer bodies leave interftices.
As often then as this ether is put into a ftate of vibration, and is tranfmitted to the eye, it excites in it the fentiment of vifion, which is,inthat cafe, nothing but a fimilar tremulous motion, whereby the fmall nervous fibres at the bottom of the eye are agitated.
You eafily comprehend, that the fenfation muff be different, according as this tremulous agitation is more or lefs frequent ; or according as the number of vibrations performed in a fecond is greater or lefs* Hence there muft refult a difference fimilar to that which lakes place in founds, when the vibrations are more or lefs frequent. This difference is clearly per* ceptible by the ear, as the character of founds in re- fpect of flat and fharp depends on it. You will re- coiled that the note marked C in the harpficord per- forms about i oo vibrations in a fecond ; note D 112; note E 125; noteF 133; note G 150; note A 166; note B 1 87 j and note C 200. Thus the nature o£
• F 4 founds
J1 THE ANALOGY BETWEEN
founds depends on the number of vibrations per- formed in a fecond.
It cannot be doubted that the fenfe of feeing may be likewife differently affected, according as the num- ber of vibrations of the nervous fibres of the bottom of the eye is greater or lefs. When thefe fibres vi- brate i ooo times in a fecond, the fenfation muft be quite different from what it would be, did they vi- brate 1 200 or 1500 times in the fame fpace.
True it is that the organ of vifion is not in a con- dition to reckon numbers fo great, ft ill lefs than the ear is to reckon the vibrations which conftitute found; but it is always in our power to diflinguifh between the greater and the lefs.
In this difference, therefore, we muft look for the caufe of difference of colour ; and it is certain that each of them correfponds to a certain number of vi- brations, by which the fibres of our eyes are ftruck in a fecond, though we are not as yet in a condition to determine the number correfponding to each parti- cular colour, as we can do with refpect to founds.
Much refearch muft have been employed before it was poflible to afcertain the numbers correfponding to all the notes of the harpfichord, though there was an antecedent conviction that their difference was founded on the diverfity of thofe numbers. Our knowledge reflecting thefe objects is neverthelefs confiderably advanced, from our being affured that there prevails a harmony fo delightful between the different notes of the harpfichord and the different colours ; and that the circumftances of the one ferve
to
COLOURS AND SOUNDS. 73
to elucidate thofe of the other. This analogy ac- cordingly furnifhes the moft convincing proofs in fupport of my fyftem. But I have reafons fall more folid to adduce, which will fecure it from every at- tack.
6th Juuet 1761.
LETTER XX.
Continuation.
NOTHING is more adapted to the communica- tion of knowledge refpecHng the nature of vifion, than the analogy difcoverable, almoft in every particular, between it and the hearing. Colours are to the eye what founds are to the ear. They differ from each other as flat and fharp notes differ. Now we know that flat and fharp in founds depends on the number of vibrations whereby the organ of hear- ing is ftruck in a given time, and that the nature of each is determined by a certain number which marks the vibrations performed in a fecond. From this I conclude, that each colour is likewife reftricled to a number of vibrations, which acl: on vifion ; with this difference, that the vibrations which produce found relide in grofs air, whereas thofe of light and colours are tranfmitted through a medium incompa- rably more fubtile and elaftic. The fame thing holds as to the objects of both fenfes. Thofe of hearing are all of them bodies adapted to the tranfmiflion of found, that is fufceptible of a motion of vibration,
74 THE ANALOGY BETWEEN
or of a tremulous agitation, which, communicating itfelf to the air, excites in the organ the fenfation of a found corresponding to the rapidity of the vi- brations.
Such are all mufical inftruments ; and, to confine myfelf principally to the harpfichord, we afcribe to each firing a certain found which it produces when ftruck. Thus one firing is named C, another D, and fo on. A firing is named C, when its ftruchire and tenlion are fuch, that being ftruck, it produces about 100 vibrations in a fecond; and if it produced lefs or more in the fame time, it would have the name of a different note, higher or lower.
You will pleafe to recollect, that the found of a firing depends on three things, its length, its thick- nefs, and the degree of tenlion ; the more it is ftretched, the fliarper its found becomes: and as long as it preferves the fame difpofition, it emits the fame found ; but that changes as foon as the other under- goes any variation.
Let us apply this to bodies which are the objects of vifion. The minuter particles which compofe the tiffue of their furface, may be confidered as firings diftended, in as much as they are endowed with a certain degree of elafticity and bulk, fo that being ftruck they acquire a motion of vibration, of which they will finilh a certain number in a fecond : and on this number depends the colour which we afcribe to fuch body. It is red, when the particles of its furface have fuch a degree of tenlion, that being agi- tated, they perform precifely fo many vibrations in
a fecond
COLOURS AND SOUNDS. 75
a fecond as are neceffary to excite in us the fenfation of that colour, A degree of tenfion which would produce vibrations more or lefs rapid, would excite that of a different colour, and then the body would be yellow, green, or blue, &c.
We have not as yet acquired the ability of afiign- ing to each colour the number of vibrations which conftitute its effence ; we do not fo much as know which are the colours that require a greater or lefs rapidity of vibration, or rather^ it is not yet deter- mined what colours correfpond with high or low notes. It is fufficient to know, that each colour is attached to a certain number of vibrations, though it has not hitherto been afcertained ; and that you have only to change the teniion or elafticity of the particles which form the furface of a body, to make it change colour.
We fee that the mod beautiful colours in flowers quickly change and difappear, from a failure of the nutritive juices : and becaufe their particles lofe their vigour or their teniion. This too is obfervable in every other change of colour.
To place this in a clearer light, let us fuppofe that the fenfation of red requires fuch a rapidity of vi- bration, that 1 ooq are performed in a fecond ; that orange require 1125, yellow 1250, green 1333, blue 1500, and violet 1666. Though thefe numbers are only fuppofed, this affects not the object I have in view. What I fay as to thefe numbers, will apply in like manner to the really correfponding numbers, if ever they are difcoveredr
A body,.
j6 HOW OPAQUE BODIES
A body, then, will be red, when' the particles of its furface put in vibration, complete iooo in a.fe- cond ; another body will be orange, when dlfpofed fo as to complete 1 1 25 in a fecond, and fo on. Hence it is -obvious that there muft be an endlefs variety of intermediate colours, between the fix principal which I have mentioned ; and it is likewife evident, if the particles of a body being agitated mould perform 1400 vibrations in a fecond, it would be of an in- termediate colour between green and blue ; green correfponding to number 1333, and blue to 1500.
Qtb J une 3 176 1. ■ . . •
LETTER XXI.
How opaque Bodies are retidered vijible.
"OU will find no difficulty in the definition I have beens giving of coloured bodies. The particles of their furface are always endowed with a certain degree of elafticity, which renders them fufceptible of a motion of vibration, as a firing is always fufceptible of a certain found ; and it is the number of vibrations which thefe particles are ca- pable of making in a fecond, which determines the fpecies of colour.
If the particles of the furface have not elafticity fufficient to admit of fuch agitation, the body muft be black, this colour being nothing elfe but a de- privation of light, and all bodies from which no rays are tranfmitted to our eyes appearing black.
I now
ARE RENDERED VISIBLE. 77
I now come to a very important queftion, refpecr.- ing which fome doubts may be entertained. It may be afked, What is the caufe of the motion of vibra- tion which conftitutes the colours of bodies ?
Into the difcovery of this indeed the whole is re- folved ; for as foon as the particles of bodies mail be put in motion, the ether diffufed through the air will immediately receive a fimilar agitation, which, continued to our eyes, conftitutes there that which we call rays , from which vilion proceeds.
I remark, firft, that the particles of bodies are not put in motion by an internal, but an external power, juft as a ftring diftended would remain for ever at reft, were it not put in motion by fome ex- ternal force. Such is the cafe of all bodies in the dark ; for, as we fee them not, it is a certain proof that they emit no fays, and that their particles are at reft. In other words, during the night, bodies are in the fame ftate with the firings of an inftru- ment that is not touched, and which emit no found ; whereas bodies rendered vifible may be compared to firings which emit found.
And as bodies become vifible as foon as they are illuminated, that is as foon as the rays of the fun, or of fome other luminous body, fall upon them, it muft follow, that the fame caufe which illuminates them, muft excite their particles to generate rays, and to produce in our eyes the fenfation of viiion. The rays of light, then, falling upon a body, put its particles into a ftate of vibration.
This appears at firft furprizing, becaufe on ex-
pofing
7§ OPAQUE BODIES, &C
poling our hands to the ftrongeft light, no ienlible impreffion is made on them. It is to be confidered, that the fenfe of touch is in us too grofs to perceive thefe fubtile and flight impreihons, but that the fenfe of light, incomparably more delicate, is powerfully affected by them; this furnifhes an inconteftable proof that the rays of light which fall upon a body poifefs fuflicient force to act upon the minuter par- . tides, and to communicate to them a tremulous agi- tation. And in this precifely confifts the action ne- cefiary to explain how bodies, when illuminated, are put in a condition themfelves to produce rays, by means of which they become vifible to us. It is fuf- ficient that bodies Ihould be luminous or expofed to the light, in order to the agitation of their particles, and thereby to -their producing themfelves rays which render them vifible to us.
The perfect analogy between hearing and light, gives to this explanation the highelt degree of pro- bability. Let a harpfichord be expofed to a great noife, and you will fee that not only the llrings in general are put into a ftate of vibration, but you will hear the found of each, almoft as if it were actually touched. The mechanifm of this phenomenon is eafily comprehended, as foon as it is known that a firing agitated is capable of communicating to the air the fame motion of vibration which, tranfmitted to the ear, excites in it the fenfation of the found which that fame ftring emits.
Now as a ftring produces in the air fuch a motion, it follows, that the air reciprocally acts on the ftring,
and
WONDERS OF THE HUMAN VOICE. 79
and gives it a tremulous motion. And as a noife is
o
capable of putting in motion the firings of a harp- fichord,and of extracting founds from them,the fame thing muft take place in the objects of vifion.
Coloured bodies are fimilar to the firings of a harpfichord, and the different colours to the different notes, in refpect of high and low. The light which falls on thefe bodies, being analogous to the noife to which the harpfichord is expofed, acts on the particles of their furface, as that noife ads on the firings of the harpfichord, and thefe particles thus put in vibra- tion, will produce the rays which (hall render the body vifible.
This elucidation feems to me fufHcient to diflipate every doubt relating to my theory of colours. I flatter myfelf at leaft, that I have eftablifhed the true principle of all colours, as well as explained how they become vifible to us only by the light whereby bodies are illuminated, unlets fuch doubts turn upon fome other point which I have not touched upon.
\%tb Juxe, 1 76 1.
LETTER XXII.
The Wonders of the Human Voice.
TN explaining the theory of founds, I confidered •*■ only two refpecls in which founds could differ ; the one regarded the force of found, and I remarked that it is greater in proportion as the vibrations ex- cited in the air are more violent. Thus the noife of 8 a difcharge
80 WONDEkS OF THE HUMAN VOICE;
a difcharge of cannon, or the ringing of a bell, has more force than that of a ftring, or of the human voice.
The other difference of founds is totally indepen- dent of this, and refers to flat and fharp, according to which we fay fome are low and others high. My remark relatively to this difference, made it to de- pend on the number of vibrations completed in a certain given time, fay a fecond ; fo that the greater fuch number is, the higher or {harper is the found, and the fmaller it is, the found is lower or flatter. < You can eaiily comprehend how the fame note may be either ftrong or faint ; accordingly we fee that the forte and piano employed by muficians, change in no refpect the nature of founds. Among the good qualities of a harpfichord, it is required that all the notes fhould have nearly the fame degree of ftrength, and it is always conlidered as a great fault when fome of the firings are wound up to a greater degree of force than the reft. Now the flat and the fliarp are referable only to the Ample founds, whofe vibrations follow regularly, and at equal intervals ; and, in mufic, we employ only thofe founds which are denominated Ample. Accords are compound founds, or the concourfe of feveral produced at once, among the vibrations of which a certain order muft predominate, which is the foundation of harmony. But when no relation among the vibrations is per- ceptible, it is a confufed noife, with which it is im- poflible to fay what note of the harplichord is in tune, fuch as the report of a cannon or muiket.
There
WONDERS OF THE HUMAN VOICE. 8 J
There is ftill another remarkable difference among the fimple founds, which feems to have efcaped the attention of philofophers. Two founds may be of equal force, and in accord with the fame note of the harpfi chord, and yet very different to the ear. The found of a flute is totally different from that of the French-horn, though both may be in tune with the fame note of the harpiichord, and equally ftrong ; each found derives a certain peculiarity from the in- ftrument which emits it, but it is impoflible to de- fcribe wherein this confifts; the fame iliing too emits different founds according as it is ftruck, touched or pinched. You can eafily diftinguifh the found of the horn, the flute, and other muficalinftruments.
The moil wonderful diverfity, to fay nothing of the variety of articulation in fpeech, is obfervable in the human voice, that aftonilhing mailer-piece of the Creator. Reflect but for a moment on the dif- ferent vowels which the mouth limply pronounces or lings. When the vowel a is pronounced or fung, the found is quite different from that of e, /, o, u, or ai pronounced or fung, though on the fame tone. We mull not, then, look for the reafon of this dif- ference in the rapidity or order of the vibrations j no inveiligation of philofophers has hitherto un- folded this myilery.
You mull be perfectly fen Able, that in order to utter thefe different vowels, a different conformation mull be given to the cavity of the mouth, and that in man the organization of this part is much better adapted to produce thefe effects, than that of ani-
Vql. II. G mals.
$2 WONDERS OF THE HUMAN VOICE.
mals. We find accordingly, that certain birds which learn to imitate the human voice, are never capable of diftinctly pronouncing the different vowels j the imitation is, at beft, extremely imperfect..
In many organs there is a flop which bears the name of the human voice ; it ufually, however, con- tains only the notes which exprefs the vocal founds ai or ae. I have no doubt, that with fome change it might be poffible to produce likewife the other vocal founds a9 e, i, o, u9 ou ; but even this would not be fufficient to imitate a fingle word of the hu- man voice; how combine them with the confonants, which are fo many modifications of the vowels ? We are fo conformed, that, however common the prac- tice, it is alrnoft impoflible to trace and explain the real mechanifm.
We diftinctly obferve three organs employed in exprefling the confonants, the lips, the tongue, and the palate ; but the nofe likewife effentially concurs. On flopping it, we become incapable of pronouncing the letters ffi and n ; the found of b and d only is then to be heard. A firiking proof of the marvel- lous ftru<5ture of our mouth for the pronunciation of the letters undoubtedly is, that all the fkill of man has not hitherto been capable of producing a piece of mechanifm that could imitate it. The fong has been exactly imitated, but without any articulation of founds, and without diftinction of the different Vowels*
The conilruction of a machine capable of exprefling founds, with all the articulations, would no doubt be
a very
PHENOMENA OF ELECTRICITY. 83
a very important difcovery. Were it polTible to exe- cute fuch a piece of mechanifm, and bring it to fuch perfection, that it could pronounce all words, by means of certain flops, like thofe of an organ or harpfichord, every one would be furprized, and juflly, to hear a machine pronounce whole difcourfes or fermons together, with the mod graceful accompa- niments. Preachers and other orators, whofe voice is either too weak or difagreeable, might play their fermons or orations on fuch a machine, as organifis do pieces of mufic. The thing does not feem to me impoflible.
i6tb June, 1 76 1.
LETTER XXIII.
A Summary of the principal Phenomena of Eleclricity,
THE fubject which I am now going to recom- mend to your attention almoft terrifies me. The variety it prefents is immenfe, and the enume- ration of facts ferves rather to confound than to in- form. The fubjecl I mean is Electricity, which, for fome time paft, has become an object of fuch im- portance in phyfics, that every one is fuppofed to be acquainted with its effects.
You muft undoubtedly have frequently heard it mentioned m converfation ; but I know not whe- ther you have ever witneffed any of the experiments. Natural philofophers of modern times profecute the ftudy of it with ardour, and are almoft every day
G 2. difcoverino-
84 .SUMMARY OF THE PRINCIPAL
difcovering new phenomena, the defcription of which would employ many hundreds of letters ; nay, per- haps, I fliould never have done.
^.And here it is I am embarraffed. 1 could not bear to think of letting you remain unacquainted with a branch of natural philofophy fo effential j but I would willingly fave you the fatigue of wading through a diffufe detail of the phenomena, which, after all, would not furnifh the neceffary information. I flatter myfelf, however, that I have difcovered a road which will lead fo directly to the object, that you fhall attain a knowledge of it much more per- fect than that of moll natural philofophers, who de- vote night and day to the inveftigation of thefe myf- teries of nature*
Without Hopping to explain the various appear- ances and effects of electricity, which would engage me in a long and tedious detail, without extending your knowledge of the caufes which produce thefe effects, I fhall purfue quite a different courfe, and begin with unfolding the true principle of nature on which all thefe phenomena are founded, however various they may appear, and from which they are all eafily deducible.
It is fufficient to remark, in general, that electri- city is excited by the friction of a glafs tube. It thereby becomes electrical : and then it alternately attracts and repels light bodies which are applied to it, and on the application of other bodies, fparks of lire are mutually extracted, which, increafed in itrength, kindle fpirits of wine and other combuftible
fubftances.
PHENOMENA OF ELECTRICITY. 85
fubftances. On touching fuch tube with the finger, you ' feel, befide the fpark, a puncture which may, in certain circumftances, be rendered fo acute as to produce a commotion through the whole body.
Inftead of a tube of glafs, we like wife employ a globe of the fame, which is made to turn round an axis, like a turning-wheel. During this motion it is rubbed with the hand, or with a cufhion applied to it ; then the globe becomes electric, and produces the lame phenomena as the tube.
Befides glafs, refinous bodies, fuch as Spanifh wax and fulphur, likewife poifefs the property of becom- ing electric by friction ; but certain fpecies of bodies only have this quality, of which glafs, fealing-wax, and fulphur, are the principal.
With no effect do other bodies undergo friction ; no fign of electricity appears : but on applying them to the nrft, when rendered electric, they immediately acquire the fame property. They become electric, then, by communication, as the touch, and frequently the approximation only, of electric bodies, renders them fuch.
All bodies, therefore, are divifible into two claries ; in the one are included fuch as become electric by friction, in the other thofe which are rendered fuch by communication, whereas friction produces no manner of effect on them,. It is very remarkable, that bodies of the nrft clafs receive no electricity from communication : when you apply to a tube or globe of glafs ftrongly electrified, other glafles, or bodies, which friction renders electric, this touch commu-
G 3 nicates
86 SUMMARY OF THE PRINCIPAL
nicates no electricity to them. The diftinction of thefe two claifes of bodies is worthy of attention, the one clafs being difpofed to become electrical by friction only, and not by communication, the other, on the contrary, only by communication.
All metals belong to this laft clafs, and the commu- nication extends fo far, that on preferring one extre- mity of a wire to an electric body, the other ex- tremity becomes fo likewife, be the wire ever fo long ; and on applying ftili another wire to the far- ther extremity of the firft, the electricity is conveyed through the whole extent of that fecond thread, and thus electricity may be tranlinitted to the molt re- mote diftances.
Water is a fubitance which receives electricity by communication. Large pools have been electrified to fuch a degree, that an application of the finger has elicited fparks, and excited pain.
The prevailing perfuafion now is, that lightning and thunder are the effect of the electricity which the clouds acquire, from whatever caufe. A thun- der ftorm exhibits the fame phenomena of electricity, on the great fcale, which the experiments of natural phiiofophers do in miniature.
20tb June, 1761.
LETTER
PHENOMENA OF ELECTRICITY. 87
LETTER XXIV.
The true Principle of Nature, on which are founded all the Phenomena of Electricity.
THE fummary I have exhibited of the principal phenomena of electricity, has no doubt excited a curioiity to know what occult powers. of nature are capable of producing effects fo furprizing.
The greateft part of natural philofophers acknow- ledge their ignorance in this refpecl. They appear to be fo dazzled by the endlefs variety of phenomena which every day prefent themfelves, and by the An- gularly marvellous- circumftances which accompany thefe phenomena, that they are difcouraged from attempting an inveftigation of the true caufe of them. They readily admit the exiftence of a fubtile matter, which is the primary agent in the production of the phenomena, and which they denominate the electric fluid ; but they are fo embarraffed about determin- ing its nature and properties, that this important branch of phyfics is rendered only more perplexed by their refearches.
There is no room to doubt, that we muft look for the fource of all the phenomena of electricity only in a certain fluid and fubtile matter ; but we have no need to go to the regions of imagination in queft of it., That fubtile matter denominated ether ^ whofe reality I have already endeavoured to demon-
G 4 ftrate,
88 ELECTRICITY FOUNDED ON THE
ftrate,* is fuflicient very naturally to explain all the furprizing effects which electricity prefents. I hope I fhall be able to fet this in fo clear a light, that you fhall be able to* account for every electrical pheno- menon, however itrange an appearance it may af- fume.
The great requifite is to have a thorough know- ledge of the nature of ether. The air which . we breathe rifes only to a certain height above the fur- face of the earth ; the higher you afcend, the more fubtile it becomes, and at laft it entirely ceafes. We muft not affirm, that beyond the region of the air there is a perfect vacuum, which occupies the im- menfe fpace in which the heavenly bodies revolve. The rays of. light which are diffufed in all directions from thefe heavenly bodies, fufficiently demonftrate that thofe vaft fpaces are filled with a fubtile matter.
If the rays of light are emanations forcibly pro- jected from luminous bodies, as fome philofophers have maintained, it muft follow, that the whole fpace of the heavens is filled with thefe rays, nay that they move through it with incredible rapidity. You have only to recollect the prodigious velocity with which the rays of the fun are tranfmitfed to us. On this hypothec's, not only would there be no vacuum, but all fpace would be filled with a fubtile matter, ancj that in a. ftate of conftant and moft dreadful agitation.
But I think I have clearly proved, that rays of li^ht are no more emanations projected from lumi-
* Vol. I. Letter XV.
nous
TRUE PRINCIPLE OF NATURE. 89
nous bodies, than found is from fonorous bodies. It is much more certain, that rays of light are nothing elfe but a tremulous motion or agitation of a fubtile matter, juft as found confifts of a fimilar agitation excited in the air. And as found is produced and tranfmitted by the air, light is produced and tranf- mitted by that matter, incomparably more fubtile, denominated ether, which confequently fills the im- menfe fpace between the heavenly bodies.
Ether then is a medium proper for the tranfmif- fion of rays of light, and this fame quality puts us in a condition to extend our knowledge of its nature and properties. We have only to reflect on the properties of air, which render it adapted to the re- ception and tranfmiffion of found. The principal caufe is its elafticity or fpring. • You know that air has a power of expanding itfelf in all directions, and that it does expand, the inftant that obftacles are re- moved. The air is never at reft, but when its elaf- ticity is every where the fame; whenever it is greater in one place than another, the air immediately ex- pands. We likewife difcover by experiment, that the more the air is comprefled, the more its elafti- city increafes : hence the force of air-guns, in which the air, being very ftrongly compreifed, is capable of difcharging the ball with aftonifhing velocity. The contrary takes place when the air is Tarefied : its elafticity becomes lefs in proportion as it is more ra- refied, or diffufed over a larger fpace.
On the elafticity of the air, then, relative to its denfity, depends the velocity of found, which makes
a progrefs
90 OF ELECTRICITY.
a progrefs of about i ooo feet in a fecond. If the elafticity of the air were increafed, its denfity re- maining the fame, the velocity of found would in- creafe : and the fame thing would take place if the air were more rare, or lefs denfe than it is, its elaf- ticity being the fame. In general, the more that any medium, fimilar to air, is elaftic, and at the fame time lefs denfe, the more rapidly will the agita- tions excited in it be tranfmitted. And as light is tranfmitted fo many thoufand times more rapidly than found, it muft clearly follow, that the ether, that medium whofe agitations conftitute light, is many thoufand times more elaftic than air, and, at the fame time, many thoufand times more rare or more fubtile, both of thefe qualities contributing to accelerate the propagation of light.
Such is the reafon which leads to conclude, that ether is many thoufand times more elaftic and more fubtile 'than air ; its nature being in other refpecls fimilar to that of air, in as much as it is likewife a fluid matter, and fufceptible of compreffion and of rarefa&ion. It is. this quality which will conduct us to the explanation of all the phenomena of elec- tricity.
Z id June, 1761,
LETTER
DIFFERENT NATURE OF BODIES. 91
LETTER XXV,
Continuation, Different Nature of Bodies relatively to Eleclricity.
ETHER being a fubtile matter, and fimilar to air, but many thoufand times more rare and more elaftic, it cannot be at reft, unlefs its elafticity, or the force with which it tends to expand, be the fame every where.
As foon as the ether in one place mail be more elaftic than in another, which is the cafe when it is more comprefled there, it will expand itfelf into the parts adjacent, comprefling what it finds there, till the whole is reduced to the fame degree of elafticity. It is then in equilibrio ; the equilibrium being no- thing elfe but the ftate of reft, when the powers which have a tendency to difturb it counterbalance each other.
When therefore the ether is not in equilibrio, the fame thing muft take place as in air, when its equi- librium is difturbed ; it muft expand itfelf from the place where its elafticity is greater, toward that where it is lefs ; but confidering its greater elafticity and fubtilty, this motion muft be much more rapid than that of air. The want of equilibrium in the air produces wind, or the motion of that fluid from one place to another. There muft therefore be pro- duced a fpecies of wind, but incomparably more fubtile, than that of air, when the equilibrium of the
ether
92 DIFFERENT NATURE OF BODIES
ether is difturbed, by which this laft fluid will pafs from places where it was more compreffed and more elaftic, to thofe where it Was lefs fo.
This being laid down, I with confidence affirm, that all the phenomena of electricity are a natural confequence of want of equilibrium in the ether, fo that wherever the equilibrium of the ether is dif- turbed, the phenomena of electricity muft take place ; confequently, electricity is nothing elfe but a de- rangement of the equilibrium of the ether.
In order to unfold all the effects of electricity, we muft attend to the manner in which ether is blended and inveloped with all the bodies which furround us. Ether, in thefe lower regions, is to be found only in the fmall interftices which the particles of the air and of other bodies leave unoccupied. Nothing can be more natural than that the ether, from its extreme fubtilty and elafticity, mould infinuate itfelf into the fmalleft pores of bodies, which are impervious to air, and even into thofe of the air itfelf. You will re- collect that all bodies, however folid they may ap- pear, are full of pores ; and many experiments in- conteftibly demonftrate, that thefe interftices occupy much more fpace than the folid parts ; finally, the lefs ponderous a body is, the more it muft be filled with thefe pores, which contain ether only. It is clear, therefore, that, though the ether be thus dif- fufed through the fmalleft pores of bodies, it muft however be found in very great abundance in the vicinity of the earth.
You will eafily compreIiend9 that the difference
of
RELATIVELY TO ELECTRICITY. 93
of thcfe pores muft be very great, both as to mag- nitude and figure, according to the different nature of the bodies, as their diverfity probably depends on the diverfity of their pores. There muft be, there- fore, undoubtedly, pores more clofc, and which have lefs communication with others ; fo that the ether which they contain is likewife more confined, and cannot difengage itfelf but with great difficulty, though its elafticity may be much greater than that of the ether which is lodged in the adjoining pores. There muft be, on the contrary, pores abundantly open, and of eafy communication with the adjacent pores ; in this cafe it is evident, that the ether lodged in them can with lefs difficulty difengage itfelf than in the preceding ; and if it is more or lefs elaftic in thefe than in the Others, it will foon recover its equi- librium.
In order to diftinguifh thefe two clafTes of pores, I fhall denominate the firft clofe, and the others open. Moft bodies muft contain pores of an intermediate fpecies, which it will be fufficient to diftinguifh by the terms more or lefs clofe9 and more or lefs open.
This being laid down, I remark, firft, that if all bodies had pores perfectly clofe, it would be impof- fible to change the elafticity of the air contained in them ; and even though the ether in fome of thefe pores mould have acquired, from whatever caufe, a higher degree of elafticity than the others, it would always remain in that ftate, and never recover its equilibrium, from a total want of communication. In this cafe, no change could take place in bodies ;
all
94 DIFFERENT NATURE OF BODIES
all would remain in the fame ftate as if the ether were in equilibrio, and no phenomenon of electricity could be produced.
This would likewife be the cafe if the pores of all bodies were perfectly open : for then, though the ether might be more or lefs elaftic in fome pores than in others, the equilibrium would be inftantly reftored, from the entire freedom of communication, and that fo rapidly, that we mould not be in a con- dition to remark the flighteft change. For the fame reafon, it would be impoffible to difturb the equili- brium of the ether contained in fuch pores ; as often as the equilibrium might be difturbed, it would be as inftantaneoufly reftored, and no fign of electricity would be difcoverable.
The pores of all bodies being neither perfectly clofe nor perfectly open, it will always be pollible to dif- turb the equilibrium of the ether which they con- tain : and when this happens, from whatever caufe, the equilibrium cannot fail to re-eftablifh itfelf : but this re-eftablifhment will require fome time, and this produces certain phenomena : and you will prefently fee, much to your fatisfaclion, that they are pre- cifely the fame which electrical experiments have dis- covered. It will then appear, that the principles on which I am going to eftablifh the theory of electri- city are extremely fimple, and at the fame time ab- folutely incontrovertible.
2 J to June, 1 76 1.
LETTER
RELATIVELY TO ELECTRICITY. 95
LETTER XXVI.
On the fame Subjecl.
I HOPE I have now furmounted the mod formi- dable difficulties which prefent themfelves in the theory of electricity. You have only to prefer ve the idea of ether, which I have been explaining ; and which is that extremely fubtile and elaftic matter diffufed not only through all the void fpaces of the univerfe, but through the minuteft pores of all bodies, in which it is fometimes more and fometimes lefs en- gaged, according as they are more or lefs clofe. This conlideration conducts us to two principal fpecies of bodies, of which the one has pores more clofe, and the other pores more open.
Should it happen, therefore, that the ether con- tained in the pores of bodies, has not throughout the fame degree of elafticity, and that it i& more or lefs comprefled in fome than in others, it will make an effort to recover its equilibrium ; and it is precifely from this that the phenomena of electricity take their rife, which, of confequence, will be varied, in pro- portion as the pores in which the ether is lodged are various, and grant it a communication more or lefs free with the others.
This difference in the pores of bodies perfectly cor- refponds to that which the firfl phenomena of elec- tricity have made us to remark in them, by which fome eafily become electrical by communication, or 1 the
^6 DIFFERENT NATURE OF BODIES
the proximity of an electrical body, whereas others fcarcely undergo any change. Hence you will im- mediately infer, that bodies which receive electricity fo eafily, by communication alone* are thofe whofe pores are open ; and that the others which are almoft infenfible to electricity, inuft have theirs clofe, either entirely or to a very great degree.
It is, then, by the phenomena of electricity them- felves, that we are enabled to conclude what are the bodies whofe pores are clofe or open. Reflecting which permit me tofuggeft the following elucidations*
Firft, the air which we breathe has its pores almoft entirely clofe ; fo that the ether which it contains^ cannot difengage itfelf but with difficulty, and mull find equal difficulty in attempting to penetrate into it. Thus, though the ether diffufed through the air is not in equilibrio with that which is contained in other bodies, where it is more or lefs compreffed, the re-eftablifhment of its equilibrium is not to be pro- duced without extreme difficulty ; this is to be un- derftood of dry air, humidity being of a different na- ture, as I fhall prefently remark.
Farther, we muft rank in this clafs of bodies, with clofe pores, glafs, pitch, refinous bodies, fealing wax, fulphur, and particularly filk. Thefe fubftances have their pores fo very clofe, that it is with extreme dif- ficulty the ether can either efcape from, or penetrate into, them.
The other clafs, that of bodies whofe pores are open, contains, firft, water and other liquors, whofe nature is totally different from that of air. For this
reafon
RELATIVELY TO ELECTRICITY. 97
reafoh when air becomes humid, it totally changes its nature with refpect to electricity, and the ether can enter or efcape without almoft any difficulty. To this clafs of bodies, with open pores, likewife muff be referred thofe of animals, and all metals.
Other bodies, fuch as wood, feveral forts of ftones and earths, occupy an intermediate ftate between the two principal fpecies which I have juft mentioned, and the ether is capable of entering or efcaping with more or lefs facility, according to the nature of each fpecies.
After thefe elucidations on the different nature of bodies, with refpect to the ether which they contain, you will fee with much fatisfaction, how all the phe- nomena of electricity, which have been confidered as fo many prodigies, flow very naturally from them.
All depends, then, on the ftate of the ether, dif- fufedor difperfed through the pores of all bodies, in as far as it has not throughout the fame decree of elafticity,' or as it is more or lefs compreffed in fome than in others ; for the ether not being then in equi- librio, will make an effort to recover it. It will en- deavour to difengage itfelf as far as the opennefs of the pores will permit, from places where it is too much compreffed, to expand itfelf and enter into pores where there is lefs compreffion, till it is through- out reduced to the fame degree of compreffion and elafticity, and is, of confequence, in equilibrio.
Let it be remarked, that when the ether paffes from a body where it was too much compreffed, into another where it is lefs fo, it meets with great ob-
Vol. II. H ftacles
98 DIFFERENT NATURE OF BODIES.
ftacles in the air which feparates the two bodies, on account of the pores of this fluid, which are almoft entirely clofe. It however panes through the air, as a liquid and extremely fubtile matter, provided its force is not inferior, or the interval between the bodies too great. Now this paffage of the ether being very much impeded, and almoft entirely prevented by the pores of the air, the fame thing will happen to it, as to air forced with velocity through fmaM apertures, a hilling found is heard, which proves that this fluid is then put into an agitation which produces fuch found.
It is, therefore, extremely natural, that the ether, forced to penetrate through the pores of the air, fhould likewife receive a fpecies of agitation. You will pleafe to recollect,1 that as agitation of the air produces found, a fimilar agitation of ether produces light. As often, then, as ether efcapes from one body, to enter into another, its paffage through the air muft be accompanied with light ; which appears fometimes under the form of a fpark,fometimes under that of a flafh of lightning, according as its quantity is more or lefs confiderable.
Here, then, is the moft remarkable circumftance which accompanies moft electrical phenomena, ex- plained to a demonftration, on the principles I have laid down. I fhall now enter into a more particular detail, which will furnifti me with a very agreeable fubject for fome following letters.
$ztbjme, 1761.
LETTER
OF ELECTRICITY. 99
LETTER XXVII.
Of pofitive and negative Electricity. Explanation of the Phenomenon of Attraction.
YOU will eafily comprehend from what I have above advanced, that a body muft become elec- trical, whenever the ether contained in its pores be- comes more or lefs elaftic than that which is lodged in adjacent bodies. This takes place when a greater quantity of ether is introduced into the pores of fuch body, or when part of the ether which it con- tained is forced out* In the former cafe, the ether becomes more compreffed, and confequently more elaftic ; in the other, it becomes rarer, and lofes its elafticity. In both cafes > it is no longer in equilibrio with that which is external ; and the efforts which it makes to recover its equilibrium, produce all the phenomena of electricity.
You fee then that a body may become electric in two different ways, according as the ether contained in its pores becomes more or lefs elaftic than that which is external ; hence refult two fpecies of elec- tricity : the one, by which the ether is rendered more elaftic, or more compreffed, is denominated in» creafed or pofitive eleBricity\ the other, in which the ether is lefs elaftic, or more rarefied, is denominated diminijhed or negative eleclricity* The phenomena of* both are nearly the fame ; a flight difference only is obfervable, which I fhall mention.
H 2 Bodies
100 OF POSITIVE AND
Bodies are not naturally electrical, as the elafticity of the ether has a tendency to maintain it in equili- brio, it muft always require a violent operation to difturb this equilibrium, and to render bodies elec- trical; and fuch operations muft act on bodies with clofe pores, that the equilibrium once deranged may not be inftantly reftored. We accordingly find that glafs,. amber, fealing-wax, or fulphur, are the bodies employed to excite electricity.
The eafieft operation, andj for feme time paft, the moft universally known, is to rub a flick of fealing wax, with a piece of woollen cloth, in order to com- municate to that wax the power of attracting fmall flips of paper and of other light bodies. Amber, by means of friction, produces the fame phenomena; and as the ancients gave to this body the name of eleflrum,the power excited by friction obtained, and preferves, the name of ekSiricity : natural philofophers of the remoteft ages having remarked, that this fub- ftance acquired by friction the faculty of attracting light bodies.
This effect undoubtedly arifes from the derange- ment of the equilibrium of the ether by means of friction. I muft begin, therefore, with explaining this well-known experiment. Amber and fealing- wax have their pores abundantly clofe, and thofe of wool are abundantly open ; during the friction, the pores of both the one and the other comprefs them- felves, and the ether which is contained in them, is reduced to a higher degree of elafticity. According as the pores of the wool are fufceptible of a compref-
fion
NEGATIVE ELECTRICITY. l6l
-lion greater or lefs than tliofe of amber or fealing- wax, it muft happen, that a portion of ether mall pafs from the wool into the amber, or reciprocally from the amber into the wool. In the former cafe? the amber becomes pofitively electric, and in the other negatively ', and its pores being clofe, it will remain in this ftate for fome time j whereas the wool, though it has undergone a fimilar change, will- prefently re- cover its natural ftate.
From the experiments which electric fealing-wax furnifhes, we conclude that its electricity is negative; and that a part of its ether has palled during the friction into the wool. Hence you perceive how a ftick of fealing-wax is, by friction on woollen clothe deprived of part of the ether which it contained, and muft thereby become electric. Let us now fee what effects muft refult from this, and how far they cor- refportd with obfervation and experience.
Let AB (plate II- Jig- 24.) be a ftick of fealing-wax, from which, by friction, part of the ether contained in its pores has been forced out ; that which remains being lefs comprefled, will therefore have lefs force to expand itfelf, or, in other words, will have lefs elafticity than that contained in other bodies in the circumambient air : but as the pores of air are ftill clofer than thofe of fealing-wax, this prevents the ether contained in the air from palling into the fealing-wax, to reftore the equilibrium ; at leaft this will not take place till after a confiderable interval of time.
; Let a fmall and very light body C, whofe pores
H 3 are
102 OF POSITIVE AND
are open, be now prefented to the ftick of fealing-wax, the ether contained in them, finding a free paffage, becaufe it has more force to expand itfelf than is op- pofed to it by the ether fhut up in the ilick at c, will fuddenly efcape, will force a paffage for itfelf through the air, provided the diftance is not too great, and will enter into the fealing-wax. This paffage, how- ever, will not be effected without very confiderable difficulty, as the pores of the fealing-wax have only a very finall aperture, and confequently it will not be accompanied with a vehemence capable of putting the ether in a motion of agitation, to excite a fenfible light, A faint glimmer' ng only will be perceptible jn the dark, if the electricity is fufEciently ftrong.
But another phenomenon will be obfervable, which is no lefs furprizing, the fmall body C will fpring to- ward the fealing-wax, as if attracted by it. To ex- plain the caufe of this, you have only to confider, that the fmall body C, in its natural ftate, is equally preffed on all fides by the air which furrounds it ; but as in its prefent ftate, the ether makes its efcape, and paffes through the air in the direction C c, it is evident, that this laft fluid will not prefs fo violently on the fmall body, on this ftde, than on any other, and that the preffure communicated to it toward c, will be more powerful than in any other direction, impelling it toward the fealing-wax as if attracted by it.
Thus are explained, in a manner perfectly intel- ligible, the attractions obfervable in the phenomena pf electricity. In this experiment, the electricity is
too
NEGATIVE ELECTRICITY. I03
too feeble to produce more furprizing effects. I fhall have the honour of prefenting you with a more ample detail in the following letters.
\*b July, 1761.
LETTER XXVIII.
On the fame Subjecl.
SUCH were the faint beginnings of the electrical phenomena ; it was not till lately that they were carried much farther. At firft a tube of glafs was employed, fimilar to that of which barometers are made ; but of a larger diameter, which was rubbed with the naked hand, or with a piece of woollen cloth, and electrical phenomenamore ftrikingwere obferved. You will readily comprehend, that on rubbing a tube of glafs, part of the ether muft pafs, in virtue of the compreflion of the pores of the glafs, and of the rubbing body, either from the hand into the glafs, or from the glafs into the hand, according as the pores of the one or of the other are more fuf- ceptible of compreflion in the friction. The ether, after this operation, eafily recovers its equilibrium in the hand, becaufe its pores are open ; but thofe of the glafs being abundantly clofe, this fluid will pre- ferve its ftate in it, whether the glafs were furcharged or exhaufted, and confequently will be electric, and will produce phenomena fimilar to thofe of fealing- wax, but undoubtedly much flronger, as its electri- city is carried to a higher degree, as well from the
H 4 greater
I04 OF POSITIVE AND /
greater diameter of the tube, as from the very nature of glafs.
Experiments give us reafon to conclude, that the tube of glafs becomes, by thefe means, furcharged with ether, whereas fealing-wax is exhaufted of it 5 the phenomena however are nearly the fame.
It muft be obferved, that the glafs tube retains its electricity as long as it is furrounded only with air, becaufe the pores of the glafs and thofe of the air, are too clofe to allow a communication fufficiently free to the ether, and to exhauft the glafs of what it has more than in its natural ftate ; fuperfluity of ether always increafing elafticity. But the air muft be very dry, for only when in that ftate are its pores fufficiently clofe ; when it is humid or loaded with vapours, experiments do not fucceed, whatever de» gree of friction you beftow on the glafs. The reafon is obvious ; for water, which renders the air humid, having its pores very open, receives every inftant the fuperfluous ether which was in the glafs, and which of courfe remains in its natural ftate. Expe- riments fucceed, then, in only very dry air; let us now fee what phenomena a glafs tube will, in that cafe, produce, (plate ILfig* 2 5. ) after having under* gone confiderable friction.
It is clear, that on prefenting to it a fmall light body C with open pores, fuch as goldJeaf, the ether in the tube more elaftic at the neareft parts D, £, will not make ineffectual efforts to difcharge itfelf and pafs into the pores of the body C. It will force a path through the air, provided the diftance be not
too
VcrlJf ^pJi/irui-a£um- oJ*t/z?lfn^/<7'i>so^JJ/aJellJW#7idJe?<<j>js
NEGATIVE ELECTRICITY. 1 05
too great ; and you will even fee a light between the tube and the body occafioned by the agitation ex- cited in the ether, which paffes with difficulty from the tube into the body. When, inftead of the body C, the finger is applied to it, you feel a pricking oc- cafioned by the rapid entrance of the ether ; and if you expofe your face to it at fome diftance, you feel a certain agitation in the air, excited by the tranfition of the ether. Thefe circumftances are likewife ac- companied, fornetimes, with a flight cracking, pro- duced undoubtedly by the agitation of the air which the ether traverfes with fuch rapidity.
I muft entreat you to keep in mind, that an agi- tation in the air always produces a found, and that the motion of ether produces light ; and then the explanation of thefe phenomena will become abun- dantly eafy.
Let the fmall light body C, be replaced in the vi- cinity of our electric tube; as long as the ether is efcaping from the tube, to enter into the pores of the body C, the air will be in part expelled from it, and confequently will not prefs fo ftrongly on the body on that fide, as in every other direction ; it will hap- pen, then, as in the preceding cafe, that the body C will be impelled toward the tube, and, being light, will come clofe up to it. We fee, then, that this ap, parent attraction equally takes place, whether the ether in the tube be too much or too little elaftic ; or, whether the elafticity of the tube be pofitive or negative. In both cafes, the paffage of the ether flops the air? and by its preffure hinders it from acting.
But
Io6 ON THE ELECTRIC ATMOSPHERE.
But while tjie fmall body C is approaching the tube, the paflage of the ether becomes ftronger, and the body C will foon be as much furcharged with ether as the tube itfelf. Then the action of the ether, which arifes from its elafticity only, entirely ceafes, and the body C will fuftain on all fides an equal preffure. The attraction will ceafe, and the body C will remove from the tube, as nothing detains it, and its own gravity puts it in motion. Now as foon as it removes, its pores being open, its fuperfluous ether prefently efcapes in the air, and it returns to its na- tural ftate. The body will then act. as at the begin- ning, and you will fee it again approach the tube, fo that it will appear alternately attracted and repelled by it ; and this play will go on till the tube has loft its electricity. For as, on every attraction, it dis- charges fome portion of its fuperfluous ether, befides the infenfible efcape of part of it in the air, the tube will foon be re-eftablifhed in its natural ftate, and in its equilibrium ; and this fo much the more fpeedily as the tube mall be fmall, and the body C light : then all the phenomena of electricity will ceafe.
-jib July, 1 761.
LETTER XXIX,
On the eleffric Atmofphere*
I HAD almoft forgot to bring forward a moft ef- fential circumftance, which accompanies all elec- tric bodies, whether po/itively or negatively fuch, and
which
ON THE ELECTRIC ATMOSPHERE. I07
which fupplies fome very ftriking elucidations for explaining the phenomena of electricity.
Though it be indubitably true that the pores of air are very clofe, and fcarcely permit any communi- cation between the ether that they contain, and what is in the vicinity, it undergoes however fome change when near to an electric body.
Let us firft confider an electric body negatively fo, as a ftick of fealing-wax v^ B, (plate III. fig. i.) which has been deprived by friction of part of the ether contained in its pores, fo that what it now contains has lefs elafticity than that of other bodies, and con- fequently than that of the air which furrounds the wax. It muft neceliarily happen, that the ether con- tained in the particles of the air which immediately touch the wax, as at m, having greater elafticity, {hould difcharge itfelf, in however fmall a degree, into the pores of the wax, and will confequently lofe fomewhat of its elafticity. In like manner, the par- ticles of air more remote, fuppofe at n, will likewife fuffer a portion of their either to efcape into the nearer at m, and fo on to a certain diitance, beyond which the air will no longer undergo any change. In this manner, the air round the ftick of wax, to a certain diitance, will be deprived of part of its ether, and be- come itfelf electric.
This portion of the air, which thus partakes of the electricity of the ftick of wax, is denominated the eleclric atmofphere ; and you will fee from the proofs which I have juft adduced, that every electric body muft be furrounded with an atmofphere. For 6 if
Io8 ON THE ELECTRIC ATMOSPHERE*
if the body is pofiil-vely eleclric, fo as to contain a Su- perfluity of ether, it will be more coinpreffed in fuch a body, and confequently more elaftic, as is the cafe with a tube of glafs when rubbed; this ether, more elaftic, then difcharges itfelf, in a fmall degree, into the particles of air which immediately touch it, and thence into particles more remote, to a certain dis- tance ; this will form another- electric atmofphere round the tube, in which the ether will be more compreiTed, and confequently more elaftic than elfe- where.
It is evident that this atmofphere which furrounds fuch bodies, muft gradually diminifh the electricity of them, as in the firft cafe there paffes almoft con- tinually a fmall portion of ether, from the furround* ing air, into the eleclric body, and which, in the other cafe, iiTues from the electric body, and paffes into the air. This is likewife the reafon why electric bodies at length lofe their electricity ; and this fd much the fooner, as the pores of the air are more open. In a humid air, whofe pores are very open, all electricity is almoft inftantly extinguiihed ; but in very dry air it continues a confiderable time.
This electric atmofphere becomes abundantly fen- iible, on applying your face to an electrified body ; you have a feeling fimilar to the application of a fpi- der's web, occafioned by the gentle tranfition of the ether from the face into the electric body, or red* procally from this laft into the face, according as it is negative or pofitive, to ufe the common expreffion.
The electric atmofphere ferves likewife more clearly
to
ON THE ELECTRIC ATMOSPHERE. 109
to explain that alternate attraction and repulfion of light bodies placed near to electric bodies, which I mentioned in the preceding letter ; in which you muft have remarked, that the explanation of repul- fion, there given, is incomplete ; but the electric at- mofphere will fupply the defect. • Let A B (plate III. Jig. 2. J reprefent an electric tube of giafs furcharged with ether, and let C be a fmall light body, with pores fufficiently open, in its natural flate. ; Let the atmofphere extend as far as the diftance D E. Now, as the vicinity of C con- tains already an ether more elaftic, this will difcharge itfelf into the- pores of the body C, there will imme- diately iflue from the tube a new ether, which will pafs from D into C, and it is the atmofphere chiefly which facilitates this paffage. For if the ether con- tained in the air had no communication with that in the tube, the corpufcle C would not feel the vicinity of the tube ; but while the ether is paiTmg from D to Q, the preifure of the air between C and D will be diminiihed, and the corpufcle C will no longer be preffed equally in all directions ; it will therefore be impelled toward D, as if attracted by it. Now in proportion as it approaches, it will be likewile more and more furcharged with ether, and will become electric as the tube itfelf, and, consequently, the elec- tricity of the tube will no longer act upon it.
But as now the corpufcle, being arrived at D, con- tains too much ether, and more than the air at E, it will have a tendency to efcape, in order to make its way to E. The atmofphere, in which the compref-
fion
110 ON THE ELECTRIC ATMOSPHERE*.
fion of the ether continues to diminifli from DtoE will facilitate this paflage, and the fuperfluous ether will in effect flow from the corpufcle toward E. By this paflage, the preffure of the air on the corpufcle will be fmaller on that lide than every where elfe, and confequently the corpufcle will be carried to* ward D, as if the tube repelled it. But as foon as it arrives at £, it difcharges the fuperfluous ether, and recovers its natural ftate ; it will then be again at- tracted toward the tube, and, having reached it, will be again repelled, for the reafon which I have juft been explaining.
It is the electric atmofphere then, chiefly, which produces thefe Angular phenomena, when we fee electrified bodies alternately attract and repel fmafl light bodies, fuch as little flips of paper, or particles of metal, with which this experiment beft fucceeds, au the fubftances have very open pores.
You will fee, moreover, that what I have juft now faid refpecting pofitive electricity, muft equally take place in negative. The tranfition of the ether is only reverfed, by which the natural preffure of the air muft always be diminifhed.
llth July, 1 76 1.
LETTER
COMMUNICATION OF ELECTRICITY. Ill
LETTER XXX.
Communication of Eleclricity to a Bar of Iron, by meant of a Globe of Glafs.
AFTER the experiments made with glafs tubes, we have proceeded to carry electricity to a higher degree of ftrength. Inftead of a tube, a globe, or round ball of glafs, has been employed, which is made to turn with great velocity round an axis, and on applying the hand to it, or a cufhion of fome matter with open pores, a friction is produced, which renders the globe completely electric.
Figure 4. of plate III. reprefents this globe, which may be made to move round an axis A B, by a me- chanifm fimilar to that employed by turners. C is the cufhion flrongly applied to the globe, on which it rubs as it turns round. The pores of the cufhion being, in this friction, compreifed more than thofe of the glafs, the ether contained in it is expelled, and forced to infinuate itfelf into the pores of the glafs, where they continue to accumulate, becaufe the open pores of the cufhion are continually fupply- ing it with more ether, which it is extracting, at leaft in part, from furrounding bodies ; and thus the globe may be furcharged with ether to a much higher degree than glafs tubes. The effects of electricity are, accordingly, rendered much more confiderable, but of the fame nature with thofe which I have de- fcribed, alternately attracting and repelling light bo- dies -f
112 COMMUNICATION OF ELECTRICITY.
dies ; and the fparks which we fee, on touching the electric globe, are much more lively.
But naturalifts have not refted fatisfied with fuch experiments, but have employed the electrical globe in the difcovery of phenomena much more fur- prizing.*
Having conitructed the machine for turning the globe round its axis AB, a bar of iron FG is fuf- pended above, or on one fide of, the globe, and to- ward the globe is directed a chain of iron or other metal ED, terminating at D, in metallic filaments, which touch the globe. It is fufficient that this chain be attached to the bar of iron in any manner whatever, or but touch it. When the globe is turned round, and, in turning, made to rub on the cufiiion at C, in order that the glafs may become furcharged with ether, which will, confequently, be more elaftic, it will eafily pafs from thence into the filaments D, for, being of metal, their pores are very open ; and from thence, again, it will difcharge itfelf by the chain DE, into the bar of iron FG. Thus by means of the globe, the ether extracted from the cuiliion C, will fuccefiively accumulate in the bar of iron FG, which likewife, of confequence, becomes electric, and its electricity increafes in proportion as you con- tinue to turn the globe.
If this bar had a farther communication with other bodies, whofe pores too are open, it would foon difcharge into them its fuperfluous ether, and thereby lofe its electricity ; the ether extracted from
* See Plate III. Fig. 3.
the
TO A BAR OF IRON. II3
the cufhion would be difperfed over all the bodies which had an inter-communication, and its greateft compreflion would not be more perceptible. To prevent this, which would prove fatal to all the phe- nomena of electricity, the bar muft, of neceflity, be fupported, or fufpended, by props of a fubftance whofe pores are very clofe ; fuch are glafs, pitch, fulphur, fealing-wax, and filk. It would be proper, then, to fupport the bar on props of glafs or pitch ; - or to fufpend it by cords of filk. The bar is thus fecured as;ainft the tranfmifiion of its accumulated ether, as it is furroundecl on all fides only by bodies with clofe pores, which grant hardly any admiffion to the ether in the bar. The bar is then faid to be ifolated, that is, deprived of all contact which could communicate, and thereby diminiih, its electricity. You muft be fenfible, however, that it is not poffible abfolutely to prevent all wafte ; for this reafon the electricity of fuch a bar muft continually diminiih, if it were not kept up by the motion of the globe.
In this manner electricity may be communicated to a bar of iron, which never could be done by the moft violent and perfevering friction, became of the opennefs of its pores. And, for the fame 'reafon, fuch a bar rendered electric by communication, pro- duces phenomena much more furprizing. On pre- senting to it a finger, or any other part of the body, you fee a very brilliant fpark dart from it, which, entering into the body, excites a pungent, and fome- times -painful, fenfation. I recollect my once having prefented to it my head? covered with my peruke and
Vol. H. I hat,
H4 Communication of electricity.
hat, and the ftroke penetrated it fo acutely, that I feit the pain next day.
Thefe fparks, which efcape from every part of the bar, on prefcnting to it a body with open pores, let on fire, at once, fpirit of wine, and kill fmall birds whofe heads are expofed to them. On plunging the end of the chain DE into a bafon filled with water, and fupported by bodies with clofe pores, fuch as glafs, pitch, filk, the whole water becomes electric; and fome authors affure us that they have feen con- liderable lakes electrified in this manner, fo that, on applying the hand, you might have feen even very pungent fparks emitted from the water. But it ap- pears to me, that the globe muft be turned a very long time indeed, to convey fuch a portion of ether, into a mafs of water fo enormous; it would be like- wife neceffary that the bed of the lake, and every thing in contact with it, fliould have their pores clofe.
The more open, then, the pores of a body are? the more difpofed it is to receive a higher degree of electricity, and to produce prodigious effects. You muft admit that all this is perfectly conformable to the principles which I at firft eltablifhed.
i^tb July, 1 76 1.
LETTER
ELECTRISATION OF ANIMALS. 115
LETTER XXXI.
Eleftrifation of Men and Animals.
AS electricity may be communicated from glafs to a bar of iron, by means of a chain, which forms that communication, it may likewife be con- veyed into the human body; for the bodies of ani- mals have this property in common with metals and water, that their pores are very open ; but the man, who is to be the fubjecr. of the experiment, muft not be in contact with other bodies whofe pores are like- wife open.
For this effect, the man is placed on a large lump of pitch, or feated on a chair fupported by glafs co- lumns, or a chair fufpended by cords of filk, as all thefe fubftances have pores fufficiently clofe to pre- vent the efcape of the ether, with which the body of the man becomes furcharged by electricity.
This precaution is abfolutely neceiTary, for were the man placed on the ground, the pores of which are abundantly open, as foon as the ether was con- veyed into his body, to a higher degree of compref- lion, it would immediately difcharge itfelf into the earth, and we muft be in a condition to furcharge it entirely with ether, before the man could become electric. Now you muft be fenfible, that the cufhion by which the globe of glafs is rubbed, could not pof- fibly fupply fuch a prodigious quantity of ether, and that were you to extract it even out of the earth it-
I % felf,
Il6 ELECTRISATION OF
felf, you could gain no ground, for you would juft take away as much on the one hand as you gave on the other.
Having, then, placed the man, whom you mean to electrify, in the manner which I have indicated, you have only to make him touch, with his hand, the globe of giafs while it turns, and the ether, ac- cumulated in the globe, will eahly pafs into the open pores of the hand, and diffufe itfelf over the whole body, from whence it cannot fo eafily efcape, as the air, and all the bodies with which he is furrounded, have their pores clofe. Inilead of touching the globe with his hand, it will be fumcient for him to touch the chain, or even the bar, which I defcribed in the preceding letter ; but in this cafe, not only the man himfelf muft be furcharged with ether, but likewife the chain with the bar of iron ; and as this requires a greater quantity, of ether, it would be neceilary to labour longer in turning the globe, in order to fup- ply a fuhicient quantity.
In this manner the man becomes entirely, electric, or, in other words, his whole body will be fur- charged with ether, and this fluid will confequently be found there in the highefl degree of comprefiion and electricity, and will have a violent tendency to efcape.
You muft be abundantly fenfible, that a ftate fo violent cannot be indifferent to the man. The body is, in its minuteft parts, wholly penetrated with ether, and the fmalleft fibres, as well as the nerves, are fo filled with it, that this ether, without doubt
pervades
MEN AND ANIMALS. l\J
pervades the principal fprings of animal and vital - motion. It is, accordingly, obferved, that the pulfe of a man electrified beats fafter, he is thrown into a fweat, and the motion of the more fubtile fluids, with which the body is filled, becomes more rapid. A certain change is likewife felt over the whole bedy, which it is impoiTible to defcribe ; and there is every reafon to believe, that this ftate has a pow- erful 'influence on the health, though fufficient ex- periments have not yet been made, to afcertain in what cafes this influence is falutary or otherwife. It may fometimes be highly beneficial to have the blood and humours raifed to a more lively circulation ; certain obftruclions, which threaten dangerous con- fequences, might thereby be prevented ; but on other occafions, an agitation too violent might prove in- jurious to health. The fubjecT: certainly well deferves the attention of medical gentlemen. We have heard of many furprizing cures performed by electricity, but we are not yet enabled fufficiently to diftinguifh the/ occafions on which we may promife ourfelves fuccefs.
To return to our electrified man ; it is very re- markable that, in the dark, we fee him furrounded with a light, fimilar to that which painters throw round the heads of faints. The reafon is abundantly ! obvious j as there is always efcaping from the body of that man, fome part of the ether with which he is furcharged, this fluid meets much refiftance from the clofe pores of the air, it is thereby put into a
J 3 ' certain
1 1 8 ELECTRISATION OF ANIMALS.
certain agitation, which is the origin of light, as I have had the honour to demonftrate.
Phenomena of a very furprizing nature are re* marked, in this ftate of a man electrified. On touch- ing him, you not only fee very brilliant fparks iffue from the part which you touch, but the man feels, befides, a very pungent pain. Farther, if the per- fon who touches him be in his natural ftate, or not •electrified, both fenfibly feel this pain, which might have fatal confequences, efpecially if he were touched in the head, or any other part of the body of acute fenlibility. You will readily comprehend, then, how little indifferent it is to us, that part of the ether contained in our body efcape from it, or that new ether is introduced, efpecially as this is done with fuch amazing rapidity.
Moreover, the light, with which we fee the man furrounded in the dark, is, an admirable confirmation of my remarks refpecting the electric atmofphere which is diffufed round all bodies ; and you will no longer find any difficulty in the moft part of elec- trical phenomena, however inexplicable they may, at firft, appear.
LETTER
SPECIES OF ELECTRICITY. II9
LETTER XXXII.
D'ljlin&ive Char after of the two Species of Eleclriclty.
YOU will pleafe to recoiled, that not only glafs becomes electric by friction, but that other fub- ftances, fuch as fealing-wax and fulphur, have the fame property, in as much as their pores are likewife clofe, fo that whether you introduce into them an ex- traordinary quantity of ether, or extract a part of it, they continue for fome time in that Hate, nor is the equilibrium fo foon reftored.
Accordingly, inftead of a globe of glafs, globes of fealing-wax and fulphur are employed, which are likewife made to revolve round an axis, rubbing at the fame time againft a cufhion, in the fame manner which I defcribed reflecting a globe of glafs. Such globes are thus rendered equally electric, and, on ap- plying to them a bar of iron which touches them only by flender filaments or fringes of metal, inca- pable of injuring the globe, electricity is immediately communicated to that bar, from which you may afterwards tranfmit it to other bodies at pleafure.
Here, however, a very remarkable difference is obfervable. A globe of dafs rendered electric in this manner, becomes furcharged with ether, and the bar of iron, or other bodies brought into com- munication with it, acquire an electricity of the fame nature ; or, in other words, the ether contained is in a ftate of too great compreffion, whofe elafticity is
1 4 increafed*
120 CHARACTER OF THE TWO
increafed. This electricity is denominated pefttive or augmented electricity. But when a globe of fealing- wax or fulphur is treated in the fame manner ; an eleclricity directly oppoiite is the refult, which is de- nominated negative, or diminijhed eleclricity, as it is perceived that, by friction, thefe globes are deprived of part of the ether contained in their pores.
You will be lurprized to fee that the fame friction is capable of producing effects altogether oppoiite; but this depends on the nature of the bodies which: undergo the friction, whether by communicating or receiving it, and of the rigidity of their particles which contain the pores. In order to explain the poffibility of this difference, it is evident, at firfl fight, that when two bodies are rubbed violently againfl each other, the pores of the one mull, in mofl cafes, undergo a greater compreffion than thofe of the other, and that then, the ether contained in the pores, is extruded, and forced to infinuate itfelf into thofe of the bodies which are lefs compreffed.
It follows, then, that in this friction of glafs againfl a cufhion, the pores of the cufhion undergo a greater compreffion than thofe of the glafs, and confequently the ether of the cufhion mufl pafs into the glafs, and produce in it a pofitive or increafed electricity, as I have already fliewed. But on fubflituting a globe of fealing-wax or of fulphur in place of the glafs, thefe fubflances being fufceptible of a greater degree of pompreffion in their pores,, than the fubftance of the cufhion with which the friction is performed, a part of the ether contained in thefe globes will be forced
out,
SPECIES OF ELECTRICITY. 121
out, and conftrained to pais into the cufhion ; the globe of fealing-wax or fulphur will, thereby, be de- prived of part of its ether, and, of courfe, receive a negative or dimi?iijhed electricity.
. The electricity which a bar of iron, or of any other metal, receives from communication with a globe of. fealing-wax or fulphur, is of the fame nature ; as is alfo that which is communicated to a man placed on a lump of pitch, or fufpended by cords of filk. When fuch a man, or any other body, with open porer., electrified in the fame manner, is touched, nearly the fame phenomena are obfervable, as in the cafe of po- fitive electricity. The touch is here likewife accom- panied with a fpark, and a puncture on both fides. The reafon is obvious : for the ether which, in this cafe, efcapes from bodies in their natural ftate, to enter into electrified bodies, being under conftraint, muft be under an agitation, which produces light. A ' fenfible difference is, however, to be remarked in the figure of the fpark, according as the electricity is po- fitive or negative. See that of pofitive electricity ; . plate HI. fig. 5. '
If the bar A B poffeffes pofitive electricity, and the finger C is prefented to it, the light which ifhies out of the bar appears under the form of rays diverging from the bar toward the finger m n> and the luminous point is feen next the finger.
But if the bar A B (plate III. Jig* 6. J is negatively electric, and the finger C is prefented to it, the lu- minous rays m n diverge from the finger, and you fee the luminous point p next the bar.
This
*22 OF THE TWO SPECIES '
This is the principal character by which pofitive is diftinguifhed from negative electricity. From whence foever the ether efcapes, the fparkis emitted in the figure of rays diverging from that point ; but when the ether enters into a body, the fpark is a lu- minous point toward the recipient body.
Zijl July, l76i.
LETTER XXXIII.
How the fame Globe- of Glafs may ftrnifh, at once, the two Species of Eleclricily.
YOU will be enabled to fee ftill more clearly the difference between pofitive and negative electri- city, after I have explained how it is poffible to pro- duce, by one and the fame globe of glafs, both the fpccies ; and this will ferve, at the fame time, farther to elucidate thefe wonderful phenomena of nature.
Let A B ( 'plate VI* jig* \-J be the globe of4 glafa, turning round its axis C, and rubbed againft by the cufhion D, in an oppofite direction to which the globe is touched by the metallic filaments F, attached to the bar of iron FG, which is fufpended by cords of filk H and I, that it may no where touch bodies with open pores.
This being laid down, you know that, by friction againft the cufhion D, the ether paffes from the cufhion into the glafs, from which it becomes more compreffed, and confequently more elaftic : it will pais, therefore, from thence, by the metallic filaments
F, into
Vol.JT.
JPIaiein
Fw,l
-JZ#T2
OF ELECTRICITY. I 23
E, into the bar of iron F G : for though the pores of glafs are abundantly clofe, as the ether in the globe is continually" accumulating by the friction, it foon becomes fo overcharged, that it efcapcs by the metallic filaments; and difcharges itfelf into the bar, by which this laft becomes equally electric.
Hence you perceive, that all this fuperfluity of ether is fupplied by the cufhion, which would fpeedily be exhausted, unlefs it had a free communication with the frame which fupports the machine, and thereby with the whole earth which is every inflant fupplying the cufhion with new ether, fo that as long as the friction continues, there is a quantity fufficient farther to comprefs that which is in the globe and in the bar. But if the whole machinery is made to reft on pillars of glafs, as M and N, or if it is fufpended by cords of fiik, that the cufhion may have no communication with bodies whofe pores are open, which might fupply the deficiency of ether, it would foon be exhaufted, and the electricity could not be conveyed into the globe and the bar, beyond a certain degree, which will be fcarcely perceptible, unlefs the cufhion be of a prodigious fize. To fupply this defect, the cufhion D is put in communication with a large mafs of metal E, the ether of which is fufficient to fupply the globe and the bar, and to carry it to fuch a high degree of compreffion.
You will thus procure to the globe and to the bar a pofitive electricity, as has been already explained. But in proportion as they become furcharged with ether, the cufhion and the metallic mafs E will lofe
the
124 - . SPECIES OF ELECTRICITY.
the fame quantity, and thereby acquire a negative electricity : fo that we have here, at once, the two fpecies of electricity ; the pofitive in the bar, and the negative in the metallic mafs. Each produces its effect conformably to its nature. On prefenting a finger to the bar, a fpark with divergent rays will hTue from the bar, and the luminous point will be feen toward the finger ; but if you prefent the finger to the metallic mafs, the fpark with divergent rays will iffue from the finger, and you will fee the lumi- nous point toward the mafs.
Let us fuppofe two men placed on lumps of pitch, to cut off all communication between them and bodies with open pores : let the one touch the bar, and the other the metallic mafs, while the machine is put in motion j it is evident that the former will become pofitively electric, or furcharged with ether, whereas the other, he who touches the metallic mafs, will ac- quire a negative eleclricity, and lofe his ether.
Here then are two electric men*, but in a manner totally different, though rendered fuch by the fame machine. Both will be furrounded by an electric atmofphere, which, in the dark, will appear like the light that painters throw about the figures of faints. The reafon is, that the fupc.rfluous ether of the one Infenfibly efcapes into the circumambient air ; and "that, with refpect to the, other, the ether contained in the air infenfibly infinuates itfelf into his body. This tranfition, though infenfible3 will be accompanied, with an agitation of ether, which produces light. 'B.
It is evident that thefe two fpecies of electricity arex
directly
THE LBYXJEN EXPERIMENr. 1 25
directly oppofite ; but in order to have a thorough conviction of it, let thefe two join hands, or only touch each other, and you will fee very vehement fparks iffue from their bodies, and they themfelves will feel very acute pain.
If they were electrified in the fame manner, which would be the cafe if both touched the bar or the me- tallic mafs, they might fafely touch each other ; no fpark, and no pain, would enfue, becaufe the ether contained in both would be in the fame ftate ; whereas in the cafe laid down, their ftate is directly oppofite.
zybjuly, 1 76 1.
LETTER XXXIV.
The Ley den Experiment.
NOW proceed to defcribe a phenomenon of elec- tricity 5 which has made a great deal of noife, and which is known by the name of the Leyden experiment, becaufe Mr. Moufchenbroeck, profeiTor at Leyden, is the inventor of it. What is moft aftonifhins; in this experiment, is the terrible ftroke refulting from it, by which feveral pcrfons at once may receive a very violent mock.
Let C be a globe of glafs, turned round by means of the handle E, and rubbed by the cufhion D D, which is preffed upon the globe by the fpring O. At Q are the metallic filaments, which tranfmit the electricity into the bar of iron F G, by the metallic chain P.
6 Hitherto
126 THE LEYDEN EXPERIMENT.
Hitherto there is nothing different from the pro- cefs already defcribed. But in order to execute the experiment in queftion, to the bar is attached ano- ther chain of metal H, one extremity of which I, is introduced into a glafs-bottle K K, filled with water; the bottle too is placed in a bafon L L, likewife filled with water. You plunge, at pleafure, into the water in the bafon another chain A, one end of which dra^s on the floor.
Having put the machine in motion for fome time, that the bar may become fufliciently electric, you know- that: if the finger were to be prefented to the extremity of the bar at #, the ufual flroke of elec- tricity would be felt, from the fpark iffuing out of it. But were the fame peifon, at the fame time, to put the other hand into the w?_ter in the bafon at A, of were he but to touch with any part of his body the chain plunged in that water, he would receive a ftroke incomparably more violent, by which his whole frame would undergo a fevere agitation.
This fiiock may be communicated to many p'er- fons at once. They have only to join hands, or to touch each other were it but by the clothes ; then the firft puts his hand into the water in the bafon, or touches the chain only, one end of which is plunged into it, and as foon as the laftperfon applies his finger to the bar, you will fee a fpark dart from it