THE

SCIENTIFIC PAPERS

OF THE HONOURABLE

HENRY CAVENDISH, F.R.S.

CAMBRIDGE UNIVERSITY PRESS

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THE

SCIENTIFIC PAPERS

OF THE HONOURABLE

HENRY CAVENDISH, F.R.S.

VOLUME I
THE ELECTRICAL RESEARCHES

Edited from the Published Papers, and the Cavendish

Manuscripts in the possession of
His GRACE THE DUKE OF DEVONSHIRE, K.G., F.R.S.

by
JAMES CLERK MAXWELL, F.R.S.

CAVENDISH PROFESSOR OF EXPERIMENTAL PHYSICS IN THE
UNIVERSITY OF CAMBRIDGE

Revised by
SIR JOSEPH LARMOR, F.R.S., M.P.

LUCAS1AN PROFESSOR OF MATHEMATICS

CAMBRIDGE

AT THE UNIVERSITY PRESS

1921

The Electrical Researches
First Edition 1879

Reprinted as Volume I of
The Scientific Papers 1921

6?

1/3

CIS
i/, I

PREFACE TO VOLUME I

THE University of Cambridge has a deep interest both in the Author and
in the Editor of the electrical investigations now presented in final form in
this volume.

Henry Cavendish matriculated in the University on 18 Dec. 1749,
from Hackney School. According to records preserved at Peterhouse he
commenced residence there on 24 Nov. 1749, and resided very regularly
and constantly as a Fellow-Commoner until 23 Feb. 1753, when he left
without proceeding to a degree. Two others of the Cavendish family were
at Peterhouse at the same time; Henry's younger brother Frederick who
was entered 10 April, 1751, and also left without taking his degree; and
his cousin Lord John Cavendish, fourth son of the Duke of Devonshire,
afterwards Chancellor of the Exchequer, who was entered 21 Feb. 1750
and became M.A. in 1753. Among his contemporaries at Peterhouse, then
as now a small society, were the Earl of Euston, afterwards as Duke of
Grafton prominent in the writings of Junius, Gray the poet and also Mason*,
and the Greek critic Markland, who was Senior Fellow of the College at
the time and always in residence.

These details are taken from a statement contributed in 1851 to
Dr G. Wilson's Life of Cavendish^ by Prof. F. Fuller, then Fellow and
Tutor of Peterhouse.

James Clerk Maxwell graduated at Cambridge in Jan. 1854. After two
years' resident activity at Cambridge, including election to a Fellowship at
Trinity College, he was appointed in April, 1856 to the Chair of Natural
Philosophy in Marischal College, Aberdeen. There he worked until 1860,
when on the fusion of the two Aberdeen Universities he became Professor
of Natural Philosophy in King's College, London. He resigned that Chair
at Easter, 1865, left London the following year and settled down at his
inherited home at Glenlair near Dalbeattie in Galloway. To quote his own
words of Feb. 1866 (Life, 1882, by L. Campbell and W. Garnett, p. 344) :
" I have now my time fully occupied with experiments and speculations
of a physical kind, which I could not undertake so long as I had public
duties." The result has contributed, more than any other cause, to the
modern revolution in the ideas and methods of physical science.

In October, 1870 William Cavendish, Duke of Devonshire, who had
graduated as second wrangler and first Smith's Prizeman in Mathematics
and a first class in Classics in 1829, and was elected in 1861 Chancellor of

* Mason was tutor to Lord John Cavendish, but was of Pembroke College, having
previously been of St John's.

t Cf. also The Cavendish Family by F. Bickley (1911), pp. 197-208.

vi Preface

the University, signified his desire to build and furnish a Physical Laboratory
for Cambridge: and in prospect of that gift the Cavendish Professorship
of Experimental Physics was founded by Grace of the Senate in Feb. 1871.
In response to appeals from the prominent Cambridge men of the time,
including Stokes, W. Thomson, and Rayleigh, Clerk Maxwell was persuaded
to offer himself for the Chair. He was formally elected the following month,
after six years of retired study and investigation which doubtless had
matured and consolidated the intellectual interests of his life, including
the preparation of the Electricity and Magnetism (Feb. 1873) and the
Theory of Heat (1870). The Laboratory was planned and furnished under
Maxwell's direction, and formally handed over to the University in the
spring of 1874. It was not however until 1877 that the Chancellor had
completed his gift "by furnishing the Cavendish Laboratory with apparatus
suitable to the present state of science"; an equipment to which Maxwell
afterwards contributed many additions. Later, Lord Rayleigh, when
Chancellor of the University, devoted the proceeds of the award of a
Nobel Prize to provide for an urgent expansion of the Laboratory of which
he had himself been Director.

The Electricity and Magnetism shows many marks of hurried final
consolidation with a view to immediate publication. It was said that the
pressing need of a textbook in the University was a paramount considera-
tion : there was no treatise of comparable depth and grasp at that time in
any language. And certainly under Maxwell's influence Cambridge was
the focus in which the new electrical ideas, inherited in outline from
Faraday, were developed and propagated, years before they were taken
up in other countries and thus became everywhere the mainspring of pro-
gress in physical science. Maxwell's own personal investigations during the
Cambridge period, in addition to a series of brilliant articles, now classical,
written for the Encyclopaedia Britannica, were concerned mainly with the
development of the other equally fundamental, but analytically much
more complex, subjects centring round the molecular theory of gases; in
this domain also he had previously (1860) been the originator of the modern
exact analysis, based on application of the mathematical principles of
statistics to the fortuitous dance of the innumerable molecules.

According to Maxwell's biographers his chief continuous literary
occupation, for the five years from 1874 to his death in October, 1879,
was the editing of the Electrical Researches of Henry Cavendish. It had
been well known that Cavendish's papers, preserved in the possession of
his kinsman the Duke of Devonshire, contained a very remarkable and
even mysterious record of progress in electrical as well as chemical science,
effected a hundred years previously by a solitary investigator, of which
only fragments had been revealed by various men of science who had seen
the manuscripts. The publication of an adequate account of the researches
of Cavendish was a task obviously incumbent on British science, for its

Preface vii

own sake ; but the difficulty and labour of the undertaking, and the learning
and historical research that it involved, had hitherto warned off the men
most competent to discharge it. The zeal of Maxwell for his new Cavendish
foundation was not thus to be deterred. Already in July, 1874, we find
him writing from Glenlair to Mr Garnett (Life, p. 389) :

In the MS. he appears to be familiar with the theory of divided currents and
also of conductors in series, but some reference to his printed paper [on the
Torpedo] is required to throw light on what he says. He made a most extensive
series of experiments on the conductivity of saline solutions in tubes, compared
with wires of different metals, and it seems as if more marks were wanted for
him if he cut out G. S. Ohm long before constant currents were invented. His
measures of capacity will give us some work at the Cavendish Laboratory,
before we work up to the point where he left it. His only defect is not having
Thomson's electrometer. He found out inductive capacity of glass, resin, wax,
etc.

According to Mr Garnett (Life, p. 555) who was in a position to be
intimately acquainted with the facts:

The amount of labour which Professor Maxwell bestowed on this work
during the last five years of his life can only be known to those who were
constantly in his company. Nearly all the MSS. he transcribed with his own hand,
the greater part being copied after midnight.... Every obscure passage or altera-
tion was the subject of a long and searching investigation: and many were the
letters written to the Librarian of the Royal Society and to scientific and literary
friends in different parts of the country, to gain information respecting the
meaning of obsolete words and symbols, or the history of individuals. And
besides this, and a comparison of Cavendish's results with those obtained by
subsequent investigators, Maxwell repeated many of Cavendish's experiments
almost in their original form, only employing modern instruments for the
purposes of measurement.

The result of five years of continual application to the subject was the
volume published in October, 1879 by the Cambridge University Press,
a few weeks before the death of its Editor, and now reprinted in different
form. The introductory sketch prepared by Maxwell, probably at the end
of his task, gives a clear and most interesting summary of the electrical
work of Cavendish: the postscript dated 14 June, 1879, describing some
manuscripts on magnetism that had just come to hand, coincides with
the beginning of his final illness.

There is perhaps no instance in the history of science in which the
unpublished records left by an investigator have been arranged and
elucidated with such minute fidelity. Careless though Cavendish was of
scientific reputation, intent on pressing on to new solitary achievement,
to the neglect of publication, due as it would seem as much to the habit of
continual postponement of final preparations for the press as to the
fascination of exercising his powers of discovery — and even, as it has

Vlll

Preface

proved, as a consequence of his recluse and self-centred life— there are
perhaps few investigators of the first rank of whose work and aims and
procedure we have now more complete knowledge than of his.

The additions appended by Maxwell, in the form of thirty-five notes
of elucidation and commentary, on modern lines, relating to Cavendish's
results and methods, constitute an example of powerful and elegant
relevant original investigation such as could hardly have been carried
through by anyone else.

Advantage has been taken of the present reprint of the Electrical
Researches, as constituting Volume I of a definitive edition of the Scientific
Writings of Henry Cavendish, to add a few brief annotations and references
such as were needed to bring Clerk Maxwell's commentary up to date.
These notes, where appended to Cavendish's text, are enclosed in curved
brackets to distinguish them from Maxwell's own. As examples, reference
may be made to pp. 374, 413, 422. The printing of the original edition had
probably proceeded at intervals, and the final consolidation must have
gone on during Prof. Maxwell's last illness in the summer of 1879. Thus it
has now been possible to improve the headings of the chapters and sections,
and the headlines of the pages, so as to convey a clearer and more rapid
view of the nature and content of the text. The index and table of contents
have been improved.

Apart from his permanent contributions to experimental laws, it is
possible to maintain that the theoretical views of Cavendish should now
command on historical grounds even more interest than they could excite
in 1878, when the Electrical Researches were made public in complete
form by Clerk Maxwell. At that time attention was largely concentrated
on the elucidation of the electric field, and the mode of transmission of
electrical influence from one body to another. The formal settlement of
that range of problems on the lines of the Faraday-Maxwell theory has
now transferred investigation to the sources of electric influence; and
problems of the distribution of electrons in conducting and insulating
bodies, their relation to the electrically polarisable molecules of matter,
their function in conduction and in radiation, even the exploration of
crystals in atomic detail by radiations of molecular wave-length, are now
opening out. These problems all involve interaction in a binary medium,
electrons and molecules controlling activities in an aether; it is now an
affair of relations of the field of transmission with electrically polar or
polarisable molecules which are its sources; and though this is very different
from Cavendish's idea of a uniform electric fluid pervading and inter-
acting with material substances by mere attraction, yet the degree of
success that had been attained by the earliei and simpler mode of repre-
sentation can become again by contrast a subject of historical scientific
interest. The title of one of Lord Kelvin's best-known memoirs, "^
atomized," is evidence for this view.

Preface ix

Numerous biographies of Cavendish have been published. He was one
of the select circle of foreign associates of the Institute of France; and
French interest in his work, stimulated by its close relations with that of
Lavoisier, was reflected in memoirs by Cuvier in the £loges Historiques de
I' Academic, vt>l. i and by Biot in the Biographic Universelle, vol. vn. These
and other biographies are drawn upon by Dr George Wilson in the very
thorough Life of Cavendish (pp. 478), including an analysis of his chemical
work, which was undertaken under the auspices of the Cavendish Society,
founded in 1846, and appeared in 1851 as one of the early volumes of their
publications.

The biographical sketch contributed by Dr Thomas Young to the sup-
plement of the Encyclopaedia Britannica about 1820 has been reprinted
here as an Appendix. Young must have been personally well acquainted
with Cavendish, and no one was better qualified to form a contemporary
judgment on his career.

The portrait prefixed to the present volume is said to have been con-
structed from surreptitious sketches made by the artist W. Alexander at
a dinner of the Royal Society Club. The original is in the print room of the
British Museum, where it was re-discovered by Charles Tomlinson, F.R.S.
who had an engraving made from it. This engraving has been reproduced
as a frontispiece to Wilson's Life, and many times since. The present photo-
graphic impression has been taken from the original picture, by permission
of the authorities of the British Museum.

It has been the custom, even among Cavendish's admirers, to brand him
as misanthropic. But there is surely another side to this judgment. The
cultivation of the highest domains of physical science is rarely consistent
with dispersal of interest in other directions. The tracking out of great
discoveries which will be a possession to the human race for all time has
indeed to be its own supreme intellectual satisfaction; and once an in-
vestigator has realized, in however modest a way, his capacity for such
achievement, he can feel that he is serving humanity in the most perfect
manner open to him by concentrating upon that work. Yet the temptation
to continual postponement of ordinary social intercourse inevitably
involves increasing isolation, and growing habits of solitude. As already
noted, there is no evidence that Cavendish's researches aimed at his
personal gratification alone : if they had not been adequately recorded by
him they could not have been recovered so completely: and it is easy to
understand how the driving force of his curiosity and conscious power
would impel him to the exploration of new fields, in temporary preference
to the final polishing of work already achieved. If he spent his life in
compelling the phenomena of physical nature to submit to exact measure
and weight, it was not from a special passion for such work, for its own
sake, but as the one means of assuring an adequate foundation for sciences
then being born : in all directions he was opening up and securing brilliant

x Preface

vistas into the philosophical explication of nature. Though standing so far
beyond most of his contemporaries in intellect and vision, there is abundant
evidence in these volumes that in the cooperative tasks which united the
scientific men of the time, largely conducted under the auspices of the
Royal Society, he was always ready to take unsparing pains, 'and to devote
himself without limit to the assistance of his colleagues. The operations
and discussions preparatory to the gravity survey of Schehallion, sum-
marised in Vol. II, are an example.

The two volumes now published may be regarded as the final garnering
of the work of one of the greatest of scientific discoverers. The acknowledg-
ments of the intellectual world will doubtless be accorded to the Cambridge
University Press for their courage in facing the great expense involved
in a complete edition of the writings of Cavendish, in a form adequate to
the subject, which was projected in the less exacting times before the
Great War. The Editors desire to record their thanks to the staff of the
Press for very efficient cooperation on the technical side of the undertaking.

J.L.
CAMBRIDGE,

February 1921.

CONTENTS

INTRODUCTION BY THE EDITOR

CAVENDISH AND HIS RESEARCHES

PAGE

Biographical data 1

Lord Charles Cavendish's experiments 1

Henry Cavendish lived with his father during his electrical researches ... 2

His laboratory in Great Maryborough Street ........ 2

His apparatus .............. 3

His attendant 5

Committee of the Royal Society on lightning conductors 5

Cavendish's researches on the electric current ........ 6

Papers on the Torpedo by Walsh, Hunter, &c. ........ 7

Experiment on the formation of nitric acid before the Royal Society .... 9

Cavendish's artificial Torpedo 9

CAVENDISH'S WRITINGS ON ELECTRICITY

The two papers in the Philosophical Transactions . . . . . . .10

The manuscripts — Sir W. Snow Harris' account of them . . . . . .10

List of the manuscripts ............ 1 2

Order of the manuscripts determined 13

Why Cavendish did not publish them 15

State of electrical science. Lord Mahon's experiments. Estimate of Cavendish by

Dr Thomas Young ............15

Coulomb's researches 18

Cavendish's method 18

Comparison of charges ............ 18

Proof of the law of force ............ 19

Experiments on coated plates — spreading of electricity 20

Specific inductive capacity ........... 21

Plates of air 21

" Whether the charge of a coated plate bears the same proportion to that of a simple

conductor, whether the electrification is strong or weak" 21

Effect of temperature 22

Effect of floor, walls, and ceiling of room ......... 23

Experiments on resistance 23

Reference to these experiments in the paper on the Torpedo ..... 23

Method of the experiments 24

Determination of the ''power of the velocity to which the resistance is -proportional " 25

Resistance of salt solution at different temperatures 26

Resistance of pure water 26

Resistance of solutions of different salts ......... 27

Chemical equivalents of different substances as given by Cavendish .... 28

Postscript relating to papers on magnetism ........ 29

xii Contents

FIRST PUBLISHED PAPER ON ELECTRICITY P. 33

AN ATTEMPT TO EXPLAIN SOME OF THE PRINCIPAL PHENOMENA
OF ELECTRICITY, BY MEANS OF AN ELASTIC FLUID

From the Philosophical Transactions for 1771 (pp. 584-667)
Part I

ARTICLES

Hypothesis 1-6

Repulsion of a cone on a particle at the vertex 7-1 1

Force between two bodies over or under charged 13-15

Equilibrium of the electric fluid 16.1?

Repulsion of a spherical shell . . . . • . • • . . 18,19

Equilibrium of electricity in a globe 20-27

Two plane parallel plates 28-38

Canals of incompressible fluid 39"53

Pressure of electric fluid against a surface 54

Circular disk 55~66

Charges of similar bodies as the n - i power of their corresponding diameters, and

independent of the material of which they are made 67-72

Charge of a thin flat plate independent of its thickness 73

Two parallel circular plates 74-83

Equilibrium of electricity in bodies communicating by a canal is independent of

the form of the canal 84-93

Whether the conditions of equilibrium are the same for two bodies communicating

by a conducting wire as if they communicated by a canal of incompressible

fluid 94-96

Molecular constitution of air 97

Part II p. 66

CONTAINING A COMPARISON OF THE FOREGOING THEORY WITH EXPERIMENT

§ i . Conductors and non-conductors 98

Electric properties of air and vacuum 99. >oo

Positive and negative electrification 101-105

§ 2. Attraction and repulsion 106-117

Electrometer in electrified air n?

§ 3. On the cases in which bodies receive electricity from or part with it to the air 1 18-122

§4. Effect of points on discharge 123-126

§ 5. Canton's and Franklin's experiments 127

§6. On the Leyden vial 128-133

§ 7. Wilcke and /Epinus's experiment of electrifying a plate of air (Mem. Berl.

1756, p. 119) 134

§ 8. Electric spark i3S-'39

PRELIMINARY PROPOSITIONS . . p. 82

From the MS. in the possession of the Duke of Devonshire, No. 4

Prop, xxix (Fig. i). If the fluid uniformly spread on a circular plate is to that collected
in the circumference as p to i the capacity of the plate is to that of the globe as p + i

to 2p + 1 '4°

Prop. xxx. Capacity of two disks at a finite distance 141

Cor. i. Capacity in terms of p H2

Cor. 2. Capacity when the density is supposed uniform 143

Cor. 3. The place in which the canal meets the disk is indifferent only when the fluid

is in equilibrium .........•••• '44

Lemma xn (Fig. 2). Repulsion of a particle on a column 145

Contents xiii

ARTICLES

Lemma xiii. Repulsion of two columns !^6

Lemma xiv r^7

Lemma xv (Fig. 3). Action of a uniform cylinder on an external point . . . 148
Cor. Potential of middle and end .......... 149

Prop, xxxi (Fig. 3). Charge of cylinder compared with that of globe .... 150

Cor. Upper and lower limits of charge . . . . . . . . .151

Prop, xxxn (Fig. 4). Charge of two equal cylinders at a finite distance . . . 152
Prop, xxxin. Ratio of charges of B and b may be deduced from the ratios of Band b to C 153
Lemma xv (Fig. 5). Repulsion on a short column close to an electrified plate . . 154

Lemma xvi (Fig. 6). Two equidistant concave plates 155

Cor. i. Definition of corresponding points, &c. ....... 156

Cor. 2. Density increasing towards the circumference . . . . . .157

Lemma xvn (Fig. 7). Concave plate compared with flat one 158

Cor 159

Prop, xxxiv (Fig. 8). Theory of a coated plate 160

Cor. i. Flat coated plate of any form 161

Cor. 2. Flat circular plate . . . . . . ... . . . 162

Cor. 3. Plate not flat but of uniform thickness . . . . . . . .163

Cor. 4. Density increasing towards the circumference . . . . . .164

Cor. 5. General conclusion . . . . . . , . . . .165

Cor. 6. Comparison with globe 166

Cor. 7. Form of plate indifferent 167

Cor. 8. Charge directly as surface and inversely as thickness 168

Prop, xxxv (Fig. 9). Theory of conducting strata in the glass plate .... 169

Prop, xxxvi (Fig. 10). Penetration of glass by fluid 170

Cor. i. Equivalent thickness of plate if there were no penetration .... 171

Cor. 2. Thickness of coatings indifferent ......... 172

Prop, xxxvii. Density more nearly uniform than if there had been no penetration . 173
Cor. Distribution probably nearly the same as in plate of air of equivalent thickness 174

APPENDIX p. 102

From MS. No. 5

Prop. i. Charge of a condenser little affected by the presence of an overcharged body 175

Cor 176

Prop. II 177

Part i. A stricter demonstration, applicable to case of penetration . . . .178

Part II 179

Cor. i 180

Cor. 2 181

Cor. 3 182

Cor. 4. Effect of an overcharged body 183

Cor. 5 184

Cor. 6 (Fig. 1 1). Two coated plates in communication little affected by an overcharged

body 185

Cor. 7. Canals may be curved as well as straight . . . . . . .186

Lemma. Potential of two equal particles compared with that of their sum at their centre

of mass .............. 1 87

Applied to case of two parallel disks 188

Mutual action of large circle and trial plate in Experiment v ..... 189

Mutual action of small circles and trial plate in Experiment v 190

[General negative conclusion] . . . . . . . . . . .192

Effect of floor and walls of the room .......... 193

Effect of earth connexion the same as if it were infinitely long ..... 194

b

xiv Contents

THOUGHTS CONCERNING ELECTRICITY P. 110

From MS. No. 18. (Probably an early draft of the theory)

ARTICLES

Hypothesis of an electric fluid . . 195

The fluid acts at a distance but does not itself extend to any perceptible distance from

electrified bodies 196

Proof of this, and objections to the hypothesis of electric atmospheres . . . 197

On the hypothesis of electric atmospheres .198

Condition of electric equilibrium between conductors in electric communication . 199
Illustration from the equilibrium of air ......... 200

Definitions of positive and negative electrification, and of over and under charge . 201

Four hypotheses 202

Cor. I, 2. Effect of two overcharged bodies approaching each other . . . . 203

Cor. 3, 4. Equally electrified bodies repel 204

Cor. 5. Electrification by induction . . . . . . . . . . 205

Cor. 6. Theory of condensers 206

Shock of the Leyden vial 207

Fifth hypothesis, on the communication of electricity between conductor and the

surrounding air 208

Effect of an overcharged body 209

Attraction and repulsion of electrified bodies 210

Electrification by induction . . . . . . . . . . .211

The electric spark 212

Vacuum formed by the spark 213

Statement of the theory of one electric fluid ....... 214-216

ACCOUNT OF THE EXPERIMENTS . . P. 118

(i) INVESTIGATION OF THE LAW OF FORCE
From MS. No. 7 (apparently prepared for publication)

The electricity of glass is here taken to be positive 217

First experiment. A globe within a hollow globe and in communication with it does

not become over or undercharged when the whole is electrified (Fig. 12) . . 218
General description of the apparatus . . . . . . . . . .219

General plan of the experiment ........... 220

The apparatus actually used 221

Mechanism for performing the required operations 222

The charging jar 223

The gauge electrometer ............ 224

Reason for using the jar 225

Theory of the experiment ............ 226

Result of the experiment ............ 227

Second method of trying the experiment 228

Advantages of the second method 229

Estimation of the degree of accuracy of the result 230

The charge of the inner globe is less than Js °f tnat °f tne outer globe . . . 23 1
Hence the electric force is inversely as the square of the distance . . . .232

Demonstration of this by Lemma 4 (Fig. 13) . 233

Limits between which the law of force must lie, n = 2 ± ^5 . . . . . 234

Second experiment. A piece of wood within a vessel formed of two wooden drawers 235

Contents xv

(2) EXPERIMENTS ON THE COMPARISON OF CHARGES
From MS. No. 9 (apparently prepared for publication)

ARTICLES

Intention of the experiments ........... 236

Definition of the ratio of the charges of two bodies, illustrated by the comparison of

a disk with a sphere ............ 237

Method of the experiment ........... 238

The [adjustable] trial plate. (Fig. 13) 239

Arrangement of the apparatus 240

Method of operation. (Fig. 14) 241

Theory of the experiment 242

Interpretation of the result ........... 243

The testing electrometer ............ 244

Method of testing ............. 245

Advantages of the method 246

Capacity of the trial plate 247

The gauge electrometer ............ 248

Form of electrometer used in the later experiments. (Fig. 30) 249

Estimation of error arising from unequal electrification in the two trials . . . 250
Comparison of the capacities of two bodies . . . . . . . .251

Demonstration 252

Why the electrification is tested by the gauge electrometer 253

The bodies to be tested were chosen of nearly equal capacity 254

Measurements of the apparatus 255

The insulating supports of waxed glass. (Fig. 16) ....... 255

Electrification of air ............. 256

Effects of the electrification of the air 257

The earth-connexions 258

The electrometer threads salted .......... 259

Leakage of the Leyden vials 260

Estimate of the accuracy of the experiments 261

Probable cause of error ............ 262

Weak charges always used 263

Reason for this .............. 264

Third experiment. On the effect of variations in the arrangement of the apparatus in

testing capacities. (Fig. 17) ........... 265

Six different arrangements ........... 266

Result of the six arrangements ........... 267

Conclusion .............. 268

Fourth experiment. Capacities of bodies of different substances, but of the same shape

and size .............. 269

Glass coated with various substances ......... 270

Method of the experiment 271

Effect of the thickness of a plate on its capacity ....... 272

Fifth experiment. Charge of two small circles compared with that of a large one.

(Fig. 18) 273

Results of the experiment 274

The experiment repeated in a different manner . . . ^ 275

Comparison with theory 276

Remarks on the calculation 277

Bearing on the theory ............ 278

Sixth experiment. Charge of two short wires compared with that of one long one . 279

Comparison with theory 280

Seventh experiment. Comparison of the capacities of several bodies .... 281

Comparison of disk with sphere . 282

bi

xvi Contents

ARTICLES

Comparison of square plate with disk

Oblong plate ... 284

Cylinder ... 285

Comparison of different cylinders

Disturbing cause 2^7

Eighth experiment. Comparison of the charge of the middle plate of three parallel
plates with that of the outer ones. (Fig. 19)

Comparison with theory 2^9

Distribution on the middle plate ........-•• 29°

GENERAL CONCLUSIONS

First experiment 29'

Second experiment .......-••••• 292

Fourth experiment ........••••• 293

Remaining experiments • 294

(3) COMPARISON OF THE CHARGES OF COATED PLATES

From MS. No. 10 (apparently prepared for publication)

New apparatus for the comparison of capacities (Fig. 20) 295

Method of making the experiment • • • • 29&

The trial plate 297

Second method 29§

Advantage of the second method 299

Spreading of electricity on the surface of the glass. (Fig. 21) 3°°

Difference between different kinds of glass in this respect . . . . • • 3°'

Determination of the velocity of spreading ..... 3°2

Attempt to check the spreading of electricity by means of cement. (Fig. 22) . . 303

Results with cement and varnish 3°4

These methods abandoned 3°S

Earth-connexion 3°°

Instantaneous spreading of electricity on the surface ; electric light around the edge . 307

Fringe of dirt 3°8

Extent of this spreading 3°9

Spreading greatest at first time of charging • .310

Recapitulation of the theory of coated plates 311

Correction of the area for spreading of electricity ... 3 > 2

Computed charge of cylindric vials 3 '3

Experiments on 10 pieces of glass from the same piece . . . . • 3'4

Table of their dimensions 3'5

Adjustment of size of coatings 3'6

Comparison of D +E + F when close together and when six inches apart . . . 3 '7

Comparison of the plates with each other . . . . . • • • • 3 ' 8

Discrepancy probably due to spreading . . . . . • • • • 3'9

Experimental investigation of spreading 32°

Slit coatings. (Fig. 23, Fig. 24) 32'

Effect of thickness of glass 322

Spreading = 0-07 on thick plates and 0-09 on thin plates 323

Table of plates with circular coatings .......•• 324

Table of the same plates with other coatings . . . . . . • • 325

Verification of the theory of spreading 32°

Effect of thickness of glass 327

Spreading not uniform throughout its extent . . . . . . • 32&

Effect of different strengths of electrification . . . . . . • • 329

Comparison of crown glass with Nairne's plates 33°

Effect of accumulation near the edge insensible . . . . . . . -33'

Contents xvii

ARTICLES

Charge of glass plates is many times greater than it ought to be by the theory . . 332

Comparison with the globe ........... 333

Consideration of the effects of external bodies on the globe and the plates . . . 334

Effect of the floor and walls of the room on the charge of the globe .... 335

Experimental investigation of this effect ......... 336

Comparison of the charges of four rosin plates with those of circles 9^3, 18-5, and

36 inches diameter ............ 337

Hypothesis about the relative effect of surrounding bodies on the capacities of different

bodies ............... 338

Application of this hypothesis to the three circles and the globe ..... 339

Charge of a plate of air ............ 340

Plate of air between glass plates with tinfoil coatings 341

Experiments with plates of air ........... 342

Table of Results with plates of air . . . . . . . . . . 343

Experiment to determine whether the air between the plates is charged . . . 344

The air is not charged ............ 345

Comparison with computed charge .......... 346

The table agrees with the theory nearly but not quite ...... 347

Suggested explanation ............ 348

Three hypotheses to explain why the charge of glass plates is rather more than eight

times what it ought to be by the theory ........ 349

First hypothesis. Electricity penetrates into the glass to a certain depth . . . 349

Second hypothesis. A conducting stratum within the glass. (Fig. 25) . . . 350
Third hypothesis. A great number of strata alternately conducting and non-conducting.

(Fig. 26) 351

Conduction only normal to the surface of the plate ....... 352

Reasons for preferring the third hypothesis ........ 353

Another reason — analogy of Newton's fits ......... 354

Effect of different degrees of electrification on the charge of a plate .... 355

Comparison of the plate D with the circle of 36 inches diameter with two different

degrees of electrification. No apparent alteration in capacity .... 356

Correction for greater amount of spreading with the stronger degree of electrification 357
Comparison with a very weak degree of electrification. Large cylinder and wire.

(Fig. 27) 358

Method of the experiment ........... 359

Result with weak electrification 360

Comparison with the usual strength of electrification 361

Comparison of the results ............ 362

Discussion of the results . . . . . . . . . . . -363

Comparison with positive and negative electrification . . . . . .364

Accumulation at the edge is greater in plates of air than in glass plates of the same

thickness .............. 365

Charge of coated glass at different temperatures. (Fig. 28) 366

The edges of the coatings kept at constant temperature 367

Table of results at different temperatures ......... 368

Glass conducts electricity better as the temperature rises ...... 369

Table of the charges of glass plates .......... 370

Table of the charges of plates of other substances . . . . . . 371

Explanation of the tables 372

Method of making plates of wax, &c. ......... 373

Difficulty of making a plate of shellac ......... 374

Dephlegmated bees wax 375

The charge of a coated plate depends on the substance of which it is made . 376

Difference between thick plates and thin ones ........ 377

The thick plate of crown glass ........... 378

xviii Contents

ARTICLES

Theory of compound plates 379

Experiments with compound plates of glass ........ 380

Experiments with glass and rosin .......... 381

Charge of hollow cylinders of glass 382

Table of results with cylindric vials .......... 383

Discussion of the results • 3^4

Appearance of the three green cylinders 385

(4) REPULSION AS SQUARE OF REDUNDANT FLUID

From MS. No. 8

The repulsion between two bodies electrified to the same degree ought, by the theory,

to be proportional to the square of the quantity of redundant fluid . . . 386

Experiment to test the theory. (Fig. 31) 38?

Comparison of the force required to produce an equal divergence of the two electro-
meters ............... 388

The Leyden jars 389

Method of the experiment 39°

Discussion of the experiment ........... 391

Method of preventing the vibration of the straws .... . 392

No sensible error due to leakage 393

Effect of want of conductivity of the straws 394

SECOND PUBLISHED PAPER ON ELECTRICITY P. 194

AN ACCOUNT OF SOME ATTEMPTS TO IMITATE THE EFFECTS
OF THE TORPEDO BY ELECTRICITY

From the Phil. Trans, for 1776 (pp. 196-225)

Walsh's experiments on the Torpedo 395, 396

Shock given by the Torpedo under water 397

Electric resistance of salt and fresh water, and of iron wire .... 398

Lines of flow of the discharge of the Torpedo ...... 399> 400

Conditions requisite for a spark and for attraction and repulsion . . . 401-408

Artificial Torpedo 409, 410

The battery and its charge 411-413

Mode of charging the battery 414

Shocks in air and under salt water. Law of divided currents .... 415-420

Torpedo in a basket ; in sand ; shock through wet shoes and through net . . 42 1 -424

Why the Torpedo gives no spark 425-435

Structure of the electric organ .......... 436

Shock through a chain without any light 437

EXPERIMENTS IN 1771 ... P. 211

From MS. No. 12

ist Night 438

2nd Night 439

3rd Night ............... 440

Two pairs of large corks made, one four times as heavy as the other. Measurement of

capacity of vial by touching eight or nine times with coated plate and wire . . 441
Thickness.

C -0601 1

Three coated plates .... 442

D -05908

F -05914

Contents xix

ARTICLES

C, D, F close together and far asunder 443

Three coated plates, 1-8 diam., 'i8 thick ......... 444

Globe and circle, 19-4 of pasteboard. Sliding plates

19 x 13

Circle of 1-8 x -18 20-2 _ 10
globe ~ 12-4" 6

Double plate, 1-75 x -285, tried with small sliding trial plate;

Double plate 1 1
globe ~ 18

Thick plate, 1-45 x -168 _ 14

"globe -13 "6

Trials of wires. Single wire, 96 x -19. Two wires, 48 x -i at 36 and 18 . . . 447

Two wires, •! x 24, at 18, 36 ........... 448

Results of wires ............. 449

Large circle on waxed glass and on silk ......... 450

Coated glass compared with non-electric body with strong and weak electricity . . 45 1

Two tin circles of 9-3, compared with one of 18-5 . 452

Brass wire, 72 x -19 453

Results. Best formula for cylinder .......... 454

Coated trial plate of two plates of glass with rosin between . . . . 455

Trial plate, Double plate A, Double plate B, Large circle (18-5?),
I7i- 18-4. 18-3. 18-5.

Globe, Globe

,8-8. circle = '^ «6

Double plates A and B, and plate air, -39 x7'95 ....... 457

Real power of plate air = computed x '243 [computed is 8 times too great] . . . 458

N, O, P,Q 459

B [2-79], D [2-73], white [2-85]. B, D, N, W tried 460

A [2-16], ist rosin 2-51, trial plates, Art. 457 461

Results for D, W, B, P, N, O, Q 462

Coated plate compared with non-electric body with strong and weak + and - electricity 463

Rosin, 3'4i x -345, compared with double B, by sliding coated plate .... 464

Side of square equivalent to trial plates ......... 465

EXPERIMENTS IN 1772 P. 224
From MS. No. 13

Plan of usual disposition of vials and bodies to be tried ...... 4°°

Exp. in 46?

Do. Dec. 14, 1771 4°8

Dec. 16, 1771. Conductivity of stone squares 4^9

Dec. 17, 1771. Exp. in 47°

Dec. 18. Exp. IV 47'

„ Exp. v, circles 9-3 and 18-5 472

Dec. 30. Exp. v, observations 473

„ Exp. v, 2nd arrangement 474

Dec. 31. Observations 475

Two wires, 36 x -i, and i of 72 x -185, Exp. VI 47^

Jan. 3, 1772. Observations ......••••• 477

Exp. vn :
Large tin circle. Double plate B, Tin cylinder, 35-9, 2-53 \

Globe, Tin plate square, 15-5 „ 54'2» '73 i • • 4?8
Double plate A. „ oblong, 17-9 x 13-4 wire, 72, -i8sJ

xx Contents

ART1CI.KS

Results: comparison with Art. 455 • • 479

Exp. IV 48°

Table omitted 48 '

Twelve plates from Nairne, A to M . 48^

D, E, F, G compared with double A and B • 483

Trial plates of Nuremberg glass, H, I, K, L. Art. 303. H, I, K, L cased with cement.

E, F, G and I, K, L of Nairne cased in cement. Plate of cement . . . 484

Spreading of electricity on cemented plates. Art. 302 . . 485

Rate of spreading 4^6

Trial of spreading by machine. (Fig. 20) . 4**7

Three sliding coated plates with brass slides. Six trial plates . 488

Feb. 4, 1772, D, E, F, G. Two double plates . . 489

E + F + G, with I, K, L, M .490

Closing of balls 4Qi

Feb. 5, 1772, I + K + L, with A + B + C + H, crown glass trial plates . . 492

A + B + C.withH 493

EXPERIMENTS IN 1773 ... P 240

From MS. No. 14 [Cavendish's Index]

PAGE The pages refer to the MS., the numbers of the Articles to the present edition

OF MS.

i-io. Spreading of electricity on the surface of glass ...... 494

n. List of thickness and coatings of some plates, see p. 27 500

12. Quantity of electricity in thick rosin compared with double plate B, and in 2nd
rosin with D, E and G of Nairne 501

13. Q and P compared with M and K of Nairne, also green cylinder 4, and white
cylinder compared with plates of Nairne by means of sliding trial plates . . 502

14. ist and 2nd green and white cylinders and white jar compared with H of Nairne

in usual manner ............ 503

15. The same in the same way, except with addition of plate M on the negative side

in some experiments 504

16. Quantity of electricity in the two coated globes, and in the two jars used in the
machine for trying plain plates 505

17. Quantity of electricity in the 4 jars, and in the 5th and 6th sliding trial plates . 506

18. Thick rosin compared with double plates A and B, and thick white and 2nd rosin

with D, E, F and G of Nairne 507

19. Thick white, 2nd rosin, D and F of Nairne and the two double plates together,
compared together; also thin white with D and E, and D and F . . . 508

20. Whitish plate, P, Q, O, old G and thin rosin compared with M . . . 509

21. Crown A and C compared with A, B and C of Nairne 510

23. Whether the shock from the plate [of] air was diminished by changing the air

between them* by moving them horizontally . . . . . . .511

25. Whether globe included within hollow globe is overcharged by electrifying outer
globe 512

26. The same thing tried by a better machine . . . . . . .513

27. Note to list of plates in p. 11 . . . . . . . . . . 514

28. ist and 2nd sliding plates compared with double plate B; also Q, P, O and thin
rosin; old G and whitish plate compared with D, E, F and M . . . . 515

30. Whether the charge of plate air is diminished by changing the air between them

by lifting up the upper plate . . . . . . . . . .516

31. Trials of plate air i, 2, 3 and 4 517

35. Lac plate and 4th rosin compared with D + E + F, also thin wax with E + F, also

thick wax and plate air 5 with D. . . . . . . . .518

* The two flat conductors between which the plate of air lies, or, in modern language, the
electrodes.

Contents xxi

PAGE
OF MS. ARTICLES

36. Lac and 4th rosin with D + E + F, also thin wax with D t E, also thick wax, 2nd

rosin and first made rosin and plate air 5 with F 519

38. Breaking of electricity through thin plates of lac, experimental rosin, and
dephlegmated bees wax . . . . . . . . . . .520

39. The quantity of electricity in a Florence flask tried with and without a magazine 521

41. Computed power of above flask 522

42. As it appeared by the foregoing experiment that the Florence flask contained
more electricity when it continued charged a good while than when charged and
discharged immediately, it was tried whether the case was the same with the
coated globes ............. 523

43. Diminution of shock by passing through different liquors ..... 524
47. Whether force with which bodies repel is as square of redundant fluid tried by

pith balls hung by threads .......... 525

5 1 . Whether the charge of plate E bears the same proportion to that of another body,

whether the electrification is strong or weak, tried by machine for Leyden vials 526

53. Plain wax and 3rd dephlegmated wax with E + F, and 5th rosin with double
plate A and B. Also small ground crown with D +E + F, and large do. with C 527

54. K, L and M, compared with D + E + F at distance and close together ; also large
ground crown with C and small one with D + E + F; also 3rd dephlegmated wax

and plain wax with E + F; also 5th rosin with double B . . . . . 528

55. K + L + M compared with A, B and C ; also A + B + C with H .... 529

56. K +L + M compared with B, with electrification of different strengths . . 530

57. K + L + M with A, B and C ; also D + E + F with K, L and M ; also small ground
crown with K, L and M, and D + E + F, and large ground crown with A, B and

C, andK + L + M 531

58. On the light visible round the edges of coated plates on charging them . . 532

59. Crown A and C and large ground crown with C ; also 3rd dephlegmated wax,
plain wax and sliding plate 3 with E + F; also 2 double plates with E, F and D 533

60. Charge of the triple plate, the three plates A, B and C placed over each other

with bits of lead between coatings 534

61. Whether the charge of plate D bears the same proportion to that of another body
whether the charge is strong or weak, tried with machine for Leyden vials . 535

62. H with slits and a crown glass with oblong coating, compared with white cylinder,

also A and C with slits compared with B . . . . . . . . 536

65. Crown with slits and H with do. compared with white cylinder, and A and C

with oblongs compared with B .......... 537

67. Experiment of p. 61, tried with small ball blown to the end of a thermometer

tube ; also fringed rings on plate of crown glass, &c. . . . . . . 538

69. Whether charge of Leyden vial bears the same proportion to that of another body
when the electrification is very weak as when it is strong ; tried by communicating

the electricity of small pieces of wire to tin cylinder and to D and E . . . 539

70. Lane's electrometer compared with straw and paper electrometers . . . 540

71. Crown and H with slits compared with white cylinder; also on the excitation

of electricity by separating a brass plate from a glass one 541

73. Whether the middle of three parallel plates communicating together is much
overcharged on electrifying the plates ........ 542

74. Charge of A, B and C laid on each other without any coatings between ; also
charge of ist thermometer tube 543

75. Lane's electrometer compared with straw and paper electrometers ; also charge of
plate rosin with brass coating made to prevent spreading of electricity . . 544

76. Second thermometer tube ; also comparison of charge of cylinder used in p. 69

with D + E 545

77. Charge of second thermometer tube; also that of rosin plate with brass coating;

also that of A, B and C laid on each other without coatings between . . . 546

78. Quantity of electricity in plate D compared with that of tin circle of 36" and

one of 30", by machine for trying simple plates ...... 547

79. Charge of plate of experimental rosin designed for compound plate of glass and
rosin, tried both when warm and when cold ....... 548

xxii Contents

PAGE
OF MS. ARTICLES

80. Whether charge of glass plate is the same when warm as when cold . . . 549

81. Crown with slit coatings and H with oblong compared with white cylinder; also
second thermometer tube with D + E + F 55°

82. Quantity of electricity in plate D, and rosin with brass coatings, compared with
that of tin circle of 36", and one of 30", by machine for trying simple plates with
different degrees of electrification SS1

83. Charge of compound plate of glass and rosin ....... 552

85. Circle of i8J" compared with double plates; also plate D, plate air, and the two
double plates compared with circles of 36" and 30" 553

86. yo&yi. The same with addit. four small rosin plates ..... 554

87. Whether the four rosin plates contain same quantity of electricity when close
together as when at a distance, tried by machine for Leyden vials . . . 555

8y. Whether charge of white glass thermometer tube is the same when hot as when

cold 556

92. Allowance for connecting wires in p. 86, &c 557

93. Whether charge of the four rosin plates is the same when close together as when
at a distance. Also on excitation of electricity by separating brass plate from

glass one 558

94. Comparison of Henly's, Lane's, and straw electrometer 559

95. Excess of redundant fluid on the positive side above the deficiency on the negative
side in glass plate and plate air, and compound plate of p. 83, compared with
charge of simple plate . . . . . • • • • • 5°°

99. Whether parallelepiped box included in a hollow box of the same shape is over-
charged on electrifying the outer box 5O1

100. Globe within hollow globe tried again 562

105. Whether the force with which two bodies repel is as the square of the redundant

fluid, tried by straw electrometers 563-?

113. Separation of Henly's electrometer by different strengths of electrification . 568

115. Separation of Henly's electrometer when fixed in the usual way and on upright

rod 569

116. Result of the comparison of different electrometers in pp. 70, 75, and 95 . . 570
118. Comparison of Lane's electrometer with light straw electrometer in different

weather 571

121. Comparison of strength of shocks by points and blunt bodies . . . 572

122. Whether shock of one jar is greater or less than that of twice that quantity of

fluid spread on four jars 573

123. Comparison of the diminution which the shock receives by passing through water
in tubes of different bores, and whether it is as much diminished in passing
through nine small tubes as through the same length of one large tube, the area

of whose bore is equal to that of the nine small ones 574

125. Comparison of the diminution of the shock by passing through iron wire or
through salt water 575

126. Measures of glass tubes used in pp. 123 and 124 more accurate, with the com-
putations of those pages over again ......... 57°

127. Comparison of conducting powers of sat. sol. S.S.* and rain water . . . 577

128. Whether the electricity is resisted in passing out of one medium into another in
perfect contact with it 57$, 579

1 29-1 3 1 . Comparison made at Nairne's of his Henly on conductor, and on upright rod 580

Here ends Cavendish's Index
* Sea salt.

Contents xxiii

M. [MEASURES] .... P. 289
From MS. No. 20

ARTICLES

Comparison of charges of jars and battery, method of repeated communication . . 581

Theory pf this method 582

Results 583

Charge of ist battery of Nairne .......... 584

Whether shock is diminished by imperfect conduction of the salt water in the jars . 585

Specific gravity of solutions of salt 586

Rule for finding the quantity of salt in water from its specific gravity . . . 586

Measurement of Lane's second and third electrometers 587

Conductivity of salted wood ........... 588

Dimensions of coatings of glass plates ......... 589

Rules for making trial plates ........... 589

Specifications for coating of plates .......... 589

Measures of thickness of 2nd rosin plate ......... 590

Measures of thickness of crown glass . . . . . . . . .591

From MS. No. 13

List of plates of glass . . . . . . . . . . . 592

Twelve plates from Nairne ........... 593

Green glass cylinders ............ 594

Coatings of jars and cylinders 595

EXPERIMENTS WITH THE ARTIFICIAL TORPEDO P. 301

From MS. No. 20

Shocks from ist Torpedo 596

Theory of divided circuits ............ 597

Shock under water 598

First leather Torpedo ............ 599

Second leather Torpedo, Tuesday, April 4 [1775] 600

Second leather Torpedo, Saturday, May 27 [1775] 601

Mr Ronayne, Mr Hunter, Dr Priestley, Mr Lane, Mr N[airne?].

Same day old Torpedo through bright and dirty links ...... 602

Tried with Lane's electrometer ........... 603

Tuesday, May 30 [1775]. Distance of discharge of Lane the same for great or small

number of jars ............. 604

Charge required to force electricity through chain ....... 605

Wednesday, May 3 1 [1775]. Comparison of rows of battery 606

Results of experiments, May 30 607

Tuesday, June 6 [1775]. Torpedos in wet sand ....... 608

Shock through salted wood 609

Monday, June 12 [1775]. Relation between quantity of electricity and number of jars

that the intensity of the shock may be the same 610

Second leather Torpedo under water 611

Tuesday, July 4 [1775]. Second leather Torpedo touched in various ways . . 612

Experiments without any Torpedo .......... 613

Anatomy of electric organs of Torpedo 614

Second leather Torpedo new covered . . . . . . . . .615

xx iv Contents

RESISTANCE TO ELECTRICITY . . P. 311
From MS. No. 19

ARTICLES
Comparison of conducting power of salt and fresh water, in the latter end of March

and beginning of April, 1776.
Method of experiment . . . . . . . . . . ...616

The experiments . . . . . . . . . . . . .617

Six jars compared with one row. Experiments 618

Examination whether salt in 69 conducts better when warm or when cold . . . 619
Examination whether the proportion which conducting power of sat. sol. and salt in

999 bear to each other is altered by heat ........ 620

Resistance of distilled water ........... 621

Salt in 2999 and salt in 150,000 622

Resistance of salt solutions ........... 623

Comparison of water purged of air and plain water ....... 624

Comparison of water impregnated with fixed air and plain water .... 625

Resistance of solutions of other salts .......... 626

Oil of vitriol, spirit of salt and f. alk. 627

Experiments in January, 1781 ........... 628

To find what power of the velocity the resistance is proportional to . . . . 629

Salt solutions .............. 630

Water and spirits of wine 631

CALIBRATION OF TUBES
Jan. 1781. From MS. No. 19

Tube 14 632

Tubes 14, 15, 22, 23, 5, 17 633

Tubes 12, 20 634

Result 635

RESISTANCE OF COPPER WIRE
From MS. No. 19

Copper wire on glass reel 636

Failure of former method ............ 637

Barometer tubes as Leyden jars ........... 638

Shock through wire plainly greater than shock received direct 639

The same with jars i , 2 or 4 640

Copper wire stretched by silk; sensation, sound and light of shock .... 641

Wire wound round a slip of glass 642

Wire from reel stretched 14 times round the garden ....... 643

Copper wire silvered put on reel 644

Comparison by sound 645

Results 646

RESULTS [OF COMPARISONS OF CHARGES] . P. 335

From MS. No. 16

Allowance for connecting wire ........... 647

Square : globe : circle :: 1-125 : J'S4 : J 648

Compared results ............. 649

Ditto. 650

Circles 36, 18-5, 9-5 651

Contents xxv

ARTICLES

Increase of charge by induction ........... 652

Double A and double B 653

Globe and circle i8| 654

D, E, F, G 655

D, E, F, M, K, L 656

A, B, C. K, L, M 657

H . . 658

Instantaneous spreading of electricity 659

Trials 660

Results 661

Tables of results ............ 662, 663

Whether charge of coated glass bears the same proportion to that of another body

whether electricity is strong or weak ......... 664

Correction for spreading with electricity strong and weak ...... 665

Experiment with tin cylinder 666

Charge corrected for spreading 667

On plate air 668

Table of plates of air 669

Table 670

Table of Nairne's plates . . . . . . . . . . . . • 671

Computations of other flat plates of glass, &c 672

Table of glass plates 673

Table of other substances ............ 674

On the glass cylinders ............ 675

Table of glass cylinders ............ 676

On the compound plates ............ 677

Experimental rosin 678

Rosin placed between glass plates .......... 679

White glass ball at various temperatures ......... 680

Two circles 681

Globe, circle, square, oblong, cylinder 682

Wires 683

RESULTS [ON RESISTANCE] . . .' P. 349

From MS. No. 19

Pump water, rain water, salt in 1000, sea water 684

Nine tubes compared with one ........... 685

Resistance as i -03rd power of velocity 686

Resistance of iron wire 687

Sat. sol. in 99=39 sat. sol. ........... 688

Experiments in 1776 and 1777 on salt solutions 689

Distilled water .............. 690

Effect of temperature . . . . . . . . . . . .691

Air in water 692

Fixed air in water 693

Other saline solutions ............ 694

Experiments in January, 1781 ........... 695

Water with different quantities of salt in it 696

xxvi Contents

NOTES BY THE EDITOR ... P. 352
[JAMES CLERK MAXWELL, 1879]

NOTE PAGE

1 . On the theory of the electric fluid 352

2. Distribution of hypothetical fluids in spheres, &c 358

3. Canals of incompressible fluid .......... 365

4. Charges of two parallel disks close together 368

5. Zero of potential ............ 369

6. Molecular constitution of air 370

7. Idea of potential 372

8. Cases of Attraction and Repulsion 373

9. Escape of electricity into the air .......... 374

10. Electromotive force required to produce a spark . 375

n. Two circular disks far apart on the same axis .... . 377

12. Capacity of a long narrow cylinder ......... 382

13. Two influencing cylinders 388

14. Condensers with curved plates 389

15. Glass as a dielectric ............ 3^9

16. Mutual influence of condensers 392

17. General theory of the experiment with trial plates 394

18. On the "Thoughts concerning Electricity" 397

Early form of Cavendish's Theory of Electricity 398

19. Experiment on the charge of a globe between two hemispheres .... 404

20. Capacity of a disk of sensible thickness 409

21. Capacity of two circles on same axis 411

22. Capacity of a square . . . . . . . . . . . • 412

23. Charge of the middle one of three parallel plates 413

24. Capacity as affected by walls of the room .415

25. Tin cylinder and wires, compared with theory 416

26. Influence of different temperatures on glass 416

27. Comparison of measurements of dielectric capacity . . . . . .418

28. Computed charge of cylindrical condenser 4'8

29. On Electrical Fishes 4»9

30. Excess of redundant fluid on positive side above deficient fluid on negative side . 423

31. Intensity of shocks 423

32. Iron wire and salt water compared as regards conductance 429

33. Salt and fresh water 429

34. Other saline solutions 43°

35. Globe and disk compared as regards capacity 433

LIFE OF CAVENDISH, BY THOMAS YOUNG . P. 435

INDEX TO CAVENDISH MANUSCRIPTS . P. 449

Contents xxvii

ILLUSTRATIONS

Henry Cavendish, from the picture by W. Alexander .... Frontispiece

FACSIMILES OF CAVENDISH'S FIGURES

FIG. PAGE

12. Globe and Hemispheres ng

15. [Adjustable] Trial Plate . I2^

14. Machine for trying simple conductors 128

30. Electrometer ............. 132

16. Insulators of waxed glass ........... 134

20. Machine for trying Leyden vials 151

23. [Perforated] coatings 163

24. [Slit coatings] 164

28. Effect of heat on glass ........... 182

Facsimile of MS. containing the words "shock melter" ..... 317

Do. containing Calc. S.S.A., &c. 320

In the late Dr George Wilson's collection of Cavendish MSS. -there is a drawing of which
the following page is a reduced copy. The words " buried at Derby" are written in pencil on
the margin.

Henry Cavendish was buried in the Devonshire Vault, All Saints' Church, Derby, but
Mr J. Cooling, Jun., Churchwarden of All Saints, inforrns me that there is no slab or monu-
ment of any kind erected in memory of him there. [See introduction to Vol. II of this
edition.]

HENRY CAVENDISH

Eldest Son of the Right Honorable

LORD CHARLES CAVENDISH,

Third Son of William^
2ND <DUKE OF "DEVONSHIRE.

Fellow of the Royal Society, and of the Society
OF ANTIQUARIES OF LONDON.

Trustee of the British Museum

and Foreign Associate in the First Class

of the INSTITUTE at Paris.

BORN October ioth j DIED February 24*
1731 J 1810

[ I ]

INTRODUCTION*

Oo little is known of the details of the life of Henry Cavendish, and so
fully have the few known facts been given in the Life of Cavendish by
Dr George Wilson f, that it is unnecessary here to repeat them except in
so far as they bear on the history of his electrical researches.

He was born at Nice on the loth October, 1731; he became a Fellow
of the Royal Society in 1760, and was an active member of that body
during the rest of his life. He died at Clapham on the 24th February, 1810.

His father was Lord Charles Cavendish, third son of William, second
Duke of Devonshire, who married Lady Anne Grey, fourth daughter of
the Duke of Kent. Henry was their eldest son. He had one brother,
Frederick, who died 23rd February, 1812.

Of Lord Charles Cavendish we have the following notice by Dr
Franklin {. After describing an experiment of his on the passage of
electricity through glass when heated to 400° F., he says, " It were to be
wished that this noble philosopher would communicate more of his ex-
periments to the world, as he makes many, and with great accuracy."

Lord Charles Cavendish has also recorded a very accurate series of
observations § on the depression of mercury in glass tubes, and these have
furnished the basis not only for the correction of the reading of baro-
meters, &c., but for the verification of the theory of capillary action by
Young, Laplace, Poisson and Ivory.

I think it right to notice the scientific work of Lord Charles Cavendish,
because Henry seems to have been living with him during the whole period
of his electrical researches. Some of the jottings of his electrical calcula-
tions are on torn backs of letters, one of which is addressed,

[The Ho]nble Mr Cavendish
at the R4 Honble
The Ld Charles
Cavendish's

Marlborough Street.

* By the Editor [James Clerk Maxwell].

f Published in 1851 as the first volume of the Works of the Cavendish Society.
} Franklin's, Works, edited by Jared Sparks, Boston, 1856, vol. v. p. 383. See
also Note 26 at the end of this book.
§ Phil. Trans. 1776, p. 382.
c. P. I. I

2 Introduction

These calculations relate to the equivalent values of his trial plates
when drawn out to different numbers of divisions. There is no date nor
any part of the original letter.

The memoranda of some experiments similar to those in Art. 588, on
the time of discharge of electricity through different bodies, are on the
back of the usual Notice of the election of the Council and Officers of the
Royal Society on the Thirtieth of November, 1774 (being St Andrew's
Day) at Ten o'Clock in the Forenoon at the House of the Royal Society
in Crane Court, Fleet Street. The address on the back of this letter is

To

The Hon Henry Cavendish

Gr* Marlborough Street.

Dr Thomas Thomson, who was acquainted with Cavendish, says in
his interesting sketch of him*,

During his father's life-time he was kept in rather narrow circumstances,
being allowed an annuity of £500 only, while his apartments were a set of
stables, fitted up for his accommodation. It was during this period that he
acquired those habits of economy and those singular oddities of character which
he exhibited ever after in so striking a manner.

The whole of the electric researches of which we are to give an account
were made before the death of Lord Charles Cavendish, which took place
in 1783. We must therefore suppose that they were made in Great Marl-
borough Street, and probably in the set of stables mentioned by Dr
Thomson. He speaks of a "fore room and a back room" in Art. 469, and
in Art. 335 he compares the size of the room in which he worked to that
of a sphere 16 feet in diameter. The dimensions of his laboratory are of
some importance in determining the electric capacity of bodies hung up
in it, and by the foot-note to Art. 335 it would appear that the room was
probably 14 feet high, which is somewhat lofty for "a set of stables,"
but I believe not much more than the height of some of the rooms in the
dwelling-houses in Great Marlborough Street.

Let us then suppose that we have been admitted by Cavendish into
his laboratory in Great Marlborough Street, as it was arranged for his
electrical experiments in 1773, and let us make the best of an opportunity
rarely, if ever, accorded to any scientific man of his own time, and
examine the apparatus by which the electric fluid, instead of startling us
with the brilliant phenomena, new instances of which were then every
day being discovered, was made to submit itself, like everything else
which entered that house, to be measured.

The largest piece of apparatus was the "machine for trying simple
bodies" of which we have a description and sketch in Art. 241, and plans

* History of Chemistry, vol. i. p. 336, quoted in Wilson's Life of Cavendish, p. 159.

Historical and Personal 3

at Arts. 265 and 273. The framework of the machine is not represented
in these figures.

We learn, however, from Dr Davy*, that

Cavendish seemed to have in view, in construction, efficiency merely, without
attention to appearance. Hard woods were never used, excepting when required.
Fir-wood (common deal) was that commonly employed.

The bodies to be "tried" and the wires and vials for trying them were
either supported on glass rods as shown in the sketch at Art. 239, or else
hung by silk strings from a horizontal bar 7 feet 3! inches from the floor
as mentioned in Art. 466. The electrical connexions were made and broken
at the proper times by means of silk strings passing over pullies attached
to the horizontal bar.

One of the bodies, the charges of which Cavendish compared by means
of this apparatus, was a globe 12-1 inches in diameter covered with tinfoil.
This globe has historical interest as it was not only the standard of capacity
with which Cavendish compared that of all other bodies, but it formed
part of the apparatus by which he established that the electric repulsion
varies inversely as the square of the distance.

There was also a set of circles of tin plate, one of 36 inches diameter,
one of 18-5 and two of 9-3; and also square and oblong tin plates, and
squared pieces of stone and slate, and a collection of cylinders and wires
of different sizes.

There was another "machine," represented, with its framework, in
Fig. 20, Art. 295, "for trying Leyden vials."

The "Leyden vials " were most of them flat plates of glass with circular
coatings of tinfoil, one on each side. They were made in sets of three,
any one of each set being nearly equal in capacity to the three of the
former set taken together. Cavendish had thus a complete set of con-
densers of known capacity by means of which he measured the capacity
of every piece of his apparatus, from the little wire which he used to
connect his coated plates, and which he found to contain -28 "inches of
electricity," up to his battery of 49 jars, which contained 321,000 "inches
of electricity f."

These "inches of electricity " can be directly compared with our modern
measurements of electrostatic capacity. Indeed the only difference is that
Cavendish's "inches of electricity" express the diameter of the sphere of
equivalent capacity, while the modern measurements express the capacity
by stating the radius of the same sphere in centimetres.

Of each of these plates of glass Cavendish has given a most minute
description, so that each, if it were found, could be identified. Mr Cottrell,
of the Royal Institution, has been kind enough to examine the catalogue
of apparatus there, which contains Cavendish's Eudiometer and Registering

* Wilson's Life, p. 178. f About half a microfarad.

I — 2

4 Introduction

Thermometer. No trace, however, of a set of glass plates could be found.
It is possible, however, that if the plates were neatly packed up, their
small bulk and their apparent uselessness may have enabled them to
survive the periodical overhaulings of some less celebrated repository, and
that they may yet gain an honourable place in the museum of historical
instruments.

But we need not expect ever to discover a piece of apparatus of still
greater historical interest — that by which Cavendish proved that the law
of electric repulsion could not differ from that of the inverse square by
more than ^. It consisted of a pair of somewhat rickety wooden frames,
to which two hemispheres of pasteboard were fastened by means of sticks
of glass. By pulling a string these frames were made to open like a book,
showing within the hemispheres the memorable globe of 12-1 inches
diameter, supported on a glass stick as an axis. By pulling the string
still more, the hemispheres were drawn quite away from the globe, and
a pith ball electrometer was drawn up to the globe to test its "degree of
electrification." A machine so bulky, so brittle, and so inelegant was not
likely to last long, even in a lumber room. A facsimile of Cavendish's
sketch of it is given at page 118. His own account of the experiment, in
Arts. 217-234, is one of the most perfect examples of scientific exposition.

We might also notice the different electrometers, most of them con-
sisting of a pair of cork or pith balls, mounted on straws or on linen threads,
and some of them capable of having their weight altered by means of
wires run into the straws; but though Cavendish had a wonderful power
of making correct observations and getting accurate results with these
somewhat clumsy instruments, we must confess that in these, the most
vital organs of electric research, Cavendish showed less inventive genius
than some of his contemporaries. When Lane and Henly brought out
their respective electrometers, Cavendish compared their indications, and
by stating in every case the distance at which Lane's electrometer dis-
charged, he has enabled us to calculate in modern units every degree of
electrification that he made use of. What was really needed for Cavendish's
experiments was a sensitive electrometer. Cavendish did the best with the
electrometers he found in existence, but he did not invent a better one.

It was not till 1785 that Coulomb began to publish the wonderful series
of experiments, in which he got such good results with the torsion electro-
meter, an instrument constructed on the same principle as that with which
Cavendish afterwards measured the attraction of gravitation ; and it was
not till 1787 that Bennett described in the Philosophical Transactions the
gold leaf electrometer, by means of which Volta afterwards demonstrated
the different electrification of the different metals.

The electrical machine, by Nairne, was one with a glass globe.

We should also notice the dividing engine, by Bird, for determining
the thickness of the glass plates, and other small distances.

Historical and Personal 5

An attendant*, "Richard," appears occasionally, to help in turning
the electrical machine, or in pulling the strings which made or broke the
electrical connexions; and sometimes he is even asked his opinion as to
the comparative strength of two electric shocks f. But there is no record
of any other person having been admitted into the laboratory during the
series of experiments to which we now refer.

The authority of Cavendish in electrical science was of course estab-
lished by his paper of 1771, and accordingly we find him nominated by
the Royal Society as one of a committee appointed in 1772 "to consider
of a method for securing the powder magazine at Purfleet J."

A powder mill at Brescia having blown up in consequence of being
struck by lightning, the Board of Ordnance applied to Mr Benjamin Wilson,
F.R.S., who held the contract for the house-painting under the Board§,
and who had some reputation as an electrician, for a method to prevent
a like accident to their magazines at Purfleet. Mr Wilson having advised
a blunt conductor, and it being understood that Dr Franklin's opinion,
formed upon the spot, was for a pointed one, the matter was referred, in
1772, to the Royal Society, and by them as usual to a committee, who
after consultation presented a method conformable to Dr Franklin's
theory || .

The Committee consisted of Cavendish, Dr, afterwards Sir William
Watson, Dr Franklin, Mr J. Robertson (Clerk and Librarian to the Royal
Society), Mr Wilson and Mr Delaval.

Dr Franklin read to the Committee a paper which is printed in his
works, vol. v. p. 435, but is not referred to in the report of the Committee,
though the report is entirely in conformity with it ^j.

The Committee went down to Purfleet and examined all the buildings
together, but I cannot trace any evidence that Cavendish did anything
to modify the report, and Franklin does not mention him in any part of
his writings, as one of the remarkable men with whom he was brought in
contact.

The most noteworthy incident of the Committee was the dissent** of
Mr Wilson, to which Mr Delaval adhered as regards that part of the report
which recommended the conductors to be pointed. Mr Wilson followed
up his dissent by a paper ff , in which he gave his reasons for preferring

* Arts. 242, 560, 565. f Art. 511.

J See Franklin's Works, vol. v. p. 430, note.

§ He also painted portraits of Franklin and of Gowin Knight, as well as of
Garrick in various characters.

|| Phil. Trans. 1772, p. 42.

f The report is printed in Franklin's Works, vol. v. p. 430, and is there stated to
be "Drawn up by Benjamin Franklin, August 21, 1772." The paper on the utility
of long, pointed rods is stated to have been read on August 27th, 1772. [On the
general subjectof atmospheric electric discharges seeC.T. R. Wilson, Phil. Trans. 1920.]

** 1-hil. Trans. 1772, p. 48. tt Ib. p. 49.

6 Introduction

blunt conductors ; but the other four members of the Committee, Messrs
Cavendish, Franklin, Watson, and Robertson, having heard and con-
sidered these objections, found no reason to change their opinion or vary
from their Report*.

But on the isth May 1777, the Board House at Purfleet was struck
by lightning, and some of the brickwork damaged. This being communi-
cated by the Board of Ordnance to the Royal Society f, a Committee was
appointed to examine the effects of the lightning and to report.

The Committee consisted of Mr Henly, Mr Lane, Mr Nairne and Mr
Planta, Secretary of the Royal Society. They reported in favour of making
a channel all round the parapet and filling it with lead, and connecting
this in four places with the main conductor on the roof of the building.

Mr Wilson, however, dissented from this Report, and communicated
to the Royal Society an account of a most elaborate and indeed mag-
nificent set of experiments conducted in the Pantheon, in which a cylinder
155 feet long, composed of 120 drums, and connected with a wire 4800 feet
long, suspended on silk strings, was electrified, and the discharge made
to strike a model of the Board House at Purfleet. The experiments were
witnessed by King George III, and seem to have been very brilliant. The
picture of the experiment, probably drawn by Mr Wilson, is, as a work
of art, considerably above the average of the plates in the Philosophical
Transactions.

The subject was referred to a larger Committee, consisting of Sir John
Pringle, President of the Royal Society, Dr Watson, Henry Cavendish,
W. Henly, Bishop Horsley, T. Lane, Lord Mahon, Edw. Nairne, and
Dr Priestley.

They reported! in favour of having an additional number of con-
ductors ten feet high, terminated with pieces of copper eighteen inches
long, and as finely tapered and acutely pointed as possible.

We give these directions (they conclude), being persuaded, that elevated
rods are preferable to low conductors terminated in rounded ends, knobs, or
balls of metal; and conceiving, that the experiments and reasons made and
alledged to the contrary by Mr Wilson, are inconclusive.

I have stated this incident at some length because it does not appear
to have been noticed by Cavendish's biographers, and because it shows
him cooperating with Franklin and others in an electrical investigation
undertaken in the interest of the nation.

Cavendish's researches on the electric current have been hitherto very
imperfectly known, as they are only alluded to in his celebrated paper on
the Torpedo. The private investigations of Cavendish are contained in
this volume, but the external events which were more or less connected
with them, were as follows:

» Phil. Trans. 1772, p. 66. f Ib- J778. P- 232- t Ib- P- 3*3-

Historical and Personal 7

On July i, 1773, Mr Walsh communicated to the Royal Society his
paper "Of the Electric Property of the Torpedo. In a Letter from John
Walsh, Esq., F.R.S., to Benjamin Franklin, Esq., LL.D., F.R.S., Ac. R.
Par. Soc. Ext., &c."

The following extracts will indicate the chief points of electrical interest.

The vigour of the fresh taken Torpedos at the Isle of Re was not able to
force the torpedinal fluid across the minutest tract of air; not from one link of
a small chain, suspended freely, to another; not through an almost invisible
separation, made by the edge of a pen-knife in a slip of tinfoil pasted on
sealing-wax.

The effect produced by the Torpedo when in air appeared, on many repeated
experiments to be about four times as strong as when in water.

The Torpedo, on this occasion, dispensed only the distinct instantaneous
stroke, so well known by the name of the electric shock. That protracted but
lighter sensation, that Torpor or Numbness which he at times induces, and from
which he takes his name, was not then experienced from the animal; but it
was imitated with artificial electricity, and shewn to be producible by a quick
succession of minute shocks. This in the Torpedo may perhaps be effected by
the successive discharge of his numerous cylinders, in the nature of a running
fire of musketry; the strong single shock may be his general volley. In the
continued effect, as well as in the instantaneous, his eyes, usually prominent,
are withdrawn into their sockets.

Walsh shows that these phenomena " are in no ways repugnant to the
laws of electricity," for "the same quantity of electric matter, according
as it is used in a dense or rare state, will produce the different conse-
quences."

Let me here remark that the sagacity of Mr Cavendish in devising and his
address in executing electrical experiments, led him the first to experience with
artificial electricity, that a shock could be received from a charge which was
unable to force a passage through the least space of air.

Walsh concludes his letter to Franklin in the following terms :

I rejoice in addressing these communications to You. He, who predicted
and shewed that electricity wings the formidable bolt of the atmosphere, will
hear with attention, that in the deep it speeds an humbler bolt, silent and
invisible: He, who analysed the electrified Phial, will hear with pleasure that
its laws prevail in animate Phials: He, who by Reason became an electrician,
will hear with reverence of an instinctive electrician, gifted in his birth with
a wonderful apparatus, and with the skill to use it*.

* That the electrical fishes still possess the power of exciting the imagination as
well as the nerves of those who have felt their power may be seen from the following
passage with which Prof. Du Bois Reymond begins his account of experiments on
a living Malapterurus in the Monatsberichte d. k. Acad. Berlin, 28 Jan. 1858.

"Fast mochte man es, im Sinne Newton's, eine Anwandlung der Natur nennen,
dass es ihr gefallen hat, aus der Unzahl der Geschopfe drei Fische, und zwar der

Introduction

However I may respect your talents as an electrician, it is certainly for
knowledge of more general import that I am impressed with that high esteem,
with which I remain,

Dear Sir,

Your affectionate

And obedient servant,

JOHN WALSH.

This paper is followed in the Philosophical Transactions by "Ana-
tomical Observations on the Torpedo," by John Hunter, F.R.S., in which
the great anatomist describes the structure of the electric organs, in
specimens of the fish furnished by Mr Walsh.

Considerable interest seems to have been excited by this account of
the Torpedo, and several papers on the Torpedo and the Gymnotus are
in the Philosophical Transactions for 1775, none of them, however, so
valuable as the original one by Walsh.

The practical electricians, however, were by no means satisfied that
the effects of these fishes were really produced by electricity.

Mr Ronayne has made a curious remark upon the supposed electricity of
the torpedo: he says, "if that could be proved, he does not see why we might
not have storms of thunder and lightning in the depths of the ocean. Indeed,
I must say, that when a Gentleman can so far give up his reason as to believe
the possibility of an accumulation of electricity among conductors sufficient to
produce the effects ascribed to the Torpedo, he need not hesitate a moment to
embrace as truths the grossest contradictions that can be laid before him*."

I am aware of only two occasions on which Cavendish, after he had
settled his own opinion on any subject, thought it worth his while to set
other people right who differed from him. One of these occasions was in

verschiedensten Art, nach Willkiir herauszugreifen, um sie mit elektromotorischen
Vorrichtungen von furchtbarer Gewalt als eine Waffe auszustatten, neben welcher
der Giftzahn der Klapperschlange, ja die nordamericanische Drehpistole, als eine
plumpe und armselige Erfindung erscheint; eine Waffe die, ohne ihren Trager der
Gefahr blosszustellen, lautlos und mit Blitzesschnelle in die Entfernung reicht, und
minutenlang eine secundendicht gedrangte Reihe von Geschossen schleudert, deren
keines fehlen kann, well alle auf alien Punkten des Raumes gleichzeitig vorhanden
sind."

In the Journal of Anatomy and Physiology for April, 1879, is a Note on a Curious
Habit of the Malapterurus Electricus, by A. B. Stirling. The author attempted to
leed Joe (the Malapterurus) with fresh worms, but he would not look at them.
Another fish, however, called Dick (Clarias), swallowed them. When Joe considered
that Dick had enjoyed his breakfast long enough, he swam up to him and gave him
such a shock that the whole was disgorged, whereupon Joe swallowed it himself.
When Dick at last succumbed to this treatment, Joe could no longer get his food
prepared for him, and gave up eating altogether.

* Extract from MS. letter of W. Henly, dated 21 May, 1775, in the Canton Papers
in the Royal Society's Library. 'Communicated to the editor by H. B.Wheatley, Esq.)

Historical and Personal 9

1778, when his experiments on the formation of nitric acid by the electric
spark from phlogisticated and dephlogisticated air (nitrogen and oxygen)
had been repeated without success by Van Marum with the great Teylerian
electrical machine, and by Lavoisier and Monge, and when Cavendish
"thought it right to take some measures to authenticate the truth of it."
For this purpose he requested Mr Gilpin, clerk to the Royal Society, to
repeat the experiment, and desired some of the gentlemen most conversant
with these subjects to be present at putting the materials together, and
at the examination of the produce*.

The other occasion, with which alone we are now concerned, is the only
one in which the presence of visitors to Cavendish's laboratory is recorded.
There can be no doubt that Cavendish had completely satisfied not only
Mr Walsh, but what was more to the purpose, himself, that the electric
phenomena of the torpedo are such as might arise from the discharge of
a large quantity of electricity at a very feeble degree of electrification.
It must therefore have been to satisfy other persons on this point that he
took the trouble to construct an artificial torpedo of wood covered with
leather, a rude model of the figure given by Walsh, with electric organs of
pewter supplied with electricity from a battery of Leyden jars, by wires
protected by glass tubes.

The accessories of this machine were equally unlike the kind of
apparatus which Cavendish made when working for himself. The torpedo
had a trough of salt water, the saltness of which was carefully adjusted,
so as to be equal to that of the sea. It had also a basket to lie in, and a
bed of sand to be buried in, and there were pieces of sole-leather, well
soaked in salt water, which Cavendish placed between the torpedo and
his hands, so that he might form some idea of what would happen if a
traveller with wet shoes were to tread on a live torpedo half buried in
wet sand.

It was on Saturday, 27th May, 1775, that Cavendish tried the effect
of his Torpedo on a select company of men of science. We find in the
Journal (Art. 601), the names of John Hunter, the great anatomist, Dr
Joseph Priestley, chemist, electrician and expounder of human knowledge
in general, Mr Thomas Ronayne, from Cork, the disbeliever in the electrical
character of the torpedo, Mr Timothy Lane, apothecary and electrician,
and Mr Edward Nairne, the eminent maker of philosophical instruments.

They got shocks from the torpedo to their complete satisfaction, and
probably learnt a good deal about electricity, but it was neither to satisfy
them nor to communicate to them his electrical discoveries, that Cavendish
admitted them into his laboratory on this memorable occasion, but simply
to obtain the testimony of these eminent men to the fact, that the shocks
of the artificial torpedo agreed in a sufficient manner with Walsh's de-

* Phil. Trans. 1788.

i o Introduction

scription of the effects of the live fish, to warrant the hypothesis that the
shock of the real torpedo may also be an electrical phenomenon.

I have now related all that I have been able to ascertain of the external .
history of Cavendish, in so far as it bears on his electrical researches. We
must in the next place consider the record of these researches — the two
papers in the Philosophical Transactions, which are here reprinted, and
the manuscripts now first published.

CAVENDISH'S WRITINGS ON ELECTRICITY

In the Philosophical Transactions for 1771 there is a paper entitled
"An attempt to explain some of the principal Phaenomena of Electricity
by Means of an Elastic Fluid: By the Honourable Henry Cavendish,
F.R.S." [Read Dec. 19, 1771, and Jan. 9, 1772, pp. 584-677.] This paper
and that on the Torpedo (Phil. Trans. 1776) are the only publications of
Cavendish relating to electricity.

Dr George Wilson, however, in his Life of Cavendish* says,

Besides his two published papers on electricity, Cavendish has left behind
him some twenty packets of manuscript essays, more or less complete, on
Mathematical and Experimental Electricity. These papers are at present in
the hands of Sir W. Snow Harris, who most kindly sent me an abstract of them,
with a commentary of great value on their contents. It will I trust be made
public.

Sir W. states that Cavendish had really anticipated all those great facts in
common electricity which were subsequently made known to the scientific world
through the investigations and writings of the celebrated Coulomb and other
philosophers, and had also obtained the more immediate results of experiments
of a refined kind instituted in our own day.

Sir William Thomson, to whom Sir William Snow Harris showed some
of Cavendish's results, thus speaks of them in a note dated Plymouth,
Monday, July 2, 1849.

Sir William Snow Harris has been showing me Cavendish's unpublished
MSS., put in his hands by Lord Burlington, and his work upon them; a most
valuable mine of results. I find already that the capacity of a disc (circular)

was determined experimentally by Cavendish as — — of that of a sphere of

2 &

same radius. Now we have capacity of disc = -a = _ '

It is much to be desired that those manuscripts of Cavendish should be
published complete; or, at all events, that their safe keeping and accessibility
should be secured to the world f.

* Works of the Cavendish Society, vol. i. Life of Cavendish, by George Wilson,
M.D.. F.R.S.E., London, 1851, p. 469.

f Reprint of Papers on Electrostatics and Magnetism, § 235, foot-note.

Description of Cavendish's Manuscripts on Electrictity \ i

The Cavendish Society, for whom Dr Wilson prepared his Life of
Cavendish, with an account of his chemical researches, did not consider
that it came within their design to publish his electrical researches.

Sir W. Harris, in whose hands the manuscripts were placed by the
Earl of Burlington, died in 1867. He makes several references to them in
his work on Frictional Electricity, edited after his death by Charles
Tomlinson, F.R.S., and published in 1867*, but he did not live to edit
the manuscripts themselves. Under these circumstances it was thought
desirable by Sir W. Thomson, Mr Tomlinson, and other men of science,
that something should be done to render the researches of Cavendish
accessible.

They accordingly represented the state of the case to the Duke of
Devonshire, to whom the manuscripts belong, and in 1874 he placed them
in my hands.

I could find no trace of Sir W. Harris' commentary referred to by
Dr Wilson, except that Dr Wilson mentions having returned it to Sir
W. Harris.

On the inside of the lid of the box which contained the manuscripts
was pasted a paper in the handwriting of Sir W. Harris, of which the
following is a copy.

The several parcels of manuscript papers by the late Mr Cavendish, which
the Earl of Burlington did me the honor to place in my hands with a view to
an examination and report on their contents may be taken at 24 in number.
Twenty of these contain sundry Philosophical papers on Mathematical and
Experimental Electricity, and Four sundry other Papers relating to Meteorology.

All these Papers are more or less confused as to systematic arrangement, and
require some considerable attention in decyphering. They are in many instances
rather notes of experiments and rough drafts intended as a basis for more
perfect productions than finished Philosophical Papers.

They are nevertheless extremely valuable and most interesting as evidence
of Mr Cavendish's great Philosophical f , and clearly prove that he had

anticipated nearly all those great facts in common electricity which at a later
period were made known to the scientific world through the writings of Coulomb
and the French philosophers.

Papers on Electricity.

Of the 20 parcels of papers on electricity 18 belong to the years 1771, 1772
& 1773, and have never yet appeared in print; the two remaining parcels are
dated 1775 and 1776, and are evidently connected with the author's celebrated
paper on the Torpedo published in the Royal Society's Transactions for 1776.

* P. 23 (straw electrometer), p. 45 (globe and hemispheres), p. 58 (specific
inductive capacity), p. 121 (measures of electricity), p. 208 (law of force), p. 223
(induction at a great distance).

t So in MS.

1 2 Introduction

The papers belonging to the years 1771, 1772 & 1773 consist of six papers on
Mathematical Electricity, nine experimental papers, one of Diagrams and
Figures, the remainder are of a miscellaneous character, and contain some
interesting Notes and Remarks and Thoughts on Electricity.

On examining the 20 parcels of manuscripts I found their contents to
be as follows :

No. i. MS. pp. i-io. Apparently an early form of the "Preliminary Propositions."

No. 2. MS. pp. 1-31. Draft of "Preliminary Propositions" as far as Prop. xxvu.

No. 3. MS. L. 3 to L. 23. Contains the same propositions in a less complete form

and not numbered, also two drafts of the propositions oh coated plates, each

12 pp., and 38 loose pages of drafts of propositions, and jottings of algebraical

calculations.

No. 4. MS. pp. 1-48. The fair copy of the " Preliminary Propositions." Props.

xxix. to xxxvu. Refers to figs. I to 10 of No. 15. See Arts. 140-174.
No. 5. MS. pp. 1-20. "Appendix." Refers to fig. n. See Arts. 175-194.
No. 6. "Computations for explanation of experiments."
MS. pp. 1-15. Drafts of the propositions.

16 pages of computations. "B. 17." Charge of a sphere within a con-
centric sphere. [This is placed here as a note to Art. 335.]

"Attractions of elect, bodies more accurate," pp. 1-4.

No. 7. MS. D. i to D. 13. Fair copy of First and Second Experiments. Refers to
Figs. 12, 13. See Arts. 217-235.

Draft of ditto marked "DIA."

No. 8. MS. pp. 1-7. Refers to Fig. 31. See Arts. 386-394.
No. 9. MS. pp. 1—51. Continuation of Experiments. See Arts. 236-294.
No. 10. MS. pp. 52-132. Part* of Experiments. See Arts. 295-385.

No. n. MS. pp. 1-8. IA. p. 10 A. 8, 9. p. 29 A. p. 32 A. i and 2. pp. 57-64.
pp. 85, 86. pp. 91-96. pp. 103-108. pp. 119-126. pp. 133-138. pp. 141, 142.
pp. 156-166.

All drafts of portions of the Account of Experiments.
No. 12. "Experiments 1771," MS. pp. 1-24. See Arts. 438-465. Also 14 loose sheets

of calculations and measurements.
No. 13. "Experiments 1772," MS. pp. 1-29. See Arts. 466-493.

M. i to M. 13. Measurements of glasses, &c. See Arts. 592-595.
No. 14. Experiment 1773, MS. pp. 1-135. See Arts. 494-580.
Index to elect, exper. 1773, pp. 1-8. See Contents.
Dimensions of trial plates, 4 pages.

•

No. 15. Figures and Diagrams.

i to 10 refer to Preliminary propositions No. 4

II Appendix No. 3

!2 ,, 13 ,, ,, Exp. i No. 7

14 ,, 19 ,, ,, Experiments, Part i No. 9

20 ,, 27 ,, ,, ,, Part 2 No. 10

30 ,, ,, Electrometer No. 9

31 ,, ,, Repulsion No. 8

* So in MS.

Description of Cavendish's Manuscripts on Electricity 1 3

No. 1 6. "Result." MS. pp. 1-2 1. See Arts. 647-683.

No. 17. "Notes." 4 pp. notes to "Thoughts concerning Electricity." These are
inserted in their proper places, Arts. 195-216.

MS. pp. 1-15. Drafts of propositions for the paper of 1771, but founded
on the theory stated in the "Thoughts." They are given in Note 18.

No. 18. "Thoughts concerning Electricity," MS. pp. 1-16. See Arts. 195-216.

No. 19. Resistance to Electricity, MS. pp. 1-23. See Arts. 616-631. "Res."
Results of ditto, pp. 1-4. See Arts. 684-696. Resistance of Copper wire, pp.
1-38. See Arts. 636-646. Calibration of Tubes. See Arts. 632-635.

No. 20. Experiments with the artificial Torpedo, pp. 1-26. See Arts. 596-615.
M. i to M. 42. Measurement of Leyden jars and batteries and of thickness of
plates. See Arts. 581-591. "Extract from Dr Williamson's exper. on elect.
Eel made in July 1773" pp. i to 14 + 4 pp. (See Phil. Trans. 1775, p. 94.)

In Art. 349, p. 175 of this book, Cavendish uses the expression "when
I wrote the second part* of this work." It appears from this that he
meant it for a book, not a paper to be communicated to the Royal Society.
Several portions of this book are contained in the manuscripts, but the
order in which they were intended to be placed can be discovered only by
help of the figures and diagrams, which are numbered from i to 31.

From these it appears that we must begin with No. 4 and No. 5, the
Preliminary Propositions f and the AppendixJ. The Preliminary Proposi-
tions refer to the printed paper of 1771. The last proposition in that paper
is numbered xxvn., and the first in the MS. is xxix.,so that one proposition
appears to be missing, but as there are several drafts, in all of which the
first proposition is numbered xxix., it is probable either that Prop. xxvm.
is not lost, but must be sought for among the enunciations in the second
part of the printed paper, or else that Cavendish made a mistake in
numbering his propositions.

The Lemmas, however, are numbered consecutively, the last in the
printed paper being Lemma xi. and the first in the MS. Lemma xn.

The other mathematical manuscripts are either drafts of these pro-
positions or jottings of calculations not intended for publication.

The paper entitled "Thoughts concerning electricity "§ (No. 18) is
placed next. It forms a suitable introduction to the account of the experi-
ments, as it indicates the leading ideas of Cavendish's researches. The
paper has no date, but its contents show that it is an earlier form of the
theory of electricity, which Cavendish had already abandoned before he
wrote the paper of 1771. The propositions in No. 17 belong to this form
of the theory, and are given in Note 18.

* This seems to refer to the second part of the paper in the Phil. Trans. 1771,
p. 670, or [p. 66] of this edition, and shows that this paper was intended to form
the first part of the " Work."

f Arts. 140 to 174. J Arts. 175 to 194.

§ Arts. 195 to 2i().

1 4 Introduction

We have next the account of the experiments, the order of which is

No. 7 Figs. 12 to 13 Exp. i. and n. Arts. 217 to 235

No. 9 Figs. 14 „ 19 Exps. in. to vm. Arts. 236 ,, 294

No. 10 Figs. 20 „ 30 Arts. 295 „ 385

No. 8 Fig. 31 Arts. 386 „ 394

The style in which these papers are written leaves no doubt that they
were intended to form a book, and to be published. They are given here
without any alteration except in the case of a few abbreviations the meaning
of which is either obvious or is explained in some other part of the MS.
I have also divided them into articles for the sake of more convenient
reference. All additions to the MS. are enclosed in square brackets.

After this I have placed the paper on the Torpedo from the Philo-
sophical Transactions for 1776. This, I think, is the whole of the "work"
which is extant, but it is by no means a complete account of Cavendish's
electrical researches. There are three forms in which Cavendish recorded
the results of his experiments :

1st. A Journal containing notes of every observation as it was made,
with the particulars of the experiments, and measurements of the
apparatus.

2nd. "Results," containing a comparison of the different measures of
quantities as recorded in the Journal, and a deduction of the most probable
result. See Arts. 647-696.

3rd. An account of the experiments written for publication.

I have reproduced the journals for 1771* and 1772! entire, because
they form a good example of Cavendish's method of work, and because
they contain all the data of some of the most important electrical measure-
ments.

The journal for 1773 j is much larger than the others, and gives an
account of many interesting and important researches.

Many pages of this journal, however, are filled with the details of the
experiments for the comparison of the coated plates which Cavendish used
as standards of capacity. These experiments differ in no respect from those
in the former journals, and all the conclusions which Cavendish deduced
from them are stated by himself in the " Results." I have therefore thought
it best to omit them from the journal, but to retain Cavendish's heading
of each experiment and its date when known, and to make the numbers
of the omitted articles run on continuously with those retained.

Many of the entries in the journals give the day of the week and of
the month, but very few of them give the year. I have therefore ascer-
tained in what years the stated days of the week and month coincided,
and have inserted the most probable year within square brackets. It thus
appears that the journal entitled "Experiments in 1773" begins with
* Arts. 438 to 465. f Arts. 466 to 493. J Arts. 494 to 580.

His work unknown to his contemporaries 1 5

experiments made in October, 1772. Cavendish appears, however, to have
got wrong in his reckoning for a good many days together during that
month. See Art. 502.

It is somewhat difficult to account for the fact, that though Cavendish
had prepared a complete description of his experiments on the charges
of bodies, and had even taken the trouble to write out a fair copy, and
though all this seems to have been done before 1774, and he continued to
make experiments in electricity till 1781, and lived on till 1810, he kept
his manuscript by him and never published it. It was not till 1784 that
he communicated to the Royal Society those "Experiments on Air," in-
cluding the production of water and of nitric acid, the absorbing interest
of which might perhaps account for some neglect of his electrical writings.

Cavendish cared more for investigation than for publication. He would
undertake the most laborious researches in order to clear up a difficulty
which no one but himself could appreciate, or was even aware of, and we
cannot doubt that the result of his enquiries, when successful, gave him a
certain degree of satisfaction. But it did not excite in him that desire to
communicate the discovery to others which, in the case of ordinary men
of science, generally ensures the publication of their results. How com-
pletely these researches of Cavendish remained unknown to other men of
science is shown by the external history of electricity.

Viscount Mahon, afterwards Lord Stanhope, a man of great ingenuity
and fertility in invention, a pupil of Le Sage of Geneva, and the inventor
of the printing press which bears his name, published in 1779 his Principles
of Electricity. The theory developed in this book is that

A positively electrified body surrounded by air will deposit upon all the
particles of that Air which shall come successively into contact with it, a pro-
portional part of its superabundant Electricity, By which means, the Air sur-
rounding that body will also become positively electrified : that is to say, it will
form round that positive body, an electrical atmosphere, which will likewise
be positive, (p. 7.)

That the electrical Density of all such Atmospheres decreases, when the
distance from the charged Body is increased, (p. 14.)

He then proceeds to determine the law of the density of the electrical
atmosphere, as it depends on the distance from the charged body. He
assumes that if a cylinder with hemispherical ends is placed in the electrical
atmosphere of a charged body, the density of the electricity at any part
of the cylinder will depend on the density of the electrical atmosphere in
contact with it.

He also shows by experiment that if the cylinder is insulated, and
originally without charge, it does not become charged as a whole by being
immersed in the electrical atmosphere of a charged body. Hence, when
the electricity of the cylinder is disturbed, the whole positive charge on

1 6 IntroauSlion

one portion of the surface is numerically equal to the whole negative charge
on the other portion.

Now if the density (on the cylinder) were inversely as the distance
from the charged body, a transverse section of the cylinder whose distance
from the charged body is the geometric mean of the distances of the ends,
would divide the charge into two equal parts (both of course of the same
kind of electricity), but if the density were inversely as the square of the
distance, the distance of the section which would bisect the charge would
be the harmonic mean of the distance of the ends. In all this he tacitly
confounds the point of bisection of the charge with the neutral point.

He then shows by experiment that the actual position of the neutral
point agrees sufficiently well with the harmonic mean, but not with the
geometric mean, and from this he concludes (p. 65),

Consequently, it evidently appears, from what was said above, that the
Density of the Electricity, of the electrical Atmosphere (in which the said
Body A , B was immersed) was in the inverse Ratio of the square of the Distance.

It is evident from this that Lord Mahon was entirely ignorant of every-
thing which Cavendish had done.

About the close of the century Dr Thomas Young, whose acquaintance
with all branches of science was as remarkable for its extent as for its
profundity, says of this neutral point § :

It was from the situation of this point that Lord Stanhope first inferred
the true law of the electric attractions and repulsion':., although Mr Cavendish
had before suggested the same law as the most probable supposition.

The same writer, in his "Life of Cavendish," in the Supplement to the
Encyclopedia Britannica*, gives the following account of the first paper on
electricity.

3. An Attempt to explain some of the principal Phenomena of Electricity by
means of an Elastic Fluid. (Phil. Trans. 1771, p. 584.) Our author's theory of
electricity agrees with that which had been published a few years before by
jEpinus.but he has entered more minutely into the details of calculation, showing
the manner in which the supposed fluid must be distributed in a variety of cases,
and explaining the phenomena of electrified and charged substances as they are
actually observed. There is some degree of unnecessary complication from the
great generality of the determinations: the law of electric attraction and repulsion
not having been at that time fully ascertained, although Mr Cavendish inclines
to the true supposition, of forces varying inversely as the square of the distance :
this deficiency he proposes to supply by future experiments, and leaves it to
more skilful mathematicians to render some other parts of the theory still more
complete. He probably found that the necessity of the experiments, which he
intended to pursue, was afterwards superseded by those of Lord Stanhope and

[* Reprinted, at the end of this volume, from Young's Miscellaneous Works, vol. n.]
§ Lectures on Natural Philosophy, London 1807, vol. I. Lecture liii, p. 664.

His ivork unknown to Young and to Coulomb 1 7

M. Coulomb; but he had carried the mathematical investigation somewhat
further at a later period of his life, though he did not publish his papers; an
omission, however, which is the less to be regretted, as M. Poisson, assisted by
all the improvements of modern analysis, has lately treated the same subject
in a very masterly manner. The acknowledged imperfections, in some parts of
Mr Cavendish's demonstrative reasoning, have served to display the strength
of a judgment and sagacity still more admirable than the plodding labours of
an automatical calculator. One of the corollaries* seems at first sight to lead
to a mode of distinguishing positive from negative electricity, which is not
justified by experiment; but the fallacy appears to be referable to the very
comprehensive character of the author's hypothesis, which requires some little
modification to accommodate it to the actual circumstances of the electric fluid,
as it must be supposed to exist in nature.

No man was better able than Dr Young to appreciate the scientific
merits of Cavendish, and it is evident that he spared no pains in obtaining
the data from which he wrote this sketch of his life, yet this account of
his electrical researches shows a complete ignorance of Cavendish's un-
published work, and this ignorance must have been shared by the whole
scientific world.

Dr Young, as it appears from the above extract, was aware of the
existence of unpublished papers by Cavendish relating to electricity, but
he supposed that these papers were entirely mathematical, and that "he
probably found that the necessity of the experiments, which he intended
to pursue, was afterwards superseded by those of Lord Stanhope and
M. Coulomb."

We now know that the unpublished mathematical papers were entirely
subsidiary to the experimental ones, and it is plain from Art. 95 that
Cavendish had actually made some of his experiments before the paper
of 1771, and that all those on electrostatics were completed before the
end of 1773.

The favourable reception which Lord Stanhope's very interesting and
popular experiments met with may have influenced Cavendish not to
publish his own, but his estimate of their value as a foundation for a
theory of electricity may be gathered from the fact, that in his "Thoughts
concerning Electricity," which appears to be his earliest writing on
the subject, he devotes two pages (Arts. 195-198) to the refutation
of the very theory of electric atmospheres which is the basis of Lord
Stanhope's reasoning; whereas in the paper of 1771, which contains his
more matured views, he does not even allude to that theory.

It was not till 1785 that the first of the seven electrical memoirs of
M. Coulomb was published. The experiments recorded in these memoirs
furnished the data on which the mathematical theory of electricity, as we
now have it, was actually founded by Poisson, and it is impossible to

* Art. 49 and Note I.

c. P. i. 2

1 8 Introduction

overestimate the delicacy and ingenuity of his apparatus, the accuracy of
his observations, and the sound scientific method of his researches ; but it
is remarkable, that not one of his experiments coincides with any of those
made by Cavendish. The method by which Coulomb made direct measure-
ments of the electric force at different distances, and that by which he
compared the density of the surface-charge on different parts of conductors,
are entirely his own, and were not anticipated by Cavendish. On the
other hand, the very idea of the capacity of a conductor as a subject of
investigation is entirely due to Cavendish, and nothing equivalent to it
is to be found in the memoirs of Coulomb.

The leading idea which distinguishes the electrical researches of
Cavendish from those of his predecessors and contemporaries, is the
introduction of the phrase "degree of electrification " with a clear scientific
definition, which shows that it is precisely equivalent to what we now
call potential.

In his first published paper (1771), he begins at Art. 101 by giving a
precise sense to the terms "positively and negatively electrified," which
up to that time had been in common use, but were often confounded with
the terms "over and under charged," and in Art. 102 he defines what is
meant by the "degree of electrification."

We find the same idea, however, in the much earlier draft of his theory
in the "Thoughts concerning Electricity," Art. 201, where the degree of
electrification is boldly, if somewhat prematurely, explained in a physical
sense, as the compression, or as we should now say, the pressure, of the
electric fluid.

We can trace this leading idea through the whole course of the
electrical researches.

He shows that when two charged conductors are connected by a wire
they must be electrified in the same degree, and he devotes the greater
part of his experimental work to the comparison of the charges of the
two bodies when equally electrified.

He ascertained by a well-arranged series of experiments the ratios of
the charges of a great number of bodies to that of a sphere 12-1 inches in
diameter, and as he had already proved that the charges of similar bodies
are in the ratio of their linear dimenions, he expressed the charge of any given
body in terms of the diameter of the sphere, which, when equally electrified,
would have an equal charge, so that when in his private journals he speaks
of the charge of a body as being so many "globular inches," or more briefly,
so many "inches of electricity," he means that the capacity of the body
is equal to that of a sphere whose diameter is that number of inches.

In the present state of electrical science, the capacity of a body is
defined as its charge when its potential is unity, and the capacity of a
sphere as thus defined is numerically equal to its radius. Hence, when
Cavendish says that a certain conductor contains n inches of electricity,

Plan of Experiments on Electrostatics 19

we may express his result in modern language by saying that its electric
capacity is \n inches.

In his early experiments he seems to have endeavoured to obtain a
number of conductors as different as possible in form, of which the
capacities should be nearly equal. Thus we find him comparing a paste-
board circle of 19-4 inches in diameter with his globe of 12-1 inches in
diameter, but finding the charge of the circle greater than that of the
globe, he ever after uses a circle of tin plate, 18-5 inches in diameter, the
capacity of which he found more nearly equal to that of the globe.

In like manner the first wire that he used was 96 inches long and
0-185 diameter, but afterwards he always used a wire of the same diameter,
but 72 inches long, the capacity of which was more nearly equal to that
of the globe.

He also provided himself with a set of glass plates coated with circles
of tin-foil on both sides. These plates formed three sets of three of equal
capacity, the capacities of the three sets being as i, 3 and 9, with a tenth
coated plate whose capacity was as 27.

Besides these he had "double" plates of very small capacity made of
two plates of glass stuck together, and also other plates of wax and rosin,
the inductive capacity of these substances being, as he had already found,
less than that of glass; and jars of larger capacity, ranging up to his great
battery of 49 jars, whose capacity was 321,000 "inches of electricity." In
estimating the capacity of his battery, he used the method of repeated
touching with a body of small capacity. (Arts. 412, 441, 582.) This
method is the same as that used by MM. Weber and Kohlrausch in their
classical investigation of the ratio of the electric units*.

Thus the method of experimental research which Cavendish adhered
to was the comparison of capacities, and the formation of a graduated
series of condensers, such as is now recognised as the most important
apparatus in electrostatic measurements.

We have next to consider the steps by which he established the
accuracy of his theory, and the discoveries he made respecting the
electrical properties of different substances.

Cavendish himself, in his description of his experiments, has shown us
the order in which he wishes us to consider them. The first experiment f
is that of the globe within two hemispheres, from which he proves that
the electric force varies inversely as the square of the distance, or at least
cannot differ from that ratio by more than a fiftieth part. The degree of
accuracy of all the experiments was limited by the sensitiveness of the
pith ball electrometer which he used. Bennett's gold leaf electrometer,
which is much more sensitive, was not introduced till 1787, but in repeating
the experiment we can now use Thomson's Quadrant electrometer, and

* Elektrodynamische Maasbestimmungen, Abb. iv. p. 235.
| Arts. 217 to 235.

2 2

20 Introduction

thereby detect a deviation from the law of the inverse square not exceeding
one in 72,000. See Note 19.

The second experiment, Art. 135, is a repetition of the first with
bodies of different shape.

The third experiment, Art. 265, shows that in comparing the charges
of bodies, the place where the connecting wire touches the body, and the
form of the connecting wire itself, are matters of indifference.

The fourth experiment, Art. 269, shows that the charges of bodies of
the same shape and size, but of different substances, are equal.

The fifth, Art. 273, compares the charge of a large circle with that of
two of half the diameter. According to the theory the charge of the large
circle should be equal to that of the two small ones if they are at a great
distance from each other, and equal to twice that of the small ones if they
are close together. Cavendish tried them at three different distances and
compared the results with his calculations.

The sixth experiment, Art. 279, compares one long wire with two of
half the length and half the diameter, placed at different distances.

The seventh, Art. 281, compares the charges of a globe, a circle, a
square, an oblong and three different cylinders, and the eighth, Art. 288,
shows that the charge of the middle plate of three parallel plates is small
compared with that of the two outer ones.

Cavendish next describes his experiments for comparison of the charges
of coated plates of glass and other substances, but begins by examining
the sources of error in measurements of this kind.

The first of these which he investigates is the spreading of electricity
on the surface of the plates beyond the coatings of tinfoil. He distinguishes
two kinds of this spreading, one a gradual creeping of the electricity over
the surface of the glass, Art. 300, and the other instantaneous, Art. 307.

He attempted to check the first kind by varnishing the glass plates
and by enclosing their edges in a thick frame of cement, but he found very
little advantage in this method, and finally adopted the plan of performing
all the operations of the experiment as quickly as possible, so as to allow
very little time for the gradual spreading of the electricity.

He next investigated the instantaneous spreading of electricity on the
glass near the edge of the coating. He noticed that at the instant of
charging the plate in the dark, a faint light could be seen all round the
edges. He also observed that after charging and discharging a coated
plate of glass many times without cleaning it, a narrow fringed ring of
dirt could be traced all round the coating, the space between this ring
and the coating being clean, and in general about -fa inch broad.

He also observed that the flash of light was stronger the first or second
times of charging a plate than afterwards.

To determine how much the capacity of a coated plate was increased
by this spreading of the electricity, he compared the capacity of a plate

Discovery of Specific Inductive Capacity 21

with a circular coating with that of the same plate with a new coating of
nearly the same area, but cut into strips, so that its perimeter was very
much greater than that of the circular coating.

In this way he found that if we suppose a strip of uniform breadth added
to the coating all round its boundary, the capacity of this coating, sup-
posing the electricity not to spread, will be equal to that of the actual
coating as increased by the spreading of the electricity. The most probable
breadth of this strip he found to be 0-07 inch for thick glass and 0-09
for thin.

When this correction was applied to the areas of the coatings of the
different coated plates, the computed charges of plates made of the same
kind of glass were found to be very nearly in the same ratio as their
observed charges.

But the observed charges of coated plates were found to be always
several times greater than the charges computed from their thickness and
the area of their coatings, the ratio of the observed charge to the com-
puted charge being for plate glass about 8-2, for crown glass about 8-5,
for shellac about 4-47, and for bees' wax about 3-5. Thus Cavendish not
only anticipated Faraday's discovery of the Specific Inductive Capacity
of different substances, but measured its numerical value in several sub-
stances.

The values of the specific inductive capacity of various substances as
determined by different modern observers are compared with those found
by Cavendish in the table in Note 27.

To make it certain, however, that the difference between the observed
and calculated capacities of coated plates really arose from the nature of
the plate and not from some error in the theory, Cavendish determined
the capacity of a "plate of air," that is to say a condenser consisting of
two circles of tinfoil on glass with air between them. The capacity of a
plate of air was found to be much less than that of a plate of glass or of
wax of the same dimensions, but it seemed to be about T'T in excess of the
calculated value. This discrepancy will be discussed in Note 17.

These may be considered the principal results of the investigations
with coated plates, but the following list of collateral experimental re-
searches will show how thoroughly Cavendish went to work.

A question of fundamental importance in the theory of dielectrics is
whether the electric induction is strictly proportional to the electromotive
force which produces it, or in other words, is the capacity of a condenser
made of glass or any other dielectric the same for high and for low
potentials?

The form in which Cavendish stated this question was as follows * : —
"Whether the charge of a coated plate bears the same proportion to that
of a simple conductor, whether the electrification is strong or weak."

* Art. 526.

22 Introduction

Cavendish, who explained the fact that the capacity of a glass plate
is greater than that of an air plate, by supposing that the electricity is
free to move within certain portions of the glass, supposed that when the
plate was more strongly electrified the electricity would be able to pene-
trate further into the glass, and that therefore its charge would be greater
in proportion to that of a simple conductor or a plate of air the stronger
the degree of electrification.

But according to the experiments he made to answer this question*
a coated plate and a simple conductor whose charges were equal for the
usual degree of electrification remained sensibly equal for higher and lower
degrees, and if, as appeared probable from the experiments on the spreading
of electricity at the edge of the coating, this spreading extended further
for high degrees of electrification than for low, it would be necessary to
admit that the charge of a glass plate became less in proportion to that
of a simple conductor as the degree of electrification increased. Cavendish,
however, concluded that the experiments were hardly accurate enough to
warrant the deduction from them of so improbable a conclusion.

He also found that the result of the comparison of a coated plate and
a simple conductor was the same whether they were charged positively
or negatively.

He tried whether the capacity of a plate of rosin altered with the
temperature, but he could not find that it didf. In glass he found that
the capacity increased as the temperature rose, but the most decided
increase did not occur till the glass began to conduct somewhat freely.
Cavendish therefore does not consider the experiment quite decisive J.

He found that the apparent capacity of a Florence flask § was greater
when it continued charged a good while than when it was charged and
discharged immediately, and he found that the same was the case with
a coated globe of glass. This phenomenon, which Faraday called "electric
.absorption," has recently been carefully studied in different kinds of glass
by Dr Hopkinsonj(. It is connected with the long-known phenomenon of
the "residual charge," and the existence of such phenomena in many
dielectrics renders it difficult to obtain consistent values of their inductive
capacities; for the more rapidly the charging and discharging is effected
the lower is the apparent value of the capacity. It is for this reason that
condensers of glass cannot be used as standards of capacity when accurate
measurements are desired.

Franklin had shown^f that the charge of a glass condenser resides in
the glass and not in the coatings, for when the coatings were removed
they were found to be without charge, and when new coatings were put
in their place the condenser thus reconstructed was found to be charged.

* Arts. 355-365- t Art- 523- + Art. 366.

§ Art. 523. || Phil. Trans. 1877, p. 599.

H Franklin's Works, ed. Sparks, vol. v. p. 201.

Experiments on Electrical Capacity and Resistance 23

Cavendish tried whether this was the case with a charged plate, of air,
by lifting one of the electrodes and changing the air between them and
then replacing the electrode. He found that the charge was not altered
during these operations, and concluded that the charge resides, not in the
air, but in the metal plates.

In Arts. 336 to 339 we find a most ingenious method of determining
by experiment the effect of the floor, walls and ceiling of a room, and of
other surrounding objects, in increasing the apparent capacity of a con-
ductor placed in a given position in the room. The method consists in
measuring the capacities of two conductors of the same shape but of
different dimensions, the centre of each being at the given point in the
room. If the experiment had been made with the conductors at an infinite
distance from all other bodies their capacities would have been in the
ratio of their corresponding dimensions, but the effect of surrounding
objects is to make their capacities vary in a higher ratio than that of their
dimensions, and from the measured ratio of the two capacities, the cor-
rection for the effect of surrounding objects on the capacity of any small
body may be calculated.

Cavendish also verified by experiment what he had already proved
theoretically, that the capacity of two condensers is not sensibly altered
when they are placed near to each other or far apart.

But besides this series of experiments on electric capacity, another
course of experiments on electric resistance was going on between 1773
and 1781, the knowledge of which seems never to have been communicated
to the world.

In his paper on the Torpedo in the Philosophical Transactions for 1776
(Art. 398) he alludes to "some experiments of which I propose shortly
to lay an account before this Society," but he never followed up this
proposal by divulging the method by which he obtained the results which
he proceeds to state — "that iron wire conducts about 400 million times
better than rain or distilled water*," and that "sea water, or a solution
of one part of salt in 30 of water conducts 100 times, and a saturated
solution of sea-salt about 720 times better than rain water."

Such was the reputation of Cavendish for scientific accuracy, that these
bare statements seem to have been accepted at once, and soon found their
way into the general stock of scientific information, although no one, as
far as I can make out, has ever conjectured by what method Cavendish
actually obtained them, more than forty years before the invention of

* This is equivalent to saying that iron wire conducts 555,555 times better than
saturated solution of sea salt. A comparison of the experiments of Matthiessen on
iron with those of Kohlrausch on solutions of sodium chloride at 18° C., would make
the ratio 451,390. The resistance of iron increases and that of the solution diminishes
as the temperature rises, and at a temperature of about 11° C. the ratio of the re-
sistances would agree with that given by Cavendish.

24 Introduction

the galvanometer, the only instrument by which any one else has ever
been able to compare electric resistances.

We learn from the manuscripts now first published, that Cavendish
was his own galvanometer. In order to compare the intensity of currents
he caused them to pass through his own body, and by comparing the
intensity of the sensations he felt in his wrist and elbows, he estimated
which of the two shocks was the more powerful.

As Cavendish does not appear to have prepared an account of these
experiments in the manner in which he usually wrote out what he intended
to publish, it may be well to describe them here, as we collect them from
different parts of his Journals.

The conductors to be compared were for the most part solutions of
common salt of known strength or of other substances. These solutions
were placed in glass tubes, more than a yard long, bent near one end.
The tubes had been previously calibrated by means of mercury.

Two wires were run into the tube, probably through holes in corks at
each end, to serve as electrodes. The length of the effective column of
the liquid could be altered by sliding the wire in the straight part of the
tube.

In order to send electric discharges of equal quantity and equal
electromotive force through two different tubes Cavendish chose six
jars of nearly equal capacity from "Nairne's last battery." The two
tubes to be compared were placed so that the wires run into their bent
ends communicated with the outside of this battery of six jars. The
wires run into the straight ends of the tubes were fastened to two
separately insulated pieces of tinfoil. The six jars were then all charged
at once by the same conductor till the gauge electrometer indicated the
proper degree of electrification. The conductor was then removed , so
that the six jars remained with their inside coatings insulated from each
other and equally charged.

Cavendish then taking two pieces of metal, one in each hand, touched
with one the tinfoil belonging to one of the tubes to be compared, and
then with the other touched the knob of jar No. i, so as to receive a
shock, the charge passing through his body and the first tube.

He next laid one of the metals on the tinfoil of the second tube, and
then touching with the other the knob of jar No. 2, he received a second
shock, the discharge passing through his body and the second tube.

In this way he took six shocks, making them pass alternately through
the first and the second tube, and proceeded to record his impression
whether the intensity of the shock through the second tube was greater
or less than that of the shock through the first, and concluded that the
tube which gave the greater shock had the smaller resistance.

He then adjusted the wire in one of the tubes so as to make the re-
sistance more nearly equal to that of the other, and repeated the experi-

Discovery of Laws of Electric Resistances of Solutions 25

ment, always recording his impression of the result, till he found that one
adjustment made the shock of the second tube sensibly greater than that
of the first, and that another adjustment made it sensibly less.

From the result of the whole series of experiments he judged what
adjustment would make the two shocks exactly equal.

Instead of using six jars only, he seems latterly to have used the whole
battery, electrifying one row to a given degree and then communicating
this charge to the whole battery, and taking the discharge of one row at
a time through the tubes alternately. He seems to have found some
advantage in thus using a discharge of greater quantity and smaller
electromotive force.

The accuracy which Cavendish attained in the discrimination of the
intensity of shocks is truly marvellous, whether we judge -by the con-
sistency of his results with each other, or whether we compare them with
the latest results obtained with the aid of the galvanometer, and with all
the precautions which experience has shown to be necessary in measuring
the resistance of electrolytes.

One of the most important investigations which Cavendish made in
this way was to find, as he expressed it, "what power of the velocity the
resistance is proportional to*."

Cavendish means by "resistance" the whole force which resists the
current, and by "velocity" the strength of the current through unit of
area of the section of the conductor.

(In modern language the word resistance is used in a different sense,
and is measured by the force which resists a current of unit strength.)

By four different series of experiments on the same solution in wide
and in narrow tubes, Cavendish found that the resistance (in his sense)

varied as the

1-08, 1-03, 0-976, and i-oo

power of the velocity.

This is the same as saying that the resistance (in the modern sense)

varies as the

0-08, 0-03, — 0-024

power of the strength of the current in the first three sets of experiments,
and in the fourth set that it does not vary at all.

This result, obtained by Cavendish in January, 1781, is an anticipation
of the law of electric resistance discovered independently by Ohm and
published by him in 1827. It was not till long after the latter date that
the importance of Ohm's law was fully appreciated, and that the measure-
ment of electric resistance became a recognised branch of research. The
exactness of the proportionality between the electromotive force and the
current in the same conductor seems, however, to have been admitted,
rather because nothing else could account for the consistency of the

* Arts. 574, 575, 629, 686.

26 Introduction

measurements of resistance obtained by different methods, than on the
evidence of any direct experiments.

Some doubts, however, having been suggested with respect to the
mathematical accuracy of Ohm's law, the subject was taken up by the
British Association in 1874, and the experiments of Professor Chrystal,
by which the exactness of the law, as it relates to metallic conductors, was
tested by currents of every degree of intensity, are contained in the Report
of the British Association for 1876.

The laws of the strength of currents in multiple and divided circuits
are accurately stated by Cavendish in Arts. 417, 597, 598.

Cavendish applied the same method of experiment to compare the
resistance of the same liquid at different temperatures*, and he found
that "salt in 69 [of water] conducts 1-97 times better in heat of 105 than
in that of 58^." He also found that "the proportion of the resistance of
saturated solution and salt in 999 to each other seems not much altered
by varying heat from 50 to 95."

Kohlrausch, who has made a most extensive series of experiments on
the resistance of electrolytes, gives results from which it appears that the
ratio of the resistances of salt in 69 at 105° F. and at 58!° F. would be
1-59. He also finds that the temperature coefficient for solutions of salt
alters very little with the strength. See Note 33.

Cavendish also tested the resistance of solutions of salt of strengths
varying from saturation to one in 20,000 of distilled water, and arrived at
the result, which Kohlrausch has shown to be nearly accurate, that for
weak solutions the product of the resistance into the percentage of salt
is nearly constant.

Of all substances, that for which different observers have given the
most different measures of resistance is pure water.

It has been found indeed that the presence of the minutest trace of
impurity in water diminishes its resistance enormously. Thus Kohlrausch
found that it was necessary to use water quite freshly distilled in platinum
vessels, for if placed in a glass vessel it rapidly diminished in resistance
by dissolving a minute quantity of the glass, and a few minutes exposure
to the air of the laboratory, by impregnating the water with a trace of
tobacco smoke, was found sufficient to spoil it for a determination of re-
sistance. Kohlrausch indeed estimates that the electric conductivity which
he observed in the purest water he could obtain might be accounted for
by the presence of no more than one ten millionth part of hydrochloric acid,
a quantity which no chemical analysis could detect. Hence the hypothesis
that water is a non-conductor of electricity, if not true, cannot be dis-
proved.

Some of these remarkable properties of water were detected by
Cavendish. He found that the resistance of pump water was 4^ times less

* Art. 091.

Cavendish's Chemical Equivalent Weights 27

than that of rain water, and that of rain water was 2-4 times less than that
of distilled water*.

In January 1777, he found that salt in 2999 conducted about 70 or
90 times better than some water distilled in the preceding summer but
only about 25 or 50 times better than the distilled water used in the year
1776 f , and that the conductivity of distilled water increased by standing
two or three hours in a glass tubej.

He also found that in order to make the conducting powers of his
weakest solutions of salt agree with the hypothesis that they are as the
quantity of salt in them, it would be necessary only to suppose that his
distilled water contained one part of salt in 120,000 §.

It was found that distilled water impregnated with fixed air from oil
of vitriol and marble conducted 2\ times better than the same water
deprived of its air by boiling ||, and that the presence of absorbed air in
a weak solution of salt seemed to increase its conductivity \

In order to find whether electricity is resisted in passing out of one
medium into another in perfect contact with it, Cavendish prepared a
tube containing 8 columns of saturated solution of sea salt enclosed be-
tween columns of mercury. He found that the shock was diminished in
passing through a mixed column in which the length of salt water was
21-8 inches as much as in passing through a single column of the same
size whose length was 22-94 inches**.

The difference would have been far greater if the comparison had been
made with an ordinary galvanometer and continued currents which rapidly
produce polarization, but with the small quantities of electricity which
Cavendish used, the effect of polarization would hardly be sensible.

He also made a compound conductor consisting of 40 bits of tin
soldered together. The shock through this appeared to be of the same
strength as through a single piece of the same size. This experiment
however is not of much value, as the resistance of the conductor was far
too small compared with that of Cavendish's body to give good results ff.

We now come to a very remarkable set of experiments which Cavendish
made on a series of salts and acids in order to determine their relative
electric resistance. They are recorded in Arts. 626, 627 and 694, and are
dated Jan. 13 and 15, 1777.

The strength of the different solutions was such, as Cavendish tells us,
"that the quantity of acid in each should be equivalent to that in a
• solution of salt in 29 of water."

* Art. 525. f Art. 690. J Art. 621.

§ Art. 630. || Arts. 625, 693. f Art. 692. ** Art. 578.

•ft Art. 579. The resistance of a man's body, from one hand to the other, varies
from about 1000 ohms when the hands are well wetted with salt water, to about
12,000 when the hands are dry. When the outer skin is removed by a blister, the
resistance is very much diminished. The resistance of the compound conductor was
probably a fraction of an ohm. See Note 31.

2 8 Introduction

The total weight of each solution was 3 pounds 10 ounces and 12
pennyweights, or 1116 pennyweights Troy. The quantity of each sub-
stance when reduced to pennyweights is in every case very nearly the
equivalent weight of that substance in the system adopted at present, in
which the equivalent weight of hydrogen is taken as unity*.

Now these experiments were made in 1777, and it is difficult to see
from what source, other than determinations of his own, he could have
derived these numbers. Wenzel's Lehre von den Verwandschaften was pub-
lished in 1777. I have not been able to consult the work itself, but from
the account of it given in Kopp's Geschichte der Chemie, the equivalent
numbers seem to have been larger than those used by Cavendish. Richter's
Anfangsgrunde der Stochyometrie was not published till 1792.

It is difficult to account for the agreement not only of the ratios but
of the absolute numbers given by Cavendish with those of the modern
system, in which the equivalent weight of hydrogen is taken as unity.
I can only conjecture from several parts of his paper on Factitious Airs
(Phil. Trans. 1766), that Cavendish was accustomed to compare the
quantity of fixed air from different carbonates with that from 1000 grains
of marble. Now the modern equivalent weight of marble is 100, so that if
Cavendish took 100 pennyweights as the equivalent weight of marble, the
equivalents of other substances would be as he has given them. This I
think is more likely than that he should have selected inflammable air
as his standard substance at a time when even his own experiments left
it doubtful whether inflammable air was always of the same kind.

In his journal, Cavendish writes down these equivalent weights just
as a modern chemist might do, without a hint that a list of these numbers
was not at that time one of the things which every student of chemistry
ought to know by heart. It is only by comparing the date of these re-
searches with the dates of the principal discoveries in chemistry, that we
become aware, that in the incidental mention of these numbers we have
the sole record of one of those secret and solitary researches, the value
of which to other men of science Cavendish does not seem to have taken
into account, after he had satisfied his own mind as to the facts.

I take this opportunity of expressing my thanks to the many friends
who have given me assistance in preparing this edition, and in particular
to Mr C. Tomlinson, who gave me valuable information about the manu-
scripts; to Mrs Sime, who lent me a manuscript book of letters, &c.,
relating to Cavendish, collected by her brother, the late Dr George Wilson;
to Mr W. Garnett, of St John's College, Cambridge, who copied out Arts.
236-294; and Mr W. N. Shaw, of Emmanuel College, who took the photo-
graphs from which the facsimile figures were executed; to Mr H. B.
Wheatley, who furnished me with information connected with the history

* See Note 34.

Magnetic Experiments 29

of the Royal Society; to Prof. Dewar, Mr P. T. Main, Mr G. F. Rodwell,
and Dr E. J. Mills, who gave me information on chemical subjects; and
Mr Dew Smith and Mr F. M. Balfour, of Trinity College, and Prof. Ernst
von Fleischl, of Vienna, who gave me information about electrical fishes,
and the physiological effect of electricity.

P.S. I4th June, 1879.

Just before sending this sheet to press I have received from Mr Robert
H. Scott, F.R.S., a small packet marked "Cavendish Papers," which had
been sent to the Meteorological Office by Sir Edward Sabine.

These papers relate entirely to magnetism, and do not fall within the
scope of this volume*, though they may supply important materials for
the magnetic history of the earth, and are in all respects excellent speci-
mens of Cavendish's scientific procedure.

I shall therefore only mention a few particulars in which these papers
throw some additional light on Cavendish's life and work.

The descriptions of Cavendish by Cuvier, Young, Thomson and Wilson
agree in representing him as living in London, and regularly attending
the meetings of the Royal Society, but in other respects leading an isolated
life, very much detached from the interests, whether social or scientific,
of other men.

It has also been hinted that Lord Charles Cavendish, who, as we have
already seen, was himself addicted to scientific pursuits, did not entirely
approve of his son's devotion to science, or at least, for some reason or
other, restricted him in the means of carrying on his work.

In these manuscripts, however, we have the details of a laborious series
of observations undertaken to determine the errors of the variation compass
and the dipping needle belonging to the Royal Society, and on Sept. 16,
1773, we find "Observations of needle in Garden by Father and Self,"
and a "Comparison of Society's compass in house and in society's] garden
with Father's compass in room."

It appears, therefore, that Lord Charles Cavendish not only placed his
instruments at his son's disposal, but made observations of the compass
in concert with him, and that these observations were undertaken in order
to make the instruments belonging to the Royal Society more available
for accurate measurements. In the same Journal there are also "Measures
taken for setting Dr Knight's magnets so that their poles shall be equi-
distant from variation] comp[ass] and dipp[ing] need[le] in 1775." The
results of this enquiry are briefly stated by Cavendish in his paper on the
Instruments belonging to the Royal Society in the "Philosophical Trans-
actions" for 1776. In the same volume there is an account of Dr Knight's
great Magazines of magnets by Dr Fothergill.

* [See Dr Chree's account of Cavendish's Magnetic Researches in vol. n.]

3°

Introduction

A considerable portion of the MS. is taken up with "Directions for
using the Dipping Needle," written out at greater or less length (probably
according to the scientific capacity of the recipient) "for Captain
Pickersgill," "for Captain Bayley," "for Dalrymple" [Hydrographer to
the Honourable East India Company] &c.

There is also a treatise of 26 pages "On the different forms of con-
struction of dipping needles."

Besides this, there is a series of observations of the magnetic variation
and also of the dip, at various times, from 1773 to August 1809 (Cavendish
died Feb. 24, 1810).

These observations were made for the most part only in the summer
months, but during that time were carried on with the greatest regularity,
and results for each year calculated from them.

We also find the record of "Trials of Nairne's needle in different parts
of England in August, 1778."

It was tried "in Garden, Aug. 8. In Garden of Observatory at Oxford,
Aug. 14. At Birmingham, in Bowling-green, Aug. 15. At Towcester, in
Garden, Aug. 17. At St Ives, in Garden, Aug. 18. At Ely, in Garden,
Aug. 18. At London, Aug. 19 and 22." From these trials he finds that
"Lines of equal dip should seem to run about 44° to south of west, and
dip should increase about 42' by going i° to N.W."

There is a long and valuable series of experiments on the magnetic
properties of forged iron, blistered steel, and cast iron. "Some bars were
got from Elwell 31! inch long, 2-1 broad, and about -5 thick. On May 29,
1776, one of each was made magnetical, the marked end being the south
pole. In trying the experiment the bars were placed perpendicularly
against a wall 25 inches distant from the center of the needle, 91°^ to west
of usual magnetic north, either the top or bottom of the bar being always
on a level with the needle. They were kept constantly with the marked
end upwards till after the observations of June 30, after which they were
kept with the marked end downwards."

Cavendish determines in every case the "fixed magnetism" and the
"moveable magnetism" of the bar, and also its magnetism when "struck
100 times on an anvil, falling 1-6 inches by its weight, and tried im-
mediately after."

There are also 23 pages of experiments on the effect of heat on magnets,
and a mathematical investigation of the bending of the dipping-needle by
its own weight as affecting the determination of the dip, together with
measurements of the elasticity of steel and of glass.

THE ELECTRICAL RESEARCHES

OF THE

HONOURABLE HENRY CAVENDISH, F.R.S.

[ 33 ]

PHILOSOPHICAL TRANSACTIONS. VOL. 61, 1771,
pp. 584-677

An attempt to explain some of the Principal Phenomena
of Electricity, by means of an Elastic Fluid

Read Dec. 19, 1771 and Jan. 9, 1772.
{See Table of Contents at the beginning of this volume.}

[PART I.]

i] Since I first wrote the following paper, I find that this way of
accounting for the phenomena of electricity is not new. ./Epinus, in his
Tentamen Theories Electricitatis et Magnetismi*, has made use of the same,
or nearly the same hypothesis that I have; and the conclusions he draws
from it agree nearly with mine, as far as he goes. However, as I have
carried the theory much farther than he has done, and have considered
the subject in a different, and, I flatter myself, in a more accurate manner,
I hope the Society will not think this paper unworthy of their acceptance.

2] The method I propose to follow is, first, to lay down the hypothesis ;
next, to examine by strict mathematical reasoning, or at least, as strict
reasoning as the nature of the subject will admit of, what consequences
will flow from thence ; and lastly, to examine how far these consequences
agree with such experiments as have yet been made on this subject. In
a future paper, I intend to give the result of some experiments I am
making, with intent to examine still further the truth of this hypothesis,
and to find out the law of the electric attraction and repulsion.

HYPOTHESIS.

3] There is a substance, which I call the electric fluid, the particler
of which repel each other and attract the particles of all other mattes
with a force inversely as some less power of the distance than the cube :
the particles of all other matter also, repel each other, and attract those
of the electric fluid, with a force varying according to the same power of
the distances. Or, to express it more concisely, if you look upon the
electric fluid as matter of a contrary kind to other matter, the particles
of all matter, both those of the electric fluid and of other matter, repel
particles of the same kind, and attract those of a contrary kind, with a
force inversely as some less power of the distance than the cube.

* [Petropoli, 1759.]

c. p. i. *

34 i 'st published Paper on Electricity

/ 4] For the future, I would be understood never to comprehend the
electric fluid under the word matter, but only some other sort of matter.

5] It is indifferent whether you suppose all sorts of matter to be indued
in an equal degree with the foregoing attraction and repulsion, or whether
you, suppose some sorts to be indued with it in a greater degree than others;
but it is likely that the electric fluid is indued with this property in a much
greater degree than other matter ; for in all probability the weight of the
electric fluid in any body bears but a very small proportion to the weight
of the matter ; but yet the force with which the electric fluid therein attracts
any particle of matter must be equal to the force with which the matter
therein repels that particle; otherwise the body would appear electrical,
as will be shewn hereafter.

To explain this hypothesis more fully, suppose that i grain of electric
fluid attracts a particle of matter, at a given distance, with as much force
as n grains of any matter, lead for instance, repel it : then will i grain of
electric fluid repel a particle of electric fluid with as much force as n grains
of lead attract it ; and i grain of electric fluid will repel i grain of electric
fluid with as much force as n grains of lead repel n grains of lead*.

6] All bodies in their natural state with regard to electricity, contain
such a quantity of electric fluid interspersed between their particles, that
the attraction of the electric fluid in any small part of the body on a given
particle of matter shall be equal to the repulsion of the matter in the same
small part on the same particle. A body in this state I call saturated with
electric fluid: if the body contains more than this quantity of electric fluid,
I call it overcharged : if less, I call it undercharged. This is the hypothesis ;
I now proceed to examine the consequences which will flow from it.

7] LEMMA I. Let EAe (Fig. i) represent a cone
continued infinitely; let A be the vertex, and Bb

and Dd planes parallel to the base ; and let the cone
be filled with uniform matter, whose particles repel
each other with a force inversely as the n power of
the distance. If n is greater than 3, the force with which a particle at A

is repelled by EBbe or all that part of the cone beyond Bb is as .--s .

For supposing AB to flow, the fluxion of EBbe is proportional to
- AB x ABZ, and the fluxion of its repulsion on A is proportional to

Afi i

2; the fluent of which is /~n~n4R«~-3' whicn when AB is mnnite

is equal to- nothing; consequently the repulsion of EBbe is proportional to

i i

° ° '

_

(n - 3) ABn~3 AH"

* [Note i, p. 352.]

Principles of Saturation 35

8] COR. If AB is infinitely small, . __3 is infinitely great; therefore

the repulsion of that part of the cone between A and Bb, on A , is infinitely
greater than the repulsion of all that beyond it.

9] LEMMA II. By the same method of reasoning it appears, that if n
is equal to 3, the repulsion of the matter between Bb and Dd on a particle

AD
at A, is proportional to the logarithm of -j-^; consequently, the repulsion

of that part is infinitely small in respect of that between A and Bb, and
also infinitely small in respect of that beyond Dd.

10] LEMMA III. In like manner, if n is less than 3, the repulsion of
the part between A and Bb on A is proportional to AB3~": consequently
the repulsion of the matter between A and Bb, on A, is infinitely small
in respect of that beyond it.

n] COR. It is easy to see from these three lemmata, that, if the
electric attraction and repulsion had been supposed to be inversely as
some higher power of the distance than the cube, a particle could not have
been sensibly affected by the repulsion of any fluid, except what was
placed close to it. If the repulsion was inversely as the cube of the distance,
a particle could not be sensibly affected by the repulsion of any finite
quantity of fluid, except what was close to it. But as the repulsion is
supposed to be inversely as some power of the distance less than the cube,
a particle may be sensibly affected by the repulsion of a finite quantity
of fluid, placed at any finite distance from it.

12] DEF. If the electric fluid in any body is by any means confined
in such manner that it cannot move from one part of the body to the
other, I call it immoveable: if it is able to move readily from one part
to another, I call it moveable.

13] PROP. I. A body overcharged with electric fluid attracts or repels
a particle of matter or fluid, and is attracted or repelled by it, with exactly
the same force as it would, if the matter in it, together with so much of
the fluid as is sufficient to saturate it, was taken away, or as if the body
consisted only of the redundant fluid in it. In like manner an under-
charged body attracts or repels with the same force, as if it consisted only
of the redundant matter; the electric fluid, together with so much of the
matter as is sufficient to saturate it, being taken away.

This is evident from the definition of saturation.

f*

14] PROP. II. Two over or undercharged bodies attract or repel each
other with just the same force that they would, if each body consisted
only of the redundant fluid in it, if overcharged, or of the redundant matter
in it, if undercharged.

For, let the two bodies be called A and B ', by the last proposition the

3—2

36 First published Paper on Electricity

redundant substance in B impels each particle of fluid and matter in A ,
and consequently impels the whole body A , with the same force that the
whole body B impels it: for the same reason the redundant substance
in A impels the redundant substance in B, with the same force that the
whole body A impels it. It is shewn therefore, that the whole body B
impels the whole body A, with the same force that the redundant sub-
stance in B impels the whole body A, or with which the whole body A
impels the redundant substance in B; and that the whole body A impels
the redundant substance in B, with the same force that the redundant
substance in A impels the redundant substance in B ; therefore the whole
body B impels the whole body A, with the same force with which the
redundant substance in A impels the redundant substance in B, or with
which the redundant substance in B impels the redundant substance in A .

15] COR. Let the matter in all the rest of space, except in two given
bodies, be saturated with immoveable fluid; and let the fluid in those
two bodies be also immoveable. Then, if one of the bodies is saturated,
and the other either over or undercharged, they will not at all attract or
repel each other.

If the bodies are both overcharged, they will repel each other.

If they are both undercharged, they will also repel each other.

If one is overcharged and the other undercharged, they will attract
each other.

N.B. In this corollary, when I call a body overcharged, I would be
understood to mean, that it is overcharged in all parts, or at least nowhere
undercharged: in like manner, when I call it undercharged, I mean that
it is undercharged in all parts, or at least nowhere overcharged.

16] PROP. III. If all the bodies in the universe are saturated with
electric fluid, it is plain that no part of the fluid can have any tendency
to move.

17] PROP. IV. If the quantity of electric fluid in the universe is
exactly sufficient to saturate the matter therein, but unequally dispersed,
so that some bodies are overcharged and others undercharged; then, if
the electric fluid is not confined, it will immediately move till all the bodies
in the universe are saturated.

For supposing that any body is overcharged, and the bodies near it
are not, a particle at the surface of that body will be repelled from it by
the redundant fluid within; consequently some fluid will run out of that
body; but if the body is undercharged, a particle at its surface will be
attracted towards the body by the redundant matter within, so that some
fluid will run into the body.

N.B. In Prob. IV, Case 3 {p. 42}, there will be shewn an exception to
this proposition ; there may perhaps be some other exceptions to it : but

Attractions of Charged Spheres 37

I think there can be no doubt, but what this proposition must hold good
in general.

18] LEMMA IV. Let BDE, bde, and /JSe (Fig. 2), be concentric spherical
surfaces, whose center is C : if the space * Bb is filled
with uniform matter, whose particles repel with a
force inversely as the square of the distance, a
particle placed anywhere within the space Cb, as
at P, will be repelled with as much force in one
direction as another, or it will not be impelled in
any direction. This is demonstrated in Newton,
Princip. Lib. I, Prop. 70. It follows also from his
demonstration, that if the repulsion is inversely as
some higher power of the distance than the square,
the particle P will be impelled towards the center ; and if the repulsion is
inversely as some lower power than the square, it will be impelled from
the center f.

19] LEMMA V. If the repulsion is inversely as the square of the
distance, a particle placed anywhere without the sphere BDE, is repelled
by that sphere, and also by the space Bb, with the same force that it would
if all the matter therein was collected in the center of the sphere ; provided
the density of the matter therein is everywhere the same at the same
distance from the center. This is easily deduced from Prop. 71, of the same
book, and has been demonstrated by other authors.

20] PROP. V. PROBLEM i. Let the sphere BDE be filled with uniform
solid matter, overcharged with electric fluid: let the fluid therein be
moveable, but unable to escape from it: let the fluid in the rest of infinite
space be moveable, and sufficient to saturate the matter therein ; and let
the matter in the whole of infinite space, or at least in the space Bfi,
whose dimensions will be given below, be uniform and solid; and let the
law of the electric attraction and repulsion be inversely as the square of
the distance : it is required to determine in what manner the fluid will be
disposed both within and without the globe.

Take the space Bb such, that the interstices between the particles of
matter therein shall be just sufficient to hold a quantity of electric fluid,
whose particles are pressed close together, so as to touch each other, equal
to the whole redundant fluid in the globe, besides the quantity requisite
to saturate the matter in Bb ; and take the space Bfi such, that the matter
therein shall be just able to saturate the redundant fluid in the globe:

* By the space Bb or Bfi, 1 mean the space comprehended between the spherical
surfaces BDE and bde, or between BDE and /38«: by the space Cb or C|3, I mean
the spheres bde or flfif.

{f Hence the only law according to a power of the distances which permits
absence of force inside a charged shell is the inverse square.}

38 First published Paper on 'Electricity

then, in all parts of the space Bb, the fluid will be pressed close together,
so that its particles shall touch each other; the space Bfi will be intirely
deprived of fluid; and in the space Cb, and all the rest of infinite space,
the matter will be exactly saturated.

For, if the fluid is disposed in the above-mentioned manner, a particle
of fluid placed anywhere within the space Cb will not be impelled in any
direction by the fluid in Bb, or the matter in Bfi, and will therefore have
no tendency to move : a particle placed anywhere without the sphere /JSe
will be attracted with just as much force by the matter in Eft, as it is
repelled by the redundant fluid in Bb, and will therefore have no tendency
to move : a particle placed anywhere within the space Bb, will indeed be
repelled towards the surface, by all the redundant fluid in that space <
which is placed nearer the center than itself; but as the fluid in that
space is already pressed as close together as possible, it will not have any
tendency to move ; and in the space Bf$ there is no fluid to move, so that
no part of the fluid can have any tendency to move.

Moreover, it seems impossible for the fluid to be at rest, if it is disposed
in any other form; for if the density of the fluid is not everywhere the
same at the same distance from the center, but is greater near b than near d,
a particle placed anywhere between those two points will move from b
towards d; but if the density is everywhere the same at the same distance
from the center, and the fluid in Bb is not pressed close together, the
space Cb will be overcharged, and consequently a particle at b will be
repelled from the center, and cannot be at rest : in like manner, if there is
any fluid in Bf$, it cannot be at rest : and, by the same kind of reasoning,
it might be shewn, that, if the fluid is not spread uniformly within the
space Cb, and without the sphere /JSe, it cannot be at rest.

21] COR. I. If the globe BDE is undercharged, everything else being
the same as before, there will be a space Bb, in which the matter will be
intirely deprived of fluid, and a space Bfit in which the fluid will be pressed
close together; the matter in Bb being equal to the whole redundant
matter in the globe, and the redundant fluid in Eft, being just sufficient
to saturate the matter in Bb : and in all the rest of space the matter will be
exactly saturated. The demonstration is exactly similar to the foregoing.

22] COR. II. The fluid in the globe BDE will be disposed in exactly
the same manner, whether the fluid without is immoveable, and disposed
in such manner, that the matter shall be everywhere saturated, or whether
it is disposed as above described; and the fluid without the globe will be
disposed in just the same manner, whether the fluid within is disposed
uniformly, or whether it is disposed as above described.

23] PROP. VI. PROBLEM 2. To determine in what manner the fluid will
be disposed in the globe BDE, supposing everything as in the last problem,

Various laws of force considered 39

except that the fluid on the outside of the globe is immoveable, and dis-
posed in such manner as everywhere to saturate the matter, and that the
electric attraction and repulsion is inversely as some other power of the
distance than the square.

I am not able to answer this problem accurately; but I think we may
be certain of the following circumstances.

24] CASE i. Let the repulsion be inversely as some power of the
distance between the square and the cube, and let the globe be over-
charged.

It is certain that the density of the fluid will be everywhere the same,
at the same distance from the center. Therefore, first, There can be no
space as Cb, within which the matter will be everywhere saturated; for
a particle at b is impelled towards the center, by the redundant fluid in
Bb, and will therefore move towards the center, unless Cb is sufficiently
overcharged to prevent it. Secondly, The fluid close to the surface of the
sphere will be pressed close together; for otherwise a particle so near to
it, that the quantity of fluid between it and the surface should be very
small, would move towards it; as the repulsion of the small quantity of
fluid between it and the surface would be unable to balance the repulsion
of the fluid on the other side. Whence, I think, we may conclude, that
the density of the fluid will increase gradually from the center to the
surface, where the particles will be pressed close together: whether the
matter exactly at the center will be overcharged, or only saturated, I
cannot tell.

25] COR. For the same reason, if the globe be undercharged, I think
we may conclude, that the density of the fluid will diminish gradually
from the center to the surface, where the matter will be intirely deprived
of fluid.

26] CASE 2. Let the repulsion be inversely as some power of the
distance less than the square; and let the globe be overcharged.

There will be a space Bb, in which the particles of the fluid will be
everywhere pressed close together; and the quantity of redundant fluid
in that space will be greater than the quantity of redundant fluid in the
whole globe BDE ; so that the space Cb, taken all together, will be under-
charged : but I cannot tell in what manner the fluid will be disposed in
that space.

For it is certain, that the density of the fluid will be everywhere the
same, at the same distance from the center. Therefore, let b be any point
where the fluid is not pressed close together, then will a particle at b be
impelled towards the surface, by the redundant fluid in the space Bb;
therefore, unless the space Cb is undercharged, the particle will move
towards the surface.

40 First published Paper on Electricity

27] COR. For the same reason, if the globe is undercharged, there
will be a space Bb, in which the matter will be intirely deprived of fluid,
the quantity of matter therein being more than the whole redundant
matter in the globe; and, consequently, the space Cb, taken all together,
will be overcharged*.

28] LEMMA VI. Let the whole space comprehended between two
parallel planes, infinitely extended each way, be filled with uniform matter,
the repulsion of whose particles is inversely as the square of the distance ;
the plate of matter formed thereby will repel a particle of matter with
exactly the same force, at whatever distance from it it be placed.

For suppose that there are two such plates, of equal thickness, placed
parallel to each other, let A (Fig. 3) be any point
not placed in or between the two plates : let BCD
represent any part of the nearest plate : draw the
lines AB, AC, and AD, cutting the furthest plate
in b, c, and d; for it is plain that if they cut one F-

plate, they must, if produced, cut the other: the
triangle BCD is to the triangle bed, as AB2 to Abz; therefore a particle of
matter at A will be repelled with the same force by the matter in the
triangle BCD, as by that in bed. Whence it appears, that a particle at A
will be repelled with as much force by the nearest plate, as by the more
distant; and consequently, will be impelled with the same force by either
plate, at whatever distance from it it be placed.

29] COR. If the repulsion of the particles is inversely as some higher
power of the distance than the square, the plate will repel a particle with
more force, if its distance be small than if it be great ; and if the repulsion
is inversely as some lower power than the square, it will repel a particle
with less force, if its distance be small than if it be great.

30] PROP. VII. PROB. 3. In Fig. 4, let the parallel lines Aa, Bb, &c.
represent parallel planes infinitely extended
each way: let the spaces f AD and EH be jj~^ir -~r~

filled with uniform solid matter: let the elec- c

trie fluid in each of those spaces be moveable

and unable to escape: and let all the rest of Is1

the matter in the universe be saturated with £ & .

immoveable fluid ; and let the electric attrac- F~~ ~~~f

tion and repulsion be inversely as the square jg

of the distance. It is required to determine in

what manner the fluid will be disposed in the

spaces A D and EH, according as one or both of them are over or undercharged.

* [Note 2, p. 358.]

f By the space AD or AB, &c. I mean the space comprehended between the
planes Aa and Dd, or between Aa and Bb.

Plane Parallel Plates 41

Let AD be that space which contains the greatest quantity of re-
dundant fluid, if both spaces are overcharged, or which contains the least
redundant matter, if both are undercharged; or, if one is overcharged, and
the other undercharged, let AD be the overcharged one. Then, first,
There will be two spaces, AB and GH, which will either be intirely de-
prived of fluid, or in which the particles will be pressed close together;
namely, if the whole quantity of fluid in AD and EH together, is less than
sufficient to saturate the matter therein, they will be intirely deprived of
fluid; the quantity of redundant matter in each being half the whole
redundant matter in AD and EH together: but if the fluid in AD and EH
together is more than sufficient to saturate the matter, the fluid in AB
and GH will be pressed close together; the quantity of redundant fluid
in each being half the whole redundant fluid in both spaces. Secondly,
In the space CD the fluid will be pressed close together; the quantity of
fluid therein being such, as to leave just enough fluid in BC to saturate
the matter therein. Thirdly, The space EF will be intirely deprived of
fluid ; the quantity of matter therein being such that the fluid in FG shall
be just sufficient to saturate the matter therein: consequently, the re-
dundant fluid in CD will be just sufficient to saturate the redundant
matter in EF; for as AB and GH together contain the whole redundant
fluid or matter in both spaces, the spaces ED and EG together contain
their natural quantity of fluid ; and therefore, as BC and FG each contain
their natural quantity of fluid, the spaces CD and EF together contain
their natural quantity of fluid. And fourthly, The spaces BC and FG will
be saturated in all parts.

For, first, If the fluid is disposed in this manner, no particle of it can
have any tendency to move : for a particle placed anywhere in the spaces
BC and FG, is attracted with just as much force by EF, as it is repelled
by CD; and it is repelled or attracted with just as much force by AB,
as it is in a contrary direction by GH, and, consequently, has no tendency
to move. A particle placed anywhere in the space CD, or in the spaces
AB and GH, if they are overcharged, is indeed repelled with more force
towards the planes Dd, Aa and Hh, than it is in the contrary direction;
but as the fluid in those spaces is already as much compressed as possible,
the particle will have no tendency to move.

Secondly, It seems impossible that the fluid should be at rest, if it is
disposed in any other manner: but as this part of the demonstration is
exactly similar to the latter part of that of Problem the first, I shall
omit it.

31] COR. I. If the two spaces AD and EH are both overcharged, the
redundant fluid in CD is half the difference of the redundant fluid in those
spaces : for half the difference of the redundant fluid in those spaces, added
to the quantity in AB, which is half the sum, is equal to the whole quantity

I
4.2 First published Paper on Electricity

in AD. For a like reason, if AD and EH are both undercharged, the re-
dundant matter in EF is half the difference of the redundant matter in
those spaces; and if A D is overcharged, and EH undercharged, the re-
dundant fluid in CD exceeds half the redundant fluid in AD, by a quantity
sufficient to saturate half the redundant matter in EH.

32] COR. II. It was before said, that the fluid in the spaces AB and
GH (when there is any fluid in them) is repelled against the planes A a
and Hh; and, consequently, would run out through those planes, if there
was any opening for it to do so. The force with which the fluid presses
against the planes A a and Hh, is that with which the redundant fluid
in AB is repelled by that in GH; that is, with which half the redundant
fluid in both spaces is repelled by an equal quantity of fluid. Therefore,
the pressure against A a and Hh depends only on the quantity of redundant
fluid in both spaces together, and not at all on the thickness or distance
of those spaces, or on the proportion in which the fluid is divided between
the two spaces. If there is no fluid in AB and GH, a particle placed on
the outside of the spaces AD and EH, contiguous to the planes A a or Hh,
is attracted towards those planes by all the matter in AB and GH, id est,
by all the redundant matter in both spaces; and, consequently, en-
deavours to insinuate itself into the space AD or EH; and the force with
which it does so depends only on the quantity of redundant matter in
both spaces together. The fluid in CD also presses against the plane Dd,
and the force with which it does so is that with which the redundant fluid
in CD is attracted by the matter in EF.

33] COR. III. If A D is overcharged, and EH undercharged: and the
redundant fluid in AD is exactly sufficient to saturate the redundant
matter in EH, all the redundant fluid in AD will be collected in the space
CD, where it will be pressed close together : the space EF will be intirely
deprived of fluid, the quantity of matter therein being just sufficient to
saturate the redundant fluid in CD, and the spaces AC and FH will be
everywhere saturated. Moreover, if an opening is made in the planes A a
or Hh, the fluid within the spaces AD or EH will have no tendency to
run out thereat, nor will the fluid on the outside have any tendency to
run in at it : a particle of fluid too placed anywhere on the outside of both
spaces, as at P, will not be at all attracted or repelled by those spaces,
any more than if they were both saturated ; but a particle placed anywhere
between those spaces, as at 5, will be repelled from d towards e; and if a
communication was made between the two spaces, by the canal de, the
fluid would run out of AD into EH, till they were both saturated.

34] PROP. VIII. PROB. 4. To determine in what manner the fluid will
be disposed in the space AD, supposing that all the rest of the universe
is saturated with immoveable fluid, and that the electric attraction and
repulsion is inversely as some other power of the distance than the square.

Bodies communicating by a canal 43

I am not able to answer this Problem accurately, except when the
repulsion is inversely as the simple or some lower power of the distance;
but I think we may be certain of the following circumstances.

35] CASE i. Let the repulsion be inversely as some power of the
distance between the square and the cube, and let AD be overcharged.

First, It is certain that the density of the fluid must be everywhere
the same, at the same distance from the planes A a and Dd. Secondly,
There can be no space as EC, of any sensible breadth, in which the matter
will not be overcharged. And thirdly, The fluid close to the planes Aa
and Dd will be pressed close together. Whence, I think, we may conclude,
that the density of the fluid will increase gradually from the middle of
the space to the outside, where it will be pressed close together. Whether
the matter exactly in the middle will be overcharged, or only saturated,
I cannot tell.

36] CASE 2. Let the repulsion be inversely as some power of the dis-
tance between the square and the simple power, and let AD be overcharged.

There will be two spaces AB and DC, in which the fluid will be pressed
close together, and the quantity of redundant fluid in each of those spaces
will be more than half the redundant fluid in A D; so that the space BC,
taken all together, will be undercharged; but I cannot tell in what
manner the fluid will be disposed in that space. The demonstrations of
these two cases are exactly similar to those of the two cases of Prob. 2.

37] CASE 3. If the repulsion is inversely as the simple or some lower
power of the distance, and AD is overcharged, all the fluid will be collected
in the spaces AB and CD, and BC will be intirely deprived of fluid. If
AD contains just fluid enough to saturate it, and the repulsion is inversely
as the distance, the fluid will remain in equilibrio, in whatever manner it
is disposed; provided its density is everywhere the same at the same
distance from the planes Aa and Dd: but if the repulsion is inversely as
some less power than the simple one, the fluid will be in equilibrio, whether
it is either spread uniformly, or whether it is all collected in that plane
which is in the middle between A a and Dd, or whether it is all collected
in the spaces AB and CD; but not, I believe, if it is disposed in any other
manner.

The demonstration depends upon this circumstance; namely, that if
the repulsion is inversely as the distance, two spaces AB and CD, repel
a particle placed either between them, or on the outside of them, with
the same force as if all the matter of those spaces was collected in the middle
plane between them.

It is needless mentioning the three cases in which AD is undercharged,
as the reader will easily supply the place.

44 First published Paper on FJectricity

38] Though the four foregoing problems do not immediately tend to
explain the phaenomena of electricity, I chose to insert them; partly
because they seem worth engaging our attention in themselves ; and partly
because they serve, in some measure, to confirm the truth of some of the
following propositions, in which I am obliged to make use of a less accurate
kind of reasoning.

39] In the following propositions, I shall always suppose the bodies
I speak of to consist of solid matter, confined to the same spot, so as not
to be able to alter its shape or situation by the attraction or repulsion of
other bodies on it: I shall also suppose the electric fluid in these bodies
to be moveable, but unable to escape, unless when otherwise expressed.
As for the matter in all the rest of the universe, I shall suppose it to be
saturated with immoveable fluid. I shall also suppose the electric attrac-
tion and repulsion to be inversely as any power of the distance less than
the cube, except when otherwise expressed.

40] By a canal, I mean a slender thread of matter, of such kind that
the electric fluid shall be able to move readily along it, but shall not be
able to escape from it, except at the ends, where it communicates with
other bodies. Thus, when I say that two bodies communicate with each
other by a canal, I mean that the fluid shall be able to pass readily from
one body to the other by that canal*.

41] PROP. IX. If any body at a distance from any over or under-
charged body be overcharged, the fluid within it will be lodged in greater
quantity near the surface of the body than near the center. For, if you
suppose it to be spread uniformly all over the body, a particle of fluid in
it, near the surface, will be repelled towards the surface by a greater
quantity of fluid than that by which it is repelled from it; consequently,
the fluid will flow towards the surface, and make it denser there: more-
over, the particles of fluid close to the surface will be pressed close together ;
for otherwise, a particle placed so near it, that the quantity of redundant
fluid between it and the surface should be very small, would move towards
it; as the small quantity of redundant fluid between it and the surface
would be unable to balance the repulsion of that on the other side.

From the four foregoing problems it seems likely, that if the electric
attraction or repulsion is inversely as the square of the distance, almost
all the redundant fluid in the body will be lodged close to the surface, and
there pressed close together, and the rest of the body will be saturated.
If the repulsion is inversely as some power of the distance between the
square and the cube, it is likely that all parts of the body will Be over-
charged: and if it is inversely as some less power than the square, it is
likely that all parts of the body, except those near the surface, will be

undercharged.

* [Note 3, p. 365.]

Electrification by induction 45

42] COR. For the same reason, if the body is undercharged, the de-
ficiency of fluid will be greater near the surface than near the center, and
the matter near the surface will be entirely deprived of fluid. It is likely
too, if the repulsion is inversely as some higher power of the distance than
the square, that all parts of the body will be undercharged : if it is inversely
as the square, that all parts, except near the surface, will be saturated:
and if it is inversely as some less power than the square, that all parts,
except near the surface, will be overcharged.

43] PROP. X. Let the bodies A and D (Fig. 5) communicate with each
other by the canal EF; and let one of them, as D, be overcharged; the
other body A will be so also.

For as the fluid in the canal is repelled by the redundant fluid in D,
it is plain, that unless A was overcharged, so as to balance that repulsion,
the fluid would run out of D into A.

In like manner, if one is undercharged, the other must be so too.

44] PROP. XI. Let the body A (Fig. 6) be either saturated or over
or undercharged; and let the fluid within it be
in equilibrio. Let now the body B, placed near
it, be rendered overcharged, the fluid within it
being supposed immoveable, and disposed in
such manner, that no part of it shall be under-
charged; the fluid in A will no longer be in
equilibrio, but will be repelled from B: there-
fore, the fluid will flow from those parts of A
which are nearest to B, to those which are more distant from it; and,
consequently, the part adjacent to MTV (that part of the surface of A
which is turned towards B) will be made to contain less electric fluid
than it did before, and that adjacent to the opposite surface RS will
contain more than before.

It must be observed, that when a sufficient quantity of fluid has flowed
from MN towards RS, the repulsion which the fluid in the part adjacent
to MAT exerts on the rest of the fluid in A, will be so much weakened,
and the repulsion of that in the part near RS will be so much increased,
as to compensate the repulsion of B, which will prevent any more fluid
flowing from MN to RS.

Fig. 6.

4.6 First published Paper on Electricity

The reason why I suppose the fluid in B to be immoveable is, that
otherwise a question might arise, whether the attraction or repulsion of
the body A might not cause such an alteration in the disposition of the
fluid in B, as to cause some parts of it to be undercharged; which might
make it doubtful, whether B did on the whole repel the fluid in A. It is
evident, however, that this proposition would hold good, though some
parts of B were undercharged, provided it did on the whole repel the
fluid in A.

45] COR. If B had been made undercharged, instead of overcharged,
it is plain that some fluid would have flowed from the further part RS to
the nearer part MN, instead of from MN to RS.

46] PROP. XII. Let us now suppose that the body A communicates
by the canal EF, with another body D, placed on the contrary side of it
from B, as in Fig. 5 ; and let these two bodies be either saturated, or over
or undercharged ; and let the fluid within them be in equilibrio. Let now
the body B be overcharged : it is plain that some fluid will be driven from
the nearer part MN to the further part RS, as in the former proposition ;
and also some fluid will be driven from RS, through the canal, to the body
D; so that the quantity of fluid in D will be increased thereby, and the
quantity in A, taking the whole body together, will be diminished; the
quantity in the part near MN will also be diminished; but whether the
quantity in the part near RS will be diminished or not, does not appear
for certain ; but I should imagine it would be not much altered.

47] COR. In like manner, if B is made undercharged, some fluid will
flow from D to A, and also from that part of A near RS, to the part near
MN.

48] PROP. XIII. Suppose now that the bodies A and D communicate
by the bent canal MPNnpm (Fig. 7) instead of the straight one EF: let
the bodies be either saturated or over or undercharged as before ; and let

Fig. 7-

the fluid be at rest; then if the body B is made overcharged, some fluid
will still run out of A into D; provided the repulsion of B on the fluid
in the canal is not too great.

The repulsion of B on the fluid in the canal will at first drive some
fluid out of the leg MPpm into A, and out of NPpn into D, till the

Electrification by induction 47

quantity of fluid in that part of the canal which is nearest to B is so much
diminished, and its repulsion on the rest of the fluid in the canal is so
much diminished also as to compensate the repulsion of B: but as the
leg NPpn is longer than the other, the repulsion of B on the fluid in it
will be greater; consequently some fluid will run out of A into D, on the
same principle that water is drawn out of a vessel through a siphon.

49] But if the repulsion of B on the fluid in the canal is so great, as
to drive all the fluid out of the space GPHpG, so that the fluid in the leg
MGpm does not join to that in NHpn; then it is plain that no fluid can
run out of A into D ; any more than water will run out of a vessel through
a siphon, if the height of the bend of the siphon above the water in the
vessel, is greater than that to which water will rise in vacuo.

50] COR. If B is made undercharged, some fluid will run out of D
into A ; and that though the attraction of B on the fluid in the canal is
ever so great.

51] PROP. XIV. Let ABC (Fig. 8) be a body overcharged with im-
moveable fluid, uniformly spread; let the
bodies near ABC on the outside be saturated
with immoveable fluid; and let D be a body
inclosed within ABC, and communicating by
the canal DG with other distant bodies satu-
rated with fluid; and let the fluid in D and
the canal and those bodies be moveable; then
will the body D be rendered undercharged.

For let us first suppose that D and the canal are saturated, and that
D is nearer to B than to the opposite part of the body, C; then will all
the fluid in the canal be repelled from C by the redundant fluid in ABC;
but if D is nearer to C than to B, take the point F, such that a particle
placed there would be repelled from C with as much force as one at D
is repelled towards C ; the fluid in DF, taking the whole together, will be
repelled with as much force one way as the other; and the fluid in FG
is all of it repelled from C : therefore in both cases the fluid in the canal,
taking the whole together, is repelled from C; consequently some fluid
will run out of D and the canal, till the attraction of the unsaturated
matter therein is sufficient to balance the repulsion of the redundant
fluid in ABC.

52] PROP. XV. If we now suppose that the fluid on the outside of
ABC is moveable; the matter adjacent to ABC on the outside will become
undercharged. I see no reason however to think that that will prevent
the body D from being undercharged; but I cannot say exactly what
effect it will have, except when ABC is spherical and the repulsion is
inversely as the square of the distance ; in this case it appears by Prob. I

48 • First published Paper on Electricity

that the fluid in the part DB of the canal will be repelled from C, with
just a smuch force as in the last proposition; but the fluid in the part
BG will not be repelled at all: consequently D will be undercharged, but
not so much as in the last proposition.

53] COR. If ABC is now supposed to be undercharged, it is certain
that D will be overcharged, provided the matter near ABC on the outside
is saturated with immoveable fluid; and there is great reason to think
that it will be so, though the fluid in that matter is moveable.

54] PROP. XVI. Let AEFB (Fig. 9) be a long cylindric body, and D
an undercharged body; and let the
quantity of fluid in AEFB be such, that
the part near EF shall be saturated. It

1 **

appears from what has been said before, F-

that the part near AB will be over-
charged; and moreover there will be a certain space, as AabB, adjoining
to the plane AB, in which the fluid will be pressed close together; and the
fluid in that space will press against the plane AB, and will endeavour
to escape from it; and by Prop. II the two bodies will attract each other:
now I say that the force with which the fluid presses against the plane AB,
is very nearly the same with which the two bodies attract each other in
the direction EA ; provided that no part of AEFB is undercharged.

Suppose so much of the fluid in each part of the cylinder as is sufficient
to saturate the matter in that part, to become solid; the remainder, or
the redundant fluid remaining fluid as before. In this case the pressure
against the plane AB must be exactly equal to that with which the two
bodies attract each other in the direction EA : for the force with which
D attracts that part of the fluid which we supposed to become solid, is
exactly equal to that with which it repels the matter in the cylinder ; and
the redundant fluid in EabF is at liberty to move, if it had any tendency
to do so, without moving the cylinder; so that the only thing which has
any tendency to impel the cylinder in the direction EA is the pressure of
the redundant fluid in AabB against AB; and as the part near EF is
saturated, there is no redundant fluid to press against the plane EF, and
thereby to counteract the pressure against AB. Suppose now all the
electric fluid in the cylinder to become fluid ; the force with which the
two bodies attract each other will remain exactly the same; and the only
alteration in the pressure against AB, will be, that that part of the fluid
in AabB, which we at first supposed solid and unable to press against
the plane, will now be at liberty to press against it; but as the density
of the fluid when its particles are pressed close together may be supposed
many times greater than when it is no denser than sufficient to saturate
the matter in the cylinder, and consequently the quantity ot redundant
fluid in AabB many times greater than that which is required to saturate

Charge on circular plate 49

the matter therein, it follows that the pressure against AB will be very
little more than on the first supposition.

N.B. If any part of the cylinder is undercharged, the pressure against
AB is greater than the force with which the bodies attract. If the electric
repulsion is inversely as the square or some higher power of the distance,
it seems very unlikely that any part of the cylinder should be under-
charged; but if the repulsion is inversely as some lower power than the
square, it is not improbable but some part of the cylinder may be under-
charged.

55] LEMMA VII. Let AB (Fig. 10) represent an infinitely thin flat
circular plate, seen edgeways, so as to appear
to the eye as a straight line; let C be the center
of the circle; and let DC passing through C,
be perpendicular to the plane of the plate ; and
let the plate be of uniform thickness, and con-
sist of uniform matter, whose particles repel
with a force inversely as the n power of the
distance; n being greater than one, and less
than three: the repulsion of the plate on a Fig. 10.

particle at D is proportional to

DC DC

DC"1-1 ~ DA"-1'

provided the thickness of the plate and size of the particle D is given.

For if CA is supposed to flow, the corresponding fluxion of the quantity
of matter in the plate is proportional to CA x CA; and the corresponding
fluxion of the repulsion of the plate on the particle D, in the direction DC,
is proportional to

CA x CA DC _ DA x DC .

DAn X DA ' DAn

for DA : CA :: CA : DA; the variable part of the fluent of which is

'-—f^--i- whence the repulsion of the plate on the particle D is

DC DC DC DC

proportional to ( — — ^^ - ^---^-^ , o o ^n-1 -

56] COR. If DC"-1 is very small in respect of CA"-1, the particle D
is repelled with very nearly the same force as if the diameter of the plate
was infinite.

57] LEMMA VIII. Let L and / represent the two legs of a right-angled
triangle, and h the hypothenuse ; if the shorter leg / is so much less than
the other, that I"-1 is very small in respect of L"-1, h3~n- L3~n will be
very small in respect of I3~n.

C.P. i. 4

50 First published Paper on Electricity

3-n / 72\3-n

-

For

therefore

/ 72\3

/ j + 1. V

'

3-n_ L3-n „ (3 - ") *2 3~»Xn-IX/«

-1 ~ ~~ ' 6

-" x 3 — » x /"~1 /3~" X3 — «x«— ix /"+1 „
""-1 1 ~ '

which is very small in respect of I3-"; as I"-1 is by the supposition very
small in respect of L"-1.

58] LEMMA IX. Let DG now represent the axis of a cylindric or pris-
matic column of uniform matter; and let the diameter of the column be
so small, that the repulsion of the plate AB on it shall not be sensibly
different from what it would be, if all the matter in it was collected in
the axis : the force with which the plate repels the column is proportional to

DC3~" + AC3~" — DA3~"',
supposing the thickness of the plate and base of the column to be given.

For, if DC is supposed to flow, the corresponding fluxion of the re-
pulsion is proportional to

DC DC x DC DC DA
DC"~2 "DA"-1 ~~ DC"-* ~ DA"~Z'

AC3~" + DC3~n — DA3~"
the fluent of which, - - , vanishes when DC vanishes.

59] COR. I. If the length of the column is so great that AC"-1 is very
small in respect of DC"-1, the repulsion of the plate on it is very nearly
the same as if the column was infinitely continued.

For by Lemma VIII AC3~" + DC3-" - DA3~" differs very little in
this case from AC3~"; and if DC is infinite, it is exactly equal to it.

60] COR. II. If AC"-1 is very small in respect of DC"-1, and the
point E be taken in DC such that EC"-1 shall be very small in respect
of AC"-1, the repulsion of the plate on the small part of the column EC,
is to its repulsion on the whole column DC, very nearly as EC3~" to AC3-".

61] LEMMA X. If we now suppose all the matter of the plate to be
collected in the circumference of the circle, so as to form an infinitely
slender uniform ring, its repulsion on the column DC will be less than
when the matter is spread uniformly all over the plate, in the ratio of

(3-n)AC\

2

Charge on circular ring 5 1

For it was before said, that if the matter of the plate be spread uni-
formly, its repulsion on the column will be proportional to

DC3-" + ACs~n - DA3-n,

or may be expressed thereby ; let now A C, the semidiameter of the plate,
be increased by the infinitely small quantity AC; the quantity of matter
in the plate will be increased by a quantity, which is to the whole, as 2A C
to AC; and the repulsion of the plate on the column will be increased by

AC
(3 - n) AC x AC2"' - AC x x (3 - n) x DA2~»,

= (3 - n) x A C x AC x

therefore if a quantity of matter, which is to the whole quantity in the
plate as 2 A C to A C, be collected in the circumference, its repulsion on the
column DC will be to that of the whole plate as

3 - n x AC x AC x — ^ - , , to DC*-" + AC*~" - DA3~";

—

and consequently the repulsion of the plate when all the matter is collected
in its circumference, is to its repulsion when the matter is spread uni-
formly, as

3 ~ n x . y _ L- -J:
2

( _ L- -J: — ^ to DC3~" 4- AC3-" — DA3~n
UO-1 DA"-1) '

62] COR. I. If the length of the column is so great, that AC"-1 is very
small in respect of DC"-1, the repulsion of the plate, when all the matter
is collected in the circumference, is to its repulsion when the matter is

o _ M
spread uniformly, very nearly as - - to AC3~n, or as 3 — n to 2.

63] COR. II. If ECn~l is very small in respect of AC"~l, the repulsion
of the plate on the short column EC, when all the matter in the plate is
collected in its circumference, is to its repulsion when the matter is spread
uniformly, very nearly as

3 — n x n — ix EC2 ,

. ,. — to EC3"1,

qAC"-1

oras3 — n x n — ix EC"-1 to ^AC"-1; and is therefore very small in
comparison of what it is when the matter is spread uniformly.

For by the same kind of process as was used in Lemma VIII, it appears,
that if EC2 is very small in respect of AC2,

* (1C"""1 ~ EA

n — i x EC2 n — i x EC2

differs very little from - „ . - , or from - -17*— - ', and if EC"~l

2EA"'1 2ACn~l

is very small in respect of AC"-1, EC2 is a fortiori very small in respect
of AC2.

4—2

5 2 First published Paper on Electricity

64] COR. III. Suppose now that the matter of the plate is denser near
the circumference than near the middle, and that the density at and near
the middle is to the mean density, or the density which it would every-
where be of if the matter was spread uniformly, as S to i ; the repulsion
of the plate on EC will be less than if the matter was spread uniformly,
in a ratio approaching much nearer to that of 8 to I, than to that of
equality.

65] COR. IV. Let everything be as in the last corollary, and let n be
taken to one, as the force with which the plate actually repels the column
DC, (DC"-1 being very great in respect of ACn~l), is to the force with which
it would repel it, if the matter was spread uniformly; the repulsion of the
plate on EC will be to its repulsion on DC, in a ratio between that of
EC3~" x 8 to AC3~n x TT, and that of EC3~n to AC3~n x -n, but will
approach much nearer to the former ratio than to the latter.

66] LEMMA XI. In the line DC produced, take CF equal to CA : if
all the matter of the plate AB is collected in the circumference, its re-
pulsion on the column CD, infinitely continued, is equal to the repulsion
of the same quantity of matter collected in the point F, on the same column.

For the repulsion of the plate on the column in the direction CD, is
the same, whether the matter of it be collected in the whole circumference,
or in the point A . Suppose it therefore to be collected in A ; and let an
equal quantity of matter be collected in -F; take FG constantly equal to
AD; and let AD and FG flow: the fluxion of CD is to the fluxion of FG,
as A D to CD ; and the repulsion of A on the point D, in the direction CD,
is to the repulsion of F on G, as CD to AD; and therefore the fluxion of
the repulsion of A on the column CD, in the direction CD, is equal to the
fluxion of the repulsion of F on CG; and when AD equals AC, the re-
pulsion of both A and F on their respective columns vanishes ; and there-
fore the repulsion of A on the whole column CD equals that of F on CG ;
and when CD and CG are both infinitely extended, they may be looked
upon as the same column.

67] PROP. XVII. Let two similar bodies, of different sizes, and con-
sisting of different sorts of matter, be both overcharged, or both under-
charged, but in different degrees; and let the redundance or deficience of
fluid in each be very small in respect of the whole quantity of fluid in
them: it is impossible for the fluid to be disposed accurately in a similar
manner in both of them*; as it has been shewn that there will be a space,

* By the fluid being disposed in a similar manner in both bodies, I mean that
the quantity of redundant or deficient fluid in any small part of one body, is to
that in the corresponding small part of the other, as the whole quantity of re-
dundant or deficient fluid in one body, to that in the other. By the quantity of
deficient fluid in a body, I mean the quantity of fluid wanting to saturate it. Not-
withstanding the impropriety of this expression, I must beg leave to make use of
it, as it will frequently save a great deal of circumlocution. [See Note i.]

Comparison of similar bodies 53

close to the surface, which will either be as full of fluid as it can hold, or

will be entirely deprived of fluid; but it will be disposed as nearly in a

similar manner in both, as is possible. To explain this, let BDE and bde

(Fig. n) be the two similar bodies; and let the

space comprehended between the surfaces

BDE and FGH (or the space BF as I shall call

it for shortness) be that part of BDE, which

is either as full of fluid a- it can hold, or

entirely deprived of it : draw the surface fgh,

such that the space bf shall be to the space

BF, as the quantity of redundant or deficient

fluid in bde, to that in BDE, and that the Fig. n.

thickness of the space bf shall everywhere bear

the same proportion to the corresponding thickness of BF : then will the

space bf be either as full of fluid as it can hold, or entirely deprived of it ;

and the fluid within the space fgh will be disposed very nearly similarly

to that in the space FGH.

For it is plain, that if the fluid could be disposed accurately in a
similar manner in both bodies, the fluid would be in equilibrio in one
body, if it was in the other : therefore draw the surface /?Se, such that the
thickness of the space /?/ shall be everywhere to the corresponding thick-
ness of BF, as the diameter of bde to the diameter of BDE; and let the
redundant fluid or matter in bf be spread uniformly over the space fif;
then if the fluid in the space fgh is disposed exactly similarly to that in
FGH, it will be in equilibrio; as the fluid will then be disposed exactly
similarly in the spaces /JSe and BDE: but as by the supposition, the
thickness of the space /?/ is very small in respect of the diameter of bde,
the fluid or matter in the space bf will exert very nearly the same force
on the rest of the fluid, whether it is spread over the space J3f, or whether
it is collected in bf.

68] PROP. XVIII. Let two bodies, B and b, be connected to each
other by a canal of any kind, and be either over or undercharged: it is
plain that the quantity of redundant or deficient fluid in B, would bear
exactly the same proportion to that in b, whatever sort of matter B con-
sisted of, if it was possible for the redundant or deficient fluid in any body
to be disposed accurately in the same manner, whatever sort of matter
it consisted of. For suppose B to consist of any sort of matter; and let
the fluid in the canal and two bodies be in equilibrio: let now B be made
to consist of some other sort of matter, which requires a different quantity
of fluid to saturate it ; but let the quantity and disposition of the redundant
or deficient fluid in it remain the same as before : it is plain that the fluid
will still be in equilibrio; as the attraction or repulsion of any body
depends only on the quantity and disposition of the redundant and

54 First published Paper on Electricity

deficient fluid in it. Therefore, by the preceding proposition, the quantity
of redundant or deficient fluid in B, will actually bear very nearly the
same proportion to that in b, whatever sort of matter B consists of; pro-
vided the quantity of redundant or deficient fluid in it is very small in
respect of the whole. [See Exp. IV, Art. 269.]

69] PROP. XIX. Let two bodies B and b (Fig. 12) be connected to-
gether by a very slender canal ADda, either
straight or crooked: let the canal be every-
where of the same breadth and thickness;
so that all sections of this canal made by
planes perpendicular to the direction of the
canal in that part, shall be equal and
similar : let the canal be composed of uniform
matter ; and let the electric fluid therein be
supposed incompressible, and of such density
as exactly to saturate the matter therein;
and let it, nevertheless, be able to move readily along the canal; and let
each particle of fluid in the canal be attracted and repelled by the matter
and fluid in the canal and in the bodies B and b, just in the same manner
that it would be if it was not incompressible * ; and let the bodies B and b
be either over or undercharged. I say that the force with which the whole
quantity of fluid in the canal is impelled from A towards D, in the direction
of the axis of the canal, by the united attractions and repulsions of the
two bodies, must be nothing ; as otherwise the fluid in the canal could not
be at rest: observing that by the force with which the whole quantity of
fluid is impelled in the direction of the axis of the canal, I mean the sum
of the forces, with which the fluid in each part of the canal is impelled in
the direction of the axis of the canal in that place, from A towards D;
and observing also, that an impulse in the contrary direction from D
towards A must be looked upon as negative.

For as the canal is exactly saturated with fluid, the fluid therein is
attracted or repelled only by the redundant matter or fluid in the two
bodies. Suppose now that the fluid in any section of the canal, as Ee, is
impelled with any given force in the direction of the canal at that place,
the section Dd would, in consequence thereof, be impelled with exactly
the same force in the direction of the canal at D, if the fluid between Ee
and Dd was not at all attracted or repelled by the two bodies ; and, conse-
quently, the section Dd is impelled in the direction of the canal, with the
sum of the forces, with which the fluid in each part of the canal is impelled
by the attraction or repulsion of the two bodies in the direction of the

* This supposition of the fluid in the canal being incompressible, is not men-
tioned as a thing which can ever take place in nature, but is merely imaginary;
the reason for making of which will be given hereafter.

Comparison of similar bodies 55

axis in that part; and consequently, unless this sum was nothing, the
fluid in Dd could not be at rest.

70] COR. Therefore, the force with which the fluid in the canal is
impelled one way in the direction of the axis, by the body B, must be
equal to that with which it is impelled by b in the contrary direction.

71] PROP. XX. Let two similar bodies B and b (Fig. 13) be connected
by the very slender cylindric or pris-
matic canal A a, filled with incompres-
sible fluid, in the same manner as '' l ' " p

described in the preceding proposition :
let the bodies be overcharged; but let
the quantity of redundant fluid in each

bear so small a proportion to the whole, that the fluid may be considered
as disposed in a similar manner in both; let the bodies also be similarly
situated in respect of the canal A a; and let them be placed at an infinite
distance from each other, or at so great an one, that the repulsion of
either body on the fluid in the canal shall not be sensibly less than if they
were at an infinite distance: then, if the electric attraction and repulsion
is inversely as the n power of the distance, n being greater than i, and
less than 3, the quantity of redundant fluid in the two bodies will be to
each other as the n — i power of their corresponding diameters AF and af.
For if the quantity of redundant fluid in the two bodies is in this
proportion, the repulsion of one body on the fluid in the canal will be
equal to that of the other body on it in the contrary direction; and,
consequently, the fluid will have no tendency to flow from one body to
the other, as may thus be proved. Take the points D and E very near to
each other; and take da to DA, and ea to EA, as a/ to AF; the repulsion
of the body B on a particle at D, will be to the repulsion of b on a particle

at d, as -j-~ to — > ; for, as the fluid is disposed similarly in both bodies,
A r aj

the quantity of fluid in any small part of B, is to the quantity in the
corresponding part of b, as AF"-1 to a/""1; and consequently the repulsion
of that small part of B, on D, is to the repulsion of the corresponding

1 i i

part of b, on d, as . F , or --}-=. , to -, . But the quantity of fluid in the
AF" AF af

small part DE of the canal, is to that in de, as DE to de, or as AF to af;
therefore the repulsion of B on the fluid in DE, is equal to that of b on
the fluid in de: therefore, taking ag to Aa, as af to AF, the repulsion of b
on the fluid in ag, is equal to that of B on the fluid in Aa ; but the repulsion
of b on ag may be considered as the same as its repulsion on A a; for, by
the supposition, the repulsion of B on A a may be considered as the same
as if it was continued infinitely; and therefore, the repulsion of b on ag
may be considered as the same as if it was continued infinitely.

56 First published Paper on Electricity

N.B. If n was not greater than i, it would be impossible for the length
of Aa to be so great, that the repulsion of B on it might be considered as
the same as if it was continued infinitely; which was my reason for re-
quiring « to be greater than i.

72] COR. By just the same method of reasoning it appears, that if
the bodies are undercharged, the quantity of deficient fluid in 6 will be
to that in B, as afn~l to AFn~*.

73] PROP. XXI. Let a thin flat plate be connected to any other body,
as in the preceding proposition, by a canal of incompressible fluid, per-
pendicular to the plane of the plate; and let that body be overcharged,
the quantity of redundant fluid in the plate will bear very nearly the same
proportion to that in the other body, whatever the thickness of the plate
may be, provided its thickness is very small in proportion to its breadth,
or smallest diameter.

For there can be no doubt, but what, under that restriction, the fluid
will be disposed very nearly in the same manner in the plate, whatever
its thickness may be ; and therefore its repulsion on the fluid in the canal
will be very nearly the same, whatever its thickness may be. [See Exp. IV,
Art. 272.]

74] PROP. XXII. Let AB and DF (Fig. 14) represent two equal and
parallel circular plates, whose centers are C and E ; let the plates be placed
so, that a right line joining their centers shall be perpendicular to the
plates; let the thickness of the plates be very small in respect of their
distance CE; let the plate AB communicate with the body H, and the
plate DF with the body L, by the canals CG and EM of incompressible
fluid, such as are described in Prop. XIX; let these canals meet their

A D

T

N-

s-

fi

B

F

Fig. 14.

respective plates in their centers C and E, and be perpendicular to the
plane of the plates; and let their length be so great, that the repulsion
of the plates on the fluid in them may be considered as the same as if they
were continued infinitely; let the body H be overcharged, and let L be
saturated. It is plain, from Prop. XII, that DFwill be undercharged, and
AB will be more overcharged than it would otherwise be. Suppose, now,
that the redundant fluid in AB is disposed in the same manner as the

Bodies connected to two parallel disks 57

deficient fluid is in DF; let P be to one as the force with which the plate
AB would repel the fluid in CE, if the canal ME was continued to C, is
to the force with which it would repel the fluid in CM ; and let the force
with which AB repels the fluid in CG, be to the force with which it would
repel it, if the redundant fluid in it was spread uniformly, as TT to i; and
let the force with which the body H repels the fluid in CG, be the same with
which a quantity of redundant fluid, which we will call B, spread uniformly
over AB, would repel it in the contrary direction. Then will the redundant

D

fluid in A B be equal to ^-- pa , and therefore, if P is very small, will

T>

be very nearly equal to — =- ; and the deficient fluid in DF will be to the

redundant fluid in AB, as i — P to i, and therefore, if P is very small,
will be very nearly equal to the redundant fluid in AB.

For it is plain, that the force with which AB repels the fluid in EM,
must be equal to that with which DF attracts it; for otherwise, some
fluid would run out of DF into L, or out of L into DF: for the same
reason, the excess of the -repulsion of AB on the fluid in CG, above the
attraction of FD thereon, must be equal to the force with which a quantity
of redundant fluid equal to B, spread uniformly over AB, would repel it,

T)

or it must be equal to that with which a quantity equal to - , spread in

the manner in which the redundant fluid is actually spread in AB, would
repel it. By the supposition, the force with which AB repels the fluid
in EM, is to the force with which it would repel the fluid in CM, supposing
EM to be continued to C, as i — P to i ; but the force with which any
quantity of fluid in AB would repel the fluid in CM, is the same with which
an equal quantity similarly disposed in DF, would repel the fluid in EM;
therefore the force with which the redundant fluid in AB repels the fluid
in EM, is to that with which an equal quantity similarly disposed in DF,
would repel it, as i — P to i: therefore, if the redundant fluid in A B be
called A , the deficient fluid in DF must be A x i — P : for the same
reason, the force with which DF attracts the fluid in CG, is to that with
which AB repels it, as A x i - P x i — P, or A x (i — P)2, to A ; there-
fore, the excess of the force with which AB repels CG above that with
which DF attracts it, is equal to that with which a quantity of redundant
fluid equal to A — A x (i — P)2, or A x (zP - P2), spread over AB, in
the manner in which the redundant fluid therein is actually spread, would

repel it : therefore A x (zP — P2) must be equal to - , or A must be equal

7T

B

to

9.P7T

75] COR. I. If the density of the redundant fluid near the middle of
the plate AB, is less than the mean density, or the density which it would

58 First published Paper on E/ectricity

everywhere be of, if it was spread uniformly, in the ratio of 8 to i ; and
if the distance of the two plates is so small, that EC"*1 is very small in
respect of AC"-1, and that ECs~n is very small in respect of AC3-", the

B AC
quantity of redundant fluid in AB will be greater than - x -^^.

2

3-n

, and

B AC3~"
less than -* x -,^
28 EC

than the former. For, in this case, PIT is, by Lemma X, Corol. IV, less

, but will approach much nearer to the latter value

EC

3-" EC

3-n

, and greater than -^-' x S, but approaches much nearer to
A C(

the latter value than the former; and if EC3'" is very small in respect
of AC3~n, P is very small.

76] REMARKS. If DF was not undercharged, it is certain that AB
would be considerably more overcharged near the circumference of the
circle than near the center ; for if the fluid was spread uniformly, a particle
placed anywhere at a distance from the center, as at N, would be repelled
with considerably more force towards the circumference than it would
towards the center. If the plates are very near together, and, consequently,
DF nearly as much undercharged as A B is overcharged, AB will still be
more overcharged near the circumference than near the center, but the
difference will not be near so great as in the former case: for, let NR be
many times greater than CE, and NS less than CE ; and take Er and Es
equal to CR and CS; there can be no doubt, I think, but that the deficient
fluid in DF will be lodged nearly in the same manner as the redundant
fluid in AB; and therefore, the repulsion of the redundant fluid at R, on
a particle at N, will be very nearly balanced by the attraction of the
redundant matter at r, for R is not much nearer to N than r is; but the
repulsion of S will not be near balanced by that of s ; for the distance of S
from N is much less than that of s. Let now a small circle, whose diameter
is ST, be drawn round the center N, on the plane of the plate; as the
density of the fluid is greater at T than at S, the repulsion of the redundant
fluid within the small circle tends to impel the point N towards C ; but as
there is a much greater quantity of fluid between N and B, than between
N and A , the repulsion of the fluid without the small circle tends to balance
that; but the effect of the fluid within the small circle is not much less
than it would be, if DF was not undercharged ; whereas much the greater
part of the effect of that part of the plate on the outside of the circle, is
taken off by the effect of the corresponding part of DF: consequently,
the difference of density between T and S will not be near so great as if
DF was not undercharged. Hence I should imagine, that if the two plates
are very near together, the density of the redundant fluid near the center will
not be much less than the mean density, or 8 will not be much less than i ;
moreover, the less the distance of the plates, the nearer will 8 approach to i.

Condensation by two parallel disks 59

77] COR. II. Let now the body H consist of a circular plate, of the
same size as AB, placed so, that the canal CG shall pass through its center,
and be perpendicular to its plane; by the supposition, the force with which
H repels the fluid in the canal CG, is the same with which a quantity of
fluid, equal to B, spread uniformly over AB, would repel it in the contrary
direction : therefore, if the fluid in the plate H was spread uniformly, the
quantity of redundant fluid therein would be B, and if it was all collected

2B

in the circumference, would be - — ; and therefore the real quantity will

3-»

zB
be greater than B, and less than

3-«

78] COR. III. Therefore, if we suppose 8 to be equal to i, the quantity
of redundant fluid in AB will exceed that in the plate H, in a greater ratio

/ _

than that of „ J — to i. and less than that of

AC

i

-to i;

j-* j-i \j -i-j din_i i^xoa 1110.11 una,L \ji /^jr

and from the preceding remarks it appears that the real quantity of re-
dundant fluid in AB can hardly be much greater than it would if 8 was
equal to i.

79] COR. IV. Hence, if the electric attraction and repulsion is in-
versely as the square of the distance, the redundant fluid in AB, supposing
8 to be equal to i, will exceed that in the plate H, in a greater ratio than
that of A C to ^CE, and less than that of AC to 2CE.

80] COR. V. Let now the body H consist of a globe, whose diameter
equals AB; the globe being situated in such a manner, that the canal CG,
if continued, would pass through its center; and let the electric attraction
and repulsion be inversely as the square of the distance, the quantity of
redundant fluid in the globe will be zB: for the fluid will be spread uni-
formly over the surface of the globe, and its repulsion on the canal will
be the same as if it was all collected in the center of the sphere, and will
therefore be the same with which an equal quantity, disposed in the
circumference of AB, would repel it in the contrary direction, or with
which half that quantity, or B, would repel it, if spread uniformly over
the plate. [See Art. 140.]

81] COR. VI. Therefore, if 8 was equal to i, the redundant fluid in
AB would exceed that in the globe, in the ratio of A C to ^CE; and there-
fore, it will in reality exceed that in the globe, in a rather greater ratio
than that of AC to ^CE; but if the plates are very near together, it will
approach very near thereto, and the nearer the plates are, the nearer it
will approach thereto.

82] COR. VII. Whether the electric repulsion is inversely as the square
of the distance or not, if the body H is as much undercharged, as it was

6o

First published Paper on Electricity

Fig. 15-

before overcharged, AB will be as much undercharged as it was before
overcharged, and DF as much overcharged as it was before undercharged.

83] COR. VIII. If the size and distance of the plates be altered, the
quantity of redundant or deficient fluid in the body H remaining the
same, it appears, by comparing this proposition with the 2Oth and 2ist
propositions, that the quantity of redundant and deficient fluid in AB

AC\3~n AC2

will be as AC"-1 x "=J , or as ECs-n - supposing the value of 8 to

remain the same*.

84] PROP. XXIII. Let AE (Fig. 15) be a cylindric canal, infinitely
continued beyond E ; and let A F be a bent canal, meeting
the other at A, and infinitely continued beyond F: let
the section of this canal, in all parts of it, be equal to I
that of the cylindric canal, and let both canals be filled
with uniform fluid of the same density: the force with
which a particle of fluid P, placed anywhere at pleasure,
repels the whole quantity of fluid in AF, in the direction
of the canal, is the same with which it repels the fluid in
the canal AE, in the direction AE.

On the center P, draw two circular arches BD and bd,
infinitely near to each other, cutting AE in B and £, and AF in D and 8,
and draw the radii Pb and Pd. As PB = PD, the force with which P
repels a particle at B, in the direction Bp, is to that with which it repels an

equal particle at D, in the direction Z)8, as ^ to ^ , or as ^ to ^~ ;

and therefore, the force with which it repels the whole fluid in Bf$, in the
direction Eft, is the same with which it repels the whole fluid in DS, in
the direction D8, that is in the direction of the canal; and therefore, the
force with which it repels the whole fluid in AE, in the direction AE, is
the same with which it repels the whole fluid in AF, in the direction of
the canal.

85] COR. If the bent canal A DF, instead of being infinitely continued,
meets the cylindric canal in E, as in Fig. 16, the repulsion of
P on the fluid in the bent canal ADE, in the direction of the
canal, will still be equal to its repulsion on that in the
cylindric canal AE, in the direction AE.

86] PROP. XXIV. If two bodies, for instance the plate
AB, and the body H, of Prop. XXII, communicate with each
other, by a canal filled with incompressible fluid, and are
either over or undercharged, the quantity of redundant
fluid in them will bear the same proportion to each other,
whether the canal by which they communicate is straight or crooked, or

[» Note 4, p. 368.]

Theory of bent connecting canal

61

into whatever part of the bodies the canal is inserted, or in whatever
manner the two bodies are situated in respect of each other; provided
that their distance is infinite, or so great that the repulsion of each body
on the fluid in the canal shall not be sensibly less than if it was infinite.
Let the parallelograms AB and DF (Fig. 17) represent the two plates,
and H and L the bodies communicating with them: let now H be re-
moved to h; and let it communicate with AB by the bent canal gc; the
quantity of fluid in the plates and bodies remaining the same as before ;
and let us, for the sake of ease in the demonstration, suppose the canal gc
to be everywhere of the same thickness as the canal GC; though the
proposition will evidently hold good equally, whether it is or not : the
fluid will still be in equilibrio. For let us first suppose the canal gc to be

Fig. 17

continued through the substance of the plate AB, to C. along the line
crC; the part crC being of the same thickness as the rest of the canal, and
the fluid in it of the same density: by the preceding proposition, the
repulsion' or attraction of each particle of fluid or matter in the plates AB
and DF, on the fluid in the whole canal Crcg, in the direction of that canal,
is equal to its repulsion or attraction on the fluid in the canal CG, in the
direction CG; and therefore the whole repulsion or attraction of the two
plates on the canal Crcg, is equal to their repulsion or attraction on CG:
but as the fluid in the plate A B is in equilibrio, each particle of fluid in
the part Crc of the canal is impelled by the plates with as much force in
one direction as the other; and consequently the plates impel the fluid
in the canal eg with as much force as they do that in the whole canal
Crcg, that is, with the same force that they impel the fluid in CG. In like

6 2 First published Paper on Electricity

manner the body h impels the fluid in eg with the same force that H does
the fluid in CG ; and consequently h impels the fluid in eg one way in the
direction of the canal, with the same force that the two plates impel it
the contrary way; and therefore the fluid in eg has no tendency to flow
from one body to the other.

87] COR. By the same method of reasoning, with the help of the
corollary to the 23rd proposition, it appears, that if AB and H each,
communicate with a third body by canals of incompressible fluid, and a
communication is made between AB and H by another canal of incom-
pressible fluid, the fluid will have no tendency to flow from one to the other
through this canal; supposing that the fluid was in equilibrio before this
communication was made. In like manner if AB and H communicate
with each other, or each communicate with a third body, by canals of
real fluid, instead of the imaginary canals of incompressible fluid used in
these propositions, and a communication is also made between them by
a canal of incompressible fluid, the fluid can have no tendency to flow
from one to the other. The truth of the latter part of this corollary will
appear by supposing an imaginary canal of incompressible fluid to be
continued through the whole length of the real one.

88] PROP. XXV. Let now a communication be made between the
two plates AB and DF, by the canal NRS of incompressible fluid, of any
length; and let the body H and the plate AB be overcharged. It is plain
that the fluid will flow through that canal from AB to DF. Now the whole
force with which the fluid in the canal is impelled along it by the joint
action of the two plates is the same with which the whole quantity of
fluid in the canal CG or eg is impelled by them ; supposing the canal NRS
to be everywhere of the same breadth and thickness as CG or eg.

For suppose that the canal NRS, instead of communicating with the
plate DF, is bent back just before it touches it, and continued infinitely
along the line Ss; the force with which the two plates impel the fluid
in Ss, is the same with which they impel that in EL, supposing Ss to be
of the same breadth and thickness as EL ; and is therefore nothing; there-
fore the force with which they impel the fluid in NRS, is the same with
which they impel that in A^RSs ; which is the same with which they impel
that in CG.

89] PROP. XXVI. Let now xyz [Fig. 17] be a body of an infinite size,
containing just fluid enough to saturate it; and let a communication be
made between h and xyz, by the canal hy of incompressible fluid, of the
same breadth and thickness as gc or GC; the fluid will flow through it
from h to xyz; and the force with which the fluid in that canal is impelled
along it, is equal to that with which the fluid in NRS is impelled by the
two plates.

If the canal hy is of so great a length, that the repulsion of h thereon

Canals of fluid compared with conducting wires 63

is the same as if it was continued infinitely, then the thing is evident:
but if it is not, let the canal hy, instead of communicating with xyz, so
that the fluid can flow out of the canal into xyz, be continued infinitely
through its substance, along the line yv : now it must be observed that a
small part of the body xyz, namely, that which is turned towards h, will
by the action of h upon it, be rendered undercharged; but all the rest of
the body will be saturated; for the fluid driven out of the undercharged
part will not make the remainder, which is supposed to be of an infinite
size, sensibly overcharged: now the force with which the fluid in the
infinite canal hyv is impelled by the body h and the undercharged part
of xyz, is the same with which the fluid in gc is impelled by them ; but as
the fluid in all parts of xyz is in equilibrio, a particle in any part of yv
cannot be impelled in any direction; and therefore the fluid in hy is im-
pelled with as much force as that in hyv; and therefore the fluid in hy is
impelled with as much force as that in gc ; and is therefore impelled with
as much force as the fluid in NRS is impelled by the two plates.

90] It perhaps may be asked, whether this method of demonstration
would not equally tend to prove that the fluid in hy was impelled with the
same force as that in NRS, though xyz did not contain just fluid enough
to saturate it. I answer not; for this demonstration depends on the canal
yv being continued, within the body xyz, to an infinite distance beyond
any over or undercharged part ; which could not be if xyz contained either
more or less fluid than that*.

91] PROP. XXVII. Let two bodies B and b (Fig. 13) be joined by a
cylindric or prismatic canal Aa, filled with real fluid; and not by any
imaginary canal of incompressible fluid as in the 20th proposition; and
let the fluid therein be in equilibrio: the force with which the whole or
any given part of the fluid in the canal is impelled in the direction of its
axis by the united repulsions and attractions of the redundant fluid or
matter in the two bodies and the canal, must be nothing; or the force
with which it is impelled one way in the direction of the axis of the canal,
must be equal to that with which it is impelled the other way.

For as the canal is supposed cylindric or prismatic, no particle of fluid
therein can be prevented from moving in the direction of the axis of it,
by the sides of the canal ; and therefore the force with which each particle
is impelled either way in the direction of the axis, by the united attractions
and repulsions of the two bodies and the canal, must be nothing, otherwise
it could not be at rest; and therefore the force with which the whole, or
any given part of the fluid in the canal, is impelled in the direction of the
axis, must be nothing.

92] COR. I. If the fluid in the canal is disposed in such manner, that
the repulsion or attraction of the redundant fluid or matter in it, on the

[* Note 5, p. 369.]

64 First published Paper on Electricity

whole or any given part of the fluid in the canal, has no tendency to impel
it cither way in the direction of the axis; then the force with which that
whole or given part is impelled by the two bodies must be nothing; or
the force with which it is impelled one way in the direction of the axis,
by the body B, must be equal to that with which it is impelled in the
contrary direction by the other body; but not if the fluid in the canal is
disposed in a different manner.

93] COR. II. If the bodies, and consequently the canal, is overcharged;
then, in whatever manner the fluid in the canal is disposed, the force with
which the whole quantity of redundant fluid in the canal is repelled by
the body B in the direction Aa, must be equal to that with which it is
repelled by b in the contrary direction. For the force with which the
redundant fluid is impelled in the direction A a by its own repulsion, is
nothing; for the repulsions of the particles of any body on each other
have no tendency to make the whole body move in any direction.

94] REMARKS. When I first thought of the aoth and 22nd proposi-
tions, I imagined that when two bodies were connected by a cylindric
canal of real fluid, the repulsion of one body on the whole quantity of
fluid in the canal, in one direction, would be equal to that of the other
body on it in the contrary direction, in whatever manner the fluid was
disposed in the canal; and that therefore those propositions would have
held good very nearly, though the bodies were joined by cylindric canals
of real fluid ; provided the bodies were so little over or undercharged, that
the quantity of redundant or deficient fluid in the canal should be very
small in respect of the quantity required to saturate it ; and consequently
that the fluid therein should be very nearly of the same density in all
parts. But from the foregoing proposition it appears that I was mistaken,
and that the repulsion of one body on the fluid in the canal is not equal
to that of the other body on it, unless the fluid in the canal is disposed
in a particular manner: besides that, when two bodies are both joined
by a real canal, the attraction or repulsion of the redundant matter or
fluid in the canal has some tendency to alter the disposition of the fluid
in the two bodies; and in the 22nd proposition, the canal CG exerts also
some attraction or repulsion on the canal EM: on all which accounts the
demonstration of those propositions is defective, when the bodies are joined
by real canals. I have good reason however to think, that those proposi-
tions actually hold good very nearly when the bodies are joined by real
canals ; and that, whether the canals are straight or crooked, or in whatever
direction the bodies are situated in respect of each other : though I am by
no means able to prove that they do : I therefore chose still to retain those
propositions, but to demonstrate them on this ideal supposition, in which
they are certainly true, in hopes that some more skilful mathematician
may be able to shew whether they really hold good or not. [See Note 3.]

Molecular constitution of air 65

95] What principally makes me think that this is the case, is that as
far as I can judge from some experiments I have made*, the quantity
of fluid in different bodies agrees very well with those propositions, on a
supposition that the electric repulsion is inversely as the square of the
distance. It should also seem from those experiments, that the quantity
of redundant or deficient fluid in two bodies bore very nearly the same
proportion to each other, whatever is the shape of the canal by which
they are joined, or in whatever direction they are situated in respect of
each other.

96] Though the above propositions should be found not to hold good
when the bodies are joined by real canals, still it is evident, that in the
22nd proposition, if the plates AB and DF are very near together, the
quantity of redundant fluid in the plate AB will be many times greater
than that in the body H, supposing H to consist of a circular plate of the
same size as AB, and DF will be near as much undercharged as AB is
overcharged.

97] Sir Isaac Newton supposes that air consists of particles which
repel each other with a force inversely as the distance: but it appears
plainly from the foregoing pages, that if the repulsion of the particles was
in this ratio, and extended indefinitely to all distances, they would compose
a fluid extremely different from common air. If the repulsion of the particles
was inversely as the distance, but extended only to a given very small
distance from their centers, they would compose a fluid of the same kind
as air, in respect of elasticity, except that its density would not be in pro-
portion to its compression : if the distance to which the repulsion extends,
though very small, is yet many times greater than the distance of the
particles from each other, it might be shewn, that the density of the fluid
would be nearly as the square root of the compression. If the repulsion
of the particles extended indefinitely, and was inversely as some higher
power of the distance than the cube, the density of the fluid would be as
some power of the compression less than f . The only law of repulsion,
I can think of, which will agree with experiment, is one which seems not
very likely; namely, that the particles repel each other with a force in-
versely as the distance ; but that, whether the density of the fluid is great
or small, the repulsion extends only to the nearest particles: or, what
comes to the same thing, that the distance to which the repulsion extends,
is very small, and also is not fixed, but varies in proportion to the distance
of the particles f.

[* Exp. Ill, Art. 265.] [f Note 6, p. 370.]

c.p, i.

66 First published Paper on Electricity

An attempt to explain some of the Principal Phenomena
of Electricity, by means of an Elastic Fluid — Part II

Containing a Comparison of the Foregoing Theory
with Experiment.

98] § I. It appears from experiment, that some bodies suffer the
electric fluid to pass with great readiness between their pores; while
others will not suffer it to do so without great difficulty ; and some hardly
suffer it to do so at all. The first sort of bodies are called conductors,
the others non-conductors. What this difference in bodies is owing to
I do not pretend to explain.

It is evident that the electric fluid in conductors may be considered
as moveable, or answers to the definition given of that term in page 6.
As to the fluid contained in non-conducting substances, though it does
not absolutely answer to the definition of immoveable, as it is not abso-
lutely confined from moving, but only does so with great difficulty; yet
it may in most cases be looked upon as such without sensible error.

99] Air does in some measure permit the electric fluid to pass through
it; though, if it is dry, it lets it pass but very slowly, and not without
difficulty; it is therefore to be called a non-conductor.

It appears that conductors would readily suffer the fluid to run in and
out of them, were it not for the air which surrounds them: for if the end
of a conductor is inserted into a vacuum, the fluid runs in and out of it
with perfect readiness ; but when it is surrounded on all sides by the air,
as no fluid can run out of it without running into the air, the fluid will
not do so without difficulty.

100] If any body is surrounded on all sides by the air, or other non-
conducting substances, it is said to be insulated: if on the other hand it
anywhere communicates with any conducting body, it is said to be not
insulated. When I say that a body communicates with the ground, or
any other body, I would be understood to mean that it does so by some
conducting substance.

101] Though the terms positively and negatively electrified are much
used, yet the precise sense in which they are to be understood seems not
well ascertained; namely, whether they are to be understood in the same
sense in which I have used the words over or undercharged, or whether,
when any number of bodies, insulated and communicating with each other
by conducting substances, are electrified by means of excited glass, they
are all to be called positively electrified (supposing, according to the usual

Positive and negative electrification 67

opinion, that excited glass contains more than its natural quantity of
electricity) ; even though some of them, by the approach of a stronger
electrified body, are made undercharged. I shall use the words in the
latter sense; but as it will be proper to ascertain the sense in which I
shall use them more accurately, I shall give the following definition.

102] In order to judge whether any body, as A, is positively or nega-
tively electrified: suppose another body B, of a given shape and size, to
be placed at an infinite distance from it, and from any other over or under-
charged body; and let B contain the same quantity of electric fluid as if
it communicated with A by a canal of incompressible fluid : then, if B is
overcharged, I call A positively electrified; and if it is undercharged, I
call A negatively electrified; and the greater the degree in which B is
over or undercharged, the greater is the degree in which A is positively
or negatively electrified.

103] It appears from the corollary to the 24th proposition, that if
several bodies are insulated, and connected together by conducting sub-
stances, and one of these bodies is positively or negatively electrified, all
the other bodies must be electrified in the same degree: for supposing a
given body B to be placed at an infinite distance from any over or under-
charged body, and to contain the same quantity of fluid as if it com-
municated with one of those bodies by a canal of incompressible fluid, all
the rest of those bodies must by that corollary contain the same quantity
of fluid as if they communicated with B by canals of incompressible fluid :
but yet it is possible that some of those bodies may be overcharged, and
others undercharged: for suppose the bodies to be positively electrified,
and let an overcharged body D be brought near one of them, that body
will become undercharged, provided D is sufficiently overcharged; and yet
by the definition it will still be positively electrified in the same degree
as before.

Moreover, if several bodies are insulated and connected together by
conducting substances, and one of these bodies is electrified by excited
glass, there can be no doubt, I think, but what they will all be positively
electrified ; for if there is no other over or undercharged body placed near
any of these bodies, the thing is evident ; and though some of these bodies
may, by the approach of a sufficiently overcharged body, be rendered
undercharged ; yet I do not see how it is possible to prevent a body placed
at an infinite distance, and communicating with them by a canal of in-
compressible fluid, from being overcharged.

In like manner if one of these bodies is electrified by excited sealing
wax, they will all be negatively electrified*.

104] It is impossible for any body communicating with the ground
to be either positively or negatively electrified: for the earth, taking the

[* Note 7, p. 372.]

5—2

68 First published Paper on Electricity

whole together, contains just fluid enough to saturate it, and consists in
general of conducting substances; and consequently though it is possible
for small parts of the surface of the earth to be rendered over or under-
charged, by the approach of electrified clouds or other causes; yet the
bulk of the earth, and especially the interior parts, must be saturated
with electricity. Therefore assume any part of the earth which is itself
saturated, and is at a great distance from any over or undercharged part ;
any body communicating with the ground, contains as much electricity
as if it communicated with this part by a canal of incompressible fluid,
and therefore is not at all electrified.

105] If any body A , insulated and saturated with electricity, is placed
at a great distance from any over or undercharged body, it is plain that
it cannot be electrified; but if an overcharged body is brought near it, it
will be positively electrified; for supposing A to communicate with any
body B, at an infinite distance, by a canal of incompressible fluid, it is
plain that unless B is overcharged, the fluid in the canal could not be in
equilibrio, but would run from A to B. For the same reason a body
insulated and saturated with fluid, will be negatively electrified if placed
near an undercharged body.

106] § 2. The phenomena of the attraction and repulsion of electrified
bodies seem to agree exactly with the theory; as will appear by con-
sidering the following cases.

107] CASE I. Let two bodies, A and B, both conductors of electricity,
and both placed at a great distance from any other electrified bodies, be
brought near each other. Let A be insulated, and contain just fluid
enough to saturate it; and let B be positively electrified. They will attract
each other ; for as B is positively electrified, and at a great distance from
any overcharged body, it will be overcharged; therefore, on approaching
A and B to each other, some fluid will be driven from that part of A
which is nearest to B to the further part: but when the fluid in A was
spread uniformly, the repulsion of B on the fluid in A was equal to its
attraction on the matter therein; therefore, when some fluid is removed
from those parts where the repulsion of B is strongest to those where it
is weaker, B will repel the fluid in A with less force than it attracts the
matter; and consequently the bodies will attract each other.

108] CASE II. If we now suppose that the fluid is at liberty to escape
from out of A, if it has any disposition to do so, the quantity of fluid in
it before the approach of B being still sufficient to saturate it; that is,
if A is not insulated and not electrified, B being still positively electrified,
they will attract with more force than before: for in this case, not only
some fluid will be driven from that part of A which is nearest to B to the
opposite part, but also some fluid will be driven out of A.

Various cases of electric distribution 69

It must be observed, that if the repulsion of B on a particle at E,
(Fig. 19) the farthest part of A, is very small in
respect of its repulsion on an equal particle placed
at D, the nearest part of A, the two bodies will
attract with very nearly the same force, whether
A is insulated or not ; but if the repulsion of B, on
a particle at E, is very near as great as on one at D, Fig Ig

they will attract with very little force if A is
insulated. For instance, let a small overcharged ball be brought near one
end of a long conductor not electrified; they will attract with very near
the same force, whether the conductor be insulated or not; but if the
conductor be overcharged, and brought near a small unelectrified ball,
they will not attract with near so much force, if the ball is insulated, as
if it is not.

109] CASE III. If we now suppose that A is negatively electrified,
and not insulated, it is plain that they will attract with more force than
in the last case ; as A will be still more undercharged in this case, than in
the last.

no] N.B. In these three cases, we have not as yet taken notice of
the effect which the body A will have in altering the quantity and dis-
position of the fluid in B ; but in reality this will make the bodies attract
each other with more force than they would otherwise do ; for in each of
these cases the body A attracts the fluid in B; which will cause some
fluid to flow from the farther parts of B to the nearer, and will also cause
some fluid to flow into it, if it is not insulated, and will consequently
cause B to act upon A with more force than it would otherwise do.

in] CASES IV, V, VI. Let us now suppose that B is negatively
electrified ; and let A be insulated, and contain just fluid enough to saturate
it ; they will attract each other; for B will be undercharged ; it will therefore
attract the fluid in A , and will cause some fluid to flow from the farthest
part of A, where it is attracted with less force, to the nearer part, where
it is attracted with more force ; so that B will attract the fluid in A with
more force than it repels the matter.

If A is now supposed to be not insulated and not electrified, B being
still negatively electrified, it is plain that they will attract with more
force than in the last case: and if A is positively electrified, they will
attract with still more force.

In these three last cases also, the effect which A has in altering the
quantity and disposition of the fluid in B, tends to increase the force with
which the two bodies attract.

112] CASE VII. It is plain that a non-conducting body saturated with
fluid, is not at all attracted or repelled by an over or undercharged body,

jo First published Paper on Electricity

until, by the action of the electrified body on it, it has either acquired
some additional fluid from the air, or had some driven out of it, or till
some fluid is driven from one part of the body to the other.

113] CASE VIII. Let us now suppose that the two bodies A and B
are both positively electrified in the same degree. It is plain, that were
it not for the action of one body on the other, they would both be over-
charged, and would repel each other. But it may perhaps be said, that
one of them as A may, by the action of the other on it, be either rendered
undercharged on the whole, or at least may be rendered undercharged in
that part nearest to B ; and that the attraction of this undercharged part
on a particle of the fluid in B, may be greater than the repulsion of the
more distant overcharged part; so that on the whole the body A may
attract a particle of fluid in B. If so, it must be affirmed that the body B
repels the fluid in A ; for otherwise, that part of A which is nearest to B
could not be rendered undercharged. Therefore, to obviate this objection,
let the bodies by joined by the straight canal DC of incompressible fluid
(Fig. 19) . The body B will repel the fluid in all parts of this canal ; for as
A is supposed to attract the fluid in B, B will not only be more overcharged
than it would otherwise be, but it will also be more overcharged in that
part nearest to A than in the opposite part. Moreover, as the near under-
charged part of A is supposed to attract a particle of fluid in B with more
force than the more distant overcharged part repels it; it must, a fortiori,
attract a particle in the canal with more force than the other repels it;
therefore the body A must attract the fluid in the canal ; and consequently
some fluid must flow from B to A , which is impossible ; for as A and B are
both electrified in the same degree, they contain the same quantity of fluid
as if they both communicated with a third body at an infinite distance, by
canals of incompressible fluid ; and therefore, by the corollary to Prop. 24,
if a communication is made between them by a canal of incompressible
fluid, the fluid would have no disposition to flow from one to the other.

114] CASE IX. But if one of the bodies as A is positively electrified
in a less degree than B, then it is possible for the bodies to attract each
other ; for in this case the force with which B repels the fluid in A may be
so great, as to make the body A either intirely undercharged, or at least
to make the nearest part of it so much undercharged, that A shall on the
whole attract a particle of fluid in B.

It may be worth remarking with regard to this case, that when two
bodies, both electrified positively but unequally, attract each other, you
may by removing them to a greater distance from each other, cause them
to repel ; for as the stronger electrified body repels the fluid in the weaker
with less force when removed to a greater distance, it will not be able to
drive so much fluid out of it, or from the nearer to the further part, as
when placed at a less distance.

Exchange of electricity with the air 71

115] CASES X and XI. By the same reasoning it appears, that if the
two bodies are both negatively electrified in the same degree, they must
repel each other: but if they are both negatively electrified in different
degrees, it is possible for them to attract each other. .

All these cases are exactly conformable to experiment.

116] CASE XII. Let two cork balls be suspended by conducting
threads from the same positively electrified body, in such manner that if
they did not repel, they would hang close together: they will both be
equally electrified, and will repel each other : let now an overcharged body,
more strongly electrified than them, be brought under them; they will
become less overcharged, and will separate less than before: on bringing
the body still nearer, they will become not at all overcharged, and will
not separate at all : and on bringing the body still nearer, they will become
undercharged, and will separate again.

117] CASE XIII. Let all the air of a room be overcharged, and let
two cork balls be suspended close to each other by conducting threads
communicating with the wall. By Prop. 15, it is highly probable that the
balls will be undercharged; and therefore they should repel each other.

These two last cases are experiments of Mr Canton's, and are described
in Philosophical Transactions 1753, p. 350, where are other experiments
of the same kind, all readily explicable by the foregoing theory.

I have now considered all the principal or fundamental cases of electric
attractions and repulsions which I can think of ; all of which appear to
agree perfectly with the theory*.

118] § 3. On the cases in which bodies receive electricity from or part
with it to the air.

LEMMA I. Let the body A (Fig. 6) either stand near some over or
undercharged body, or at a distance from any.
It seems highly probable, that if any part of
its surface, as MN, is overcharged, the fluid
will endeavour to run out through that part,
provided the air adjacent thereto is not over-
charged.

For let G be any point in that surface, and
P a point within the body, extremely near to it ;
it is plain that a particle of fluid at P must be repelled with as much force
in one direction as another (otherwise it could not be at rest) unless all the
fluid between P and G is pressed close together, in which case it may be
repelled with more force towards G than it is in the contrary direction : now
a particle at G is repelled in the direction PG, i.e. from P to G, by all the
redundant fluid between P and G ; and a particle at P is repelled by the

[* Note 8, p. 373.]

72 First published Paper on Electricity

same fluid in the contrary direction ; so that as the particle at P is repelled
with not less force in the direction PG than in the contrary, I do not see
how a particle at G can help being repelled with more force in that direction
than the contrary, unless the air on the outside of the surface MN was
more overcharged than the space between P and G.

In like manner, if any part of the surface is undercharged, the fluid
will have a tendency to run in at that part from the air.

The truth of this is somewhat confirmed by the third problem ; as in
all the cases of that problem, the fluid was shewn to have a tendency to
run out of the spaces AD and EH, at any surface which was overcharged,
and to run in at any which was undercharged.

119] COR. I. If any body at a distance from other over or under-
charged bodies be positively electrified, the fluid will gradually run out
of it from all parts of its surface into the adjoining air; as it is plain that
all parts of the surface of that body will be overcharged : and if the body
is negatively electrified, the fluid will gradually run into it at all parts
of its surface from the adjoining air.

120] COR. II. Let the body A (Fig. 6) insulated and containing just
fluid enough to saturate it, be brought near the overcharged body B;
that part of the surface of A which is turned towards B will by Prop. II
be rendered undercharged, and will therefore imbibe electricity from the
air ; and at the opposite surface RS, the fluid will run out of the body into
the air.

121] COR. III. If we now suppose that A is not insulated, but com-
municates with the ground, and consequently that it contained just fluid
enough to saturate it before the approach of B, it is plain that the surface
MN will be more undercharged than before; and therefore the fluid will
run in there with more force than before; but it can hardly have any
disposition to run out at the opposite surface RS ; for if the canal by which
A communicates with the ground is placed opposite to B, as in figure 5,
then the fluid will run out through that canal till it has no longer any
tendency to run out at RS; and by the remarks at the end of Prop. 27, it
seems probable, that the fluid in A will be nearly in the same quantity,
and disposed nearly in the same manner, into whatever part of A the canal
is inserted by which it communicates with the ground.

122] COR. IV. If B is undercharged the case will be reversed; that is,
it will run out where it before run in, and will run in where it before
run out.

As far as I can judge, these corollaries seem conformable to experi-
ment : thus far is certain, that bodies at a distance from other electrified
bodies receive electricity from the air, if negatively electrified, and part
with some to it if positively electrified : and a body not electrified and not

Discharge by points 73

insulated receives electricity from the air if brought near an overcharged
body, and loses some when brought near an undercharged body: and a
body insulated and containing its natural quantity of fluid, in some cases,
receives, and in others loses electricity, when brought near an over or
undercharged body.

123] § 4. The well-known effects of points in causing a quick dis-
charge of electricity seem to agree very well with this theory.

It appears from the 20th proposition, that if two similar bodies of
different sizes are placed at a very great distance from each other, and
connected by a slender canal, and overcharged, the force with which a
particle of fluid placed close to corresponding parts of their surface is
repelled from them, is inversely as the corresponding diameters of the
bodies. If the distance of the two bodies is small, there is not so much
difference in the force with which the particle is repelled by the two bodies ;
but still, if the diameters of the two bodies are very different, the particle
will be repelled with much more force from the smaller body than from
the larger. It is true indeed that a particle placed at a certain distance
from the smaller body, will be repelled with less force than if it be placed
at the same distance from the greater body; but this distance is, I believe,
in most cases pretty considerable; if the bodies are spherical, and the
repulsion inversely as the square of the distance, a particle placed at any
distance from the surface of the smaller body less than a mean proportional
between the radii of the two bodies, will be repelled from it with more
force than if it be placed at the same distance from the larger body.

I think therefore that we may be well assured that if two similar bodies
are connected together by a slender canal, and are overcharged, the fluid
must escape faster from the smaller body than from an equal surface of
the larger; but as the surface of the larger body is greatest, I do not know
which body ought to lose most electricity in the same time; and indeed
it seems impossible to determine positively from this theory which should,
as it depends in great measure on the manner in which the air opposes
the entrance of the electric fluid into it. Perhaps in some degrees of
electrification the smaller body may lose most, and in others the larger.

124] Let now ACB (Fig. 18) be a conical point standing on any body
DAB, C being the vertex of the cone; and let DAB
be overcharged: I imagine that a particle of fluid
placed close to the surface of the cone anywhere
between b and C, must be repelled with at least as
much, if not more, force than it would, if the part
AabB of the cone was taken away, and the part aCb Fig. 18.

connected to DAB by a slender canal; and conse-
quently, from what has been said before, it seems reasonable to suppose
that the waste of electricity from the end of the cone must be very great

74 First published Paper on Electricity

in proportion to its surface ; though it does not appear from this reasoning
whether the waste of electricity from the whole cone should be greater or
less than from a cylinder of the same base and altitude*.

All which has been here said relating to the flowing out of electricity
from overcharged bodies, holds equally true with regard to the flowing in
of electricity into undercharged bodies.

125] But a circumstance which I believe contributes as much as any
thing to the quick discharge of electricity from points, is the swift current
of air caused by them, and taken notice of by Mr Wilson and Dr Priestly
(vide Priestly, pp. 117 and 591) ; and which is produced in this manner.

If a globular body ABD is overcharged, the air close to it, all round
its surface, is rendered overcharged by the electric fluid which flows into
it from the body ; it will therefore be repelled by the body ; but as the air
all round the body is repelled with the same force, it is in equilibrio, and
has no tendency to fly off from it. If now the conical point ACB be made
to stand out from the globe, as the fluid will escape much faster in pro-
portion to the surface from the end of the point than from the rest of the
body, the air close to it will be much more overcharged than that close
to the rest of the body ; it will therefore be repelled with much more force ;
and consequently a current of air will flow along the sides of the cone,
from B towards C; by which means there is a continual supply of fresh air,
not much overcharged, brought in contact with the point; whereas other-
wise the air adjoining to it would be so much overcharged, that the
electricity would have but little disposition to flow from the point into it.

The same current of air is produced in a less degree, without the help
of the point, if the body, instead of being globular, is oblong or flat, or
has knobs on it, or is otherwise formed in such manner as to make the
electricity escape faster from some parts of it than the rest.

In like manner, if the body ABD be undercharged, the air adjoining
to it will also be undercharged, and will therefore be repelled by it; but
as the air close to the end of the point will be more undercharged than
that close to the rest of the body, it will be repelled with much more force ;
which will cause exactly the same current of air, flowing the same way,
as if the body was overcharged ; and consequently the velocity with which
the electric fluid flows into the body, will be very much increased. I
believe indeed that it may be laid down as a constant rule, that the faster
the electric fluid escapes from any body when overcharged, the faster will
it run into that body when undercharged.

Points are not the only bodies which cause a quick discharge of
electricity ; in particular, it. escapes very fast from the ends of long slender
cylinders; and a swift current of air is caused to flow from the middle of
the cylinder towards the end: this will easily appear by considering that

[* Note 9, p. 374.]

Electric 'wind 75

the redundant fluid is collected in much greater quantity near the ends of
the cylinders than near the middle. The same thing may be said, but I
believe in a less degree, of the edges of thin plates.

What has been just said concerning the current of air, serves to explain
the reason of the revolving motion of Dr Hamilton's and Mr Kinnersley's
bent pointed wires, vide Philosophical Trans. Vol. LI., p. 905, and Vol. LIII.,
p. 86; also Priestly, p. 429: for the same repulsion which impels the air
from the thick part of the wire towards the point, tends to impel the
wire in the contrary direction.

126] It is well known, that if a body B is positively electrified, and
another body A, communicating with the ground, be then brought near
it, the electric fluid will escape faster from B, at that part of it which is
turned towards A, than before. This is plainly conformable to theory;
for as A is thereby rendered undercharged, B will in its turn be made
more overcharged, in that part of it which is turned towards A, than it
was before. But it is also well known that the fluid will escape faster
from B, if A be pointed, than if it be blunt; though B will be less over-
charged in this case than in the other ; for the broader the surface of A ,
which is turned towards B, the more effect will it have in increasing the
overcharge of B. The cause of this phenomenon is as follows :

If A is pointed, and the pointed end turned towards B, the air close
to the point will be very much undercharged, and therefore will be strongly
repelled by A, and attracted by B, which will cause a swift current of air
to flow from it towards B ; by which means a constant supply of under-
charged air will be brought in contact with B, which will accelerate the
discharge of electricity from it in a very great degree : and moreover, the
more pointed A is, the swifter will be this current. If, on the other hand,
that end of A which is turned towards B is so blunt, that the electricity
is not disposed to run into A faster than it is to run out of B, the air
adjoining to B may be as much overcharged as that adjoining to A is
undercharged; and therefore may by the joint repulsion of B and attrac-
tion of A , be impelled from B to A , with as much or more force than the
air adjoining to A is impelled in the contrary direction ; so that what little
current of air there is may flow in the contrary direction.

It is easy applying" what has been here said to the case in which B is
negatively electrified.

I27] § 5- In the paper of Mr Canton's, quoted in the second section,
and in a paper of Dr Franklin's Philosophical Transactions 1755, p. 300,
and Franklin's letters, p. 155, are some remarkable experiments, shewing
that when an overcharged body is brought near another body, some fluid
is driven to the further end of this body, and also some driven out of it,
if it is not insulated. The experiments are all strictly conformable to the

j6 First published Paper on Electricity

nth, I2th, and I3th propositions: but it is needless to point out the
agreement, as the explanation given by the authors does it sufficiently.

128] § 6. On the Leyden vial.

The shock produced by the Leyden vial seems owing only to the great
quantity of redundant fluid collected on its positive side, and the great
deficiency on its negative side ; so that if a conductor was prepared of so
great a size, as to be able to receive as much additional fluid by the same
degree of electrification as the positive side of a Leyden vial, and was
positively electrified in the same degree as the vial, I do not doubt but
what as great a shock would be produced by making a communication
between this conductor and the ground, as between the two surfaces of
the Leyden vial, supposing both communications to be made by canals
of the same length and same kind.

It appears plainly from the experiments which have been made on
this subject, that the electric fluid is not able to pass through the glass;
but yet it seems as if it was able to penetrate without much difficulty to
a certain depth, perhaps I might say an imperceptible depth, within the
glass ; as Dr Franklin's analysis of the Leyden vial shews that its electricity
is contained chiefly in the glass itself, and that the coating is not greatly
over or undercharged.

It is well known that glass is not the only substance which can be charged
in the manner of the Leyden vial ; but that the same effect may be produced
by any other body, which will not suffer the electricity to pass through it.

129] *Hence the phenomena of the vial seem easily explicable by
means of the 22nd proposition. For let ACGM , Fig. 20,
represent a flat plate of glass or any other substance
which will not suffer the electric fluid to pass through
it, seen edgeways ; and let BbdD, and EefF, or Bd and
Ef, as I shall call them for shortness, be two plates of
conducting matter of the same size, placed in contact
with the glass opposite to each other; and let Bd be
positively electrified; and let Ef communicate with
the ground; and let the fluid be supposed either able
to enter a little way into the glass, but not to pass
through it, or unable to enter it at all; and if it is
able to enter a little way into it, let b/38d, or bS, as I
shall call it, represent that part of the glass into which
the fluid can enter from the plate Bd, and e<f>, that

* The following explication is strictly applicable only to that sort of Leyden vial,
which consists of a flat plate of glass or other matter. It is evident, however, that
the result must be nearly of the same kind, though the glass is made into the shape
of a bottle as usual, or into any other form; but I propose to consider those sort of
Leyden vials more particularly in a future paper.

The Ley den vial 77

which the fluid from Ef can enter. By the above-mentioned proposition,
if be, the thickness of the glass, is very small in respect of bd, the diameter
of the plates, the quantity of redundant fluid forced into the space Bd, or
B8, (that is, into the plate Bd, if the fluid is unable to penetrate at all into
the glass, or into the plate Bd, and the space b8 together, if the fluid is
able to penetrate into the glass,) will be many times greater than what
would be forced into it by the same degree of electrification if it had been
placed by itself; and the quantity of fluid driven out of E<f> will be nearly
equal to the redundant fluid in B8.

If a communication be now made between B8 and E<f>, by the canal
NRS, the redundant fluid will run from 58 to E$; and if in its way it
passes through the body of any animal, it will by the rapidity of its motion
produce in it that sensation called a shock.

130] It appears from the 26th proposition, that if a body of any size
was electrified in the same degree as the plate Bd, and a communication
was made between that body and the ground, by a canal of the same
length, breadth and thickness as NRS; that then the fluid in that canal
would be impelled with the same force as that in NRS, supposing the
fluid in both canals to be incompressible ; and consequently, as the quantity
of fluid to be moved, and the resistance to its motion is the same in both
canals, the fluid should move with the same rapidity in both: and I see
no reason to think that the case will be different, if the communication
is made by canals of real fluid.

Therefore what was said in the beginning of this section, namely, that
as great a shock would be produced by making a communication between
the conductor and the ground, as between the two sides of the Leyden
vial, by canals of the same length and same kind, seems a necessary con-
sequence of this theory ; as the quantity of fluid which passes through the
canal is, by the supposition, the same in both; and there is the greatest
reason to think, that the rapidity with which it passes will be nearly if
not quite the same in both. I hope soon to be able to say whether this
agrees with experiment as well as theory.

131] It may be worth observing, that the longer the canal NRS is,
by which the communication is made, the less will be the rapidity with
which the fluid moves along it ; for the longer the canal is, the greater is
the resistance to the motion of the fluid in it; whereas the force with
which the whole quantity of fluid in it is impelled, is the same whatever
be the length of the canal. Accordingly, it is found in melting small wires,
by directing a shock through them, that the longer the wire the greater
charge it requires to melt it.

132] As the fluid in B8 is attracted with great force by the redundant
matter in £$, it is plain that if the fluid is able to penetrate at all into

78 First published Paper on Electricity

the glass, great part of the redundant fluid will be lodged in 68, and in
like manner there will be a great deficience of fluid in e<f>. But in order
to form some estimate of the proportion of the redundant fluid which
will be lodged in 68, let the communication between Ef and the ground
be taken away, as well as that by which Bd is electrified ; and let so much
fluid be taken from BS, as to make the redundant fluid therein equal to
the deficient fluid in E(j>. If we suppose that all the redundant fluid is
collected in 68, and all the deficient in e<f>, so as to leave Bd and Ef satu-
rated; then, if the electric repulsion is inversely as the square of the
distance, a particle of fluid placed anywhere in the plane bd, except near
the extremities b and d, will be attracted with very near as much force
by the redundant matter in etf>, as it is repelled by the redundant fluid
in 68 ; but if the repulsion is inversely as some higher power than the square,
it will be repelled with much more force by 68, than it is attracted by e<f>,
provided the depth 68 is very small in respect of the thickness of the glass;
and if the repulsion is inversely as some lower power than the square, it
will be attracted with much more force by e<j>, than it is repelled by 68.
Hence it follows, that if the depth to which the fluid can penetrate is
very small in respect of the thickness of the glass, but yet is such that
the quantity of fluid naturally contained in 68, or e<f>, is considerably more
than the redundant fluid in B&; then, if the repulsion is inversely as the
square of the distance, almost all the redundant fluid will be collected
in 68, leaving the plate Bd not very much overcharged; and in like manner
Ef will be not very much undercharged : if the repulsion is inversely as
some higher power than the square, Bd will be very much overcharged,
and Ef very much undercharged : and if the repulsion is inversely as some
lower power than the square, Bd will be very much undercharged, and
Ef very much overcharged.

133] Suppose, now, the plate Bd to be separated from the plate of glass,
still keeping it parallel thereto, and opposite to the same part of it that it
before was applied to; and let the repulsion of the particles be inversely
as some higher power of the distance than the square. When the plate
is in contact with the glass, the repulsion of the redundant fluid in that
plate, on a particle in the plane bd, id est, the inner surface of the plate,
must be equal to the excess of the repulsion of the redundant fluid in 68
on it, above the attraction of E<f) on it; therefore, when the plate Bd is
removed ever so small a distance from the glass, the repulsion of the
redundant fluid in the plate, on a particle in the inner surface of that
plate, will be greater than the excess of the repulsion of 68 on it, above the
attraction of E(f>; for the repulsion of 68 will be much more diminished
by the removal, than the attraction of E<f>: consequently, some fluid will
fly from the plate to the glass, in the form of sparks: so that the plate
will not be so much overcharged when removed from the glass, as it was

Penetration into glass 79

when in contact with it. I should imagine, however, that it would still
be considerably overcharged.

If one part of the plate is separated from the glass before the rest, as
must necessarily be the case, if it consists of bending materials, I should
guess it would be at least as much, if not more, overcharged, when sepa-
rated, as if it is separated all at once.

In like manner, it should seem that the plate Ef will be considerably
undercharged, when separated from the glass, but not so much so as when
in contact with it.

From the same kind of reasoning I conclude, that if the repulsion is
inversely as some lower power of the distance than the square, the plate Bd
will be considerably undercharged, and Ef considerably overcharged, when
separated from the glass, but not in so great a degree as when they are
in contact with it.

X34] § 7- There is an experiment of Mr Wilcke and ^Epinus, related
by Dr Priestly, p. 258, called by them, electrifying a plate of air: it
consisted in placing two large boards of wood, covered with tin plates',
parallel to each other, and at some inches asunder. If a communication
was made between one of these and the ground, and the other was
positively electrified, the former was undercharged; the boards strongly
attracted each other; and, on making a communication between them,
a shock was felt like that of the Leyden vial.

I am uncertain whether in this experiment the air contained between
the two boards is very much overcharged on one side, and very much
undercharged on the other, as is the case with the plate of glass in the
Leyden vial ; or whether the case is, that the redundant or deficient fluid
is lodged only in the two boards, and that the air between them serves
only to prevent the electricity from running from one board to the other :
but whichever of these is the case, the experiment is equally conformable
to the theory*.

It must be observed, that a particle of fluid placed between the two
plates is drawn towards the undercharged plate, with a force exceeding
that with which it would be repelled from the overcharged plate, if it was
electrified with the same force, the other plate being taken away, nearly
in the ratio of twice the quantity of redundant fluid actually contained
in the plate, to that which it would contain, if electrified with the same
force by itself ; so that, unless the plate is very weakly electrified, or their
distance is very considerable, the fluid will be apt to fly from one to the
other, in the form of sparks.

J35] § 8. Whenever any conducting body as A, communicating with
the ground, is brought sufficiently near an overcharged body B, the electric

[* See Articles 344, 345, 511, 516.]

80 First published Paper on Electricity

fluid is apt to fly through the air from B to A, in the form of a spark:
the way by which this is brought about seems to be this. The fluid placed
anywhere between the two bodies, is repelled from B towards A , and will
consequently move slowly through the air from one to the other: how it
seems as if this motion increased the elasticity of the air, and made it
rarer: this will enable Ihe fluid to flow in a swifter current, which will
still further increase the elasticity of the air, till at last it is so much
ratified, as to form very little opposition to the motion of the electric fluid,
upon which it flies in an uninterrupted mass from one body to the other.
In the same manner may the electric fluid pass from one body to
another, in the form of a spark, if the first body communicates with the
ground, and the other body is negatively electrified, or in any other case
in which one body is strongly disposed to part with its electricity to the
air, and the other is strongly disposed to receive it.

136] In like manner, when the electric fluid is made to pass through
water, in the form of a spark, as in Signor Beccaria's* and Mr Lane's f
experiments, I imagine that the water, by the rapid motion of the electric
fluid through it, is turned into an elastic fluid, and so much ratified as to
make very little opposition to its motion: and when stones are burst or
thrown out from buildings struck by lightning, in all probability that effect
is caused by the moisture in the stone, or some of the stone itself, being
turned into an elastic fluid.

137] It appears plainly, from the sudden rising of the water in Mr
Kinnersley's electrical air thermometer J, that when the electric fluid
passes through the air, in the form of a spark, the air in its passage is
either very much rarified, or intirely displaced: and the bursting of the
glass vessels, in Beccaria's and Lane's experiments, shews that the same
thing happens with regard to the water, when the electric fluid passes
through it in the form of a spark. Now, I see no means by which the
displacing of the air or water can be brought about, but by supposing its
elasticity to be increased, by the motion of the electric fluid through it,
unless you suppose it to be actually pushed aside, by the force with which
the electric fluid endeavours to issue from the overcharged body: but I
can by no means think, that the force with which the fluid endeavours
to issue, in the ordinary cases in which electric sparks are produced, is
sufficient to overcome the pressure of the atmosphere, much less that it
is sufficient to burst the glass vessels in Beccaria's and Lane's experiments.

138] The truth of this is confirmed by Prop. XVI. For, let an under-
charged body be brought near to, and opposite to the end of a long
cylindrical body communicating with the ground, by that proposition the

* Elettricismo artificial e naturale, p. no. Priestly, p. 209.

f Phil. Trans. 1767, p. 451.

{ Phil. Trans. 1763, p. 84. Priestly, p. 216.

The electric spark 8 1

pressure of the electric fluid against the base of the cylinder is scarcely
greater than the force with which the two bodies attract each other,
provided that no part of the cylinder is undercharged; which is very
unlikely to be the case, if the electric repulsion is inversely as the square
of the distance, as I have great reason to believe it is ; and, consequently,
if the spark was produced by the air being pushed aside by the force with
which the fluid endeavours to issue from the cylinder, no sparks should
be produced, unless the electricity was so strong, that the force with
which the bodies attracted each other was as great as the pressure of the
atmosphere against the base of the cylinder: whereas it is well known,
that a spark may be produced, when the force, with which the bodies
attract, is very trifling in respect of that*.

139] One may frequently observe, in discharging a Leyden vial, that
if the two knobs are approached together very slowly, a hissing noise will
be perceived before the spark; which shews, that the fluid begins to flow
from one knob to the other, before it passes in the form of a spark; and
therefore serves to confirm the truth of the opinion, that the spark is
brought about in the gradual manner here described.

[* Note 10, p. 375.]

C P. I.

PRELIMINARY PROPOSITIONS

[From the MS. in the possession of the Duke of Devonshire, N°. 4 ; hitherto

unpublished.]

{See Table of Contents at the beginning of this volume.}

In this and all the following propositions and lemmata the electric attraction
and repulsion is supposed to be inversely as the square of the distance.

140] PROP. XXIX. Let a thin circular plate be connected to a globe [of the
same diameter] placed at an infinite distance from it by a straight canal of
incompressible fluid such as is described in Pr. XIX, perpendicular to the plane
of the plate and meeting it in its center, and let them be overcharged.

If we suppose that part of the redundant fluid in the plate is spread uni-
formly, and that the remainder is disposed in its circumference, and that the
part which is spread uniformly is to that which is disposed in the circumference
as p to one, the quantity of redundant fluid in the plate will be to that in the
globe as p + i to 2p + i.

For by Prop. XXII, Cor. V, the force with which that part of the redundant
fluid in the plate which is disposed in the circumference repels the fluid in the
canal is the same with which an equal quantity placed in the globe repels it in
the contrary direction, and the repulsion of that part which is spread uniformly
is the same as that of twice that quantity placed in the globe, and therefore the
repulsion of a quantity of fluid equal to p + i disposed in the plate as expressed
in the proposition is equal to that of the quantity 2p + i placed in the globe.

141] PROP. XXX. Fig. i. Let two equal thin circular plates AB and ab
communicate with each other, and also with a third circular plate EF of the
same size and shape and placed at an infinite distance from them, by the straight
canal CD of incompressible fluid. Let the three plates be all parallel to each

T)

Fig. i.

other and be placed so that CD shall pass through their centers and be per-
pendicular to their planes, and let the plates be overcharged. The quantity of
redundant fluid in each of the plates AB and ab will be to that in EF as the
repulsion of the plate ab on the canal cD to the sum of the repulsions on cD

Ratios of capacities 83

and fD (cf being taken equal to cC), supposing that the redundant fluid in all
three plates is disposed in the same manner.

For first, as the plates AB and ab are at an infinite distance from any other
over or undercharged body, the repulsion of A B on the canal Cc in one direction
must be equal to that of ab on it in the contrary, and therefore the redundant
fluid in AB must be equal to that in ab.

Secondly, the sum of the repulsions of AB and ab on the canal cD must be
equal to that of EF on it in the contrary direction, as otherwise some fluid
must flow from ab to EF or from EF to ab. But as all three plates are of the
same size, and the fluid in them is disposed in the same manner, the repulsions
of EF and ab on cD will be to each other as the quantity of redundant fluid in
them, and therefore the quantity of redundant fluid in ab will be to that in EF
as the repulsion of ab on CD to the sum of the repulsions of AB and ab on it,
that is, as the repulsion of ab on cD to the sum of its repulsions on fD and cD,
for the repulsion of AB on cD is equal to the repulsion of ab on/D*.

142] COR. I. If the fluid in these plates is disposed in the same manner as
in Prop. XXIX the quantity of redundant fluid in each of the plates AB and ab
will be to that in EF as

AC(p+\) to ACQ + V+p (Ac - Cc) +

For by Lemma X the repulsion of a given quantity of fluid spread uniformly
over ab on the column cD; the repulsion of the same fluid on cf; the repulsion
of the same quantity of fluid collected in the circumference of the plate ab on
the column cD ; and the repulsion of the same fluid on cf are to each other as

, ac , ac ac2
ac; ac + cf — af; — and >,

2 2 2af

and therefore the whole repulsion of the plate ab on cD is to its repulsion on cf as

ac ... ac ac2

pxac+ 2 : p x (ac + cf- «/) + -_ —^

and therefore the repulsion of ab on cD is to the sum of its repulsions on cD
and/Z) as

acx(p + l):ac(2p+i)-p (ac + cf- af) - ™ + ?L,

acz
or as ac(p + $:ac(p + \}+p(af-cf) + —j.

143] COR. II. Therefore if all the redundant fluid in the plates is spread
uniformly, the redundant fluid in each of the plates AB and ab will be to that
in EF as AC : AC + Ac — Cc, and if it is all collected in the circumference, as

AC*

AC :AC + A~~.
Ac

144] COR. III. By Prop. XXIV it appears that the redundant fluid in the
plate AB or ab will bear the same proportion to that in EF though they com-

[* Note ii, p. 377.]

6—2

84 Preliminary Propositions

municate with EF by separate canals, and whether the canals by which they
communicate with it are straight or crooked, or in whatever direction EF is
placed in respect of them, provided the situation of AB and ab in respect of
each other remains the same. Only it must be observed that if the fluid in the
plates is not disposed so as to be in equilibrio, as will most likely be the case
if it is disposed as in the two preceding corollaries, it is necessary that the canals
should meet them in their centers, for if the fluid in a plate is not in equilibrio,
its repulsion on a canal of infinite length will not be the same in whatever part
the canal meets it, as it will if the fluid in the plate is in equilibrio.

145] LEMMA XII. Fig. 2. Let BA be an infinitely slender cylindric column
of uniform matter infinitely continued beyond A : the repulsion of a particle of

C

Fig. 2.

matter K on this column in the direction BA is proportional to or may be
represented by -^ • supposing the size of the particle and [the] base of the
column to be given.

For draw KC perpendicular to AB continued, and let the point B flow
towards C, the fluxion of the repulsion of K on the column equals

-OT CB _ - KB'
KB* X KB ~ KB* '

the fluent of which, ^5 , is nothing when KB is infinite.
ti.ts

146] LEMMA XIII. Suppose now KC to represent an infinitely slender
cylindric column of uniform matter: the repulsion of KC on the infinite column
BA is to the repulsion of the same quantity of matter collected in the point C

tKC + KB^ KC
on the same column as the nat. log. of ^r^ — to -^ .

For the repulsion of all the matter therein, when collected at C, on BA is

KC
proportional to prp , and supposing the column CK to flow, the fluxion of its

O.D

CK' KC -L Kfl
repulsion on BA is equal to T*W, the fluent of which is the nat. log. of - — ^= ,

and is nothing when CK is nothing.

147] LEMMA XIV. The repulsion of CK on a particle at B, in the direction

CK
CB, is proportional to -—& ^ , supposing the base of CK and the size of

f\LJ X ' / '

the particle B to be given.

Repulsion by columns 85

For supposing CK to flow, the fluxion of its repulsion on B in the direction
CB is proportional to ^rg-2 x VR> ^e fluent °f which is ,^p rr> . and is

nothing when CK is nothing.

148] LEMMA XV. Fig. 3. Let GEFHMN be a cylinder whose bases are
GEF and HMN and whose axis is CK. Let the convex surface of this cylinder
be uniformly coated with matter, and let GC be small in respect of CK. Let

Fig. 3-

GA be a diameter of the base produced, and D any point therein. The repulsion
of the convex surface of the cylinder on the point D in the direction CD is very
nearly the same as if all the matter therein was collected in the axis CK and
spread uniformly therein.

For let MED and meD be two planes infinitely near to each other, parallel
to CK and passing through D, and cutting the convex surface in ME and NF
and in me and nf, which will consequently be right lines equal to each other
and perpendicular to ED; and draw CP perpendicular to ED.

The repulsion of NnfF on D in the direction CD is proportional to

Ff x FN PD Ee x EM PD
pD ;un x rff • ancl tliat °* MmeE ls proportional to ^ ^^ x -

Ff Ee

But Ff is to Ee as FD to ED, therefore ^^ and v^. are each equal to

^=- = nf: — , therefore the sum of the repulsions of MmeE and NnfF
ru + L.L) 2rL)

is proportional to

(Ff+Ee)CKxPD / i _i_\ _ (Ff + Ee)CK /_i_ _i_\
2.PD x CD \ND + MD) 2CD \ND """ MDj '

But the repulsion of the same quantity of matter collected in CK is proportional

(Ff+ Ee) x CK
- — ~ — -

to

2 , „„ I

x -~~. , and, as CG is small in respect of CK, +

86 Preliminary Propositions

2 *
differs very little from -&-=: , therefore the sum of the repulsions of MmeE and

NnfF is very nearly the same as if all the matter in them was collected in CK,
and consequently the repulsion of the whole convex surface of the cylinder will
be very nearly the same as if all the matter in it was collected in CK.

149] COR. Therefore if BA represents an infinitely thin cylindric column
of uniform matter infinitely extended beyond A, the repulsion of the convex
surface of the cylinder thereon in the direction BA is very nearly the same as
if all the matter therein was collected in CK, and therefore is to the repulsion
of the same quantity of matter collected in the point C thereon very nearly as

CK + KB . CK zCK A CK "

nat. log. — ^rs -- to -^D> that is very nearly as nat. log. -^- to ^ • In

like manner the repulsion on the infinite column DA is to the repulsion of the

4- KD CK
same quantity of matter collected in C very nearly as nat. log. — ^== — to ^ .

150] PROP. XXXI. Fig. 3. Let the cylinder GEFHMN be connected to
the globe W, whose diameter is equal to GB and whose distance from it is
infinite, by a canal TR of incompressible fluid of any shape, and meeting the
cylinder in any part, and let them be overcharged: the quantity of redundant
fluid in the cylinder will be to that in the globe in a less ratio than that of CK

to nat. log. -^=- , and in a greater ratio than that of -= to nat. log. -~5 •

provided CB is small in respect of CK.

By Prop. XXIV the quantity of redundant fluid in the cylinder will bear
* As neither MD nor ND differ from KD by so much as CB, it is plain that

II 2

j-fri + TFVJ cannot differ from -=^j= in so great a proportion as that of BC to KD,

but in reality it does not differ from it in so great a ratio as that of CB2 to KD1,
but as it is not material being so exact, I shall omit the demonstration. See A. I.
[From MS. " A. i "] Demonstration of note at bottom of page 8,
CB = r, CP = b, PF = d, PD = a, CR* + CD* = ea,
b* - d* = /», e2 - /2 = g*.

*-*+£

g e "*" e3 '

ND* = CR* + a* - 2ad + d* = e°- - b* - 2ad + d* = e* - f* - 2ad
- g2 - 2ad,
g2 + 2nd,

I ad

g + g3 + 3 2g& _ 2

I ad a*d* ~g

g g3
2 /» aW _2 b* a*d* _ d*

which is less than

2 b* d* _ 2

~~

e e3 e* ~~ e e3

Comparison of charges 87

the same proportion to that in the globe in whatever part the canal meets the
cylinder, therefore first I say the redundant fluid in the cylinder will bear a

C ' K

greater proportion to that in the globe than that of - _„ to nat. log.

For let the canal TR be straight and perpendicular to BL, and let it meet
the cylinder in R, the middle point of the line BL, and let it, if produced, meet
the axis in S, which will consequently be the middle point of CK; then, if the
redundant fluid in the cylinder was spread uniformly on its convex surface,
the quantity of redundant fluid therein would be to that in the globe very nearly

CK . . . CK
as to nat. log. .

For in that case the repulsion of the cylinder on the canal RT would be to
the repulsion of the same quantity of redundant fluid collected in C very nearly

2SK . SK CK . CK

as nat. log. -=^- to •=„• or as nat. log. -^ to —^ , and the force with which
o/v jJK Co 20/3

the globe repels the canal in the direction TR is the same with which a quantity
of redundant fluid equal to that in the globe placed at S would repel it in the
contrary direction.

But there can be no doubt but that almost all the redundant fluid in the
cylinder will be collected on its surface, and also will be collected in greater
quantity near the ends than near the middle, consequently the repulsion of the
cylinder on RT will be less than if the redundant fluid was spread uniformly
on its convex surface, and therefore the quantity of redundant fluid in it will
bear a greater proportion to that in the globe than it would on that supposition.

Secondly, the quantity of fluid in the cylinder will bear a less proportion

to that in the globe than that of -^-^ to nat. log. _

For suppose the canal to meet the cylinder in B and to coincide with BA .
Then, if the redundant fluid was spread uniformly on the convex surface, the

C 'K
quantity therein would be to that in the globe very nearly as -^-= to nat. log.

O/5

-7^-5- , and the real quantity of redundant fluid in it will bear a less proportion
CD

to that in the globe than if it was spread uniformly on the convex surface.

151] COR. Therefore the quantity of redundant fluid in the cylinder is to
that in a globe whose diameter equals CK in a ratio between that of 2 to nat.

2CK CK*

log. -^o- and that of i to nat. log. -^ .

152] PROP. XXXII. Fig. 4. Let ADFB and adfb be two equal cylinders
whose axes are EC and ec, let them be parallel to each other and placed so that
Cc, the line joining the ends of the axes, shall be perpendicular to the axes,
and let the lines EC and fb be bisected in G and g, and let them be connected
by canals of incompressible fluid of any shape to a third cylinder of the same
size and shape placed at an infinite distance from them, and let them be over-

[* Note 12, p. 382.]

88 Preliminary Propositions

charged : the quantity of redundant fluid in each of them will be to that in the

third cylinder in a ratio between that of log ^ to log ^ + log — T^T- and

2EC . 2EC EC + Eb

that of log -_„- to log y,R + log — ^r — , provided the redundant fluid in

the third cylinder is disposed in the same manner as in the other two.

C JS

JO

Fig. 4.

For let us suppose that ADFB and adfb are connected to the third cylinder
by the canal GM, then, if the redundant fluid in each cylinder is disposed
uniformly on its convex surface, the sum of the repulsions of ADFB and adfb
on the canal gM will be to the repulsion of the third cylinder thereon (supposing
the quantity of redundant fluid in it to be equal to that in each of the two others)
2EG . , EG + Eg ,_ ,__.2EG

as log 7^- + log -

to log

"Gg b CB •

Let us now suppose the fluid in the first two cylinders to be disposed so as
to be in equilibrio, and consequently to be disposed in greater quantity near
their extremities than near their middles, and let the fluid in the third cylinder
be disposed in the same manner, and be the same in quantity as before. The
repulsion of ADFB on Gg will be diminished in a greater ratio, and consequently
its repulsion on gM will be diminished in a less ratio than that of adfb on gM,
consequently the sum of the repulsions of ADFB and adfb on gM will be
diminished in a less ratio than that of the third cylinder thereon, and therefore
the sum of the repulsions of ADFB and adfb on gM will be to that of the third
cylinder thereon in a greater ratio than that of

2.EG EG

log - + log —

Eg ^ 2EG
to log - .

Therefore the real quantity of redundant fluid in each of the first two
cylinders will be to that in the third cylinder in a less ratio than that of
2EG 2EG EG + Eg

In like manner, by supposing them to be connected to the third cylinder
by the canal bD, it may be shewn that the quantity of redundant fluid in either
of the first two cylinders is to that in the third in a greater ratio than that of

2EC . 2EC EC + Eb*

log -rrr to log -j^- + log

CB

CB

Cb

[* Note 13, p. 388.]

Equidistant concave plates

89

153] PROP. XXXIII. If two bodies B and b are successively connected by
canals of incompressible fluid to a third body C placed at an infinite distance
from them, and are overcharged, that is, if one of them, as B, is first con-
nected to G and afterwards B is removed and b put in its room, the quantity
of redundant fluid in C being the same in both cases, it is plain that the quantity
of redundant fluid in B will bear the same proportion to that in b that it would
if B and b were placed at an infinite distance from each other, and connected
by canals of incompressible fluid.

154] LEMMA XV. Fig. 5. Let AB be a thin flat plate of any shape what-
soever, of uniform thickness and composed of uniform matter. Let CG be an
infinitely slender cylindric column of uniform matter perpendicular to the plane
of AB and meeting it in C and extended infinitely beyond G. Let ab be a thin
circular plate perpendicular to cG whose center is c. Let the area of ab be equal
to that of AB, and let the quantity of matter in it be the same, and let it be
disposed uniformly.

Fig. 5-

Let B be that point of the circumference of AB which is nearest to C. If
EC is small in respect of CB, the repulsion of the plate AB on the short column
EC is to the repulsion of ab on the infinite column cG nearly as EC to cb.

For let BD be a circle drawn through B with center C, as EC is very small
in respect of CB, the repulsion of the circle BD on EC is to its repulsion on CG
very nearly as EC to CB, and therefore is to the repulsion of ab on cG very
nearly as EC to cb. But the repulsion of AB on EC is very little greater than
that of DB, for the repulsion of DB is very near as great as it would be if its
size was infinite.

155] LEMMA XVI. {Fig. 6.} Let ACB and DEF be two thin plates, not flat
but concave on one side, let their distance be everywhere the same, and let it be
very small in respect of the radius of curvature of all parts of their surface.
Let C be any point of the surface of AB, and let CE be perpendicular to the
surface in that point. Let Tt be a flat plate perpendicular to CE.

Let R be any point in AB and S the corresponding point in DF, and let T

9o

Preliminary Propositions

be the corresponding point in Tt*: the sum of the repulsions of R on the column
CE in the direction CE and of S on the same column in the opposite direction
EC is very nearly equal to the force with which they would repel the same
column in the direction CE if they were both transferred to T, provided CR*

Fig. 6.

•

is very small in respect of the square of the least radius of curvature of the
surface of AB.

Let RS be continued till it meets CE continued in V, draw EM and SN
perpendicular to CR.

Let CM = C,RE-RM = E, SC - NC = S, and SE - NM = D.

As CE is very small in respect of the least radius of curvature of AB, and
CV is not less than the least radius of curvature, CM and NR are each very
small in respect of CR, and therefore CN, MR, and ES differ from CR in a
very small ratio. Moreover as CR2 is very small in respect of CF2, CM2 and
RN2 are very small in respect of CE2, and therefore ME and NS differ in a very

CE2
small ratio from CE ; and, moreover, 2 x (TE — TC) is greater than ==- .

Now the repulsion of the point R on the column CE in the direction CE is

_ A jffr f?r*

r = ^7; ™ , and the repulsion of the point 5 on the same column

RC RE RC x RE

SC — SE
in the opposite direction is ^^r — ~p-, and the sum of the repulsions of R

oO X o jC-

and S is

RE-RC SC -SE E-C

RC x RE

SC x SE
E

RC x RE

S

S + C-D

SC x SE'
D

C

C

~ RC x RE ^ SC x SE ^ SC x SE RC x RE ^ SC x SE'

* If RS is drawn perpendicular to the surface of A B at the point R cutting DF
in S, I call S the corresponding point of the plate DF, and if CT is taken in the
intersection of the plane RCE with that of the plate Tt equal to the right line CR,
I call 2" the corresponding point of Tt.

f Lemma XII [Art. 145].

Corresponding points 9 1

and the repulsion of the two particles when transferred to T on the column CE,

TE — TC
or the repulsion of T, as I shall call it for shortness, is 2 ~rr — ^ .

But as ME differs in a very small ratio from CE, and RM differs in a very
small ratio from RC, RE - RM or E differs in a very small ratio from TE — TC.
In like manner SC — NC or S differs in a very small ratio from TE — TC, and
ER and CS both differ in a very small ratio from TE, and SE differs in a small
ratio from TC.

Therefore =7; ^p + c-^~r-cr differs very little from 2 x == — =^ , that

RC x RE SC + SE 7 E x TC

is, from the repulsion of T.

Moreover, as EM and SN differ very little from each other, D is very small in
respect of TE — TC, and ^ ^= is very small in respect of the repulsion of T.

.. RC - SE . CM + RN CE , RE - SC .

Moreover, — ^^ — is less than =^ or than -^=-7 , and jj^ is

KL KL L V Kt.

RM - CN , RC -SE

hardly greater than - , and is therefore still less than ^^ ;

Kc, A.C

RC RE

therefore =-=- and ^ each differ from one in a less ratio than that of CE to

o/i oO

RC x RE

CV, and therefore ^= — - differs from one in a less ratio than that of 2CE
SE x SC

toCV.

r C C -C f RC x ~

Consequently, - ^-^ + ^-^ or ^^^ x (i - g

^= ^

SE x SC

is

less than ^^ =-= x -^^ , which is less than

KL x Kh Lv -^

CE x RC zCE 2CE*

x

CV x RC x RE CV CV2 x RE '

zCE2
which is very small in respect of ~=. ™ 5^ , that is, of the repulsion of T.

/ / , X ./ O X i \ i '.

Therefore the sum of the repulsions of R and S differs very little from the
repulsion of T.

N.B. Though the distance CR is ever so great, it may be shewn that the
sum of the repulsions of R and 5 cannot be more than double that of T*.

156] COR. I. Let the edges of the plates ACB and DBF correspond, that is,
let them be such that if a line is erected on any part of the circumference of
one plate perpendicular to the [tangent] plane of the plate in that part, that
line shall meet the other plate in its circumference. Let the two plates be of
an uniform thickness, and let the thickness of DF bear such a proportion to
that of AB that the quantity of matter shall be the same in both. Consequently
the quantity of matter in each part of DF will be very nearly equal to that in
the corresponding part of AB. Also let the size of the plates be such that CE

[* Note 14, p. 389.]

92 Preliminary Propositions

shall be very small in respect of the distance of C from the nearest part of the
circumference of AB, and let the least radius of curvature of the surface of AB
be so great in respect of CE that a point R may be taken such that CR shall
be small in respect of that radius of curvature, and yet very great in respect
of CE.

Let Pp be a flat circular plate whose center is G and whose plane is per-
pendicular to GZ, and let its area be equal to that of AB, and let the quantity
of matter in it be also equal to that in AB, and let it be disposed uniformly:
the sum of the repulsions of AB and DF on CE in the opposite directions CE
and EC will be to the repulsion of Pp on the infinite column GZ very nearly
as 2CE to GP.

For suppose each particle of matter in all that part of AB whose distance
from C is not greater than CR and in the corresponding part of DF to be
transferred to its corresponding point in Tt, so as to form a circular plate whose
radius is CR.

If we suppose thJt the thickness of the plates Tt and Pp are both equal to
that of AB, the matter in all parts of Tt will be very nearly twice as dense as
that in AB or as that in Pp. Therefore the repulsion of Tt on CE will be very
nearly twice the repulsion of Pp on Gg, supposing Gg to be equal to CE.

But from the foregoing lemma it appears that the sum of the repulsions
which the above-mentioned part of AB and DF exerted on CE before the
matter was transferred is very nearly equal to that which Tt exerts thereon
after the matter is transferred, and the sum of the repulsions of the remaining
part of AB and DF, or that whose distance from C is greater than CR, is very
small in respect of that part whose distance is less, therefore the sum of the
repulsions of the whole plates AB and DF on CE is to the repulsion of Pp
on GZ very nearly as 2.CE to GP.

It may perhaps be supposed from this demonstration that it would be
necessary that CE should be excessively small in respect of CV, in order that
the sum of the repulsions of the plates on CE should be very nearly equal to
the repulsion of Pp on Gg, but in reality this seems not to be the case, for if
the plates are segments of concentric spheres whose center is V, the sum of
their repulsions will exceed twice the repulsion of Pp on Gg in a not much

CE
greater ratio than that of i + ^. to i, and if the radius of curvature of their

surfaces is in some places greater than CV, and nowhere less, I should think
that the sum of their repulsion could hardly exceed twice the repulsion of Pp
in so great a ratio as that.

157] COR. II. If we now suppose that the matter of the plate AB is denser
near the circumference than near the point C, and that the density at and
near C is to the mean density (or the density which it would everywhere be of
if the matter was spread uniformly) as S to one, and that the quantity of matter
in each part of DF is equal to that in the corresponding part of AB as before,
the sum of the repulsions of the plates on CE will be less than if the matter

Concave plate compared with flat one 93

was spread uniformly in a ratio approaching much nearer to that Of 8 to one
than to that of equality.

For if any particle of matter is removed from that part of AB which is
near C to that point which is at a distance from it, and an equal alteration is
made in the plate DF, the sum of the repulsions of these particles will be much
less after their removal than before.

158] LEMMA XVII. Fig. 7. Let ACB be a thin plate, not flat but concave
on one side, let the radius of curvature of its surface be nowhere less than CV,
and let M V be perpendicular to its surface at C; let MC be very small in respect
of CV, and let Tt be a plane perpendicular to MC: the difference of the repulsion

of any particle of matter as R in the plate ACB on the point M in the direction
CM, and of its repulsion on the point C in the same direction, is very nearly
the same as if the particle was transferred to T (CT being equal to the right
line CR), provided CR is small in respect of CV.

Draw RN perpendicular to MC, the difference of the repulsions of R on the

. _ MN CN MC CN CN ,._

points M and C = 3 - = 3 + - -3 , and the difference of the

MC

but

+

repulsions of the same particle placed at T on the same points =
MR* = (MC + CAT)2 + RN2

= MC2 + CR2 + 2MC x CN
= MT2 + 2MC x CN,

CR2
and CN is not greater than —~~ , and therefore zMC x CN is not greater than

MC x CR2
— -^= -- , and therefore is very small in respect of CR2 or MT2.

O Y

Therefore MR2 differs very little from MT2, and TT™ from
This being premised there are two cases to be considered.

94 Preliminary Propositions

First, if CR is considerably greater than MC, as
CR> - MR* - MC- - 2MC x CN = MR* x {i - *ejJg+_2OV) J ,

i i I 3MC(MC + 2CN)\

£^3 differs not much from ^-3 x |i - - - MRi

CN CN . CN - iMC (MC + zCN)

,
and

MR* ~ CR*

MC - 3CN (MC + zCN) , MC

or from x - — V™ — • wnicn is very small in respect of ^p ,

provided CR is small in respect of CV.

CR*

For as CN is less than -?=-. ,
20 r

3CN (MC + 2CN) . 3CR* x MC

2M#2 2

"CF" 4CF2'
Therefore as j™ - =™ is very small in respect of ^^ , and as

x C7 4Mfl2 x CF2 '
3MC 3C#2
""

differs very little from , 3 + 3-3. or the difference of the

AfC
repulsions of R on the points M and C differs very little from JTTJ^ , the

difference of the repulsions of T on the same points.

Secondly, if CR is not considerably greater than MC, CN must be very
small in respect of CR, and consequently must be very small in respect of MC.

Therefore p™ - T™ is very small in respect of , and therefore the

MC
difference of the repulsions of R on C and M differs very little from

159] COR. Therefore by the same method of reasoning as was used in Cor.
to Lemma XVI, the difference of the repulsions of the whole plate ACB on
the points M and C is very nearly the same as if each particle of matter in it
was transferred to the plane Tt and placed at the same distance from C as
before, and therefore its repulsion on M is very nearly equal to its repulsion
on C, provided MC is very small in respect of the least distance of the circum-
ference of the plate from C, and that the thickness of the plate is everywhere
very nearly the same, except at such a distance from C as is very great in
respect of MC.

160] PROP. XXXIV*. Fig. 8. Let NnvV be a plate of glass or any other
substance which does not conduct electricity, of uniform thickness, either flat,
or concave on one side and convex on the other, and let the electric fluid be
unable to penetrate at all into the glass or to move within it.

Let ACB and DEF be thin coatings of metal, or any substance which
conducts electricity, applied to the glass.

* This proposition is nearly the same as Prop. XXII, only made more general.

Theory of a coated plate 95

Let these coatings be of any shape whatsoever, and let their edges correspond
as in Lemma XVI, Cor. I.

Let AB communicate with the body H, and DF with the body L, by the
straight canals CG and EM of incompressible fluid.

Let the points C and E be so placed that the two canals shall form one right
line perpendicular to A B at the point C, and let the lengths of these canals be so

w

71

Fig. 8.

great that the repulsion of the coatings on the fluid in them shall be not sensibly
less than if they were infinite, and let H be overcharged and let L be saturated.

It is plain from Prop. XII that DF will be undercharged, and that AB will
be more overcharged than it would otherwise be.

Let Ww be a thin flat circular plate whose center is C, perpendicular to CE,
and whose area is equal to that of AB, let the force with which the redundant
fluid in AB would repel the short column CE (if ME was continued to C) be
called m, and let the force with which it would repel CM, or with which it repels
CG (for they are both alike), be called M. Let the force with which the same
quantity of redundant fluid disposed in DF, in the same manner in which the

deficient fluid therein is actually disposed, would repel \pr\ be called * , let

the force with which the same quantity of redundant fluid uniformly disposed
on Ww would repel CG be called W, and let the force with which H repels CG
be the same with which a quantity of fluid, which we will call B, uniformly
distributed on Ww would repel it in the contrary direction: then will the

GW
quantity of redundant fluid in AB be B x ,-j ~ — , which, if M and G

Mg + Gm — mg

are very nearly alike, and m and g are very small in respect of G, differs very

BW

little from - , and the deficient fluid in DF will be to the redundant fluid
g+ m

in AB as M — m to G, and therefore on the same supposition will be very
nearly equal to it.

For the force with which AB repels the fluid in EM must be equal to that
with which DF attracts it, for otherwise some fluid would run out of DF into L,
or out of L into DF. For the same reason the excess of the repulsion of AB
on CG above the attraction of DF thereon must be equal to the force with which
a quantity of redundant fluid equal to B spread uniformly on Ww would repel it.

g 6 Preliminary Propositions

By the supposition the force with which AB repels the canal EM is M — m,
and the force with which the same quantity of redundant fluid, spread on DF
in the same manner in which the deficient fluid therein is actually disposed,
repels it is G, therefore if the redundant fluid in A B is called A, the deficient

fluid in DF will be A x — ~ - ; therefore the force with which DF attracts

Cr

CG is (G — g) — T*—~ • and the excess of the force with which AB repels CG

above that with which DF attracts it is

(G-g) (M-m) _ Mg+Gm-mg

G G

which must be equal to the force with which a quantity of fluid equal to B

T>

spread uniformly over Ww would repel it, that is, it must be equal to W j ;

BGW
therefore A equals Mg+Gm_mg-

161] COR. I. If the plate of glass is flat, and its thickness is very small in
respect of the least distance of the point C from the circumference of AB, and
the fluid in AB and DF is spread uniformly, the quantity of redundant fluid

B x CW
in DF will differ very little from — ^g— , and the deficient fluid in DF will

be very nearly equal to the redundant fluid in AB.

For as the plate of glass is flat, the two coatings will be equal to each other,
and therefore M and G are equal to each other, and so are m and g, and

CE*
s.. differs very little from prp- , and moreover g is very small in respect of G.

162] COR. II. If the plate is flat and the two coatings are circular, their
centers being in C and E, the quantity of redundant fluid in AB will be more

B x CW CW

accurately equal to - g^— x cw _ cj~ , CV being in this case equal to the

semi-diameter of the coatings, and the deficient fluid in DF will be to the
redundant in AB nearly as CW - CE to CW.

For in this case ^ is accurately equal to

CW-VCE*+CW*

CW

and therefore _

2m _ m? 2CEVCW*+CE*-2CE*
W Wz~ CW*

which, if CE is small in respect of CW, differs very little from

2CE (CW - CE)
CW>

* Lemma XV [Art. 148.]

Coated plate compared with globe 97

163] COR. III. If the plate of glass is not flat, and its thickness is very
small in respect of the radius of curvature of its surface at and near C, every-
thing else being as in Cor. I, the quantity of redundant fluid in AB will still

B x CW
be very nearly equal to

For as CE is very small in respect of the radius of curvature, the two
coatings will be very nearly of the same size, and therefore G differs very little
from M , and m + g is to W very nearly as CE to CW*, and moreover m and g
are both very small in respect of M and G f.

164] COR. IV. If we now suppose that the density of the redundant fluid
in AB is greater at its circumference than it is near the point C, and that its
density at and near C is less than the mean density, or the density which it
would everywhere be of if it was spread uniformly, in the ratio of 8 to one,
and that the deficient fluid in DF is spread nearly in the same manner as the
redundant in AB, the quantity of redundant fluid in AB will be greater than
before in a ratio approaching much nearer that of one to 8 than to that of
equality, and that whether the glass is flat or otherwise.

For by Lemma [XVI, Cor. II], m and g will each be less than before in the
above-mentioned ratio.

165] COR. V. Whether the plate of glass is flat or concave, or whatever
shape the coatings are of, or whatever shape the canals CG and EM are of,
or in whatever part they meet the coatings, provided the thickness of the plate
is very small in respect of the smallest diameter of the coatings, and is also
sufficiently small in respect of the radius of curvature of its surface in case it
is concave, the quantity of redundant fluid in AB will differ very little from
B x CW
2.CE '

For suppose that the canal GC meets the coating AB in the middle of its
shortest diameter, and that the point in which ME meets DF is opposite to L,
as in Prop. [XXII, Art. 74], the thickness of the glass will then be very small
in respect of the distance of the point C from the nearest part of the circum-
ference of AB, and moreover, by just the same reasoning as was used in the
Remarks to Prop. XXII, it may be shewn that 8 will in all probability differ
very little from one, and consequently by Cors. I and III the redundant fluid
in AB will be as above assigned. But by Prop. XXIV the quantity of fluid in
the coatings will be just the same in whatever part the canals meet them, or
whatever shape the canals are of.

166] COR. VI. On the same supposition, if the body H is a globe whose
diameter equals Ww, id est the diameter of a circle whose area equals that of

* Lemma XVI. Cor.

t As the demonstration of the sixteenth Lemma and its corollary is rather
intricate, I chose to consider the case of the flat plate of glass separately in Cor. I,
and to demonstrate it by means of Lemma XV.

c. p. i. 7

98 Preliminary Propositions

the coating AB, the redundant fluid in AB will be to that in H very nearly as
CW to

For the quantity of redundant fluid in H will be 28.

167] COR. VII. On the same supposition the redundant fluid in AB will
be very nearly the same whether the glass is flat or otherwise, or whatever
shape the coatings are of.

168] COR. VIII. On the same supposition, if the size and shape of the
coatings and also the thickness of the glass is varied, the size and quantity of
redundant fluid in H remaining the same, the quantity of redundant fluid in
AB will be very nearly directly as its surface, and inversely as the thickness of
the glass.

169] PROP. XXXV (Fig. 9). Let Pp, Rr, Ss, Tt represent any number of
surfaces whose distance from Nn, and consequently from each other, is the
same in all parts, and let everything be as in the preceding proposition, except
that the fluid in the spaces PprR, SstT, &c., that is, in the spaces comprehended
between the surfaces Pp and Rr, and between 5s and Tt, &c. is moveable*, in
such manner, however, that though the fluid in any of these spaces as PprR
is able to move freely from Pp to Rr or from Rr to Pp, in a direction perpen-
dicular to the surface Pp or Rr, yet it is not able to move sideways, or in a

Fig. 9.

direction parallel to those surf aces f, and let the fluid in the remaining spaces
NnpP, RrsS, TtvV, &c. be immoveable: the quantity of redundant fluid in AB
and the deficient fluid in DF will be very nearly the same that they would be
if the whole fluid within the glass was immoveable, and its thickness was only
equal to NP + RS + TV, &c., that is, to the sum of the thicknesses of those
spaces in which the fluid is immoveable, provided that NV, the thickness of
the glass, is very small in respect of the smallest diameter of AB, and also in
respect of the radius of curvature of the surface of the glass.

* To avoid confusion I have drawn in the figure only two spaces in which the
fluid is supposed to be moveable, but the case would be just the same if there were
ever so many.

t [Note 15.]

Theory of conducting strata in glass plate 99

Let the canals GC and EM be perpendicular to the plate of glass and opposite
to each other, so as to form one right line, and let them meet AB and DF in
the middle of their shortest diameters. The coating AB will be very much
overcharged, and DF almost as much undercharged, in consequence of which
some fluid will be driven from the surface Pp to Rr and from 5s to Tt. Moreover
the quantity of fluid driven from any portion of the surface Pp near the line
CE will be very nearly equal to the quantity of redundant fluid lodged in the
corresponding part of AB, or more properly will be very nearly equal to a mean
between that and the quantity of deficient fluid in the corresponding part of DF.

For a particle of fluid placed anywhere in the space PprR near the line CE
is impelled from Pp to Rr by the repulsion of AB and the attraction of DF,
and it is not sensibly impelled either way by the spaces SstT, &c., as the attraction
of the redundant matter in Ss is very nearly equal to the repulsion of the re-
dundant fluid in Tt; and moreover the repulsion of AB on the particle and the
attraction of DT are very nearly as great as if their distance from it was no
greater than that of Pp and Rr, and therefore the particle could not be in
equilibrio unless the quantity of fluid driven from Pp to Rr was such as we have
assigned.

As to the quantity of fluid driven from Pp to Rr at a great distance from
CE, it is hardly worth considering. It is plain, too, that the quantity of fluid
driven from Ss to Tt will be very nearly the same as that driven from Pp to Rr.

Let now G, g, M, m and W signify the same things as in the preceding
proposition, and let the quantity of redundant fluid in AB be called A as
before, and let NP + RS + TV + &c., id est, the sum of the thicknesses of
those spaces in which the fluid is immoveable, be to NV, or the whole thickness
of the glass, as S to i, and let PR + ST + &c., or the sum of the thicknesses
of those spaces in which the fluid is moveable, be to NV as D to one.

Take £11 equal to PR, the repulsion of the space PprR on the infinite
column EM is equal to the repulsion of the redundant fluid in Rr on EH, and
therefore is to the repulsion of AB on CE very nearly as £11 or PR to CE.
Therefore the repulsion of all the spaces PprR, SstT, &c. on EM is to the
repulsion of A B on CE very nearly as D to one, or is equal to mD, and therefore
the sum of the repulsions of AB and those spaces together on EM is very nearly
equal to M — m + mD or to M — mS.

But the attraction of DF on EM must be equal to the above-mentioned sum
of the repulsions, and therefore the deficient fluid in DF must be very nearly

, . A(M-mS)
equal to — — ^ — - .

By the same way of reasoning it appears that the force with which CG is
repelled by AB, DF, and the spaces PprR and SstT, &c. together is very nearly

equal to

(M - mS) (G -g) Mg P mgS

M - — -! - gD, or to 6 + mS -- - - gD,

which, as M differs very little from G, and - is very small in respect of

7—2

IOO

Preliminary Propositions

mS or gS, is very nearly equal to g + mS — gD or to (g + m) S, therefore the

BW
quantity of redundant fluid in AB will be very nearly equal to , ~ ,

and will therefore be greater than if the fluid within the glass was immoveable
very nearly in the ratio of one to S, or will be very nearly the same as if the
thickness of the glass was equal to CE x S, and the fluid within it was im-
moveable.

170] PROP. XXXVI. Fig. 10. Let every thing be as in the preceding pro-
position, except that the electric fluid is able to penetrate into the glass on the
side Nn as far as to the surface Kk, and on the side Vv as far as to Yy ; in such
manner, however, that though the fluid can move freely from A B to aft or from

Fig. 10.

a/3 to AB, and also from DF to &<f> or from 8<f> to DF, in a direction perpen-
dicular to those surfaces, yet it is unable to move sideways, or in a direction
parallel to those surfaces: the quantity of redundant fluid on one side of the
glass, and of deficient fluid on the other, will be very nearly the same as if the
spaces NnkK and VvyY were taken away and the coatings AB and DF were
applied to the surfaces Kk and Yy.

For by [Art. 132] of former Part, almost all the redundant and deficient
fluid will be lodged on the surfaces a/3 and S<f>, and the coatings AB and DF
will be not much over or undercharged. Now if the whole of the redundant
and deficient fluid was lodged in a/3 and S(f>, it is evident that the quantity of
redundant and deficient fluid would be exactly the same as if the spaces NnkK
and VvyY were taken away, and therefore it will in reality be very nearly the
same.

171] COR. I. Therefore the quantity of redundant fluid on the positive side
of the glass, that is, in the coating AB, and the space AaftB together, as well
as the quantity of deficient fluid on the negative side of the glass, will be very
nearly the same that they would be if the fluid was unable to penetrate into

Penetration of glass by charge 101

the glass or move within it, and that the thickness of the glass was equal only
to the sum of the thicknesses of those spaces in which the fluid is immoveable.

172] COR. II. Whether the electric fluid penetrates into the glass or not, it
is evident that the quantity of redundant fluid on one side the glass, and of
deficient fluid on the other, will be very nearly the same, whether the coatings
are thick or thin.

173] PROP. XXXVII. It was shewn in the remarks on Prop. XXII in the
first Part, that when the plate of glass is flat, and the fluid within it is im-
moveable, the attraction of the deficient fluid in DF makes the redundant fluid
in A B to be disposed more uniformly than it would otherwise be. Now if we
suppose the fluid within the glass to be moveable as in the preceding proposition,
and that the deficient fluid in the planes Pp, Ss, &c. and the redundant fluid
in the planes Rr, Tt, &c. is equal to, and disposed similarly to that in DF, the
redundant fluid in AB will be disposed more uniformly than it would be if the
fluid within the glass was immoveable, and its thickness no greater than the
sum of the thicknesses of those spaces in which the fluid is immoveable.

For let the intermediate spaces be moved so that Tt shall coincide with Vv
and Rr with Ss, &c., but let the distance between Tt and Ss and between Rr
and Pp, &c. remain the same as before, that is, let the thickness of the spaces
in which the fluid is moveable remain unaltered. The distance of Pp from Nn
will now be equal to the sum of the thicknesses of the spaces TtVv, RrSs, NnPp,
&c. in which the fluid is immoveable.

Now, after this removal, the effect of the planes Tt and DF and of Rr and
Ss, &c. will destroy each other, so that the intermediate spaces and DF together
will have just the same effect in rendering the redundant fluid in AB more
uniform than the plane Pp alone will have, that is, the fluid in AB will be
disposed in just the same manner as if the thickness of the glass was no greater
than the sum of the thicknesses of the spaces in which the fluid is immoveable,
and the whole fluid within the glass was immoveable.

But the effect of the intermediate spaces in making the fluid in AB more
uniform was greater before their removal than after, for the effect of the two
planes Pp and Rr together, and also that of Ss and Tt together, &c. is the
greater the nearer they are to AB.

174] COR. The redundant and deficient fluid in the intermediate spaces will
in reality be not exactly equal and similarly disposed to that in DF, and in all
probability the quantity of deficient fluid disposed near the extremity of DF
will be greater than that in the corresponding parts of Pp, Ss, &c., or than the
redundant fluid in the corresponding parts of Rr, Tt, &c., so that the redundant
fluid in AB will perhaps be disposed rather less uniformly than it would be if
the deficient and redundant fluid in those spaces was equal to and similarly
disposed to that in DF; but on the whole there seems no reason to think that
it will be much less, if at all less, uniformly disposed than it would be if the thick-
ness of the glass was equal to the sum of the thicknesses of the spaces in which
the fluid is immoveable, and the whole fluid within the glass was immoveable.

IO2 Appendix to Preliminary Propositions

APPENDIX: FROM MS. NO. 5.

175] As the following propositions are not so necessary towards under-
standing the experiment as the former, I chose to place them here by way of
appendix.

PROP. I. Let everything be as in Prop. XXXIV, except that the bodies
H and L are not required to be at an infinite distance from the plates of glass;
let now an overcharged body N be placed near the glass in such manner that
the force with which it repels the column CG towards G shall be to that with
which it repels the column EM towards M as the force with which the deficient
fluid in DF attracts the column CG is to that with which it attracts EM: it
will make no alteration in the quantity of redundant fluid in AB, provided thu
repulsion of N makes no alteration in the manner in which the fluid is disposed
in each plate.

For increase the deficience of fluid in DF so much as that that coating and N
together shall exert the same attraction on EM as DF alone did before, they
will also exert the same attraction on CG as DF alone did before, and conse-
quently the fluid in the two canals will be in equilibrio.

176] COR. In like manner, if the forces with which the body N repels the
columns CG and EM bear the same proportion to each other as those with
which the plate AB repels those columns, and therefore bear very nearly the
same proportion to each other as those with which EM repels those columns,
the quantity of deficient fluid in DF will be just the same as before N was
brought near, and the redundant fluid in AB will be diminished by a quantity
whose repulsion on CG is the same as that of N thereon.

Therefore, if the repulsion of N on CG is not greater than that of H thereon,
the diminution of the quantity of redundant fluid in AB will bear but a very
small proportion to the whole. For the quantity of redundant fluid in AB is
many times greater than that which would be contained in it if DF was away,
id est, than that whose repulsion on CG is equal to the repulsion of H thereon
in the contrary direction.

177] PROP. II. From the preceding proposition and corollary we may con-
clude that if the force with which N repels the columns CG and EM bears very
nearly the same proportion to each other as the force with which DF attracts
those columns, the quantity of redundant fluid in AB will be altered by a
quantity which will bear but a very small proportion to the whole, unless the
repulsion of N on CG is much greater than that of H thereon.

If the reader wishes to see a stricter demonstration of this proposition, as
well as to see it applied to the case in which the fluid is supposed moveable in
the intermediate spaces, as in Prop. XXXV, he may read the following:

178] PART i. Take Ee = £ thickness of those spaces in which the fluid is
moveable, draw def equal and similar to DEF, and let the deficient fluid therein
be equal to that in DF: the repulsion of the intermediate spaces on EM is to the

Charge of condenser little affected by surroundings 103

difference of the attractions of DF on eAf and ep. (supposing Ee and M/j. to be
equal to CE) very nearly as twice EC to CE, and is therefore very nearly equal
to twice the difference of the attraction of df and DF on EM.

Fig. ioa.

In like manner the attraction of the intermediate spaces on CG is very
nearly equal to twice the difference of the attraction of DF and df thereon.

Suppose now the quantity of deficient fluid in DF to be increased in the
ratio of i + / to i, the redundant fluid in AB remaining the same as before, a
new attraction is produced on EM, very nearly equal to

/ x (attraction of DF on EM) - '- x 2 (diff. attr. of df and DF on EM),

that is, very nearly equal to/ x (attraction of df on EM).

In like manner a new attraction is produced on CG, very nearly equal to
/ x (attraction of df on CG), therefore, the new attraction produced on EM is
to that produced on CG very nearly as the attraction of df on EM is to its
attraction on CG, and therefore in order that the quantity of redundant fluid
in AB shall not be altered by the approach of N, the repulsion of N on EM
must be to its repulsion on CG very nearly as the attraction of df on EM to its
attraction on CG.

179] PART 2. Lp t the fluid within the glass be either moveable, as in Prop.
[XXXV, Art. 169], or let it be immoveable, and let the distance of H and L
from the glass be either great or not.

fCC (ff

Let the repulsion of H on | ,,,.. in direction GC be | „ , and let the sum

of these repulsions = S.

(GC in direction CG = A

Let the repulsion of ,/V on •[_.,,. ,. .. ,,,,, D, and let the repulsion

[EM in direction EM = B

which N should exert on CG in order that the redundant fluid in AB should
remain unaltered be to that which it should exert on EM : : i : P.

The quantity of redundant fluid in AB will be increased in the ratio of
B - PA i + p
S ~ P + p
from that of

B- PA

to i, which, if P differs very little from i, differs very little

i 4-

to i.

104 Appendix to Preliminary Propositions

For the force •! „ may be divided into two parts, namely

PA- B pA+ B
P+p " P+p
PpA + pB PpA + PB
P+p P+p

(pA + B
PpA + PB

\ f •
I P + p

, has no

tendency to alter the redundant fluid in AB, but the first part, or the force
PA -B

P + P (CG in direction CG

- PpA + pB a' 1 (EM in direction EM '

or -

P + p

{ -PA + B
P + P

(CG in direction GC

- PpA + pB a ;1 (EM in direction EM

to i.

P + p

(GC -PA + B
as they are to the repulsion of H on j ^ as — „ -- to H,

or as (- PA + B) J^-^ to S,

increases the redundant fluid in the ratio of

B- PA i + p
S P + p

180] COR. I. If the lengths of the columns CG and EM are such that the
repulsion and attraction of AB and DF on them are not sensibly less than if
they were of an infinite length, the attraction of DF on CG will be very nearly
equal to its attraction on EM, and therefore, if the forces with which N repels
the columns CG and EM are very nearly equal to each other, the quantity of
redundant fluid in AB will be very little altered thereby.

N.B. If the size of H is much greater than that of AB, it is possible that its
distance from the glass may be such as to exert a very considerable repulsion
on EM, and yet that the action of AB and DF on CG shall be not sensibly less
than if it was of an [infinite length],

181] COR. II. Let the bodies H and L be of the same size and shape and
at an infinite distance from the glass, and let the fluid be in equilibrio. Let
now an equal quantity of fluid be taken from H and L, the quantity of redundant
fluid in AB will be very little altered thereby.

For the repulsion of the whole quantity of fluid in L on the canal EM will
be as much diminished as that of H on CG, so that it comes to the same thing
as placing an overcharged body N in such manner that its repulsion on CG

Coated plates in communication little affected 105

shall be equal to that on EM; which by the preceding proposition will make
very little alteration in the quantity of redundant fluid in AB.

182] COR. III. Let the bodies H and L be at an infinite distance, and either
of the same or different size, and let the fluid be in equilibrio. Let now the body
H be brought so near to AB that its repulsion on GC shall be sensibly less than
before. The quantity of redundant fluid in A B will be very little altered thereby,
provided the repulsion of the two plates on the column CG is not sensibly
diminished.

For whereas when H was at an infinite distance from AB it exerted no
repulsion on EM, now it is brought nearer it does exert some, and its repulsion
on EM is very nearly equal to the diminution of its repulsion on CG, so that
it comes to the same thing as placing a body N in such manner as to repel EM
with very nearly the same force that it does CG in the contrary direction.

183] COR. IV. Let the body H be brought near A B as in the preceding
corollary, and let the fluid be in equilibrio; let now an overcharged body R
be placed near H, the quantity of redundant fluid in H must be so much
diminished, in order that the fluid may remain in equilibrio, supposing the-
fluid in AB to remain unaltered, as that the diminution of its repulsion on the
two columns GC and EM shall be equal to the repulsion of R on the same
columns. Consequently, if the repulsion of R on them is to the repulsion which
H exerted on them before the approach of R as n to i, the quantity of re-
dundant fluid in H will be diminished in the ratio of i — n to i.

For supposing the quantity of fluid in H to be thus diminished, I say, the
quantity of fluid in A will remain very nearly the same as before. For the
repulsion of H and R on the two columns will be the same as that of H was
before, but it is possible that their repulsion on GC may be a little less, and their
repulsion on EM as much greater than that of H was before, but this, by the
preceding corollaries, will make very little alteration in the quantity of fluid
inAB.

184] COR. V. It appears from Prop. XXIII that the repulsion of the
body R on the two columns GC and EM will be the same in whatever direction
it is placed in respect of H and the canal, provided its distance from the point G
is given, and consequently the diminution of the quantity of fluid in the body H
will be very nearly the same in whatever direction R is situated, provided its
distance from G is given.

185] COR. VI. Fig. n. Suppose now that instead of the body H there is
placed a plate of glass Kkil, coated as in Props. XXXIV and XXXV, with
the plates Tt and Ss, whereof Tt communicates with AB by the canal GC, and
the other 5s communicates by the canal gP with the body P, placed at an
infinite distance and saturated with electricity, and let AB and consequently
Tt be overcharged, and let the fluid be in equilibrio.

Suppose now that an overcharged body R is brought near the glass Kkil,
I say that the proportion which the redundant fluid in Tt bears to that in AB
will be very little altered thereby, supposing the length of the canal CG to be

io6

Appendix to Preliminary Proposition.1:

such that the repulsion of the coatings AB and DF thereon shall be not sensibly
less than if it was infinite, and that the thickness of the glass Gg is very small
in respect of the distance of R from it, and that the repulsion of R does not
sensibly alter the disposition of the fluid in Tt and Ss, and also that the re-

pulsion of R on GC and EM together is not much less than if GM was infinite,
and also not much greater than the repulsion of the glass NnvV on CG.

For let the quantity of fluid in Tt and Ss be so much altered that the united
repulsion of R and tihpse two coatings on the two canals GC and EM together,
and also their repulsion" *pn gP, shall be the same as that of the two coatings
alone before the approach oi 'i&

By Prop. II, Cor. i the quantity '.of fluid in Tt will be very little altered
thereby, for the repulsion of R on the c^anal gP is very nearly the same as its
repulsion on gC and EM together.

As the repulsion of Tt, Ss and R together von the two canals GC and EM
together is the same as before the approach of R, it follows that if their re-
pulsion on gC is less than before, their repulsion onh\M will be as much increased.

Let now the quantity of fluid in AB and DF be s-o much altered that their
repulsion on gC shall be as much diminished as that i of Kkil and R on the
same column is diminished, and that their repulsion on > EM shall be as much
diminished as that of Kkil and R on the same is increased-1, it is plain that the
fluid in ah1 three canals will be exactly in equilibrio, and' by the preceding
corollary the quantity of fluid in AB will be very little altered, and therefore
the proportion of the redundant fluid in AB and Tt to each ot her will be very
little altered*. V

186] COR. VII. By Prop. [XXIV, Art. 86] all which is saicfc in this pro-
position and corollaries holds good equally whether the canals Q7C, EM and
GP are straight or crooked.

LEMMA.
* [Note 16, p. 392.]

Testing large ami small circles by trial plate 1 07

187] Let DE be an uniform canal of incompressible fluid infinitely con-
tinued towards E, and let A and B be given points in a right line with D, and
let AB be bisected in C; the force with which any particle of fluid repels this
canal (supposing the repulsion to be inversely as the square of the distance)
is inversely as its distance from the point D, and therefore the sum of the forces
with which two equal particles of fluid placed in A and B repel this canal is to the
sum of the forces with which they would repel it if both collected in the point C,

I I . _2_

* AD + BD : CD '
or as C£>2 : CZ>2 - CB*,

CB*

or as i : i - =-^ .

188] Let us now examine how far the proportion of the quantity of fluid
in the large circle and the two small ones in Experiment V [Art. 273] Fig. 18,
bear to each other will be affected by the circumstances mentioned in [Art. 276],
supposing the plates to be connected by canals of incompressible fluid.

First it appears from Cor. [VII, Art. 186], that the quantity of redundant
fluid in the large circle, and also in the two small ones, will bear very nearly
the same proportion to that in the jar A as it would if it had been placed at an
infinite distance from A, for the distance of the plate from the jar was in neither

Fig. 18.

experiment less than 63 inches, and neither the length nor the diameter of the
coated part of the jar exceeded four inches, so that the repulsion of the jar on
the canal connecting it to the plate could not differ by more than ^ part from
what it would be if the canal was infinitely continued, and would most probably
differ from it by not more than J or ^ part of that quantity*; for the same

* The repulsion of a globe 4 inches diameter on a straight uniform canal of
incompressible fluid extending 63 inches from it differs by only ^ part from what
it would be if the canal was infinitely continued, but the repulsion of a Leyden
vial of that size on the same column differs probably not more than J or J of that
quantity from what it would be if infinitely continued.

io8 Appendix to Preliminary Propositions

reason the deficience of fluid in the trial plate will bear very nearly the same
proportion to that in the jar, &c. as it would if it had been placed at an infinite
distance from it.

• It is plain that if the plates had been placed at such a distance from the jar
that the quantity of fluid in them had been considerably less than if they had
been placed at an infinite distance, still the quantity in the large circle would
bear very nearly the same proportion to that in the two small ones as it would
if they had been placed at an infinite distance.

189] Secondly, it is plain that in trying the large circle, the repulsion of
that circle increases the deficience of fluid in the trial plate, and the attraction
of the trial plate increases the redundance in the circle. Now the repulsion of
the plate Ee on the canal mMNa, and the attraction of the trial plate T on
rRSA (supposing mMNa and rRSA to be infinitely continued beyond a and A)
are by [Cor. IV, Art. 183] very nearly the same as if the redundant fluid in Ee
and the deficient fluid in T were both collected in the centers of their respective
plates, and the quantity of redundant fluid in Ee may be considered as equal
to the deficient in T, and consequently the repulsion of Ee on mMNa is very
nearly equal to the attraction of T on rRSA. Moreover, the repulsion of Ee
on its own canal rRSA must be equal to the attraction of T on mMNa, as the
jars with which they communicate are both equally electrified, and therefore,
by Cor. [IV], the quantity of redundant fluid in Ee will be increased in very
nearly the same ratio as the deficient in T.

190] In like manner, in trying the two small circles, the quantity of re-
dundant fluid in them is increased in very nearly the same ratio as the deficient
in T, for as half the distance of the two circles never bore a greater proportion
to em than that of 18 to 72, the repulsion of the two circles on the canal mMNa
will be very nearly the same, and the deficience of fluid in T will be increased
in very nearly the same ratio as if all the redundant fluid in them were collected
in e, the middle point between them.

The quantity of redundant fluid in Bb indeed will be increased in a rather
greater ratio, and that in Cc in a rather less ratio than if it was placed at e,
but the ratio in which the quantity of fluid in Bb is increased must very nearly
as much exceed that in which it would be increased if it was placed at e as that
in which Cc is increased falls short of it, as the attraction of T on the canal
fRSA exceeds that on rRSA by nearly the same quantity as its attraction
gRSA falls short of it, and therefore the quantity of redundant fluid in both
circles together is increased in very nearly the same proportion as that in a
circle placed in e would be, and consequently the redundance in the two circles
is increased in very nearly the same ratio as the deficience in the trial plate.

191]* The attraction of the trial plate on the canals fRSA and gRSA and the
repulsion of the circles Bb and Cc on the canal mMNu is very nearly the same as
if the deficient or redundant fluid in the plates was collected in the center of their
respective plates, and therefore the repulsion of the circles Bb and Cc on the canal

* Memorandum relating to the second article.

Affect of floor and walls of the room 109

tnMNn is inversely as the distances of their centers from m, and the increase of the
quantity of redundant fluid in the circles Bb and Cc by the attraction of T is in
the same proportion.

Therefore take the point a so that the repulsion of a particle at a on that canal
shall be a mean between the repulsions of the same particle thereon when placed
at B and C, the charge of T will be increased in the same proportion as it would be
by the repulsion of a plate containing as much redundant fluid as the two plates
together whose center was a, and the charge of the two circles together will also be
increased in the same proportion as that of the circle whose center is a would be
thereby.

192] Consequently, in trying either the large circle or the two small ones,
the trial plate must be opened to very nearly the same surface to contain the
same charge as them as it must be if they were placed at an infinite distance
from the trial plate, and consequently no sensible alteration can be produced
in the phsenomena of the experiment by the repulsion and attraction of the
circles and trial plate on each other.

193] Thirdly, for the same reason it appears that as the circles and the trial
plate are both at much the same distance from the ground and walls of the room,
no sensible alteration can be produced in the experiment by the ground near
the circles being rendered undercharged and that near the trial plate over-
charged.

It must be observed, indeed, that the distance of the circles and trial plate
from the ground is much less than their distance from each other, and conse-
quently the alteration of the charge of the two circles and trial plate produced
by this cause will not be so nearly alike as that caused by their attraction and
repulsion on each other; but as, on the other hand, the whole alteration of their
charge produced by this cause is, I imagine, much less than that produced by
the other, I imagine that this cause can hardly have a more sensible effect in
the experiment than the preceding.

194] Fourthly, we have not as yet taken notice that the canals by which
the jars A, a communicate with the ground are but short, and meet the ground
at no great distance from the jars.

But it may be shewn by the same kind of reasoning used in Prop. [II,
Art. 178], with the help of the second corollary to the preceding proposition,
that the quantity of redundant fluid in the circles will bear very nearly the same
proportion to that in the positive side of the jar A, whether the canal by which
A communicates with the ground is long or short.

Besides that, if it was possible for this circumstance to make much alteration
in the proportion which the redundant fluid in the circles bears to that in A ,
it would in all probability have very nearly the same effect in trying the two
small circles as in trying the large one, so that no sensible alteration can be
produced in the experiment from this circumstance.

It appears, therefore, that none of the above-mentioned circumstances can
cause any sensible alteration in this experiment*.

* [Note 17, p. 394.]

THOUGHTS CONCERNING ELECTRICITY

[From MS. N° 10: probably an early draft of the theory.]
{See Table of Contends at the beginning of this volume. J

195] Electricity seems to be owing to a certain elastic fluid inter-
spersed between the particles of bodies, and perhaps also surrounding the
bodies themselves in the form of an atmosphere.

196] This fluid, if it surrounds bodies in the form of an atmosphere,
seems to extend only to an imperceptible distance from them*, but the
attractive and repulsive power of this fluid extends to very considerable
distances.

197] That the attraction and repulsion of electricity extend to con-
siderable distances is evident, as corks are made to repel by an excited
tube held out at a great distance from them. That the electric atmospheres
themselves cannot extend to any perceptible distance, I think, appears
from hence, that if two electric conductors be placed ever so near together
so as not to touch, the electric fluid will not pass rapidly from one to the
other except by jumping in the form of sparks, whereas if their electric
atmospheres extended to such a distance as to be mixed with one another,
it should seem as if the electricity might flow quietly from one to the other
in like manner as it does through the pores of any conducting matter.

But the following seems a stronger reason for supposing that these
atmospheres cannot extend to any perceptible distance from the body
they surround, for if they did it should seem that two flat bodies whenever
they were laid upon one another should always become electric thereby,
for in that case there is no room for the electric atmosphere to extend to
any sensible distance from those surfaces of the bodies which touch one
another, so that the electric fluid which before surrounded those surfaces
would be forced round to the opposite sides, which would thereby become
overcharged with electricity, and consequently appear electrical, which is
contrary to experience.

198] Many Electricians seem to have thought that electrified bodies
were surrounded with atmospheres of electric matter extending to great
distances from them. The reasons which may have induced them to think
so may be first, that an electrified body affects other bodies at a con-
siderable distance. But this may, with much more probability, be supposed

* There are several circumstances which shew that two bodies, however smooth
and strongly pressed together, do not actually touch each other. I imagine that
the distance to which the electric atmospheres, if there are any, extend must be
less than the smallest distance within which two bodies can be made to approach.

Conductors in communication ill

owing to the attraction and repulsion of the electric matter within the
body or close to its surface. And, secondly, because a body placed near
a positively electrified body receives electricity itself, whence it is supposed
to receive that electricity from the electrified body itself, and therefore
to be within its atmosphere. But, in all probability, the body in this case
receives its electricity from the contiguous air, and not immediately from
the electrified body, as will be further explained in its place.

199] Let any number of bodies which conduct electricity with perfect
freedom be connected together by substances which also conduct elec-
tricity. It is plain that the electric fluid must be equally compressed * in
all these bodies, for if it was not, the electric fluid would move from those
bodies in which it was more compressed to those in which it was less
compressed till the compression became equal in all. But yet it is possible
that some of these bodies may be made to contain more than their natural
quantity of electricity, and others less. For instance, let some power be
applied to some of these bodies which shall cause the electric fluid within
their pores to expand and grow rarer f, those bodies will thereby be made
to contain less electric matter than they would otherwise do, but yet the
electric matter within them will be just as much compressed as it would
be if this power were not applied.

On the other hand, if some power were applied which shall diminish
the elasticity of the electric fluid within them and thereby make it grow
more dense, those bodies will be made to contain more electricity, but
yet the compression will remain still the same.

200] To make what is here said more intelligible, let us suppose a long
tube to be filled with air, and let part of this tube, and consequently the
air within, be heated, the air will thereby expand, and consequently that
part of the tube will contain less air than it did before, but yet the air in
that part will be just as much compressed as in the rest of the tube.

In like manner, if you suppose the electric fluid to be not only confined
within the pores of bodies, but also to surround them in the form of an
atmosphere, let some power be applied to some of those bodies which
shall prevent this atmosphere from extending to so great a distance from

* Note by Editor. [That is, must sustain an equal pressure. In modern scientific
language the words compression, extension, distortion, are used to express strain,
or change of form, while pressure, tension, torsion, are reserved to indicate the
stress or internal force which accompanies this change of form. Cavendish uses the
word compression to indicate stress. The idea is precisely that of potential.]

•f [No such power has been discovered. There is nothing among electrical
phenomena analogous to the expansion of air by heat. — ED.] {Nowadays the free
electrons in a metal, or on a large scale in an incandescent star, are often treated
theoretically as constituting the molecules of a gaseous medium, responding to
change of temperature. It is interesting to compare the text with electron theories
of conductance and equilibrium. j

1 1 2 "Thoughts concerning Electricity

them, those bodies will thereby be made to contain less electricity than
they would otherwise do, but yet the electric fluid that surrounds them
will be just as much compressed as it would [be] if that power was not
applied.

It will surely be needless to warn the reader here not to confound
compression and condensation.

201] I now proceed to my hypothesis.

DEF. i. When the electric fluid within any body is more compressed
than in its natural state, I call that body positively electrified: when it
is less compressed, I call the body negatively electrified.

It is plain from what has been here said that if any number of con-
ducting bodies be joined by conductors, and one of the bodies be positively
electrified, that all the others must be so too.

DEF. 2. When any body contains more of the electric fluid than it
does in its natural state, I call it overcharged. When it contains less,
I call it undercharged.

202] HYP. ist. Every body overcharged with electricity repels an
overcharged body, and attracts an undercharged one.

HYP. 2nd. Every undercharged body attracts an overcharged body,
and repels an undercharged one.

HYP. 3rd. Whenever any body overcharged with electricity is brought
near any other body, it makes it less able to contain electricity than before.

HYP. 4th. Whenever an undercharged body is brought near another
it makes it more able to contain electricity.

203] COR. I. Whenever any body at a distance from any other
electrified body is positively electrified it will be overcharged, and if
negatively electrified it will be undercharged.

COR. II. If two bodies, both perfectly insulated, so that no electricity
can escape from them, be positively electrified and then brought near to
each other, as they are both overcharged they will each, by the action of
the other upon it, be rendered less capable of containing electricity, there-
fore, as no electricity can escape from them, the fluid within them will
be rendered more compressed, just as air included within a bottle will
become more compressed either by heating the air or by squeezing the
bottle into less compass; but it is evident that the bodies will remain
just as much overcharged as before.

204] COR. III. If two bodies be placed near together, and then equally
positively electrified, they will each be overcharged, but less so than they
would [be] if they had not been placed near together.

It may perhaps be said that this is owing to the electric atmosphere
not having so much room to spread itself when the two bodies are brought

Hypotheses regarding the electric fluid 1 1 3

near together as when they are at a distance; but I think it has already
been sufficiently proved that these atmospheres cannot extend to any
sensible distance from their respective bodies.

COR. IV. If two bodies are placed near together and then equally
negatively electrified, they will each be undercharged, but less so (id est,
they will contain more electricity) than if placed at a distance.

This phenomenon cannot be accounted for on the foregoing sup-
position.

205] COR. V. If a body overcharged with electricity be brought near
a body not electrified and not insulated, part of the electric fluid will be
driven out of this body, and it will become undercharged.

But if the body be insulated, as in that case the electric fluid cannot
escape from it, it will not become undercharged, but the electric fluid
within it will be more compressed than in its natural state, id est, the
body will become positively electrified, and will remain so as long as the
overcharged body remains near it, but will be restored to its natural state
as soon as the overcharged body is taken away, provided no electricity
has escaped during the meantime.

This is in effect the same case as that described in the 5th experiment
of Mr Canton's paper in the 48th vol. of [the Philosophical] Transactions,
p. 353, and is explained by him much in the same manner as is done here.

206] COR. VI. If a body positively electrified in such a manner that
if it is by any means made more or less capable of containing electricity,
the electric fluid shall run into it from without or shall run out of it, so
as to keep it always equally electrified, be brought near another body
not electrified and not insulated, the second body will thereby be rendered
undercharged, whereby the first body will become more capable of con-
taining electricity, and consequently will become more overcharged than
it would otherwise be with the same degree of electrification. This again
will make the second body more undercharged, which again will make the
first body more overcharged, and so on.

It must be observed here, that if the two bodies are brought so near
together that their action on one another shall be considerable, the
electricity will jump from one to the other; otherwise if the two bodies
were brought so near together that their distance should not be greater
than the thickness of the glass in the Leyden bottle, it seems likely that
the first body might receive many times as much additional electricity as
it would otherwise receive by the same degree of electrification ; and that
the second body would lose many times as much electricity as it would
by the same degree of negative electrification.

If the second body be negatively electrified, the same effect will be
produced in a greater degree.

c. P?I. 8

1 1 4 Thoughts concerning Electricity

It may also happen that the second body shall be made undercharged
though it is positively electrified, provided it be much less electrified than
the first body, and that the two bodies be placed near enough to each
other.

207] The shock produced by making a communication between the
two surfaces of the Leyden vial seems owing only to the glass prepared
in that manner containing vastly more electricity on its positive side than
an equal surface of metal equally electrified, and vastly less on its negative
side than the same surface of metal negatively electrified to the same
degree, so that if two magazines of electricity were prepared, each able
to receive as much additional electricity by the same degree of electrifi-
cation as one of the surfaces of a Leyden vial, and one of the magazines
was to be positively electrified and the other negatively, there is no doubt
but what as great a shock would be produced by making a communication
between the two magazines as between the two surfaces of the Leyden
vial.

I think, therefore, that the phenomena of the Leyden vial may very
well be accounted for on the principle of the 6th Corollary, for in the
Leyden vial the two surfaces of the glass are so near together, that the
electric matter on one surface may act with great force on that on the
other, and yet the electricity cannot jump from one surface to the other,
by which means perhaps the positive side may be made many times more
overcharged, and the negative side many times more undercharged, than
it would otherwise be.

208] HYP. 5th. It seems reasonable to suppose that when the electric
fluid within any body is more compressed than it is in the air surrounding
it, it will run out of that body, and when it is less compressed it will run
into the body.

COR. I. Let the body A , not electrified, be perfectly insulated, and let
an overcharged body be brought near it. The body A will thereby be
rendered less capable of containing electricity, and therefore the electric
fluid within it, as it cannot escape, will be rendered more compressed.
But the electricity in the adjoining air will, for the same reason, be also
compressed, and in all probability equally so, therefore the electricity will
have no disposition either to run in or out of the body.

COR. II. It is evidently the same thing whether A be insulated, or
whether it be not insulated, but electrified in such manner that the fluid
within it be as much compressed as it was before by virtue of the insula-
tion. Therefore if the body A be now not insulated, but positively
electrified, and an overcharged body be brought to such a distance from
it that the electric fluid in the adjacent air be equally compressed with
that in A, such a quantity of electricity will thereby be driven out of A
that it will retain only its natural quantity. So that A will be neither

Communication of electricity 1 1 5

overcharged nor undercharged, nor will the electricity have any disposition
to run either in or out of it.

209] If the overcharged body be now brought nearer, A will become
undercharged, and the electricity will run into it from the surrounding
air. If the overcharged body be not brought so near A will be overcharged,
and the electricity will run out of it. If an undercharged body be brought
near A it will become more overcharged than before, and the electricity
will run out stronger than before.

COR. III. If the body A be negatively electrified, and an undercharged
body be brought near it till the electric fluid in the adjoining air is as
much compressed as that in the body A, the electricity will have no dis-
position to run either in or out of A , nor will it be either overcharged or
undercharged, as will appear from the same way of reasoning as was
used with regard to the 2nd Corollary.

If the undercharged body be now brought nearer, A will become over-
charged, and the electricity will also run out of it. If the undercharged
body be removed farther off, A will become undercharged, and the elec-
tricity will also run into it. If an overcharged body be brought near to A,
it will become more undercharged than before, and the electricity will
also run in faster than before.

On the whole, therefore, it appears that whenever a body is under-
charged the electricity will run into it, and whenever it is overcharged it
will run out.

210] It has usually been supposed that two bodies, whenever the
electricity either runs into or out of both of them, repel each other ; but that
when it runs into one and out of the other, they attract. In the beginning
of this paper I laid down a different rule for the electric attraction and
repulsion, namely, that when the two bodies are both overcharged or both
undercharged they repel, but attract when one is overcharged and the
other undercharged.

But by what has been just said it appears that these two rules agree
together, or at least if they do differ, they differ so little that there is no
reason to think my rule will agree less with experiment than the other.

The reasoning here used would have been more satisfactory if the
bodies were capable of containing electricity only on one side, namely,
on that which is turned towards the other body. But I do not imagine,
however, that this will make much difference in the effect.

211] What has been here said holds good only in cases where the size
of the body A is small in respect of the distance of the electrified body
from it, so that the influence of the electrified body may be nearly the
same on all parts of the body A as is the case in bits of cork held near an
excited tube; but when the size of the body A is such that the influence

8—2

1 1 6 Thoughts concerning Electricity

of the electrified body may be much greater on that part of A which is
directly under it than on that which is farther removed from it, as is the
case in electrifying a prime conductor by an excited tube, then the case
is very different, for then on approaching the electrified tube, part of the
electric fluid will be driven away from that part of the prime conductor
which is nearest the excited tube to the remoter parts where its influence
is weaker, whereby that part of the conductor nearest the tube will be
undercharged, and consequently the compression of the electric fluid in
that part will be less than in the contiguous air, consequently some electric
matter will flow into it from the adjoining air, whereby the conductor
will be overcharged, and therefore on taking away the tube will be posi-
tively electrified.

Thus if the excited tube or other electrified body is not brought within
a certain distance, the conductor receives its electricity only from the
contiguous air, as was before said, and not immediately from the electrified
body; but if the body be brought near enough, the electric matter jumps
from the electrified body to the conductor in form of a spark.

212] The means by which this is brought about seems thus — When
the part of the conductor nearest the excited tube has received any
electricity from the contiguous air, that air will be undercharged, and will
receive electricity from the adjacent air between it and the tube, by which
means the electric matter will flow in gentle current between the particles
of air from the excited tube to the conductor. It seems now as if the
particles of air were by this means made to repel each other with more
force, and thereby to become rarer; this will suffer the electric fluid to
flow in a swifter current, which again will increase the repulsion of the
particles of air, till at last a vacuum is made, upon which the electric fluid
jumps in a continued body to the conductor.

213] That a vacuum is formed by the electric fluid when it passes in
the form of a spark through air or water appears, I think, from the violent
rising of the water in Mr Kinnersley's electrical air-thermometer (Priestley,
p. 216), and still more strongly from the bursting the vial of water, in
Mr Lane's experiment, by making the electrical fluid pass through the
water in the form of a spark.

If I am not much mistaken I have frequently observed, in discharging
a Leyden vial, that if the two knobs are approached together very gently,
a hissing noise may be perceived before the spark, which shews that the
electricity does begin to flow from one knob to the other before it moves
in the form of the spark, and may therefore induce one to think that the
spark is brought about in the gradual manner here described.

214] The attraction and repulsion of electrified bodies, according to
the law I have laid down, may perhaps be accounted for in the following

Attraction and repulsion 1 1 7

manner. Let a fluid consisting of particles mutually repelling each other,
and whose repulsion extends to considerable distances, be spread uni-
formly all over the globe, except in the space A , which we will suppose to
contain more than its proper quantity of the fluid. The fluid placed in
any space B within reach of the repulsion of A will be repelled from A
with more force than it will [be] in any other direction. But as it cannot
recede from A without an equal quantity of the fluid coming into its
room which will be equally repelled from A, it is plain that it will have
no tendency to recede from A , any more than a body of the same specific
gravity as water has any tendency to sink in water. Let now the space B
be made to contain more than its natural quantity of this fluid, it will
then really have a tendency to recede from A , or will appear to be repelled
by it, just as a body heavier than water tends to descend in it, and, on
the contrary, if B is made to contain less than its natural quantity of the
fluid, it will have a tendency towards A, or will appear to be attracted
by it.

215] Let now the space A be made to contain less than its natural
quantity of the fluid (as the fluid in B is now repelled from A with less
force than it is in any other direction, id est, apparently attracted towards
it), if B also contain less than its natural quantity of the fluid it will tend
to recede from A , id est, appear to be repelled by it ; but if B contain more
than its natural quantity, it will then tend to approach towards A , id est,
appear to be attracted by it.

216] If the electric fluid is diffused uniformly through all bodies not
appearing electrical and the repulsion of its particles extends to con-
siderable distances, it is plain that the consequences are such as are here
described ; but how far that supposition will agree with experiment I am
in doubt*.

* [Note 18, p. 397.]

[ "8 1

EXPERIMENTS ON ELECTRICITY

{See the reasoned summary of methods and results in the latter part of
Prof. Clerk Maxwell's 'Introduction.'}

{I.} EXPERIMENTAL DETERMINATION OF THE LAW OF
ELECTRIC FORCE.

[From MS. N°. 7: apparently prepared for publication. See Table of Contents
at the beginning of this volume.]

217] I now proceed to give an account of the experiments, in all of
which I shall suppose, according to the received opinion, that the elec-
tricity of glass is positive, but it is not at all material to the purpose of
this paper whether it is so or not, for if it was negative, all the experi-
ments would agree equally well with the theory.

218] EXPERIMENT I. The intention of the following experiment was
to find out whether, when a hollow globe is electrified, a smaller globe

inclosed within it and communicating with the outer one by some con-
ducting substance is rendered at all over or undercharged; and thereby
to discover the law of the electric attraction and repulsion.

Apparatus for experiment 'with globes \ 1 9

219] I took a globe 12-1 inches in diameter, and suspended it by a
solid stick of glass run through the middle of it as an axis, and covered
with sealing-wax to make it a more perfect non-conductor of electricity.
I then inclosed this globe between two hollow pasteboard hemispheres,
13-3 inches in diameter, and about -fa of an inch thick, in such manner
that there could hardly be less than •& of an inch distance between the
globe and the inner surface of the hemispheres in any part, the two
hemispheres being applied to each other so as to form a complete sphere,
and the edges made to fit as close as possible, notches being cut in each
of them so as to form holes for the stick of glass to pass through.

By this means I had an inner globe included within an hollow globe
in such manner that there was no communication by which the electricity
could pass from one to the other.

I then made a communication between them by a piece of wire run
through one of the hemispheres and touching the inner globe, a piece of
silk string being fastened to the end of the wire, by which I could draw it
out at pleasure.

220] Having done this I electrified the hemispheres by means of a
wire communicating with the positive side of a Leyden vial, and then,
having withdrawn this wire, immediately drew out the wire which made
a communication between the inner globe and the outer one, which, as
it was drawn away by a silk string, could not discharge the electricity
either of the globe or hemispheres. I then instantly separated the two
hemispheres, taking care in doing it that they should not touch the inner
globe, and applied a pair of small pith balls, suspended by fine linen threads,
to the inner globe, to see whether it was at all over or undercharged.

221] For the more convenient performing this operation, I made use
of the following apparatus. It is more complicated, indeed, than was
necessary, but as the experiment was of great importance to my purpose,
I was willing to try it in the most accurate manner.

ABCDEF and AbcDef (Fig. 12) are two frames of wood of the same
size and shape, supported by hinges at A and D in such manner that each
frame is moveable on the horizontal line AD as an axis. H is one of the
hemispheres, fastened to the frame ABCD by the four sticks of glass
Mm, Nn, Pp, and Rr, covered with sealing-wax, h is the other hemisphere
fastened in the same manner to the frame AbcD. G is the inner globe,
suspended by the horizontal stick of glass 5s, the frame of wood by which
Ss and the hinges at A and D are supported being not represented in the
figure to avoid confusion.

Tt is a stick of glass with a slip of tinfoil bound round it at x, the place
where it is intended to touch the globe, and the pith balls are suspended
from the tinfoil.

I 20 Determination of the law of electric force

The hemispheres were fixed within their frames in such manner that
when the frames were brought near together the edges of the hemispheres
touched each other all round as near as might be, so as to form a complete

c

Fig. 12.

sphere, and so that the inner globe was inclosed within them without
anywhere touching them, but on the contrary being at nearly the same
distance from them in all parts.

222] It was also so contrived, by means of different strings, that the
same motion of the hand which drew away the wire by which the hemi-
spheres were electrified, immediately after that was done, drew out the
wire which made the communication between the hemispheres and the
inner globe, and immediately after that was drawn out, separated the
hemispheres from each other and approached the stick of glass Tt to the
inner globe. It was also contrived so that the electricity of the hemi-
spheres and of the wire by which they were electrified was discharged as
soon as they were separated from each other, as otherwise their repulsion
might have made the pith balls to separate, though the inner globe was
not at all overcharged.

The inner globe and hemispheres were also both coated with tinfoil to
make them the more perfect conductors of electricity.

223] In trying the experiments a coated glass jar was connected to
the wire by which the hemispheres were electrified, and this wire was
withdrawn so as not to touch the hemispheres till the jar was sufficiently
charged. It was then suffered to rest on them for two or three seconds
and then withdrawn, and the hemispheres separated as above described.

224] An electrometer also was fastened to the prime conductor by

Results of experiment 'with globes 121

•

which the coated jar was electrified, by which means the jar and conse-
quently the hemispheres were always electrified in the same degree. This
electrometer as well as the pith balls will be described in [Arts. 244 and
248] ; the strength of the electricity was the same as was commonly used
in the following experiments, and is described in [Arts. 263, 329, 359, 520].

225] My reason for using the glass jar was that without it it would
have been difficult either to have known to what degree the hemispheres
were electrified or to have kept the electricity of the same strength for a
second or two together, and if the wire had been suffered to have rested
on the hemispheres while the jar was charging, I was afraid that the
electricity might have spread itself gradually on the sticks of glass which
supported the globe and hemispheres, which might have made some error
in the experiment.

226] From this manner of trying the experiment it appears:

First, that at the time the hemispheres are electrified, there is a perfect
communication by metal between them and the inner globe, so that the
electricity has free liberty to enter the inner globe if it has any disposition
to do so, and moreover that this communication is not taken away till
after the wire by which the hemispheres are electrified is removed.

Secondly, before the hemispheres begin to be separated from each
other, the wire which makes the communication between them and the
globe is taken away, so that there is no longer any communication between
them by any conducting substance.

Thirdly, from the manner in which the operation is performed, it is
impossible for the hemispheres to touch the inner globe while they are
removing, or even to come within T%ths of an inch of it.

And Fourthly, the whole time of performing the operation is so short,
that no sensible quantity of electricity can escape from the inner globe,
between the time of taking away the communication between that and
the hemispheres, and the approaching the pith balls to it, so that the
quantity of electricity in the globe when the pith balls are approached to
it cannot be sensibly different from what it is when it is inclosed within
the hemispheres and communicating with them.

227] The result was, that though the experiment was repeated several
times*, I could never perceive the pith balls to separate or shew any
signs of electricity.

228] That I might perceive a more minute degree of electricity in the
inner globe, I tried the experiment in a different manner, namely, before
the hemispheres were electrified, I electrified the pith balls positively,
making them separate about one inch. When the hemispheres were then
separated, and the tinfoil, x, brought in contact with the globe, and
[* Dec. 18-24, 1772, Arts. 512, 513, and April 4, 1773, Art. 562.]

I 2 2 Delicacy of the experiment

consequently the electricity of the pith balls communicated to the globe,
they still continued to separate, though but just sensibly. I then repeated
the experiment in the same manner, except that the pith balls were
negatively electrified in the same degree that they before were positively.
They still separated negatively after being brought in contact with the
globe, and in the same degree that they before did positively.

229] It must be observed that if the globe was at all overcharged the
pith balls should separate further when they were previously positively
electrified than when negatively, as in the first case the pith balls must
evidently separate further than they would do if the globe was not over-
charged, and in the latter case less.

Moreover, a much smaller degree of electricity may be perceived in
the globe by this manner of trying the experiment than the former, for
when the pith balls have already got a sufficient quantity of electricity
in them to make them separate, a sensible difference will be produced in
their degree of divergence by the addition of a quantity of fluid several
times less than what was necessary to make them separate at first. It is
plain that this method of trying the experiment is not just, unless the
hemispheres are electrified in nearly the same degree when the pith balls
are previously electrified positively as when negatively, which was pro-
vided for by the electrometer.

230] In order to find how small a quantity of electricity in the inner
globe might have been discovered by this experiment, I took away the
hemispheres with their frames, leaving the globe and the pith balls as
before. I then took a piece of glass, coated as a Leyden vial, which I
knew by experiment contained not more than Jyth of the quantity of
redundant fluid on its positive side that the jar by which the hemispheres
were electrified did, when both were charged from the same conductor.

I then electrified this coated plate to the same degree, as shewn by
the electrometer, that the jar was in the former experiment, and then
separated it from the prime conductor, and communicated its electricity
to the jar, which was not at all electrified. Consequently the jar contained
only ^th part of the redundant fluid in this experiment that it did in
the former, for the coated plate and jar together contained only 5Vth. and
therefore the jar alone contained only g^th.

By means of this jar, thus electrified, I electrified the globe in the same
manner that the hemispheres were in the former experiment, and im-
mediately after the electrifying wire was withdrawn, approached the pith
balls. The result was that by previously electrifying the balls, as in the
second way of trying the experiment, the electricity of the globe was
very manifest, as the balls separated very sensibly more when they were
previously electrified positively than when negatively, but the electricity

Discussion of the results as to law of force 123

of the globe was not sufficient to make the balls separate, unless they were
previously electrified.

It is plain that the quantity of redundant fluid communicated to the
globe in this experiment was less than ^th part of that communicated to the
hemispheres in the former experiment, for if the hemispheres themselves had
been electrified they would have received only ^th of the redundant fluid
they did before, and the globe, as being less, received still less electricity.

231] It appears, therefore, that if a globe 12-1 inches in diameter is
inclosed within a hollow globe 13-3 inches in diameter, and communicates
with it by some conducting substance, and the whole is positively elec-
trified, the quantity of redundant fluid lodged in the inner globe is certainly
less than g'^th of that lodged in the outer globe, and that there is no reason
to think from any circumstance of the experiment that the inner globe is
at all overcharged.

232] Hence it follows that the electric attraction and repulsion must
be inversely as the square of the distance, and that when a globe is posi-
tively electrified, the redundant fluid in it is lodged intirely on its surface.

For by Prop. V [Art. 20], if it is according to this law, the whole
redundant fluid ought to be lodged on the outer surface of the hemispheres,
and the inner globe ought not to be at all over or undercharged, whereas,
if it is inversely as some higher power of the distance than the square,
the inner globe ought to be in some degree overcharged.

233] For let ADB (Fig. 13) be the hemispheres and adb the inner globe,
and Aa the wire by which a com-
munication is made between them.
By Lemma IV [Art. 18], if the elec-
tric attraction and repulsion is in-
versely as some higher power of the
distance than the square, the re-
dundant fluid in ABD repels a
particle of fluid placed anywhere in
the wire A a towards the center, and
consequently, unless the inner globe
was sufficiently overcharged to pre-
vent it, some fluid would flow from
the hemispheres to the globe.

But if the electric attraction and
repulsion is inversely as some lower power of the distance than the square,
the redundant fluid in ABD impels the particle in the contrary direction,
that is, from the center, and therefore the inner globe must be undercharged.

234] In order to form some estimate how much the law of the electric
attraction and repulsion may differ from that of the inverse duplicate

Fig. 13-

124 Experiment with conductor of any form

ratio of the distances without its having been perceived in this experiment,
let AT be a diameter of the two concentric spheres ABD and abd, and let
A a be bisected in e. Ae in this experiment was about -35 of an inch and
Te 13-1 inches, therefore if the electric attraction and repulsion is inversely
as the 2 + ^'jjth power of the distance, it may be shewn that the force
with which the redundant fluid in ABD repels a particle at e towards the
center is to that with which the same quantity of fluid collected in the
center would repel it in the contrary direction as I to 57.

But as the law of repulsion differs so little from the inverse duplicate
ratio, the redundant fluid in the inner globe will repel the point e with
very nearly the same force as if it was all collected in the center, and
therefore if the redundant fluid in the inner globe is J7th part of that in
ABD the particle at e will be in equilibrio, and as e is placed in the middle
between A and a, there is the utmost reason to think that the fluid in the
whole wire A a will be so too. We may therefore conclude that the electric
attraction and repulsion must be inversely as some power of the distance
between that of the 2 + ^th and that of the 2 — ^th, and there is no
reason to think that it differs at all from the inverse duplicate ratio*.

235] EXPERIMENT II. A similar experiment was tried with a piece of
wood 12 inches square and 2 inches thick, inclosed between two wooden
drawers each 14 inches square and 2 inches deep on the outside, so as to
form together a hollow box 14 inches square and 4 thick, the wood of
which it was composed being -5 to -3 of an inch thick.

The experiment was tried in just the same manner as the former. I
could not perceive the inner box to be at all over or undercharged, which
is a confirmation of what was supposed at the end of Prop. IX [Art. 41]—
that when a body of any shape is overcharged, the redundant fluid is
lodged entirely on the surface, supposing the electric attraction and re-
pulsion to be inversely as the square of the distance f.

DEMONSTRATION OF COMPUTATIONS IN [ART. 234].

Let aef be a sphere, c its center, b any point within it, af a diameter,
plane perpendicular to af.

Let cb = a, ba = d, bf = s and ad = #, and let the
repulsion be inversely as the n power of the distance.
The convex surface of the segment Eae is to that of
the whole globe as ad : af, and therefore if the point d
is supposed to flow towards/, the fluxion of the surface
Eae is proportional to x, and the fluxion of its re-
pulsion on b in the direction dc is proportional to

Ee any

* [Note 19, p. 404.]

t [Art. 561.]

Mathematical computation for law of force 125

or may be represented thereby, but

be* = (d - x)2 + x (2a + 2d - x) = d* + 2ax,
therefore the fluxion of the repulsion is

*(*-*)

n+l'

(d* + 2ax) 2
the variable part of the fluent of which is

- 2ad - d2 d*

zax)

but when x is nothing, d2 + 2ax, or be2 = d2, and when x = af, or s + d, it = s2,
therefore the whole fluent generated while b moves from a to f is

2ad + d2 / i i \ d3~n — s3~"

2a* (n - i) W"-1 s"-1/ 2«2 (3 - «) '
but the repulsion of all the fluid collected in the center on b

_s + d
a" '

and a = —

2

and 2«rf + d2 = ds,

therefore the repulsion of the surface of the globe is to that of the same quantity
of fluid collected in the center as

ds s"-1 - d"-1 d3-" — s3-" 2 (s + d)

x -

sn-l_<fn-l d3-"-S3-" (S + d) 2"-l

(n - i) (ds)"~2 + 3 - n ' (s- d)n~*

n — i (ds)n~l 3~ n an~2 '

W-

or dividing by s3-11, as

n - 1 S-M ' ^ P'2 -P) •

supposing - to be called p.

[{II.} EXPERIMENTS ON THE CHARGES OF BODIES.]

[From MS. N03. 9 and 10: apparently prepared for publication.
See Table of Contents at the beginning of this volume.]

236] The intention of the remaining experiments was to find out the
proportion which the quantity of redundant fluid in bodies of several
different shapes and sizes would bear to each other if placed at a con-
siderable distance from each other and connected together by a slender
wire, or, which comes to the same thing, to find the proportion which the
quantity of redundant fluid in them would bear to each other if they
were successively connected by a slender wire to a third body placed at
a great distance from them, supposing the quantity of redundant fluid in
the third body to be the same each time; and to examine how far that
proportion agrees with what it should be by theory if the bodies were
connected by canals of incompressible fluid.

237] To avoid circumlocution I shall frequently in the following pages
make use of a term the meaning of which is given in the following definition.

DEF. When in relating any experiment in which two bodies B and b
were successively connected to a third body and overcharged, I say that
the charge of B was found to be to that of b as P to i, I mean that the
quantity of redundant fluid in B would have been to that in b in the above
proportion, provided the quantity of redundant fluid in the third body
was exactly the same each time, everything else being exactly the same
as in the experiment, that is, the bodies being situated exactly as in the
experiment. But when I say simply that the charge of one body is to that
of another in any particular proportion, for instance, when I say that the
charge of a thin circular plate is to that of a globe of the same diameter
as i to 1-57, I would be understood to mean that if the circular plate and
globe are successively connected to a third body by a thin wire the re-
dundant fluid in the plate would be to that in the globe in that proportion,
provided they were placed at a very great distance both from the third
body and from any other over- or undercharged matter, and that the
quantity of redundant fluid in the third body was exactly the same each
time.

238] The method I took in making these experiments was by com-
paring each of the two bodies I wanted to examine, or B and 6 as I shall
call them, one after another with a third body, which I shall call the trial
plate, in this manner. I took two Leyden vials and charged both of them
from the same conductor; I then electrified B positively by the inside of
one of the vials, and at the same time electrified the trial plate negatively
by the coating of the other vial. Having done this I tried whether the

On the comparison of charges 127

redundant fluid in B was more or less than sufficient to saturate the re-
dundant matter in the trial plate, by making a communication between
them by a piece of wire; for if the redundant fluid in B was more than
sufficient to saturate the redundant matter in the trial plate, they would
both be overcharged after the communication was made between them;
if, on the other hand, the redundant fluid in B was not sufficient to saturate
the redundant matter in the trial plate, they would be undercharged.
Having by these means found what size the trial plate must be made so
that the redundant matter in it should be just sufficient to saturate the
redundant fluid in B, I tried the body b in the same manner, and if I
found that it required the trial plate to be of the same size, in order that
the redundant matter in it should be just sufficient to saturate the re-
dundant fluid in b, I was well assured that if B and b were successively
made to communicate with a third body and positively electrified they
would each of them contain the same quantity of fluid, supposing the
quantity of redundant fluid in the third body to be the same each time;
that is, that the charge of B was equal to that of b.

Having thus given a general idea of the method I used, I proceed to
describe it more particularly.

239] The trial plates I made use of consisted of two flat tin plates
ABCD and abed (Fig. 15), made to slide one upon the other, so that by

making the side be of one plate extend more or less beyond the side BC
of the other it formed a plate of a greater or less size, and which conse-
quently contained more or less electricity*.

240] The apparatus used in making these experiments is represented
in Fig. 14, where the parallelogram T represents the trial plate and B one
of the bodies to b« compared together, each supported on non-conductors.
dDS is the wire for making a communication between them, having a

* [See table for trial plate at Art. 468.]

128

Experiments on the Charges of Bodies

Apparatus and mode of use \ 29

joint in it at D, where it is supported by a non-conductor, and where are
also hung two small pith balls to show whether B and T are over- or
undercharged after the communication is made between them. A and a
are the two vials; Ee is a wire communicating with the inside coating of
A , aCc a wire communicating with the same coating of a ; and Ff and Gg
are wires fastened to the outside coating of a; rRSs is a wire for making
a communication between B and the vial A, having joints in it at R and 5,
where it is supported by non-conductors, and mMNn is another wire of
the same kind for making a communication between T and the vial a*.

241] In order to try the experiment I proceed in this manner: the
wires Dd and D8 are lifted off from the plates B and T so as not to touch
them, and consequently so that there is no communication between B
and T : the wires Rr and Mm are suffered to rest on B and T, and the
wires 5s and Nn are lifted up so as not to touch Ee and Ff. The vials are
then charged by means of the wire bt which rests on Ee and Cc, and
communicates by the wire Pp with the prime conductor, a communication
being made between the outside of the vial A and the ground, and the
vial a being made to communicate with the ground by the wire xyz,
which rests on Gg, and is suspended from the wire bt by silk strings repre-
sented in the figure by dotted lines. When the vials are sufficiently charged,
the wire bt is lifted up till xy bears against the bottom of Cc, xy being still
suffered to communicate with the ground as before, and the communica-
tion between the outside of the vial A and the ground being still preserved.
At the same time the wires 5s and Nn are let fall upon Ee and Ff. For
the sake of doing this more commodiously I make use of the silk strings
represented in the figure by dotted lines and passing over the pulley H.
A weight is fastened to the string at w, which is supported while the vials
are charging in such manner that the wires 5s and Nn are lifted up so as
not to touch Ee and Ff, and the wire bt is suffered to rest on Ee and Cc,
and the wire xy on Gg; and when the vials are sufficiently charged the
weight is let down, by which means 5s and Nn are suffered to fall down
upon Ee and Ff, and the wire bt is lifted up till xy bears against the bottom
of Cc.

242] From what has been said it appears that whilst the vials were
charging, the outsides of each of them communicated with the ground,
and consequently the inside of each vial is overcharged and the outside
undercharged. As soon as the vials are charged the communication of
each of them with the prime conductor is taken away, and at the same
time the communication between the outside of the vial a and the ground
is taken away, so that it is entirely insulated, and, immediately after, a
communication is made between its inside and the ground, and at the
same time the body B is made to communicate with the inside of the

* [See plan. Fig. 17, p. 137.]

c. p. i. 9

130 Experiments on the Charges of Bodies

vial A, and the trial plate with the outside of the vial a; consequently the
body B will be overcharged as it communicates with the overcharged part
of the vial A , while the undercharged side communicates with the ground ;
and the trial plate will be undercharged, as it communicates with the
undercharged side of the vial a, while the overcharged side communicates
with the ground.

Immediately after this operation is performed the wires Rr and Mm
are lifted up, so as to cut off the communications of the bodies B and T
with the vials, and, instantly after, the wires Dd and D8 are let down, so
as to make a communication between the body B and the trial plate.
For the sake of expedition this operation was performed nearly in the
same manner as the former, by means of the silk strings passing over the
pullies L and /, and represented in the figure by dotted lines. I also
employed an assistant to turn the electrical machine and to manage the
silk strings passing over the pulley H, while I stood ready near D to per-
form the last mentioned operation as soon as the wires Ss and Nn were
let down, and also to see whether the pith balls separated or not.

243] From the manner of performing the last mentioned operation it
appears that the communication is not made between B and T till after
their communication with the vials and all other bodies is cut off; conse-
quently, if the quantity of redundant fluid communicated to B is more
than sufficient to saturate the redundant matter in T, they will be over-
charged after the communication is made between them, and the pith
balls at D will separate positively, but if the redundant fluid in B is not
sufficient to saturate the redundant matter in T they will be undercharged,
and the pith balls will separate negatively.

244] The balls were made of pith of elder, turned round in a lathe,
about one-fifth of an inch in diameter, and were suspended by the finest
linen threads that could be procured, about 9 inches long.

245] In making these experiments I did not open the trial plate to
such a surface that the pith balls should not separate at all on making
the communication between B and T, and assume that for the size which
must be given to the trial plate in order that the deficience of fluid in it
should be equal to the redundance in B (or for the required surface of the
trial plate, as I shall call it for shortness) ; but I first made the surface of
the trial plate such that the deficient fluid therein should exceed the re-
dundant in B, and that the pith balls should separate negatively, just
enough for me to be sure they separated : I then diminished the surface of
the trial plate till I found, on repeating the experiment, that the pith
balls separated positively as much as they before separated negatively
and the mean between these I concluded to be the required surface of the
trial plate.

Testing by trial plate I 3 1

246] This way of making the experiment I found much more accurate
than the other, for supposing the required surface of the trial plate to be
expressed by the number 16, I found that its surface must be increased
to about 20 before I could be certain that the pith balls would separate
negatively, and that it must be diminished to about 12 before they would
separate positively; whereas I found that increasing its surface from 20
to 21 would make the balls separate sensibly further, and that diminishing
its surface from 12 to n would have the same effect; so that I could
determine the required surface of the trial plate at least four times more
exactly by the latter method than by the former.

247] It will be shewn hereafter* that the quantity of deficient fluid
in the trial plate is in proportion to the square root of its surface ; conse-
quently the redundant fluid in B must exceed, or fall short of, the deficient
fluid in the trial plate by about £th part, in order that the balls should
separate, and moreover the increasing or diminishing the deficience of
fluid in the trial plate by about ^ part will make a sensible difference in
the separation of the balls.

248] It is plain that this way of finding the required surface of the
trial plate is not just, unless the vials are charged equally in both trials,
namely, that in which the balls separate positively and that in which they
separate negatively; I therefore fastened an electrometer to the wire Pp,
at a sufficient distance from the vials, consisting of two paper cylinders
about three-quarters of an inch in diameter and one inch in height, sus-
pended by linen threads about eight inches long, and in changing the
vials took care always to turn the globe f till these cylinders just began
to separate.

249] In all the later experiments, however, I made use of a more
exact kind of electrometer, consisting of two wheaten straws, Aa and Bb
(Fig. 30), eleven inches long, with cork balls A and B at the bottom, each
one-third of an inch in diameter, and supported at a and b by fine steel
pins bearing on notches in the brass plate C, and turning on these pins
as centers. This electrometer was suspended by the piece of brass C from
the prime conductor, and a piece of pasteboard, with two black lines
drawn upon it, was placed six inches behind the electrometer on a level
with the balls, in order to judge of the distance to which the balls sepa-
rated, the eye being placed before the electrometer at thirty inches distance
from them (a guide for the eye being placed for that purpose J), and the

* [Arts. 284, 479, 682.] f [Of Nairne's electrical machine, see Art. 563.]

t It is necessary that the eye should always be placed nearly at the same dis-
tance from the electrometer, 'as it is evident that the nearer the eye is placed the
further the balls will appear to separate. But as the distance of the balls from the
eye is so much greater than their distance from the pasteboard, a small alteration
in the distance of the balls either from the eye or the pasteboard will make no
sensible alteration in the distance to which the balls appear to separate.

9—2

132 Construction and use of electrometer

electrical machine was turned till the balls appeared even with those lines.
By these means I could judge of the strength of the electricity to a con-

rt

siderable degree of exactness. In order to make the straws conduct the
better they were gilt over.

250] In order to estimate what error may arise from the vials being
not equally charged in both trials, let the required surface of the trial
plate be called 16; then must the surface which must be given to it in
order that the balls may separate negatively be 20, or 16 + 4, supposing
(he vials to be charged with the usual degree of strength. Suppose now
that in the next trial, in which the balls are to separate positively, the
vials are charged stronger than before, in the ratio of x to i, so that the
quantity of redundant fluid in B shall be greater than before, in the
ratio of x to i, and that the deficience in the trial plate should be greater
than before in the same ratio, provided its surface remained unaltered;
then must the surface which must be given to the trial plate, in order
that the balls shall separate positively as much as they did negatively,

be 16 - -; for, if this surface is given to it, it is plain that the redundant

X

fluid in B will as much exceed the deficient in the trial plate as it before
fell short of it. The mean between these two surfaces is 16 + -

2X

whereas it ought to have been 16, so that the error which will proceed
from thence in finding the required surface of the trial plate is -

and, consequently, is less than half of the error which we are liable to in
finding it the other way (or that in which we endeavour to find that
surface of the trial plate with which the balls do not separate at all),

Comparison of capacities 133

though x is ever so great ; for in that way it was before said that we were
liable to an error of four. But if x is equal to f , which is as great an error
of strength as I think can well arise in charging the vials, even when the
first mentioned electrometer is used, the error in finding the required
surface is only ^ of the whole surface, or only J» part of what might arise
the other way.

251] Having thus found what surface must be given to the trial plate,
in order that the deficience of fluid in it shall be equal to the redundance
in B, I take away the body B and put the other body b, which I want to
compare with it, in its room, and if I find on repeating the experiment
that the trial plate must be drawn out to the same surface as before, in
order that the deficience of fluid in it shall be equal to the redundance
in b, or, in other words, if the required surface of the trial plate is the same
in trying b as in trying B, I am well assured that if B and b were succes-
sively made to communicate with one of the vials, or with any other
third body, and were positively electrified, they would each of them contain
the same quantity of redundant fluid, supposing the quantity of redundant
fluid in the third body to remain the same each time. On the other hand,
if I find that the required surface of the trial plate is greater in trying b
than in trying B in the ratio of t2 to T2, I am well assured that the quantity
of redundant fluid in b would exceed that in B in the ratio of t to T, sup-
posing, as was said before, that the deficience of fluid in the trial plate is
in proportion to the square root of its surface.

252] If the reader should think that this conclusion requires any proof
it may be thus demonstrated :

Suppose that in trying B it was found that the required surface of
the trial plate was T2 and that in trying b it was tz, and let us first suppose
that the vials are charged in exactly the same degree in trying b as in
trying B, then is the conclusion evident, for then are B and b successively
made to communicate with the vial A, the charge of this vial being
exactly the same each time, and the quantity of redundant fluid com-
municated to b is, actually, to that communicated to B as t to T. But it
is plain that the conclusion is equally just, though the vials are charged
higher in trying one than in trying the other. For though, in this case,
the redundant fluid actually communicated to b will not be to that com-
municated to B in the ratio of / to T, yet we are sure that it would have
been so if the vials had been charged in the same degree each time, for the
required surfaces which must be given to the trial plate in trying b must
evidently be the same whether the vials are charged to the same degree
as they were in trying B, or to a different degree.

253] Though it is of no signification whether the vials are charged to
the same degree in trying b as in trying B, yet it is necessary, as I said
before, that in trying either B or b the vials should be charged nearly

134 Experiments on the Charges of Bodies

with the same strength when the balls are to separate positively as when
they are to separate negatively, as otherwise a small error will arise in
finding the required surface of the trial plate.

254] In all the following experiments I took care to proportion the
size of the bodies B and & in such manner that the quantity of redundant
fluid in one should not be very different from that in the other, so that,
though the deficience of fluid in the trial plate should not be very nearly
as the square root of its surface, it would make very little error in the
conclusion.

255] The usual distance of the centers of B and J in these experiments
was 83 inches, the distance of B from the vial A 106 inches, and that
of T from a 86 inches, and the distance of the two vials about 10 inches*.
The usual height of the body B and the trial plate above the ground was
50 inches ; they were commonly supported upon pillars such as are repre-
sented in Fig. 16, where Ee, Bb and Dd are three upright pillars of baked

wood about 40 inches long, and ee, 6,8, and d8 are sticks of glass 10 inches
long and J inch thick let into the wood, and covered with sealing-wax.
ACGF is a piece of board which the pillars are fastened into. The points
M, N, R, and S were each supported by a pillar of the same kind, and the
point D was supported nearly in the same manner. In some experiments,
however, the body B was suspended by silk strings. The wires dD8, rRSs,
and mMNn were about T'T inch thick.

256] It is well known that the air of a room is easily rendered over-

or undercharged, in particular if a wire such as rRSs [Fig. 14] is positively

* [See plan at Art. 265, details at Art. 466, and theory in Note 17.]

Insulation and earth-connections \ 3 5

electrified, though even in no greater degree than in these experiments,
and kept so for a second or two, and its electricity then destroyed, the
air near it will be sensibly overcharged, as may be thus shewn. Take a
pair of pith balls, like those hung at D, and suspend them within a few
feet of the wire from some body communicating with the ground. The
balls will instantly separate on electrifying the wire on account of the
repulsion of the redundant fluid in it, but they will also continue to
separate, though in a less degree, after the electricity of the wire is de-
stroyed, which can be owing only to the air being rendered overcharged
by it.

257] It may be suspected that this electrification of the air by the
wires may affect the separation of the pith balls at D and thereby cause
an irregularity in the experiments, but it must be considered that the
wire mMNn is made as much undercharged as rRSs is overcharged, and
the pith balls are placed about equally distant from both, so that the
undercharged air near one wire will nearly balance the effect of the over-
charged air near the other. Besides that, if it had any effect upon the
separation of the balls, it would have much the same effect in trying B
as in trying b, and therefore could hardly cause any error in the result of
the experiment. However, still further to obviate any error from that
cause, I had a contrivance by which the electricity of the wires rRSs and
mMNn, as well as that of the vials, was destroyed as soon as the wires
rR and mM were lifted up from B and T.

258] It is necessary that the outside of the bottle A and the wire yx
should have as perfect a communication with the ground as possible, as
otherwise it might happen that the body B and the trial plate might not
receive their full degree of electrification before the wires rR and mM
were lifted up. I therefore made them to communicate by a piece of wire
with the outside wall of the house. This I found to be sufficient, for if
I charged a vial, making the outside to communicate with the outside
wall, and then made a communication by another wire between the inside
of the vial and another portion of the outside wall of the house at several
feet distance from the other, I found the vial to be discharged instantly;
but if I made the wires to communicate only with the floor of the room
instead of the wall of the house, I found it took up some time before the
vial was discharged.

It must be observed that in this case, where you want to carry off
the electricity very fast by an imperfect conductor, such as the wall, the
best way is to apply a pretty broad piece of metal to the wall, so as to
touch it in a considerable surface, and to fasten the wire to that, which
was the way I last made use of, for if you only apply the wire against the
wall, as it will touch the wall only in a few points, the electricity will not
escape near so fast.

136 Experiments on the Charges of Bodies

259] In dry weather the linen threads by which the pith balls arc
suspended are very imperfect conductors, so that the balls are apt not to
separate or close immediately on giving or taking away the electricity.
To remedy this inconvenience I moistened the threads with a solution of
sea-salt, which I found answered the end perfectly well, for the threads
after having been once moistened conveyed the electricity ever after very
well, though the air was ever so dry.

260] As the charge of the vials A and a is continually diminishing
from the time that the communication between them and the electrical
machine is taken away, both by the electricity running along the surface
of the vial from the inside to the outside, and by the waste of electricity
from the wires rRSs and mMNn and their supports, it is necessary that
the operation of electrifying B and T and lifting up the wires rR and mM
should be performed as soon as possible, and, above all, it is necessary
that the communication should be made between B and T as soon as
possible after lifting up the wires rR and mM. This end was obtained
very well by the manner, already described, of performing the operation.

261] Before I begin to relate the experiments, it will be proper to say
something more about the accuracy that is to be expected in them. 1
before said that increasing or diminishing the surface of the trial plate
by ^ of what I called the required surface, i.e., that surface in which the
deficience was equal to the redundance in B, made a sensible alteration
in the distance to which the pith balls separated. In reality I found that
increasing or diminishing it by only ^4 part of the required surface would
in general make a sensible alteration, but I could not be certain to nearly
so small a quantity, for it would frequently happen that after having
determined the surface of the trial plate at which the balls separated to
a given degree, that on repeating the experiment a little after, the balls
would separate differently from what they did before, and that I was
obliged to alter the surface of the trial plate by T'^ and sometimes even |
of the required surface in order to make the balls separate in the same
degree as before. Therefore, as increasing the surface of the trial plate
by ^j part increases the deficience of fluid therein by fa part, it appears
that if the bodies B and b really contain the same quantity of redundant
fluid, it might seem from the experiments as if B contained fa or even
T^ part more or less redundant fluid than b, so that I am liable to make
an error of -fa or -fa part in judging of the proportion of the quantity of
redundant fluid in two bodies. I imagine, however, that it will not often
happen that the error will amount to as much as 3^.

262] I do not very well know what this irregularity proceeded from.
Part of it might arise from the difference in the strength with which the
vials were charged, but 1 believe that part of it must arise from some other

Estimate of accuracy 137

cause which I am not acquainted with. For greater security I always
compared each body with the trial plate 6 or 7 times running.

263] It appears from the description of the electrometer fastened to
the wire Pp that the vials were charged extremely weakly in these experi-
ments (they were indeed charged so weakly that if tried by Lane's electro-
meter they would not discharge themselves, if the distance of the knobs
was more than ^ of an inch*), and it perhaps may be asked why I chose
to charge them so weakly, as it is plain that the stronger the vials are
charged the less alteration in the size of the trial plate would it have
required to produce the same alteration in the separation of the pith balls.

264] My reason was this, — that the electricity seems to escape re-
markably faster from any body, both by running into the air and by
running along the surface of the non-conductor on which it is supported,
when the body is electrified strongly than when it is weak, which made
me afraid that if I had charged the vials much stronger the experiment
might have been too much disturbed by the diminution of the quantity
of redundant fluid in B and the deficience in the trial plate between the
lifting up of the wires Rr and Mm and letting fall the wires Dd andZ)8,
and also by the diminution of the charge of the vials between lifting up
the wire bt and lifting up the wires Rr and Mm; and indeed it seemed,
from some trials I made with a heavier electrometer fastened to Pp, as
if the experiments were not more exact, if so much so, when the vials
were charged stronger, as when they were charged in the usual degree.

I now proceed to relate the experiments I have made.

265] EXP. III. This experiment was made with a view to discover
whether the quantity of -redundant fluid communicated to the body B

Fig. 17. [Scale A-]
* [Difference of potentials about n-8. See Art. 329 and Note 10.]

i 3 8 Experiments on the Charges of Bodies

was different according to the different situations in which it was placed
in respect of the vial A, or according to the different shape of the wire
sSRr by which it was touched, or according to the different parts in which
it was touched by that wire. The body which I used for this purpose was
a square tin plate, 12 inches each way, and the different ways in which
it was tried are drawn in Fig. 17, which represents a plan of the disposition
of the whole apparatus, in which the letters B, d, D, 8, t, m, M, N, a,
A, S, R and r represent the same things as in Fig. 14.

266] 1st Way. The tin plate was placed in a vertical plane so as to
be represented in the plan by the line 6/J, the wires Rr and Dd when let
down resting on the edge of the plate as in the figure.

2nd. The tin plate was placed horizontal, as represented by the square
Bcfg, the plate being placed so that the wire Rr touched it near the
middle. N.B. The wire Rr was bent at right angles about f of an inch
from the end r, so that -f of an inch was in a vertical situation, and the
rest horizontal. Consequently the wire touched the plate only by its
extremity.

3rd. The same as the last, except that the wire Rr touched the plate
not far from the side fg, and pretty near the middle of that side.

4th. The same as the last, except that a cross wire eE was fastened
horizontally across the wire Rr, so as to be parallel to the side fg, and
about one inch distance from it.

5th. The plate in the same situation as before, but the wire Rr was
bent into an arch, like tTR, only the plane of that arch was vertical. The
wire touched the plate near the middle.

6th. The plate in the same situation as before, but the wire Rr was
removed into the situation yx, the communication between y and 5 being
by the wire yzS bent into an arch, as in the figure, the plane of which was
vertical. The wire yx touched the plate near the middle.

N.B. In all these ways the tin plate was supported on silk lines.

267] The charges of the plate in the different situations were found
to be to each other in the following proportions?1:

1st Way. . . . 11-7,

2nd „ . . . . 11-7,

3rd „ . . 12-0,

4th „ . . 10-8,

5th „. . . . 11-5,

6th „. . . . 10-8.

* [Art. 470, Dec. 17, 1771. The numbers there found are here multiplied by a
constant, so as to make the result by the 3rd way equal to 12.]

Influence of variation of the arrangements 139

The plate was tried in some of these situations another night, when
the charges came out in the following proportions * :

2nd Way. . . . 11-9,

3rd „ . . . . 12-0,

5th „.'-. . n-8,

6th „ . ii-o.

268] It should seem from these experiments that the charge of the
tin plate is not exactly the same in all the ways of trying it, as the extremes
seem to differ from each other by above T'5 part, which is more than could
arise from the error of the experiments; but, excepting the 4th and 6th
ways, the others seem to differ by less than ^. This I think we may be
well assured of, that no sensible error can arise in the following experi-
ments from any small difference in the manner in which the bodies are
touched by the wire.

269] EXP. IV. These experiments were made with intent to see
whether the charge of a body of a given shape and size was the same
whatever materials it consisted of, as it ought to be according to Prop.
XVIII f, and also to see how far the charge of a flat plate depended on
its thickness J. The substances used for this purpose were all flat plates
about one foot square. The results of the experiments are given in the
following Table §:

Side

Names of substances used

Mean side
of square

Thick-
ness

Charge

increased
by ij of

Reduced
charge

thickness

A tin plate ...

I2-OO

•02

11-92

12-0^

11-89

A hollow plate composed of tin

j

plates soldered together

11-03

I-OI

12-30

12-38

11-92

Another of the same kind, but

thinner ...

11-62

•37

12-08

12-11

11-97

A piece of pasteboard such as used

•J 1

for the covering of books

1 2 -O2

•087

n-95

I2-I4

11-81

A piece of Portland stone

I2-OO

•40

12-44 •

12-53

11-91

A sandstone known in London by

the name of Bremen stone

I2-O4

•42

12-44

12-60

11-84

A slate such as used for the cover-

ing of houses

I2-OO

•16

I2-2O

12-21

11-99

N.B. The three pieces of stone were all ground flat, and of an uniform
thickness.

270] As it would have been difficult to try the following substances
by themselves, I coated panes of crown-glass with them on one side and
tried them in that manner, which, as glass does not conduct electricity,

* [Art. 468.]

J [Prop. XXI, Art. 73.]

f [Art. 68.]

§ [Arts. 293, 471, 480, 481.]

14° Capacities of bodies of different substances

seems as unexceptionable as it would have been to have tried them by
themselves, supposing it had been possible to have done so.

Names of substances with which the
glass was coated

Mean side
of square

Thickness
of glass

Thickness
of coating

Charge

Reduced
charge

Gold leaf

Il-o8

•0^6

11-87

11-89

Thin tinfoil

*• * V v

11-96

wjvy

•058

•00113

/

n-55

n-59

Several folds of thick tinfoil stuck

together with gum-water

11-98

•056

•017

ii-93

u-95

Gum Arabic laid on in the form of

gum- water and suffered to dry . . .

12-05 "064

12-17

12-12

The same mixed up with a good

deal of salt

1 1 -96

•061

n-95

i t-99

Charcoal powder mixed with a little

gum-water

12-04

II-95

11-91

Water thickened with a little gum

11-96

•06 1

1 1 -80

11-84

The last mentioned substance was quite fluid, but had sufficient
tenacity to prevent its flowing immediately to the lowest part of the
plate. In those substances in which the thickness of the coating is not
set down it was not measured, but the thickness was small.

271] All these things were supported on the pillars of baked wood
and waxed glass described at [Art. 255]. The panes of glass were laid on
these pillars with their coated sides uppermost, so that the wires Rr and
Dd fell on their coated sides. As many of the substances used were but
imperfect conductors of electricity, I fastened bits of tinfoil about an
inch square on the places on which the wires Rr and Dd touched the
plate in order to make the electric fluid spread more readily over it, and
I satisfied myself beforehand that with this precaution they conducted
readily enough for my purpose, as I found by discharging a Leyden vial,
and making these substances part of the circuit.

272] It appears from these experiments that the charge of a thick
plate is greater than that of a thin one of the same base, as might be
guessed from the theory*, and it seems to be equal to that of a very thin
one whose side exceeds that of the thick one by about i$ of its thickness.
Let us therefore increase the mean side of each of these plates by i^ of
its thickness, where that quantity is worth regarding, and alter the charge
found by experiment in the ratio of 12 inches to the side thus increased,
which will give us the charge of a plate of the same materials and shape
whose increased side is 12 inches, when the charge of each substance will
stand as in the last column of the preceding Table. These numbers do
not differ from each other by more than what may fairly be supposed
owing to the error of the experiment, and therefore I think we may
conclude — firstly, that the charge of a body of a given shape and size is
the same whatever materials it consists of, and, though the experiment
was tried only with square plates, yet I think there can be no doubt but

* [Note 20, p. 409.]

Capacities of bodies of similar forms 141

the case will be the same with bodies of any other shape ; secondly, that
the charge of any thin plate is very nearly the same whatever its thickness
may be, provided its thickness is very small in respect of its breadth or
smallest diameter ; and there can be no doubt also but what this will hold
good in thin plates of any shape, though it was tried only with square
ones ; and thirdly, if the plate is square and its thickness is several times
less than its side, though not small enough to be disregarded, its charge
is equal to that of a very thin square plate whose side exceeds that of the
former by about i^ of its thickness.

This last circumstance seems far from being repugnant to the theory;
but as I do not know how to calculate the charge of such a plate within
tolerably near limits, I shall not trouble the reader any further about it.

273] EXP. V. This experiment was made with a view to find what
proportion the charges of similar bodies of different sizes bear to each
other, and whether it is the same that it ought to be by the theory on a
supposition that the electric attraction and repulsion is inversely as the
square of the distance, and that the bodies are connected to the jar by
which they are electrified by canals of incompressible fluid. It was tried
by taking two circular tin plates of 9 inches diameter, and comparing the
charge of these two circles together with that of one of twice the diameter.
The circles were placed in a vertical situation, and were disposed as in
Fig. 18, where the letters D, 8, m, T, M,N, a, A, S and R stand for the

Fig. 18.

same things as in Fig. 17. Bb and Cc are the two small circles placed
parallel to each other, which, as they are in a vertical situation, appear
in the plan as straight lines. Rf and Rg are the wires by which they are
electrified, which are bent near /and g so as to enable them to rest on the
edges of the circles. Dd is the wire for making a communication between

142 Capacities of disks as modified by approach

them and the trial plate; Ee is the large circle placed half way between
the two small ones, and Rr the wire by which it is electrified. . But it must
be observed, that in trying the large circle the two small circles and the
wires Rf and Rg are taken away and the wire Rr put in their room ; and
in like manner, when the small circles are tried, the circle Ee and the wire
Rr are removed.

274] It must be observed that the charge of the two small circles
together will not be as much as double the charge of one circle, unless
the distance of the two circles from each other is extremely great. In
order, therefore, to know better what allowance to make on this account,
I tried the experiment with the two small circles placed at three different
distances, namely, at 18, 24, and 36 inches from each other, the circles
being always placed so that the middle point between them was at the
same distance from D. Their charges came out in the following propor-
tion * :

The large circle i-ooo,

The two small ones at 36 inches distance '899,

24 „ „ -859,

,, ,, ,, 18 „ ,, -811.

275] I repeated the experiment in the same manner, except 1st, that
the distances of the vials from the circles and trial plate were different
from what they were before, namely, in the foregoing experiment the
distance To, from the middle of the trial plate to the vial a was 87 inches
and eA, or the distance from the center of Ee to the vial A, was 106 inches,
whereas in this experiment Ta was 98 inches and eA 63 inches; the
distance Te was 83 inches in both experiments ; and 2ndly, that I placed
a frame of wood about 5 feet square under the circles 14 inches from the
ground. The reason of these alterations will be shewn by and byf. Their
charges came out as follows:

The large circle i-ooo,

The two small ones at 36 inches distance '894,

24 „ „ -840,

18 „ „ -798.

276] Let us now endeavour to find out what proportion the charges
ought to bear to each other by the theory on the above-mentioned sup-
position of their being connected by canals of incompressible fluid, and
of the electrical attraction and repulsion being inversely as the square of
the distance. This cannot be done exactly without knowing the manner
in which the redundant fluid is disposed in the circles, which I am not
acquainted with, but if we suppose the fluid to be spread uniformly over

* [Arts. 452, 454, 472-475.].

f [Arts. 277, 339, 474 and Note 17.]

Comparison with theory 143

the plates.it will appear, by calculating according to Prop. XXX [Art. 141],
that their charges should be in the following proportion :

The large circle i-ooo,

The two small ones at 36 inches distance -933,
24 „ „ -911,

18 „ „ -890.

If we suppose that the whole redundant fluid is collected in the cir-
cumference, they should be as follows :

The large circle i-ooo,

The two small ones at 36 inches distance -890,
24 „ „ -844,

18 „ ,, -805;

and if we suppose that \\ of the whole redundant fluid is collected in the
circumference, and the remainder, or \\, spread uniformly, they should
be as follows:

The large circle i-ooo,

The two small ones at 36 inches distance -920,
24 ,. „ -890,

18 „ „ -863.

277] I think this latter proportion of the charges much the most likely
to agree with the truth*, as it appears from an experiment which will be
mentioned hereafter, that the charge of a circular plate bears the same
proportion to that of a globe that it would do if the fluid was disposed
in that manner. But it must be observed that in these calculations the
circles are supposed to be placed at an infinite distance from the vial by
which they are electrified, and also from any other over- or undercharged
body, whereas in these experiments the circles were at such a distance from
the vial that their repulsion on the canal by which they communicated
with it was sensibly less than if it was infinite, and moreover the attraction
of the undercharged trial plate on the wire mMNn has some tendency
to increase the quantity of fluid in the circles, and the repulsion of the
circles tends to diminish the quantity of fluid in the trial plate, and
moreover the floor and walls of the room will be made undercharged
near the circles and overcharged near the trial plate, which will also have
some tendency to alter the quantity of fluid in the circles and trial plate.
It was with a view to find out what error could proceed from these
causes that I tried the experiment in the two different ways above men-
tioned. It will be shewn, however, in the appendix f, that the first two
of these causes cannot produce any sensible alteration in the experiment,
* I would not be understood by this to suppose that the fluid is actually dis-
posed in this manner in a circular plate, but only that the charges will bear the
same proportion to each other that they ought to do on this supposition.

f [Art. 1 88, and Notes 17 and 21.] {Prof. Maxwell has supplied a series of very
elegant calculations of capacity, for the cases measured by Cavendish, in Notes 20 to 25.)

1 44 Theoretical conclusions

and that it is not likely that the last should. This is also confirmed by the
near agreement of the results in both ways of trying the experiment, as
the difference in the proportion of the charges in these two ways of trying
the experiment was not greater than what might well be owing to the
error of the experiment.

278] It seems reasonable to conclude, therefore, that the proportion
which the charges ought to bear to each other in the theory on the sup-
position of their being connected by canals of incompressible fluid, and
of the electrical attraction and repulsion being inversely as the squares
of the distances, must be nearly as in the last Table, and therefore it
should seem that the observed charges of the two small plates were rather
less in proportion to that of the large one than they ought to have been
by theory on the above-mentioned supposition ; but the difference is not
great, and perhaps not more than what may be owing to our not being
able to compute the true proportion with sufficient accuracy, and to the
error of the experiment, though I am more inclined to think that the
difference is real. This, however, can by no means be looked upon as a
sign of any error in the theory, but, on the contrary, I think that the
difference being so small is a strong sign that the theory is true. For it
cannot be expected that the charges of bodies connected together by wires
should bear exactly the same proportion to each other that they should
do if they were connected by canals of incompressible fluid; and, indeed,
the third experiment shews that they do not, as the charge of the tin
plate was found to be a little different according to the situation in which
it was placed and the disposition of the wire by which it was touched,
which should not be the case if it was connected to the vial by a canal of
incompressible fluid.

279] EXP. VI. This experiment was made with the same view as the
last, and consisted in comparing the charge of two brass wires together,
with that of a single one of twice the length and thickness. The small
wires were 3 feet long and Jffth of an inch thick; they were placed hori-
zontal and parallel to each other, as represented by the lines Bb and Cc
in Fig. 18, and were tried at three different distances from each other,
viz.: — 18, 24, and 36 inches. The long wire was 6 feet long and Jth of
an inch in thickness, and was placed in the same direction as the small
ones, as represented by Ee, They were electrified by the same wires and
in the same manner as the circles, only they were placed so as to be touched
by the wires//?, rR, and gR, very near their extremities b, c, and c. Their
charges were as follows :—

The long wire i-ooo,

The two short ones at 36 inches distance -903,

24 „ „ -860,

18 „ ,, -850.

Capacities of bodies of various forms determined 145

280] The charges of the two small wires at the several distances of
36, 24, and 18 inches ought by theory to have been to that of the long
wire in a proportion between that of -923, -905, and -883 to i and that
of -893, -860, and -835 to i, supposing them to be connected to the vial
by canals of incompressible fluid, but, as it should seem from the next
experiment, ought in all probability to approach much nearer to the
former proportion than the latter. The observed charges were actually
between these two proportions, but approached much nearer to the latter,
so that they agreed as nearly with the computation as could be expected*.

281] Exp. VII. Being a comparison of the proportional charges of
several bodies of different shapes: the result is as follows: —

A globe 12-1 inch in diameter i-ooo

A tin circle 18-5 ,, „ -992

A tin plate 15-5 inches square -957

An oblong tin plate 17-9 inches by 13-4 inches . . -965
A brass wire 72 inches long and -185 thick . . -937
A tin cylinder 54-2 inches long and -73 in diameter . -951
A tin cylinder 35-9 inches long and 2-53 in diameter -999
The globe was the same that was used in the first experiment. The
wire and cylinders were placed in the same manner as the large wire in
the preceding experiment, and were touched in the same manner f.

282] Remarks on this experiment.

First, the proportion which the charge of the circular plate bears to
that of the globe agrees very well with the theory, for by Prop. XXIX
[Art. 140] the proportion should be between that of -76 to i and that of
1-53 to i, and the observed proportion is that of -992 to i. We may
conclude also from this experiment that the charge of a circular plate is
to that of a globe of the same diameter as 12 to i8£, which by the above-
mentioned proposition is the proportion which ought to obtain if ^f of
the whole quantity of redundant fluid in the plate was spread uniformly
[over the surface] , and the remainder, or ^\, was spread uniformly [round
the circumference], that is, if the value of p in that proposition equals |f {.

283] 2ndly. The charge of a square plate is to that of a circle whose
diameter equals the side of the square, as 1-153 to I, or its charge is to that
of a circle whose area equals that of the square as 1-02 to i§.

284] 3rdly. The charge of the oblong plate is very nearly equal to
that of a square of the same area, and consequently as the length of the
trial plates used in these experiments never differed from their breadth
(whether the trial plate was more or less drawn out) in a greater proportion
than those of this oblong plate do, and as the charges of similar bodies

* [Arts. 453, 476, 477, 683, and Note 13.] t [Arts- 4?8, 682.]

J [Arts. 654, 68 1, and Note 2.] § [Arts. 479, 682, and Note 22.]

c. p. i. 10

146 Influence of the connecting wires

of different sizes are as their corresponding diameters, or sides, I think
we may safely conclude that the charges of these trial plates were as the
sides of a square of the same area, agreeable to what was said in [Art. 247].

285] 4thly. By Prop. XXXI [Art. 150] the charge of a cylinder whose
length = L and diameter = D is to that of a globe whose diameter = L

2L dL

in a ratio between that of i to log, -yr and that of 2 to log, ~ , and

therefore the charges of the brass wire, long cylinder and short cylinder,
should be to that of the globe, supposing them to be connected with the
vial by which they were electrified by canals of incompressible fluid, in
a ratio between that of -894, -896 and -887 to i and that of 1-619, I-573
and 1-469 to i. The observed charges are as -966, -980 and 1-028 to i,
which are between the two above-mentioned proportions, but approach
much nearer to the former than the latter, as might have been expected ;
so that the observed charges agree very well with the theory*.

286] Sthly. If we suppose that the redundant fluid is disposed in the
same manner in a cylinder, whether the length is very great in respect
of the diameter or not, it is reasonable to suppose that the charges of the
brass wire, long cylinder and short cylinder, should be to each other in
a proportion not much different from that of -894, -896 and -887, or that
of -966, -968 and -959. The observed charges do not differ a great deal
from that ratio, only the charges of the two cylinders, especially the
shorter, are rather greater in proportion to that of the brass wire than
they ought [to be], so that according to this supposition the observed
charges do not agree exactly with computation. But if we suppose that
the redundant fluid is spread less uniformly in a cylinder whose length
is not very great in proportion to its diameter than in another, that is,
that there is a greater proportion of the redundant fluid lodged near the
extremities, which seems by no means an improbable supposition, the
observed charges may perhaps agree very well with what they should be
by theory, if they were connected by canals of incompressible fluid.

287] With regard to the small disturbing causes mentioned in [Art.
277], as the length of the brass wire bears so great a proportion to its
distance from the trial plate and to its distance from the ground, it is
possible that its effect in increasing the deficiency of fluid in the trial plate
may be sensibly less, and also that the increase of charge, which it receives
itself from the ground near it being under-charged, may be sensibly
different from what it would be if it had been of a more compact shape,
so that perhaps some alterations may have been made in the experiments
by these two causes. I should imagine, however, that they could be but
small. It must be observed that the first of these two causes tends to make
the charge of the wire appear greater than it really was, and consequently

* [Note 12, p. 382.]

Charges on three equidistant disks 1 47

to make the observed charges appear to agree nearer with the theory than

they really did. Which way the second cause should operate I cannot say.

On the whole it should seem as if the true charge of a cylinder whose

length is L and diameter D is to that of a globe whose diameter is L nearly

as | to natural logarithm -=^ , or as -489 to Tabular log. -^ .

288] EXP. VIII. Let AB, ab and eg (Fig. 19) be three equal thin
parallel plates equidistant and very near to each
other, and let Cf, the line joining their centers, be
perpendicular to their planes, and let all three
plates communicate with each other and be posi-
tively electrified: it may easily be shewn that ac-
cording to the theory the quantity of redundant
fluid in the middle plate will be many times less
than that in either of the outer plates, or than that
which it would receive by the same degree of

electrification if placed by itself. I therefore took three tin plates, each
12 inches square, and placed them as above described, and electrified
them by means of a wire fixed to a Leyden jar, the end of the wire being
formed in such manner as to touch all three plates at once. As soon as
the electrifying wire was taken away I drew away the outer plates, and
at the same time approached a pair of cork balls to the middle plate in
the same manner as I did to the globe in the first experiment and observed
how much they separated, care being taken to take away the electricity
of the outer plates as soon as drawn away. I then removed the outer
plates and, by the same means that I used in the first experiment, made
the quantity of redundant fluid in the jar less than before in a given ratio,
and by means of this jar electrified the middle plate by itself and ap-
proached the cork balls as before. In this manner I proceeded till I found
how much it was necessary to diminish the quantity of redundant fluid
in the jar in order that the corks might separate as much as before, and
consequently how much less the quantity of redundant fluid in the middle
plate when placed between the two other plates was than that which it
would have received by the same degree of electrification if placed by itself * .

The result was that when the distance of the outer plates was \

1 1 -05

to

inches, the quantity of redundant fluid in the middle plate was about \

times less than it would be if electrified in the same degree when placed
by itself.

289] It is plain that according to the theory the quantity of redundant
fluid in each of the outer plates should be the same, and that the quantity

* [Art. 542 and Note 23.]

1 48 Theory for three parallel disks

in the middle plate should be such that the repulsion of AB and ab together
on the column cf shall be equal to that of the plate eg thereon in the
contrary direction, and the redundant fluid in each of the outer plates is
not much more than one-half of that which it would receive by the same
degree of electrification if placed by itself. Now it will appear by com-
puting, according to the principles delivered in Prop. XXX [Art. 141],
that the quantity of redundant fluid in the middle plate will be so ex-
cessively different according to the different manner in which the fluid is
disposed in the plates that there is no forming any tolerable guess how
much it ought to be; but if we suppose that part of the redundant fluid
in each plate is spread uniformly and the rest collected in the circum-
ference, and that in the outer plates the part that is spread uniformly is
^ of the whole, as we supposed in Experiment V, the quantity of re-
dundant fluid in the middle plate when the distance of the outer plates
is 1-15 inches will not agree with observation, unless we suppose that not
more than the 2ist part of it is spread uniformly; but if we suppose that
f of the redundant fluid in the outer plates is spread uniformly the quantity
in the middle plate will agree with observation, if we suppose that about
J of it is spread uniformly and the rest collected in the circumference.

When the distance of the outer plates is 1-65 inches there is no need
of supposing so great a proportion of the fluid in the middle plate to be
disposed in the circumference in order to reconcile the theory with obser-
vation.

N.B. The more uniformly we suppose the fluid to be spread in the
outer plates and the less so in the middle, the greater should be the
quantity in the middle plate.

The above computations were made on the supposition that the plates
were circles of 14 inches diameter, that is, nearly of the same area that
they actually were of.

290] It will appear by just the same method of reasoning that was
used in the remarks on the 22nd Proposition [Art. 74], that a vastly
greater proportion of the redundant fluid in the middle plate will be
collected near its circumference than would be if the outer plates were
taken away, and perhaps this circumstance may make the fluid in the
outer plates be spread more uniformly than it would otherwise be, so
that it seems not improbable that the fluid in the plates may be disposed
in such manner as to make the experiment agree with the theory.

The circumstance of its being necessary to suppose a greater proportion
of fluid in the middle plate to be lodged in the circumference when the
plates are at the smaller distance from each other than when they are at
the greater agrees very well with the theory, for it is plain that the nearer
the outer plates are to each other the greater proportion of the fluid in
the middle plate should be lodged in the circumference.

Summary of results 149

On the whole I see no reason to think that the experiment disagrees
with the theory, though the middle plate was certainly more overcharged
than I should have expected.

General Conclusion.

291] The ist experiment shews that when a globe is electrified the
whole redundant fluid therein is lodged in or near its surface, and that
the interior parts are intirely, or at least extremely nearly, saturated,
and consequently that the electric attraction and repulsion is inversely
as the square of the distance, or to speak more properly, that the theory
will not agree with experiment on the supposition that it varies according
to any other law.

292] The 2nd experiment shews that this circumstance of the whole
redundant fluid being lodged in or near the surface obtains also in other
shaped bodies, as well as in the globe, conformably to the supposition
made in the remarks at the end of Prop. IX [Art. 41]. These two experi-
ments, at the same time that they determine the law of electric attraction
and repulsion, serve in some measure to confirm the truth of the theory,
as it is a circumstance which, if it had not been for the theory, one would
by no means have expected.

293] From the 4th experiment it appears, first, that the charge of
different bodies of the same shape and size, all ready conductors of elec-
tricity, is the same, whatever kind of matter they are composed of; and
secondly, that the charge of thin plates is very nearly the same whatever
thickness they may be of, provided it is very small in respect of their
breadth or smallest diameter ; but if their thickness bears any considerable
proportion to their breadth, then their charge is considerably greater than
if their thickness were very small. These two circumstances are perfectly
conformable to the theory, and are a great confirmation of the truth of it.

294] The remaining experiments contain an examination whether the
charges of several different sized and different shaped bodies bear the
same proportion to each other, which they ought to do according to the
attempts made in different parts of these papers to compute their charges
by theory, supposing, as we have shewn to be the case, that the electric
attraction and repulsion is inversely as the square of the distance: with
regard to this it must be observed that, as in computing their charges I
was obliged to make use of a supposition, which certainly does not take
place in nature, it would be no sign of any error in the theory if their
actual charges differed very much from their computed ones ; but, on the
other hand, if the observed charges agree very nearly with the computed
ones, it not only shews that the actual charges of different bodies bear
nearly the same proportion to each other that they would do if they were

'5°

Experiments on the Charges of Bodies

connected by canals of incompressible fluid, but is also a strong confirma-
tion of the truth of the theory. Now this appears to be the case, for,
first the charge of a tin plate was found to be nearly, though not quite,
the same in whatever part it was touched by the electrifying wire, or in
whatever direction it was placed in respect of the jar by which it was
electrified. Secondly, the charge of a single plate or wire was found to
bear nearly, though, in the first case, I believe, not quite the same pro-
portion to two similar plates or wires of half the diameter or length which
it ought to do according to computation. Thirdly, the proportion which
the charges of a thin circular plate and of three cylindrical bodies of
different lengths and diameters bear to that of a globe agree with com-
putation; but it must be observed that, as the proportion of the charges
of the bodies to that of the globe is determined by the theory within only
very wide limits, their agreement cannot be looked upon as so great a
confirmation of the theory as it would otherwise be, yet as their shapes
are so very different I think that their agreement, even within those
limits, may be considered as a considerable confirmation of it.

'5' ]

PART *. — [{III.} EXPERIMENTS ON COATED {DIELECTRIC}

PLATES.]

Hitherto unpublished: see Table of Contents at the beginning of this volume.]

295] This part consists chiefly of experiments made to determine the
charges of plates of glass and other electric substances coated in the manner
of Ley den vials. The method I used in doing this was nearly of the same
nature as that by which I determined the charges of the other sort of
bodies in the preceding part, but the apparatus was more compact and

<&

\

?

•^r—

•M

7

?

-\

Fig. 20.

portable and is represented in Fig. 20, where Hh is a horizontal board
lying on the ground, LI and LI are two upright pillars supporting the two
horizontal bars Nn and Pp, both at the same height above the ground,
and parallel to each other.

* [Not numbered by Cavendish.]

I 5 2 Experiments on Coated Plates

To these two bars are fastened four upright sticks of glass covered
with sealing wax; they are represented in the figure and shaded black,
but are not distinguished by letters to avoid confusion. To these sticks
of glass are fastened four horizontal pieces of wire A a, Bb, Dd, and Ee,
and to Bb is fastened another wire mM supported at the further end by
a stick of waxed glass.

Rr is a wooden bar reaching from the wire Ee to the pillar LI, and along
the upper edge of this bar runs a wire, one end of which is wound round the
wire Ee and the other reaches to the ground and serves to make a communi-
cation between Ee and the ground. Cc and Kk are two wires fastened firmly
together at k serving to electrify the plate. They are moveable upon K as
a center where they communicate with the inside coating of one or more
large glass jars, and the same electrometer that was used in the former
experiments is fastened to the prime conductor by which the jars are elec-
trified, in order that they may be charged to the same degree each time.

To the ends C and c of the wire Cc is fastened a silk string, as repre-
sented in the figure, passing over the pulley S, with a counterpoise w at
the other end which serves to lift Cc from off the wires Aa and Bb, or to
let it down upon them at pleasure. Gg is a wire the end G of which is bent
into a ring, through which passes the wire Ee, so that Gg turns upon Ee
as a center. Ff is a wire turning in the same manner on Dd. The ends
g and /of these wires are fastened by silk strings to C and c as represented
in the figure, in such manner that when Cc rests on the wires A a and Bb,
Gg and Ff rest on Dd and Ee, but on lifting up Cc, Gg and Ff are also
lifted off from Dd and Ee.

The counterpoise w is so heavy as to overcome the weight of Cc, and
to lift it up till the wires Gg and F/bear against A a and Bb, which prevents
Cc from rising any higher.

Fig. 20 a.

[Note. This Figure was found among the MS. It is not numbered, nor does
any part of the MS. seem to refer to it, but it is inserted here to shew some of the
details of a piece of apparatus similar to that described in the text.]

Methods of making the comparisons 153

296] In making the experiment one of the plates whose charges we
want to compare together, or the plate B as we will call it, is laid on the
bars Nn and Pp, between the sticks of glass and end N, the upper coating
thereof being made to communicate with Bb and Mm by a wire V resting
on Mm, and the lower coating is made to communicate with the ground
by a springing wire 5 fastened to Rr, and by its elasticity bearing against
the lower coating of the plate.

Another coated plate is laid on the same bars between the sticks of
glass and n by way of trial plate, the upper coating of which communicates
with Aa by the wire /?, and the lower coating communicates with Dd by
the springing wire 8. A pair of pith balls also, such as were used in the
former experiments, were suspended from D as represented in the figure.

In trying the experiments, the jars, and consequently the wire Cc,
are charged, the wire Cc being all that time lifted up as high as it will
go by means of the counterpoise. When the jars are charged to the proper
degree as shewn by the electrometer, the wire Cc is let down on the wires
A a and Bb by lifting up the counterpoise. This instantly charges both
the coated plates, for when Cc rests on A a and Bb, and consequently Ff
and Gg rest on Ee and Dd, the lower coatings of both plates communicate
with the ground, and their upper coatings with Cc.

Immediately after this the counterpoise is let go, by which means Cc
is lifted up, and Gg and Ff along with it, till the two last mentioned wires
bear against Aa and Bb, so that immediately after the coated plates are
charged, the communication between them and the wire Cc, by which
they were electrified, is taken away, and at the same time the communica-
tion between the lower coating of the trial plate and the ground is taken
away, and immediately after that a communication is made between the
upper coating of the plate B and the lower coating of the trial plate, and
also a communication is made between the upper surface of the trial plate
and the ground, so that the upper coating of the trial plate and the lower
coating of the plate B both communicate with the ground, and the upper
coating of B and the lower coating of the trial plate communicate with
each other and the wire Dd.

Consequently, if the quantity of redundant fluid communicated to the
wires Bb and Mm and the upper side of the plate B together is equal to
the deficient fluid on the under side of the trial plate, they and the wire
Dd will be neither over nor undercharged after the operation is completed;
but if the redundant fluid in them exceeds the deficient fluid on the lower
side of the trial plate, Dd will be overcharged, and the pith balls will
separate positively. On the other hand, if it is less than the deficient fluid,
the pith balls will separate negatively.

297] The trial plate consisted of a flat plate of glass, or other electric
substance, the lower surface of which was coated all over with tinfoil,

IJ4 The trial plate

but on the upper side there was only a small coating of tinfoil. I had
also fiat plates of brass of different sizes which I could lay on the upper
surface, and slip backwards and forwards, and thereby increase or diminish
the size of the upper coating at pleasure, for the area of the upper coating
is equal to the area of the plate of brass added to that of so much of the
tinfoil as is left uncovered by the brass*.

By this means I could increase or diminish the quantity of deficient
fluid on the lower side of the trial plate at pleasure, for I could alter the
size of the upper coating at pleasure, and the quantity of deficient fluid
on the under side of the plate is not much greater than it would be if the
lower coating was no greater than the upper, and consequently depends
on the size of that upper coating.

As it is necessary that the trial plate should be insulated, it was not
laid immediately on the bars Nn and Pp, but was supported by sticks
of waxed glass fastened to those bars.

Having by these means found what size it was necessary to give to
the upper coating of the trial plate in order that the pith balls should
separate positively just sensibly, and what size it was necessary to give
to it that they might separate as much negatively, I removed the plate B
and placed the plate or plates which I intended to compare with it (or
the plate b as I shall call it) in its room and repeated the experiment in
just the same manner as before. Then, if I found that the size which it
was necessary to give to the upper coating of the trial plate in order to
exhibit the same phenomena was the same as before, I concluded that
the charge of the plate b was the same as that of B. If, on the other hand,
I found that it was necessary to make the area of the upper coating of
the trial plate greater or less than before in any ratio, I concluded that
the charge of b was greater or less than that of B in the same ratio, for
the quantity of deficient fluid on the lower side of the trial plate will be
pretty nearly in proportion to the area of the upper coating.

N.B. In the following experiments it was always contrived so that
the charges of the plates to be compared together should be pretty nearly
alike, so that if the quantity of deficient fluid on the lower surface of the
trial plate was not exactly in this proportion, it would make very little
error in the proportion of the charges.

298] The method above described is that which I made use of in my
first experiment, but I afterwards made use of another method a little
different from this, and which I found more exact, though rather more
complicated, namely, for each set of plates that I wanted to compare

* N.B. In order to estimate how much of the tinfoil was left uncovered, I drev
parallel lines upon it at small equal intervals from each other, and took notic
which of these lines the edge of the brass plate stood at. [Arts. 442, 488.]

Second method of experiment 1 5 5

together I prepared two trial plates, which I shall call L and /, not coated
as that above described, but in the usual way, namely, with the coatings
of the same size on both sides*.

The first of these plates, or L, was of such a size that when used as
a trial plate with the plate B or b on the other side, the quantity of de-
ficient fluid in it was rather more than ought to be in order that the pith
balls should just separate negatively, and the second plate I was rather
greater than it ought to be in order that they should just separate posi-
tively.

I also prepared a sliding plate of the same kind as the trial plate used
in the former method, but whose charge was many times less than that
of the plate B or b. This sliding plate I placed along with the plate B or b
on the side N, and on the other side I placed the trial plate L and found
what size it was necessary to give to the coating of the sliding plate in
order that the balls should just separate negatively. I then removed the
plate B and put b in its room, and found what sized coating it was necessary
to give to the sliding plate in order that the balls should separate the same
as before. Having done this, I removed the trial plate L and put / in its
room, and tried each of the plates B and b as before, finding what coating
it was necessary to give to the sliding plate that the balls might just
separate positively.

Having done this, if I found that it required the coating of the sliding
plate to be of the same size in order to exhibit the same phenomena in
trying the plate B as in trying b, it is plain that the charges of B and b
must be both alike, but if I found that it was necessary to give less surface,
one square inch for instance, to the coating of the sliding plate in trying B
than in trying b, then it is plain that the charge of B exceeds that of b
by a quantity equal to that of the charge of the sliding plate when its
surface is one square inch, supposing, as is very nearly the case, that the
charge of the sliding plate is in proportion to the surface of its upper
coating.

In this way of trying the experiment, it is plain that, in order to
determine the proportion which the charges of B and b bear to each other,
we must first know what proportion the charge of the sliding plate, when
its coating is of a given size, bears to that of B. This I found by finding
what sized coating must be given to the sliding plate that its charge should
be equal to that of another plate, the proportion of whose charge to that
of B I was acquainted with.

It is plain that, if it is necessary to give one inch less surface to the
coating of the sliding plate in trying B than in trying b when the trial
plate L is made use of, it will be necessary to make the same difference
in the surface of the sliding plate when the trial plate / is made use of,

* [Art. 457.]

i 56 Experiments on Coated Plates

so that I might have saved the trouble of making two trial plates. How-
ever, for the sake of more accuracy, I always chose to make two trial
plates and to take the mean of the results obtained by means of each
trial plate for the true result.

299] One reason why this method of trying the experiment is more
exact than the former, or that by means of a sliding plate only, is that
in the former method I was liable to some error from inaccuracy in judging
how much of the tinfoil coating of the trial plate was left uncovered by
the sliding brass plate, whereas in this method, as the charge of the sliding
plate is but small in respect of that of B, it was not necessary to be accurate
in estimating its surface. But I believe the principal reason is that an
error which will be taken notice of by and by, and which proceeds from
the spreading of the electricity on the surface of the glass, is greater in
a sliding plate than in one coated in the usual manner.

In general I think it required scarcely so great an increase of the charge
of the trial plate to make a sensible alteration in the degree of separation
of the pith balls in the following experiments as in the preceding, and
therefore it should seem as if these experiments were capable of rather
more exactness than the former, but this was not the case, as the different
trials were found not to agree together with quite so much exactness in
these experiments as the preceding. For this reason, and also because
they were attended with less trouble, I repeated the experiments oftener,
as I not only compared each plate with the trial plate «for more times
together as I did in the preceding experiments, but in general I repeated
the experiment on several different days.

300] The circumstance which gave me the most trouble in these ex-
periments was the spreading of the electricity on the surface of the glass.
To understand this, let ABab, Fig. 21, be a flat plate of coated glass,
cd and CD being the two coatings, and let CD be positively electrified, and
let cd communicate with the ground.

c — d.

Fig. 21.

It is plain that the electric fluid will flow gradually from CD and
spread itself all round on the surface of the glass, and nearly the same
quantity of fluid will flow from the opposite side of the glass into cd, so
that those parts of the glass which are not coated gradually become charged,
those parts becoming so soonest which are nearest the edge of the glass.

On discharging the plate the uncoated part of the glass gradually
discharges itself, as on the side AB the fluid will flow gradually from the

Spreading of charge on glass 157

uncoated part of the glass into CD, and on the opposite side it will flow
into the uncoated part of the glass from cd.

301] There is a great deal of difference in this respect between different
kinds of glass, as on some kinds it spreads many times faster than on
others. The glass on which it spreads the fastest of any I have tried is
a thin kind of plate-glass, of a greenish colour, much like that of crown-
glass, and which I have been told is brought from Nuremberg*. On the
English plate-glass it does not spread near so fast, but there is a great
deal of difference in that respect between different pieces. On the crown-
glass it spreads not so fast as on the Nuremberg, but I think faster than
on the generality of English plate-glass. On white glass I think it spreads
as slowly as any.

302] The way in which I compared the velocity with which it spread
on different plates was as follows f. I took away the wire Ff (Fig. 20)
and placed the plate which I wanted to try where the plates L or I used
to be placed, the lower coating communicating as usual with Dd by the
wire 8, but the wire /J being drawn up by a silk string so as not to touch
the upper coating. The wire Cc is suffered to rest on Aa and the jars
electrified. When they are sufficiently charged /J is let down on the upper
coating, which instantly charges the plate to be tried, and immediately
the wire Gg is lifted up from Dd, but not high enough to touch A a. Con-
sequently, immediately after the plate is charged, the communication
between Dd and the ground is taken away, and consequently as fast as
any fluid flows from the uncoated part of the under surface of the glass
to the lower coating, some fluid will flow into Dd and overcharge it, and
consequently make the pith balls separate.

303] In order to prevent, if possible, the ill effects proceeding from this
spreading of the electricity, I took some coated plates of glass, and covered
all the uncoated part with cement to the thickness of J or \ an inch, as
in Fig. 22, which represents a section passing through the middle of the

i

U c

' 1 D a

1 .

1

-7=

j a,

Fig. 22.

plate perpendicular to its plane, and in which the glass plate and coatings
are represented by the same letters as before, and the dotted lines re-
present the cement | . Thinking that it would be impossible for the
electricity to spread between the cement and the glass, in which case

* [Art. 497.] t [See Arts- 485' 486- 487- Also Arts- 494 to 499.]

t [Art. 484.]

158 Experiments on Coated Plates

this method must have been perfectly effectual, as it would be necessary
for the electricity to spread itself not only on the perpendicular surface
ef, but also to some distance on the horizontal surface fg, before the
quantity of redundant fluid lodged on the surface of the cement could
bear any sensible proportion to that in the coating CD.

304] The result was that in dry weather the electricity seemed to
spread as fast on those plates which were covered with cement as on the
others, but in damp weather not so fast, the difference between dry and
damp weather being less in those plates which were covered with cement
than the others; and besides that there seemed as much difference between
the swiftness with which it spread on the surface of the Nuremberg and
English plates after they were covered with cement as before, which shews
plainly that the electricity spread between the cement and the glass, and
not on the surface or through the substance of the cement. It could not
be owing, I think, to its passing through the substance of the glass, for
if it was, there would hardly be much difference in the uncoated plates
between damp and dry weather, whereas, in reality, there was a very
great one.

I also tried what effect varnishing the glass plates would have, but I
did not find that it did better, if as well, as covering them with cement.

305] As there seemed, therefore, to be very little advantage in covering
the plates with cement or varnishing them, and as it was attended with
a good deal of trouble, I did not make use of those methods, but trusted
only to letting the wires down and up pretty quick, so as to allow very
little time for the electricity to spread on the surface of the plates, and this
I have reason to think was sufficiently effectual, as I never found much
difference in the divergence of the pith balls, whether the wires were let
down and up almost as quick as I could, or whether they were suffered
to rest a second or two at bottom.

306] As the wire Cc is suffered to rest so short a time on Aa and Bb,
it is plain that the lower coatings of the trial plate and plate to be tried
must have a very free communication with the ground and the outside
coating of the jars, or else there would not be time for them to receive
their full charge. I accordingly took care that the wires which made the
communication should be clean and should touch each other in as broad
a surface as I could conveniently. As for the method I took to have a
ready communication with the ground, it is described in [Art. 258].

307] Besides this gradual spreading of the electricity on the surface
of the glass, there is another sort which is of much worse consequence,
as I know no method of guarding against it, namely, the electricity always
spreads instantaneously on the surface of the glass to a small distance
from the edge of the coating, on the same principle as it flies through the

Instantaneous spreading of charges

'59

air in the form of a spark. This is visible in a dark room, as one may see
a faint light on the surface of the glass all round the edges of the coating,
especially if the glass is thin, for if it is thick it is not so visible*.

[From a photograph taken in the Cavendish Laboratory of a plate of glass with
a circular tinfoil coating on one side, a larger coating being applied to the other side
of the glass. The electrification of the coatings was produced by an induction coil.]

308] There is another circumstance which shews this instantaneous
spreading of the electricity, namely, after having charged and discharged
a coated plate of glass a great many times together without cleaning it,

* [See Art. 532, Feb. i, 1773.]

160 Formula for capacity of plate condenser

I have frequently seen a narrow fringed ring of dirt on the glass all round
the coating, the space between the ring and the coating being clean, and
in general about T\y inch broad*. This must in all probability have pro-
ceeded from some dirt being driven off from the tinfoil by the explosions,
and deposited on the glass about the extremity of that space over which
the electricity spreads instantaneously, and therefore seems to show that
the distance to which the electricity spreads instantaneously is not very
different from -fo of an inch.

309] From some experiments which will be mentioned by and byf,
I am inclined to think that the distance to which the electricity spreads
instantaneously is about ^ of an inch when the thickness of the glass
is about I of an inch and about ^ of an inch when its thickness is about
•jij of an inch; or more properly the quantity of redundant fluid which
spreads itself on the surface of the glass is the same that it would be if
the distance to which it spread was so much, and that the glass in all
parts of that space was as much charged as it is in the coated part.

310] If I charged and discharged a coated plate several times running,
in the dark, with intervals of not many seconds between each time, I
commonly observed that the flash of light round the edges of the coating
was stronger the first or second time than the succeeding ones, which
seems to shew that the electricity spreads further the first or second time
than the succeeding ones. Accordingly I frequently found in trying the
following experiments that the pith balls would separate rather differently
the first or second time of trying any coated plate than the succeeding ones.
Observing that I now speak of the half dozen trials which, as I said in [Art.
299], I commonly took with the same plate immediately after one another.

311] Before I proceed to the experiments it may be proper to remind
the readerj that if a plate of glass or other non-conducting substance,
either flat or concave on one side and convex on the other, provided its
thickness is very small in respect of its least radius of curvature, is coated
on each side with plates of metal of any shape, of the same size and placed
opposite to each other, its charge ought by the theory to be equal to that
of a globe whose diameter is equal to the square of the semidiameter of
a circle whose area equals that of the coating divided by twice the thick-
ness of the glass, supposing the coated plate and globe to be placed at
an infinite distance from any over or undercharged body, and to be
connected to the jar by which they are electrified by canals of incom-
pressible fluid ; provided also that the electricity does not penetrate to any
sensible depth into the substance of the glass, and that the thickness of

* [See Art. 538, Feb. 13, 1773.] f [See below, Arts. 314 to 323.]

} [See Art. 166, Prop. XXXIV, Cor. VI.] { The generalisation, to values of capacity
and distribution for condensers with varying thickness of dielectric, had to await
Green's Easay of 1828, where it follows immediately from his use of the potential
function. Cf. end of Note 3, p. 366.}

Correction for spreading of charge 161

the glass bears so small a proportion to the size of the coating that the
electricity may be considered as spread uniformly thereon.

312] It was before said that the electricity spreads instantaneously
to a certain distance on the surface of the glass, so that the surface of the
glass charged with electricity is in reality somewhat greater than the area
of the coating. Therefore, if the plate is flat, let the area of the coating
be increased by a quantity which bears the same proportion to the real
coating as the quantity of redundant fluid spread on the surface of the
glass beyond the extent of the coating does to that spread on the coated
part of the glass. That is, let the area of the coating be so much increased
as to allow for the instantaneous spreading of the electricity, and let a
circle be taken whose area equals that of the coating thus increased. I call
the square of the semidiameter of this circle, divided by twice the thickness
of the glass expressed in inches, the computed charge of the plate, because,
according to the above-mentioned suppositions, its charge ought to be
equal to that of a globe whose diameter equals that number of inches.

313] In like manner, in what may more properly be called a Leyden
vial, that is, where the glass is not flat, but convex or concave, let a circle
be taken whose area is a mean between that of the inside and outside
coatings, allowance being made for the spreading of the electricity. I call
the square of the semidiameter of this circle, divided by twice the thickness
of the glass, the computed charge of the vial. In like manner, if the real
charge of any plate is found to be equal to that of a globe of x inches
in diameter, I shall call its real charge x.

I now proceed to the experiments.

314] I procured ten square pieces of plate-glass all ground out of the
same piece of glass, three of them 8 inches each way and about -fife inch
thick; three more of about the same thickness 4 inches each way, the
rest were as near to ^ of that thickness as the workman could grind them,
one being 8 inches long and broad, and the other 4 inches. They were
not exactly of the same thickness in all parts of the same piece, but the
difference was not very great, being no where greater than f of the whole.
The mean thickness was found both by actually measuring their thickness
in different parts by a very exact instrument and finding the mean, and
also by computing it from their weight and specific gravity and the length
and breadth of the piece*. The mean thickness, as found by these two
different ways, did not differ in any of them by more than 2 thousandths
of an inch.

315] All these plates were coated on each side with circular pieces of
tinfoil, the opposite coatings being of the same size and placed exactly
opposite to each other. The mean thickness of the plates, which for more

* A cubic inch of water was supposed in this calculation to weigh 253! grains
Troy. [See Arts. 592, 593.]

c. p. i. ii

162

Coated Plates of same kind of glass

convenience I have distinguished by letters of the alphabet, together with
the diameters of the coatings, and their computed charge, supposing the
electricity not to spread on the surface of the glass, are set down in the
following table*.

Plate

Mean
thickness

Diameter
of coating

Computed
charge

A

•2112

6-57

25-5

B

•2132

6-6

25-5

C

•2065

6-5

25-6

D

•2057

2-155

2-82

E

•2065

2-16

2-82

F

•2115

2-175

2-8o

H

•07556

6-8

76-5

K

•07712

2-265

8-3I

L

•08205

2-335

8-3l

M

•07187

2-195

8-38

316] The sizes of the coatings were so adjusted that the computed
charges of D, E, and F are all very nearly alike. Those of K, L and M
were intended to be three times as great as those of the former, and
consequently the diameters of their coatings nearly the same. The com-
puted charges of A , B and C were intended to be three times as great as
those of K, L and M, and consequently the diameter of their coatings
about three times as great, and the computed charge of H was intended
to be three times as great as that of A. By some mistake, however, the
coatings of K, L and M were made rather too small, but the error is very
trifling.

317] My first trials with these plates were to examine whether the
charge of the three plates D, E, and F together was sensibly less when
they were placed close together than when they were placed at 6 inches
distance from each other, that is at as great a distance as my machine
would allow of. I could not perceive any difference. This is conformable
to the theory, as is shewn in [Art. 185]. I chose to make the experiment
with these three plates, as the difference should be more sensible with
them than with any of the others.

318] Secondly. I compared together each of the plates D, E and F.
I could not perceive any sensible difference in their charges f.

Thirdly. The charge of the plate K was found to exceed that of the
three plates D, E and F together in the proportion of 1-016 to i. The
charge of L was not sensibly different from that of K, and that of M very
little different.

Fourth. The charge of each of the plates A, B and C was to that of
the three plates L, K and M together, as 0-905 to i.

* [Art. 482.] f [See Art. 489, Feb. 4, 1772.]

Experiments of comparison and combination 163

Fifth. The charge of H was equal to that of the three plates A, B
and C together.

Therefore the charges of D, K, A and H were to each other as
i. 3'05, 8-28 and 24-9*.

319] It appears, therefore, that the proportion which the charge of K
bears to that of D, and which H bears to that of A, is very nearly the same
as that of their computed charges, but the proportion which the charge
of A bears to that of K is near T'5 part less than it ought to be.

This in all probability proceeds from the effect of the instantaneous
spreading of the electricity bearing a greater proportion to the whole in
the plate K than it does in A , the diameter of whose coating is near three
times as great.

320] In order to form some judgment, if possible, how great the effect
of this instantaneous spreading of the electricity was, I took off the coatings
from the plates A and B], and put on others of just the same area in the
form of a rectangular parallelogram (that of A was 6-414 long and 5-310
broad, and that of C 6-398 long and 5-201 broad), and compared their
charges with that of the plate B, whose charge, as was before said, was
just the same as those of these two plates before their coatings were
altered.

321] I then took off these coatings J, and on A I put a square coating
6-388 each way with slits cut in it, as in Fig. 23, each -fa broad, so as to
divide it into 9 smaller squares, each 1-863 inches each way. The narrow
communications marked in the figure between these squares were each
Y^ of an inch broad.

« .
9

On C I put an oblong coating 6-377 l°ng an<^ 6-343 broad, with four
parallel slits cut in it, as in Fig. 24, each T% broad, the narrow space left
between these slits and the outside being ^ broad. Having done this,
I compared their charges with that of the plate B as before.

* [See also Arts. 656 to 658.] f [C, see Art. 536.] J [Art. 537.]

II — 2

1 64 Experiments on Coated Plates

It must be observed that the area of these slit coatings was somewhat
less than that of the circular or oblong ones, but their whole circumference,
including the circumference of the slits, is more than three times as great
as that of the circular or oblong ones, so that the surface of glass charged

by means of the instantaneous spreading of the electricity was more than
three times as great in these coatings as the former, and consequently
the quantity of that surface may be determined thereby, supposing that,
if it was not for the spreading of the electricity on the surface, the charge
of a coated plate would be the same whatever shape its coating is of,
provided the area of the coated surface is given.

322. In order to find whether the electricity spread to the same dis-
tance upon thin glass as thick, I also took off the coatings from the plate H ,
and in its room put on first a square coating 6-03 inches each way, and then
an oblong one 6-708 long and 6-514 broad, with four slits in it, as in Fig. 24,
each -fa broad, and ascertained the proportion which its charge with each
of these coatings bore to that with the circular coating by comparing it
with another plate, the proportion of whose charge to that of the circular
coating I had before ascertained*.

323] It appeared from these experiments that if we suppose the
electricity to spread instantaneously about -07 of an inch on the thick
glass plates such as A and C, and about -09 on the thin ones, not only
the charges of A , C and H with the three different coatings, but also the
charges of all the plates will agree very well with the theory, as will
appear by the following table ; whereas, if we suppose that the electricity
does not spread sensibly on the surface of the glass, the charge of the
plate H with the slit coating would be greater in proportion to its charge
with the circular or oblong coating than it ought to be in the ratio of
7 to 6, and the error in the plates A and C would not be much less.

* [Arts. 659-663.]

Verification of theory of spreading of charge
324] Plates with circular coatings.

Plates

Diameter

Increased
diameter

Thickness

Computed
charge

Observed
charge

D

2-155 2-295

•2057

3-20

3-21

E

2-16

2-3

•2065

3-20

3-21

F

2-175 2-3I5 -2115

3-17

3-21

K

2-265 2-445 -07712

9-69

974

L

2-335 2-515 -08205

9-63

974

M

2-195 2-375 -07187

9-81

9-84

A

6-57 6-71

•2112

26-6

26-6

B

6-6

6-74

•2132

26-6

26-6

C

6-5

6-64

•2065

26-7

26-6

H

6-8

6-98

•07556

80-6

79-8

325] The same plates with other coatings.

Area which

Plates

Area
of
coating

Circum-
ference

electricity
spreads
over

Increased
area

Computed
charge

Observed
charge

A with oblong

34'i

23-4

1-64

3574

26-9

26-8

A with slits

31-8

73'5

5-15

36-95

27-8

27-8

C with oblong

33'3

23-2

1-62

34-92

26-9

27-0

C with slits

30-4

76-5

5'35

35-75

27-5

27-7

H with oblong

36-4

24-1

2-17

38-57

81-2

80-7

H with slits

33'3

80- 1

7-21

40-51

85-3

85-5

By the observed charge in the foregoing table, I mean only the pro-
portion which the observed charges bore to each other, not the real
observed charges. [See Art. 671.]

326] From the circumstance of the light mentioned in [Art. 307], it
appears plainly that the electricity does actually spread instantaneously
to a small distance on the surface, and from the rings of dirt taken notice
of in Art. 308 it seems likely that the distance to which it spreads is not
very different from what we have here supposed ; moreover, if the distance
to which the electricity spreads is such as we have supposed, the charges
of all these plates bear very exactly the same proportion to each other
that they ought to do by theory, whereas if the distance to which the
electricity spreads is different from that here assigned, and consequently
the proportion of the charges of different plates to each other different
from that furnished by theory, it seems very strange that their charges
should all have happened to agree with computation, notwithstanding
that their thickness and the size and shape of their coatings are so very
different. I think therefore that we may fairly infer both that the distance
here assigned to the spreading of the electricity is right, and that, if it
was not for this spreading of the electricity, the charge of any plate of

*i66 Spreading of charge on Coated Plates

glass would be as the square of the radius of the circle equal in area to the
coated surface divided by twice the thickness of the glass, that is, that
the actual charges are in proportion to the computed ones.

327] Though it seems likely from these experiments that the electricity
spreads further on the surface of thin glass than it does on thick, yet I
can not be sure that it does, as the difference observed is not greater than
what might proceed from the error of the experiment. However, as there
seems nothing improbable in the supposition, I shall suppose in the
following pages that it does really do so.

328] When I say that the electricity spreads T^ff of an inch on the
surface of the glass, I mean that the quantity of electricity thereby spread
on the uncoated part of the glass is the same that it would be if it actually
spread to that distance, and if all that part of the glass which it spread
over was charged in the same degree as the coated part, and consequently
that the charge of the plate is the same as if the size of the coating was
increased by a ring drawn round it -07 of an inch broad, and that the
electricity was prevented from spreading any further. But I would by
no means be understood to mean that no part of the electricity spreads
to a greater distance than that, as it seems very likely that it does so,
but that the part furthest from the coating is less charged with electricity
than that nearest to it.

329] What is said above must be understood of the distance to which
the electricity spreads with that degree of strength which I commonly
made use of in my experiments, but I also made some trials with the
plates A and C to determine to what distance it would spread with two
other degrees of electricity.

If a jar with Lane's electrometer fixed to it* was charged to the higher
degree, it would discharge itself when the knobs of the electrometer were
at -053 inches distance; when it was charged to the lower degree, it dis-
charged itself when they were at about half that distance, or at -027 of
an inch; and when it was charged to the usual degree, it discharged itself,
as was before said, at -04 of an inch, so that the usual degree of electricity
was about a mean between these twof.

It seemed as if the electricity spread about ^ of an inch further with
the stronger degree of electricity than with the weaker, but the experi-
ment was not accurate enough to determine it with certainty.

330] I made an experiment of the same kind to determine whether
the electricity spread to the same distance on crown-glass as on this. It

* [Art. 540, Feb. 16, 1773.]

f [By Macfarlane's experiments (Trans. R. S. Edin. vol. xxvin, Part n, 1878)
the electromotive force required to produce sparks between flat disks at those
distances would be 14, n-8, and 9 units respectively.]

Lane's discharging electrometer

167

1 68 Specific effect of the glass dielectric

seemed to spread about ^ of an inch on it, that is, rather less than on
the plate H, though its thickness was, of the two, rather less. But whether
this difference is real, or owing to the error of the experiment, I cannot tell.

331] There seems no reason, from the foregoing experiments, to think
that the charge of any of these plates is sensibly greater than it would be
if the electricity was disposed uniformly on their coated surfaces, as their
charges agree very well together without such a supposition. If we suppose
that the charges of any of them are sensibly greater than they would be if
the fluid was disposed uniformly, it will be necessary to suppose that there
is a still greater difference between the distance to which the electricity
spreads on the surface of thin plates and that of thick ones than what we
have assigned. But I shall speak more on this subject at the end of
Art. [365].

332] But though it appears from the foregoing experiments that the
charges of plates of glass of different thicknesses with coatings of different
shapes and sizes bear the same proportion to each other that they ought
to do by theory, yet their charge is many times greater in proportion to
that of a globe than it ought to be on a supposition that the electricity
does not penetrate to any sensible depth into the substance of the glass,
as will appear by the following experiment.

333] In order to compare the charge of the plate D with the globe
of i2T\j inches used in the former part, I made two plates coated as a
Leyden vial, the charge of each of which was about \ that of D, each
consisting of two plates of glass cemented together and coated on their
outside surfaces with circular pieces of tinfoil about if inch in diameter*.

I then compared the charge of each of these double plates with that
of the globe in the same manner that I compared together the charges
of different bodies in the former part, the only difference being that, in
trying either of these double plates, I made a communication between
the lower coating of the plate and the ground, the wires Mm and Dd
(Fig. 14) being contrived so that they were sure to fall on the upper
coating f.

By this means the charge of each of these double plates was found to
be just equal to that of the globe. The charge of the plate D was then
compared with that of the two double plates together, and was found to
be less than that in the proportion of 263 to 272, and consequently the
charge of the plate D is to that of the globe as 26-3 to 13-6.

334] Before we go further it will be proper to consider what effect
the three circumstances taken notice of in Art. 277 will have in altering

* If they had been made of a single piece of glass, the coatings must have been
so small as would have been inconvenient unless the glass had been of a greater
thickness than could have been easily procured. [Arts. 446, 451, 649, 653, 654.]

t [Arts. 455, 456, 478.]

Disturbing influence of adjacent bodies 169

the proportion of the charge of the double plate to that of the globe.
With regard to the two first, it appears that the charge of the globe and
double plate will neither of them be sensibly different from what they
would be if they were placed at an infinite distance from the jar by which
they are electrified, and moreover, in trying the globe, the repulsion of
the redundant fluid in the globe increased the deficience of fluid in the
trial plate as much as the attraction of the trial plate increased the quantity
of redundant fluid in the globe*, so that it required the same size to be
given to the trial plate as it would have done if the globe and trial plate
had exerted no attraction or repulsion on each other; and in trying the
coated plate, the coated plate could not sensibly increase the deficience
in the trial plate, nor could the attraction of the trial plate sensibly increase
the redundance in the coated plate, so that neither of these two causes
had any tendency to alter the proportion of the charges of the globe and
coated plate to each other.

335] But the third cause will have a sensible effect, for in trying the
globe the floor and sides of the room near it would be made undercharged,
which would increase the charge of the globe, whereas in trying the coated
plate the floor would not be made sensibly undercharged, nor, if it was,
would it have any sensible effect in increasing the charge of the plate.

So that the charge of the globe bore a sensibly greater proportion to
that of the coated plate than it would have done if it had been placed
at an infinite distance from any other bodies.

How much the charge of the globe should be increased hereby I can
not tell, but I should imagine it should be at least by -J^th part, for if
the room had been spherical and 16 feet in diameter (about its real
size) and the globe placed in its center, it should have been increased
as much as thatf, and as the globe was really placed three times as

* [Note 17.]

f Let the globe Bbfi, whose centre is C, be insulated in the hollow globe Dd8
concentric with [it]. Let the inner globe be pos. electrified by the canal BE not

communicating with the outer globe, and let the outer globe communicate with the
ground. The quant, dene, fluid in the outer globe must be equal to the redundant

170 Comparisons of plates of rosin with disks

near to the floor as to the ceiling*, I suppose the effect to have been still
greater.

336] In order to find out, if possible, how much the charge of the globe
was increased hereby, I made four flat plates of a mixture of rosin and
bees waxf, about 4 inches square and -22 thick, and coated each of them
with circles of about 1-8 inches in diameter, and compared the charge of
each of them separately with that of a circular plate of tin, 9-3 inches in
diameter. I then compared the charge of two of these plates together
with that of a tin circular plate 18^ inches in diameter, and lastly I
compared the charge of all together with that of a circle of 36 inches
diameter J.

337] By a mean of the different experiments it appears that the charge
of each of the rosin plates was alike, and that the charge of any one of
them was to that of the circle of 9-3 inches as 10-34 to 9'3> that the charge
of the circle of i8£ inches was to that of two of the rosin plates together
as 20-19 to 21-96, and that the charge of the circle of 36 inches was to that
of all four plates as 43-75 to 42-06.

But the charge of the four plates together will not be exactly four
times the charge of one plate singly, as some allowance must be made for
the charge of the wire connecting their upper surfaces, and, besides that,
the charge of the plates when placed close together will not be quite so
great as if placed at a distance fron each other §.

in the inner globe, and the attraction of the outer globe on the canal BE is to the
repulsion of the inner one thereon as

i i
CD '' I3C'

and therefore the quantity of redun. fluid in the inner globe is to that which it
would contain if the outer globe were away as

If room was spherical, 16 feet in diameter, globe in middle of it, its charge should
be increased in ratio of 1 6 to 15 by reason of undercharged floor, &c.

* [This is the only indication of the Height of the room. The circles were sus-
pended by silk strings from a horizontal bar (Art. 466) 87-5 inches from the floor.
By Art. 474 the platform 14 inches high diminished the height of the bodies in the
ratio of 2 to 3. Hence the height of the center of the bodies from the floor was
42 inches, and the height of the room 4 x 42 inches, or 14 feet. This would agree with
the height of the top of the circle of 18 inches being 51 inches from the floor (Art. 472).]

f These plates are non-conductors of electricity, and may be charged as Leyden
vials. The manner in which I made them will be described in the following pages
[Arts. 373, 514]. My reason for making them of these materials is that the charge
of such a plate is much less than that of a plate of glass of the same dimensions.

J It must be observed that, in the two last mentioned comparisons, the rosin
plates were placed close together and their upper surfaces connected by a piece of
wire.

§ [Art. 5570

Capacity as ajfected by floor and walls of the room 1 7 1

By trying the charge of all four rosin plates together by the machine,
Fig. 20, both when placed close together and at as great a distance from
each other as I could, I found their charge when close together to be to
their charge when placed at a distance nearly as 41 to 41^, and, from some
other experiments I made, I am inclined to think that the charge of each
of the wires which connected the upper coatings of the plates was to that
of one plate alone as 28 to 930*.

From these circumstances, I am inclined to think that the charge of
two plates together is to that of one plate alone as 21-96 to 10-34, and
that the charge of the four plates together is to that of one alone as
42-06 to 10-34, an(i consequently that the charges of the tin circles of
9-3 inches, i8£ inches and 36 inches are to each other as 9-3, 20-19 and
4375 1-

338] Though I do not know how to calculate how much the charge
of the circles ought to be increased by the attraction of the undercharged
ground, yet I think there can be little doubt but that if the charge of the
plate of i8J inches is increased in any ratio whatever as that of xto x — i8|,
the charge of the plate of 36 inches will be increased in the ratio of x to
x — 36, and that of the plate of 9-3 inches in the ratio of x to x — 9-3 ;
therefore if we suppose that the charge of the i8J inch plate is increased
in the ratio of 9 to 8, or of i66£ to i66J — i8i, the charges of the three
plates should be to each other as

36 x i66| i8£ x i66J , 9-3 x i66£

— , - and '

130^ 148 I57'2

that is, as 43-37, 19-65 and 9-3,

which agrees very nearly with experiment, and nearer so than it would
have done if we had supposed the charge of the i8£ inch plate to have
been increased in any other proportion which can be expressed in small
numbers J.

339] I think we may conclude therefore that the charge of the 12-1 inch
globe was increased by the attraction of the undercharged ground nearly
in the proportion of 9 to 8, for I think there can be little doubt but that
the charge of the globe must be increased thereby in nearly the same
ratio as that of the i8£ inch plate, and therefore we may conclude that the
charge of the plate D is to the charge which the 12-1 inch globe would
receive, if it was placed at a great distance from any over or undercharged
matter, nearly in the proportion of 26-3 to 12-1, or, in other words, the
charge of the plate D is 26-3, which is rather more than eight times greater
than it ought to be if the electric fluid did not penetrate into the glass.
I shall speak further as to the cause of this in [Art. 349].

* [Arts. 555, 558, also 443.] t [Art. 649.]

J [Art. 652, and Note 24.]

172 Experiments on Coated Plates

340] In order to try the charge of what Jipinus* calls a plate of air,
I took two flat circular plates of brass, 8 inches in diameter and J thick,
and placed them on the bars Nn and Pp of the machine (Fig. 20), the two
plates being placed one over the other, and kept at a proper distance from
each other by three small supports of sealing-wax placed between them,
the supports being all of the same height, so that the plates were exactly
parallel to each other. Care was also taken to place the plates perpendicu-
larly over each other, or so that the line joining their centers should be
perpendicular to their planes.

The lowermost plate communicated with the ground by the wire RS,
and the uppermost communicated with Mm by the wire V, just as was
done in trying the Leyden vials.

I then found its charge, or the quantity of redundant fluid in the
uppermost plate, in the usual manner, by comparing it with the plate D,
and found it to be to that of D asf....

341] As I was desirous of trying larger plates than these, and was
unwilling to be at the trouble of getting brass plates made, I took two
pieces of plate-glass J n£ inches square, and coated each of them on one
side with a circular plate of tinfoil 11-5 inches in diameter, and placed
them on the machine as I did the brass plates in the former experiment,
with the tinfoil coatings turned towards each other, and kept at the
proper distance by supports of sealing-wax as before, care being taken
that the tinfoil coatings should be perpendicularly over each other.

For the more easy making a communication between the circular
coating of the lower plate and the ground, and between that of the upper
plate and the wire Mm, I stuck a piece of tinfoil on the back of each plate,
communicating by a narrow slip of the same metal with the circular
coatings on the other side.

I then tried the charge as before, the lower plate communicating with
the ground and the upper with the wire Mm.

As glass does not conduct electricity, it is plain that the quantity of
electric fluid in the pieces of tinfoil will be just the same that it would be
if the glass was taken away, and the pieces of tinfoil kept at the same
distance as before.

The distance of the two circular coatings of tinfoil was measured by
the same instrument with which I measured the thickness of the plates
of glass, and may be depended on to the loooth or at least to the 5ooth
part of an inch§.

* \Mirn. Berl. 1756, p. 119.]

•f The memoranda I took of that experiment are lost, but to the best of my
remembrance the result agreed very well with the following experiment.

J [Art. 517.]

§ [See Art. 459, "Bird's instrument," and "dividing machine," Art. 517. Also
594. 595-]

Results for plates of air 173

342] In this manner I made the experiment with the plates at four
different distances, namely -910, -420, -288 and -256, and when I had made
a sufficient number of trials with the plates at each distance, I took off
these circular coatings and put on smaller, namely of 6-35 inches diameter,
and tried the experiment as before with the plates at -259 inches distance.
The result of the experiments is given in the following table :

343*]

No. of
Experi-
ment

Distance
of the
tinfoil
coatings

Diameter of
the coatings
corrected for
the spreading
of electricity

Computed
charge

Observed
charge

Observed
charge by
computed
charge

Diameter
of coatings
by distance
of ditto

I
2

•910
•4.2O

n-5

18-2

3Q'4

27
«2

1-49

1*^2

12-6

27-4

•3

•288

S7'4

72-1

1-26

4O

A

•2<i6

64-6

78- T

I'2I

A*\

5

•259

6-35

19-5

/« 0
26-5

1-36

24-5

It is plain that some allowance ought to be made in these trials for
the spreading of the electricity on the surface of the glass. In the above
table I have supposed it to spread -05 of an inch, but the effect is so small
that it is of very little signification whether that allowance is made or not.

344] In my former paper [Art. 134] I expressed a doubt whether the
air contained between the two plates in this experiment is overcharged
on one side and undercharged on the other, as is the case with the plate
of glass in the Leyden vial, or whether the redundant and deficient fluid
is lodged only in the plates, and that the air between them serves only to
prevent the electricity from running from one plate to the other, but the
following experiment shews that the latter opinion is true.

I placed the two brass plates on the machine (Fig. 20), and tried their
charge as before, except that, after having charged the plates f, I im-
mediately lifted up the upper plate by a silk string so as to separate it
two or three inches from the lower one, and let it down again in its place
before I found its charge by making the communication between Bb
and Dd and between A a and Ee.

The way I did this was that as soon as I had let down the wire Cc
on A a and Bb, and thereby charged the plates, I lifted it up again half
way so as to take away the communication between Cc and the upper
plate &c., but did not lift it quite up, so as to make the communication
between Bb and Dd, and between A a and Ee, till after I had separated
the upper plate from the lower, and put it back in its place.

* [See Arts. 669, 519.]

f [Arts. 511, 516, Dec. 18, 26, 1772.]

174 No specific effect of plates of air

I could not perceive any sensible difference in the charge, whether I
lifted up the upper plate in the above-mentioned manner, or whether
I tried its charge without lifting it up.

345] It is plain that in lifting up the upper plate from the lower and
letting it down again, the greatest part of the air contained between the
two plates must be dissipated and mixed with the other air of the room,
so that if the air contained between the two plates was overcharged on
one side and undercharged on the other, the charge must have been very
much diminished by lifting up the upper plate and letting it down again,
whereas, as I said before, it was not sensibly diminished.

I think we may conclude, therefore, that redundant and deficient fluid
is lodged only in the plates, and that the air between them serves only
to prevent the electricity from running from one plate to the other.

346] As this is the case, the charge of these plates ought, according
to the theory, to be equal to that of a globe whose diameter equals the
square of the radius of the plate or circular coating divided by twice their
distance, that is, to their computed charge, provided the electricity is
spread uniformly on the surface of the plates, and therefore in reality
the numbers in the last column but one ought to be rather greater than
in the last but two, and moreover the less the distance of the plates is in
proportion to the diameter of the coating, the less should be the proportion
in which those numbers differed, and if the distance is infinitely small in
proportion to the diameter, the proportion in which those numbers differ,
should also be infinitely small.

347] This will appear by inspecting the table to be the case, only it
seems from the manner in which the numbers decrease, that they would
never become equal to unity though the distance of the plates was ever
so small in respect of their diameter, and I should think, or rather I
imagine, would never be less than i-i, so that it seems as if the charge
of a plate of air was rather greater in proportion to that of the globe than
it ought to be, and I believe nearly in the proportion of n to 10*.

348] The reason of this, I imagine, is as follows. It seems reasonable
to conclude from the theory that when a globe or any other shaped body
is connected by a wire to a charged Leyden vial, and thereby electrified,
the quantity of redundant fluid in the globe will bear a less proportion
to that on the positive side of the jar than it would do if they could be
connected by a canal of incompressible fluid f, but in all probability when
a plate of air is connected in like manner to the Leyden vial, the quantity
of redundant fluid on its positive side will bear nearly the same proportion
to that in the vial that it would do if they were connected by a canal of

* [Art. 670.]

f This seems likely from Appendix, Coroll. V [Art. 184].

Possible explanations of specific effect of the dielectric 175

incompressible fluid, and consequently the charge of the plate of air in
these experiments ought to bear a greater proportion to that of the globe
than if they had been connected to the vial by which they were electrified
by canals of incompressible fluid.

349] It was said in Art. 339 that the charges of the glass plates were
rather more than eight times greater than they ought to be by the theory,
if the electric fluid did not penetrate to any sensible depth into the glass.
Though this is what I did not expect before. I made the experiment, yet
it will agree very well with the theory if we suppose that the electricity,
instead of entering into the glass to an extremely small depth, as I thought
most likely when I wrote the second part of this work*, is in reality able
to enter into the glass to the depth of -^ of the whole thickness of the glass,
that is, to such a depth that the space into which it can not penetrate is
only £ of the thickness of the glass, as in that case it is evident that the
charge should be as great as it would be if the thickness of the glass was
only | of its real thickness, and the electricity was unable to penetrate
into it at all.

350] There is also a way of accounting for it without supposing the
electricity to enter to any sensible depth into the glass, by supposing that
the electricity at a certain depth within the glass is moveable, or can
move freely from one side of the glass to the other.

Thus, in Fig. 25, let ABDE be a section of the glass plate perpen-
dicular to its plane, suppose that the electricity from without can pene-

Fig. 25.

trate freely into the glass as far as the line db or ed but not further,
suppose too that within the spaces abfla and edSe the electric fluid is
immoveable, but that within the space a/?8e it is moveable, or is able to
move freely from the line aft to 8e. Then will the charge of the plate be
just the same as on the former supposition, provided the distances aa
and ee are each -fa of the thickness of the plate f.

* [Refers to Art. 132.]

| The only reason why I suppose the electric fluid to be able to enter into the
glass from without as far as the lines ab and ed is that Dr Franklin has shewn that
the charge resides chiefly in the plate of glass and not in the coating, and conse-
quently that the electricity is able to penetrate into the glass to a certain depth.
Otherwise it would have done as well if we had supposed the fluid to be immoveable
in the whole spaces ABfta and ED8e, and that the distance A a and Et are each

of AE.

176 Specific effect of the dielectric

351] But I think the most probable supposition is that there are a
great number of spaces within the thickness of the glass in which the
fluid is alternately moveable and immoveable.

d

Fig. 26.

Thus let ABDE (Fig. 26) represent a section of the plate of glass as
before, and let the glass be divided into a great number of spaces by the
parallel lines ab, a/3, ed, eS, &c., and suppose that in the two outermost
spaces ABba and EDde the fluid is moveable, that in the two next spaces
ab^a and ed8e it is immoveable, and that in the two next spaces it is
moveable, and so on. The charge will be the same as before, supposing
the sum of the thickness of the spaces in which the electricity is immove-
able to be % of the whole thickness of the glass, as it is shewn that the
charge of such a plate will be the same as that of a plate in which the
electricity is entirely immoveable, whose thickness is equal to the sum of
the thicknesses of those spaces in which we supposed the fluid immove-
able*.

352] It must be observed that in those spaces in which we supposed
the fluid to be moveable, as in the space ABba for example, though the
fluid is able to move freely from the plane Ab to ab, that is, though it
moves freely in the direction Aa or aA, or in a direction perpendicular
to the plane of the plate, yet it must not [be] able to move lengthways,
or from A to B, for if it could, and one end of the plate AE was electrified,
some fluid would instantly flow from AE to BD, and make that end
overcharged, which is well known not to be the case. The same thing must
be observed also with regard to the two former ways of explaining this
phenomenon.

353] The chief reason which induces me to prefer the latter way of
accounting for it is that in the two former ways the thickness of the
spaces in which the fluid is moveable must necessarily be very considerable.
In thick glass, for example, in a plate of the same thickness as D, it must
be not less than •$$ of an inch in the first way of explaining it, and in
the second way it must be still greater. Now if the electric fluid is able
to move through so great a space in the direction AE, it seems extra-
ordinary that it should not be able to move in the direction AB, whereas
in the latter way of accounting for it the thickness of the spaces in which
the electricity is moveable may be supposed infinitely small, and conse-

* [Prop. XXXV, Art. 169, and Note 15.]

not influenced by strength of charge 1 77

quently the distance through which the electricity moves in the direction
AE also infinitely small.

354] Another thing which inclines me to this way of accounting for
it is that there seems some analogy between this and the power by which
a particle of light is alternately attracted and repelled many times in its
approach towards the surface of any refracting or reflecting medium. See
Mr Michell's explanation of the fits of easy reflection and transmission
in Priestley's Optics, page 309.

355] To whichever of these causes it is owing that the charges of these
plates are so much greater than they should be if the electric fluid was
unable to enter into the plate, it was reasonable to expect that the greater
the force with which the plate was electrified, the greater should be the
depth to which the electric fluid penetrates into the glass, or the greater
should be the thickness of the spaces in which we supposed the fluid to
be moveable, and consequently in comparing the charge of the plate D
with the circle of 36 inches diameter, or with any other body, the greater
the force with which they are electrified the greater proportion should
the charge of the glass plate bear to that of the circle.

356] I therefore compared the charge of the plate D with that of the
circle of 36 inches with electricity of two different degrees of strength,
namely the same which I made use of in [Art. 329], in trying whether
the distance to which the electricity spread on the surface of glass was
different according to the strength of the electricity.

The way in which I compared their charges was just the same that I
made use of in comparing the rosin plate with the tin circles in [Art. 337].
The event was that I could not perceive that the proportion which their
charges bore to each other with the stronger degree of electricity was
sensibly different from what they did with the weaker*.

357] But it must be remembered that it seemed from the experiment
related in [Art. 329], that the electricity spread ^ of an inch further on
the surface of the glass with the stronger degree of electricity than with
the weaker. The difference of charge owing to this difference in the
spreading of the electricity is -fe part of the whole, so that it seems that
if the electricity had been prevented from spreading on the surface of the
glass, the proportion of the charge of the glass plate to that of the tin
circle would have been less with the stronger degree of electricity than
with the weaker, and that nearly in the proportion of 16 to 17.

358] I also made an experiment to determine whether the charge of
a coated plate of glass bore the same proportion to that of another body
when the electricity was very weak as when it was of the usual strength f.

* [Arts. 547, 551, 553, also Arts. 451, 463, 526, 535, 538, 664.]
t [Arts. 539, 666.]

C. P. I. 12

178 Spreading is dependent on strength of charge

For this purpose I first found what proportion the charge of a tin
cylinder 15 feet long and 17 inches in circumference bore to that of the
two plates D and E together when the electricity was very weak. This
I did in the manner represented in Fig. 27, where AB is the tin cylinder

Fig. 27.

supported horizontally by non-conductors. DC is a brass wire 37 inches
long and about £ inch in diameter supported also horizontally by non-
conductors, the end C being in contact with the cylinder, and a pair of
fine pith balls being suspended from the other end D. FE is a piece of
wire communicating with the prime conductor, and between it and DC
is suspended by a silk string the wire FT in a vertical situation.

359] The cylinder AB, and consequently the wire DC, were first
electrified negatively to such a degree as to make the pith balls separate
to the distance of one diameter of the balls. The prime conductor and
wire FE being then charged to the usual degree, as shewn by the usual
electrometer hung down from it, one end of the wire W was brought in
contact with E so as to be electrified by it, and was then immediately
removed and brought in contact with DC so as to communicate its elec-
tricity to the cylinder*.

Now I found that if the wire W was 29 inches long, and $ in diameter,
and its electricity was twice communicated in this manner to the cylinder,
the pith balls would separate as much positively as they before did nega-
tively, consequently the cylinder AB and the wires DC and W together,
when electrified to such a degree as to make the pith balls separate one
diameter, contain as much electricity as the wire W alone does when
electrified in the usual degree.

The cylinder AB was then removed, and the two glass plates D and E
placed under the wire DC in its room, their upper coatings communicating

* [See plan at Art. 539.]

Results slight and uncertain 179

with DC, and their lower coatings with the ground, and the operation
performed as before. I found that I was obliged to change the wire W
for one of the same thickness, and only 22 inches long, in order that the
pith balls should separate the same as before.

360] Therefore the charge of the two plates D and E and the wire DC
together is to that of the tin cylinder and wire DC together as the charge
of a wire J inch thick and 22 inches long to that of a wire of the same
thickness and 29 inches long, that is, as i to 1-26, and consequently, as
the charge of the wire DC is but small in comparison of that of the two
plates, the charge of the two plates will be to that of the tin cylinder pretty
nearly in the same proportion of i to 1-26*.

Having thus found what proportion the charges of the plates and
cylinder bear to each other when electrified in a very weak degree, I tried
what proportion they bore with the usual degree of electrification.

361] To this purpose I placed the two plates on the machine repre-
sented in Fig. 20 between M and m in the usual manner, and on the other
side I placed a sliding coated plate, and found as usual what size must
be given to the coating of this plate that the pith balls should just separate
positively, and what size must be given to it that they should just separate
negatively.

I then removed the two plates and suspended the tin cylinder so as
to touch the wire Mm, but without touching any other part of the machine,
and found what size it was necessary to give to the coating of the sliding
plate that the pith balls should separate as before.

By this means the charge of the tin cylinder was found to be to that
of the two plates as 1-33 to i. Therefore the charge of the two plates
seems to bear pretty nearly the same proportion to that of the cylinder
whether the electricity is of the usual strength or very weak. But if we
suppose that the electricity spreads -07 inches on [the] surface of glass
with the usual degree of electrification, and that it does not spread sensibly
with the weak degree of electrification, then the proportion which the
charge of the glass plates bears to that of the cylinder should be less with
the usual degree of electrification than with the weak one, and that by
about A part.

This difference, however, is not more than what might very well
proceed from the error of the experiment.

362] On the whole, I am uncertain whether the charge of a glass plate
would really bear a rather less proportion to that of a globe or other body
when the electricity is strong than when it is weak, provided the electricity

* I believe the true proportion is between that of i to 1-28 and that of i to 1-37,
but as the experiment is not capable of much accuracy, I think it needless to
trouble the reader with the computation. [See Art. W>6, and Note 25, p. 416.]

12—2

180 Discussion of results on spreading of charge

was prevented from spreading on the surfaces as it should seem by these
experiments, or whether it was not rather owing partly to the error of
the experiment, and partly to there not being so much difference in the
distance to which the electricity spreads on the surface of the glass ac-
cording to the different degree in which it is electrified, as I imagined.

If the first of these suppositions is true, I do not know how to reconcile
it with the theory, except by supposing that the greater the force with
which the plate is electrified the less is the depth to which the electricity
penetrates into the glass, or the less is the thickness of the spaces in which
we supposed the fluid to be moveable.

Though it seemed natural to expect that the electric fluid should
penetrate further into the glass, or that the fluid within the glass should
move through a greater space when the glass was strongly electrified than
when weakly, that is, when the force with which the fluid was impelled
was great than when it was small, yet it is not strange that it should be
otherwise, as it is very possible that the electric fluid may penetrate with
great freedom to a certain depth within the glass, and that no ordinary
force shall be able to impel it sensibly further, and in like manner it is
very possible that the fluid may be able to move with perfect ease in the
space ae (Fig. 25) and yet that no ordinary force shall be able to move
the fluid at all beyond that space.

But it would be very strange that the fluid should penetrate to a less
depth within the glass, or that the fluid within the glass should move
through a less space when the glass is strongly electrified than when weakly.

363] The reader perhaps may be tempted from this circumstance to
think that the reason of the actual charge of the glass plates so much
exceeding their computed charge is not owing to the electric fluid pene-
trating into the glass, or to any motion of the fluid within the glass, but
to some error in the theory. But I think the experiments on the plate
of air [Art. 344] form a strong argument in favour of its being owing to
the penetration of the electric fluid into, or its motion within the glass,
for it appears plainly from these experiments that the electric fluid does
not penetrate into the air, and on account of the fluidity of the air it
seems very improbable that the electric fluid within the air should be
able to move in the manner we supposed it to do within the glass ; whereas
it appears plainly from Dr Franklin's analysis of the Leyden vial, that
the electric fluid does actually penetrate into the glass.

Therefore as this excess of the observed charge above the computed
does not take place in the plate of air, where it could not do it consistently
with the theory, but does in the glass plate, where it may do so consistently
with the theory, I think there seems great reason to think that it is not
owing to any defect in the theory, but to some such motion of the electricity
as we have supposed.

Dielectric influence of temperature \ 8 1

364] I could not find that there was any difference in the proportion
which the charge of a glass plate bore to that of another body whether
they were electrified positively or negatively*.

365] It was said in Art. [331], that there seemed no reason to think
that the charge of the plate D, or of any other of those glass plates was
sensibly greater than it would be if the electricity was spread uniformly
on their surfaces, whereas the charge of most of the plates of air was found
very considerably greater than it would be on that supposition. But this
is by no means inconsistent, for according to the first way of accounting
for the great excess of the real charge of those plates above the computed,
namely supposing that the electricity penetrates into the glass to the
depth of T7jj of its thickness, the increase of its charge on account of the
electricity being not spread uniformly, should be not greater than it would
be if the glass was only \ of its real thickness, and the electricity was
unable to penetrate into it at all, and therefore should not be greater than
it is in a plate of air in which the thickness is ^ of the diameter, and
should therefore in all probability be quite imperceptible.

And by Prop. XXXVI [Art. 170], the increase of charge should hardly
be much, if at all, greater according to the second or third way of ac-
counting for this phenomenon.

366] In order to tryf whether the charge of coated glass is the same
when hot as when cold, I made use of the apparatus in Fig. 28, where
ABCba represents a short thermometer tube with a ball BCb blown at
the end and another smaller ball near the top. This is filled with mercury
as high as the bottom of the upper ball, and placed in an iron vessel
FGMN filled with mercury as high as FN. Consequently the ball BCb
was coated as a Leyden vial, the mercury within it forming the inside
coating, and that in the vessel FGMN the outer one.

In trying it, I set the vessel FGMN on the wooden bars of the machine
represented in Fig. 20, near the end NP, and dipt a small iron wire bound
round the wire Mm into the mercury within the tube, so as to make a com-
munication between the wire Mm and the inside coating, the outside coating,
or the mercury in FGMN, being made to communicate with the ground.

It was heated by a lamp placed under FGMN, and its charge was
frequently tried while heating by comparing with a sliding coated plate
placed on the other end of the wooden bars.

When it was sufficiently heated, the lamp was taken away, and the
charge frequently tried in the same manner while cooling, a thermometer
being dipt every now and then into the mercury in FGMN to find its heat.

367] As it was apprehended that the electricity might spread further
on the surface of the glass while hot than while cold, a paper coating

* [Art. 463.] f [Art. 556, March 21, 1773. See also Arts. 548, 549, 680.]

182

Experiments on Coated Plates

Glass becomes conducting as temperature rises 1 8 3

DBbd was fastened on the tube, so that as the outside coating was made
to extend as far as Dd, that is three or four inches above the mercury in
FGMN, where the tube was very little heated, and as the inside coating
reached still higher, that is to the bottom of the upper ball, no sensible
error could proceed from thence.

The use of the upper ball was to prevent the mercury within the tube
from overflowing when hot.

368] By a mean between the experiments made while the ball was
heating and while cooling, its charge answering to the different degrees
of heat was as follows.

Heat

Charge

Difference
of heat

Difference
of charge

55

IOO

IO2

4

157
222

295

104
116
136

65

73
10

12
20

5

305

141

369] At 295° the electricity passed through the glass pretty freely,
but at 305° much faster. It appears, therefore, that the charge of glass
is considerably greater when heated to such a degree as to suffer the
electricity to pass through than when cold, but that its charge does not
begin to be sensibly increased till it is heated to a considerable degree*.

370] On the charges of plates of several different sorts of glass, and also
of plates of some other substances which do not conduct electricity, charged
in the manner of Leyden vials.

The result of the experiments I made on this subject is contained in
the two following tables: —

TABLE OF GLASS PLATES f.

!

Observed

Thickness

Diameter

Ditto
corrected

Computed
charge

Observed
charge

charge
by com-
puted

Specific
gravity

charge

Flint glass ground flat

•2115

2-23

2-37

3-32

26-3

7-93

3-279

Ditto a thinner piece

•104

2-215

2-385

6-84

52-3

7-65

3-284

Plate glass P

•127

2-85

3-02

8-98

71-9

8-01

2-752

W

•I72

3-435

3-585

9-34

74-8

8-01

2-787

G

•1848

3-575

3-725

9-38

75-5

8-05

2-973

N

•106

2-12

2-29

6-18

5'-4

8-31

2-682

0

•106

2-505

2-675

8-44

75

8-89

2-5M

Q

•076

2-065

2-245

8-29

76-5

9-23

2-504

Crown glass

•0682

3-495

3-675

24-76

211-3

8-54

2-537

Ditto another piece

•0659

3'43

3-61

2472

208-7

8-44

2-532

Crown glass ground
Part of same piece

•07
•0693

2-035
3-54

2-215
3-72

8-76
24-96

76-5
215-1

8-73
8-62

} 2-535

Mean of the 10 pieces used in former experiments

8-22

2-678

[Note 26.]

t [See Art. 673.]

1 84 Dielectric effects on various substances

371] Plates of other substances*.

Thickness

Diameter ^.g^

Observed
^charge

Obscrvi-.l
charge by
computed

Gum Lac

•I25

4-23 17-89

80

4-47

f1

•4845

3'75 3-63

13-5

Mixture of rosin

and bees wax. Plate
4

•192
•103
•103

3-355 7-22

4-247 21-89
4-525 24-85

25-2
69
78-9

3'49
3-15
3-18

^5

•103

1-79

3-89

13

3-34

I1

•303

3-78

5'90

24-5

4-16

Dephlegmated beeswax. Plate -{2

•I2O

12-95

46-1

3-56

(3

•063

2-74

14-90

50-5

3-39

Plain bees wax

•119

3-475

12-69

51-3

4-04

372] The coatings of all these plates were circular.

In computing the charge of the glass plates, the diameter of the coating
was corrected on account of the spreading of the electricity as in the
fourth column, the electricity being supposed to spread -07 of an inch if
the thickness is -21 and -09 if the thickness is -08, and so on in proportion
in other thicknesses. But no correction is made in computing the charges
of the other plates, as I was uncertain how much to allow.

373] The method I used in making all the plates of the second table
was this. I first cast a round plate of the substance, three or four times
as thick as I intended it should be, and rather thinner near the edges than
in the middle, taking care to cast it as free from air bubbles as I could.

I then heated it between two thick flat plates of brass, till it was
become soft, and then pressed it out to the proper thickness by squeezing
the plates together with screws f. In order to prevent its sticking to the
brass plates, I put a piece of thin tinfoil between it and each plate, and
I found the tinfoil did not stick to it so fast but what I could get it off
without any danger of damaging them.

374] The heat necessary to melt shell lac is so great as to make it
froth and boil; which makes it impossible to cast a plate of it free from
air bubbles. The plate mentioned in the preceding table was as free from
them as I could make it. It contained, however, a great quantity of
minute bubbles, but no large ones.

375] Bees wax melts with a heat of about 145°. If it is then heated
to a degree rather greater than that of boiling water, it froths very much,
and seems to lose a good deal of watery matter, and if it is kept at this heat
till it has ceased frothing, it will then bear being heated to a much higher
degree without frothing or boiling. Bees wax thus prepared I call
dephlegmated.

In order that the plates of dephlegmated bees wax should all be equally
so, I dephlegmated some bees wax with a pretty considerable heat, and
* [See Art. 674.] f [Art. 514.]

Apparent influence of thickness of the plate 1 8 5

suffered it to cool and harden, and out of this lump I made all three plates,
taking care in casting them not to heat them more than necessary.

I used the same precautions also in casting the plates of a mixture of
rosin and bees wax, the proportion of the rosin to the bees wax was forgot
to be set down.

What are called in the table the 4th and 5th plate of rosin and bees
wax are in reality the same plate as the 3rd, only with a smaller coating.

376] It appears from these experiments, first, that there is a very
sensible difference in the charge of plates of the same dimensions according
to the different sort of glass they consist of, the charge of the plates 0
and Q, which consisted of the greenish foreign plate glass mentioned in
[Art. 301], being the greatest in proportion to their computed charge of
any, next to them the crown glass, and the flint glass being the least of all.

Secondly. The charge of the Lac plate is much less in proportion to
its computed charge than that of any glass plate, and that of a plate of
bees wax, or of the mixture of rosin and bees wax, still less.

But it must be observed that there is a very considerable difference
between the three different plates of dephlegmated bees wax in that
respect. The same thing, too, obtains in the mixture of rosin and bees
wax*.

377] As the proportion of the real charge to the computed is greater
in the thick plates than the thin ones, one might be inclined to think that
this was owing to the electricity being not spread uniformly. But as the
difference seems to be greater than could well proceed from that cause,
I am inclined to think that it must have been partly owing to some
difference in the nature of the plates. Perhaps it may have been owing to
some of the plates having been less heated, and consequently having
suffered a greater degree of compression in pressing out than the others.

378] The piece of ground crown glass mentioned in the first of the
foregoing tables was made out of a piece of crown glass about Jf of an
inch thick, and ground down to the thickness mentioned in the table, care
being taken by the workman to take away as much from one side as the
other, so that the plate consisted only of the middle part of the glass.

My reason for making it was that as there appears to be a considerable
difference in the charge of different sorts of glass, it was suspected that
there might possibly be a difference between the inside of the piece and
the outside, and if there had, it would have affected the justness of the
experiments with the ten pieces of glass ground out of the same piece.

* 'Note 27, p. 418.]

+ There are pieces of that thickness sometimes blown for the use of the Opticians.

i 86 Theory of multiple dielectric plates

But by comparing the charges of the plates of crown glass with those
of the two other pieces of crown glass in the table, there does not seem to
be any difference which can be depended on with certainty.

The experiment indeed would have been more satisfactory if the piece
of ground glass and the pieces with which it was compared had been all
made out of the same pot. But as it would have been difficult procuring
such pieces, and as I have found very little difference in the specific gravity
of different pieces of crown glass, and as I am informed it is all made at
the same glass house, I did not take that precaution.

379] Let two or more flat plates of different non-conducting substances,
as AabB, BbcC and CcdD, (Fig. 29) be placed close
together and coated in the manner of a single plate
with the coatings Ee and Ff. Let the charge of the
plate AabB, supposing it placed by itself and coated
in the usual manner, be equal to that of a plate of
glass whose thickness is A and whose coatings are of
the same size as those of AabB.

In like manner let the charge of BbcC be equal to
that of a plate of the same glass whose thickness is
equal to B, and let that of CcdD equal that of one
whose thickness is C.

Then whichever of the three ways of accounting
for the excess of the real charge of glass plates above
the computed we prefer, it is a necessary consequence
of our theory that the charge of this compound plate
AadD should be equal to that of a single plate of glass whose thickness
equals A + B + C, and whose coatings are of the same size as Ee and Ff.

380] In like manner if two or more plates of the same kind of glass
are placed together and coated as above, the charge of this compound
plate should be equal to that of a single plate of the same glass whose
thickness is equal to that of all the plates together. This appears from the
following experiments to be the case, for

1st. I took the three plates of glass A, B and C*, and laid them on
one another, having first taken off their old coatings and coated the outside
surfaces as in Fig. 29 with circles of tinfoil 6-6 inches in diameter. The
charge of this compound plate was found to be to that of the three plates
D, E and F together as -944 to i. The sum of the thicknesses of A, B
and C together is -6309, and the computed charge of a plate of that
thickness with coatings 6-6 in. diameter is to that of D, E and F together,
allowing in the same manner as in [Art. 328] for the instantaneous spreading
of the electricity, as -94 to one. So that the charge of this compound plate
is exactly the same that it ought to be according to the foregoing rule.

* [Arts. 534, 544, 546, 677.]

JE

F

C

f

a 6 c d

Fig. 29.

verified by experiment

187

381] 2ndly, I made a plate of a mixture of rosin and bees wax *, about
8 inches square and somewhat more than -12 thick, and coated it with
circles 6-61 in. diameter. Its charge was found to be to that of the plates
K, D and E together as 56 to 55, and therefore should be equal to that of
a plate of glass of the same kind as K whose thickness is -345 and the
diameter of whose coatings is the same as those of the rosin plate, namely
6-61 inches.

This plate was then inclosed between the glass plates B and //f, the
coatings being first taken off, and the outside surfaces of B and H coated
with circles 6-6 inches in diameter. Its charge was found to be to that of
K as 7-56 to 8.

According to the foregoing rule, its charge should be the same as that
of a plate of glass of the same kind as B -634 of an inch thick with coatings
6-6 inches in diameter, and should therefore be to that of K as 7-34 to 8,
which is very nearly the same that it was actually found to be.

382] On the charges of such Leyden vials as do not consist of flat
plates of glass.

These experiments were made with hollow cylindrical pieces of glass,
open at both ends, and coated both within and without with pieces of
tinfoil surrounding the cylinder in the form of a ring, the breadth of the
ring being everywhere the same, and the inside and outside coatings being
of the same breadth, and placed exactly opposite to each other. Only as
the inside diameter of the two thermometer tubes was too small to admit
of being coated in this manner, they were filled with mercury by way of
inside coating.

The thickness of the glass was found by suspending the cylinder by
one end from a pair of scales with its axis in a vertical position, and the
lower part immersed in a vessel of water, and finding the alteration of
the weight of the cylinder according as a greater or less portion of it was
under water J.

383] The result of the experiments is contained in the following table §.

Mean
thick-
ness

Mean
outside
semi-dia-
meter

Length
of
coating

Com-
puted
charge

Observed
charge

Observed
charge
by com-
puted

Specific
gravity

Outside
diameter
by thick-
ness

Part of a jar of flintl
glass ' /

•084

1-62

4'4

85-9

717

8-35

3-254

19-3

A cylinder of ditto

•0704

•645

9-86

87-I

650

7-46

3-281

9-2

Thermometer tube I.

•094

•14

ii

I I'D

80-2

7-31

3-098

I'5

„ II.

•130

•16

1.5-5

II-I

80-7

7-26

3-243

1-24

Cylinders of green 1 2
bottle glass |j

•045
•060
•078

•50
•53
•48

7-16
8-55

7

77-2
76-6
40-8

754
690

353

9'77
9
8-65

2-665
2-664
2-665

n-3
8-8
6-2

[Arts. 548, 678.J
[Art. 594.]

t [Arts. 552, 679.]

§ [See Art. 676, and Note 28.]

i 88 Curved dielectric plates not different from flat

The lengths of the coating here set down are the real lengths. But in
computing the charges of the white jar and cylinder and the three green
cylinders, these lengths were increased on account of the spreading of
the electricity according to the same supposition as was used in computing
the charges of the flat plates.

But in computing the charges of the thermometer tubes no correction
was made, as I was uncertain how much to allow, but as the length of
their coatings is so great, this can hardly make any sensible error.

384] It should seem from these experiments as if the proportion of
the real to the computed charge was rather less in a cylinder in which
the thickness of the glass is \ of the semidiameter than in one in which
it is only ^, and most likely rather less in that than in a flat plate, but
then it seems to be not much less in a cylinder in which the inside diameter
is many times less than the outside, that is, in which the thickness of the
glass is almost equal to the outside semidiameter, than it is in the first
mentioned cylinder.

Nothing certain, however, can be inferred as to this point, as in all
probability the four pieces of flint glass used in these experiments and
the two flat pieces used in [Art. 370] did not consist exactly of the same
kind of glass, as indeed appears from their specific gravities.

385] The three green cylinders, indeed, were all made at the same
time and out of the same pot, so that it seems difficult to suppose that
there should be any difference of that kind between them*. But then I
had no flat plates to compare them with.

On the whole, I think we may with tolerable certainty infer that the
ratio of the real to the computed charge is not very different from what
it is in flat plates, whatever is the proportion which the thickness of the
glass bears to the diameter of the cylinder, though it seems to be not
exactly the same.

* Though it seems not likely that there should be any difference in the nature
of the glass of which the three green cylinders consisted, yet I am not sure that
there was not, for the inside of the glass, that is, that part which was nearest to the
inside surface, was manifestly more opaque and of a different colour from the
outside, and the separation between these two sorts of glass appeared well defined,
so that the cylinder seemed to consist of two different coats of glass lying one over
the other. The distinction was the most visible in those cylinders which consisted
of the thickest glass and in the thickest part of those cylinders. The specific
gravities, however, do not indicate any difference in the nature of the glass. What
was the reason of the above-mentioned appearance I cannot tell.

{IV.} WHETHER THE FORCE WITH WHICH TWO BODIES
REPEL IS AS THE SQUARE OF THE REDUNDANT FLUID,
TRIED BY STRAW ELECTROMETERS*.

[From MS. N°. 8: hitherto unpublished. See Table of Contents at the
beginning of this volume.]

386] If two bodies, A and B, placed near to each other, are both
connected to the same overcharged Leyden jar, and the force with which
this jar is electrified is varied, everything else remaining unaltered, the
force with which A and B repel each other ought by the theory to be as
the square of the quantity of redundant fluid in the jar, supposing the
distance of the bodies A and B to remain unaltered. For the quantity
of redundant fluid in A is directly as the quantity of redundant fluid in
the jar, and therefore the force with which each particle of redundant
fluid in B is repelled by A is also directly as the quantity of redundant
fluid in the jar, and therefore as the number of particles of redundant
fluid in B is also as the quantity of redundant fluid in the jar, the force
with which B is repelled by A is as the square of the quantity of redundant
fluid in the jar.

387] In order to try whether this was the case, I made use of the
following apparatus f .

CD (Fig. 31) is a wooden rod 43 inches long, covered with tinfoil and
supported horizontally by non-conductors. At the end C is suspended, as

Fig. 31.

in the figure, the electrometer described in Art. 249, and at the other end D
is suspended a similar electrometer, only the straws reached to the bottom
of the cork balls A and B, but not beyond them, and were left open so
as to put in pieces of wire, and thereby increase their weight and the
force with which they endeavoured to close. The lower ends of these

* [Title supplied from Cavendish's Index to {the results ofj his experiments.
Art. 563.]

f [Arts. 563, 567, also Art. 525.]

190 Repulsion with Different Degrees

wires when used were just even with the bottom of the cork balls, and
were kept in that situation by wax, the wax being cut off even with the
bottom of the corks, so as to leave no roughnesses to carry off the electricity.
In like manner, when the wires were not used, the ends of the straws were
closed up with wax.

388] The proportion which the force with which the balls of this
electrometer endeavoured to close when the wires were inserted bore to
that with which they endeavoured to close without the wires was thus

(A
found. The weight of the straw \r> with its ball and centre pin but

(7-6
without its wire was found to be V, , grains, and the distance of its

center of gravity from the center of suspension was I „ inches, as was

found by balancing it on the edge of a knife. Consequently the force with
which this straw, when put in its place, endeavours to descend towards
the perpendicular, supposing it to be removed to a given distance from
(7-6 x 5-36

• WaS as 0.65 x 5-285 '

The weight of the wire inserted was \ grains, and half its length

was \ Z 2^ inches, so that as the distance of the bottom of the cork balls
(i-oo

from the center of suspension was n-i inches, the distance of its center
of gravity from the center of suspension was j . inches, and therefore

the excess of the force with which the ball endeavours to descend towards
the perpendicular when the wire is inserted above that with which it
endeavours to descend without [the wire] is to the force with which it

(12-05 x 0-87 , [7-6 x 5-36
endeavours to descend without the wire as 4 y lfi.fi -ft-'

2*Q2

or as \ 0 to one. Therefore the force with which the electrometer en-
(2'Oo

deavours to close when the wires are inserted is to that with which it
endeavours to close without the wires as 3-9 to i.

389] E and F are two coated Leyden vials, nearly of the same size.
The outside coatings of both communicate with the ground, and the
inside coating of E communicates with CD, but not that of F.

390] The way in which I tried the experiment was as follows. I first
compared the electrometer C with the electrometer D without the wires,
and found that when the jar E was electrified to such a degree as to make

D separate \ divisions, C separated \ \ divisions, so that the

same

of Electrification 1 9 1

(jo

degree of electrification which made C separate \ divisions made D
separate j f divisions.

I then put the wires into the electrometer D, and put the larger of the
two vials in the place of E, and electrified E and consequently the rod CD

(jo

and the two electrometers till D separated \ divisions.

(12

The wire by which E was electrified was then immediately taken away
and a communication made between E and F, so that the redundant fluid
in E and CD and the electrometers was communicated to F.

It was found that the electrometer C then separated \ ~ * divisions.

(X4

The experiment was then repeated in the same manner, except that
the smaller vial was placed at E. It was found that if E was electrified

till D separated j divisions, then on making a communication between

(jql

E and F, C separated < * divisions.
(I25

391] From hence we may conclude that if the vials had been exactly
equal and E had been electrified till D separated ] ^ divisions, then on

(12

making a communication between E and F, C would have separated

t divisions.
13*

But it appears from the first mentioned part of the experiment, that

the same degree of electrification which makes C separate \ ' f divisions

(X3s

j JO

is sufficient to make D without the wires separate \ „ divisions. From

I"!

whence it appears that if the jars are exactly equal, and one of them is
electrified till the electrometer D with the wires separates j divisions,

and its electricity is then communicated to the other vial, the electricity
will be of that degree of strength which is necessary to make the same

electrometer without the wires separate ] . divisions, that is, very

(IJs

nearly the same as before, or as it did with the wire before the com-
munication of the electricity.

But if the vials are equal, the quantity of redundant fluid in the first
vial, after its electricity is communicated to the second, will be very little
more than half of what it was before the communication, for the quantity
of redundant fluid in the rod DC and the electrometers is trifling in com-

192 Repulsion with Different Degrees

parison of that in the vial*, and consequently it appears that the distance
to which the electrometer with the wires in it separates with a given
quantity of redundant fluid in the vial is very nearly the same as that to
which it separates without the wires when there is only half that quantity
of redundant fluid in the vial.

Therefore as the force with which the electrometer endeavours to close
by its weight when the wires are in is to that with which it endeavours
to close without the wires as 3-9 to i, it appears that the force with which
the balls of the electrometer are repelled with a given quantity of re-
dundant fluid in the vial, is to that with which they are repelled when
there is only half that quantity of redundant fluid in the vial as 3-9 to i
(supposing the distance of the balls to be the same in both cases), that is,
very nearly as the square of the quantity of redundant fluid in the vial,
the difference being not more than what might very easily be owing to
the error of the experiment. So that the experiment agrees very well
with the theory.

392] It was found that if the communication was made between the
two vials by a piece of metal, the electricity was diminished so suddenly
as to set the straws a vibrating, and it was some time before they stopt,
for which reason the communication was made by a piece of moist wood,
which, though it communicates the electricity of one vial to the other very
quickly, did not do it so instantaneously as to make the straws vibrate
much.

393] The electricity of the vial was found to waste very slowly, so
that it could not be sensibly diminished during the small time spent in
communicating the electricity from one vial to the other and reading off
the divisions, so that no sensible error could proceed from that cause.

394] I tried the experiment before in the same manner, and with the
same electrometers, except that the straws were not gilt, but only moist-
ened with salt. It then seemed as if the force with which the balls of the
electrometer were repelled with a given quantity of redundant fluid in
the vial was to that with which they were repelled with only half that
quantity in the vial as 4 to §.

As I suspected that this small difference from the theory was owing
to the straws not conducting sufficiently readily, I gilt the straws, when,
as was before shewn, the experiment agreed very well with theory.

It must be observed that if the straws do not conduct sufficiently
readily, the balls of the electrometer will not be so strongly electrified

* [In a sentence which Cavendish has scored out in his MS. we read — ]
The charge of the two vials together was found to be 2168 inches. The diameter
of the rod CD was at a medium about J of an inch. [This would make the com-
puted charge of the rod 9-7 inches. — En.]

of 'Electrification 1 9 3

and will not separate so much as they ought to do, and in all probability
the difference will be greater in the stronger degree of electricity, in which
the electricity wastes much faster, than it is in the weaker, and will there-
fore diminish the degree of separation more in the stronger degree of
electricity than in the weaker, and will therefore make the force with
which the balls repel with the stronger degree of electricity appear to be
less in proportion to that with which they repel with the weaker degree
than it ought to be.

C.P.I. 13

PHILOSOPHICAL TRANSACTIONS. VOL. 66, 1776,
PART I, pp. 196-225

account of some attempts to imitate the effects
of the Torpedo by Electricity

Read Jan. 18, 1775.
{See Table of Contents at the beginning of this volume.]

395] Although the proofs brought by Mr Walsh *, that the phenomena
of the torpedo are produced by electricity, are such as leave little room
for doubt; yet it must be confessed, that there are some circumstances,
which at first sight seem scarcely to be reconciled with this supposition.
1 propose, therefore, to examine whether these circumstances are really
incompatible with such an opinion; and to give an account of some
attempts to imitate the effects of this animal by electricity.

396] It appears from Mr Walsh's experiments, that the torpedo is not
constantly electrical, but hath a power of throwing at pleasure a great
quantity of electric fluid from one surface of those parts which he calls
the electrical organs to the other; that is, from the upper surface to the
lower, or from the lower to the upper, the experiments do not determine
which ; by which means a shock is produced in the body of a person who
makes any part of the circuit which the fluid takes in its motion to restore
the equilibrium.

397] One of the principal difficulties attending the supposition, that
these phenomena are produced by electricity, is, that a shock may be
perceived when the fish is held under water; and in other circumstances,
where the electric fluid hath a much readier passage than through the
person's body. To explain this, it must be considered, that when a jar
is electrified, and any number of different circuits are made between its
positive and negative side, some electricity will necessarily pass along
each; but a greater quantity will pass through those in which it meets
with less resistance, than those in which it meets with more. For instance,
let a person take some yards of very fine wire, holding the end in each
hand, and let him discharge the jar by touching the outside with one end
of the wire, and the inside with the other; he will feel a shock, provided
the jar is charged high enough; but less than if he had discharged it without

* [Philosophical Transactions, 1773, pp. 461-477. Of the Electric Property of
the Torpedo. In a letter from John Walsh, Esq., F.R.S., to Benjamin Franklin,
Esq., LL.D., F.K.S., &c. Read July i, 1773.

Electric resistance of iron wire compared with water 195

holding the wire in his hands; which shews, that part of the electricity
passes through his body, and part through the wire. Some electricians
indeed seem to have supposed that the electric fluid passes only along the
shortest and readiest circuit; but besides that such a supposition would
be quite contrary to what is observed in all other fluids, it does not agree
with experience. What seems to have led to this mistake is, that in dis-
charging a jar by a wire held in both hands, as in the above-mentioned
experiment, the person will feel no shock, unless either the wire is very
long and slender, or the jar is very large and highly charged. The reason
of which is, that metals conduct surprisingly better than the human body,
or any other substance I am acquainted with; and consequently, unless
the wire is very long and slender, the quantity of electricity which will pass
through the person's body will bear so small a proportion to the whole, as not
to give any sensible shock, unless the jar is very large and highly charged.

398] It appears from some experiments*, of which I propose shortly
to lay an account before this Society, that iron wire conducts about 400
million times better than rain or distilled water; that is, the electricity
meets with no more resistance in passing through a piece of iron wire
400,000,000 inches long, than through a column of water of the same
diameter only one inch long. Sea water, or a solution of one part of salt
in 30 of water, conducts 100 times, and a saturated solution of sea salt
about 720 times, better than rain water.

399] To apply what hath been here said to the torpedo; suppose the
fish by any means to convey in an instant a quantity of electricity through
its electric organs, from the lower surface to the upper, so as to make the
upper surface contain more than its natural quantity, and the lower less ;
this fluid will immediately flow back in all directions, part over the moist
surface, and part through the substance of its body, supposing it to conduct
electricity, as in all probability it does, till the equilibrium is restored:
and if any person hath at the time one hand on the lower surface of the
electric organs, and the other on the upper, part of the fluid will pass
through his body. Moreover, if he hath one hand on one surface of an
electric organ, and another on any other part of its body, for instance the
tail, still some part of the fluid will pass through him, though much less
than in the former case ; for as part of the fluid, in its way from the upper
surface of the organ to the lower, will go through the tail, some of. that
part will pass through the person's body. Some fluid also will pass through
him, even though he does not touch either electric organ, but hath his
hands on any two parts of the fishes body whatever, provided one of those
parts is nearer to the upper surface of the electric organs than the other.

400] On the same principle, if the torpedo is immersed in water, the
fluid will pass through the water in all directions, and that even to great
distances from its body, as is represented in Fig. i, where the full lines

* [Arts. 576, 577, 084, (.87.!

13-2

196 Memoir on the Torpedo as imitated by electricity

represent the section of its body, and the dotted lines the direction of the
electric fluid; but it must be observed, that the nearer any part of the
water is to the fishes body, the greater quantity of fluid will pass through
it. Moreover, if any person touches the fish in this situation, either with
one hand on the upper surface of an electric organ, and the other on the
lower, or in any other of those manners in which I supposed it to be touched
when out of the water, some fluid will pass through his body ; but evidently

Fig. i.

less than when the animal is held in the air, as a great proportion of the
fluid will pass through the water: and even some fluid will pass through
him, though he does not touch the fish at all; but only holds his hands
in the water, provided one hand is nearer to the upper surface of the
electric organs than the other.

401] The second difficulty is, that no one hath ever perceived the
shock to be accompanied with any spark or light, or with the least degree
of attraction or repulsion. With regard to this, it must be observed, that
when a person receives a shock from the torpedo, he must have formed
the circuit between its upper and lower surface before it begins to throw
the electricity from one side to the other; for otherwise the fluid would
be discharged over the surface of the fishes body before the circuit was
completed, and consequently the person would receive no shock. The only
way, therefore, by which any light or spark could be perceived, must be
by making some interruption in the circuit. Now Mr Walsh found, that
the shock would never pass through the least sensible space of air, or even
through a small brass chain. This circumstance, therefore, does not seem
inconsistent with the supposition that the phenomena of the torpedo are
owing to electricity; for a large battery will give a considerable shock,
though so weakly charged that the electricity will hardly pass through
any sensible space of air; and the larger the battery is, the less will this
space be. The principle on which this depends will appear from the
following experiments.

402] I took several jars of different sizes, and connected them to the
same prime conductor, and electrified them in a given degree, as shewn
by a very exact electrometer; and then found how near the knobs of an
instrument in the nature of Mr Lane's electrometer must be approached,

Experiments elucidating absence of any sparking 197

before the jars would discharge themselves. I then electrified the same
jars again in the same degree as before, and separated all of them from
the conductor except one. It was found, that the distance to which the
knobs must be approached to discharge this single jar was not sensibly
less than the former. It was also found, that the divergence of the electro-
meter was the same after the removal of the jars as before, provided it was
placed at a considerable distance from them : from which last circumstance,
I think we may conclude, that the force with which the fluid endeavours
to escape from the single jar is the same as from all the jars together*.

403] It appears, therefore, that the distance to which the spark will
fly is not sensibly affected by the number or size of the jars, but depends
only on the force with which they are electrified; that is, on the force with
which the fluid endeavours to escape from them: consequently, a large jar,
or a great number of jars, will give a greater shock than a small one, or
a small number, electrified to such a degree, that the spark shall fly to
the same distance; for it is well known, that a large jar, or a great number
of jars, will give a greater shock than a small one, or a small number,
electrified with the same force.

404] In trying this experiment, the jars were charged very weakly,
insomuch that the distance to which the spark would fly was not more
than the 2Oth of an inch. The electrometer f I used consisted of two straws,
10 inches long, hanging parallel to each other, and turning at one end on
steel pins as centers, with cork balls about J of an inch in diameter fixed
on the other end. The way by which I estimated the divergence of these
balls, was by seeing whether they appeared to coincide with parallel lines
placed behind them at about 10 inches distance; taking care to hold my
eye always at the same distance from the balls, and not less than thirty
inches off. To make the straws conduct the better, they were gilded, which
causes them to be much more regular in their effect. This electrometer
is very accurate ; but can be used only when the electricity is very weak.
It would be easy, however, to make one on the same principle, which should
be fit for measuring pretty strong electricity.

405] The instrument by which I found to what distance the spark
would fly is represented in Fig. 2 ; it differs from Mr Lane's electrometer }

[Art. 604.]

Fig. 2.

t LArt. 249.]

[Art. 329.]

198 Memoir on the Torpedo as imitated by electricity

no otherwise than in not being fixed to a jar, but made so as to be held
in the hand. The part ABCDEFGKLM is of baked wood, the rest of
brass; the part GKL being covered with tinfoil communicating with the
brass work at FG; and the part ABM being also covered with a piece of
tinfoil, communicating with the brass work at CD.

406] I next took four jars, all of the same size; electrified one of them
to a given degree, as shewn by the electrometer; and tried the strength
of the shock which it gave; and found also to what distance the spark
would fly. I then took two of the jars, electrified them in the same degree
as before, and communicated their electricity to the two remaining. The
shock of these four jars united, was rather greater than that of the single
jar; but the distance to which the spark would fly was only half as great*.

407] Hence it appears, that the spark from four jars, all of the same
size, will not dart to quite half so great a distance as that from one of those
jars electrified in such a degree as to give a shock of equal violence; and
consequently the distance to which the spark will fly is inversely in a
rather greater proportion than the square root of the number of jars,
supposing them to be electrified in such a degree that the shock shall be
of a given strength. It must be observed, that in the last mentioned
experiment, the quantity of electric fluid which passed through my body
was twice as great in taking the shock of the four jars, as in taking that
of the single one; but the force with which it was impelled was evidently
less, and I think we may conclude, was only half as great. If so, it appears
that a given quantity of electricity, impelled through our body with a
given force, produces a rather less shock than twice that quantity, im-
pelled with half that force; and consequently, the strength of the shock
depends rather more on the quantity of fluid which passes through our
body, than on the force with which it is impelled.

408] That no one could ever perceive the shock to be accompanied
with any attraction or repulsion, does not seem extraordinary ; for as the
electricity of the torpedo is dissipated by escaping through or over the
surface of its body, the instant it is produced, a pair of pith balls sus-
pended from any thing in contact with the animal will not have time to
separate, nor will a fine thread hung near its body have time to move
towards it, before the electricity is dissipated. Accordingly I have been
informed by Dr Priestley, that in discharging a battery he never could
find a pair of pith balls suspended from the discharging rod to separate.
But, besides, there are scarce any pith balls so fine, as to separate when
suspended from a battery so weakly electrified that its shock will not
pass through a chain, as is the case with that of the torpedo.

409] In order to examine more accurately, how far the phenomena of
the torpedo would agree with electricity, 1 endeavoured to imitate them

* [Arts. 573, bio, 613.]

Artificial electric torpedo 199

by means of the following apparatus. ABCFGDE, Fig. 3, is a piece of
wood, the part ABCDE of which is cut into the shape of the torpedo,
and is i6f inches long from A to D, and lof broad from B to E; the part
CFGD is 40 inches long, and serves by way of handle. MNmn is a glass
tube let into a groove cut in the wood. Ww is a piece of wire passing
through the glass tube, and soldered at W to a thin piece of pewter Rr

\

Fig- 3-

lying flat on the wood, and intended to represent the upper surface of the
electric organs. On the other side of the wood there is placed such another
glass tube, not represented in the figure, with a wire passing through it,
and soldered to another piece of pewter of the same size and shape as Rr,
intended to represent the lower surface of those organs. The whole part
A BCDE is covered with a piece of sheep's skin leather.

410] In making experiments with this instrument, or artificial torpedo
as I shall call it, after having kept it in water of about the same saltness
as that of the sea, till thoroughly soaked, I fastened the end of one of the
wires, that not represented in the drawing for example, to the negative
side of a large battery, and when it was sufficiently charged, touched the
positive side with the end of the wire Ww; by which means the battery
was discharged through the torpedo: for as the wires were inclosed in

Fig. 4.

glass tubes, which extended about an inch beyond the end of the wood FG,
no electricity could pass from the positive side of the battery to the nega-
tive, except by flowing along the wire Ww to the pewter Rr, and thence
either through the substance of the wood, or along the wet leather, to the
opposite piece of pewter, and thence along the other wire to the negative
side. When I would receive a shock myself, I employed an assistant to
charge the battery, and when my hands were in the proper position,

aoo Memoir on the Torpedo as imitated by electricity

to discharge it in the above mentioned manner by means of the wire Ww.
In experiments with this torpedo under water, I made use of a wooden
trough ; and as the strength of the shock may, perhaps, depend in some
measure on the size of the trough, and on the manner in which the torpedo
lies in it, I have, in Fig. 4, given a vertical section of it ; the torpedo being
placed in the same situation as in the figure. ABCDE is the trough; the
length BC is 19 inches; the depth A B is 14; and the breadth is 13; conse-
quently, as the torpedo is two inches thick in the thickest part, there is
about 5^ inches distance between its sides and those of the trough.

411] The battery was composed of 49 jars, of extremely thin glass,
disposed in 7 rows, and so contrived that I could use any number of rows
I chose. The outsides of the jars were coated with tinfoil; but as it would
have been very difficult to have coated the insides in that manner, they
were filled with salt water. In a battery to answer the purpose for which
this was intended, it is evidently necessary that the metals serving to
make the communications between the different jars should be joined
quite close : accordingly care was taken that the contacts should be made
as perfect as possible. I find, by trial, that each row of the battery contains
about 15! times as much electricity, when both are connected to the same
prime conductor, as a plate of crown glass, the area of whose coating is
100 square inches, and whose thickness is T^,j of an inch ; that is, such that
one square foot of it shall weigh 10 oz. 12 dwts. ; and consequently, the
whole battery contains about no times as much electricity as this plate*.

412] The way by which this was determined, and which, I think, is
one of the easiest methods of comparing the quantity of electricity which
different batteries will receive with the same degree of electrification, was
this: First of all, supposing a jar or battery to be electrified till the balls
of the above-mentioned electrometer separated to a given distance, I
found how much they would separate when the quantity of electricity in
that jar or battery was reduced to one-half. To do this, I took two jars,
as nearly equal as possible, and electrified one of them till the balls sepa-
rated to a given degree, and then communicated its electricity to the other;
and observed to what distance the balls separated after this communi-
cation. It is plain, that if the jars were exactly equal, this would be the
distance sought for; as in that case the quantity of electricity in the first
jar would be just half as much after the communication as before; but as
I could not be sure that they were exactly equal, I repeated the experi-

* I find, by experiment, that the quantity of electricity which coated glass of
different shapes and sizes will receive with the same degree of electrification, is
directly as the area of the coating, and inversely as the thickness of the glass;
whence the proportion which the quantity of electricity in this battery bears to that
in a glass or jar of any other size, may easily be computed. [See Art. 584. The
charge of the first row of jars was 64,538, and that of the whole battery about
481,000 inches of electricity.]

Measurement of charge of artificial torpedo 201

ment by electrifying the second jar, communicating its electricity to the
first, and observing how far the balls separated; the mean between these
two distances will evidently be the degree of separation sought, though
the jars were not of the same size. Having found this, I electrified one row
of the battery till the balls separated to the first distance, and repeatedly
communicated its electricity to the plate of coated crown glass, taking
care to discharge the plate each time before the communication was made,
till it appeared by the electrometer, that the quantity of electricity in
that row was reduced to one-half. I found it necessary to do this between
ii or 12 times, or n£ times as I estimate it. Whence the quantity of
electric fluid in the row may be thus determined.

413] Let the quantity in the plate be to that in the row as x to i ;
it is plain, that the electricity in the row will be diminished each time it
is communicated to the plate, in the proportion of i to i + x, and conse-
quently after being communicated iij times will be reduced in the

_ _i

proportion of i to (i + #)"*; therefore, (i + x)"* = 2; and i + x = 2)"*.
Whence the value of x may easily be found by logarithms. But the readiest
way of computing it, and which is exact enough for the purpose, is this:
multiply the number of times which you communicated the electricity of
the row to the plate, by 1,444 '> and from the product subtract the fraction £ ;

the remainder is equal to - , or the number of times by which the elec-

X

tricity in the row exceeds that in the plate*.

414] The way by which I estimated the strength of the charge given
to the battery, was taking a certain number of jars, and electrifying them
till the balls of the electrometer separated to a given distance, and then
communicating their electricity to the battery. This method proved very
convenient; for by using always the same jars, I was sure to give always
the same charge with great exactness; and by varying the number and
size of the jars, I could vary the charge at pleasure, and besides could
estimate pretty nearly the proportion of the different charges to each
other. It was also the only convenient method which occurred to me ; for
I could not have done it conveniently by charging the whole battery till
an electrometer suspended from it separated to a given distance ; because
in most of the experiments the electricity was so weak, that a pair of fine
pith balls suspended from the battery would separate only to a very small
distance ; and counting the number of revolutions of the electrical machine
is a very fallacious method.

415] I found, upon trial f, that though a shock might be procured
from this artificial torpedo, while held under water, yet there was too
great a disproportion between its strength, when received this way, and

* [Arts. 441, 582.] t [Art. 596.]

2O2 Memoir on the Torpedo as imitated by electricity

in air; for if I placed one hand on the upper, and the other on the lower
surface of the electric organs, and gave such a charge to the battery, that
the shock, when received in air, was as strong as, I believe, that of the
real torpedo commonly is; it was but just perceptible when received under
water. By increasing the charge, indeed, it became considerable; but then
this charge would have given a much greater shock out of water than the
torpedo commonly does. The water used in this experiment was of about
the same degree of saltness as that of the sea; that being the natural
element of the torpedo, and what Mr Walsh made his experiments with.
It was composed of one part of common salt dissolved in 30 of water,
which is the proportion of salt usually said to be contained in sea water.
It appeared also, on examination, to conduct electricity not sensibly better
or worse than some sea water procured from a mineral water warehouse.
It is remarkable, that if I used fresh water instead of salt, the shock seemed
very little weaker, when received under water than out; which not only
confirms what was before said, that salt water conducts much better than
fresh; but, I think, shews, that the human body is also a much better
conductor than fresh water : for otherwise the shock must have been much
weaker when received under fresh water than in air.

416] As there appeared to be too great a disproportion between the
strength of the shock in water and in air, I made another torpedo*, exactly
like the former, except that the part ABCDE instead of wood was made of
several pieces of thick leather, such as is used for the soles of shoes, fastened
one over the other, and cut into the proper shape; the pieces of pewter
being fixed on the surface of this, as they were on the wood, and the whole
covered with sheep skin like the other. As the leather, when thoroughly
soaked with salt water, would suffer the electricity to pass through it very
freely, I was in hopes that I should find less difference between the strength
of the shock in water and out of it, with this than with the other.

417] For suppose that in receiving the shock of the former torpedo
under water, the quantity of electricity which passed through the wood
and leather of the torpedo, through my body, and through the water,
were to each other as T, B, and Wf; the quantity of electricity which
would pass through my body, when the shock was received under water,
would be to that which would pass through it, when the shock was received

r> J3

out of water, as r> , T , w to ;g~T~T' as m tne nrst case> ^e quantity

D

which would pass through my body would be the g — -= — ,„ part of the

D

whole; and in the latter the „ „ part. Suppose now, that the latter
torpedo conducts N times better than the former; and consequently, that

* [Arts. 599, 600.] f [Arts. 597, 598.]

Law of dhnded discharges 203

in receiving its shock under water, the quantity of electricity which passes
through the torpedo, through my body, and through the water, are to
each other as NT, B, and W; the quantity of electricity which will now
pass through my body, when the shock is received under water, and

D D

out of water, will be to each other as •,=,— ^r,r to 5 JT™; which two

D + £\ 1 + W D + 1\ 1

T)

quantities differ from each other in a less proportion than -„ — T±W

T>

and p — j,: consequently, the readier the body of the torpedo conducts,

the greater charge will it require to give the same shock, either in water
or out of it ; but the less will be the difference between the strength of the
two shocks. It should be observed, that this alteration, so far from making
it less resembling the real torpedo, in all probability makes it more so;
for I see no reason to think, that the real torpedo is a worse conductor
of electricity than other animal bodies; and the human body is at least
as good, if not a much better conductor than this new torpedo.

418] The event answered my expectation ; for it required about three
times as great a charge of the battery, to give the same shock in air, with
this new torpedo as with the former ; and the difference between its strength
when received under water and out of it, was much less than before, and
perhaps not greater than in the real torpedo. There is, however, a con-
siderable difference between the feel of it under water and in air. In air
it is felt chiefly in the elbows; whereas, under water, it is felt chiefly in
the hands, and the sensation is sharper and more disagreeable. The same
kind of shock, only weaker, was felt if, instead of touching the sides, I
held my hands under water at two or three inches distance from it.

419] It is remarkable, that I felt a shock of the same kind, and nearly
of the same strength, if I touched the torpedo under water with only one
hand, as with both. Some gentlemen * who repeated the experiment with
me thought it was rather stronger. This shews, that the shock under
water is produced chiefly by the electricity running through one's hand
from one part to the other; and that but a small part passes through one's
body from one hand to the other. The truth of this will appear with more
certainty from the following circumstance ; namely, that if I held a piece
of metal, a large spoon for instance, in each hand, and touched the torpedo
with them instead of my hands, it gave me not the least shock when
immersed in water; though when held in air, it affected me as strongly
if I touched it with the spoons as with my hands. On increasing the charge,
indeed, its effect became sensible: and as well as I could judge, the battery
required to be charged about twelve times as high to give the same shock
when the torpedo was touched with the spoons under water as out of it.

* [See Art. 601, 27 May, 1775. Mr Ronayne, Mr Hunter, Dr Priestley, Mr Lane,
Mr N[airne].]

204 Memoir on the Torpedo as imitated by electricity

It must be observed, that in trying this experiment, as my hands were out
of water, I could be affected only by that part of the fluid which passed
through my body from one hand to the other.

420] The following experiments were made with the torpedo in air.
If I stood on an electric stool, and touched either surface of the electric
organs with one hand only, I felt a shock in that hand; but scarcely so
strong as when touching it in the same manner under water. If I laid a
hand on one surface of the electric organs, and with the other touched
the tail, I felt a shock; but much weaker than when touching it in the
usual manner; that is, with one hand on the upper surface of those organs,
and the other on the lower. If I laid a thumb on either surface of an
electric organ, and a finger of the same hand on any part of the body,
except on or very near the same surface of the organs, I felt a small shock.

In all the foregoing experiments, the battery was charged to the same
degree, except where the contrary is expressed: they all seem to agree
very well with Mr Walsh's experiments.

421] Mr Walsh found, that if he inclosed a torpedo in a flat basket,
open at the top, and immersed it in water to the depth of three inches,
and while the animal was in that situation, touched its upper surface with
an iron bolt held in one hand, while the other hand was dipped into the
water at some distance, he felt a shock in both of them. I accordingly
tried the same experiment with the artificial torpedo ; and if the battery
was charged about six times as high as usual, received a small shock in
each hand*. No sensible difference could be perceived in the strength,
whether the torpedo was inclosed in the basket or not. The trough in
which this experiment was tried was 36 inches long, 14^ broad, and
1 6 deep ; and the distance of that hand which was immersed in the water
from the electric organs of the torpedo, was about 14 inches. As it was
found necessary to charge the battery so much higher than usual, in order
to receive a shock, it follows, that unless the fish with which Mr Walsh
tried this experiment were remarkably vigorous, there is still too great a
disproportion between the strength of the shock of the artificial torpedo
when received under water and out of it. If this is the case, the fault
might evidently be remedied by making it of some substance which con-
ducts electricity better than leather.

422] When the torpedo happens to be left on shore by the retreat of
the tide, it loosens the sands by flapping its fins, till its whole body, except
the spiracles, is buried; and it is said to happen sometimes, that a person
accidentally treading on it in that situation, with naked feet, is thrown
down by it. I therefore filled a box, 32 inches long and 22 broad, with

* As well as I could judge, the battery required to be charged about 1 6 or 20
times as high, to give a shock of the same strength when received this way as when
received in the usual manner with the torpedo out of water. [Art. 615.]

Shock from Torpedo under various conditions 205

sand, thoroughly soaked with salt water, to the depth of four inches, and
placed the torpedo in it, intirely covered with the sand, except the upper
part of its convex surface, and laid one hand on its electrical organs, and
the other on the wet sand about 16 inches from it. I felt a shock, but
rather weak; and as well as I could judge, as strong as if the battery had
been charged half as high, and the shock received in the usual way*.

423] I next took two thick pieces of that sort of leather which is used
for the soles of shoes, about the size of the palm of my hand; and having
previously prepared them by steeping in salt water for a week, and then
pressing out as much of the water as would drain off easily, repeated the
experiment with these leathers placed under my hands. The shock was
weaker than before, and about as strong as if received in the usual way
with the battery charged one-third part as high. As it would have been
troublesome to have trod on the torpedo and sand, I chose this way of
trying the experiment. The pieces of leather were intended to represent
shoes, and in all probability the shoes of persons who walk much on the
wet sand will conduct electricity as well as these leathers. I think it
likely, therefore, that a person treading in this manner on a torpedo, even
with shoes on, but more so without, may be thrown down, without any
extraordinary exertion of the animal's force, considering how much the
effect of the shock would be aided by the surprise.

424] One of the fishermen that Mr Walsh employed assured him, that
he always knew when he had a torpedo in his net, by the shocks he re-
ceived while the fish was at several feet distance; in particular, he said,
that in drawing in his nets with one of the largest in them, he received
a shock when the fish was at twelve feet distance, and two or three more
before he got it into his boat. His boat was afloat in -the water, and he
drew in the nets with both hands. It is likely, that the fisherman might
magnify the distance; but, I think, he may so far be believed, as that he
felt the shock before the torpedo was drawn out of water. This is the
most extraordinary instance I know of the power of the torpedo; but I
think seems not incompatible with the supposition of its being owing to
electricity; for there can be little doubt, but that some electricity would
pass through the net to the man's hands, and from thence through his
body and the bottom of the boat, which in all probability was thoroughly
soaked with water, and perhaps leaky, to the water under the boat: the
quantity of electric fluid, however, taking this circuit, would most likely
bear so small a proportion to the whole, that this effect cannot be ac-
counted for, without supposing the fish to exert at that time a surprizingly
greater force than what it usually does.

425] Hitherto, I think, the effects of this artificial torpedo agree very
well with those of the natural one. I now proceed to consider the circum-

* [Art. 608.]

2o6 Memoir on the Torpedo as imitated by electricity

stance of the shock's not being able to pass through any sensible space
of air. In all my experiments on this head, I used the first torpedo, or that
made of wood ; for as it is not necessary to charge the battery more than
one-third part as high to give the same shock with this as with the other,
the experiments were more likely to succeed, and the conclusions to be
drawn from them would be scarcely less convincing: for I find, that five
or six rows of my battery will give as great a shock with the leathern
torpedo, as one row electrified to the same degree will with the wooden
one ; consequently, if with the wooden torpedo and my whole battery, I
can give a shock of a sufficient strength, which yet will not pass through
a chain of a given number of links, there can be no doubt, but that, if
my battery was five or six times as large, I should be able to do the same
thing with the leathern torpedo.

426] I covered a piece of sealing wax on one side with a slip of tinfoil,
and holding it in one hand, touched an electrical organ of the torpedo
with the end of it, while my other hand was applied to the opposite surface
of the same organ. The shock passed freely, being conducted by the
tinfoil; but if I made, with a penknife, as small a separation in the tinfoil
as possible, so as to be sure that it was actually separated, the shock would
not pass, conformably to what Mr Walsh observed of the torpedo.

427] I tried the experiment in the same manner with the Lane's
electrometer described in Art. 405, and found that the shock would not
pass, unless the knobs were brought so near together as to require the
assistance of a magnifying glass to be sure that they did not touch.

428] I took a chain of small brass wire, and holding it in one hand, let
the lowest link lie on the upper surface of an electric organ, while my other
hand was applied to the opposite surface. The event was, that if the link,
held in my hand, was the fifth or sixth from the bottom, and consequently,
that the electricity had only four or five links to pass through besides
that in my hand, I received a shock; so that the electricity was able to
force its way through four or five intervals of the links, but not more. One
gentleman, indeed, found it not to pass through a single interval; but in
all probability the link which lay on the torpedo happened to bear more
loosely than usual against that in his hand. If instead of this chain I
used one composed of thicker wire, the shock would pass through a great
number of links; but I did not count how many. It must be observed,
that the principal resistance to the passage of the electrical fluid is formed
by the intervals of the lower links of the chain; for as the upper are
stretched by a greater weight, and therefore pressed closer together, they
make less resistance. Consequently the force required to make the shock
pass through any number of intervals, is not twice as great as would be
necessary to make it pass through half the number. For the same reason
it passes easier through a chain consisting of heavy links than of light ones.

Transmission of the shock 207

429] Whenever the electricity passed through the chain, a small light
was visible, provided the room was quite dark. This, however, affords
no argument for supposing that the phenomena of the torpedo are not
owing to electricity; for its shock has never been known to pass through
a chain or any other interruption in the circuit; and consequently, it is
impossible that any light should have been seen.

430] In all these experiments, the battery was charged to the same
degree; namely, such that the shock was nearly of the same strength as
that of the leathern torpedo, and which I am inclined to think, from my
conversation with Mr Walsh, may be considered as about the medium
strength of those of a real one of the same size as this. It was nearly
equal to that of the plate of crown glass in Art. 411, electrified to such
a degree as to discharge itself when the knobs of a Lane's electrometer
were at ,0115 inches distance; whence a person, used to electrical experi-
ments, may ascertain its strength*. The way I tried it was by holding
the Lane's electrometer in one hand, with the end resting on the upper
surface of the plate, and touching the lower surface with the other hand,
while an assistant charged the plate by its upper side till it discharged
itself through the electrometer and my body. There is, however, a very
sensible difference between the sensation excited by a small jar or plate
of glass like this, and by a large battery electrified so weakly that the
shock shall be of the same strength; the former being sharper and more
disagreeable. Mr Walsh took notice of this difference; and said, that the
artificial torpedo produced just the same sensation as the real one.

431] As it appeared, that a shock of this strength would pass through
a few intervals of the links of the chain, I tried what a smaller would do.
If the battery was charged only to a fourth or fifth part of its usual height,
the shock would not pass through a single interval ; but then it was very
weak, even when received through a piece of brass wire, without any link
in it. This chain was quite clean and very little tarnished; the lowest link
was larger than the rest, and weighed about eight grains. If I used a
chain of the same kind, the wire of which, though pretty clean, was grown
brown by being exposed to the air, the shock would not pass through a
single interval, with the battery charged to about one-third or one-half
its usual strength.

432] It appears, that in this respect the artificial torpedo does not
completely imitate the effects of the real one, though it approaches near
to it; for the shock of the former, when not stronger than that of the
latter frequently is, will pass through four or five intervals of the links of
a chain; whereas the real torpedo was never known to force his through
a single interval. But, I think, this by no means shews, that the phenomena

* [Charge of plate = 4100 inches of electricity = 5207 centimetres capacity.
Electromotive force = 5-5. See Note 10.]

208 Memoir on the Torpedo as imitated by electricity

of the torpedo are not produced by electricity; but only that the battery
I used is not large enough. For we may safely conclude, from the experi-
ments mentioned in Arts. 402, 406, 407, that the greater the battery is,
the less space of air, or the fewer links of a chain, will a shock of a given
strength pass across. For greater certainty, however, I tried, whether if
the whole battery and a single row of it were successively charged to such
a degree, that the shock of each should be of the same strength when
received through the torpedo in the usual manner, that of the whole
battery would be unable to pass through so many links of a chain as that
of a single row*. In order to which I made the following machine f.

433] GM, Fig. 5, is a piece of dry wood; Ff, Ee, Dd, Cc, Bb, and Aa,
are pieces of brass wire fastened to it, and turned up at bottom into the

Fig. 5-

form of a hook, on which is hung a small brass chain, as in the figure, so
as to form five loops, each loop consisting of five links; the part G is
covered with tinfoil, which is made to communicate with the wire Aa.
If I held this piece of wood in one hand, with my thumb on either of the
wires Ff, Ee, &c. and applied the part G to one surface of an electric
organ, while with a spoon, held in the other hand, I touched the opposite
surface, I received a shock, provided the battery was charged high enough,
the electricity passing through all that part of the chain between Aa,
and my thumb; so that I could make the shock pass through more or
fewer loops, according to which wire my thumb was placed on; but if
the charge was too weak to force a passage through the chain, I felt no
shock, as the wood was too dry to convey any sensible quantity of elec-
tricity. The event of the experiment was, that if I charged the whole
battery to such a degree that the shock would but just pass through two
loops of the machine, and then charged a single row to such a degree as
appeared, on trial, just sufficient to give a shock of the same strength as
the former, it passed through all five loops ; whether it would have passed
through more I cannot tell. If, on the other hand, I gave such a charge
to the whole battery, and also to the single row, as was just sufficient to
force a passage through two loops of the chain, the shock with the whole
battery was much stronger than that with the single row.

434] It must be observed, that in the foregoing machine, each loop
consisted of the same number of links, and the links of each loop were
stretched by the same weight ; so that it required no more force to impel

* The battery, as was before said, was divided into seven rows, each of which
could be used separately. j [Arts. 605, 607.]

Structure of the electric organ 209

the electricity through one loop than another, which was my reason for
using this machine rather than a plain chain. Considerable irregularities
occurred in trying the above experiments, and indeed all those with a
chain; for it frequently happened, that the shock would not pass with
the battery charged to a certain degree, when perhaps a minute after, it
would pass with not more than three-fourths of the charge. The irregu-
larity, however, was not so great but that, I think, I may be certain of
the truth of the foregoing facts; especially as the experiments were re-
peated several times. The uncertainty was at least as great in the experi-
ments with Lane's electrometer, when the knobs were brought so close
together, as is necessary in experiments of this kind.

435] It appears therefore, that if the whole battery, and a single row
of it, are both charged in such a degree as to give a shock of the same
strength, the shock with the whole battery will pass through fewer loops
of the chain than that with the single row; so that, I think, there can be
no doubt, but that if the battery had been large enough, I should have
been able to give a shock of the usual strength, which yet would not have
passed through a single interval of the links of a chain.

436] On the whole, I think, there seems nothing in the phenomena of
the torpedo at all incompatible with electricity; but to make a compleat
imitation of them, would require a battery much larger than mine. It
may be asked, where can such a battery be placed within the torpedo?
I answer, perhaps it is not necessary that there should be anything
analogous to a battery within it. The case is this; it appears, that the
quantity of electric fluid, transferred from one side of the torpedo to the
other, must be extremely great; for otherwise it could not give a shock,
considering that the force with which it is impelled is so small as not to
make it pass through any sensible space of air. Now if such a quantity
of fluid was to be transferred at once from one side to the other, the force
with which it would endeavour to escape would be extremely great, and
sufficient to make it dart through the air to a great distance, unless there
was something within it analogous to a very large battery. But if we
suppose, that the fluid is gradually transferred through the electrical
organs, from one side to the other, at the same time that it is returning
back over the surface, and through the substance, of the rest of the body;
so that the quantity of fluid on either side is during the whole time very
little greater or less than what is naturally contained in it; then it is
possible, that a very great quantity of fluid may be transferred from one
side to the other, and yet the force with which it is impelled be not sufficient
to force it through a single interval of the links of a chain. There seems,
however, to be room in the fish for a battery of a sufficient size; for
Mr Hunter* has shewn, that each of the prismatical columns of which

* "Anatomical observations on the Torpedo." By John Hunter, F.R.S. Phil.
Trans. LXIII (1773), p. 485. See Art. 614.

c. p. i. 14

2 1 o Memoir on the Torpedo as imitated by electricity

the electrical organ is composed, is divided into a 'great number of parti-
tions by fine membranes, the thickness of each partition being about the
I5oth part of an inch; but the thickness of the membranes which form
them is, as he informs me, much less. The bulk of the two organs together
in a fish 10^ inches broad, that is, of the same size as the artificial torpedos,
seems to be about 24^ cubic inches ; and therefore the sum of the areas of
all the partitions is about 3700 square inches. Now 3700 square inches of
coated glass T^ of an inch thick will receive as much electricity as 30,500
square inches ,055 of an inch thick * ; that is, 305 times as much as the plate
of crown glass mentioned in Art. 411, or about 2f times as much as my
battery, supposing both to be electrified by the same conductor; and if the
glass is five times as thin, which perhaps is not thinner than the mem-
branes which form the partitions, it will contain five times as much
electricity, or near fourteen times as [much as] my battery.

437] It was found, both by Dr Williamson f and by a committee
appointed by the Philosophical Society of Pennsylvania, that the shock
of the Gymnoius would sometimes pass through a chain, though they never
perceived any light. I therefore took the same chain which I used in the
foregoing experiments, consisting of 25 links, and suspended it by its
extremities from the extreme hooks of the machine described in Art. 433,
and applying the end of the machine to the negative side of the battery,
touched the positive side with a piece of metal held in the other hand, so
as to receive the shock through the chain without its passing through the
torpedo; the battery being charged to such a degree that the shock was
considerably stronger than what I usually felt in the foregoing experi-
ments. I found that if the chain was not stretched by an additional
weight, the shock did not pass at all: If it was stretched by hanging a
weight of seven pennyweights to the middle link, it passed, and a light
was visible between some of the links ; but if fourteen pennyweights were
hung on, the shock passed without my being able to perceive the least
light, though the room was quite dark; the experiment being tried at
night, and the candle removed before the battery was discharged J. It
appears, therefore, that if in the experiments made by these gentlemen
the shock never passed, except when the chain was somewhat tense, which
in all probability was the case, the circumstance of their not having per-
ceived any light is by no means repugnant to the supposition that the
shock is produced by electricity §.

* Vide note in p. 200.

f " Experiments and Observations on the Gymnotus Electricus, or Electrical
Eel." By Hugh Williamson, M.D. Communicated by John Walsh, Esq., F.R.S.
Phil. Trans. LXV (1775), p. 94.

f [Art. 613.] § [See Note 29, p. 419 and Introduction.]

EXPERIMENTS, 1771

{ The Journal of Experiments, of which a formal description is contained ante in
Art. 217 onward. From MS. N°. 12. See Table of Contents at the beginning of this
volume. The footnotes refer back to the formal account of results.}

IST NIGHT*.

438] East plate neg[ative] standing east and west. West plate positive]
north and south. East plate touched perpendicularly] by wire near midd[le].
West wire bearing against north side of west plate.

East
10*
12
12

West

12 a small matter positive.

loj nearly same perhaps rather less negative.

10 a good deal more.

East plate touched flat near west side.

12 io£ separated] very little, scarce enough to say

whether positive or negative,
xoj 12 I thought rather more pos.

Position of east and west plates reversed. Plates touched by wires as last
time.

io£ 12 Seemed to separate rather more than before

positive.
12 io£ did but just separate.

' 439] 2ND NIGHT.

vee EnegaSvee Both plates east and west, wires straight,
oj Tin, pasteboard, and tinfoil, each 12 inches;

separated a little and equally negative. With
paper of 12 inches, in one or two first trials it
seemed to separate much the same. Afterwards
it did not separate at all, owing, as was supposed,
to its being too dry to conduct well, but after
being moistened it seemed to separate like the
rest.

3j The same things being tried, the corks separated

more than before and were positive, and I
believe pretty equally.

* [Probably the first trials of the apparatus described in Art. 240.]

14—2

2 1 2 "Journal of Experiments, 1 77 1

440] 3RD NIGHT.

West

East

pos.

neg.

ioj

12

Separated visibly, I guess about i diameter.

—

Ilf

Seemed to separate rather less.

—

n£

Scarcely separated.

paper of 12

Separated much the same as tin of 12.

12

i°i j

Nearly the same as in first experiment but of [the]

ZIi

= I

2 separated rather more.

*3i I2

Nearly the same as in first experiment.

nf

Seemed as if it was rather more.

ni

Sensibly more than with 12.

From the two other nights' experiments it seemed as if the positive bottle
electrified the plates sensibly stronger than the negative one: why there was
not the same difference this night I cannot tell.

Plates east and west. Wires straight.

441] Two pair of large corks were made, each of which was found to
separate with the same force. The weight of one pair of them was then made
four times as great by the addition of lead to them.

The quantity of electricity in 3rd made vial was then compared by means
of these corks with that of a glass plate with circular coating 2-4 inches in
diameter and about -06 thick, by touching the glass 8 or 9 times the electricity
was reduced from strength requisite to make heavy corks separate to that
requisite to make light corks separate, or was reduced to J, therefore the vial
should contain 12 times as much electricity as the glass plate and wire by
which communication was made, which was about 12 inches long*.

442] Three coated plates were made

CDF

Thickness -06031 -05908 -05914 inches.

Diameter of coating 1-82 1-79 i'?85

Therefore square of diameter of \

coating by thickness, or com- 1 54-92 54'23 53'88

puted power of plate J

Mean 54-34. (D is cased with cement.)

A circular coating 5-39 inches diameter was made to thick plate in place
where its thickness seemed -178, therefore its computed power is equal to the
sum of foregoing three plates. The proportion of thickness to diameter is nearly
the same.

Two sliding coated plates were made for trying the foregoing, the trial plates
being electrified negatively, the others positively.

*• [See Arts. 413, 582.]

Trials of charges on coated plates

213

Breadth of

trial plate

C

12

D

—

D

13

F

12

C

17

C

16

C

15

D

16

D

17

F

17

separated pos.
rather more,
scarce at all.
same as C.
separate neg.

do.

not at all.
scarce sensibly,
about as much as C at 16.
about as much as C.
Therefore F seems to contain about as much electricity as C, and D to
contain about TV more.

443] The three foregoing plates

Large plate
placed close together

placed as far asunder as possible
The above mentioned large plate

[Art. 442]

23

23
23
21
20
30

separated pos.

a trifle more

rather less than No. i

same as No. I.

same as No. 2.

separated a very little neg.

No.

i

2

3

All 3 plates together

444] Three coated plates were made on thick plate each 1-8 inches diameter,
the mean thickness of glass being supposed -18, therefore the computed power
of all three together = 54.

4 separated pos.

5 did not separate,
ii

10
12
ii

4

3

WithC

sep. neg.
did not separate,
sep. neg.
did not.
sep. neg.
did not.
N.B. The breadth of the sliding plate is not known.

445] Small sliding plate not drawn out 14 x 9-4.
Large 19 x 13.

Globe hung on silk strings negative.
Sliding plates on waxed glass positive.

Globe — plate 19 x 13

14
15
16

Globe — plate 14 x 10-4
n-4
12-4

did not separate

doubtful

separated pos.

seemed rather more

separated neg.

doubtful

did not separate

[Equivalent*]

157
16-3
16-9
17-4

12

12-6

13-2

* [This column gives the side of a square equivalent to the trial plate. See
Art. 465.]

214 'Journal of Experiments ; 1771

Pasteboard circle 19-4 inches diameter hung on silk strings.

[Equivalent]
Circle — plate 19 x 14 did not separate 16-3

15 did rather doubtful 16-9

16 did very little 17-4

17 did more 18-
Circle — plate 14 x 12-7 did 13-2

13-4 did rather doubtful 13-7
14-4 did not 14-2*

With circle 1-8 inches diameter on glass -18 thick it separated a little nega-
tively with plate 19 x 19, and would most likely not separate at 19 x 21 or
19 x 22 = 20 or 2o£. Therefore quantity of electricity therein most likely is
to that of globe as 20-2 to 12-4 or as 10 : 6.

446] Thickness of double plate of glass at centre of circle = -285. Diameter
of coating = 1-75.

Being tried against small plate not drawn out, separated considerably
positive, therefore quantity of electricity therein might perhaps be to that in
globe as ii to 18, and therefore its actual power would be to that of thick
plate as 6-6 to 18. The computed power is to that of thick plate as 10-8 to 18.

A coating 1-45 inches diameter was made on thick plate where the thickness
is supposed = -168, therefore computed power = 12-5. This being tried against
sliding plates was as follows:

Small Large

sliding sliding

plate

3
4

5

therefore quantity of electricity therein seems to be to that of globe as 13-7
to 12-6, or 17-4 to 16-3, id est as 14 to 13,
therefore actual power = n-6

diam. plate
In thick plate 1-8 diam.. ^.^ =

do. 1-45 8-1

double plate 6-14

TRIALS OF WIRES.

447] The wires placed horizontally and parallel to each other, one end
supported by silk, the other by waxed glass.

The trial wire consisted of iron wires -14 thick sliding on each other, sup-
ported in [the] same manner.

* [The charges of the globe and the circle of 19-4 inches appear from these
numbers to be as 28-9 : 30-7. The diameter of the tin circle, 18-5, was probably
calculated from these experiments so that its charge might be equal to that of the
globe. The correct diameter would have been 19 inches.]

Equivalent

plate Equivalent

13-2

separated negative

2

did not sep.

16-9

137

separated

3

doubtful

17-4

14-2

did not

4

separ. pos.

18

Trials of charges on wires 2 1 5

Single wire -19 inch thick, 96 inches long.

Trial wire drawn out 8 inches separated neg.

loi did not.

32 did not.

34 separated very little pos.

Two wires -r inch thick, 48 inches long, placed 36 inches asunder.
Trial wire drawn out 24 inches separated pos.
22 did not.

o sep. very little neg.

2 did not.

The same wires at 18 inches distance.

174 sep. pos. rather doubtful.

18 did.

16 did.

I3J did not.

By these it should [seem] as if trial wire required to be drawn out 9 less
with the wires at 36 inches distance than with single wire, and 17 less with two
wires at 18 inches, whence I should suppose that [the quantity of] elfectricity]
in these three cases was as 96, 87 and 79.

The trial wire not drawn out was 70 inches, but the straight part of it was
only 54.

448] Wires of half that length tried in the same manner with a shorter
trial wire.

Two wires -i thick, 24 long, at 18 inches distance.
Trial wire drawn out r inch sep. neg.

3 very little.

5 rather doubtful.

7 did not.

12 did not.

14 sep. pos. very little.

The same at 36 inches distance.

[trial wire] at 20 sep. pos.

18 doubtful.

16 did not.

ii did not.

9 did not.

7 did a good deal.

Wire 48 inches long, touched by end of touching wire,
[trial wire] at 9 did not.

7 sep. neg.

20 did.

18 did not.

2 1 6 "Journal of Experiments, \ 77 1

Same wire touched by middle of touching wire.
18 doubtful.

20 did.

9 did not.

7 doubtful.

5 did.

449] From these experiments the quantity of electricity in

long wire touched at end -j should / 96

middle I seem | 94

short wires 36 dist. (to | 96

do. 18 - J be as I 87

450] Experiments to determine whether the quant, el. in the large circle
was the same whether it was supported on waxed glass* or on silk strings, the
trial plates, which were of wood covered with tinfoil, being supported on waxed
glass, the large trial plate drawn out to n inches being expressed by L — n, the
small ditto by S — n.

Large circle supported on silk strings.
L — 5 sep. pos. very sensibly if I staid some time before letting down the wires,

but scarce sensibly if I did not.

L — 4 seemed to separate, but rather doubtful if I staid, but not if I did not.
8 — 5 sep. neg. if I did not stay, but not if I did.
L — 5 tried again, sep. very little whether I staid or not.

The circle supported on waxed glass.
L - 5 sep. very little whether I staid or not.
S - 5 sep. very little whether I staid or not.

From these experiments there seems no reason to think that there is any
sensible difference in the quantity of electricity whether the circle is supported
on silk or on waxed glass. I believe the air was moderately but not very dry when
these experiments were tried. The next experiment was made the same night.

451] Experiment to determine whether quantity of electricity in coated
glass bears the same proportion to that in a non-electric body whether electrifi-
cation is strong or weakf.

Two pair of corks were made; each separated with rather a less degree of
electrification than those used in former experiments. Some lead was then added
to those of one pair, so as to double their weight and consequently to make
them require 2ce the force to make them separate.

The plate of glass used was the double plate called A in the following ex-
periments, but with coating 1-78 inches diameter.

Tried with light corks.
L - 3 sep. a little pos.
S — 4 as much neg.

* [See Art. 255.] t [See Art. 355.]

Trials of charges on disks 2 1 7

Tried with heavy corks.

L - 2 separated pos.
S - 5f as much neg.

If these experiments could be depended on as perfectly exact the coated
plate should contain TTgth part more electricity in proportion when electrified
with heavy corks than with light, but this difference is much too small to be
depended on.

452] Comparison of two tin circles* 9-3 inches diameter with one of 18-5,
the tin plates supported on waxed glass and touched in the same manner as
wires, the trial plates supported on silk strings.

The two circles at 36 in. distance.

Side of square equivalent to trial plate.

S — i sep. very little neg.
S — 2 did not

L — i sep. very little

L - doubtful

11-26

I5-03

Large circle touched by middle of touching wire.

L — 2 sep. very little pos.
S - i£ sep. very little neg.

15-57
11-83

Do. circle touched by extremity of touching wire.

S — 3^ very little neg.
L - 4 very little pos.

12-62
16-64

Small plates at 36 inches distance tried again,
sep. very little with L - i, which is the same as before.

Small plates at 24 inches.

S — 7 very little pos. equivalent to 14-26.
Do. at 18 inches S - 5^ very little pos i3'55-

453] A brass wiref, 72 inches long and -19 thick, was then tried, touched
by middle of touching wire.

L - 2 sep. pos. 15-57

S - 2| very little neg. 12-07

454] From these experiments it should seem as if electricity] in

Large circle touched at extremity

at middle

Two small circles at 36 inches

do. at 24

do. at 18

were
as

14-63
13-55
I3-I5
12-26

"•55

If the two circles were placed at the same distance from each other in the

[Art. 273 and Notes n and 21.]

f [Art. 279.]

2 1 8 "Journal of Experiments, 1 77 1

same manner as in coated plates, and were electrified by wires touching their
centers perpendicularly, the quantity of electricity should be

Large circle 14-02

Two at 36 13-15

24 12-72

18 12-28

The quantity of] elfectricity] in the wire 72 inches long and -19 thick seems
to be nearly equal to that in the circle of 18-5 inches. Therefore if we suppose
quantity of electricity in a cylinder to be proportional to its length divided by
the logarithm

•982

1-096 to N. log.

I I-2II

, length quantity of elec-
of -r^- — , M . .. J. -4266

thickness tncity in cyhn-

, length der is to that in

ofr -, ,. .4761 to tab. log. < —or as

£ thickness globe whose dia-

of length meter = length

J thickness ' of cylinder as
and the quantity of electricity therein is to that in a circle of the same dia-
meter as

•6627 1-526 f-

•74 to tab. log. or as 1-704 to N. log. J
-8173 1-882 l-

455] A trial plate for Leyden vials consisting of two plates with rosin

between.

S — 2j sep. neg. rather doubtful

L — i pos. rather doubtful

Double plate A, computed power = 11-04.
L - 3^ sep. a little pos. ,

S - 4 a little neg.

Double plate B, computed power = n-i.
L - 3 a little pos. ,

S - 4^ a little neg.

Large circle on silk strings.
L — 3^ a little pos. „

S — 4! a little neg.

Globe on silk strings.
L — 4^ a little pos. j_

S - 4f a little neg.

456] Therefore the quant, el. in these bodies seems as follows :

Trial plate 17^

A 18-4

B 18-3

circle 18-5

globe 18-8

* [See Note 12.]

Trials of charges in plates of air 219

Diameter of the globe = 12-1, therefore quantity of electricity in globe is
to D° in circle of same diameter as 1-56 to i*.

457] Two trial plates were made on a piece of the large bit of ground glass,
one 2-37 inches diameter on place where the thickness = 1-80, computed
power =31-2; the other 2-57 inches diameter where thickness = 1-90, com-
puted power = 34-8.

The first is called S the other L.

fThe plates of ground glass E and F were each coated on one side with a
circle 7-95 inches diameter communicating with coating on the other side.
These plates were kept from touching by three bits of sealing-wax. When the
coatings were kept at distance -39 from each other this is called plate of air
•39 thick, &c.

A piece of wire of the same thickness as the other was made to slide thereon.

When the plate of air was tried against trial-plate S with wire drawn out
12 inches it is expressed

plate air — S + 12 &c.

Double plates A and B S + 29^ sep. a little pos.
L + 17 sep. a little neg.

plate air -343 S + o did not sep.

[L] + 3 a little pos.

plate air -39 S + 18 sep. a little pos.

L + 3 sep. a little neg.

same plate air L + 38 sep. pos.^f

S + 18 did same.

Tried again in afternoon of the same day.

A and B 8 + 27 sep. a little pos.

plate air -39 S + 19 do.

A and B 8 + 29 do.

A and B L + 15 sep. a little neg.

plate air -39 L + 4 do.

458] The wire not drawn out is about 40 inches, and may therefore contain
about 10 cyl. } inc. of electricity, id est, as much electricity as is contained in
circle of 10 inches diameter. Quantity of electricity in additional wire is sup-
posed to be equal to its length [divided] by 4-4.

Both the trial plates together, whose computed power = 66, is equi-
valent to 2A + 26 + 80 inches of wire + 45 of additional wire, id est, to
73-4 + 20 + io- 1 = 103-5 inches of electricity, therefore i inch of computed
power in the glass of which trial plates are made should be equivalent to
1-41 inches of electricity.

By the experiment marked ^f in [457], a difference of computed power in
the trial plates = 3-6, which is equivalent to 5-08 inches of electricity, was

* [See Art. 653 and Preface.] t [See Art. 341.]

J [Probably "circ." See Art. 648.]

22O "Journal of Experiments, 1771

equivalent to drawing out wire 20 inches, which is supposed = 4-54 inches of
air, which is as near an agreement as can be expected.

By a medium of the experiments, the plate of air -39 thick required wire
to be drawn out n£ inches less than A and B, the different experiments varying
from 9 to 14, therefore the plate of air contains 2-6 inches more electricity
than A and B, id est, it contains 39-3 inches of electricity. The plate of air
'343 seemed by i experiment to contain 42-7 of electricity.

Therefore plate of air -39 contains 4-94 times more electricity than a circle
of same diameter, therefore quantity of electricity therein is to that in circle
of same diameter as radius to thickness x 2-06 or quantity of electricity = com-
puted power x -243.

459] Four irregular pieces of glass, N, O, P, Q, were coated with circles.
The thickness, specific gravity of glass and diameter of circles are marked in
[Art. 370], the thickness of glass being found by taking thickness with calipers
at center of proposed circle, and finding a part of outside of same thickness
and measuring that part by Bird's instrument*; the computed power of all
being just 40. The experiments were tried with sliding wire as former[ly].

Tried with large trial plate.

N

. 2

+ o

separated constantly neg.

+ 3

sep. but not certain.

P

. I

+ 6

sep.

+ 9

doubtful.

P

. I

+ 0

did not.

Q

. I

+ 0

did not.

N

. again

+ 3

sep.

+ 6

rather doubtful.

With small trial plates.

N . + 9 seP- Pos-

+ 6 did not.

Q +o sep. considerably.

O + o sep. considerably, but not so much as Q.

P +6 doubtful.

+ 9 sep. plainly.

The afternoon when these were tried, hygrometer corks closed in about
20 seconds.

The trial plates being inlarged, tried with large trial plate.
P +42 doubtful.

+ 39 do.
+ 24 sep.
+ 28 doubtful.

O + o very little, rather doubtful.

Q + o did not sep.

N +21 sep. a little.

P +24 sep. a little.

* [Arts. 341, 517.]

Charges on coated plates of different substances 221

With small trial plate.

P +28 did not.

+ 36 did.

Q 4- o separated rather more.

O +9 sep. a little.

+ 18 sep. about as much as Q at o.

N +28 sep. a little.

These experiments were tried in the morning. In the afternoon hygrometer
corks closed in about 30 seconds.

460] The plate B was coated with a circle 279 inches diameter, computed
power = 40, and the plate D was coated with a circle 2-73, computed power = 46.

A piece of the white glass was also coated with a circle 2-85 in. diameter
where the thickness was -182, computed power 44-6.

They were tried with the same trial plates.

With large trial plate.
D + o sep. neg.

+ 3 very little, rather doubtful.
B +33 very little.
N +21 very little.
D + 3 rather doubtful.

With small plate.

B +48 very little.

D +15 do.

N +39 do.
White + 32 sep. a little pos.

B +48 did not quite sep.
White + 18 nearly same as B.

+ 24 sep. supposed nearly same as ist time.

N +27 sep. very little.

+ 30 nearly same or rather more than W at 24 with large plate.

N +14 sep. a little neg.

W + 10 do.

B +32 do.

W + 8 do.

N +14 do.

461] The plate A was coated with a circle 2-16 inches diameter, computed
power = 22-6 ; a plate of rosin also, the first which was pressed out after hard-
ening, was coated with a circle 2-51, thickness -102, computed power = 2-51*;
they were tried with the trial plates described in p. 16 [Art. 457].

Tried with small plate.
Rosin + 19 sep. a little pos.

A + 36 do.

Double plates A & B + 36 do.

Rosin + 16 do.

* [Should be 61-7.]

222 "Journal of Experiments, \ 77 1

With large plate.

Rosin + o sep. very little, rather uncertain.

A + 17 sep. a little, rather uncertain.

+ 14 sep. a little.
Double plate + 15 do.

462] Hence it appears that A contains as much electricity as the two
double plates. The rosin plate required the wire to be drawn out 18 inches
less than them, therefore rosin plate contains 40-7 inches of electricity, and
therefore quantity of electricity therein = comp. power x *.

A contains 36-7 inches of electricity, and therefore as A and B are of the
same kind of glass, the quantity of electricity in them = computed power x
1-62 = -21056, and B contains 64-96 inches of electricity.

The whitish glass plate required the wire to be drawn out 27 inches less
than B, D requires 33 less and N requires 14 less, P requires 3 more than N,
0 21 less, and Q 37 less than N, therefore W contains 71-2 of electricity, D 72-5,
N 68-2, P 67-5, O 73 and Q 76-7.

Therefore f D — 1-58

W = 1-60
B = 1-62

P = 1-69 spe. gra.
N = 1-71
O = 1-83

Q = 1-92

Quant, el. in.f
comp. power

2-973
2-787
2-674
2-752
2-682

2-514
2-504

463] Experiments to determine whether the quantity of electricity in coated
plates bore the same proportion to that in other bodies whether el. was weak
or strong, or whether it was positive or negative J.

On the side of corks was placed plate A with circle 2 inches in diameter,
containing 31 inches of electricity. On the other side there was no coated plate,
but the wire was drawn out 23 inches and made to rest at further end on the
sliding wooden plates. The heavy corks required more than 2ce the force to
make them separate than the light ones.

With light corks S — o sep. a very little neg.
heavy S — 5 sep. a little.

L — 5^ sep. a little pos.
light L - 7 do.

* [So in MS. See note to Art. 464.]

f [The "real charges" here given are in "circular inches," and the computed
power is 8 times the true value, so that the numbers here given must be multiplied
by 8/1-57 = 5-I to compare them with those given in Art. 370. The diameters of
the coatings in these experiments are not the same as those in Art. 370 which are
taken from Arts. 508-515 and 672.]

t [Art. 355.]

Whether capacity is independent of charge

Tried with the usual corks.

With the electricity neg. L - z\ sep. a little.

pos. L - 3f do.

neg. L — 2j do.
According to these experiments the plate should seem to contain

223

4 x

4 _ 7

3 - TFT —

1 th

r*orf

Part

more electricity in proportion when electrified by heavy corks than light, and
about ¥Vh more when electrified pos. than neg.

464] A plate -345 inches thick was pressed out of exper. rosin and coated
with circle 3-41 inches diameter, therefore computed power = 337. This was
compared with double plate B by help of the sliding coated plate mentioned
in [Art. 442].

Breadth of coating on sliding plate

Rosin 29 sep. a little neg.

22 sep. a little pos.

B 20 sep. a little pos.

26^ sep. a little neg.

Therefore the plate contains 18-3 x -^y = 20 inches of electricity*.

465] Side of square equivalent to trial plate.
Small plate o = 1072

drawn out to i = 11-26

2 = 11-80

-54

3 = 12-35

4 = 12-83

5 = I3-3I

6 = 13-78 \ -48

7 = 14-26

8 = 14-74
Large plate o = 14-49

drawn out to i = 15-03

2 = 15-57 \ '54

3 = 16-10

4 = 16-64 '

5 = i7-J2

6 = 17-60

7 = 18-08

8 = 18-56 \ -48

9 = 19-04
ro = 19-52
ii = 20-00

* [This would make the specific capacity of rosin 20 x 5-1/33-7 = 3. The
numbers in Art. 462 make it 3-3.]

[ 224 ]

EXPERIMENTS, 1772*

{Journal: from MS. N°. 13. See Table of Contents at the beginning of this volume.
The footnotes refer back to the formal account of results. }

466] Plan of usual disposition of vials and bodies to be tried &ca drawn in
the true proportion and shapef.

8 is the trial plate, B the body to be tried, A and a the vials, mM and rR
the touching wires.

mM} MN = 41, XT . n

rm = 83 inches, \ = 27, „,, N« = 24, AC = 10.

rK. ) Kb = 01,

Height of body and trial plate above ground = 4-2

below horizontal bar = 3-1 1.
All the wires were about -07 thick.

[East]

[North |

[South]

\E
[West. Scale A]

467] Comparison of quantity of electricity in a tin plate one foot square,
according to the different situations in which it was electrified. The trial plate
was suspended on waxed glass, the plate to be tried on silk strings J.

Description of the different ways in which it was tried.

Fore Observation — The plate horizontal and placed as in figure, the touching
wire also as in figure but extending to different distances upon the plate [called
2nd and 3rd way in Art. 266].

* [This is the heading of this bundle of the Journal, though the dates up to
Art. 475 belong to 1771.]

f [See Art. 240.] } [See Exp. in. Art. 265.]

Variation of capacity due to connecting wire 225

Bent Wire — the same as former except that the touching wire was bent
into the shape rTR, the distance rR remaining as before, the arch rTR being
vertical and its greatest distance from the straight line rR being about 15 inches
[5th way].

Cross Wire — The same except that the touching wire rR had a cross wire Ee
placed horizontally fastened on within 3 inches of r, the touching wire being
of the same length as before, and Ee 23 inches long. The touching wire was
made to extend so much on the plate that Ee was about i inch distant from the
edge of the plate [4th way].

Back Observation — The touching wire removed into the situation xy, the
wire yzS being 13 feet 5 inches long and passing nearly perpendicularly over B
and at the height of 3'. 7" above it [6th way].

Plate Vertical — The plate hanging in a vertical plane nearly perpendicular
to the right line joining it and the vial. The touching wire touched it about
the middle of the upper side [ist way].

468] Sat. Dec. 14 [1771]. Th. 53°. S. H. 19. C. H. + 7*.

Back observation. Touching wire extends 4 inches.

Side of
equivalent
square diff. J sum

B - 2 sep. a little neg.
r£ very little
I very little, rather doubtful
D 3 do.

12-33

1 2 -O6
1178

8-93

| 2-85

io-35

2 sep. pos.

8-45

Fore observation. Touching wire extends 9 inches over.

D - 5 very little, rather doubtful

9-84

4 sep.
B - 3 sep. a little
2j very little, rather doubtful

9'39
12-85
12-59

2-75

11-21

Fore observation, wire extends very little over.

B - 3 very little, rather doubtful
B - 3^ sep. a little
D - 5 very little, rather doubtful

12-85
13-10
9-84

[ 3-(>i

"•34

4 sep.

9'39

Touched by bent wire near middle.

D - 3£ sep. a little
4 very little, rather doubtful
B - 3j extremely little
3 rather doubtful

9-17

9-39
13-10
12-85

-3-46

11-12

Th. 55°. Smeaton's Hygrometer i8J. Common Hygrometer + 5.

* [Th. — Fahrenheit's Thermometer: S. H. — Smeaton's Hygrometer. See "De-
scription of a new Hygrometer by John Smeaton." Phil. Trans. 1771, p. 198.
C. H. — Common Hygrometer.]

c. p. i. 15

226

Journal of Experiments, 1 6 Dec. 1 77 1

469] Monday, Dec. 16 [1771]. Trials of time in which electricity of stone
square, &c. was destroyed.

The squares were supported on glass, and a piece of tinfoil about i| inch
square fastened on each corner. On one of these pieces was fastened a wire
from which the pith balls were suspended. The square was then electrified by
applying a charged vial, and then a wire communicating with the wall was
applied to the other piece of tinfoil.

With slate the corks closed in 10"
Portland 15

Bremen 8

gummed glass 5

The stones had been kept in fore room for several days. The gummed glass
had been kept in fore room till the gum began to crack. It was then kept in
back room for about 5 hours, and then kept in fore room about ij hour.

Th. 54. S. H. 22. C. H. + 14.

Hygrometer corks closed in 4'. The glass being then wiped they closed in 7'.
Being then suffered to stand uncovered lor 2 or 3 hours, the corks closed in 5'.

Th. 54. S. H. 2oJ. C. H. n.

470] Tuesday, Dec. 17 [1771]. Th. 53. S. H. 20. C. H. + 9.
Experiments of [Art. 468] continued.

Plate vertical. Side sq equiv ^
C — 2 sep. a little pos. 10-09

B - 3^ do. neg. 13-10 • 3-14

D — 5 do. pos. 9-84 ,

Fore observation. Wire extends very little over.

C — 2 sep

D-5
B — 4 sep

. a little pos. 10-09 1
more 9-84 j- 3-25
. a little 13-34 }

Fore observation.

Wire extending 9 inches over.

B-4
C- i

?• I3'3? 3-78
do. 9-56

Bent wire.

C- J
B-3i

do. 9-28
3-82
do. 13-10

Cross wire.

B-2
D- 2|

do. 12-33
do. 8-69

Back observation.

.

D- ^\

B-2

do. 8-69
3-64
do. 12-33

Th. 55. S. H. i8J. C.H. + (

J sum

n-53

11-71

n-45

11-24

10-51

10-51

Capacities of similar bodies

Plate vertical

Fore obs. at extremity

do. wire 9 inches over

Bent wire

Cross wire

Back observation

471] Wednesday, Dec. 18 [1771]. Th. 50°. S. H. 17^ C. H. + 3.
Trials of flat plates of different substances about i foot square*.

227

This

night

ist night

11-71

- -18

- -0

11-34- °

- -26

- 'IS

•47

- '22

— i -20

— I-2O

- -99

Tm plate

Slate
Portland stone

Bremen stone

Glass coated
with tinfoil

Pasteboard

Glass coated with
salt and gum-water
Do. with charcoal
powder

C — 2 sep. about TV in.

_ g do -

-5f

- 2j do.

Side of
equiv. square diff.

3'73

\ sum
"'95

I4'°6}
10-35 /

371 12-20

g_

J

~ '

— i?
-5

Z 5j

fC — 2
JB - 5

fB - 5

\C - 2

fC - 2\

\B-5i

14-29!

3'7°

12-44

10-59}

3-70

12-44

9-96)
I3-82/

3-86

n-89

13-941
9-96J

3-98

ir-95

13-82}

3-73

"•95

I3-82J

3-73

"•95

10-22")
I3-94/

3-72

1*08

same as first tried

Th. 50°. S. H. 17.

The subject is continued in Art. 480.

3-86 11-89

C. H.

472] Comparison of two tin circles 9-3 inches in diameter with one of 18-5 ;
the two circles being placed in vertical planes parallel to each other and per-
pendicular to the vertical plane joining their centers and the trial plate, their
centers being both in the above-mentioned plane f.

There was a distinct touching wire to each plate meeting each other at R,
the two wires were kept asunder by a slender glass tube, and about i inch of
the end of the wires bent at right angles horizontally in order to touch the
plates by being let fall on their edges. When the large circle was tried, this

[Exp. iv, Art. 269.]

f [Exp. v, Art. 273.]

15—2

228 journal of Experiments, 30 Dec, 1771

double touching wire was removed and a single one used in its room, which was
sometimes fastened to the middle of the glass tube, and sometimes used without
it, as will be expressed.

The height of the top of the circles above floor = 4'. 3".

The center of the large circle when that was used, or the middle point

(of i(\"
/ //

/ " -J

from lvial ^

(middle of trial plate) '

The circles were suspended by silk strings. The length of the touching wires
for the circles was 36 inches.

473] Monday Dec. 30 [1771]. Th. 50°. S. H. 18.
Two small circles at 18 inches from each other.

Equivalent diff. J sum Proportion

B — S scp. about TV 13-821

3-47 12-08 i-ooo
C - -2\ do. 10-35}

The same at 26 inches distance.

C — 4 do. 11-07)

B-6J do. 14-51} 3'44 I2'79 I'°59

at 36 distance.

C - 4^ do. 11-31

B - \ do. 11-37 4'°8 13-38 1-108

A — 14^ do. 15-42
Large circle, touching wire being fastened to glass tube.

A - 17* do. 16-04

B- 3 do. 12-85 4'°9 I4'89 I-233
Do. without glass.

B - 3 12-85

4-00 14-80 1-233
A - 17^ 16-94

The Proportions by theory, vide P. 14 of calculations*, are as follows f.

Calculation Experiment

.Small circles at 18 i-ooo i-ooo

at 26 1-044 I'°59

at 36 1-074 1-108

single plate 1-160 1-233

474] The same experiments repeated in the same manner except that the
distance of the center of the large circle, or of the middle point between the

* ["P. 14 of Calculations" refers to a rough calculation in parcel No. 6, which
is an early form of Props. XXIX and XXX. See Arts. 140-143. "P. 14" contains
the following remark, which fixes its date after Art. 456, "By exp. P. 15 [Art. 456]
quant, el. in circle is to that in globe of same diam. as i : 1-56 :: £ : -78, therefore

= -78." Here n is the reciprocal of p in Art. 140.!
2 + 2W

f [See Art. 68 1 and Notes u and 21.]

Capacity affected by proximity to other bodies 229

centers of the small ones, was 5'. 3" from the vial, and the middle point of the
trial plate 8'. 2" from vial, and that some boards forming a floor about 4 or
5 feet square was placed under the circles 14 inches from the ground, and that
a perpendicular bar of the same breadth as those of the frame was placed
5 inches nearer to the circles than the other, so that the distance of the center
of the large circle from the vial and the ground, and also the distance of the
nearest small circle from the perpendicular bar when they were placed at
36 inches distance, were diminished in about the ratio of 2 to 3*.

475] Tu. Dec. 31 [1771]. Th. 51°. S. H. 18.
Small circles at 18 inches distance.

B — 6 sep.
C - 4 do.

14-29
11-07

3-

Do. at 26.

B-
B-

isep.
8 do.

11-51
I5-I7

3'

Do. at 36.

B-

A-

2 do.
15!

12-33
16-07

3'

Large circle

with glass.

A-
B-

i8f

5

17-54
13-82

3-

Do.

without glass.

B-
A-

5i

20

14-06
18-11

4"

Th. 53-

S. H.

15*.

12-68

Proportion
I-OOO

I3-34 I-052

I4-20

I-I2O

15-68 1-237

16-08 1-268

476] Comparison of 2 wires 3 feet long and Tlff inch in diameter with i of
6 feet long and -185 in diameter f.

The wires were placed parallel to each other, horizontal and perpendicular
to the horizontal bar. They were touched almost close to one extremity by the
same wires and in the same manner as the circles in the former experiment.

That end of the wires near the part which was touched was suspended by
silk, the other end was supported on waxed glass. The distances were the same
as in [Art. 472].

477] Fr. Jan. 3 (1772). Th. 50°. S. H. rgj. C. H. + 2.
Short wires at 18 inches distance.

L — 4 sep. 11-07

B-8 do. 15-17

at 24.
A I 14* £15

13-12

3-64 13-33

Proportion

-847

-860

[Art. 275.]

f [Exp. vi, Arts. 279 and 683.]

230 ^journal of Experiments, 3 Jan. 1772

Short wires at 36 inches distance. Proportion

Single wire without glass.

B- 3isep.
A - 191 do.
A -19 sep.less

B- 3isep. 13-10

A - 191 do. 17-89

B- 4 do. 13-34

Two wires at 18, repeated.

Th. 52°. S. H. 18. C. H. 44.

By theory [Art. 152], the proportions should be between those of

i -9323 -9053 -8827

and i -8926 -8597 -8353

478] Comparison of different substances tried in the usual manner*.
The large tin circle suspended by silk.

B- 4jsep. [Article]

B-^*-* ,£. „ I5.85 w

B- 5 do.
The globe suspended on silk.

A: 4 £ %% ™ ** w

Coated double glass plate Af.

A -20 do. 18-11 fr t]

B - 5J do. 14-06

Double plate B.

":/„ r 3S «•« "•* w

The large circle supported on waxed glass.

B:26}

A tin plate 15-5 square, on do.

B- 5
A - 20

A tin plate 17-9 by 13-4, on do.

£~2°, l8'^ 4-05 16-08 [7]

B - 5i 14-06

* [See Arts. 653, 654, 682.]

f Double plate ground glass A, thickness -3, diam. coating 1-82, comp. power 11-04.
- B, - -31.- 1-855. - "-I-

- 5 13-82 6

A - 20 18-11

Capacities of different bodies compared 231

A tin cylinder 35-9 inches long and 2-53 in diameter, on do.

[Art.]
l~,l Sg 3-83 .6-64 n

A tin cylinder 54-2 long and -73 in diameter, on do.
A - igi 17-89

B- 5 13-82 4'°7 I5'85 @

Brass wire 72 inches long and -185 in diameter, on do.

B — 44 13-58

4-08 15-62 [iol
A - 19 17-66

Th. 50°. S. H. i6J. C. H. -8*.

479] According to the 5th and 6th articles of last .page, the quantity of
electricity in the square is to that in a circle of the same area as 1-08 to i,
and that in square to that in oblong of the same area as -991 to i.

By comparing the 2nd article with the 3 last, the quantity of electricity in
/"thick cylinder

I thin cylinder may be to that in a globe whose diameter equals the length of
[wire

cylinder length I<l8J f 2« length

JL- as -962 to N. log 3L_ , or X.ll6 to N. L. 3 , or as 1-271

•980 1-103 1-218

4 times length

to IN . L . -, . .- — .

thickness

Therefore, if we suppose that the real quantity of electricity in any cylinder
is to that in the globe whose diameter equals the length of the cylinder as i£

2ce lenath 2ce length

t0 N' L' thickness ' °r aS -4964 t0 tab' 10g thickness ' U wil1 agree Very WeU
both with theory and experiment.

Or by comparing this with the first article, the quantity of electricity in
any cylinder is to that in a circle whose diameter is equal to the length of the

2ce length
cylinder as -759 to tab. log thickness -

Comparative charges of bodies tried in the former experiment.

By means of this experiment and that of 1771. [Arts. 455, 456.] If the
charge of the globe is called i, that of the circle will be -992, therefore, by
comparing 6th and 7th articles with 5th, the charges of the square and oblong
will be -957 and -965.

By comparing arts, i and 5, the charge of circle on waxed glass is greater
than on silk strings in ratio 1-042 to i, and therefore if charge of cylinders and
wire on waxed glass are supposed greater than on strings in the ratio -1-021
to i f , the charges of thick cylinder, thin cylinder and wire will be

1-028 -980 and -966.

* [Exp. vil, Art. 281.]

•f [The cylinders and wire were supported on waxed glass at one end only.]

232 ""journal of Experiments, '"Jan. 1772

480] Sat. Jan. . Th. 53°. S. H. 23. C. H. uj.

Comparison of different substances tried in the usual way* except that in
the first experiment the touching wire rR and the wire RS were of brass -185
thick.

Tin plate with thick touching wire.

^ i?£ 378 n-45

B - 4 i3'34

The same plate with the common touching wire.

Hollow tin plate, i-oi thick.

3-71 12-20
B - si 14-06

Glass covered with thick coat of tinfoil.

B-4i 13-58 II-8

C - 2 10-09

- Thin coat of do.

9-56 8

B - 4 13-34

— gold leaf.

B-4J 13-58 62

C - if 9-96

- gum.

C — 2 IO-OQ

B-51 14-06

Water with a little gum.

B-44 13-58

C - ii 9-83

The same tin plate as before.

C - 2 IO-OQ

3-07 12-07
B - 54 i4-o6

Th. 55° -5. S. H. 22-5. C. H. 10.

481] Result of this and Art. 471. [Same as Table, Arts. 269, 270.

* [Exp. iv, Art. 269.]

Capacities of Ley den vials

233

TRIALS OF LEYDEN VIALS.

I

482] The plates from Nairne made out of the same piece of glass were coated
with circles of tinfoil as below *.

Diameter Computed

Plates Thickness of coating power

D

•2057

2-16

22-74

E

•2065

2-16

22-60

F

•2115

2-IQ

22-68

G

•2022

2-I4

22-65

H

•07556

6-79

610-2

I

•07797

2-299

67-78

K

•07712

2-286

67.78

L

•O82O5

2-358

6775

M

•07187

2-207

67.78

A

•2112

6-55

203-1

B

•2132

6-586

203-4

C

•2065

6-482

203-4

The old ground glass plates R were coated with tinfoil square, com-

puted power 2 ., , to be used as trial plates.
33 '°°

483] Friday, Jan. . Th. 52°. S. H. 15. C. H. - 9.

The plates D, E, F, G of Nairne were compared with the double plates A
and B by means of the trial plates A and B and an additional wire sliding on
the electrifying wire Mm.

The ,. of the wire Mm is ^ inches, the additional wire is of the

thickness -15

same thickness. The wire Bb is g|- inches long.

sep. near i diam. closed soon. Called Ist way.

rather more, closed soon, 2nd way.

sep. i diam. closed much slower, 3rd way.

3rd way.

2nd way.

2nd way.

3rd

3rd

2nd
2nd

3rd

* [See Art. 315. The computed power as given in this part of the Journal is
the square of the diameter divided by the thickness, which is eight times the com-
puted power as defined in Art. 311, and calculated in Art. 315.]

Plates

Additional

Trial

tried

wire

plate

2 double
plates

15
18

3

A
A
B

D

6

B

15

A

E

15

A

6

B

F

3

B

18

A

G

18

A

6

B

234 "Journal of Experiments, 1772

Plates
tried

Double
plates
D

Additional
wire

3
6

Trial
plate

B

E

6

F

6

G

6

G

o

G

12

G

18

A

F

18

E

18

D

18

U

12

Double
plates

15

sep. full i diam. did not close soon.

do.

do.

do.

do.

seemed more, but not quite certain.

seemed pretty certainly less.

sep. about I diam. closed faster.

do.

do.

do.

sep. but certainly less.

sep. about i diameter*.

484] Two of the old ground glass plates H, I, K, L of Nuremberg glass f,
were coated with oblong squares to serve for trial plates to the plates I, K, L, M
of Nairne, but the observations were found to be so irregular that nothing could
be made of them, owing, as was supposed, to the spreading of the electricity
on the surface of the glass.

To prevent this, all the four plates H, I, K and L were coated with oblong
squares, and cased in cement composed of 2 parts rosin, i of bees' wax, and
3 of brick dustf.

In making it the bees' wax was first melted and imperfectly dephlegmaied,
the rosin was then added and melted with as little heat as possible, and then
the brick dust, previously heated so as to be very dry, was added. By this
means the cement is more safe and sticky than if more heat is used in making it.
In some of the mixtures also a small part of the rosin, never exceeding Jth of
the whole, was exchanged for as much pitch, which was added after the rest
was melted and mixed.

The plates E, F, G, and I, K, L of Nairne were cased in the same cement,
about -165 thick.

A plate of the same cement was also cast by pouring it out on a tin plate.
This was coated with circles about 2-2 in diameter.

485] The spreading of the electricity on the surface of the trial plates
seemed not to be prevented by casing them in cement, for putting the plate L
of Nairne on the positive side, and the trial plate H on the negative, then if the
apparatus was let down and drawn up again immediately J, the pith balls sepa-
rated about half an inch negatively, but if the apparatus was suffered to rest
at the bottom about half a minute, and then drawn up immediately, they
separated considerably more than i inch, and if it was suffered to rest at the

[See Art. 655.]

f [See Art. 303.]

J [See Art. 302.]

Spreading of electricity on glass 235

bottom but a very short time, and then kept mid way for \ minute, and then
drawn up, the balls at first separated positively but closed very soon, and after
a long time separated negatively.

If a sliding plate containing about \ part of the electricity in the plate L
was put on the positive side as an additional plate, and the apparatus was let
down and drawn up immediately, the balls separated about i diameter nega-
tively, but if it rested at the bottom \ a minute and was then drawn up im-
mediately they separated about i inch negatively.

486] In order to see how fast the electricity spread on the surface of the
glass, the heavy paper cylinders* were placed in the usual place, and the light
ones on the wire Bb, the wires Gg and Ff were detached from Cc and rested at
bottom, and a coated plate on the positive side. The wire Cc was suffered to
rest on A a and Bb while the jars were charging, and the wire V drawn up so
as not to rest on the coated platef.

When the heavy cylinders, and a fortiori the light ones, separated, the wire V
was let down on the plate and the wire Cc immediately drawn up, and the
time elapsed till the closing of the light cylinders counted, which was as follows:

L reversed 50"
Trial plate H 7
D° reversed 5

487] Another way was taken to try the same thing, namely, the wire Ff
was taken off and Gg placed so as to lye below the wire Dd and to be drawn up
against it by a string. The coated plate to be tried was placed on the negative
side, the wire 8 touching its bottom coating. The jars were then charged, the
wire Cc resting all the while on Aa and Bb, and Gg drawn against Dd, and /3
drawn up so as not to rest on the plate. When the jars were sufficiently charged
|8 was let down on the plate, and the wire Gg dropt immediately after, so as to
take away the communication between Dd and the ground, so that the pith balls
which were hung to D shewed whether much electricity passed round to under
side of plate or spread on the surface.

When the pith balls communicated with the ground they separated about
•£$ of an inch negatively by the repulsion of the wires on them.

Coated
plates

D of Nairne |

not in cement/
E of Nairne

in cement
F do.
G do.
I do.

Gj of Nairne all 20"
E [ inclosed in 25

Dl of Nairne not 20'
MJ inclosed in cement. 35

F) cement. 20

M reversed 36

F reversed 23

L of N. in cement 50

Balls closed
in seconds

3" or 4"

25"

25
20

35

Separated
again in

30" in 3' separated about
2'. 30" in 4' separated about

i'. 40" in 4' separated about

* [Art. 248.]

f [See Fig. 20, Art. 295.]

236 "Journal of Experiments, Feb. 4, 1772

Coated Balls closed Separated

plates in seconds again in

K of Nairne }
in cement /

L 10 did not separate again in several minutes

Double 1 A 15 i'. 15"

plates J B 10 i'. 30"

closed almost instantly, separated again in about 10".

488] Three sliding coated plates were made, each covered all over with
tinfoil on one side, with a slip of tinfoil 1-8 by -9 in. on the other. Two flat
pieces of brass were also prepared, one 1-8 by -9 and the other 1-8 square.

The tinfoil was divided in breadth into 6 equal parts, and the breadth of
the coated surface is expressed in those divisions or in 6th parts of the breadth*.

The first plate was one of exper. rosin -345 thick.

The 2nd, 2 plates of glass with rosin between.

The 3rd, a bit of the large piece of whitish plate glass. .

The rosin sliding plate when the breadth of coating = 24)

^ contains as much

2nd = I2J

electricity as the double plate A.

The 3rd sliding plate when its breadth => io§ contains as much electricity
as plate F of Naime.

Therefore i division on

2nd sliding plate contains -Jf I of the electricity

3rd
in plate D, E, F, or G of Nairne.

7 inches of additional wire answers to r inch of computed power in plates
of Nairne.

2 trial plates were made for the plates I, K, L and M of Nairne out of 2 of
the ground plates first got from Nairne. The dimensions of the coating of the
small one was about 3-3 by 3-1, and that of the large one 3-7 by 3-4, the
thickness of glass unknown.

Two trial plates were also made for the plates A, B and C of Nairne out of
the old ground plates E and F. F, the smallest, was 5-7 square, and E was
6-3 by 6 nearly.

Two trial plates were made of crown glass for the plate H of Nairne, the
small one 5-7 by 5-1, the other 6 by 5-9.

489] Tuesday, Feb. 4 [1772]. Th. 47°. S. H. 17. C. H. - 5.

Trial of plates D, E, F and G of Nairne, and of the 2 double plates, the
plates E, F and G being cased with cement : tried by means of additional wire f.

* [See Art. 297.] f [Art. 318.]

Capacities of condenser plates compared

237

Length of

Plates additional Trial

tried wire plate

D q B

G

o

B

F

o

B

G

2

B

2 doublel

plates /

9

B

D

9

B

D

16

A

2 double!

plates /

18

A

G

9

A

F

7

A

G

7

A

2 double

plates

y

I If let down and up immediately, sep. neg.
about -Jy inch. If it rested at bottom 2"
or 3", rather less,
do.
do.
do.

do., but closed sooner.

do.
sep. about ^ pos.; much the same if it rested

at bottom 2" or 3".

do. if let down and up immediately, rather
more if resting at bottom 2 or 3".
do.
do.
do.

do.

490] Feb. 4 continued. Comparison of the three plates E, F and G together
with the plates I, K, L and M, tried by the two above-mentioned trial plates
and the i8' and 2n" sliding plate*.

Sliding

Plates
tried

plate and
breadth of
coating

Trial
plate

; thereon

E(F, G

Is1 9

S

I

24

E, F, G

9

M

— 16

K

24

L

24

K
I
E, F, G

M
E, F, G

2nd 17

17
15

7
9

7

sep. pos. about T\p D° if resting 2 or 3".

sep. rather less than ^v, rather more if resting 2 or 3".

same as before.

sep. about ^. D° if resting 2 or 3".

DO

DO
Large. Sep. neg. about y1^: rather less if resting 2 or 3",

the separation more after a little time than at

first, and closed very slow.

DO

D"

DO

DO
DO

[Art. 318.]

238 "Journal of Experiments, Feb. 5, 1772

491] Trials of the same kind as those in [Art. 487].

Large trial plate for the experiments of this page — balls closed in 13"

Small do.
Trial plate A
B

E of Nairne
F
G
D

Double plate B
A

M of Nairne
I

K
L —

10 or 15
15
15

20

20

20

5

5

7

20
20

35
25

492] Wed. Feb. 5 [1772]. Th. 49°. S. H. 17^. C. H. 4$.

Comparison of I, K, and L together, with A, B and C by means of the trial
plates E and F, and of A, B and C together, with H by means of the two
crown glass trial plates*.

sep. about ^ pos. Much the same if resting at
bottom 2 or 3".

•

sep. i diam. neg. Much the same if kept at bottom

2 or 3". Kept increasing for a short time,
do.
do.

the same, only rather less if resting at bottom 2 or 3".
the same as before,
the same as before.

Sliding

Plates

plate and

Trial

to be tried

breadth of

plates

coating

F ?

I, K, L

2 ml 8

B

3r<1 8

D«

A

3r,l 8

D°

C

DO

D°

I, K, L

2n(1 10

D°

C

3r" 8

D°

E s

C

3r" 10

A

3r(1 10

{

B

ii

K, L

6

t

C

ii

t

I, K, L

— 6

t

* [Art. 318.]

Capacities of condenser plates compared
493] Comparison of A, B, C together, with H*.

239

Plates
to be tried

Sliding
plate and
breadth of

coating

A.B.C

3'" 18

H

DO

A, B,C

D°

H

D°

H

3r" 6

—

24

H

3r<l 24

A,B,C

D°

H

DO

—

3 18

Trial
plates

Large. Sep. neg. about i diam., the same if it rested

at bottom 2 or 3".
DO
D"
DO

visibly rather more,
very visibly less than last, and seemingly less than

former.
Small — sep. near ^ inch pos. Same if it rested at

bottom 2 or 3".
DO
DO
sensibly less.

Trials of same kind as those of [Art. 487].

I closed in 65" H in 55" Trial plate

B 20

K

20

20

A 20 Large trial plate for H

C 35 Small

E in 35"
F 7

5
5

'[See Art. 658.]

[ 240 j

EXPERIMENTS, 1773*

{From MS. N°. 14: see Table of Contents at the beginning of this volume.
The footnotes refer back to the formal account of results. [

494] Spreading of electricity on surface of glass plates.

4 plates of English glass were cut out of same piece and coated with bits
of tinfoil of the same size. One of these plates was covered at different times
with thick solution of lac, which ran into heaps in drying, another with trans-
parent varnish which also ran into heaps, another with solution of lac and
vermilion which lay smooth, and the other left as it was.

They were all done in the end of the summer and suffered to dry in the
open air. The spreading of the electricity on their surface was tried in the
manner described 1772, p. 22 [Art. 486].

Tu. Oct. 13 [1772]. Th. 63. N. 2o|. C. - 7.
D of Nairne, corks closed immediately.
G do. in cem. in 3" or 4".

Plate with lac closed immediately, sep. again in 3" or 4".
Lac and verm. D°, but much more.
Transparent varnish same as lacquer.
Plate not varnished closed immediately, sep. again in 5" or 6".

495] To see whether the machine used for trying Ley den vials f conducted fast.

The heavy and light paper cylinders being both hung to conducting wire,
and globe J turned till heavy ones separated, the light ones closed in i'. i"
after the others when the conducting wire communicated with machine, and
about i'. 20" when it did not.

496] The plate covered with solut. lac was undone, and that and the plate
not varnished were lacquered in Nairne's manner, one with vermilion, the
other without. Neither of them were dried after the operation.

The old Lac and vermilion and the transparent varnish were dried before
fire, heat uncertain.

Frid. Oct. 16 [1772]. Th. 63. N. 20. C. — 10.

The two plates lacquered in Nairne's manner discharged the electricity of
the jars presently.

Lac and verm, in i8' manner closed in about 10".
Transparent varnish uncertain, from 5" to 20".

* [This is the heading of this bundle of the Journal, though many of the dates
belong to 1772.]
t [Art. 295.]
| FOf electrical machine. See Arts. 248, 563. 568, 569.]

Loss of charge by spreading 241

Sat. Oct. 17 [1772]. The last varnished plates being dried before fire.
Th. 65. N. 21. C. - 7.

Ist lac and vermil. closed in 2" or 3", did not sep. in i'.

2 D° closed rather sooner.

Transparent closed and sep. again in about 4".

Tu. Oct. 19 [1773*]. The varnished glasses were baked over stove, the heat
being kept for 2 hours at about 170.

Wed. Oct. 20 [1773*]. Th. 64. N. 22. C. - 5.
Lac & verm, closed in about 15".
Old lac & verm. D°.
Transparent in i or 2".

D° rubbed with cloth, closed and sep. again in i or 2".
On Wednesday, the varnished plates were baked for above 2 hours, the
heat the greatest part of the time about 210, but part of the time the £ rose
a little way into the ball. I suppose must be at least 235 or 240.

Fr. . Th. 60. N. 22. C. - 5.

Transparent closed and sep. again immed.

Last lac & verm, closed & sep. again almost immed.

Ist D° closed and sep. again in about 2".

497] Glasses for exper. on spreading of elect.

9 plates of English glass & 8 of Nuremberg coated with plates of same size.

Sun. Oct. 24 [1773*]. Th. 63. Comm. — 6. N. 21$.
Closing of corks.

E. 9 closed in about 2".

8 rather sooner.

7 DO.

6 DO.

5 D° 4, 3, 2, i D° i did not sep. in i'.

N. 8 closed and sep. again in less than 2" but did not sep. much.

7 closed in i or 2" but did not sep. again soon.

6 closed presently and sep. again more than 8.

5, 4, 3, 2, i D° but seemed to sep. at first, to sep. more before it
began to close, it was pos. after closing.

Sun. & Mon. N i, 2, 3, 4 & 8 were baked with heat from 130 to 200. The
tinfoil of the lowest plate was blistered.

Sun. Th. 62. Com. - 15. N. 18.

E 2, 3, 4, 5 closed in about 2", 2 and 3 sep. again in 30 or 4(0]. E i closed
not quite so fast.

E 9 not baked closed in about 7", 7 & 6 in about 4", & 8 in about 3".

The 5 baked Nuremberg immediately separated wide, some without closing
first, others with.

* [Probably 1772. See note to Art. 502.]

c. p. i. 16

242 Journal of Experiments^ Nov. 4, 1772

N 6 closed and sep. almost immediately, 7 closed and sep. almost immed.
but did not sep. wide. 5 closed and sep. again in 5" or 7". N 8 washed with
spta of wine did not close so soon as before.

N 8 & E 4 were washed with sp. wine & a little ros. varnish & then varnished
with rosin.

Sun. eve. Th. 60. Com. - 20. N. 16.
E. 4 did not close in i'.
N. 8 closed in 2 or 3".
N. 3 closed and sep. again immed.

N. 8 & E. 4 were then cased in soft cement. The plates N. i & £.3 were
varnished with lac varnish, & the plates N. 2 & E. 2 with a mixture of 6 parts
of varnish & i of vermilion, & afterwards baked for about 5 hours with a heat
part of the time up to 200, and most of the time above 150, & N. 3 & E. 5
were varnished in the same manner, and then cased in a cement composed of
14 of rosin to 12 of brick dust. N.B. E. 5 was heated in drying the varnish to
a great degree, so as to make it smoke violently.
Wed. Nov. 4 [1772]. Th. 59. N. i6J. C. - 18.
E. 4 closed in about 4".
E. 5 in 3" or 4".

N. 8 closed and sep. again in 3 or 4".
N. 3 seemed to do the same rather sooner.

Fr. Nov. 6 [1772], the plates E. i and N. 4 were varnished with rosin and
the plates E. 2 & N. 2 varnished with a mixture of 4 parts of rosin varnish to i
of vermilion & afterwards baked. They were a good deal heated both in
varnishing and baking, so as to be somewhat blistered.

The plates E. 3 & N. i were also varnished before then and dried before fire.

Sat. Nov. 7 [1772]. N. 5 and E. 8 were varnished with rosin, and N. 6 and

E. 6 varnished with 8 parts of solut. rosin & 3 of vermilion, and then baked for

about 2 hours with heat which part of the time rose to 146, but commonly did

not exceed 130.

Sun. Nov. 7 [1773*]. Th. 63. Com. — 2. N. 22 J.
N. 3 closed and sep. wide immed.
N. 8 closed & sep. again in 2" or 3".
N. 6 rather slower.
N. 5 closed and sep. wide immed.
N. 4 more so.
N. 2 DO.
N. i D°.

E. 6 closed in 3 or 4".

E. 8 closed and sep. again in 2 or 3" about i inch.
E. 3 closed and sep. wide immed.
E. 2 DO.
E. i closed and sep. again in about i'.

* [Probably Nov. 8, 1772. See note to Art. 502.]

Spreading of charge on varnished plates 243

E. 5 closed in about 2".
E. 4 did not close in \ min.

498] Order in which the elect, spread.

N E

6 rosin & verm, last done
8 in soft cem.

5&3

(Varnished with ros. last
I done and hard cem.
( rosin alone, 2 Ist

' 1 rosin and verm. Ist

4 soft cement

6 rosin and verm, last done

5 hard cem.

8 rosin last done

1 rosin alone

2 & 3 ros. and verm. Ist ros. alone Ist

4-21 of the lac varnish contains 12 gra. of lac.
Th. Nov. Th. 58. Com. - 13. N. ig.

N. 8 in soft cem. closed almost immed. sep. again in 3 or 4".

E. 4 in D° did not quite close in J min.

E. 8 in ros. closed and sep. again almost immed.

E. 6 ros. and verm, closed and sep. wide immed.

N. 5 ros. more so.

N. 6 ros. & verm, same as E. 6.

Th. Nov. Th. 58. Com. - 7. N. 21.

E. 4 at first approached a little nearer, afterwards did not.

N. 8 closed and sep. again in about 3".

E. 2 Lac and verm, closed and sep. wide immed.

E. 3 Lac. not so soon.

N. 2 Lac and verm, rather quicker.

N. i Lac. D°.

E. i not varn. closed in about 8".

N. 4 closed and sep. again in about 2".

499] Sat. Nov. E. 8 & N. 5 were varnished with ros. & E. 6 & N. 6

were varnished with 8 parts of solut. rosin & 3 of vermilion. They were after-
wards baked over boiling water for about 2 hours, the heat between 115 & 120.

Sun. Nov. E. i & N. 4 were varnished with 6-0 of thick solut.

lac, 3-3 of verm. & 19 of sp'8, and E. 2 & N. i were varnished with 6-0 of solut.
lac, 4-16 of verm. & 9 of sp"1. The quantity of this last mixture spread on the
glasses was 8-0.

Mon. Nov. 16 [1772]. Th. 52. Com. — n. N. igj.
N. i closed in i or 2", sep. again in about 4.
E. 2 did not quite close in £ min.
E. i nearly the same.
N. 4 nearly the same as N. i.
E. 6 closed and sep. again immed.
N. 6 do.

N. 5 not quite so soon.
E. 8 closed and sep. again in about 3".

16 — 2

244 "Journal of Experiments, Oct. 17, 1772

N. 8 in soft cem. same as N. I.

N. 2 not covered, closed rather sooner and sep. rather more than N. i.

E. 3 closed in about 5", did not sep. in \ min.

500] Trials of quant, el. in Leyden vials, &c.
The following plates were coated as follows*.

Mean Diam. Comp. Log.

thick. coat. power D°

Thick white

•2115

2-252

23-98

1-3799

Thin DO

•104

2-234

48

1-6812

N

•106

2-136

43-04

I-6339

O

•106

2-522

59-99

1-7781

P

•127

2-87

64-87

1-8120

Q

•076

2-082

57-04

1-7562

G

•1848

3-596

69-97

1-8449

White plate

•172

3-444

68-98

1-8387

Crown C

•0659

3-45

180-6

2-2567

iJ A\

•0682

3-51

180-6

2-2568

Thick rosin

•4845

3-760

29-18

1-4651)

2nd do.

•195

3-374

58-37

1-76621 [See Art. 514]

3ri1 do.

•103

4-247

175-1 -'-434!

Two trial plates were made with two plates of glass with rosin between,
for comparing thick rosin with the double plates A and B.

Two trial plates were also made on a piece of the white plate glass for com-
paring N and thin white with D + E.

501! Sat. Oct. 17 [1772]. Th. 65. N. 21. C. 7. Inc- el-
answering

. , Addit. Trial to addit.
Plates tried wire p,ate wjre

D of Nairne
varnished with lac

7

A

sep. a little pos.

1-58

G of N in cem[ent]

7

—

rather more

'

much the same as D

•— ^^~

o

or rather less

o

ED°

—

—

DO

E

IO

B

did not sep.

G

—

—

DO

D

—

—

scarce separated

2nd ros. plate

18

A

sep. a little

4-07

D

7

A

DO

1-58

Thick ros.

3i

small

DO

•79

Doub. plate B

—

—

DO

Thick ros.

if

large

very little

•40

Doub. pi. B

if

D»

less

D

3i

A

sep.

•79

Thick white

7

A

DO

i-58

* [See Arts. 370, 371.]

Influence of the Dielectric 245

Hence it should seem that the plate D contained about r-6 inc. el. less than
the plates E or G, which is nearly conformable to p. 26, 1772 [Art. 489].

The thick rosin plate seems to contain just the same as doub. pi. B, and
the 2n" rosin plate to contain 2-49 inc. el. less than D. The thick white seemed
to contain -79 inc. el. less than D.

502] Q and P compared with M and K of Nairne, also green cylinder 4 and
white cylinder compared with plates of Nairne by means of sliding trial plates.

Mon. Oct. 18*. Th. 64$. N. 17 J. C. - 15.
[13 observations, Art. 660].

[Result.] Therefore K seems to contain 5 inc. el. less than M, conformable
to 1772, p. 26 [Art. 489].

O contains 16 inc. less, and P 16 less.

The comp. power of white cyl. = 537-5, and [it] appears to contain 756 inc. el.
Therefore inc. el. by comp. power = 1-41.

The comp. power of green cyl. is 318-2, and [it] appears to contain 540 x f £
inc. el., therefore inc. el. by comp. power = i-62f.

503] Ist and 2nd green and white cylinders and white jar compared with H of
Nairne in usual manner.

[12 observations.]

[Result.] Hence it should seem that the white cyl. contained as much el.
as H; the 2nd green contained 45 inc. el. more than H; the Ist green uncertain,
and the white jar seemed to contain 74 inc. el. more.

504] Trials of the same cylinders and jar in same manner except that in trying
the white jar and Ist green cylinder the plate M of Nairne was placed on the neg.
side as an additional trial plate.

Sat. Dec. 5 [1772]. Th. 56. N. 20.
[13 observations. Art. 660.]

[Result.] Hence iflt green cylinder should cont. 135 inc. el. more than H
2nd 56

white cyl. 7

white jar 88

* [As the records of the actual observations in the following articles are of pre-
cisely the same nature as those already given, they will be omitted, and as the
author has summed up the results for each day, these statements only will be given,
except in cases of more than ordinary importance. According to the day of the
week and month the dates for these experiments should belong to 1773, but as the
experiments seem continuous with those of dates before and after which are certainly
in 1772, I think Cavendish made a mistake in the day of the month which he did
not find out till 4"" November.]

•f [These measures of specific inductive capacity must be multiplied by 5-1.
See note to Art. 462.]

1170

600-7

1-84

1023

600

1-70

976

684-1

i-43

1060

680-7

1-56

246 Journal of Experiments, Dec. 3, 1772

By means of this and preceding page, the quant, el., comp. power and
quant, el. by comp. power are as follows*:

Quant, el. Comp. power

Ist green
2nd do.
white cyl.
white jar

505] The quant, el. in the 2 coated globes was tried by putting the white
cylinder and the 6th sliding plate on neg. side.

[6 observations.]

ftjlobe 2 (1782

[Result.l Therefore \ , seems to contain < ' [circ.l inc. el.

Iglobe 3 U555 L

Trials of jars used in the i" sort of experiments: [Art. 240] tried by putting
a sliding plate with or without the white cylinder on neg. side.

Th. Dec. 3 [1772]. Th. 55. N. 22.

[6 observations.]

[Result.] There seems some mistake in the 3rd exper., therefore if we make

use only of those exper. in which they sep. pos. the jar for j contains

more than H;

id est inc. of el., but if we made use only of the other exper. it would be

972

fneg. side 1233
Ipos. side 1043 '

506] Trials of the 4 large jars, the jars being placed on the neg. side.
Fr. Dec. 4 [1772]. Th. 59. N. 19 J.
[8 observations.]

[Results.] By mean

g c i + C
jar i equals w. cyl. + g. c. 2 + B + - - + 5, 6 = 3184

jar 4 w. c. + g. c. 2 + B + + 5 - 10 = 2675

jar 3 w. c. + g. c. 2 + g. c. i + B + 5 - 7^ = 3635

jar 2 w. c. + g. c. 2 + - - + 5 - 16 = 3050

507] Trials of the 5** and 6th trial plates, the trial plate being placed on neg.
side.

Result. Therefore trial plate 6 - 56 = H.

[Trial plate] 6 — 18 rather more than C'.

By mean 6 — 18 = C, and trial plate 5 - 17 = C.

* [See Art. 383.]

•(• [These measures of specific inductive capacity must be multiplied by 5-1. See
note to Art. 462.]

Specific inductive capacity 247

The trial plate 4 is on same plate as 5, and the area of one division on it is
to that of 5 on trial plate 5 as r82 to 9.

508] Thick white, 2nd rosin, D and F of Nairne, and the two double plates
together, compared together, also thin white with D and E and D and F.

Sat. Dec. 5 [1772] in evening. Th. 56. N. 28^.

[24 observations.]

N.B. Before these exper. were tried, the plates E and F were freed from
cemfent] and coated afresh with plates of same size. The plate D was also
freed from the varnish and coated afresh, and the trial plate B was freed from
cement and coated with rather larger plates.

Hence it should seem that thick ros. contained n inc. el. less than the
doub. plates A or B, id est 18-2 inc. el., that the thick white contained same
as D, id est 36 inc., and that 2nd ros. contained 2-03 inc. less, id est 34 inc., which
differs very little from p. 12 [Art. 501].

509] Whitish plate, P, Q, O, old G and thin rosin compared with M.

Sun. Dec. 6 [1772]. Th. 54. N. 20.

[19 observations, Art. 655.]

[Result.] By these exper. the two double plates should contain about
1-13 inc. el. more than D, that thick white contained same as D, that the 2nd
rosin contained 2-26 less, that the thin white contained -45 less than D + E,
and that N contained 1-81 less.

Sunday evening. Th. 57^. N. 17^.
[18 observations.]

510] Crown A and C compared with A, B and C of Nairne.

Mon. Dec. 7 [1772]. Th. 55. N. i8J.

[10 observations.

21 observations of spreading of electricity on the different plates.j

By the above exper. Crown A and C should contain 15 inc. el. less than A.

511] Whether the shock from the plate air was diminished by changing the air
between them by moving them horizontally*.

Sat. Dec. 18 [1773 f]. Th. 60°. N. 23^.

It was tried whether shock in charging plate air was sensibly diminished by
moving the 2 plates horizontally, and thereby changing the air between them
in the manner represented in figure, where AB represents the two 8-inch brass
plates with sealing wax between them suspended by the silk strings AC and BD.

AE and BF are silk strings fastened to the frame on which lower plate
rests, and passing over wire hooks E and F, and stretched by weights so that
the plates would move from E towards F and rest in any position.

The electrifying wire was suspended by the string G with a counterpoise.

* [See Arts. 345, 516.] f [Probably Dec. 19, 1772. See Art. 502.]

248

'Journal of Experiments, Dec. 18, 1772

The plates were electrified, holding my finger to bottom plate, they were
then moved 24 inches by lifting up the weight M, and then discharged by
holding my little finger to lower plate and touching upper plate with brass
knob held in the other hand. I could feel a small pulse in little finger, having
tried this I electrified and discharged the plates in same manner only without

c

moving them first and endeavouring to preserve the same distance of time
between the electrification and discharge. I was not able to perceive any
difference in the feel. I endeavoured to ascertain the time by the vibrations
of a pendulum, but without much success. It seemed needless, however, as I
could perceive scarce any difference in the sensation whether I discharged it
immediately or waited as long as when the plates were moved. The usual
time between the electrification and discharge was about 2\".

The experiment was also made by Richard, who did not perceive any
difference.

The heavy paper electrometer was used. The bits of sealing wax between
the plates were those made in 1771 [Art. 457].

512] Whether globe included within hollow globe is overcharged by electrifying
outer globe*.

It was tried whether the globe enclosed within hollow paper globe was
overcharged when the outer globe was electrified.

This was first tried by making the 2 hemispheres slide on 2 sticks of glass
by means of 2 tin hooks and a stick of glass fixed to the back of the hemisphere.

The wire by which it was elect, was suspended about 4 inches above the
hemispheres while the vials were charging. It was then let down, and it was
so contrived that the same motion of the hand which lifted up again the elect,
wire, lifted up the wire which connected the inner globe with the outer, drew
back the hemispheres, and drew up the pith balls fastened to a stick of glass
till they touched the inner globe.

It was found that if the elect, of the hemispheres was discharged before
they were separated, but after the communication between them and the inner

* [See Exp. i, Art. 218.]

Determination of law of electric force 249

globe was taken away, that the pith balls did not sep., but if they were sepa-
rated before their elect, was discharged, then the pith balls would at first sep.
about an inch or so, but quickly closed, whereas if the inner globe was electrified
after the hemispheres were separated, it was found to be a great while before
the pith balls closed. It was found that this was owing to the sticks of glass
on which the hemispheres slid being electrified thereby, as the same phenomena
were produced by electrifying those sticks when the hemispheres were taken off.
N.B. These sticks were not covered with sealing wax, and as appeared by
this exper. suffered the electric, to run along them pretty readily. The stick
of glass run through the globe had all that part without the globe covered with
sealing wax.

513] The same thing tried by a better machine.

Wed. Dec. 23 [1772]. Th. 52°. N. i8£.

The exper. was tried in a different manner, the hemispheres being fastened
by sticks of glass covered with sealing wax within wooden frames turning on
hinges.

If the pith balls were made to sep. pos. about i inch before the globe was
elect, they separated i£ or two diameters on touching the globe. If they
separated only r inch before touching, they did not sep. at all on touching the
globe. If they separated negatively i£ or 2 inches before touching, they did
not sep. at all after touching.

The event was just the same whether the wires for discharging the elect,
of the globes when separated were placed so as to touch the hemispheres as
soon as they were sep. an inch from each other, or whether they were placed
so as not to touch them till they were separated almost the whole distance.

N.B. Each hemisphere was drawn back about n inches from its first
situation.

It appears from hence that the inner globe was a small matter overcharged,
but not enough so to make the balls sep. unless they were before positively
electrified, so that the redundant fluid in it could hardly be ^ of that which
it would have received by the same degree of electrification if the outer hemi-
spheres had been taken away, and probably not more than \ as much.

[Exper. rosin*.}

514] These rosin plates were made out of a mixture of 4 parts rosin and
r of bees wax mixed together with a considerable heat, towards the beginning
of the year 1771. Towards end of 1772 some round plates were cast out of this
by gentle heat, which were pared to a proper size and shape and then pressed
out between brass plates heated in wooden box over furnace (the tin lining
being not then made), the bits of tinfoil were at first fastened on by just wetting
it in a few places with gum water and sticking it on, but as this was found not
to do well, the bits of tinfoil were afterwards rubbed with melted wax and
fastened on by keeping them some time pressed with slight weights with flannel
between them.

* [See Arts. 337, 373, and 500.]

250 "Journal of Experiments^ Dec. 25, 1772

515] I9t and 2nd sliding plates compared with double plate B, also P, Q and O
and thin rosin. Old G and whitish plate compared with D, E, F, and M.

The isl and 2nd sliding coated plates were compared with double plate B
[6 observations]. The 25 divisions] on slfiding] pl[ate] were measured by using
brass plate 3 inc. by ij and 9 div. of the tinfoil.

2 trial plates were made for plates M &c. out of a white glass hemisphere
[8 observations. Art. 656].

Fr. Dec. 25 [1772]. Th. 49. N. 20.

[19 observations, and 3 on insulation. Art. 656.]

By this exper. with \ ,. trial plate 0 contains < inc. el. less than
Ismail I -7

D, E & F, P 7'3 less, O 4'4 less, old G 2'9 less, whitish plate 4'4 less, and thin
"7 7'3 7'3 9'5

rosin less.
17-2

By mean P contains 9-5 less, 0 5-8 less, old G 5-1 less, whitish plate 7 less,
thin rosin 16 less, and Q -3 less.

The wires used in the machine were all cleaned between this experiment
and the next.

516] Whether the charge of plate air is diminished by changing the air between
them by lifting up the upper plate*.

In order to try whether in electrifying plate air the electricity was lodged
in the air or in the plates, the two brass 8-inch plates were placed on each other
with supports of sealing wax to keep them at about -4 inc. distance from each
other and placed on the machine f with the end M of the wire Mm resting on it ;
the uppermost plate being fastened by a stick of waxed glass and 3 pieces of
silk to the end of a lever so that it could be lifted up and down. It was also
contrived so that in lifting up the plate the wire Mm was first lifted up from
it about J inch, for fear that if Mm rested on the plate when lifted from the
under one, some electricity might escape from the ends of the wire Bb, &c.
The third sliding trial plate was put on the negative side.

If the wire Cc was let down and up immediately without lifting up the
upper plate, the pith balls separated negatively very little with 18 divisions
of sliding plate.

If the wire Cc was let down and immediately drawn up halfway, but not
drawn quite up till the upper plate had been drawn up and let down again, the
balls separated very little more.

The event was the same also if the trial plate was drawn out so that the
balls should separate a little positively.

The upper plate was lifted up 2 or 3 inches. The sliding plate was let out
to 12 divisions that the balls should separate positively.

* [See Arts. 344, 511.] f [Art. 295.]

Dielectric influence of plate of air 251

517] Trials of plate air i, 2, 3 and 4. [See Arts. 341 and 668.]
Two plates of glass nj inches square were coated with tinfoil about 11-4
inches diam. a slip of tinfoil extending from the coating to the other side. These
plates were placed upon each other with coated sides to[wards] each other and
kept asunder by 3 supports of sealing wax, the supports being placed a little
on outside of coated part and tried in the usual manner.

Sun. Dec. 27 [1772]. Th. 50. N. 18.
[4 observations.]

Mon. Dec. 28 [1772]. Th. 53. N. 17$.

The exper. tried in same manner except that only i corner of the under
plate rested on machine, the rest being supported by 2 wooden pillars, the
places where it was supported being nearly under wax supports.

[15 observations. Art. 668.]

By this exper., plate air i contains i inc. el. more than D, plate air 2, -i inc.
el. less than D + E, and plate air 3, loj inc. less than D + E + F.

Wed. Dec. 30 [1772]. Th. 55. N. 15.

The supports of plate air 3 altered and called plate air 4.

[12 observations.]

One of the pith balls was destroyed by accident, and another put in its
room.

The plate air i was made to rest intirely on machine.

[3 observations.]

By this exper., plate air 4 contains i inc. el. less than D + E + F, plate
air 2, i inch less than E + F, and plate air i, i inch more than E. It should
seem also that the wire Mm contained 2 inches less el. when the plate rested
intirely on the machine than when it rested on it only by one corner.

The thickness of these plates of air was found by laying these plates on
bracket fastened to dividing machine* with or without wax supports between
them, and finding the division at which the new machine stood right, the knob
of the new machine resting on the middle of upper plate, and the under plate
being supported under the wax supports. By this means the thicknesses of
these plates of air were as follows:

plate i = -910

2 = -420

3 = -288

4 = -256

Some experiments were made by putting bits of tinfoil between the plates
whether the glasses were flat, and consequently whether the measures thus
found were true. It seemed as if when the plates lay on each other the middle
of the coatings could not want more than -002 or -004 of touching, but it did

* [Arts. 341, 459, 591.]

252 "Journal of Experiments, Dec. 30, 1772

not appear that it wanted so much, and it seemed as if the outside did not
want anything of touching, so that the above measures seem pretty just.

The diameter of the coating was 11-4.

The above coatings were taken off from these plates of glass, and coatings
6-254 in diameter put in their room, these with the small wax supports placed
between them is called plate air 5.

N.B. 8 folds of the tinfoil used for these coatings was found to be ^ inch
thinner than the same number of folds of that used for former coatings, so that
this plate air is about -003 thicker than plate air 4.

The coatings were also taken from thin rosin and coatings 4-525 put in their
room.

A plate of pure lac was also pressed out -125 thick, and the coatings used
before for thin rosin put on, which were found at a medium 4-23 in diameter.

Two plates of dephlegmated * bees wax pressed out the year before were
also coated.

N.B. The bees wax was heated very hot in dephlegmating, and melted with
gentle heat when cast into plates.

The thickness of the A. ' of these plates was , and the diameter of
thickest -303

their coatings ^ .

518] Lac plate and 4th rosin compared with D + E + F; also thin wax with
E + F; also thick wax and plate air 5 with D.

Mon. Jan. 4 [1773]. Th. 51. N. 17.

[23 observations.]

By these exper. Lac plate contains i£ inc. el. more than D + E + F; 4th
rosin from 3 inc. more to 2 inc. less, by mean much the same as D + E + F;
thin wax 4 inc. less than E + F ; thick wax 2} less than D ; plate air 5 J more,
and Ist made rosin J more.

In the preceding experiments the plates of rosin &c. were exposed to the
heat of the fire during trials, which seemed to cause an irregularity. To avoid
that, in the following days' experiments the plates were laid on table at same
distance from fire as the machine for some time before they were tried, and a
screen was placed between all of them (except plate air) and fire while trying.

519] Lac and 4th rosin with D + E + F; also thin wax with D + E; also
thick wax, 2od rosin and i8' made rosin and plate air 5 with F.

Tu. Jan. 5 [1773]. Th. 50. N. 17.

[22 observations.]

By these exper. 4th rosin contains from 2 inc. more to 2\ less than D + E + F;
by mean, the same as D + E + F.

Lac from 4 more to \ less, by mean 2\ more than D + E + F.

Thin wax from 4 less to i less, by mean 2\ less than D + E.

* [Art. 375.]

Tests of electric strength of dielectrics 253

Thick wax 3 less than F.

2nd rosin, if less, plate air 5 J more, and Ist made rosin same as F.

N.B. The Ist made rosin was made of the same proportion of rosin and
bees wax as the others, but not of the same parcel : it is uncertain how much
it was heated in making the mixture.

Result of the exper. on plate air.

Diam.

Thick.

Comp.
pow.

Inc.
el.

Inc. el.

by comp.
pow.

Do.»
8x12-1

Inc. el.

Last col. into
excess preceding
above unity

' 18-8

diam.

Ist plate

11-4

•910

H3

37

•259

1-34

3-25

I'll

2nd

•42

310

71

•229

1-18

6-23

I-I2

3rd

•288

451

97^

•216

i-n

8-55

•95

4

•256

508

107

•211

i -09

9'39

•84

5

6-254

•259

'51

•240

1-24

5-80

i'39

520] Breaking of electricity through thin plates of lac, exper. rosin and dephleg.
bees wax.

Thin plates were pressed out of lac, experimental rosin and dephlegmated
bees wax, very thin at one end and thicker at the other. The tinfoil was stript
from one side of these plates but the other left on, and was fastened to a piece
of glass with gum water, and a piece of tinfoil fastened to the under side of glass
communicating with the other.

These plates were placed on [the] negative side of the machine with wire 8
bearing against bottom and a flat piece of brass at top on which wire j8 was
suffered to rest. The machine was electrified in usual degree, and the bit of
brass shifted from thicker to thinner part, till the electricity broke through the
plate and discharged the jars.

A piece of the plate with the tinfoil under it was then cut out of the size of
the brass plate, as near as possible to the place where the electricity broke
through, and the thickness of the plate found by weighing it and also the
tinfoil after the plate was separated from it.

The thickness of the plates thus found was as follows f, the specific gravity

being
\ rosin >• , •?!•

supposed
Uac li-

I" wax
J. rosin

955
i -06

wax at Ist place -0130
2nd -0123
rosin -0131

lac '0143

* [See Art. 343. The inches of electricity are circular inches, and to reduce
them to globular inches must be multiplied by 12-1, the diameter of globe, and
divided by 18-8, the diameter of a circle which has the same charge. The com-
puted power here is the square of the diameter divided by the thickness, and this
must be multiplied by 8 to get the computed power as denned in Art. 311.]

•f [With the "usual degree of electrification" Lane's electrometer discharged at
•04 inch. See Art. 329. The electric strength of wax, rosin, and lac is therefore
about three times that of air.]

254 "Journal of Experiments^ y an. 1773

521] The quantity of electricity in a Florence flask tried with and without a
magazine.

The quant, el. in a Florence flask was tried by putting it on negative side,
and some of the jars &c. on the other, the battery of 6 Florence flasks being
used instead of the jars.

With the i8', 2nd, 3rd jar with sliding plate 6 — 40 sep. neg. rather more
than i diam.

4 jars + white cyl. sep. a little pos.

i, 2, & 3 jars + 6 — 48 D° neg.

Sat. Jan. . Th. 56. N. 19.

The same thing tried again in same manner
with the 4 jars and white cyl. sep. about i diam. pos.
with i, 2, & 3 jar D° neg.

4 jars + white cyl. D° pos.

Tried without mag.

With 4 jars and white cyl. sep. at Ist about i diam. but soon closed,
with i, 2, & 3 jar sep. a good deal neg.

with i, 2, & 3 jar + wh. cyl. + gr. cyl. 2 after a time sep. near i diam.
With 4 jars and the 2 cyl., sep. at Ist a good deal, after a time sep. about I diam.
Sun. Jan. Th. 56. N. 21.

A coating of tinfoil to a part of the Florence flask out of water.

With 4 jars + wh. cyl. + gr. cyl. 2 sep. rather more than i diam.
The case was much the same whether wire was suffered to rest at bottom
2" or 3", or less than i".

With 4 jars + wh. cyl. + 6 — 16 sep. less than i diam.
With i, 2, & 3 jars + 6 - 16 D° neg.

Without mag.

With 4 jars sep. a little neg., increased after a time to full i diam.
By the Ist night's experiments the flask contains 12126 inc. el.
by the 2nd 11694

and by the 3rd "495

Without magazine by 2nd night it contained 13205 inc. el.
The true quantity is supposed 11700

522] Computed power of above flask.

The diameter of the flask at the surface of the water in tin pan on Saturday
was 1-7; the height of that part above the bottom 5-1 ; the height of top of tinfoil
coating above bottom 6-55; and the diameter of that place, -68; and the cir-
cumference at the widest part 13.

The weight of that part under water was i .. 2 .. 7*, and that of the part
between that and the top of coating was 2 .. 4.

* [Troy weight.]

Residual charge : comparison of resistances 255

If the spheroid agdm does not differ much from a sphere, and ab does not
differ much from ad, the surface afea is nearly

equal to the circumference of gm x ab x - — j^— ,

^surface
the -! thickness of the part under water was

Icomp. pow.

( 62 (-5-3

| -0127, and that of the part above J -0179, and the
1 6200 1.375

comp. power of the whole part below top of coating 6575, the specific gravity
of the glass being supposed 2-68.

Therefore inc. el. by comp. pow. = 1-78.

523] As it appears from the above experiments that the Florence flask
contains more electricity when it continues charged for a good while than when
charged and discharged immediately, it was tried whether the white globes
would do the same.

This was done by putting the globe 3 on positive side and the white cylinder
and trial plate 6 on negative side, and first charging and discharging them in
the common manner, and then discharging the magazine and charging it again,
while the end c of the wire Cc rested on Bb, while the end C was prevented
from resting on A a by a silk string. When the magazine was charged, and had
continued so for a little time, the end C was let down on Aa and the wire Cc
immediately drawn up again so as to discharge the globe &c. The event was
as follows,

in common way, wh. cyl. + 6 — 20 sep. near i diam. pos.

globe elect, first, +6-24 D°.

in common way, +6 — 47 D° neg.

globe elect, first, +6-48 D°.

By these experiments the globe contains 45 inc. el. or about ^1T less when
electrified in the common way than when charged before the rest, which is as
much as is contained in i inch in length of the uncoated part of the neck (the
whole neck being ij inches), so that supposing the experiment exact it seems
as if the globe contained rather more electricity when it continued charged a
considerable time than when charged and discharged immediately *.

524] Diminution of shock by passing through different liquors^.
Tried in November [1772].

The electricity was made to pass through 42 inches of a saturated solution
of sea salt in a thermometer tube of a wide bore, and the two jars charged in

* [These phenomena are connected with the "residual charge." A careful in-
vestigation of them has been made by Dr Hopkinson, Phil. Trans, vol. 167 (1877),
P- 599'] {Reprinted in his collected Scientific Papers.}

•f [This is the first experiment on electric resistance.]

256 Journal of Experiments, Nov. 1772

such manner as that a slight shock should be felt in [the] elbows : it was then
made to pass through rain water in a tube of a rather greater capacity, and the
electricity made rather stronger. The wires were obliged to be placed within
•18 of each other in order to feel the shock in the same degree. Therefore the
electricity meets with more than 230 times the resistance in passing through
rain water than salt.

The above jars were electrified till light paper cylinders began to separate,
and the shock made to pass through a tube filled with rain water. The wires
were obliged to be brought within -48 inches of each other in order that the
shock should be just felt in the elbows.

When the same tube was filled with saturated solution of sea salt diluted
with 29 its bulk of rain water, a much greater shock was felt when the wires
were at i6J inches from each other.

Therefore electricity meets with much more than 34 times the resistance
from rain water than from a saturated solution of sea salt with 29 of rain water.

When the same tube was filled with kitchen salt in 1000 of rain water, the
wires must be brought within 4-4 inches; with pump water within 2 inches,
and with spirit of wine almost close ; therefore the resistance of

Pump water } . (4!

„ ., . ... } is < " less than that ot ram water.

S. salt in 1000 of ram water) [9

Mon. Nov. 16 [1772] with straw electrometer. With sea water a shock was
felt when the wires were igj inches distant; with rain water when they were
at about -19 inches distant. Therefore resistance of sea water is about 100
times less than that of rain water.

G
A

525] Exper. Whether force with which two bodies repel is as square of re-
dundant fluid in them*.

Tried by pith balls hung by threads.

A and B are the coated plates A and B, the bottoms of which communicate
with the ground, D and d are two bits of wood resting on them, supporting the
pith balls E and e. G is a bit of wood for making a communication between
them. The wire for electrifying the plates rests on B, and is so contrived that
when that is lifted up the wood G is let fall on the plates.

The pith balls E had bits of wire made to run into them in order to increase
their weight.

A paper with divisions was placed 6 inches behind the pith balls and a
guide for the eye 30 inches before them.

* [Arts. 386, 563, 567.]

Relation of Repulsion to charges 257

Tu. Oct. 26 [1773]. Th. 60. Com. - 6J. N. 2i£.

One of the balls E with its string weighed -5 gr. and its wire 1-4, the other
•6 gr. and its wire 1-7.

The two balls and strings together — the weight of one of the strings, weighed
1-05 gr., the weight of the string about -05, the weight of the two wires together
was 3-2.

When the wires were taken out of the balls E, and a communication made
between the two plates, while the electrifying wire rested on B, then when

balls r sep. ] , balls E sep. -!

U-o8 (.!•]

•14

The wires were put into balls E and the jars electrified while the electrifying
wire rested on B. When the balls E sep. 1-3 inc. the electrifying wire was lifted
up and the electricity of the plates taken away, immediately after which the
electrifying wire was let down and immediately drawn up again when the balls e
separated to 1-44. The electrifying wire being then let fall on B and suffered
to remain, the balls E separated to 1-14.

The jars were charged, and the electricity diminished by alternately drawing
up and down the electrifying wire and discharging the electricity of the plates
till the balls e separated to 1-2; then letting the electrifying wire rest on B,
the balls E separated to 1-08.

Wed. morn. The new heavy electrometer made with large wood ball and
pith ball separates when the balls E separate to 1-52, and new light electrometer
separates when the balls e separate to 1-44.

When balls e separate to 1-44, balls E separate to -96.

The new heavy electrometer above mentioned separates about J or J inch
when old light cylinder electrometer just separates.

Result of these experiments.

Balls E without weight separate .-\ farther than balls e with the same degree
of electrification.

1*22

If balls separate with i part of redundant fluid, balls of \ weight

separate with A part of redundant fluid.
1-25

If balls of given weight separate 1-5 with given degree of electrification,
balls of 4 times weight separate -96, therefore if balls of given size are electrified

in given degree, the distance to which they separate is inversely as -- power
of their weight.

Therefore, in last paragraph, if balls of given weight separate J , balls of

I*Q 1*22

* their weight will separate to _ , therefore if balls of given weight with
c. p. i. 17

258 Journal of Experiments, Oct. 1773

given quantity of redundant fluid separate to given distance balls of , that
weight separate to same distance with half that quantity of redundant fluid.

526] Whether the charge of plate E bears the same proportion to that of another
body whether the electrification is strong or weak: tried by machine for Ley den vials.

Wed. Oct. 27 [1773]. Th. 61. Com. 8J. N. 2oJ.

Plate E of Nairne on neg. side against sliding tin plates placed at end of
long wire [20 observations].

Result. Therefore with light electrom. the plate E is balanced

, 14-03 + 8-17
by a square of - — ' + x = n-i + x,

IO-OQ + 12-33
with heavy el. by - 2 - + x = 11-21 + x,

10-50 + 11-23

— + x = 10-91 + x.

2

The plate E is balanced by 37 inc. el.

527] Plain wax and 3rd dephlegmated wax with E + F and 5th rosin with
double plate A and B. Also small ground crown with D + E 4- F, and large do.
with C.

The coatings were taken off from 4th rosin, and coatings 1-79 inc. diam. put
in their room. This is called 5th rosin.

A plate of dephlegmated bees wax was also made [-120]* inc. thick and
coatings put on 3-525 inc. in diam. This is called 3 dephlegmated bees wax.

A plate of plain bees wax was also pressed out [-119] * inc. thick and coatings
put on 3-475 inc. diam.

A piece of thick crown glass was procured from Nairne about -26 thick and
ground down equally on both sides to about -07 inc. thick. Two circular coatings
were put on, one 3-54 inc. in diam. the other 2-035.

Wed. Jan. Th. 56. N. 27 £ [16 observations].

528] K, L and M compared with D + E + F at distance and close together; also
large ground crown with C and small one with D + E + F; also 3rd dephlegmated
wax and plain wax with E + F; also 5th rosin with double B.

Friday, Jan. 29 [1773]- Th. 3$. N. i6£.

Tried with middle sized cork balls and a new white large trial plate [18
observations. Art. 656].

529] K + L + M compared with A, B, and C; also A + B + C with H.
Sat. Jan. 30 [1773]. Th. 50^. N. i6£. [20 observations. Art. 657.]

* [These measures are left blank in the Journal. I have supplied them from
Art. 371.]

Law of partition of charges 259

530] K + L + M compared with B with electrification of different strengths.
Sun. Jan. 31 [1773]. Trial plate F enlarged.

[14 observations with light and heavy electrometer alternately. Arts. 656,
658.]

531] K + L + M with A, B, and C; also D + E + F with K, L, and M;
also small crown with K, L, and M; and D + E + F and large ground crown
with A, B and C and K + L + M.

Mon. Feb. i [1773]. Th. 48. N. 16.
[20 observations. Art. 657.]

532] On light visible round edges of coated plates on charging them*.

Mon. Feb. i [1773]. Th. 48. N. 16.

Some coated glass plates were placed on pos. side and electrified in usual
manner in dark room in order to see whether any light was visible round their
edges. With the plates M and L of Nairne and with the small ground crown
glass a light was visible round the edges when the light electrometer was used,
and nearly equally so with the large ground crown glass. The light seemed of
the 2 rather stronger with the plates F and A of Nairne; no light was visible
when light electrometer was used, but it was with the heavy electrometer.

533] Crown A and C and large ground crown with C; also 3rd dephlegmated
wax, plain wax and sliding plate 3 with E + F; also 2 double plates with E, F,
and D.

Mon. evening. Th. 53. N. 15. [25 observations. Art. 655.]

534] Charge of the triple plate— the three plates A, B and C placed over each
other, with bits of lead between coatings].

The three plates A, B and C were placed over one another with the coatings
nearly perpendicularly over each other, with bits of lead between them, so as
to keep them at the distance off inches from each other. This compound
plate was tried in the usual manner.

Tu. Feb. 2 [1773]. Th. 50. N. 17$. [9 observations. Art. 677.]

535] Whether the charge of plate D bears the same proportion to that of another
body whether the charge is strong or weak: tried with machine for Leyden vials§.
[Art. 664.]

Th. Feb. 4 [1773]. Th. 48^. N. 13*.

Tried with smallest cork balls and the light straw balls as electrometers'.

The plate D placed on the neg. side and the sliding tin plates at 23^ inc.
dist. from wire.

17 — 2

* [Art. 307.] f [A""*- 38°-]

} [So in MS.] § [Arts. 356, 664.]

260

^Journal of Experiments, Feb. 1773

Div. on
electrometer] *

Div. on
sliding plate

Side square
equiv. to
trial plate

Diff.

Sum.

I + 3

2-2
4 17

sep. neg.
D° pos.

10-09
16-70

6-61

26-79

Tin plates at 17^ inches dist.

i + 3

2 5

D° pos.
D° neg.

17-42

n-54

5-88

28-96

3+ i

3 Ti

4 15

D° neg.
D° pos.

12-06
15-68

3-62

27-74

i + 3

4 *8£

2 5

D° pos.
D° neg.

17-42
11-54

5-88

28-96

3+ I

3 ij

DO

12-06

^88

28-00

4 X5i

D° pos.

15-94

The same repeated with neg. elect.

4-15

3 4

2 4i

4 i7i

D«

D° neg.
D»

D° pOS.

15-68

12-06

11-31
16-94

3-62

5-63

27-74
28-25

536] H with slits and a crown glass with oblong coating compared with white
cylinder; also A and C with slits compared with B.

The coatings were taken off from the plates A, C and H, and oblong coatings
with slits put in their room; an oblong coating without slits was also put to
a piece of crown glass, vide Measures [Art. 593].

Tu. Feb. 9 [1773]. Th. 50. N. 12^. 50 observations. [Art. 660.]
These plates were tried with middle cork balls.

Spreading of el. on surf.
A & C. Balls at first sep. wider. Closed in about 10".

B. D°, but rather sooner. As it was supposed that this proceeded from
the wires not conducting ready enough, the machine was moved slower, there
was then but little of this and B was a great while before it closed, C about
5", H a great while.

It was suspected that this increase of separation of the balls before they
closed was owing to the wire designed to carry off el. to earth f not conducting
fast enough. To try this, the next evening a long wire was insulated, and the
cork balls hung to it. It was electrified sufficiently to make them sep. about
an inch. They closed instantly on touching the wire with a bit of iron either
communicating with wire for carrying off el. to ground, or whether it was only
held in the hand. The air was as dry as the night before.

* [Divisions and quarter divisions.]

f [Art. 258.]

Spreading of electricity 261

537J Crown with slits and H with D° compared with white cylinder; and A
and C with oblongs compared with B *.

The coatings were taken off from the plates A and C and oblong coatings
without slits put in their room. The coatings were also taken from the crown
glass, and oblong coatings with slits like those put to C put in their room.

Fr. Feb. 12 [1773]. Th. 49. N.
[34 observations, Art. 660.]

538] Experiment of p. 61 [Art. 535] tried with small ball blown to the end of
a thermometer tube.

A ball rather less than | inch diam. was blown at end of glass tube and was
coated on outside with tinfoil, the inside being filled with $. This was used
instead of plate D in exper. to see whether charge of Leyden vial bore the
same proportion to that of another body whatever force it was electrified with.
It was found that 12 inches of this tube when coated contained as much el.
as K + jj^D, and therefore the spreading of the el. ^ inch on surface of this
tube increases its charge by ^%D, whereas the spreading of el. ^ on surface

of D increases its charge by — j D.

5s

Th. 49. N. 13$. Tin plates at 17 inches from wire.
With electrometer at I + 3.

Div. on
sliding plate

4 22

3 3i

3 ' 6

4 *9i

sep. about i diam. pos.
D° neg.

With electrometer
DO
D°

Equiv. to
trial plate

Diff.

19

5'9

t 3 + I-

I4-3
17-9

3-6

Sum.

32-1

32-2

Fringed rings on plate of crown glass &c. f

Sat. Feb. 13 [1773].

It was found on looking at the plate of crown glass that there were narrow
fringed rings of dirt all round the edges of the coatings, the space between these
rings and the coating being clean. This was supposed to be done by the ex-
plosions.

The distance of these rings from the edge of the coating seemed nearly the
same both within the slits and without, but of the 2 seemed less within the
slits. The mean distance seemed about -105 inc. which seems to shew that the
electricity spreads pretty nearly the same both within the slits and without.

'Something of this kind has been frequently observed in the sliding trial
plate i and sometimes I believe in some of the coated glass plates.

Sun. Feb. 14 [1773]. Th. 49. N. 17. Last exper. repeated.
[At 1 + 3, Sum = 29-6, at 3 + i, Sum = 28-3. Plate D gave 26 and 27-5
respectively. See Art. 664.]

* [Art. 321.] f [Art. 308.]

262

journal of Experiments, Feb. 1773

JS7

539] Experiment to determine whether the charge of a Leyden vial bears the
same proportion to that of another body when elect, is very weak as when it is
strong *.

AB is a tin cylinder 14 feet 8-7 inches long and 17-1 inches in circumference.
DC is a brass wire 37-1 inches long and -15 in.
diameter; both supported by non-conductors;
with the middle sized cork balls hung at D.

FE communicates with the prime conductor
and is charged till light paper electrometer sepa-
rates. A brass wire is suspended by silk, so as
to be made alternately to touch E and DC.

Mon. Feb. 15 [1773]. Th. 55. N. 22.

The cylinder AB and wire DC were elec-
trified negatively till the balls separated about
i diameter. On touching DC twice with the wire,
the corks separated about as much positively.

The wire was 27-6 inches long and -15 in.
diameter.

The cylinder AB was then taken away and
the plates D and E placed under the wire DC.
The wire was obliged to be changed for one 20-8
inches long to exhibit the same phenomenon. [See Art. 666.]

Tu. Feb. 16 [1773]. Th. 57. N. 20.
Same exper. repeated.

Cylinder touched twice with wire 31 inches long; changed from about
i diam. neg. to D° pos.

D and E with wire 24 inches D°.
cyl. with wire 31 D°.
cyl. with 27^ did not. [See Art. 666.]

540] Lane's electrometer compared with straw and paper electrometers.
In the afternoon. Th. 56$. N. 19. I tried the distance to which the spark-
would fly by Lane's electrometer.

Distance
[Lane]

Knobs touched
•027
•038
•044
•047
•051

•053

•038

knobs at -965 inc. dist .

Divisions on
electrometer -f-

o+5

0 + 48

i+ 5
i+ 15

1 -I- 20
1 + 25
1 + 27*
i+ 5

25 + 28

Straw elect, sep. 1 + 3
2 + ij

2 + 2\

2 + 3

3 + oi

3+ i
light paper elect, just sep.

* [See Arts. 358, 606, and Note 25.]

f [Revolutions and 6o"> parts of a revolution. One revolution = -038 inch.]

Measures with condensers 263

541] Crown and H with slits compared with white cylinder; also on the exci-
tation of electricity by separating a brass plate from a glass one.

Wed. Feb. 17 [1773]. Th. 55. N. 21. [6 observations, Art. 660.]
Fr. Feb. 19 [1773]. Th. 53^. N. i8J.

A plate of glass nj inches square, coated with tinfoil 8 inc. in diameter,
was supported on waxed glass. A brass plate 8 inc. in diameter was supported
over it by silk strings in such manner as to lye on the plate perpendicularly
over the tinfoil, and to be drawn up till it touched a piece of wire supported
on waxed glass with the middle sized cork balls suspended from it. This was
done in order to see how much of the charge of the plate was contained in the
coating.

It was found that though the plate was not electrified, yet on lifting up the
brass plate the balls separated some inches if the tinfoil communicated with
the ground, but if it did not communicate, the balls, as well as I remember,
separated considerably less. Some bits of thin silk thread were placed between
the glass and brass plate.

In the afternoon. Th. 54. N. 17^.

The experiment repeated with bits of card between the glass plate and
brass.

. , .. fcommun. ) . , fi .

When tinfoil { ,., > with ground, balls sep. about {, inch,

(.did not commun.J (.f

When there was nothing between the glass and brass plate, they sep. 1-4 inc.
whether the tinfoil communicated with the ground or not.

In all these cases the brass plate was negative.

The glass plate was found to be pos. if the tinfoil did not communicate with
the ground, but I could not perceive it to be at all electrified if it did com-
municate.

The next morning the experiment was repeated, but the balls separated
much less than before. The temper, of the air was much the same.

542] It was tried whether when three tin plates i foot square were placed
near to and parallel to each other, the line joining their centers being perpendi-
cular to their planes, the middle plate would receive much electricity on electri-
fying the plates*.

The experiment was tried with the same apparatus and nearly in the same
manner as the experiment with the globe f, except that the two outer plates
were suspended by two sticks of waxed glass turning on hinges. The wire too
by which the plates were electrified was made so as to touch all three plates
at the same time. Four bits of sealing wax were stuck to the middle plate,
two on each side, to prevent the outer plates coming too near.

* [Exp. vin, Art. 288 and Note 23.] t [Art. 218.]

264 "Journal of Experiments, 21 Feb. 1773

Sun. Feb. 21. Th. supposed about 55. N. 2oJ.

If the bits of sealing wax were of such size that the distances of the outer
plates were about j , the middle sized cork balls separated about j | .

The light paper electrometer was used in this experiment. If the globe 2
was electrified in the same degree, and its electricity communicated to

and the middle tin plate electrified by one of these jars (the
(i, 2 & 4 ]ars

two outer being drawn aside) and the cork balls then drawn up against the

plate, they separated about 1 1 .

<.s

Ist (8

In the nd case the electricity of the globe was diminished < , [times], and

therefore when the outside plates were at j , the quantity of electricity in

the middle plate was about < * of what it would have received by the same

IT
degree of electrification if placed by itself.

543] Charge of A, B, and C laid on each other without any coatings between;
also charge of I8t thermometer tube.

The coatings were taken from the 3 plates A, B and C of Nairne, and the
plates cleaned and placed one on the other without anything between them,
and stuck together by dropping some melted wax on the edges. The outside
surfaces were then coated with circles 6-6 inc. diam. This is called Triple Plate*.

A thermometer tube was coated with coatings n inch long, the inside being
filled with $, with wire let into one end, and the ends stopped with cement.
The tube was 12-7 inc. long; weighed i .. 3 .. o, and the bore held 22.gra. of
water, the specific gravity of a piece of the same tube weighed twice over was

II-

N.B. The comp. pow. of this tube is about goj.

This is called Tube i f.

Mon. Feb. 22 [1773]. Th. 53 J. N. 20 J. [8 observations. Art. 675.]

544] Lane's electrometer compared with straw and paper electrometers; also
charge of plate rosin with brass coating made to prevent spreading of electricity.

Lane's elect. Revolutions] Divisions]
Light paper just sep. when [Lane's] el. at i 13

Straw at i + 3 o 54

3+i i 36

Knobs touched at o 7!

* [Art. 380.] t [Art. 382.]

Comparisons of electrometers 265
A plate of rosin and bees wax of the same proportions as for exper. rosin
A c

was cast of the shape of figure, ABDC and abed being brass plates 2-45 in.
diam. their distance before the rosin was poured in being about -12 inc.

Tu. Feb. 23 [1773] in afternoon, the rosin plate being cast that morning,
the hygrom. as well as I remember being about 22.
[4 observations, comparison with E.]
Wed. Feb. 24 [1773]. Th. 54. N. 20. [4 observations.]
Spreading of electricity on surface.
Rosin closed in about 7", sep. again in 35.
E was irregular.

545] Second thermometer tube; also comparison of charge of cylinder used in
[Art. 539] with D + E.

A thermometer tube whose length was 22-1 inc., weight = 2, 17, 21 and
weight water which filled bore 14 gra. was coated with tinfoil 15-5 long, conseq.
comp. power = * the spec. gra. of a part of the same tube being 3-243.

Fr. Feb. 26 [1773]. Th. 52. N. 20 £.

The cyl. used in [Art. 539] compared with the plates D and E, the wire Mm
of machine being drawn out to 39^ inches, and resting on the cylinder as in
that experiment. A sliding trial plate on neg. side.

[6 observations. See Art. 666.]

546] Charge of second thermometer tube; also that of rosin plate with brass
coating; also that of A, B, and C laid on each other without coatings between. [10
observations. Art. 675.]

The same things were tried the day before, Th. 55, N. 17^, but the wire for
making communication between machine and ground was forgot to be fixed.
[14 observations. See Art. 666.]

547] f The quantity of electricity in plate D compared with that in a tin circle
of 36 and another 0/30 inches diameter by means of the machine used for comparing
simple plates J, the trial plate being a tin cylinder inches long, and § in
circumference, fastened to the end of the usual sliding trial plates, with another
cylinder of the same size sliding within it.

T«ried with elect, of usual strength and with the middle sized corks.
Also the double plate A compared with the circle of i8J inc.

* [So in MS.] • t [Arts. 356, 664.]

t [Art. 240.] § [So in MS.]

266 "Journal of Experiments, March, 1773

Wed. March 3 [1773]. Th. 56. N. 21. [16 observations.]

548] Charge of plate of experimental rosin designed for compound plate of
glass and rosin; tried both when warm and when cold *.

A plate of experimental rosin near 8 inches square was pressed out between
two glass plates with tinfoil coatings fastened on by oil, the heat being such
that it required very little weight to press out the5 rosin.

The thickness of the plate was much less toward one end than the other,
varying in different parts of the coated plate from -137 to -108, but the mean
thickness was -122.

It was coated with circles of tinfoil 6-61 in. diameter.

Its charge was compared with that of the plates K, D and E of Nairne by
means of a sliding trial plate made of the plate f of Nairne.

Sat. March 6 [1773]. Th. 55$. N. 17.

Tr. si. pi.

K + D + E

ros. plate

In the afternoon. Th. 57^. N. 16
ros. plate

K4- D+ E

24
19

25
19

sep. neg.
D° pos.

D° neg.

sep. pos.
D° neg.
D".

The rosin plate was then warmed before the fire between two glass plates
with flannel between them and the rosin till it would not support its own
weight without bending. As soon as it was strong enough to bear its own
weight it was compared as before.

rosin plate

sep. pos.
did not sep.
In about 2 or 3 hours after, when it was quite cold, it was tried again :

2o£
26

rosin 25 sep. pos.

19 D° pos.

i8J DO.
24^ D° neg.
549] Whether charge of glass plate is the same when warm as when cold.

The same afternoon the charge of a glass plate when hot and cold was
compared together in the same manner.

The glass was nj inches square, used for jEpinus experiment {, coated on
one side with a circle of 8 inc. diameter, and a brass plate of same diameter
used for the other coating.

The glass and brass plate were both heated before the fire till almost as hot
as I could bear my hand on, and then tried by the help of the 6th sliding plate,

* [Arts. 381, 678.] t [So in MS.] } [Arts. 134, 341, 517.]

Measures with various dielectrics 267

when the breadth of the sliding plate was required to be 37 in order that it
should sep. pos.

After the plate was cold it was tried again, the breadth of the sliding plate
was obliged to be 36.

Hence it would seem as if the charge both of glass and of rosin plate was
the same when hot as when cold, the small difference between them being most
likely owing to the electricity spreading more on the surface of the warm plate
than of the cold one.

550] Crown with slit coat-ings and H with oblong compared with white cylinder;
also second thermometer tube with D + E + F.

The slit coatings were taken from H and plain coatings, 6-03 square, put in
their room.

Sun. March 7 [1773]. Th. 56. N. 15.

Straw elect, at 2 + 3, which is equivalent to light paper electrometer [4 obs.].
Elect, at 3 + i [6 obs.]. Elect, at i + 3 [7 obs. Art. 660].

Mon. Mar 8 [1773]. Th. 54. N. 14^. [4 obs.].

551] Quantity of electricity in plate D and rosin with brass coatings compared
with that of tin circle of 36" and one of 30" by machine for trying simple plates*;
with different degrees of electrification].

Tu. Mar. 9 [1773]. Th. 51. N. 15.

The exper. of p. 78 [Art. 547] repeated, only using square tin plates of different
sizes made to fasten on to sliding cylinder instead of the sliding trial plates.
The tin circles and the square plates both supported on silk.
Straw el. at inner marks N° 2.

Square

Inc. cyl.

plate

drawn out

circ. 36"

5

24

sep. a little neg.

—

3

II

DO pos.

E

i

26

DO.

5

9

D° neg.

rosin

3

X7

D°.

i

4

D° pOS.

circ. 30"

i

20

D° pOS.

3

28

D° neg.

Electrometer] at outer

marks.

circ. 30

3

20

DO.

i

29

D° pOS.

circ. 36

4

34

D° neg.

2

28

D° pos.

E

4

21

D° neg.

2

24

D°.

* [Art. 240.] f [Art. 664.]

268 journal of Experiments, March ', 1773

The electricity was found to break through the rosin plate when electrified
with this strength, but there was no hole made in the plate, as it was found not
to break through after that with the weak degree of electrification. It seemed
not to pass over the surface, as no light was perceived.

552] Charge of compound plate of glass and rosin.

The rosin plate of p. 79 [Art. 548] without its coatings was included between
the plates B and H of Nairne and the outside surfaces coated with circles
6-6 inc. diam. and is called Compound Plate.

Th. Mar. n [1773]. Th. 53. N. 17. [4 comparisons with K.]

Fr. Mar. 12 [1773]. Th. 53^. N. 13$. [20 observations, Art. 664.]

553] Circle of i8£" compared with double plates, also plate D, plate air and
the two double plates compared with circles of 36" and 30".

A sliding trial plate was made of deal, with an additional piece to fit on,
the breadth was 31 inches, the length when not drawn out, and without the
additional piece, was 15, and the additional piece increased the length rof inches.

The number in the 2nd column shews the number of inches by which the
sliding piece is drawn out.

March 3

Inc. el. Difi.

Mean

Circle 30
on silk

I*

30

27'3_ .8
34'3

26-5
7-0

33'5

30-0

D° on glass

14-7

4
36

27-0
35-6 +I'°

28-9
36-6 7 7

327

D° on silk

n-3

5*

36

24-6

+ 1-7
32-9

*4 »>

30-4

E

157

i*

38

T3 + 1-9

36-1

T 8'8

33-6

Circle 30"

•11 I8-7
on silk

8

33'9 °

33-9

Tu. Mar. 9. [Electrometer] At inner marks. At outer marks.

Difif. Mean Diff. Mean

Circle 36" n-6 35-6 5-8 36-3

E 12-2 32-5 6-9 33-2

Circle 30" 11-4 30-4 7 30-8

March 12. [14 observations.]

Sat. Mar. 13. Th. 55. N. 12. [12 observations. See Art. 649.]

Mon. Mar. 15. Th. 54. N. 14. [15 observations. See Arts. 649, 655.]

554] The same with addit. four small rosin plates.

Four plates of rosin and bees wax were cast 4 inches square and about
•22 thick and coated with circles 1-8 in. diam. A tin trial plate was also made
6 inches long and 5 broad. It is called N. The plates of rosin were connected
by bits of brass wire like that used for connecting the two double plates.

Compound dielectrics 269

Fr. Mar. 19. [20 obs. Arts. 649, 651.]
Tu. Mar. 23. [21 obs. Art. 649.]
Wed. Mar. 24. [22 obs. Art. 649.]

555] Sun. Mar. 2iat [1773]. Th. about 55. N. about 15.

It was tried whether the 4 rosin plates contained the same quantity of
electricity whether they were placed close together or at a distance, and what
is to be allowed for the connecting wires, &c.

This was tried with the usual machine*, the rosin plates being placed on
the positive side and sliding plate 3 on the negative side, the sliding plate re-
maining always at the same division, the small variations of the charge being
found by the additional wire.

They were tried in 5 different ways.

Ist way. The plates placed close together near the end m, the usual wires V
resting on the plates, with the connecting wires put on the plates.

2nd way. D° without the connecting wires.

3rd way. The connecting wires suffered to remain, and also one of the
wires V, but the 3 others removed towards end M , placed at 4 inches distance
from each other, and supported in their usual situation by silk strings.

4th way. The same, except that the 3 wires V were taken quite away.

5th way. The rosin plates placed at as great a distance from each other as
possible id est f inches with the usual wires V, but without the connecting
wires.

3rd way, with connect,
wires, usual ones re-
moved to end

4th way, without usual
wires

Ist way, with connect-
ing wires and usual
also

2ni1 way, without con-
necting wire

5th way, removed to
distance

556] Whether charge of white glass thermometer tube is the same when hot as
when cold\.

Sun. Mar. 21 [1773] afternoon. Th. about 55. N. about 15.
A ball about I inch in diameter was blown at the end of a thermometer
tube with a bulb 4-3 inches above. This was filled with § sufficient to rise into

* [Art. 295. See Art. 337.] f [So in MS.] J [See Art. 366 and Note 26.]

Inc. el.
on addit.
wire

Sliding
plate

Inc. el.
on addit.
wire

Sliding
plate

ect.
re-

t °

3---I4

sep. pos.

I

3...I2f

D° neg.

;ual

} a*

DO

2

DO

sct-
ual

| i

DO

2

DO

on-

2

DO

2i

DO

to

1 X|

DO

4

DO

270 Journal of Experiments, March, 1773

the bulb. The tube was coated 3-4 inches from the ball with gummed paper
dipped in salt water and bound on with iron wire. This ball was placed in a
glass of $ surrounded with iron filings and placed on machine near M, and
heated by a spirit lamp, the $ in which the ball was immersed being made to
communicate with the ground, and a bit of iron wire bound round the wire Mm
being dipped into the $ in bulb.

The crown glass plate * and the plate A of Nairne, which was coated
as a sliding plate, being put on negative side.

The Ist column being the number of square inches which it was necessary
to give to the coating of the sliding plate in order that the balls might sep.
pos. and the 2nrt column that they might sep. neg. The charge of the crown
glass plate being equal to that of the sliding plate when its coated surface is
33 square inches.

Sep. pos.

Sep. neg.

Heat of 5 in which ball was immersed

12-9

15
21
26-6
29-4

3i-8
29-4
19-6
17-2
14-8
12-9

29-4
33

cold
170
210
27O

300 elect, passed through glass pretty fast.
305 passed through much faster.
290

235
160

145
cold

33
30-6

Tu. Mar. 23 and Wed. Mar. 24. [43 obs. Art. 649.]

557] Allowance for connecting wires in p. 86. [Art. 554.]

The allowance to be made for the charge of the connecting wires was en-
deavoured to be found by suspending the two circles of 9-3 inc. horizontally
by silk lines at n inches distance from each other and finding their charge by
means of the forked electrifying wire as in 1772 p. 7 [Art. 472], both when the
plates were connected by a wire similar to that used for connecting the rosin
plates, and without any connection.

The event was as follows.

Fr. Mar. 26th [1773. 8 obs. See Art. 647.]

2i
Therefore the plates contain about J square inc., or 1-41 inc. el. more with

the connecting wire than withoutf-

Sat. Mar. 27 [1773].

It was tried by usual machine whether the 4 rosin plates contained more
el. when at a distance than near. The trial plate B id est the largest trial plate
used for D &a being placed on neg. side.

* [So in MS.] f [See Art. 647.]

Tests 'with various electrometers

271

With a quantity of additional wire = to gj inc. el. the balls sep. pos. when
the plates were at as great a distance as possible. When they were placed close
together they seemed to require rather more
additional wire, and as well as I could judge,
a quantity = about | inc. el.

558] Excitation of electricity by separating
brass plate from glass one.

Sat. afternoon. Th. 60. N. 9.

The experiment of p. 71 [Art. 541] was
repeated. It was found that the brass plate
was electrified on lifting up as before, though
the plate was not electrified before. But if the
plate was first charged and discharged again
before the plate was lifted up, it was found to
be stronger electrified.

I then took a piece of tinfoil of the same
size as the brass plate, with a silk string fast-
ened to it near the edge, and laid it on the glass
and lifted it up gently by the silk string. The
tinfoil was found to be electrified thereby.

559] Comparison of Henly's, Lane's, and
straw electrometer.

Th. about 58. N.

Sun. Mar. 28 [1773].
about 8.

The two conductors of Nairne were placed
end to end, and Henly's electrometer placed
on that furthest from globe* parallel to con-
ductor and the cork pointing from globe. The
four jars were also joined to the usual wire with
the straw electrometer hung to it, the wire and
jars being placed at such a distance from the
conductors that the electricity was found not
to flow sensibly from them to the jars.

The globe 3 f was then applied to that con-
ductor nearest the globe and electrified till
Henly's electrometer stood at 90°. The globe 3
was then removed from the conductors and its
electricity communicated to the jars{.

The straw electrometer separated to 2 + J.

* [Of Nairne's electrical machine.]

f [Globes 2 and 3 are glass globes coated as Leyden jars. See Art. 505 for their
charges.]

J [For the charges of these jars see Art. 506.]

[Henly's Electrometer, from
the original figure, Phil. Trans.
2. P- 359-]

272 "Journal of Experiments, March, 1773

The experiment was repeated several times and was found to agree together
pretty well.

The jars were then electrified, they and the straw electrometer standing in
the same place, and it was found that Lane's electrometer fastened to one of
them discharged at 0-53^ with that degree of electrification, the same jar being
applied to the conductor and electrified till Henly's electrometer stood at 90°,
Lane's discharged at 12-15.

The conductors being then taken away and the jars and straw electrometer
placed in usual position, Lane's discharged at 1-17 when straw stood at 2 + 3,
and at I + 2 when light paper electrometer just separated. The knobs touched
at 0-4.

Sun. eve. Th. 58. N. 8.

The globe 3 electrified till Henly stood at 90°, and its electricity com-
municated to i, 2, and 3 jars, straw electrometer separated to 2 + if. Lane's
with that degree of electrification discharged at 1-7.

When Henly's stood at 90°, Lane's discharged at 12 -20.

Jar 2 charged till straw electrometer separated to 4, and electricity com-
municated to jar i, straw separated to 2 + \.

When straw electrometer separated to 4 Lane's discharged at 2-0

2 + i -52

2 + 3 1-19

light paper just separated i-i

560] Excess of redundant fluid on positive side above deficient fluid on negative
side in glass plate and plate air &c. *

Mon. Mar. 29'" [1773]. Th. 58. N. 7.

The ii J inch plate coated with circles of 8 inches diameter was supported
on waxed glass. I charged this by touching the top with a vial charged till
the straw electrometer separated to 2 + 3 while I touched the bottom with a
wire. At the same time an assistant stood ready with a bent wire in his hand
ready to discharge it as soon as I took the jar away, the wire was fastened to
a stick of waxed glass and had the pair of cork balls commonly made use of
hanging to it, the cork balls separated about i inch.

I then charged the jar 4 to the same degree and communicated its electricity
to the jars i & 2 and touched the upper side of the plate with one of the jars,
but without touching the bottom with the wire. The corks separated very
nearly the same as before, but of the 2 rather more. I then charged the jar till
the straw electrometer separated to 2 + 2 and diminished its electricity as
before, the corks now separated rather less than the first time. The experiment
was repeated several times with very nearly the same event.

I could perceive no difference in the separation of the cork balls whether
the wire of the jar with which I touched the plate was 17 inches long or only 2f .

* [See Note 30.]

Difference of charges on parallel disks 273

If the four jars were charged to 2 + 3 and its electricity communicated to
globe 3, it was diminished to 2 4- 2.

The plate air 4 was charged by jar charged till straw electrometer stood at
2 + o, and if jar 4 was charged to the same degree and its electricity communi-
cated to jar 2, the corks separated the same if bottom was not touched.

With plate air i the charge was obliged to be reduced by communicating
jar 2 to jar 4 to make the same separation when bottom was not touched as
when it was.

Tu. Mar. 30 [1773]. Th. 56. N. 8.

The same experiment was repeated, only putting a piece of sealing wax with
marks on it supported by glass about 2 inches below the corks to serve by way
of comparison.

Compound plate
of [Art. 552]
Plate air i
Plate air 4

2+1
2+i
2+1

Jar i commun.
to 2 + 4
jar i to 2
i to 2

2 4. TJ
* ~ A 2

2+1
2

The second column is the distance to which the straw electrometer separated
in charging jar with [which] the plate was electrified when the bottom was
touched in order that the cork balls should separate equal to marks on wax.
The third column is the ratio in which the electricity of the jar was diminished
when the bottom was not touched, and the fourth column shews the degree in
which the jar was electrified (as expressed by distance to which the electro-
meter separated) in order that ..he balls should separate to the required distance.

N.B. The paper of divisions used for the electrometer was different from
that used before, but the divisions nearly of same strength. The marks on
sealing wax used for compound plate were nearer than those for plate air.

The jars i, 3 & 4 being charged till straws separated to 3 + o and the elec-
tricity communicated to jar 2, they separated to 2 + i, and the electricity of
jar 2 being destroyed and the electricity of the others again communicated to
it, they separated to i + 3*.

Therefore diminishing the electricity in ratio of 95 to 126 diminishes distance
to which the balls separate in ratio of 126 to 165, or diminishing the electricity
in ratio 1-33 to i diminishes distance in ratio 1-31 to i.

Result.

On Monday the excess of redundant fluid on the positive side above de-
ficient fluid on negative side in

ii £ inch plate with 8 inch coating \

•3 J

Plate air i L is

Plate air 4

1-88
i

/ 2-14

* The smaller divisions are equal to ^ of large ones.
C.P.I. 1 8

274 "Journal of Experiments, April, 1773

of the quantity of electricity which is given to it with the same degree of
electrification if the bottom plate is not touched.

Compound plate
On Tuesday D° excess in Plate air i

I'OO

Plate air 4

2-16

561] Fr. Apr. 2 [1773]. Th. about 55. N. about 10.

It was tried whether a parallelepiped box included within another box of
the same shape and communicating with it would receive any electricity on
electrifying the outer box*.

The experiment was tried just in the same manner as that with the globe
in p. 26 [Art. 513]. The inner box was 12 inches square and 2 thick. The outer
box was 14 inches square and 4 thick on the outside, and 13 square and 3-4
thick within.

The boxes were made of wainscot and well salted. I could not perceive that
the inner box was at all over or undercharged, for if I previously electrified the
cork balls positively sufficiently to make them separate in touching the inner
box, they would separate as much if I previously electrified them negatively
in the same degree.

Globe within hollow globe tried again f .
562] Sun. Apr. 4 [1773]. Th. 58. N. n.

The globe included between the 2 hemispheres was tried again in the same
manner, except that the hemispheres were coated with tinfoil and were made
to shut closer.

I could not perceive the inner globe to be at all electrified either way.

In order to see how small a degree of electricity I could perceive this way,
I separated the two hemispheres as far as in the experiment, and electrified
the 2na thermometer tube with the same strength of electricity as was used in
the experiment, and communicated its electricity to the jars i and 2, then
touched the inner globe with one of those jars and drew up the cork balls,
previously positively electrified, against the globe. I found them to separate
very visibly.

I then repeated the experiment in the same manner except that the balls
were negatively electrified in the same degree.

The elect, of the thermometer tube was diminished by communicating to
the 2 jars in the ratio of 105 to 6339 J, or of r to 60, so that if the redundant
fluid in the globe had been so much as ^ of that in the hemispheres, I must
have perceived it.

* [Exp. n, Art. 235.] t [ExP- I- Art. 218.]

J [Charge of 2n<l thermometer tube = 80-7 glob. inc. = 124-3 ciic. inc., by
Art. 675, jar i + jar 2 = 6234, by Art. 506.]

Test of law of inverse squares 275

As it might be suspected that in the principal experiment the neighbourhood
of the hemispheres communicating with [the] ground would enable the globe
to hold more than it would otherwise do, and that therefore the cork balls
would not separate so much as they would do if the hemispheres were taken
away and the quantity of redundant fluid in the globe was the same, and
consequently that the above computation of the quantity I could perceive is
not just, I took away the hemispheres, made the corks touch the globe, and
electrified it till they separated, then holding the hemispheres in my hands as
near the globe as in the experiment, I did not perceive any alteration in the
separation of the corks.

The outside diameter of the hemispheres was 13-3 inches.

563] Experiment to see whether the force with which two bodies repel is as the
square of the redundant fluid in them*: tried with straw electrometer and glass globes.

The two electrometers were hung at opposite ends of a horizontal stick of
wood 43 inches long, supported on sticks of waxed glass and communicating
near the middle with one of the globes f. The same string also which lifted up
the electrifying wire let down a piece of wood for making a communication
between the two globes. The board with divisions was placed 6 inches behind
the electrometers, and the guide for the eye 30 inches before it.

The electricity of the globes wasted very slowly, so that it could not be
sensibly diminished in the time between reading off divisions to heavy electro-
meter and those to light one.

The electrifying wire rested on horizontal wood while globe f was turned,
two jars being used as a magazine to prevent the globe Leyden vial from charging
too fast. The globe J was turned till the heavy electrometer separated to rather
more than the intended division, after which I waited till it came right, when
by the string I lifted up the electrifying wire and made the communication
between the two globes and looked at the division of light electrometer. The
electricity of the magazine was discharged as soon as the electrifying wire was
lifted up.

564] One of the straws used for the heavy electrometer was black in some
places, and is called "blighted," the other is called "fair."

Sun. Jan. 24 [1773].

Blighted straw
Fair straw

Weight

Length

Cent. gr.
from
needle

Wire
length

Added
weight

Weight with
addit. tried
immed.
after

6

II-I
II-I

5'I
4-99

2-2
1-8

10-7

8-8

I7-8
14-8

* [See Art. 386.]

t [The coated globes 2 and 3. Their charges are given in Art. 505 as 1782 and
1555 circ. inc., or 1159 and 1009 glob, inc., the sum of which, 2168, agrees with
Art. 391.]

J [Of Nairne's electrical machine.]

1 8— 2

276 Journal of Experiments, January, 1773

The additional wire was ran into straw very easily, and was fastened by
putting a little wax on the end, which by heat was pressed quite smooth against
the end of the straw.

Mon. morn. Jan. 25. Th. 55. N. 2oJ.

The globe 3 was made to communicate with horizontal wood, then if heavy

f 8
electrometer separated to J 9 divisions, the light electrometer separated, on

1 10
communicating electricity to globe 2, to the same number of divisions.

565] Trials of time in. which the electricity of jar t was diminished by these
straws, from degree in which the heavy electrometer used in former experiments of
this kind to that in which the pith balls began to close.

Weight

Light electrometer

2

fair

35

27

7-8
6-8

14-8

15 17-8

Heavy electrometer blighted

In the afternoon the blighted straw was by mistake for the other covered
for an hour with paper soaked in salt water. After standing about an hour to
dry, it was found that when heavy electrometer was made to separate 10
divisions, light separated nj.

The , . straw discharged the electricity as before in •* , weight of

blighted straw 17-8.

The fair straw was then kept in salted paper in the same manner for about
3 hours.

Tu. morning. Th. 57. N. 23.

If heavy electrometer separates to 15, 10, 9, 8, light electrometer separates
about J less.

Fair straw discharged the electricity almost immediately, blighted in
about 5".

When fair straw rested on cork ball it was about 30", the. blighted was much
longer.

Weight of fair straw 14-95.

Ball of fair straw moistened with salt water.

Heavy electrometer at , light at

10 ' 10

The blighted straw was kept in salted paper for i£ hours, and then set to
dry till the afternoon. In the afternoon its ball was moistened with salt water.

When heavy el. at < • , light at |

lio' (9 +

Conductance of straw electrometers 277

Fair ) 2"

Rl' ht H ( straw c'osed in about „ when resting on straw, and about 5"

or 7" when resting on cork ball.

In about ij hours after they were tried again without any alteration having
been made.

When heavy at { ^ , light at

, > closed •! f on straw { on ball,
blighted] (2j (.10

The light straw N° i was soaked in salt paper at night for 3^ hours.

Wed. Jan. 27. Th. 57. N. 23.

When heavy sep. to 15, light at 14, but increased after a time to near 15.
As it was suspected that this increase might be owing to the air being electrified,
I tried and found the air to be much electrified in all parts of the room.

( straw , 2" or 3" .

N° i resting on < , „ closed in

(ball 90

straw 20"

N° 2 on , .. closed in ,

ball very slow.

The ball of N° i was then moistened with salt water.

Heavy sep. to 15, light to 13, but increased to near 14.

In order to avoid in some measure the inconvenience from electrifying the
air, Richard turned the globe, by which means the electricity was not made so
strong.

heavy to , light to

10 10

N° i closed in about 4" whether resting on ball or straw.

N° 2 was soaked in salt water for 2\ hours till 3 in afternoon, about 5 or 6
it was tried.

heavy to , light to , Ist time, for several times after to 14.
10

On straw

On ball

N° 2

4"

4

I

3 or 4

3 or 4

fair

2 or 3

8

blighted

2 or 3

9

Wed. Feb. 3. Th. 46^ N. 12.

As it was found the preceding day that the straws conducted ill, they were
kept about 3 or 4 hours in the morning in salted paper, at about 3 they were
taken out of the paper and hung up to dry. In the afternoon they were tried,
a screen being placed to keep them from the fire.

278

Journal of Experiments , February, 1773

Globe 3 elect.

Globe 2 elect.

Heavy Light

Heavy

Light

15

i6J

15

17!

15

16

15

J7i

12

12

15

Z7i

12

I2i

12

I4j

10

loi

12

13^

10

io|

12

13

8

8J

10

iii

8

8

IO

"I

8

8J

8

9l

8

cS

9i

10

3

IO

nj

10

10

10

nj

10

10

12

14

12

13

12

I3j

12

12

15

17^

12

12

15

J7i

15

16

15

X5l

15

15^

The blighted heavy straw

closed in

fair

On straw

25"
10

On ball

I . 30"
not near closed in 2'

Weight with
addition

Without

Distance of
pin from
cent. grav.

Fair
Blighted

14-85
17-85

6-05
7-05

5-07
5-155

566] After the additional wire had been taken from the heavy electrometer,
the two electrometers were electrified and compared together without the
process of communicating the electricity from one globe to the other, when
they stood as follows.

Heavy straw electrometer
without additions

17
15
13
12

If globe 2 was electrified till D° electrometer separated to 17, on com-
municating electricity to globe 3 it separated to gj.

The light straw electrometer was then placed instead of the paper electro-
meter, and a paper with divisions placed behind it. It was found that when

Heavy

Light

8

9

Heavy paper

•2

TTT

10

iof

electrometer

very little

12
15

ia|
15}

Light do.

TTJ

very little

12

12}

IO

IOJ

8

84

Sensitiveness of electrometers

279

heavy straw electrometer separated to ', divisions, the light straw electrometer

separated to

Small
divisions

Large
divisions

567] As the straws seemed not to conduct well enough, they were gilt.
The gilding was not perfect in several places, but it was sufficient to conduct
the shock of a jar very weakly electrified.

Added
weight

12

Weight

Cent. grav.
from pin

Wire
length

N. r

7'55

5-25

2'45

N. 2

6-55

5-17

2-OI

CN
Heavy electrometer < '

Tu. Apr. 13.

The globe 2 electrified and communicated to globe 3.

IO-I

Heavy el.

13
12
IO

8

Light

154

14

12

104

8
ro

12
13

Globe 3 communicated to 2
8

Wed. Apr. 14. Th. 51. N. 13.

Globe 2 communicated to 3

94
n|

14
154

It was found that some electricity ran from the electrifying wire to the
knob of the globe to which electricity was to be communicated, on which the
knob was removed to such a distance that no sensible electricity ran from
one to the other.

10
12
13

104
13

14

Globe 3 communicated to 2

13
12

10 iqj

8 8|

Globe 2 communicated to 3

13

12

14

N.B. The holes where the wires were put in were gilt over.

N. 2

N

' > of heavy electrometer were found to weigh

16-65
19-65 '

The wires were then taken out, the holes stopped up with wax and gilt
over. It was then found on electrifying the globe without communicating its
electricity to the other, that when the heavy electrometer stood at

8 9

™ the light stood at "f
13 14!

280

"Journal of Experiments, April, 1773

N. i
N. 2

Weight

7-6
6-65

Cent. grav.
from pin

5-36
5-285

35'i
136-1

N. I N. 2

Force requisite to separate straws without wires 40-8

with wires 159^9

Therefore force required to separate heavy electrometer falls short of four
times force required to separate light electrometer in the ratio of 296 to 303-6,
or of I to 1-027.

568] Separation of Henry's electrometer by different strengths of electrification.

Nairne's jar being tried against the two trial plates for plate H, the pith
balls separated a little after a short time the same way as the two trial plates.
Therefore Nairne's jar is supposed to contain about ±£ of plate H, or 16 times
as much as plate M.

The two conductors of Nairne were set end to end with [Henly's] electro-
meter on furthest, and the jar applied to the same, the furthest conductor
being without any point, and the plate M was placed near it, set on a conductor
communicating with the ground. When the electrometer was raised a little
above 90°, the nearest conductor was removed and the electricity of globe
taken away. Then as soon as the electrometer was sunk to 90° a communication
was made between conductor and plate M and immediately taken away again,
and the figure to which the electrometer sunk wrote down and the electricity
of plate M discharged, after which a communication was again made between
the conductor and plate M.

The results of the experiments are contained in the following Table, where
the first^column is the number of times that a communication has been made
between the conductor and M.

Number
of times

Elect,
in jar

ISt

Mum

2

oers on e
3

lectron
4

leter
5

6

Difi.

Supposed tn

Elect. Number
in jar on elcctr.

1C

Diff.

2nd difl
by first

I
2
3

4
5

•938

•879
•824

•773
•725

70
32

20
16

M

73
36
21

16
14

73
44
23
17
15

79

63
31
19

16

77
58

35
18
14!

80
63

3°
i8J

151

063
59
55

8

I-OOO

•938
•879
•824

•773

90
80

63
32
18-5

IO
!7

31
.13-5

3

160
290

564
262
62

6

•679
•637
•597

12
IO

9

12
II
10

13

12

ioi

H

12
II

13
ITi

10 J

I2i
nf

IOJ

T1

46
42

•725
•679

•637

J5'5
13
n-5

*)

2'5

i'5

T

55
35

9

•560

8

9

10

IO

IO

9i

4°

•597

10-5

£

2(>

10

•525

1\

8

§1

37

1 C

•560

9'5

J

II

•492

7

7\

8

J.T

•525

8-5

12

•461

6

<>.'.

7

33

•492

8

"5

T

13

M

•433
•406

5i

5

6
5l

61

5i>

31
28

•j -7

•461
•433

7
0-5

•5
j

25

15

•380

5

27

•406

5'5

16

•357

44

I7>

•334

4

18

•313

4

19

•294

3*

20

•276

3

Calibration of Hen ly electrometer

281

The second column shows the quantity of electricity in the jar, which must
diminish each time in the ratio of 15 to 16, and the other column is the number
which the electrometer stood at in the different experiments.

The above experiment is supposed to have been made in the autumn of 1772.

569] Separation of Henly's electrometer when fixed in the usual way and on
an upright rod.

Aug. 13, 1773. Th. about 78.

Henly's electrometer was stuck on a thin wooden rod 25 inches long, the
end of which was fixed into the hole made in the conductor for receiving the
electrometer, being parallel to the conductor as usual. The conductor to which
this was fixed was connected to the other conductor which received the elec-
tricity from, the machine by a brass wire about 10 inches long, and a jar with
Lane's electrometer fastened to it was made to communicate with this last
conductor, so that the rod to which the electrometer was fastened was about
* inches from the globe and * inches from the jar.

Henly's electrometer was then compared with Lane's while in this situation,
and when this was done the wooden rod was taken away and Henly's placed
on the conductor in the usual manner, everything else being the same as before,
and compared with Lane's as before.

N.B. In both trials the cork ball of Henly's was turned from the globe f.

The result was as follows: —

Hence it appears that when
Henly's [electrometer] is fixed on
the rod it is more sensible towards
the beginning of its motion than
afterwards, whereas when put in
the usual way it is the contrary.

570] Result of P. 70, 75, & 95 [Arts. 540, 544, 559], being a comparison of
the different electrometers.

Lane

Henly

Rev. div.

On rod

Usual way

4-30
6-30
8-30

21

37
38

5
10

18

10-30

40

32

Straw electrometer at

P. 70

Th. 5(4

N. ly

P. 75 P. 94
Th. 53i Th. 58

N. 2oJ N. 8

P. 95
Th. 58

N. 8

i + 3

43

4Ci

2+ i

48

2+ |

5«

2 + ij

Co

2+ if

63

2 + 2|

70

2 + 3~

75

73

75

3+ i

80

3+ i

824

88£

4

nC

Light paper elect, just sep.

Co

64^

58

Henly's at 90°

73 1

736

[bo in MS.]

[Of the electrical machine.]

282

"Journal of Experiments, Aug. 13, 1773

The three last columns are the distances at which Lane's electrometer dis-
charged, expressed in divisions, or 6oth parts of a revolution of the screw.

By p' ^ [Art. 551] the distance at which Lane's discharges is as the j

power of the quantity of electricity in the jar, and the quantity of electricity
when the straw electrometer is at 2 + 3, id est the usual charge is to that when

Henly's is at 90° as i to | ,_ j* .

571] Comparison of Lane's electrometer with light straw electrometer in different
weather.

Lane's electrometer was compared with the light straw electrometer by
the apparatus represented above. A being the globe, B a conductor, CD a wooden
rod supported on two waxed glass pillars, having a pin at D almost in contact
with the conductor, the straw electrometer being hung to C. £ is a jar with
Lane's electrometer fastened to it, supported on a bracket fixed to glass pillars,
the wire of which touches CD.

The distance of C from the globe is 54^ inches and from the nearest glass
pillar 32 inches. The height of the pith balls above the floor is 36} inches.

A small board with divisions on it, not represented in the figure, supported
on an upright wooden rod, is placed behind the straw electrometer 25 inches
from it, and a bit of tin with a narrow notch in it for an eye sight is placed at
the same distance before the electrometer.

The outward divisions on the board, or those called the 4th, are at 5 inches
asunder, the 3r" at 4 inches, the 2nd at 3 inches, and the Ist at 2.

As I found it impracticable looking attentively at both balls of the electro-
meter, I looked only at one, which, as my eye was guided by a narrow slit, was
sufficient, and when I had made the experiment looking at one ball I repeated
it looking at the other, so that the mean would be right though the slit was not
right placed.

A wire was continued from the coating of the jar to the earth.

Shock related to character of the discharge 283

Wed. Aug. 18, 1773.

Th. 63°. N. 19. Bar. 29-64.

With two more jars communicating with E by wire.

Knobs of Lane's electrometer touched at 0-29.

st ( 2"d i1'43

I 3™ division; Lane discharged at J2-27.
Ct at i 4th U-ii

With only one jar; straw at 3rd division, Lane discharged at 2-27. A slip
of tinfoil was then pasted on CD the whole length so as to touch the wire of the
jar and the frame of the straw electrometer. The result with only one jar was
then as follows.

Sri' 2*26

Straw at ,. division. Lane at

4th 3'i

Th. Sept. 2. Th. 65°. N. 19. Bar. 29-865.

ord I-SSi

Straw at .. division. Lane at .

4th 2-41

Wed. Sep. 8th. Th. 62°|. N. 19$. C. 18. Bar. 29-235.

ord 2*22

Straw at ,. division. Lane at

4th 3'i

In the afternoon. Th. 62°. N. 19. C. 17. Bar. supp. 29-37.

ord 2"^^

Straw at ... division. Lane at .
4th 3'0

Fr. Sept. 17. Th. 58°^. N. 28^. C. 29. Bar. 29-61.

Straw at Lane at

4 2-59

572] Comparison of strength of shocks by points and blunt bodies.

The wooden rod used in P. 118 [Art. 571] was supported on waxed glass
with the straw electrometer at the end, and some tinfoil wound round part of
the rod. The white glass cylinder was put in contact with it, electrified in such
a degree that I felt a slight shock in discharging it with a piece of brass wire
with a round knob at the end. If it was then electrified in [the] same degree,
and discharged [with] a like brass wire with a needle fastened to the end, I
could perceive no shock, and but a very slight sensation, even though the point
was approached pretty quick. The distance to which the straw electrometer
separated was about 1-8 inches.

The white cylinder was then changed for one of the large jars, the shock
was not very different whether it was discharged by the knob or point unless
the point was approached very slow. The distance to which the electrometer
separated was about -9 inch.

The wooden rod was taken away, and the white glass cylinder made to rest
on the conductor with Henly's electrometer on it, and electrified till it stood

284 "Journal of Experiments, NOT.}. 1773

at 90°, and to prevent the shock being too strong it had its choice whether it
would pass through my body or some salt water, the wires in the salt water
being brought within such a distance that the shock was weak when taken
by the blunt body. I then found that if I took it with the point I could scarce
perceive any spark.

The experiment was tried in the same manner with a large jar. The shock
was very sensibly less though the point was approached almost as fast I could.

573] Whether shock of one jar is greater or less than that of twice that quantity
of fluid spread on four jars*.

It was found that if the jars 3 and 4 were electrified in a given degree, and
their electricity communicated to the jars i and 2, the shock produced by dis-
charging them was nearly the same, or of the two rather more, than that pro-
duced by discharging the jar i or 2 by itself. The shock of the jar 3 was found
to be very sensibly greater than that of jar 4.

It was tried with the wooden rod, the jars to be electrified being placed in
contact wtih the tinfoil thereon, and when they were sufficiently electrified
those to which the electricity was to be communicated being approached till
they touched the rod, all four standing on the same tin plate. The jars were
electrified till the straws separated -9 inch.

N.B. The jars i and 2 contain pretty nearly the same quantity of electricity
and their sum is nearly equal to the sum of jars 3 and 4. The quantity of elec-
tricity in jar 3 exceeds that in jar 4 in the ratio of 37 to 27, or of 4 to 3 nearly f.

574] Comparison of the diminution which the shock receives by passing through
water in tubes of different bores, and whether it is as much diminished in passing
through 9 small tubes as through the same length of one large tube the area of whose
bore is equal to that of the 9 small ones%.

Nov. 1773. It was tried whether a shock was as much diminished by passing
through a glass tube filled with water, 37 inches of which held 250 grains of
water, as in passing through 9 tubes, 37 inches of all which together held 258
grains of water, the length of water which it passed through being the same in
both cases, namely about 40 inches.

Two jars were used, and charged till the straw electrometer separated to
3 + o. The water in the tubes was mixed with a very little salt, and the shock
just enough to be perceived.

I could not be certain that there was any difference, but if any, that with
the single tube seemed greatest. The shock was then made to pass through
7 of the small tubes, 37 inches of which hold about 200 grains of water. The
shock was then sensibly less than with the large tube.

It was afterwards tried through what length of a tube, 37 inches of which
held 44 grains, the shock must pass, so as to be as much diminished as in passing
through 44^ of the large one.

* [Art. 406 and Note 31.] f [Art- 685-] t LSee Art- 5°6.]

Resistance of iron wire and salt water compared 285

It was found that when it passed through 5-2 inches the shock was sensibly
greater, and when it passed through 8-4 sensibly less than with the large one,
so that it is supposed it would be equal if it passed through 6-8.

44

i -08

6-8

44i 250
so that the resistance should seem as the ro8 power of the velocity.

N.B. The quantity of water which the tubes held was not measured very
exactly.

575] The tubes used in p. 123 [Art. 574] were measured by
follows :

and are as

NO

Length
col. $

Weight
[Troy]
[oz. pwt. gr.]

Length o
column wh

Straight end

: same
en near

Bent end

Weight of
37 inches
in grains

I

37-i

16 . 12

20-9

20-2

395

2

37'3

14 . 2

23-65

22-9

335

3

38-4

1.0.8

24-5 21-8

470

4

38

ii . 6

24-5 24-7

263

5

377

17 . 17

21-7 23-3

417

6

36-8

14 . 10

20-4 20-3

348

7

38-8

15 . 22

26-6 22-3

364

8

38-6

17 . 17

24-8 21-6

407

9

39-8

16 . 18

26-3 22-2

374

10

37-8

I . 10 . 0

16-9 17-4

7°5

ii

37-3

I . 3 . 20

22-8

22-2

567

large

447

8 . 15 . 8

3480

37 inches of the 9 first tubes, which are what was used in p. 123 [Art. 574],
held together 3373 grains, therefore the shock was very nearly the same, but if
anything rather greater when it passed through one tube, 37 inches of which
held 3480 grains of $, than when it passed through 9 tubes, 37 inches of all
which together held 3373 grains.

By p. 124 the shock is as much diminished in passing through 6-8 inches
of a tube, 37 inches of which hold 567 grains, as through 44^ of one, 37 inches
of which hold 3480, so that resistance should seem as the 1-03 power of the
velocity.

576] Comparison of diminution of shock by passing through iron wire or
through salt water*.

In order to compare the conducting power of iron wire and salt water, the
shock of two jars had its choice whether it would pass through 2540 inches of
nealed iron wire, 12 feet of which weighed 14-2 grains, or through my body,
each end of the iron wire being fastened to a pretty thick piece of brass wire
which I grasped tight, one in one hand and the other in the other, and with
them discharged the jars.

* [Art. 398 and Note 32.]

286 yournal of Experiments, Nov. 1773

It was found that when the straw electrometer separated to i + o, I just
felt a shock in my wrists, and when it separated to 2 -f- o, I felt a pretty brisk
one in them but not higher up.

I then gave the shock its choice whether it would pass through my body,
or 5-1 inches of a column of a saturated solution of sea salt contained in a glass
tube, i inch of which holds 9-12 grains of fresh water, the wires running into
the salt water being fastened to brass wires as before.

I found the shock to be just the same as before, and found too that in-
creasing the length of the column of salt water not more than J of an inch made
a sensible difference in the strength of the shock.

Therefore the electricity meets with the same resistance in passing through

2540 inches of wire whose base is 0 - - = — as through 5-1 inches of salt

78 x 144 79

water whose base is 9-12.

Therefore, if the resistance is as the 1-08 power of the velocity, the resistance
of iron wire is 607,000 times less than that of a column of salt water of the same
diameter*.

577] Comparison of conducting powers of saturated solution of sea salt and
distilled water.

The shock of i jar charged till the straw electrometer separated to i + o£,

( *8
discharged through a column of < inches of a mixture of saturated solution

t greater
of sea salt with 99 of distilled water in tube 6, was -j ? than when it was

discharged through 35^ inches of saturated solution of sea salt in tube 2.

By a former experiment, the shock passed through ' > of the mixed water

was j| r than through 40 J of saturated solution.

By a mean, the resistance of one inch of the mixed water is equal to that of
38 of the saturated solution, therefore allowing for the different bases of the
tubes, the resistance of the mixed water is 39 times greater than that of the
saturated solution.

The shock of two jars, charged to 4 + 0, and discharged through ~~

( CTf*3.tf*I*

of distilled water in tube 5, was < ° ' than when it was discharged through

23 J of the above-mentioned mixed water in tube 8.

( *R
By a former experiment, the shock passed through | of distilled water

was |f than through 23 J of the mixed,

(less

* [If the resistance is as the velocity, resistance of saturated solution of salt is
355.4°° times that of iron wire. By Matthiessen and Kohlrausch it should be about
502,500. See Note 32.]

Whether there is surface resistance 287

By the mean, the resistance of 1-3 of distilled water = that of 23^ of mixed.

10-9 inches of tube 5 in the place where used holds 120 grains of $, or 37
inches holds 408 grains, which is the same as tube 8: therefore the resistance
of distilled water is 18 times greater than that of mixed, or 702 times greater
than that of a saturated solution of sea salt.

578] Whether the electricity is resisted in passing out of one medium into
another in perfect contact with it.

The Qth tube of P. 126 [Art. 575] was filled with 8* columns of saturated
solution of sea salt inclosed between columns of £, the end columns being §•
The tube 7 was filled with one short column of § at the bent end, and a long
column of saturated solution of sea salt.

It was found that the shock of one jar, charged till the straw electrometer
separated to i-o£, passed through a column of the salt water in tube 7,

' [• inches long, was rather j diminished than in passing through the

mixed column in tube 9, the wires used in tube 9 being immersed in the end
columns of £, and those used in tube 7 being immersed one in the short column
of $ at the end and the other in the column of salt water.

The length of the mixed column in tube 9 was 43-5 inches, its weight was
10-5, the weight of a column of £ of the same length was 18-10, therefore the sum
of the lengths of all the columns of salt water was 21-8 inches, and by the
experiment the shock was as much diminished by passing through 24-4 inches
of salt water in tube 7 as through this. But as the bore of tube 7 in that part

which was used was greater than tube 9 in the ratio -±- ' x — — = 1-06 to i

22-3 37'4

nearly, the shock should be as much diminished in passing through a column
22-94 long in tube 9 as through one of 24-4 in this. Therefore the shock is as
much diminished in passing through a mixed column, in which the length of
salt water is 21-8 inches, as through a single column of the same size whose
length is 22-94 inches.

The difference is much less than what might proceed from the error of the
experiment.

579] A slip of tin was made consisting of 40 bits soldered together, all
i\i inch broad and all about \ inch long. They were made to lap about ^ inch
over each other in soldering. I could not perceive that the shock of a jar was
sensibly less when received through this than through a slip of tin of same
length and breadth of one single piece.

If the jar were charged pretty high and a double circuit made for it, namely
through this piece of tin and my body, I could not perceive the least sensation.

580] Made at Nairne's with his large machine.

A long conductor was applied to the electrical machine and a smaller con-
ductor to its end, a Henly's electrometer was placed on the middle of the long

* [8° in MS. Perhaps 80.]

288 'Journal of Experiments, Nov. 1773

conductor, and a small jar with a Lane's electrometer fastened to it was made
to touch the short one. When Henly's stood at

3° Lane's dis- <7 + 35 = "668

55 charged at '7 + 5« = -678 inch.

70 19 + 30 = -741

The jar was then changed for one of rather more coated surface and a much
smaller knob. When Henly's stood at 30 or 35, Lane's discharged at 17-7 = -650,
so that Lane's discharged at nearly the same distance with the same charge,
whichever jar was used.

Henly's electrometer was then placed on an upright rod, touching the long
conductor near the furthest end, Lane's electrometer with the first jar being
placed as before.

Henly then rose to 55 or 60 before Lane discharged at 17-55 = -681 inch.
Henly being then lifted higher it rose to 65, Lane remaining as before. It was
then lifted still higher, when it rose to

6s I7'55 = '631

before Lane s

discharged at
35 or 40 6-55 = -263

Lane's being then separated to 27-55 = 1-060, the jar once discharged over
surface of glass and once to the electrometer, but there seemed reason to think
that Henly's rose no higher than before, namely 65.

My Henly's electrometer usually rose to 90 when Lane's discharged at
12-20 = -467 inches.

Therefore the distance at which Lane's discharges, answering to different
numbers on Henly's, is as follows :

I [Lane]
Henly on highest rod 65 1-060

65
50

35 or 40
Henly on conductor .70

55
30

•68 1

•377
•263

•741
•678
•668
•469

My Henly on conductor 90

The distance at which Lane's discharges with a given jar is nearly propor-
tional to the quantity of electricity in the jar, for if a jar is charged to a degree
at which Lane is found to discharge at a given distance, and its electricity is
communicated to another jar of the same size, so as to contain only J as much
electricity as before, Lane will then discharge at nearly \ the former distance.

[ 289 ]

M[EASURES]

(From MS. N°. 20. See Table of Contents at the beginning of this volume.}

[These "Measures" are on a set of loose sheets of different sizes marked M. i to
M. 21, and another set marked M. i to M. 12.]

581] Comparative charges of jars and battery

*

M. i. If jar i is electrified till straw electrometer separates to ij, and its
electricity is communicated to jars 2 + 4, pith electrometer separates 5j. There-
fore charge required to make pith balls separate 5f is to that required to make
straw electrometer separate i\ as 3184 to 8909, and that to make pith separate
5j to that to make straw separate if as 2920 to 8909.

f5
Jars i and 2 being electrified by wire and jar 1 6 by coating till pith electro-

(-7
meter separated ij and a communication being then made between them in

51
the manner used for trying Leyden vials, pith balls separate 5^ negative,

5i

5 ri3i6t

therefore charge of jar 6 should be -j 1273 .

7 (.1231

Charge of 1 + 2 + 3 + 4= I2544-

Jars 1 + 2 + 3 + 4 being compared in the same manner with jar

pith balls did not separate at all.

M. 2. If the charge of jars i + 2 + 3 + 4 is called 4

jar i or 2 is nearly = i

5. 6, or 7 4

I row of battery = 22

whole battery = 154

Jar 8 being electrified it was found that it must be touched 7^ times by
white cyl. to reduce the quantity of electricity to J. The 4 jars must be touched
8£ times by do. Therefore charge of jar 8 = 3|.

A piece of crown glass i foot square of which weighed 10-12 was coated with
tinfoil about 10 inches square.

* [Art. 411.]

f [These numbers are given as in the MS. They should be each multiplied
by 10. See also Art. 585, where the numbers seem to be deduced from some other
experiment.]

C.P.I. 19

290 Records of Measures

M. 3. The charge of each row of the battery was found by charging to a
given degree by electrometer and touching it repeatedly with jar 4 till the
separation of electrometer was reduced to that answering to \ the charge.

*The Ist, 2nd, 3rd, 4th, 5th, 6th, 7'" row required to be touched 18, 19, 17,
i8£, 17, 17, 18 times, therefore charge

Ist row = 26 charge of jar 4

2nd = 27-4

3'd = 24-6

4"> = 26-7

5" = 24-6

6»» = 24-6

7th = 26

and charge of whole battery = 180 times that of jar 4

and real charge = 321000

and if real charge by computed of white glass = 7-5,

computed charge = 42800
which answers to 187 square feet of glass whose thickness = T'ff.

Therefore charge of jar 4 answers to 1-04 square feet of D° thickness. The
coating is about T^- of a square foot, and therefore the mean thickness = -058.

582] M. 4. Let jar be touched n times f by jar which is to first as x to i,
it will be reduced in ratio of i to (i + x)n, therefore if it is reduced to \ thereby

(l + x)n = 2.

Therefore let N. L 2 = a and N. L (i + x) = px,

pxn = a,

i pn
and

x a

x^ / x\
but N. L (l + x) = x nearly, = x ( I J ,

therefore p = i - - nearly, = i - — - nearly,

therefore - = - ( i ) nearly,

x a \ 2nJ

= " - J nearly,
whence we have the following

Rule for finding ratio of charge of 2 jars, supposing the charge of first to
be reduced to J by touching n times by 2nd.

Charge of Ist is to that of 2nd :: i '44471 - \ to i.

* N.B. The left-hand row is supposed to be called the Ist row. [If Jar 4 = 2675
circ. inc. (see Art. 506) whole battery = 481,500 circ. inc. or 321,000 glob, inc.,
counting i glob. inc. = 1-5 circ. inc., as Cavendish seems to do here.]

t [Art. 413.]

Comparison of Ley den jars ana1 batteries 291

583] M. 5. jar i -i 3184 [circ. inc.]

2 = 3050
3= 3635
4= 2675

5 = 11816

6 = 12544

7 = 11816

8 = 10761
jst row = 64538*

Quantity of electricity communicated to whole battery f by

B + 2A = 3-61 + 2A

2B + 2A = 7-07 + 2A

3B + 2A = 10-36 + 2A

36 + C + 2A = 13-16 + 2A

R = 20-58

R + B = 23-66 D = \

R + 26 = 26-74

R + 36 = 29-83

Quantity of electricity communicated to i8' row by

A = -95 B + 2A = 2-56^

2A=i-8 26+ =4-58 1

3A=2-6 36+ -6-17 1

4A = 3-3 {?4} 3B + = 7-54]

Charge of Ist battery of Nairne.

584] M. 6. Electricity of Ist row of old battery was reduced to J by touching
nj times by crown glass of 10 inches square. Therefore charge of Ist row to
that of crown glass as 15! to i. The first row of new battery appeared by that
means to contain 10-7, the 2nd row II, and the 3rd 11-4 times the charge of the
same plate.

The mean area of the convex coating of each jar seemed to be 14 x iz\ = 175
inches, to which adding 5, id est T% of area of bottom, whole coating may be
estimated at 180 square inches of same thickness as sides.

fist ( 10

2 row of new battery was reduced to J by touching -j loj
3 1 10

j-13'94
times by jar i, therefore charge = jar i x \ 14-66, and charge mean row

U3-94
= jar I x 14-18 = 45,149 inc. el.

* [See Art. 506.]

f [Here A seems to be the charge of one of the first 4 jars taken as unit, B that
of one of the others taken as 4, and K that of the row taken as 22, the battery being
154, as in M. 2.]

19 2

292 Records of Measures

By top leaf its charge should be - '• — — = 46390 inc. el., therefore

J / 3

its computed charge = = 30100, and thickness of glass should seem

_ 180 x 6 x « x fj = 1
30100

585] M. 7. Whether shock of battery is sensibly diminished by imperfect con-
duction of the salt water in the jars.

An uncoated glass jar like the coated ones was filled with fresh water and
put into a glass jar of fresh water, a brass wire with knob being put into it,
and a slip of tinfoil into the outer jar, it was charged till straw electrometer
separated to 8 and tried by shock melter* filled [with] sea water, wires about
3 inc. dist.

The water in inner jar was then changed for sat. sol. s. s. f and that in outer
for about equal parts of D° and fresh water, and tried in the same manner.
The shock seemed rather greater, but was plainly less when electrometer was
at 7.

When shock was taken without shock melter* it was as strong with el.
at 5 as with D° at 8. Jar 2 being charged to 8 and its electricity communicated
to jar, the electrometer separated to 4^.

586] M. 8. Feb. 28, 1775.

Specific gravity bottle filled with salt water from torpedo trough weighed
8.4.18 by ingraved weights. Th. at 49. Specific gravity = 1-0254.

Being mixed with ^-^ = -3525 its weight of rain water, specific gravity
bottle weighed 8.4.1, Th. at 49 \, specific gravity 1-0190.

Excess of specific gravity above unity of stronger is to that of weaker as
1-335 to i. The quantity of salt in them is as 1-3524 [to i].

Therefore the excess of specific gravity above i differs pretty nearly, but
not quite, in as great a ratio as the quantity of salt in them.

M. 9. April i. D° Specific gravity bottle with water from torpedo trough
weighed 8 . 4 . 22 by D° weights.

April 29. Torpedo trough filled with water to within i inch of top, and
58 oz. salt added.

Specific gravity bottle filled therewith, Th. at 70°, weighed 8.4.12. At 54 J
same water weighed 8.4.16^.

One bottle of sea water weighed 8.4.11, Th. at 67. Another bottle weighed
8.4.19!, Th. DO.

Specific gravity bottle with rain water weighs 8. i . 22^.
[M. 10 blank.]

* [This word occurs also in Arts. 622 and 637. See facsimile at Art. 622.]
t [Saturated solution of sea salt.]

Investigations on salt water 293

M. II. Rule for finding the quantity of salt in water by its specific gravity.

, quantity of salt
Let the specific gravity of the solution at 46^ = S, and - .,,,,,,;„„ = *•

If S is above

1-0675

1-0261 - = ^

solution

I

•779

S - i + -0033
•719

X

S — I + -O022
•789

779 = 9-8917
L -719 = 9-8568

•784 = 9-8942
vide Heat p. 98*.

587] In 2nd Lane's electrometer or Ist detached do.
40 threads screw = i£ inches, or i division of plate =
For 3rd Lane D°.

incn-

588] M. 12.

June ii.

altin

Bt

Not salting

2 .

19 .

5

3

- 15

- 15

2 .

16 .

10

3

. 8

. 21

3 •

ii .

I

4

• 5

. 8

3 •

J4 •

IO

4

• 7

• 9

2 .

4 •

10

2

• 13

. 12

2 .

ii .

8

2

. 18

• 13

2 .

12 .

14

3

• 4

. 22

Mahogany

Wainscot

Beech

Ash

Alder

Lime

Deal

Weight of the unsalted ones on June 18, and number of vibrations of a
pendulum J inches long, in which the electricity of i row of the battery was
reduced from 2 to i by pith balls by touching with them, the ends being wrapt
round with tinfoil fastened on with gum.

Weight

Number of
vibrations

Loss of
weight

Mahog.

3

• 14 •

12

34

I • 3

Wainscot

3

• 7 •

2O

19

I . I

Beech

3

• 15 •

5

36

10 . 3

Ash

4

. 0 .

16

6

6 . 17

Alder

2

. II .

18

200

i . 18

Lime

2

• 15 •

14

22

2 . 23

Deal

3

• 3 •

12

60

I . IO

* [Mr Vernon Harcourt, in his Address to the British Association (B.A. Report,
1839, p. 48), has given extracts from Cavendish's MS. on Heat, p. i to p. 50, but he
does not mention any page 98.] {See Vol. n of this Edition.}

t [Art. 609.] { [So in MS.]

294 Records of Measures

M. 13. The salted ones taken out of water two or three hours weighed

Mahogany

Wainscot

Beech

Ash

Alder

Lime

Deal

3 • 15 • 14
3.9.0
4.8.0

4 . 14 . 12
3 . 9 . 22
3 . 17 . ii

3-1-4

June 19'". Bits of tinfoil were fastened round the ends of these pieces of
wood with gum.

26 being electrified to ij and its electricity communicated to the whole
battery gave a slight shock when received through the Lime, Alder, Ash and
Beech, but most through the Lime.

iR + 36 through wainscot and 2R + 36 through deal gave much the same
shock, and 3R was just sensible through Mahogany.

589] M. 14. Dimensions of coatings made to pieces of glass D, E, F, G;
A, B, C, I, K, L, M, H. [See Art. 324.]

M. 15. Bluish-green ground glass from Nairne called R and S,

M. 16. Logarithms for calculations of these plates.

M. 17. Do.

M. 18. Straight piece of elect[rifying] wire, thickness -15, length 30.

Increase of quantity of electricity in wire of that thickness by increasing
its length from 33 to 53 inches = 4-53 inches, therefore increase of quantity of
electricity in wire = increase length x -226.

The two trial plates of white plate glass, which contain together 66 inches of
computed power, or 66 x 1-6 inches of electricity, were balanced by twice the
sum of the double plates A and B + 48 of additional wire = 73-4 + 10-85 = 84-2
inc. el., therefore 10-7 inc. el. is to be allowed for the usual length of the
wire.

[Rules for making trial plates.}

M. 19. By p. 21 [Art. 459] it should seem that the difference between two
trial plates ought to be to their sum as L + S + 20 inc. of wire to L + S, or as

20 x -226 .
3-6 -I 7 — to 66, or as 32 : 330.

{D 12-16

E of Nairne are to be coated with circles -j 2-16 in diameter.
F [2-19

The mean quantity of electricity in the trial plates should be 47-4 inc. if
nothing is allowed for additional wire, therefore if this is increased by ^ to

allow for uncertainty, and the plate „ is used for , a trial plate, the com-

Conductances of salted substances 295

puted power should be ' ,'j , and [M. 20] the coating should be a square
33'°°

whose side =

2-27

Quantity of electricity in small thin plates to be uo-r, computed power
= 67-8, diameter of circles to be

I = 2-299
K = 2-286
L = 2-358
M = 2-207

The trial plates to them to be made of plates I and L quant" el" of that

comp. power
glass supposed = 1-95.

Computed power of mean between the two plates to be I2° x -- - = 68

1-95 10

= a square of 1-933, the thickness of the glass being -07, therefore

Small = L) , (2-126 ,

Large = I } = ''933 long and {^ Abroad.

1-62 IL

1-74 were made to I
Oblong coatings 1-82 long and \

(2

2-14 K

M. 21. j > trial plate for large thick plates |F to be coated with oblong

square |^ by 6.

Dimensions of trial plates.

Length

Breadth

A

16-4

II-8

B

13

97

C

10-4

7-8

D

8-5

6-4

Sliding Plates.
Value of i division in

Number of Plate Inc. el. Parts of D

Ist -75 -0208

2nd 1-50 -0416

3rd 3'37 -0940

4th 8-57 -238

5'" 19-0 -530

6th 18-0 -500

I inch additional wire -226 -0063

296

Records of Measures

[From this table it appears that D is supposed to contain 36 "inc. el.
Now, by Art. 655, D contains 26-3 "globular inches," which is equal to 41
"circular inches," or 36-7 "square inches."]

[Specimen of Measurements of thickness by dividing engine.]
590] 2nd rosin plate, [Arts. 371, 500] mean diameter 5-6.

M. 23. At 2- 1 10 knobs coincided,

2-306 1

05 1 center 2-3057
06 1

} one inch [from center] 2-3045

04

047

2- no coinc.

2-IIO

coinc.

2-306'

04
06

05

oo

02

ij inc. from center

02

2-303

OO

02

02

02

2-110 come.
Mean thickness =-195.

591] M. 32. Measures of thickness of crown glass [Arts. 370, 500] measured
in the middle of each i6th square part, the numbers being placed in the same
situation as the squares.

C. At i-88r the knobs coincided.

1-944 48 51 48

48 52 52 44

53 53 46 38

53 46 40 34
mean 1-947, thickness -066.

Measures of glasses for condenser plates 297

{From MS. N°. 13.}

592] M. r*. List of Plate glasses.

First got.

Made into trial plates and cased in cem[ent] of a
greenish colour inclining to blue with a great want
Of transparency.

not used.

coated, comp. pow. = 46.

Same sort of glass as A and B, but from their greater

length and breadth I could not so well judge of their

... ,
colour. Made up into trial plates.

Same kind as C and D. Remains not approp.

H is marked on side with single scratchof file, I with 2,

and so on to L.

Made into trial plates and broke except L.
More transparent than the thick plates,
not used.

The thickness was measured in the middle of each side, beginning with that
side to right of letter, the letter being held towards eye.

Thickness Diam. coating Comp. power

Double plate ground glass A -3 1-82 11-04

B -31 1-855 "'I

Ist got from Nairne.

2 thickish plates of 8 inc. made into trial plates for 2nd sort, called S and L.
Another cut into 4 pieces for trying effect of different varnishes.
A 4th not used.

2 thin ones of bluish glass coated in order to serve for trial plates to largest
plate, and called L and S, but not used.

2 thick plates and i thin one rough.

2 white glass plates from Nairne.

4 pieces out of same piece with different sorts of surface.

A large piece of whitish plate glass divided into 3 pieces, one used for sliding
trial plate.

4 irregular shaped pieces called N, O, P, Q. [Art. 459.]

2 thinnish pieces 5 inches square with very thin plate rosin between.

M. 2. i piece of much the same kind fastened to piece of crown glass with
cement between, used for sliding plate.

* [Here follows another series of measures oil loose leaves of different sizes.]

298

Records of Measures

593] M. 3. N airne's plates of same piece *.
Out of water Loss in water

4 thin pieces

7- 1-14

2. 12. 21

7-079

4 thick do.

19. 3.11

7- 3- 4

19-173

large thin piece

7. 0. 2

2.12. 7

7-004

A

19. 6.17

7. 4.10

19-335

B

I9.I2.II

7. 6.13

19-623

19. 1.16

7. 2.13

19-083

2-644

2-6774

7-158

2-6785

2-6i5

2-6785

7-221

2-6776

7-327

2-6782

7-127

2-6775

Mean 2-6779

I cub. inc. water = -5278 oz.
I oz. of glass = 9-84973 cub. inc.

[The weights in Ist & 2nd column are in ounces, pennyweights and grains
(Troy), in the 3rd and 4th in decimals of an ounce, and the 5th is the specific
gravity. The number 9-84973 is the logarithm of the number of cubic inches
in an ounce of glass.]

M. 4. [Gives Ist the length of each side of each piece of glass, and the
distance between the middles of opposite sides to hundredths of an inch.

2nd the thickness at each corner and middle of each side to thousandths of
an inch.

3rd specific gravity and mean thickness deduced from it for plates A to M
of Nairne.

The results are given in M. 5. The thicknesses are as follows:

Thickness
calculated

Measured

Diff.

A

•2112

•2095

•0017

B

•2132

•2109

23

C

•2065

•2057

8

D

•2057

-2047

10

E

•2065

•2055

10

F

•2115

•2IOI

14

G

•2O22

•2103

9

H

•07556

•0735

21

I

•07797

•0759

21

K

•07712

•0755

16

L

•08205

•0804

16

M

•07187

•0707

12

[The thicknesses given in Art. 324 are those calculated from the weight in
and out of water and the measurement of the sides. They are greater than
the measured thicknesses in every case.]

594] M. 6. Measures of thickness &a of green glass cylinder.
Longest cylinder : a mark made with file near middle.
The i8' column is the distance in inches of the point to which cylinder is
immersed in water from the scratch.

* [Art. 314.]

List of measured cylinders and Ley den jars 299

The 2nd column is weight required to balance it in that position.
The 3rd is the same thing in the 2nd trial.

The 4th is the difference of these numbers, or bulk of intermediate portion
of glass.

The 5th is the same thing in 2nd trial, and

The 6th is the mean between them.

The 7th is the circumference in the middle of that space.

Bulk int. space

Towards

I»<

2nd

by

wide end

tri[al]

tri.

,st

2"<1

Mean

Circum.

13

II . 12 . 15

12 . 22

1 . 13

I . 12

I . 12 . 5

3-595

12

II . II . 2

II . IO

2 . 22

2 . 22

2 . 22

3-435

10

II . 8. 4

8 . 12

2.18

2.17

2 • 17 • 5

3-265

8

II . 5 . 10

5 -19

2 . 20

2 . 21

2 . 20 . 5

3-140

6

II . 2 . 14

2 . 22

2 . l6

2.18

2.17

3-020

4

IO . 19 . 22

17 . io

2.18

2 . l8

2.18

2-940

2

10.17. 4

17 . io

2 .23

2 . 21

2 . 22

2-905

0

10 . 14 . 5

14 • 13

[after this a table for the narrower half of Ist cylinder, and in M. 7 for
2nd, 3rd and 4th cylinders. M. 8 and M. 9 is a table of n columns.
Ist column, distance from mark.
2nd Mean loss [of weight] for 2 inches.
3rd Suppfosed] mean circumference.
4th Log. loss.

5th Log. supp. circumference].
6th Log. thickfness] x p.

7 Thick, x py> = ratio of circumference to diameter].

8 True mean circ. *

9 Log. do.

10 Log. comp. power of i inch.

11 Comp. power of i inch.]

M. io. Measures of the circumference and substance of glass in jars and
cylinder.

Marks with file are made at the extremities of the whole space, and the
numbers begin with the space marked with double mark.

* By mean circumference is meant the mean between the inside and outside
circumference.

300 Records of Measures

The circumference was measured by a slip of tinfoil put round, and the
intersection marked with knife.

The substance of glass was found by hanging it to end of sliding ruler
fastened to one end of balance, and weighing it in water; and by sliding the
ruler I made more or less of it to be immersed, and knew the difference of the
space immersed.

M. ii. Specific gravity of different pieces of white glass.

Large jar

3-253

3-253

small D°

3-256

3-257

long cylinder

3-281

3-279

thick flat glass

3-280

3-279

thin do.

3-280

3-284

The small jar being broke, a 2nd was measured.

Thickness measured by calipers in 4 different rows parallel to axis and in
5 different places in each row, beginning at a scratch with a file near bottom.

[Here follow the measures.]

The thickness was then tried in 4 different parts of circumference at 4-4 inc.
distance from scratch.

It was then weighed in water in the same manner as the others.

The jar was dried before each trial, and before the 3rd was rubbed with
solut. p. ash*, which made the water stick less to side, for which reason it is
supposed most exact.

The circumference was measured in two parts of the middle space, and
they came out both the same.

595] M. 12. Measures of coatings to jars and cylind.]

A coating made to 2nd small jar extending to 4-4 inqhes from scratch. Comp.
power = 680-7.

Coating to white cylinder extends 9-86 inches from double mark. Comp.
power = 684-1.

A coating made to 4th green cyl. extending 7 inches from mark. Comp.
power = 318-2.

A mark was made on wide part, extending 7-16 inc. from new mark. Comp.
power 600-7.

M. 13. A mark made on 2nd green cylinder 11 inches from first towards
thick end, and the tube cut off about i inch from Ist mark.

A coating made to the thick part extending 8-55 inches from 2nd mark.
Comp. power = 600.

* [Pearl ash.]

f [See Art. 383. The computed power here is 8 times the true value, and there
is no correction for spreading of electricity.]

EXPERIMENTS WITH THE ARTIFICIAL
TORPEDO [1775]

{From MS. N°. 20. See Table of Contents at the beginning of this volume.}

596] Torp. i in water touching sides*.

3 rows ijf felt plain shock in hands.

4 - more brisk in D°.
7 - more violent in D°.
2 plain in D°.
I sensible.

+ 2 + 3t
4+1 + 5 + 6+ 7 — but just sensible.

Out of water.

4+1 uncertain.

4+1 + 2 sensible.

4+1 + 2 + 3 D°.

5 + 4+1 sensible in elbows.

5 + 6 gentle in elbows.

5 + 6 + 7+1 + 2 + 3 + 4 strong in elbows,
i row more violent.

Uncoated, out of water.

4 scarce percept.
4+1 sensible.
4+1 + 2 gentle.

In water.

5 + 6 + 7 perceptible.

Without any torped. jar 4 was perceptible.

I could not perceive any sensible difference in the conducting power ot the
water I used & of sea water, but the difference caused by mixing ^ part of
rain water with the sea water was scarcely perceptible.

(distilled water\ I i

are to each < Tfi

go io

§N.B. resistance of -jsat. sol. in "j. other nearly •< IOO

(sat. sol. as (702

* [Art. 415.]

f [3 rows of battery electrified till the electrometer separated to ij.]

{ [These numbers are those of the jars of the first row of the battery. See
Art. 583.]

§ [This should be conducting power, instead of resistance. The numbers then
agree with those in Art. 684.]

302 Torpedo 'Experiments^ April, 1775

so that there seems no reason to think that the resistance of water about the
saltness of sea water varies in a quicker ratio than that of the quantity of salt
in it.

Without torpedo jar 1 + 2 + 4 was very sensible in elbows, but 1 + 2 was
felt only in wrists.

597] Let a given charge be passed by double circuit through your body and
another circuit; let the quantity of electricity which passes along the second
circuit be to that which passes through your body as * to i ; the rapidity with
which the fluid passes through your body is the same whatever is the value
of x, and the quantity which passes through your body is * as i + x.

If the resistance which the electricity meets with before it comes to the
double circuit is to that which it would meet with in passing through your
body alone as a to i, the force required to drive electricity through the whole

circuit in given time is as a + - - , and therefore the time in which it is

i + x

I T. I V

discharged = = , and the velocity with which it passes

i i + a + ax
a + -

i + x

through your body is as — , and the strength of shock is as

i + a + ax

(i + x} (i + a + ax) '

In trying resistance of liquors by double circuit, if the quantity of elec-
tricity which passes through the liquor is to that which passes through your
body as x to [i], the quantity of electricity which passes through your body

is as - — , and the rapidity with which it passes through your body is given.

I ~T~ X

In trying it with single circuit, if resistance el. in passing through liquor
is to that in passing through your body as x to i, velocity of electricity is as

- , and the quantity is given, therefore in both ways of trying it, the

I ~T~ X

greater x is, the more exact will be the method, and both methods will be equally
exact if x is given or very great, supposing the strength of the shock to be as
the quantity of electricity into its velocity f.

(16

598] Shock produced by charge -i 22 in water bears the proper proportion

(44

f 6
to that caused by charge j 8 out of water.

Ii6

* [Should be inversely as i + x. The rest is a correct statement of the strength
of derived currents according to the law afterwards published by Ohm. See Art.

4I7-]

f [The "velocity" is what is now called the strength of the current. The
strength of the shock is assumed to be proportional to the energy of the discharge.
See Arts. 406, 573, 610, and Note 31.]

Electric current in divided circuits 303

It is supposed that it required about 2f the charge to give a proper shock
in water as [it does] out, or it is supposed to require 5 times quant, el. It is
supposed too that it requires 2ce charge of 3 times quant, el. to give same
shock with torp. out of water as without torp.

I body | i

torp. be as J2 , if quant, el. which
water la

passes through torp. is increased to zn, quant, el. which passes through your

body ||

in wat. ... ,

, will be 4 , therefore

out wat.

a + 2 + i

must = - , or

in + i 3x5

i5« + 30« + 15 = 2na + 6n + a + 3,
n (za + 6 — 30) = 14* + 12,

140 + 12

n = - - . which if a = 60. is

2« - 24

I4« 7 * 5 =

20. x | 4

and therefore it should require about 9 times quant, el., or about 5j times the
charge, to give the same shock out of water as at present.

599] Tu. Mar. First leather Torpedo*.

Out of water.

i row jars el. to ij by straw el. and commun. to rest, a shock just sensible
in elbows.

1 + 2 + 3 + 4 + 5 + 6+7: just sensible in hands.
D° + r row: stronger than NO i.

In water.

2 rows : plain in hands,

1 row: just sensible,

3 rows : rather stronger than 2 D° out of water.

600] Tu. Apr. 4 [1775]. 2nd leather Torpedo.
Out of water,
5 + 6 + 7 : very slight in fingers.

2 rows : only in hands, there seemed to be something wrong.

4 rows: brisk in elbows.

2 rows: briskish in elbows.

* [Art. 416.]

304 Torpedo Experiments, May, 1775

In water.

2 rows just sensible in hands.

3 rows stronger.

4 rows pretty strong D°.

Ist leather Torpedo in water.

4 rows nearly same, but I believe not so strong as last.
2 rows very slight.

Out of water.
2 rows slight in elbows.
4 rows strong in elbows.

601] Sat. May 27 [1775] with 2nd leather Torpedo under water, 3 rows
charged to i\ on electrom. *

Shock with one hand to one person seemed stronger, to another weaker
than with both.

Communication being made with metals instead of the hands, no shock
was felt, but when all the rows were charged to 3, Mr Ronayne felt a small
shock.

With wooden Torpedo, i row to i\; shock passed across 27 links of heavy
chain with light. It also passed across 4 links of small chain with light, but
not across 6.

Without Torpedo, 5 + i + 2 to i|; shock passed with light through elec-
trom., no candle in room; also with torp. charged as in trial.

On a former night in trying wooden Torp., charged I believe much the
same as this time, no light was perceived, though Mr Hunter felt a shock, but
very weak.

One candle in room, hid as well as possible behind screen.
With Gymnotus, all rows charged to 3$.
Doubtful.

Dr Priestfley] and Mr Lane touching with i hand at same time, Dr Priestly
felt shock extend to elbow.

A former night, 3 rows charged to \\, Mr N. thought the shock extended
to elbow; no one else thought so.

Sat. May 27 [1775].

602] Old Torp. out of water 26 + A (8-i)f, tried with metals, weak shock;
New torp. B + A (4-6) as strong as former.

The old Torp. tried with one hand holding metal against bottom side, in
other hand holding bright link.

* [Art. 419. The (artificial) Gymnotus is not elsewhere mentioned.]
f [The numbers in brackets are the charge communicated to the battery or the
row. See Art. 583.]

Shocks in and out of water

3°5

3A (3) no shock, with B (3-6) a very slight shock when torp. was just wetted,
none else.

With long link, not bright, 3 A, (3), sometimes left it, not always; with
2 A never.

With wire of same size bright without link, seemed not to feel it so well.

With small link not bright no shock with B + A (4-6), but there was with
B + 2 A (5-6); with bright wire without link felt shock with B + A (4-6), but
not with B (3-6).

With dirty link 2B + A (8-1), sometimes a small shock, not always; with
28 + 2A (9-1), certain.

603] Tried with Lane's electrom. ; dirt unaltered.

Rows of
batt. to
which el.
is comm.

Jars el.

Equiv.*

I

R+ 2B

26-7

shock

7 1

R+ B

237

none.

I

I J

B + 2A

4-56 small

shock.

1 1

B + A

3-56 : none.

7 I

R-f- B

23-7 shock

7 1

R

20-6

none.

-7 I

R+ 26

26-7 shock

7 1

R+ B

237

none.

I I

B + 3A

5-6

shock

1 \

B + 2A

4-6

none.

7 1

R+ 26

26-7

shock

7 (

R+ B

237

none.

r 1

B + 3A

5-6

shock

1 i

B + 2A

4-6

none.

Tu. May 30 [1775].

604] It was tried whether distance on Lane's electrom. at which jars dis-
charged was the same at the same separation of straw & pith ball electrom.
whether number of jars was great or small f.

This was tried first by laying small knob'd Lane on wire while jars were
charging, and afterwards by charging jars, without Lane lying on wire, to a
little greater and little less degree by electrom. than what it was before found
that they discharged at; then touching them with Lane, I could not perceive
that the number of jars made any difference.

It was tried by comparing i & 4 jars with straw el. at 2 and by comparing
i and 7 rows of battery with pith balls at i.

It was also tried whether the number of jars electrified affected the separa-
tion of straw el.: by connecting 4 jars to the wire & then withdrawing 2 of
them. It was not found to be at all affected.

* [See Art. 583.]

f [Art. 402.]

c. P. i.

20

306 Torpedo Experiments, May, 1775

Tu. May 30 [1775].

605] Charge required to force el. through 4 links of small chain, and also
through 2 loops of machine*, 5 links of chain in each loop.

Rows
of
Batt.

Jars
el.

Equiv.

7

R

20-6

passed through 4 links

38 + C + 4A

17-1

did not

old

R

20-6

passed through 2 loops

torp.

3B + C + 4A

I7-I

did not

36 + C + 4A

I7-I

passed through 4 links

26 + 4A

II-I

did not

new

R

20-6

passed through 2 loops

torp.

36 + C + 4A

17-1

did once, failed once

R

20-6

passed through 4 links '

36 + C + 4A

17-1

did not

2nil

R + 36 + C

33

passed through 2 loops

h leather

R

20-6

did once, failed once

torp.

36 + C + 4A

17-1

did not ,

leather torp. R = 20-6'

old 2B + A = 8-1 gave same

new B + 3A = 6-6 shock.

without torp. A + D — 1-5

Tried with new Torpedo.

Rows
Batt.

Jars
el.

Equiv.

7

I

B + A
3A + D

4-6
3

I gave same shock.

7

2B + 2A

9-1

gave same

B + 3A

5'4

I shock.

Trial of charge required to pass through 4 links of chain.

i

3A

2-6

sometimes passed, sometimes not.

7

36 + C + 4A

17-2

D°.

i

4A

3'3

passed.

7

R

20-6

passed.

7

i

36 + C + 4A
3A

17-2

2-6

> did not.

Tried with 2 loops of machinef.

[Rows Jars el. Equiv.]

7

36 + C + 4A

17-2

[ did not.

I

4A

3-3

f

I

B + A

3-6

1 did.

7

R

20-6

1

i

B + 2A

4-6

did not.

i

B + 3A

5-6

did.

7

R

20-6

did.

i

B + A

3'5

did not.

i

B + 2A

4'5

did.

i

B + A

3'5

did not.

i

B + 2A

4'5

did.

* [Art. 433.] f [Arts. 433, 605.]

Shock through loops of chain 307

3B + C + 2A = (9-2) commun. to i row, 2ce passed through 2 loops, once
missed, once did not pass through 3, never through 5.

R communicated to 7 rows = 20-6 was tried 3 times without ever passing
through 3 rows.

Wed. May 31 [1775].

606] i jar was elect, and commun. to i row of battery, and shock taken
without torpedo. There seemed a little difference in the strength of the shock
according to which row it was communicated to, but hardly more than was
observed at different times from the same row.

Result of exp. May 30.

607] By mean, quant, el. req. to give same shock with 7 rows is to that
with i :: 18-3 : 11-5 :: 1-6 : i*.

Charge req. to force through j b with 7 rows is to that with I in rat.

(6-6 to i Sr j6-2 to i KTI mn ^ j6~4 to i

to i '

^— . w^-w

(6-6 to i „ (6-2 to i (6-4

between < & < , by means as {

\5-7toi 1 3-7 to i' (4-8

Tu. June 6 [1775].

608] The 2nd leather Torp. was tried in sandf wetted with salt water. The
Torp. lay flat on sand and was covered by it all but pos. elect, parts & middle
of back. With 3 rows charged to ij, felt a shock whether I laid bare hands on
torp. & on sand 16 inc. dist. from nearest part of D°, or whether I touched torp.
with metals. In latter case shock seemed much the same as shock 10 inch plate

crown glass { received through Lane's el. at - - inc.

If I laid pieces of sole leather§ which had been soaked in salt water for a
week and then pressed between paper with £ hundred weight for J day to drain
out moisture on torp. and on sand, and received shock with metal that way,

shock was about equal to that of 10 inc. plate with Lane at -

1600

The torp. taken out of sand and tried with metals in usual way gave shock
about equal to D° plate, Lane at i8J.

Being tried in same manner with i row, shock was weaker than in sand
through leathers, & with 2 rows stronger than without leathers.

The spe. gra. bottle with water which came from sand weighed 8.4.11.
Th. at 69, so that the water with which it was moistened appears to be of
right strength.

609] Bits of beech, wainscot & deal|| about f inch square were soaked in
salt water for 3 or 4 days, then taken out and wiped and exposed to the air
in dry room for about 6 hours.

* [Arts. 406, 573, 610, and Note 31.] t [Art. 422.]

J [Arts. 411, 430.] § [Art. 423.] || [Art. 588.]

20 2

308 Torpedo Experiments, June, 1775

The shock of the Torp. was received touching pos. el. part with metal and
neg. with one of these bits, the end which touched the torp. and that part
which I held in hand being bound round with tinfoil.

With 6 rows elect, to ij, I felt slight shock through wainscot: dist. tinfoils
2 inc.

With D° charge through deal, tinfoils at i inc., none.

With 3 rows to ij; received shock through beech, tinfoils at 4f inc. dist.,
about as strong as with ij rows when touched with metals on both sides.

With D° charge through 4^ inches of dry deal dipt in salt water and tried
the instant it was taken out, none.

Taking hold of tail in one hand & touching pos. side with metal, brisk
shock. When touching neg. side with metal much slighter, the exper. tried
with each pos. and each neg. part.

Mon. June 12 [1775].

610] Jar i elect, to 2j by pith el. seemed to give shock of same strength
as B + 2A comm. to whole battery; it was weaker than 2B and stronger than
B commun. to D°, but as there is a good deal of difference between the sensa-
tions of the 2, it is not easy comparing them.

According to this exp. the numb, jars which el. should be divided amongst
in order to produce given shock should be as the 2| power of quant, el., and
therefore el. 2 jars should be comm. to 5^ more in order to produce same shock
as i jar*.

Mon. June 18 [1776 f].

iR + 36 + C + 2 A comm. to 7 rows = (34^), & el. to a given mark on
pith el. gives shock equal or rather greater than i row el. to same degree and
not commun. to rest.

iR + 36 + C + 2 A elect, to i J on straw el. and comm. to rest always passed
through i loop of machine. The same elect, to i sometimes passed, sometimes
failed.

i row charged to i and not commun. to any more passed 3 times through
5 loops without once failing.

iR + 36 + C + 2A el. to i and comm. to rest would never pass through
2 loops.

611] 2nd Leather torpedo tried under water with metals with glass tubes
on them, all rows charged to 4 gave briskish shock, which was much greater
than shock out of water with i row to i \, but rather less than with 2 rows to D°.

The shock received in same manner with i row not communicated to rest
was less when el. to ij, and about equal when el. to 2j.

* [Arts. 406, 573, and Note 31.] f [Probably June 19, 1775.]

Shock through various substances 309

With 7 rows el. to i £ shock of D° Torp. when received through the salted
lime tree wood gave slight shock about equal to 3A passed through same wood
without torpedo.

Charge of 7 rows el. to 4 is to that of if row el. to ij as - — =— : i : : 12 to i.

3

612] Tu. July 4 [1775]. 2nd leather torp., the wire belonging to convex
side fastened to outside of battery and inside of battery touched by wire of
flat side.

3 rows of battery charged to i\ and comm. to remainder. Under water no
sensible diff. whether I touched convex or flat side with one hand.

Out of water, touching tail with one hand and one side of one elect, organ
with metal, a much greater shock if I touched convex side than flat side. The
event was the same if it was elect, by neg. elect.

Touching convex side of both organs with one hand, only standing on
electrical stool, a shock in that hand, but I think scarcely so strong as under
water.

Touching flat side in same way, much the same.

Laying i finger on convex surface of one organ & another finger of same
hand on the middle of the convex surface, a very slight shock.

Laying one finger on convex surface of one organ & the other on the nearest
edge of the torpedo, a considerably greater shock, but not strong.

Laying one finger on convex and another on flat side of same organ, a con-
siderably greater shock, but do not know how to compare it in point of strength
with that taken the usual way.

Tried without any torpedo *.

613] 36 being comm. to 7 rows and passed through i loop of 26 links of
small chain. If the chain was not stretched by any additional weight, the
shock did not pass. If the middle link was stretched by a weight of 7 pwt. it
passed, & the light was visible in a few links. If it was stretched by a weight
of 13^ pwt. no light was seen. There was no remarkable difference in the strength
of the shock, whether it was received through chain tended by 13^ pw. or without
chain.

The chain was fastened to the same machine that was used in a former
experiment, it was 7-9 inc. long and the distance of the supports 5-1.

The room was quite dark, it being tried at night without any candle in the
room.

3 rows of battery were elect, till pith el. sep. to i, its el. was then comm.
to the rest of the battery, & I received the shock of I row, the elect, having its
choice whether it would pass through my body or through some salt water.

* [Art. 437.]

310 Torpedo Experiments, July, 1775

I then elect, i row of battery till pith el. sep. to same degree, and commun. its
elect, to rest of battery and received the shock of 5 rows of it in same manner.
The shock seemed to be nearly of same strength, perhaps rather less.

Therefore shock of 5 rows elect, to a given degree seems about equal or
perhaps rather less than that of i row el. to 3 times that degree.

614] The mean thickness of the section of the elect, organ in the section
given in Mr H.* paper, in which the breadth is 10-3 inches, that is, the same as

I2l
my torpedo's, is 1-3 inc.; the area of one organ is 2-5 x 5j x = gj sq. inc.,

as found by cutting out a piece of paper of that size and weighing it.

And according to Mr H. there are about 150 partitions in i inch, therefore
comp. charge both organs reckoned in old way is

19 x 1-3 x 150 x ^ x 150 = 748,000,

and the real charge is 1122,000 inches of el. supposing the partitions to consist
of plates of white glass ^^ inc. thick, which is about 2\ times as much as my
battery, that being = 451,000 inc. el.

615] Tried with the 2nd leather torpedo, new covered, in large trough full
of water, the torpedo laid flat as in figure,
the electrical organ being (as supposed) 3
inches under water.

If torpedo was tried out of water with
i row to i\ comm. to 7 and touched with
hands in usual manner, the shock was just
felt in hands, and if touched with metals,
was just sensible in elbow.

Tried under water in above-mentioned manner with 7 rows el. to 4, the
upper surface being touched with the pestle of a mortar held in one hand, the
other hand dipt into water as far as wrist, a shock in the wrist of the hand in
the water I believe full as strong as the former.

The place where the hand was dipt into water was about n inc. from the
front of the fish, and conseq. about 14 from elect, organ.

Tried in the same manner as before, except that the fish lay in an open
wicker basketf, just big enough to receive it, and which had been soaked for
some days in salt water. The shock seemed much the same.

Holding hand in water in same manner as before without touching torpedo
— no sensation.

With three rows to ij out of water, the shock was stronger if I touched
convex side with one hand laid flat on elect, organs than if I touched flat side
in same manner, but the difference was not great.

Charge of 7 rows el. to 4 is to that of i row el. to ij as 19-6 to i.

The water appeared by its spe. gra. to contain .^ of salt.

* ["Anatomical observations on the torpedo." By John Hunter, F.R.S., [Phil.
Trans. 1773]. Art. 436.] t [Art. 421.]

[ 3" ]

[EXPERIMENTS ON] RESISTANCE TO
ELECTRICITY [1776]

•From MS. N°. 19. See Table of Contents at the beginning of this volume.
See also near the end of the Introduction.}

616] Comparison of conducting power of salt and fresh water in the latter
end of March and beginning of April, 1776.

Tried with Nairne's last battery, 6 jars being chose, each of which held
very nearly the same quantity of electricity; the wires run into the bent ends
of the tubes being made to communicate with the outside of the battery, and
the wires run into the straight ends being fastened to separate pieces of tinfoil.

The six jars were all charged by the same conductor: the communication
with that and each other was then taken away, and the jars discharged through
the tubes, one after the other, by touching the above-mentioned bit of tinfoil
by metal held in one hand, and the wire of the jar by metal held in the other
hand, the shock being received alternately through each tube.

617] Exp. i.

Distance of wires
In tube 15 t4

6-5 inc.
5-8
3'5
4-2

5'3

40-7

Sat. sol. S.S.* in tube .14,
salt in 69 of water in tube 15

in short
tube than
in long
one

very sensibly less
sensibly less
sensibly greater
scarce sensibly
just sensibly less

Straw electrom. = 4. Th. = 57. [Resistance = 390000 Ohms, f]
Resistance of 4-7 inches in tube 15 supposed equal to 40-7 in 14. Therefore
sat. sol. conducts 8-6 times better than salt in 69 of water.

Exp. 2. The same solution tried in tubes 22 and 23.

Tube 23 22 electrom. at i \. Th. = 58. [R. = 118000] f.

3'3
5'5

sensibly greater.

less in same proportion.

4-4 inches in tube 23 = 41 in tube 22.
Therefore sat. sol. conducts 8-94 times better than salt in 69 of water.

* [Saturated solution of sea salt.]

•f [The resistance of the saturated solution in Ohms, calculated from the measure-
ments in Art. 635 by Kohlrausch's data, is given for each tube within brackets to
indicate the absolute value of the resistances compared.]

312 On Resistance to Electric Current

Exp. 3. A new saturated solution and solution in 69 of water made and tried
in tubes 15 and 14. [R. = 390000.]

3-5 40-7 just sensibly greater. Electrom. = 3.
3- 1 very plain. Th. = 57.

5-5 sensibly less.

5-0 just sensibly less.

Therefore new saturated solution conducts 9-61 times better than new
solution in 69.

Exp. 4. Salt in 69 of water compared with salt in 999 of water in tube 22
and 23.

•

[R. = 1230000.]
23 22 Electrometer = if.

3-1 41-1 sensibly greater. "*• = 57-

3-5 scarce sens.

4-3 scarce sensibly less.

4-9 just sensib.

5-3 very sensib.

Resist. 4-1 in tube 23 supposed equal to 41-1 in 22.

Therefore salt in 69 conducts 9-57 times better than salt in 999.

Exp. 5. Salt in 999 compared with distilled water in tubes 12 and 20.

[R. = 462000.]

20 12 Electrom. = 3.

Th. = 58.

•78 43-5 sensib. greater.
1-2 scarce sensib. less.

1-4 diff. more sensib. than in i" trial.

1-05 supposed right.

Therefore salt in 999 conducts 36-3 times better than distilled water.
The distilled water changed for rain water.

1-9
3-3
2-55

sensib. greater. Electrom. = 3. Th. = 58°.
less, rather more sensib. than former,
supposed right.

Therefore rain water conducts 2-4 times better than distilled water, or
15-2 times worse than salt in 999.

The rain water changed for distilled water with ^fo^ of salt in it.

5-3
2-7

sensib. less.

about as much greater.

Therefore salt in 20,000 of distilled water conducts [3-67] times better than
distilled water, or 9-92 worse than salt in 999.

Solutions of sea salt compared 3 i 3

[6] Saturated solution and salt in 69 of water (the new solutions) compared in
the same manner, only using the jars i and 2 instead of the battery; with the
tubes 5 and 17.

17 5 [R. = 25100.]

2-6 41-1 sensib. greater.
5-5 sensib. less.

Therefore saturated solution conducts 10-05 times better than salt in 69 of
water.

618] The electricity of the 6 jars was found to be as much diminished by
being communicated to 3 rows of the battery as that of i row is by being
communicated to 4 rows, therefore quantity of electricity in the 6 jars is to
that in one row as 3 to 4.

Exp. 7. Saturated solution and salt in 69 (the new solutions) tried in the same
manner with battery; i row being electriffed to 2, and its electricity communicated
to remaining rows, and one row used at a time.

Tried in tube 5 and 17. [R. = 25300.]
i? 5

5-4 41-4 plainly less.

2-6 about as much greater.

3-0 scarce sensibly greater.

5-0 just sensib. less.

3-95 supposed right. Therefore sat. sol. conducts 10-31 times better than
salt in 69.

Exp. 8. Saturated solution compared with salt in 29 in tubes 22 & 23 with
Nairne's jars.

8-7
4-8

22

24-9

Electrometer i. Th. 63. [R. = 65000.]

just sensibly less,
about as much greater.

The bore of that part of tube 23 which was used is supposed ^ greater than
that of whole tube together. Therefore sat. sol. conducts 3-51 times better
than salt in 29 of water.

Exp. 9. The solution in 29 diluted with i J of water, id est, solution of salt
in 69, compared with sat. solution in same tubes.

23 22 Electrom. = i. Th. = 63. [R. = 65000.]

2-0 24-9 greater.

3-8 about as much less.

Therefore sat. sol. conducts 7-79 times better than the diluted solution,
and the diluted solution conducts 2-2 times worse than solution in 29.

3*4

On Resistance to Electric Current

Exp. 10. Saturated solution compared with salt in 69 in same tubes.

23

22

[R. = 65000.]

3-1 24-9 sensib. less. Electrom. = i. Th. = 63.
1-9 as much greater.

Therefore sat. solut. conducts 9-02 better than the solution in 69.

619] Examination whether salt in 69 conducts better when warm than when cold.

Salt in 69 in tube 17 placed in water; solution in 29 in tube 23 out of water,
the distance of wires in tube 17 being not measured, but remaining always the
same.

Electrometer = f .
23

8-1 . sensib. less

5 about as much greater)

4 plainly less ) . , ,

v heat of water = 105.
2-6 as much greater j

Therefore salt in 69 conducts 1-97 times better in heat 105 than in that
of 58J*.

620] Examination whether the proportion which conducting power of sat. sol.
and salt in 999 bear to each other is altered by heat.

Sat. sol. in tube 15, salt in 999 in tube 19, both in water; distance of wires
in tube 15 not altered.

19 Electrom. =

r} h«

of water = 58 J.

3-25
2-15
2-25

3'5

sensib. less \

sensib. greater)
just sensib. greater

heat of water 50.

electrom . = i.

rather more sensib. less) heat of water 95.
Therefore the proportion seems very little altered by heatf.

621] Jan. i, 1777. Salt in 2999 of water compared with water distilled in
preceding summer in tubes 12 and 20.

Electrom. = 4^.

20

1-4

12

43-5 rather greater. Column of 1-6 in tube 20.

plainly less. Supposed equal to 43-5 in tube 12.
greater.

Therefore allowing for different bores of tubes, salt in 2999 conducts 24
times better than distilled water.

* [By the experiments of Kohlrausch, this ratio would be 1-59. See Art. 691
and Note 33.]

| [This agrees, with the results of Kohlrausch.]

Distilled and salt water compared 3 1 5

Jan. 2 M. Same experiment repeated with the same water, which had been
left in the tubes all night.

20 12

1-4 plainly greater.

1-9 seemingly less.

2-1 plainly less.

Therefore salt in 2999 conducts 22 times better than distilled water.

The same experiment repeated, only the water in the tubes was changed
for fresh by pouring out the old and putting in fresh by small funnel, without
taking out the wires.

plainly less.

i-i
•35
7

plainly greater,
plainly less.

Therefore salt in 2999 conducts 72 times better than distilled water.

The same experiment repeated, only the distilled water changed for that
used in the preceding year.

•4 considerably greater,

i-i plainly less. -8 supposed equal.

Therefore salt in 2999 conducts 47 times better than distilled water.

Jan. 3. Experiment repeated with the same water left in.

•8 plainly greater.

1-2 plainly less.

Therefore salt in 2999 conducts 38 times better than the distilled water.
The distilled water changed for the new distilled water.

•28 plainly greater.

•6 plainly less.

Therefore salt in 2999 conducts 86 times better than distilled water*.

Salt in 2999 compared with salt in 150,000 in same tubes.

1-2 43-5 sensib. greater. Electrom. = 4j.
1-7 sensib. less.

Therefore salt in 2999 conducts 26 times better than salt in 150,000.

The experiment repeated with the same waters, only the wires in tube 12
brought nearer.

•3 12-5 sensib. greater. Electrom. = ij.
•45 sensib. less.

* [See Art. 690.]

3 1 6 On Resistance to Electric Current

622] Examination whether comparative resistance of salt in 2999 and salt in
150,000 was the same when tried in the above-mentioned manner, or when passed
through 2 wires in glass of wafer, as in fig. *

Jan. 6. The tubes 12 and 20 filled with salt in about 105 of water: salt in
150,000 of water in glass. 2 jars electrified to if and communicated to the rest.

oo.e flcSS

If the distance of wires in tube 12 was the shock was sensibly {

18-5 ' (greater

than that through the wires in glass.

The same tried as before, only with the jars electrified to 2 and the shock
received with shock melter*.

If the distance of wires in tube was f ^ ^ shock was plainly / than

\2O-3 i greater

through wires in glass.

The glass filled with salt in 2999 and the shock compared with that through
tube 20 with same solution of salt in 105.

The jar electrified to 2 and received with shock melter f.

If dist. wires in tube 20 was / shock was (f r than through wires

\i- \less

in glass.

N.B. Great irregularity was found in trying this last experiment, the cause
of which I am unacquainted with.

Therefore salt in 2999 conducts 31-5 times better than salt in 150,000.

The same salt in 150,000 which was used in this experiment was saved and
compared with salt in 2999 in the usual manner with tubes 12 and 20, electro-
meter at 4^.

( T«2 I PTf13.tfir

If distance of wires in tube 20 was -! shock was plainly -! than

^1-85 (.less

through tube 12 with wires at 42-4 inches distant.

Therefore salt in 2999 conducts 24-6 times better than salt in 150,000.

The thermometer in all the foregoing experiments of this year supposed to
be about 45°.

623] Exp. ii. Saturated solution in tube 14 compared with salt in 149 of water
in tube 15.

Tube 15

1-6
2-6

41-8

Electrometer at 3^. Th. = 45.
[R. = 474000.] "

sensib. greater,
sensib. less.

Sat. sol. conducts 20-5 times better than salt in 149.

* [See figure in facsimile of MS. on opposite page.]

f [The reading here is doubtful; see facsimile of MS. on opposite page. Cavendish
says, Arts. 601, 602, 616, that he took the shock with metals in each hand, but the
word here cannot be read "metal." The word occurs also in Arts. 585 and 637.]

Shock melter

3 1 7

/'

9iSa#*i

Cf

C •
'

3 1 8 On Resistance to Electric Current

Exp. 12. Jan. 8. Sat. sol. in tube 22 compared with salt in 149 in tube 23.
'Tube 23 Tube 22 Electrom. i\. Th. = 42. [R. = 146000.]

i-6

i-8

2-4
2-2
2-O
1-8

1-8 + 2-1 .

plainly greater.

seeming, greater, but doubtful.

plainly less.

rather less.

not sensib. different.

seemed greater.

in tube 23 supposed = 41 in tube 22.

m

Therefore sat. sol. conducts 19-6 times better than salt in 149.
Exp. 13. Salt in 149 in tube 5 compared with salt in 2999 in tube 17.

317

5

Electrometer = .

1-8

2-8

40-5

sensib. greater,
sensib. less.

Salt in 149 conducts 17-3 times better than salt in 2999.
By new measure of tubes.

Exp. 14. Same solutions in tubes 18 and 19.

Tube 19

2-2
2-4
3-o
2-8

18
42-8

Electrometer = if. [R. = 308000.]

sensib. greater.
» not sensib.
sensib. less,
seemed less, but doubtful.

2*2 I 2'Q

- in tube 19 supposed equal to 42-8 in tube 18.
Salt in 149 conducts 16-7 times better than salt in 2999.

Exp. 15. Jan. 9. Sat. sol. in tube 22 compared with salt in 29 in tube 23.

Tube 23

22

97
9.4

6-6
6-9
6-3

35-8

Electrometer = ij. Th. = 42.

[R. = 128000.]
sensib. less.

seemed less, but doubtful,
seemed greater,
not sensib. gr.
sensib. greater.

6-5 + 9-7 supp. = 35-8 in tube 23.

Sat. sol. conducts 4-38 times better than salt in 29.

Solutions of "various salts compared 319

624] Comparison of water purged of air by boiling and plain water.
Jan. 12. Salt in 2999 in tube 12. Salt in 150,000 in tube 20.
Tube 20 . 12 Electrometer = 4^. Th. = 50.

1-2 plainly greater.

1-4 seemed greater, but doubtful.

1-8 seemed less, but doubtful.

2-0 plainly less.

The water was then boiled over lamp in the same vial in which it had been
kept some time, and then cooled in water and compared in the same manner.

2-0 sensib. less.

1-8 seemed less, but doubtful.

1-2 seemed greater, but doubtful.

i-o plainly greater.

Therefore if anything water conducted better before boiling than after, but
the difference might very likely proceed from the error of the experiment.

In order to see whether the water had absorbed much air by being exposed
to the air in the trial, some of the boiled water was exposed to the air as much
as that which was tried in the tube was supposed to have been, and boiled over
again in a vial. It did not begin to discharge air till it was heated to 190°, and
then discharged but little. Some more of the boiled water which had not been
poured out of the vial seemed to discharge as much air. But some distilled
water which had not been boiled began to discharge air almost as soon as heated,
and discharged a great deal before it began to boil*.

625] Comparison of water impregnated with fixed air and plain water.

Some distilled water was impregnated with fixed air produced by oil of
vitriol and marble, and compared with salt in 2999 in same tubes and manner
as in former experiments.

Electrometer = 4^. Th. = 55.

1-6

1-4

2-4

2-6
2-8

seemed greater, but doubtful.

plainly greater.

not sensibly less.

sensibly less, scarce doubtful.

plainly less.

The same water deprived of its fixed air by boiling, and tried as before.
Tube 20

1-2
i-o

•9
•6

7

12

[See Art. 692.]

plainly less.

sensib. less.

seemed less, but doubtful.

plainly greater.

not sensib. greaterf.

t [See Art. 693.]

320

Chemical equivalents

,*

JLlectric resistances of solutions of 'various salts 321

626] 2-3 of Sal. Amm., 3-2 of Sal. Sylvii, 3-17 of Quadr. nitre, 2-21 of calcined
Glauber's salt and 14-10 of calc. S. S. A.* were dissolved in water, the solution
of each being 3.10.12, that is, such that the quant, acid in each should be
equiv. to that in a solut. salt in 29 of water.

Jan. 13. Sal. Sylvii in tube 15 compared with salt in 29 in tube 22.

Electrometer = 2. Th. = 55.
[R. = 253000.]

seemed greater, but doubtful.

plainly greater.

seemed less, but doubtful.

seemed less.

plainly less.

right.

Jan. 14. Sal. amm. tried same way.

seemed less, but doubtful,
plainly less,
sensibly greater.

Tube 15

22

5

18-2

' 4'5

7

77

8-2

7'4 + *i

— — n-7 cnrtrinc^/-!

7-2
7-9

5'3
5-8

seemed greater, but doubtful.

Calc. S. S. tried same way.
4-0

4'5
6-0

5'5

plainly greater,
scarce sensib. gr.
plainly less,
sensib. less.

Salt in 29.
4'5

7-0
6-5

Glauber's salt.
Tube 15

4-2
3-8
4-2

4-4
4-6

3'4
3-6

22

plainly greater,
scarce sensib. greater,
plainly less,
scarce sensib. less.

plainly less.

no sens. diff.

scarce sens. less.

do.

just sens. less.

sensibly greater.

scarce sensib. less.

* [See facsimile on the opposite page. The results are given in Art. 694. See
Note 34, p. 430, and Introduction.]

C. P. I. 21

322

On Resistance to Electric Current

Quadrang. nitre
4-0

4-3
6-0
6-2

plainly greater,
seemed greater, but doubtful,
seemed less, rather doubtful,
plainly less.

627] 2-0 of oil of vitriol, 2, 5-10 of spirit of salt 2, and 5-19 of f. alk. D,
were diluted with water, the solution being 3 . 10 . 12. Consequently the quantity
of acid in 2 first were equivalent to that in salt in 59 of water, and the alk. in
last was equivalent to that in salt in 29; compared in the same manner as the
former.

scarce sensib. greater.

seemed greater, but doubtful.

plainly greater.

plainly less.

seemed less, but doubtful.

sensib. greater.
not sensib.
sensib. less.
not sensib.

seemed less, rather doubtful,
seemed greater, rather doubtful.

Jan. 15

F. alk. Th. = 5

4'5

4-0

37

57

5-4

Diluted

oil of vitriol.

4-0

4'3

47

Diluted spirit of salt.

n-8
8-0

Another diluted spirit of salt was made of same strength as the former.
Being tried with wires at 9-9 inch, distance no sensible difference was per-
ceived, which agrees with former.

Another diluted oil of vitriol was made and tried, Jan. 16.

5-2

77

sensib. greater,
sensib. less.

EXPERIMENTS IN JANUARY, 1781 *.
628] Some basket saltf was dried before fire, and a saturated solution made

with it which contained

378

of saltj, and also other solutions of different

strengths, all being made with distilled water.

* [The results of these experiments are collected in Art. 695. See Note 33.]
f ["Salt made up in form of sugar loaves, in small wicker baskets, which is
thence called loaf salt or basket salt." Rees' Cycloptzdia.]

{ [26-45 per cent. Saturated solution at 18° C. is 26-4 per cent, by Kohlrausch.]

Dependence on concentration of solution
Sat. sol. in tube 14, salt in 69 in tube 15. [R. = 399000.]

323

3-6

5-8
5'4

14

39' i

Electrometer 3^. Th. = 53.

sensib. greater.

plainly less.

sensib. less 4'5 suPPosed "ght-

Sat. sol. conducts 8-63 times better than salt in 69.

Same solutions in same tubes.

5'4 plainly less.

seemed rather less.

scarce sensib. greater. 4'3 SUPPOSed n8ht'

sensib. greater.

3-6
3-3

Sat. sol. conducts 9-03 times better than salt in 69.
Sal. sol. in tube 14, salt in 29 in tube 15. El. = 3^.

7'3

II-O

sensib. greater.

sensib. less. 9' i supposed nght.

Sat. sol. conducts 4-1 times better than salt in 29.
The same solutions in same tubes.

107

7'5
7-8
97

seemed rather less,
sensib. greater,
seemed rather greater,
supposed right.

Sat. sol. conducts 3-85 times better than salt in 29.

The same solutions in same tubes. El. = ij. [R. = 136000.]

2-6

2-6

37
3'5
3'3

13-3

seemed rather greater.

D° scarce sensib.

plainly less.

sensib less. 2-95 supposed nght.

seemed rather less.

Sat. sol. conducts 3-95 times better than salt in 29.
Sat. sol. in tube 14. Salt in n in tube 15. El. if.

15

14

[R. = 1360

47

13-3

sensib. greater.

8

plainly less.

7-6

do.

7-2

sensib. less.

5-95 supposed true.

Sat. sol. conducts 1-92 times better than salt in II.

21 — 2

On Resistance to Electric Current

The same again.

7

4'9
5'1

seemed rather less.

sensib. greater. 6-05 supposed right.

seemed rather greater.

Sat. sol. conducts 1-88 times better than salt in n.

The same again.

4'9

7

seemed rather greater, but doubtful.

sensib. greater.

sensib. less. 5'95 supposed true.

Sat. sol. conducts 1-92 times better than salt in n.

629] Salt in 142 put in tubes 5 and 15 in order to find what power of velocity
the resistance is proportional to.

Electrometer = 3. [R. = 579°°°-]

plainly less.

do.

scarce sensib. less. supposed right.

plainty greater.

DO.

sensib. greater,
seemed rather greater,
sensib. less.

Therefore log. vel. in 15 by do. in 5 = 1-2122,
log. length in 5 by do. in 15 = 1-1829.

= -976 power of velocity.

J5

5

3'3

41-9

2-9

2

2-2

2-4

2-6

Therefore resistance is as
The same repeated.

1-2122

15

3
2-6

2-7

sensib. less.

hardly sensib.

seemed sensib. greater.

sensib. greater. 2>g5 supposed true.

hardly sensib.

Log. vel. in 15 by D° in 5 = 1-2122,
Log. length in 5 by D° in 15 = 1-2122.
Therefore resistance is directly as velocity*.

* (This is the first experimental proof of what is now known as Ohm's Law.]

Ohms Law of resistance determined
630] Salt in 69 in tube 22. Salt in 999 in 23.

Electrometer = 3^. [R. = 1335000.]

plainly less.

325

23

22

4'9
4-6

41-5

4-3
3-6

37

3'4

3'4

scarce sensib. less,
sensib. greater,
scarce sensib. greater,
seemed greater,
plainly greater,
sensib. greater.
Salt in 69 conducts 9-91 times better than salt in 999.

The same repeated.

3 '4 seemed greater.

3'6 scarce sensib. greater.

3'2 sensib. greater.

4'3 scarce sensib. less.

4'5 sensib. less.

Salt in 69 conducts 10-3 times better than salt in 999.

The same liquors in tubes 5 and 17.

4 supposed true.

3-85 supposed true.

17

5

Electronic

4-2

42-2

plainly less.

4

sensib. less.

3-8

hardly sensib.

3'i

sensib. greater.

3-3

hardly sensib.

3-55 supposed right.

Salt in 69 conducts 11-31 times better than salt in 999.
The same repeated.

5

3'3 hardly sensib. greater.

3-1 sensib. greater.

4 not sensib. less.

4-2 seemed rather less.

4'3 DO.

4-4 sensib. less.
Salt in 69 conducts 10-75 times better than salt in 999.

Salt in 999 in tube 12; distilled water in tube 20. El. = 2\

[R. = 494000.]
20 12

43-3

seemed rather less.

-326

On Resistance to Electric Current

2 or 3 hours after it seemed rather greater at -5.

Next morning was plainly greater at -7.

The water being changed for fresh, seemed rather less at -3.

The distilled water changed for salt in 20,000.

2-1 sensib. less.

2 not sensib. less.

1-7 sensib. greater.

1-8 seemed rather greater. 1-95 supposed right.

1-9 not sensib. greater.

2-1 sensib. less.

Salt in 999 conducts 20 times better than salt in 20,000.

Salt in 20,000 conducts about 7 times better than distilled water; therefore
if distilled water contains j^^nis °f sa^t their conducting powers will be as the
quantity of salt in them.

The same repeated. Electrometer — 2.

2-1 not sensib. less.

2-2 seemed rather less.

2-3 D°.

2-4 D°.

2-5 plainly less.

2 supposed nght.
2-3 seemed rather less.

1-7 seemed rather greater.

1-6 plainly greater.

Therefore salt in 999 conducts 19-5 times better than salt in 20,000.

The waters changed for fresh. El. = z\.
20 12

2 scarce sensib. different.

1-9 D°.

1-8 sensib. greater.

2-1 not sensib. less. 2-05 supposed right.

sensib. less.

Salt in 999 conducts 19 times better than salt in 20,000.
The same repeated. El. = 2.

42-9

sensib. less,
scarce sensib. less.

seemed rather greater.

_ 1-95 supposed nght.

sensib. greater.
Salt in 999 conducts 19-8 times better than salt in 20,000.

2-3

2-1
1-8
1-7
1-6

Resistance of mixed liquids
Salt in 69 in tube 22. Salt in 142 in tube 23.

327

7'3
7-5
6-3
6

22

I2-65

El. = 2. [R. = 407000.]

seemed rather less,
sensibly less,
not sensib. greater,
sensib. greater.
Salt in 69 conducts 174 times better than salt in 142.

6-75 supposed right.

6-45 supposed right.

The same repeated.
6

5-8
5-6
5-8
7-3

7
6-8

Salt in 69 conducts 1-84 times better than salt in 142.

Salt in 999 in tube 12, distilled water in tube 20. El. = 2\.

[R. = 494000.]

seemed rather greater,
doubtful,
plainly greater,
not sensib. greater,
plainly less,
seemed rather less,
scarce sensibly less.

•83
7

sensib. less. N.B. The tubes had been measured
sensib. greater. between the last trial and this.

The distilled water was then changed for fresh.
•3 | | sensib. less.

Another bottle was filled with distilled water and tube 20 filled up again
with that.

•3 | | seemed rather less.

631] The tube 20 filled with the same distilled water mixed with ?fas of spirits
of wine.

•3 | | seemed not sensibly less.

Same mixture mixed with -fa more of spirits of wine, id est, sp* wine in 18 of
distilled water.

. -3 | | scarce sensib. less.

Equal bulks of sp* wine and distilled water.

•3 | | seemed scarce sensib. less.

Pure spirits of wine.

•3 | | seemed of 2 rather greater.

Therefore there is not much difference between the resisting power of the
above distilled water and spirits of wine and mixtures of the 2 : but of the 2,
spirits of wine resists least.

728

On Resistance to Electric Current

632] Tube 14.

[CALIBRATION OF TUBES.]

Dist. mid.
col. from
str. end

Length
col.

3-6

4-08

9-2
13-6
18-1

4-03
3'9
3-7

25-5
36-8

• 3-54
3-46
3-09

42

2-8

Tube 15.

- 3-6
+ 1-7

5-32

5-16

+ 7-9

4-95

+ 9'9

4-47

col. = 2-45.
40-6 inc. = 28-5 gr.
4-26 = 3 gr.

12-2 inches of tube next to bend contain \ part of
of that in col. 42-5 long.

col. = 3-25 gr.

4-67

After it was measured 7 inches were cut off from straight end, and the
numbers in the first col. are the distances from the shortened end. A new bend
was also made 12-8 from new end, and the part where the tube is equal to tube
14 is at 10-3 from D°.

633] Jan. 1781. The following tubes were measured over again by intro-
ducing a col. $ and measuring its length in 3 different places, the beginning of
the Ist col. being at J inch from bend, and the beginning of the second at the
end of the first. Another column was afterwards introduced whose length was
pretty nearly equal to the sum of the 3 former, and weighed.

NO of

ist

2nd

3rd

tube

col.

col.

col.

14

12-2

14-3

16

41-8 inc.

= 29-3 gr.

15

3-47

371

3-86

n-55

= 77

22

13-03

I3-65

14-6

41-8

= 100

23

3-6

3'3

3-09

10

24-5

5

12-65

14

13-5

42-1

= 489

17

3-25

3'iS

3-08

9.9

= 116

634] The two following tubes were measured by stopping up the end near
bend and weighing them with different quantities of $ in them, and measuring
the distance of the top of the column from straight end, whence it was found

that in

long beginning 1448

at \ inch = 2777

from bend 4033

long beginning 270
at \ inch from 543
bend weighed 881

14-8

N° 12 a col. 28-6
42-8

3-17

N° 20 a col. 6-27
9.97

Calibration of tubes

329

635] In the following result the column whose length is given in the 2nd
column is supposed to begin at \ inch from the bend.

By the resistance of each is meant

grains £ in each inch

[The resistance of a column of mercury one inch long weighing one grain
is -13 Ohms, and the resistance of saturated solution of salt at t° Centigrade is
to that of mercury as io8 is to 2015 + 45-1 (t — 18). Hence the resistance as
given by Cavendish must be multiplied by 6907 + 82-2 (59 — T) to convert it
into Ohms when the tube contains saturated solution at T° Fahrenheit.]

RESULT.

N°.

Length
column

Resist.

Log-
do.

Resist,
for each
inch

Log.
do.

14

12-2
26-5
42-5

14-99
35-58
61-36

1-1758
I-55I2
1-7879

1-229

1-343
1-444

•0894
•1280
•1595

15

3'47
7-18
11-04

4-907
10-518
16-591

•6908
1-0219
1-2199

1-414
1-465
I-503

•1505
•I658
•1769

22

13-03
26-68
41-28

5-157
10-817
17-294

•7124
1-0341
1-2379

•3958

•4054
•4190

9-5975
9-6079
9-6222

23

3-6
6-9
9-99

I-588
2-923
4-093

•2009
•4658
•6l20

•4412

•4237
•4096

9-6446
9-6270
9-6124

5

12-65
26-65
40-15

1-030
2-291
3-463

•OI26
•3600
•5395

•08138
•08596
•08626

8-9105
8-9343
8-9358

17

3-25
6-43
9-51

•2844
•5566
•8121

9-4539
9-7455
9-9096

•08750
•08656
•08539

8-9420

8-9373
8-9314

12

14-8
28-6
42-8

•1513
•2946

•4552

9-1798
9-4692
9-6582

•01022
•OIO3O
•01064

8-0095
8-0128
8-0268

2O

3-17
6-27
9-97

•03722
•07243
•11293

8-5708
8-8599
9-0528

•OII74
•OII55
•OII33

8-0697
8-0626
8-0541

330 On Resistance to JLlectric Current

COMPARISON OF RESISTANCE OF COPPER WIRE WITH THAT OF SAT. SOL.

636] The wire was wound on reel on bars of glass about f inch broad, the
distance of one round of wire from the next on same bar being -6.

The mean circumference of reel = 46-7 x a\/2*.

There were 8 rows of glass bars, and 28 rounds of wire on each row, and
on one row there was \ round over. Therefore whole length of wire

= 93-4 x \/2 x 8 x 28 + \ = 29,623 inches.

This weighed 2967 grains, consequently there are 9-984 inches to i grain.
N.B. There were many knots in the wire.

637] The resistance of this wire was attempted to be compared with that
of sat. sol. in tube 17 by shock melterf as in former experiments, but without
success. It was therefore compared by the sound of the explosion by discharging
the jars by a wire without its passing through my body; but in this there was
considerable difficulty, as the light of the spark passed through the wire was
very different from that passed through the water, the first being reddish and
the latter white. The sound also was of a different kind, the latter being sharper.

Distance of wires in tube 17.

El. = 4.

•68 not sensib. diff.

•6 scarce sensib. stronger.

•55 doubtful.

•5 seemed rather greater.

•45 sensib. greater.

•9 seemed sensib. less.
i do.
1-2 sensib. less.

- El. =

•g scarce sensib. less,

i not sensib. less.

1-2 seemed rather less.

•6 plainly greater.

•7 not sensib. greater

•4 not sensib. gr.

•3 seemed rather gr.

•2 plainly gr.

•8 seemed rather less.

1-2 plainly less.

* [The reel was probably square, with glass bars at the corners, the length of
the diagonal being 46-7 inches.]
f [See Arts. 585 and 622.]

Copper wire compared with solutions in tubes
1-2 plainly less.

331

•8 scarce sensib. less.

•4 sensib. gr.

•5 scarce sensib.

•5 sensib. gr.

•6 seemed rather gr.

•7 not sensib. diff.

i seemed rather less.

El. = 3-

El. = 4.

638] Two Leyden vials were made of barometer tubes filled with £ and
coated on outside with tinfoil. The quantity of electricity in them was found
to be very nearly the same, but that in N° i rather the greatest.

The charge of each of these tubes is about 714 inches, and that of the large
jars about 6100, and that of the three jars i, 2 and 4 together is also 6100*.

The shock of these tubes was received through my body in the same manner
as in trying the large jars, either by making the shock pass through the copper
wire or through the sat. sol. or receiving it in the simple manner without passing
through either: the experiment being tried as usual by charging both tubes
from the same conductor and receiving the charges of one one way and the
other the other.

639] It was found by repeated trials that the shock received through the
copper wire was plainly greater than the simple shock. When received through
the sat. sol. with wires f

in contact not sensib. less than simple.

at -i dist. seemed rather less, but doubtful.

•5
i
2
4
6-6

D°. scarce doubtful.

not doubtful.
D°.

considered less.

The tubes charged to ij by old electrometer.

640] It was also found by the small jars i, 2 or 4 that the shock received
through the wire was stronger than the simple shock.

The shock through the wire was also much greater than the simple shock
when the covering which was put over the wire to defend it from accidents
was taken away.

It was also plainly greater when the shock passed through only 3 rows of
the wire instead of the 8.

* [Probably globular inches. The numbers do not agree with those in Art. 583.]
•f {See end of Note 31.}

332 On Resistance to Electric Current

If the shock was received through 166 inches of the same wire not stretched
upon glass, without any knots in it, it seemed not at all greater, but if anything
less than the simple shock. It was the same if received through a piece of wire
of about the same length with 37 knots in it.

641] Some more of the same wire was stretched by silk into 32 x 12 rows,
each 78-7 inches long; consequently the whole length was 30,220 inches. It
weighed 3272 grains, id est, 9-24 inches to a grain.

The shock of the above-mentioned tubes was sensibly greater when received
through this last wire than when received simply, but was considerably less
than when received through the first wire.

They were then compared by sound with the same tube charged to sj,
when the sound of the shock passed through the new wire was sharper, and
the other fuller.

The sound of the shock passed through the new wire seemed full as brisk,
and the light as white as of that passed through -55 of sat. sol., but not near
so strong as when the wires in sat. sol. were in contact, the sound and light,
however, seemed nearly of the same kind. When distance in tube was i-i the
sound was evidently less loud than that with the wire.

When the shock was allowed to pass through both wires, the sound, I
thought, seemed much of the same kind as when passed through new wire
singly.

The shock passed through both wires felt plainly greater than the simple
shock, and the difference seemed greater than that between the new wire
simply and the simple shock.

In the foregoing the shock passed at the same time through both wires,
but it was then tried so that it should first pass through old and from thence
through new wire.

The shock felt then evidently stronger than the simple shock or that through
new wire alone, but I could not tell whether it was greater or less than that
through the old wire alone.

642] A piece of the same wire was wound about 150 times round one of
the slips of glass, and was laid flat on another of these slips which lay flat on
a table.

The shock of these tubes seemed rather greater when received through this
wire than when received simply, but the difference was not considerable, but
it seemed evidently less than the shock received through the new wire.

643] The wire was taken from off the reel with the slips of glass, and all
except a small part of it stretched round the garden in 14 rounds. The shock
of the above-mentioned tubes received through this wire felt plainly greater

Copper wire compared with solutions in tubes 333

than that passed through the wire stretched by the silk threads, and much
greater than the plain shock.

The shock passed through the sat. sol., wires in contact, seemed about
equal to the plain shock.

The spark passed through garden wire seemed rather redder than that
through the silk wire, but the difference was not remarkable.

The spark passed through garden wire seemed about as strong as that through
about -8 of an inch of saturated solution, but sensibly redder.

644] The reel was altered, and some copper wire silvered stretched upon it.

The mean circumference of reel = 44-05 x 2 Vz.

There were 12 rows of glass bars and 42 rounds of wire on each row, therefore
whole length of wire = 88-1 x A/2 x 12 x 42 = 62,790 inches. This weighed
5747 grains. Consequently there are 10-93 inches to i grain.

The shock received through this wire felt vastly stronger than the simple
shock; the shock of tube 2 received through the wire with electrometer at ij
seeming little less strong than the simple shock with the same tube and the
electrometer at if, but considerably stronger than with electrometer at ij.

645] The above-mentioned wire compared with sat. sol. by sound.

1-46. Seemed more brisk. The light of salt water white, the other very red.

1-7 D°\

2-5 DO

3-5 EL = -

5-5

8-7 I believe nearly the same.

8-3 seemed much weaker. El. = 3.

6 seemed rather greater.

7-5 doubtful.

8-5 seemed rather weaker.

6 seemed rather stronger.

7-2 doubtful. El. = 3.

8-5 seemed rather weaker.

6 doubtful.
5 D".

4 seemed stronger.
8-5 seemed rather weaker.
8-5 doubtful.

9-5 I believe rather less, certainly a sharper sound, but I believe rather
less loud.

7 seemed greater.

334

Resistance of Copper Wire
1-65 _

2

1-8

= '9

^=•55

U . .65

1-6

= •8

14-5

2

12-5

= 7-25

= 6-25

2 = 8'25

372

- 74

21-75

= 7-25

646] 74 of sat. sol. in tube 17 is equivalent to 29,623 inches of copper wire,
9-984 inches of which = i grain.

7-25 of sat. sol. in do. = 62,790 of copper wire, 10-93 of which = i grain*.

[Length of
wire

29,623
62,790

Resistance of pure copper

calculated from Matthiessen

annealed hard drawn

Resistance of saturated

solution in tube 17

calculated from

Kohlrausch

424
984

433
1004

413
4046]

[ 335 ]

RESULTS (OF EXPERIMENTS ON COMPARISON
OF CHARGES. ARTS. 438—595}

{From MS. N°. 16. See Table of Contents at the beginning of this volume.}

647] 1773, p. 92 [Art. 557]. The connecting wire to the two plates of
9-3 inches contains 1-4 inc. el. The connecting wire to the rosin plates of p. 86
[Art. 554], should contain rather more in proportion to its length than this,
id est, rather more than -28.

By p. 93 [Art. 557], the 4 rosin plates seemed to contain about \ inc. el.
less when placed close together than at dist. Let us therefore suppose that the
charge of 2 rosin plates placed close together with connecting wire between
them exceeds twice the charge of i plate by -28 inc. el., and that the charge
of 4 plates exceeds 4 times the charge of i by z\ times that quantity, or -7 inc.
el. Let us suppose, too, that the charge of the 2 double plates A & B with
connecting wire exceeds twice the charge of I by -28.

648] 8 square inches of elect. = 9 circular inches.

L.*

•1880.

Res. p. 5 [Art. 654].
= -649 = 9-8120.

glob. inc. el.
circ. inc. el.
circ. inc. el.

glob. inc. el.
N.B. By inc. el. is meant circular inches of electricity.

649] Mar. 13. P. 85 [Art. 553].

[Side of square equivalent to trial
plate when the balls separate

negatively,

positively.]

Difference

Mean

Circle i8i

17-66

13-34

4-32

I5-50

Double B

17-89

13-34

4-55

15-61

Double A

17-89

13-34

4-55

15-61

Circle 36

33-65

26-56

7-09

30-10

2 doub.

3I-38

24-08

7-30

27-73

D

29-61

22-53

7-08

26-07

* [These logarithms are correct only to three places of decimals, they should be
0-1875 ar"d 9-8122. See Note 35.]

336

Results of Experiments

Mon. Mar. 15. P. 85.

[Side of square equivalent to trial
plate when the balls separate

negatively, positively.]

Difference

Mean

Circ. 36

33-65 27-18

6-47

30-41

Circ. 30

28-42
28-10

Plate air

30-87

24-39

6-48

27-63

•2 doub.

3I-I3

24-39

6-74

27-76

D

29-86

22-84

7-02

26-35

Doub. B

18-22

13-82

4-40

16-02

Doub. A

18-22

13-82

4-40

16-02

Circle i8£

18-11

I3-58

4-53

15-84

Mar. 19. P. 86.

Circle 9

9-28

6-48

2-80

7-88

Rosin i

10-59

7-13

3-46

8-86

2

10-47

6-91

3-56

8-69

3

10-59

7-24

3-35

8-91

4

10-35

7-02

3-33

8-68

1 + 2 Rosin

18-56

I4-5I

4-°5

i6-53

3 + 4

18-67

14-62

4-05

16-64

Circle i8£

18-00

13-82

4-18

I5-91

Circle 36

33'9°

27-49

6-51

30-74

4 rosin

32-14

25-94

6-20

29-04

Mar. 23. P. 90 [Art. 554].

Circle . 9-3

9-28

6-48 2-80

7-88

Rosin i

10-22

7-13 3-09

8-67

2

IO-O9

7-02 3-07

8-55

3

IO-22

7-I3

3-09

8-67

4

10-22

7-13

3-09

8-67

Rosin 1 + 2

I8-56

14-06 4-50

16-31

3 + 4

I8-56

14-06 4-50

16-31

Circle i8J

17-66

13-34 4-32

I5-50

Circle 36

34-40

26-56 7-84

30-48

4 rosin

33-40

26-25 7-15

29-82

Mar. 24. P. 91.

Circle 36

33-65

27-49

6-16

30-57

Plate air i

30-75

25-01

5-74

27-88

4 rosin

31-76

25-32

6-44

28-54

rosin 1 + 2

18-34

I4-5I

3-83

16-42

3 + 4

18-78

I4-5I

4-27

16-64

Circle 18

18-11

13-82

4-29

15-96

Circle 9-3

9-56

6-48

3-08

8-02

Rosin i

10-83

7-35

3-48

9-09

2

10-83

7-46

3-37

9-14

3

10-83

7-46

3-37

9-14

4

10-83

7-46

3-37

9-14

on comparison of charges 337

650] [Results of Art 649.] By Mar. 13. [Art 553.]
Double plate = circ. i8J + -n sq. inc., or -12 inc. el.

Circ. 36 = 2 doub. + 2-67 inc. el. without allowance for communi-
cating wire, &c., or 2-95 with.

D = 2 doub. — i -60 with allowance.

Circ. 36"! (+ 3-19

\ = Circ. i8i x 2 { *.
D J \- 1-36

By Mar. 15 [Art. 553].
Doub. pi. = i8J + -20.

D I ,- -91 (- 1-51

pi. air ! = circ. i8J x 2 \ + -53 = 2 doub. j I- -13 with allowance,
circ. 36) (+ 3-66 1+ 3-26

651] All the following are with allowance.

Mar. 19 [Art. 554]. i ros. = circ. 9-3 + i-oi.

circ. i8J = 2 ros. - -47 = circ. 9-3 x 2 + 1-55.
circ. 36 = 4 ros. + 2-61 = circ. i8J x 2 + 3-55.

Mar. 23 [Art. 554]. i ros.= circ. 9-3 + -85.

circ. i8f = 2 ros. - -63 = circ. 9-3x2 + 1-07.
circ. 36 = 4 ros. + 1-44 = circ. i8J x 2 + 2-76.
1-32

Mar. 24 [Art. 554]. i ros. = circ. 9-3 + 1-25.

circ. i8J = 2 ros. - -36 = circ. 9-3 x 2 + 2-14.

circ. 36 = 4 ros. + 2-98 = circ. i8£ x 2 + 3-70.

Plate air i = circ. 36 - 3-03 = circ. i8J x 2 + -67,

By mean of all

circ. 36 = circ. i8| x 2 + 3-37.
circ. i8£ = circ. 9-3x2+ 1-59.

Therefore charge of circle of

37 inc. , i8i by 4-47

1, . exceeds 2ce charge of circ. of ,

i8£ inc. 9^ by 1-69

37 inc. exceeds 4 times charge of g| by 7-85.

652] *If charge circle is greater than it would be if placed at a great dis-
tance from any other body in ratio of a : a — 36,

charge circ. of i8£ should exceed in ratio of a : a - i8J and so on.
Therefore, if we suppose a = 167,

1 36 (9-89

charge circ. Ji8J should exceed its true charge by ^2-31 ,

b-3 I '55

and charge circ. 36 should exceed

2ce charge of i8J by 4-27 , . f -90 greater

' , which is \
4 times charge of 9-3 by 6-49 |/oo less

* [See Art. 338, and Note 24.]
c.p. i. 22

338 Results of Experiments

than by experiment, and charge circ. i8J should exceed 2ce charge of 9-3 by
i-ii, which is -58 less than by experiment.

We will therefore suppose that the charge of circ. i8J or of globe 12-1, as
found by experiment, exceeds the true charge in the ratio of 9 to 8, as it should
do if a = 167.

653] 1771. P. 15 [Art. 456].

doub. B contains A f-2i

. . V sq. inc. or { circ. inc. less than circ. i8i.
doub. A contains J {-14

1772. P. 12 [Art. 478].

doub. B , . -ii -12 .

. contains sq. me. or , circ. inc. more than circ. 18*.
doub. A -23 -26

1773. P. 85 [Arts. 553 & 650]. Each doub. plate contains -16 circ. inc.
more than circ. i8£.

1*25

654] P. 15. 1771 [Art. 456]. Globe cont. - - sq. inc. or -35 circ. inc. more

4
than circ. 18-5.

P. 12. 1772 [Art. 478]. Globe contains same as circ.
By mean, globe of 12-1 = circ. of 18-67, or

globe of 12 inc. = circ. of 18-5.

Therefore i circ. inc. = -65 glob. inc.

or i sq. inc. = -73 glob. inc.

DEF. The charge of globe i inc. diam. placed at great dist. from any other body
is called i glob. inc.

The circ. 18-5 = 13-5 glob. inc. *

The doub. plate A or B is supp. = 13-6 glob. inc.

655] P. 18, 1772 [Art. 483],

D, E, F & G cont. -68 inc. el. less than 2 doub.
P. 19, 1773 [Art. 509],

D & F cont. i inc. less than do.

P 59. 1773 [Art. 533],

D, E & F cont. 1 1 inc. less than do.
P. 85, 1773 [Art. 553],

— D cont. 1-6 less than 2 doub.

— D cont. 1-31 less than do.

D cont. 1-36 less than 2ce circ. i8J.

D cont. -91 less than do.

D is supposed to cont. 1-3 circ. inc. or -85 glob. inc. less than 2 doub., id est,
26-3 glob. inc.

* [See Note 35, p. 433.1

on spreading of electricity

656] 1773- P. 28 [Art. 515],

M cont. i inc. el. more than D + E + F.

P. 29 [Art. 515],

M cont. same as

P. 54 [Art. 528],

M cont. 2i)
K & L _ more than D + E + K N. i6|.

1773, P. 57 [Art. 530],

M cont. 2
K £ L r more than D + E + F. N. I4J.

P. 57 [Art. 530],

K & L C more than D + E + F. N. 16.

It is supp. that 7 more than D + E + F, id est, 8°'7 glob.

K & L — 1-5 79.9 5

inc. el.

657] 1773, P. 55 [Art. 529],

B or r cont. 3| 3 inc. el. less than K + L + M. N. 15.

P. 57 [Art. 530],

each cont. 33-7 less than do. N. 14^.

P. 58 [Art. 531],

each cont. 38-6 less. * N. 16.

It is supp. that A, B, and C each cont. 34-8 inc. less than K + L -t- M, id est,
29-1 less than gD, id est, 217-8 glob. inc.

658] By exper. of 1772,

F or G cont. 2 inc. more than D.
E 1-6

M cont. 3-86 less than E + F + G.
K & L 12-02 less.

F 10-72 less.

Therefore E + F + G cont. 5-6 more than 3D.

M 1-7 more.

K or L 6-4 less.

F 5-1 less.

A, B & C each contain 15-2 less than F + K + L.
or 33-1 less than cjD.

22 — 2

340 Results of Experiments

1773. P- 56 [Art. 530],

H cont. 10 inc. more than A + B + C.

1772, P. 29 [Art. 493],

H cont. the same as A + B + C.

H is supposed to contain 654 glob. inc.

*

659] Instantaneous spreading of el.\ Measures P. 19 [Art. 593].

A = 33-9 20-6

The area of the old coatings of C = 33-2 and circumf. - 20-4

H = 36-3 21-4

A = 31-8 /73'5

Area of slit coatings of -_ and circumf. j '

crown = 24-7 (69-6

A = 34-1 23-4

0 — ^^''•? 2^*2

Area of oblong coatings of .. & circumf.

H = 36-4 24-1

crown = 29-0 21-6

660] P. 15, 1773 [Art. 504],
White Cyl. cont. 7 inc. el. less than H.

P. 13 [Art. 502], 5

By mean it cont. 6 less than H.

P. 62 [Art. 536],

H with slit coat. cont. 77-5 more than white cyl.
crown with oblong coat. 33-7 N. 1.2.

P. 63 [Art. 536],

H with D° cont. 99-1 more than wh. cyl. N. II.

crown 43-8

P. 65 [Art. 537],

H with D° 70-8 more than wh. cyl. N. 14.

crown with slits 34

P. 66 [Art. 537],
crown D° cont. 20 more than wh. cyl. N. i2j.

P. 71 [Art. 541],

H D° cont. 74-1 more than wh. cyl. N. 21.

crown 67-3

* [See Art. 318.] \ [See Art. 3i<».l

P. 8r [Art. 550],

H with obi. cont.

H
crown

H
crown

on spreading of electricity

20-2 more than wh. cyl., st. el.* at 2 + 3
34 3+i

57-3

9 less than wh. cyl. i + 3

14-6 more than

341

P. 82 [Art

550],

H

18-5 more than wh. cyl.

A and C with circ.

coatings are supposed to contain same as B.

P. 62 [Art.

536],

A

r with slit coat.

cont. ] more than B

us. el.t

v<

13-5

1

A

C

i + 3

A

337

I N-

C

337

1 irreg. /

P. 63 [Art.

536],

A
C

18-51

15-2)

us. el.

A
C

13-5)
lo-ij

i + 3

A

18-51

C

18-5}

3+1 very irreg.

P. 65 [Art.

537].

with obi. - 4 1 more than B
\* 5-IJ

us. el.

A

5-i

C

1-7

1 + 3

A

o

C

17 less than B

3+ i

P. 66 [Art.

537].

A

more than B

us. el.

C

5-r

N. 15.

N.

N. ii.

14.

N. 12$.

661] By mean H with slits cont. 78 inc. el.l

\ more than wh. cyl.
with oblong 19 — — J

Crown with slits contains 27 inc. el. more than wh. cyl.
oblong 39 -

N.B. This is meant in dry weather & with usual deg. el.
The crown with slits exceeded wh. cyl. by 427 more with electrom. at
3+1 than at i + 3, and H with oblong exceeded wh. cyl. by 43 more with

* [Straw electrometer. See Art. 560, note.]

f [Usual degree of electrification. See Art. 329 and Note 10.]

34 2 Results of Experiments

electrom. at 3 + i than at i + 3, but it must be observed that this was only
one day's observ.

A 16

With usual deg. el. p exceeded B by

with electrom. at i + 3 by

&at

3+ i by

14-3
ii

26-1
26-1

A

with oblong exceeded B with us. el. by

with electrom. at i + 3 by

1-7

and at 3 + i by

662] Hence we have the following results: —

L. inc. el.
in each sq.
inc. circ. or
obi. coa.

Inc. el. in
slit coat,
more than
in oblong

Sq. inc.
coating
answering
toD"

Sq. inc.
of slit
coat,
equiv.
to obi.

Sq. inc.
in obi.

Dili.

Excess

s& SP,«f «*
above
oblong

A with us. el.

9-959

12-6

I-27

30-53

34-i

3-57

50-1 -072

el. at i + 3

9-2

•93

30-87

3-23

•065

el. at 3 + i

26-1

2-63

29-17

4-93

•098

C with us. el.

0-050

9-4

•91

29-49

33-3

3-81

53-3

•071

el. at i + 3

9'3

•92

29-48

3-82

•072

3 + !

27-8

2'75

27-65

5-65

•106

H with us. el.

4-437

59

2-12

31-18

36-4

5-22

45'0

•094

Crown do.

- 12

- '33

25-03

29-0 | 3-97

48-0

•083

663]

Inc. el.
In oblong
coating
- D° in
circular

Sq. inc. of
coating
equiv.
toD°

Sq. inc. of

circular
coa tin K
equiv. to
oblong

Sq. inc.
in oblong

Diff.

Excess
circumf.
oblong
above
circular

Sq. inc. equiv. to
excess of spreading
of elect, in oblong
above that in circular

A

3-4

•34

34-24

34'1

•14

2-8

•20

C

5-1

•51

33-71

33-3

•41

2-8

•20

H

i-3

•46

36-76

36-4

-36

2-7

•25

It is plain that the numbers in the 8th or last col. ought to be equal to those
in the 6th, as is nearly the case.

664] Whether charge of coated glass bears the same proportion to that of another
body whether el. is strong or weak *.

P. 61 [Art. 535], E on neg. side tried against sliding tin plates on pos.

Charge of E was B?ff part less with straw el. at 3 + i than at 1 + 3, the
diff. between neg. and pos. el. was much too small to be certain of.

* [Arts. 356, 451, 463, 535, 539, 551.]

on dielectric plates of air 343

P. 66 [Art. 538], a ball blown at end of therm, tube tried in same manner.
Charge just the same whether electron! . at i + 3 or 3 + i.

P. 68 [Art. 538], charge D° ^ less with el. at 3 + i than at i + 3.

P. 82 & 84 [Arts. 551 & 555], tried with machine for finding quant, el. in
common plates. No perceptible diff. between charge of E whether tried with
el. at i + 3 or 3 + i.

665] By P. 9 [Art. 661], it should seem that el. spread. -034 inc. more on
surface with greater degree of el. than with smaller, and therefore, as the diam.
coating of E or D is 2-16.

So that it should seem as if the charge of a coated plate in which the
spreading of the el. was prevented would be at least ^ less with the stronger
degree el. than with the weaker.

666J By exper. of P. 69 [Art. 539], it appeared that the charge of tin cyl.
was to that of D + E when electrified very weakly as 1-28 to i, and by P. 70
[Art. 539] as 1-24 to i. By mean as 1-26 to i*.

By mean of P. 76 [Art. 545], the charge of the same cyl. was to that of
D + E when electrified in the usual degree as 1-33 to I.

By mean of P. 77 [Art. 546], it came out as 1-37 to i, but this last can not
be depended on, as wire for making communication with ground was forgot
to be fixed f.

667] It should seem that the charge of D and E is increased \^ by spreading
of el. when elect, in usual degree, therefore if we suppose that the spreading is
insensible when electrified in very small degree, the charge of a glass plate is
less in proportion to that of another body when electrified with usual degree
el. than when elect, with a very small one in ratio of 1-26 to 1-51, or of 5 to 6.

668] On plate air •{.
[By Art. 517],

P. 32 pi. air i cont. i inc. el. more than D) ,

> by mean I more than D.
33 f I

The same plate air contained 2 inc. el. less when resting intirely on machine
than when resting by i corner.

* [See Arts. 358, 539, 545.]

f The comp. charge of the cyl. is 48-4 glob. inc. The real charge, supposing
that the wire contains 3-6 glob. inc. less when joined to cyl. than to D + E = 73-6,
and therefore its real charge exceeds the computed in the ratio of 1-52 to i. [See

Note 25.]

{ [See Art. 340.]

344 Results of Experiments

[By Art. 517], PI. air 2 cont. i inc. el. less than D + E.

P. 32, pi. air 3 10-5 inc. el. less than D + E + F.

P. 33, pi. air 4 i inc. el. less than D + E + F.

P. 36, pi. air 5 J more than D.

P. 37, Do.
By res. P. 5 [Art. 653], D, E, and F cont. 26-3 glob. inc.

Therefore pi. air i contains 27 glob. inc.

2 52

3 72-1

4 78-3

5 26-5

669] [Table of plates of air given in Art. 343.]
670]

Plate

air

Log. diam.
by thickness

I

1-1017

•7919

7452

6928

6332

2

1-4375

•9426

8689

7799

6679

3

1-6013

1-0163

9235

8054

6427

4

I-6525

•9747

8566

6939

4307

5

I-3895

•9458

8809

8045

7117

The- *

diam. real charge

(pet rrJnmnc arA Tru> Incr nt v PYPPQ<I —

thickness " " computed charge

above N, the value of N in 3ri1 {?} col. being i, in 2nd 1-05, in 3rd i-i, and in 4th 1-15.

The numbers in the 3rd column seem most uniform, and therefore it seems

diam. real charge

likely that [if] the ... . - was very great, - would equal i-i*.

thickness comp. charge

671] If we suppose the el. to spread -07 inc. on surf, thick plates and -09
on surf, thin ones, the result of Nairne's plates is as follows f.

i

Keal

Keal

_.

J-JlcLIfi.

DO.

Thick-

Computed

Real

charge

charge

corrected

ness

charge

charge

by com-

by

puted

diam.

D

2-155

2-295

•2057

3-2O

26-3

8-22

1

E

2-16

2-3

•2065

3-20

26-3

8-22

n-4

F

2 '175

2-3I5

•2115

3-17

26-3

8-30

J

K

2-265

2-445

•07712

9-69

79-9

8-29

L

2-335

2-5I5

•08205

9'°3

79'9

8-29

M

2-195

2;375

•07187

9-81

80-7

8-23

'j'jff\

A

6-57

6-71

•2112

26-6

217-8

8-18

32 o

B

6-6

6-74

•2132

26-6

217-8

8-18

C

6-5

6-64

•2065

26-7

217-8

8-16

H

6-8

6-98

•07556

80-6

654

8-n

93-7

* [See Art. 347.]

f [In Art. 324 the "Real charges" of this table are multiplied by • 1-2-2 for easy
comparison with the computed charges.]

on coated plates and cylinders
672] Computations of other flat plates of glass, &c.

345

Mean

charge

[Art. 507] P. 18

thick white

= D

[Art. 508] P. 19

DO.

26-3

P.

thin white

= D + E - -5

•33

52-3

P. 19

N

= D + E - 1-8

1-2

5I-9

[Art. 509] P. 20

P

= M-i5

97

71

)

[Art. 515] P. 28

= D + E + F - 9-5

6-1

72-8

f 7I-9

[Art. 509] P. 20
[Art. 515] P. 28

Q

= M-g
= D + E + F- i-i

57

7

74-8
78-2

[ 76-5

[Art. 509] P. 20

o

= M — 9

57

74-8

1 _-

[Art. 515] P. 28

= D + E + F - 5-8

3'8

f 75

[Art. 509] P. 20

white plate

= M - 77

5

757

[Art. 515] P. 28

= D + E + F - 77

5

73'9

[Art. 509] P. 20

oldG

= M - 7-3

4-8

75'9

[Art. 515] P. 28

= D + E + F - 5-8

3'8

[Art. 510] P. 21

crown A

-A--I3

8-5

[Art. 533] P. 59

-67

4.4

211-3

[Art. 510] P. 21
[Art. 533] P. 59

crown C

= A-i3

- 15

8-5
9-8

I 208-7

[Art. 527] P. 53

small ground crown

= D + E + F - 44)

[Art. 528] P. 54

-ail

2-4

76-5

[Art. 531] P. 57

-3 1

[Art. 527] P. 53

large ground crown

-C-I31

[Art. 528] P. 54

- 2

[Art. 531] P. 57

0

2-7

215-1

[Art. 533] P. 59

-17)

[Art. 507] P. 18

exper. rosin i

= doub. B - i

•06

13-5

rosin 2

E- 2

[Art. 519] P. 36

- 1-7

i-i

25-2

[Art. 509] P. 20

rosin 3

= M- 17

n-i

\ fr

[Art. 515] P. 28

= D + E + F-i6

10-4

| "9

[Art. 518] P. 35
[Art. 519] P. 36

rosin 4

= D + E+F

= DO.

} 78-9

[Art. 527] P. 53

rosin 5

= doub. B — i

.AC

[Art. 528] P. 54

- i

°5

I3

[Art. 518] P. 35
[Art. 519] P. 36

Ist made ros.

= D+2|

oj

•6

26-9

[Art. 518] P. 35

deph. bees wax i

T.R

^ A * C

[Art. 519] P. 36

-3

I o

24 5

[Art. 518] P. 35

deph. bees wax 2

=E+F-4 )

2, -r

crvC

- 2-5}

L

5° 5

[Art. 527] P. 53

deph. bees wax 3

[Art. 528] P. 54

I ?? j

30

TT

6-5

46-1

[Art. 533] P. 59

-11)

[Art. 527] P. 53

plain bees wax

= E + F-3-5)

[Art. 528] P. 54

0

»
-5

1-3

5J'3

[Art. 533] P. 59

-2-5)

[Art. 518] P. 35

lac

= D + E + F+ 1-5

37

[Art. 519] P. 36

+ 2-2

2

i-i

673] [Table given in Art. 370.]

The diam. was corrected on supposition that elect, spreads -07 if the thickness
of glass = -21, and -09 if thickness = -08, and so in proportion in other thicknesses.

346 Results of Experiments

674] [Table given in Art. 371.]

The correction of the diameter is the same as would be used according to
the preceding rule to a glass plate of 2ce the thickness, only the correction used
is never less than J^ inch.

675] On the glass cylinders.

inc. el.

D+I4-3 = 690 glob. me.

5«3,

p.

M,

gr. cyl. 2.

= H

+

45

inc. cl.

1

504,

p.

i5,

H

+

55

•6

"*"

-

503,

F.

14.

white jar

= H

+

74

-

H +

M-

34

Iw

504,

P.

15-

H +

M-

20

r

504,

P.

15,

gr. cyl. I

TT

+

M

+

30

5°2-

P.

T •»

13.

gr- cyl. 4

= C

T"\

+

K

T?

+

J x

T? ,

23
^

i

=754
=353

545, P. 75, therm, tube i=D+E+F+2 inc. el. = 80-2

546, P. 77, therm, tube 2 = D+E+F+2-8 = 80-7

676] [Table given in Art. 383.]

The white jar and cyl. and the 3 green cyl. are corrected for the spreading
of the electricity in the same manner as the flat plates, but the 2 therm, tubes
are not.

677] On the compound plates *.
P. 60, Art. 534.

The 3 plates A, B and C placed over each other with bits of lead between
contained 8-9 inc. el. less than K or L, therefore its charge = 74 inc. The
3rd part of the charge of A, B, or C is 72-6 inc.

The coatings taken from the 3 plates A, B, & C, the plates placed close
together and the outside surfaces coated with circles 6-6 in diam.
544, P. 75, it contained 7-5 inc. less than D + E + F.
546, P. 77, 6 less.

By mean it contains 6-7 less, therefore charge = 74-5.

The thickness of the 3 plates together is -6309. The computed charge of
a plate of that thickness with a coating 6-6 in diam. supposing the el. to spread
•07 inc. is 9-00, and the real charge of such a plate according to the mean ratio
of the real and computed charges of D, E, and F is 74-2.

678] A plate of exper. rosin about 8 inc. square was pressed out, thickness
irregular, but at a medium about -122. It was coated with circles 6-61 in diam. f

Art. 548, P. 79, its charge = K + D + E x i + -^
in afternoon x i + t\.

By mean it=K + D+Ex i + ^ = 135.

The real charge of this plate is to its computed, supposing the el. to spread
•07 inc., as 2-89 to i.

The charge of this plate is the same as that of a glass one -345 thick, sup-
posing ratio of real and computed charge the same as in A or B.

* [Arts. 379, 534.] f [Arts- 381- 552-]

on capacities of bodies of simple form 347

679] The coatings being taken from this plate it was included between the
plates B and H, and the outside surfaces coated with circles of 6-6 in. diam.

552, P. 83, it cont. 6-9 inc. el. less than K,

6-5

5-2 less than D + E + F,

by mean it contains 75-5 glob. inc.

The charge of plate glass of the same sort as Nairne's -634 thick (id esl,
equal to the sum of the thicknesses of the two glass plates and a glass plate
equiv. to the rosin) = 73-3, supposing the el. to spread the same on this plate
as on the rosin.

680] [Same as Art. 368.]

681] By res. P. 5 [Art. 654] a globe of 12 inc. contains as much el. as a
circle of 18-5 *, therefore by Prop. XXIX, p = \^, therefore

Charge of both plates
when distant

18 26 11

Sing. pi.

if p = 1£

i

1-046

1-078

1-172

o

I

1-062

1-108

1-249

infinite]

i

1-035

1-059

1-126

up = &

•353

•892

•920

i

0

•So i

•851

•887

i

inf.

•888

•919

•940

i

By Ist exp. 1772 [Art. 473] the proportions were

thus
By 2nd exp. [Art. 475]

•811
•798

•859

•840

-899
•894

it

i

682] The charges of the following bodies are supposed to bear the following
proportions to each other J.

globe 12- 1 diam. = i
circle 18-5 diam. = -992
square of 15-5 -958

oblong 17-9 x 13-4 -964

cyl. 35-9 by 2-53
54-2 -73

72 -185

1-028
-978
-966

Charge fsh[°rt] CyL f'887 ^

h th ° f 'on£ cy'' *s b°tween 1 '^9° & 1'573 tnat

globe being one, and

wire

1-894 1-619

* [Note 35.] t [Note 21.]

J [Exp. VII, Art. 281. The numbers here are different. See Art. 478.]

348 Results of Experiments on capacities of wires

if charge cyl. is supposed to be to that of globe whose diam. = length

cvl: : : | : N. L. 2!ength , their charge = 1-008 .
diam.

i -006

This ratio approaches about 5 times nearer to the first proportion than
the 2nd*.

The area of the oblong is the same as that of the square, and their charges
are very nearly the same.

The charge of a square is to that of a circle whose diam. = side square as
1-153 to if.

683] In exper. P. n, 1772 [Art. 477], the large wire should contain about
,,'.. less el. than if its diam. was double the small ones. Allowing for this, the
charges of the large wire at 36, 24 & 18 inc. dist. should be between the two
following proportions:

i -942" -915 -891,

i -901 -868 -844,

but I believe ought to approach about 5 times nearer to the former. The
observed proportions arej

i -903 -860 -850.

* [Note 12.]

t [This ratio is given in Art. 283 as 1-53 by a mistake of the Editor in copying,
see Note 22.]
t [Note 13.]

[ 349 ]

RESULTS {OF EXPERIMENTS ON RESISTANCE
OF SOLUTIONS, ARTS. 616—646}

{From MS. N°. 19. See Table of Contents at the beginning of this volume.}

Pump- water is 4Jh

684] Resistance of Salt in 1000 of rain water 9 - times less than that

Sea water 100 I

of rain water*.

685] A shock is diminished very nearly the same, but if anything rather
more, by passing through 9 tubes, 37 inches of which hold 3373 grains of $,
than through one tube, 37 inches of which hold 3480 grains of £ f.

686] A shock is as much diminished in passing through 6-8 inches of a tube,
37 inches of which hold 567 grains, as through 44^ of one 37 inches of which
hold 3480. So that resistance should seem as 1-03 power of velocity*.

687] If resistance is as -! j? power of velocity, the resistance of

times less than that of saturated solution of sea salts.
(607000

688] Resistance of sat. sol. S. S. in 99 of distilled water is 39 times greater
than that of the sat. sol.

Resistance of distilled water is 18 times greater than that of sat. sol. in
99 of distilled water ||.

689^] Experiments in 1776 and 1777.

No. of Conducts times T , Electro-

Exp. better than meter

1 Sat. sol. 8-6 salt in 69 14 & 15 4

2 8-94 22 & 23 rj

3 9-61 14 & 15 3 New solutions.

-< 5&I i D°Ja

iron wire is

o batery
7 10-31 5 & 17

10 9-02 22 & 23 I

9 7-79 salt in 29 diluted 22 & 23 i

with ij of water
supp. z\.

* [Arts. 398, 524.] f [Arts. 574, 575, &c.] J [Arts. 575, 629.]

§ [Arts. 398, 576, and Note 32.] || [Art. 577.]

K [Arts. 617-623.]

350 Results of Experiments

No. of Conducts times T . Electro-

Exp. better than meter

8 sat. sol. 3-51 salt in 29 22 & 23 I

15 4-38 22 & 23 i;

11 sat. sol. 20-5 salt in 149 14 & 15 3

12 19-6 22 & 23 I;;

4 salt in 69 9-57 salt in 999 22 & 23 ij •

5 salt in 999 9-92 salt in 20,000 12 & 20 if

13 salt in 149 17-3 salt in 2999 5 & 17 3

14 16-7 18 & 19 if

N.B. It is not said what water the solutions were made with. By the com-
parison of salt in 999 with salt in 20,000, it should seem either that they were
not made with distilled water, or that some mistake was made in the experi-
ment.

690] In Jan. 1777, salt in 2999 conducted about 70 or 90 times better than
some water distilled in the preceding summer, or about 25 or 50 times better
than the distilled water used in the year 1776 *.

Salt in 2999 conducted about 25 times better than salt in 150,000.

691] Salt in 69 conducts 1-97 times better in heat of 105° than in that of
58°tf.

The proportion of the resistance of sat. sol. and salt in 999 to each other
seems not much altered by varying heat from 50° to 95° J.

692] Salt in 150,000 seemed to conduct rather better than the same water
deprived of air by boiling in the same vial in which it was kept, and cooled
quick in water to prevent its absorbing much air. But the difference was not
more than might arise from error of experiment §.

693] Distilled water impregnated with fixed air from oil of vitriol and
marble conducted 2j times better than the same water deprived of its air by
boiling ||.

694] Conducting power of other saline solutions compared with that of
salt in 29 of water ^f.

Sal. Sylvii 1-08

Sal. amm. 1-13

Calc. S. S. -852

Glaub. salt -696

Quadran. Nitre -887

F. alk. -819

Spt. salt 1-72

Oil vitr. -783

D° another parcel 1-12

* [Art. 621.] f [Art. 619.] { [Art. 620.]

§ [See Art. 624.] || [Art. 625.] f [Art. 626 and Note 34.]

on electric resistance of solutions 3 5 i

N.B. The solutions of the neutral salts were all of such strength that the
acid in them was equiv. to that in salt in 29.

The f. alk. also was equiv. to that in salt in 29, but the acids were equiv.
to that in salt in 59.

695] Experiments in Jan., 1781*.

Sat. Sol.

o

o

3

1'

salt in 69

Tubes
14 & 15

Electro-
meter

8-8

Cot Sol

£

n

U)

O

1

o.«r

0"

3 °5

<-t-

T3 +

• o 97

Sat Sol

95

<T>

IsT

T3

9*

T-S8

(-*•

rr

Xf

p

i 91

Salt in 69

92
1-74

T>RA

salt in 142

22 & 23

2

I 1-79

Salt in 69

9-91

salt in 999

3i

J

10 3

,

10-57

11-31

K. 17

Ii

Salt in 999

10 75

20

salt in 20,000

12 & 2O

|

r>l

19-6

X9

™.S

2t

Salt in 20,000 conducts about 7 times better than distilled water.

696] Therefore the resistance of water with different quantities of salt in
[it] are as follows J :

Qu^tiy

Resistance

Log. do.

Resist,
x quant, salt

Log. do.

i by 3-78

I

12

1-91

•2810

•602

9-7793

30

3-97

•5988

•500

9-6992

70

8-8

•9445

•475

9-6769

143

15-75

I-I973

•416

9-6195

1000

93-02

1-9686

•352

9-5461

2OOOO

1823

3-2608

•345

9-5373

' [Art. 628.] f {Stated in Art. 628 as if} J [See Note 33.]

[ 352 ]

NOTES BY THE EDITOR

{JAMES CLERK MAXWELL}

i See Table of Contents at the beginning of this volume. }

NOTE i, ARTS. 5 AND 67.
On the theory of the Electric Fluid.

The theory of One Electric Fluid is here stated very completely by
Cavendish*. The fluid, as imagined by him, is not a purely hypothetical sub-
stance, which has no properties except those which are attributed to it for the
purpose of explaining phenomena. He calls it an elastic fluid, and supposes
that its particles and those of other matter have certain properties of mutual
repulsion or of attraction, just as he supposes that the particles of air are
indued with a property of mutual repulsion, but according to a different law.
See Art. 97 and Note 6. But in addition to these properties, which are all that
are necessary for the theory, he supposes that the electric fluid possesses the
general properties of other kinds of matter. In Art. 5 he speaks of the weight
of the electric fluid, and of one grain of electric fluid, which implies that a
certain quantity of the electric fluid would be dynamically equivalent to one
grain, that is to say, in the language of Boscovich and modern writers, it would
be equal in mass to one grain.

We must not suppose that the word weight is here used in the modern sense
of the force with which a body is attracted by the earth, for in the case of the
electric fluid this force depends entirely on the electrical condition of the earth,
and would act upward if the earth were overcharged and downward if the
earth were undercharged.

Cavendish also supposes that there is a limit to the quantity of the electric
fluid which can be collected in a given space. He speaks (Art. 20) of the electric
fluid being pressed close together so that its particles shall touch each other.
This implies that when the centres of the particles approach to within a certain
distance, the repulsion, which up to that point varied as the «th power of the
distance, now varies much more rapidly, so that for an exceedingly small
diminution of distance the mutual repulsion increases to such a degree that
no force which we can bring to bear on the particles is able to overcome it.

We may consider this departure from the simplicity of the law of force as
introduced in order to extend the property of "impenetrability " to the particles
of the electric fluid. It leads to the conclusion that there is a certain maximum

* For an earlier form of Cavendish's theory of electricity, see "Thoughts con-
cerning electricity" (Arts. 195-216), and Note 18.

The theory of a single electric Jiuid 353

density beyond which the fluid cannot be accumulated, and that therefore the
stratum of the electric fluid -collected at the surface of electrified bodies has a
finite thickness.

No experimental evidence, however, has as yet been obtained of any limit to
the quantity of electricity which can be collected within a given volume, or any
measure of the thickness of the electric stratum on the surface of conductors*,
so that if we wish to maintain the doctrine of a maximum density, we must
suppose this density to be exceedingly great compared with the density of the
electric fluid in saturated bodies.

A difficulty of far greater magnitude arises in the case of undercharged
bodies. It is a consequence of the theory that there is a stratum near the
surface of an undercharged body which is entirely deprived of electricity, the
rest of the body being saturated. Hence the electric phenomena of an under-
charged body depend entirely upon the matter forming this stratum. Now,
though on account of our ignorance of the electric fluid we are at liberty to
suppose a very large quantity of it to be collected within a small space, we
cannot make any such supposition with respect to ordinary matter, the density
of which is known.

In the first place, it is manifestly impossible to deprive any body of a greater
quantity of the electric fluid than it contains. It is found, indeed, that there
is a limit to the negativef charge which can be given to a body, but this limit
depends not on the quantity of matter in the body but on the area of its surface,
and on the dielectric medium which surrounds it. Thus it appears from the
experiments of Sir W. Thomson and those of Mr Macfarlane, that in air at the
ordinary pressure and temperature a charge of more than 5 units of electricity
[per cm.2,] positive or negative, can exist on the surface of an electrified body
without producing a discharge. In other media the maximum charge is different.
In paraffin oil, and in turpentine, for instance, it is much greater than in air J.
In air of a few millimetres pressure it is much less, but in the most perfect
vacuum hitherto made, the charge which may be accumulated before discharge
occurs is probably very great indeed.

Now this charge, or undercharge, whatever be its magnitude, can be accu-
mulated on the surface of the thinnest gold leaf as well as on the most massive

* [The modern molecular theories of the phenomena of galvanic polarization
touch on this subject.]

t [The phenomena of discharge in dielectrics, especially of negative electrons as
indicated in the text, are of course now much more thoroughly understood. Of.
Sir J. J. Thomson's treatise on Conduction of Electricity through Gases, or Prof. J. S.
Townsend's book on The theory of ionization...by collision.]

J By Messrs Macfarlane and Playfair's experiments the maximum electromotive
intensity is 364 for paraffin oil and 338 for turpentine. For air it is 73, between
disks one centimetre apart. (Trans. R. S. Ed. 1878.) They have since found that
the electric strength of the vapour of a certain liquid paraffin at 50 mm. pressure is
1-7 times that of air at the same pressure, and that the electric strength of a solid
paraffin which melts at 22°-^ C. is 2-5 when liquid and 5 when solid, that of air
being i.

c. p. i. 23

354 Note i : on the theory of the electric jiuid

conductors. Suppose that there is a deficiency of five units of electricity for
each square centimetre of the surface on both sides of a sheet of gold leaf whose
thickness is the hundred thousandth part of a centimetre. We have no reason
to believe the gold leaf to be entirely deprived of electricity, but even if it were,
we must admit that every cubic centimetre of gold requires more than a million
units of electricity to saturate it.

But we have by no means reached the limit of our experimental evidence.
For Cavendish shows in Art. 49 that if in any portion of a bent canal the re-
pulsion of overcharged bodies is so great as to drive all the fluid out of that
portion, then the canal will no longer allow the fluid to run freely from one end
to the other, any more than a siphon will equalize the pressure of water in two
vessels, when the water does not rise to the bend of the siphon.

Hence if we could make the canal narrow 'enough, and the electric repulsion
of bodies near the bend of the canal strong enough, we might have two con-
ductors connected by a conducting canal but not reduced to the same potential,
and this might be tested by afterwards connecting them by means of a con-
ductor which does not pass close to any overcharged body, for this conductor
will immediately reduce the two bodies to the same potential.

Such an experiment, if successful, would determine at once which kind of
electricity ought to be reckoned positive, for, as Cavendish remarks in Art. 50,
the presence of an undercharged body near the bend of the canal would not
prevent the flow of electricity.

But even if the electric fluid were not all driven out of the canal, but only
out of a stratum near the surface, the effective conducting channel would thereby
be narrowed, and the resistance of the canal to an electric current increased.

Now we may construct the canal of a strip of the thinnest gold leaf, and we
may measure its electric resistance to within one part in ten thousand, so that
if the presence of an overcharged body near the gold leaf were to drive the
electric fluid out of a stratum of it amounting to the ten thousandth part of
its thickness, the alteration might be detected. Hence we must admit either
that the one-fluid theory is wrong, or that every cubic centimetre of gold con-
tains more than ten thousand million units of electricity.

The statement which Cavendish gives of the action between portions of
the electric fluid and between the electric fluid and ordinary matter is nearly,
but not quite, as general as it can be made.

Since the mode in which the force varies with the distance is the same in
all cases, we may suppose the distance unity. Two equal portions of the electric
fluid which at this distance repel, each other with a force unity are defined to
be each one unit of electricity.

Let the attraction between a unit of the electric fluid and a gramme of
matter be a. Since we may suppose this force different for different kinds of
matter, we shall distinguish the attraction due to different kinds of matter by
different suffixes, as a1 and «2. Let the repulsion between two grammes of
matter entirely deprived of electricity be rn, these two portions of matter
being of the kinds corresponding to the suffixes i and 2.

Saturated bodies 355

Now consider a body containing M grammes of matter and F units of the
electric fluid. The repulsion between this body and a unit of the electric fluid

at distance unity is

F - Ma. (i)

If this expression is zero, the body will neither repel nor attract the electric
fluid. In this case the body is said to be saturated with the electric fluid, and
the condition of saturation is that every gramme of matter contains a units
of the electric fluid. From what we have already said, it is plain that a must
be a number reckoned by thousands of millions at least. The definition of
saturation as given by Cavendish is somewhat different from this, although on
his own hypothesis it leads to identical results. He makes the condition of
saturation to be (in Art. 6) " that the attraction of the electric fluid in any small
part of the body on a given particle of matter shall be equal to the repulsion of
the matter in the same small part on the same particle." Hence this condition

is expressed by the equation

Fa = Mr. (2)

But as the essential property of a saturated body is that it does not disturb
the distribution of electricity in neighbouring conductors, we must consider
the true definition of saturation to be that there is no action on the electric fluid.

Now [following Cavendish's ideas] consider two bodies of different kinds of
matter Ml and M2, and let each of them be saturated.

The quantity of electric fluid in the first will be

F! = Mjalt (3)

and that in the second F2 = M 2a2 . (4)

The repulsion between the two bodies will be

FIF* ~ FiMza2 - F2Af ^ + MjMfu , (5)

or, substituting the values of Fl and F2 , and changing the signs, it will be an

attraction equal to

AfjAf.teaj-fu). (6)

Now we know that the action between two saturated bodies is an attraction

equal to

M^Jt, (7)

where k is the constant of gravitation.

Hence we must make

•A - »u "" * (8)

for every two kinds of matter, k being the same for all kinds of matter.

According to Baily's repetition of Cavendish's experiment for determining
the mean density of the earth*,

(centimetre)3

k = 6-506 x io-* - —3 . (9)

gramme . second

* Baily's adopted mean for the earth's density is 5-6604, which, with the values
of the earth's dimensions and of the intensity of gravity at the earth's surface used
by Baily himself, gives the above value of k as the direct result of his experiments.
[Cavendish's value 5-45 has been shown by modern determinations to be too small
by less than two per cent.]

23 2

356 Note I : on the theory of the electric Jiuid

This number is exceedingly small compared to the product a^, which is
of the order zo20 at least. Hence rlt, the repulsion between two grammes of
matter entirely deprived of electricity, is of the same order as a^.

If we consider the attraction of gravitation as something quite independent
of the attractions and repulsions observed in electrical phenomena, we may

suppose

-

so that two saturated bodies neither attract nor repel each other.

Now we have adopted as the condition of saturation, that neither body
acts on the electric fluid in the other. But since neither body acts on the other
as a whole [gravitation now being a separate phenomenon] , each has no action
on the matter in the other, so that our definition of saturation coincides with
that given by Cavendish.

Lastly, let the two bodies not be saturated with electricity, but contain
quantities F1 + El and F2 + Ez respectively, where Fl = a^M^, and F2 = a^M^,
and El and E2 may be either positive or negative, provided that F + E must
in no case be negative.

The repulsion between the bodies is
(Fl + EJ (F2 + E2) - (F, + £x) M2«2 - (F2 + E2) M.a,
and this by means of equations (3) (4) and (10) is reduced to

Theory of Two Fluids.

In the theory of Two Electric Fluids, let V denote the quantity of the
Vitreous fluid and R that of the Resinous.

Let the repulsion between two units of the same fluid be b, and let the
attraction between two units of different fluids be c.

Let the attraction between a unit of either fluid and a gramme of matter
be a, and let the repulsion between two grammes of matter be r.

If a body contains V1 units of vitreous, Rt units of resinous electricity, and
M 1 grammes of matter, its repulsion on a unit of vitreous electricity will be

VJ) - Rf - M&,

and the repulsion on a unit of resinous electricity

- VjC + RJ - M ,«!.

The definition of saturation is that there shall be no action on either kind of
electricity. Hence, equating each of these expressions to zero, we find as the
conditions of saturation

The theory of two fluids 357

The total repulsion between the two bodies is

If we now put V1 = A/\ ~— + ^S,^ + ££1(

o — c

the total repulsion becomes

„ „ b + c „ „ b — c
£,£2 — + S,S2 -j- -

The first term of this expression, with its sign reversed, represents the
attraction of gravitation, and the second term represents the observed electric
action, but the other terms represent forces of a kind which have not hitherto
been observed, and we must modify the theory so as to account for their non-
existence.

One way of doing so is to suppose b = c and a^ = «2 = o. The result of this
hypothesis is to reduce the condition of saturation to that of the equality of
the two fluids in the body, leaving the amount of each quite undetermined. It
also fails to account for the observed action between the bodies themselves,
since there is no action between them and the electric fluids.

The other way is to suppose that S1 = S2 = o, or that the sum of the
quantities of the two fluids in a body always remains the same as when the body
is saturated. This hypothesis is suggested by Priestley in his account of the
two-fluid theory, but it is not a dynamical hypothesis, because it does not give
a physical reason why the sum of these two quantities should be incapable of
alteration, however their difference is varied.

The only dynamical hypothesis which appears to meet the case is to suppose
that the vitreous and resinous fluids are both incompressible, and that the
whole of space not occupied by matter is occupied by one or other of them.
In a state of saturation they are mixed in equal proportions.

The two-fluid theory is thus considerably more difficult to reconcile with
the facts than the one-fluid theory.

358 Note 2: distribution of attracting ftuid

NOTE 2, ARTS. 27 AND 282.
[Distribution in spheres and ellipsoids.}

The problem of the distribution, in a sphere or ellipsoid, of a fluid, the
particles of which repel each other with a force varying inversely as the nth
power of the distance, has been solved by Green*. Green's method is an ex-
tremely powerful one, and allows him to take account of the effect of any
given system of external forces in altering the distribution.

If, however, we do not require to consider the effect of external forces, the
following method enables us to solve the problem in an elementary manner.
It consists in dividing the body into pairs of corresponding elements, and
finding the condition that the repulsions of corresponding elements on a given
particle shall be equal and opposite.

(i) Specification of Corresponding Points on a line.

Let A^AZ be a finite straight line, let P be a given point in the line, and
let Ql and Q2 be corresponding points in the segments A-f and PA% respectively,
the condition of correspondence being

It is easy to see that when Ql coincides with Alt Q2 coincides with Az, and
that as Ql moves from Al to P, Q2 moves in the opposite direction frOm At
to P, so that when Ql coincides with P, Q2 also coincides with P.

Let Qi and Q2' be another pair of corresponding points, then

i i i i

Qt'P Af ~ PQt' PA2 •

Subtracting (i) from (2)

— — — —
Q,'P Q,P PQ2' PQ2'

QiQi C/Pi

QSP . Q,P PQ2' . PQZ •

If the points Ql and Qv' are made to approach each other and ultimately to
coincide, QjQi ultimately becomes the fluxion of Q, which we may write Qi,
and we have

* "Mathematical Investigations concerning the laws of the equilibrium of fluids
analogous to the electric fluid, with other similar researches," Transactions of the
Cambridge Philosophical Society, 1833. Read Nov. 12, 1832. See Mr Ferrers' Edition
of Green's Papers, p. 119.

in an ellipsoid 359

or corresponding elements of the two segments are in the ratio of the squares
of their distances from P.

Let us now suppose that A^PA^ is a double cone of an exceedingly small
aperture, having its vertex at P; let us also suppose that the density of the
redundant fluid at Ql is plt and at Q2 is pz; then since the areas of the sections
of the cone at Q1 and Q2 are as the squares of the distances from P, and since
the lengths of corresponding elements are also, by (5), as the squares of their
distances from P, the quantities of fluid in the two corresponding elements
at Q1 and Q2 are as piQ^P* to p2PQ2*. If the repulsion is inversely as the «th
power of the distance, the condition of equilibrium of a particle of the fluid
at P under the action of the fluid in the two corresponding elements at Ql

and<?'is

*. ...... (6)

We have now to show how this condition may be satisfied by one and the
same distribution of the fluid when P is any point within an ellipsoid or a
sphere. We must therefore express p so that its value is independent of the
position of P.

Transposing equation (i) we find

i i i i

' HA ' r>n " T~P • ...... (7 1

QJP

Multiplying the corresponding members of equations (i) and (7) and omitting
the common factor A^P .PAt,

we may therefore write, instead of equation 6,

Pi (A 1Q1 . Q1A ^ = p, (A jQs
Let us now suppose that A^A2 is a chord of the ellipsoid, whose equation is

aa 6" ca
If we write

X2 V2 Z'

A2 lir\

- 02- p-^2-/)>

then the product of the segments of the chord at (?j is to the product of the
segments at Q2 as the values of p2 at these points respectively, or

We may therefore write, instead of equation (9),

If, therefore, throughout the ellipsoid,

p = Cp"-*, (14)

where C is constant, every particle of the fluid within the ellipsoid will be in
equilibrium.

360 Note 2: distribution of an attracting fluid

We have in the next place to determine whether a distribution of this kind
is physically possible.

Let E be the quantity of redundant fluid in the ellipsoid; then

/•. C I p"-* \Ttabc p (i - p'rfdp
.'a

= 4-nabcC pn~3 (i - />2)4 dp ...... (15)

r r

2

Let p0 be the density of the redundant fluid if it had been uniformly spread
through the volume of the ellipsoid, then

...... (17)

and if p is the actual density of the redundant fluid,

When n is not less than 2, there is no difficulty about the interpretation of
this result.

The density of the redundant fluid is everywhere positive.
When n = 4 it is everywhere uniform and equal to p0 .

When n is greater than 4 the density is greatest at the centre and js zero at
the surface, that is to say, in the language of Cavendish, the matter at the
surface is saturated.

When n is between 2 and 4 the density of the redundant fluid at the centre
is positive and it increases towards the surface. At the surface itself the density
becomes infinite, but the quantity collected on the surface is insensible compared
with the whole redundant fluid.

When n is equal to 2, F (— — J becomes infinite, and the value of p is

zero for all points within the ellipsoid, so that the whole charge is collected on
the surface, and the interior parts are exactly saturated, and this we find to
be consistent with equilibrium.

When n is less than 2 the integral in equation (15) becomes infinite. Hence
if we assume a value for C in the interior parts of the ellipsoid, we cannot
extend the same law of distribution to the surface without introducing an
infinite quantity of redundant fluid. We might therefore conclude that if the
quantity of redundant fluid is given, we must make C = o, and suppose the
redundant fluid to be all collected at the surface, and the interior to be exactly

in an ellipsoid 361

saturated. But, on trying this distribution, we find that it is not consistent
with equilibrium. For when n is less than 2, the effect of a shell of fluid on a
particle within it is a force directed from the centre. If, therefore, a sphere of
saturated matter is surrounded by a shell of electric fluid, the fluid in the sphere
will be drawn towards the shell, and this process will go on till the different
parts of the interior of the sphere are rendered undercharged to such a degree
that each particle of fluid in the sphere is as much attracted to the centre by
the matter of the sphere as it is repelled from it by the fluid in the sphere and
the shell together. This is the same conclusion as that stated by Cavendish.

Green solves the problem, on the hypothesis of two fluids, in the following
manner.

Suppose that the sphere, when saturated, contains a finite quantity, E, of
the positive fluid, and an equal quantity of the negative fluid, and let a quantity,
Q, of one of them, say the positive, be introduced into the sphere.

Let the whole of the positive fluid be spread uniformly over the surface of
the sphere whose radius is a, so that if P' is the surface-density,

Green then considers the equilibrium of fluid in an inner and concentric
sphere of radius b, acted on by the fluid in the surface whose radius is a, and
shows that if the density of the fluid is

p = 2 P'a sin "-^ 77 (a2 - 62)^" (a2 - r2)-1 (62 - r2) ~2~ ,

there will be equilibrium of the fluid within the inner sphere.

The value of p is evidently negative if n is less than 2.

Green then determines, from this value of the density, the whole quantity
of fluid within the sphere whose radius is b, and then by equating this to — E,
the whole quantity of negative fluid, he determines the radius, b, of the inner
sphere, so that it shall just contain the whole of the negative fluid.

The whole of the positive fluid is thus condensed on the outer surface, the
whole of the negative fluid distributed within the inner sphere, and the shell
between the two spherical surfaces is entirely deprived of both fluids.

At the outer surface, the force on the positive fluid is from the centre, but
the fluid there cannot move, because it is prevented by the insulating medium
which surrounds the sphere.

In the shell between the two spherical surfaces the force on the positive
fluid would be from the centre. Hence if any positive fluid enters this shell, it
will be driven to the outer surface, and if any negative fluid enters, it will be
driven to the inner surface.

But all the positive fluid is already at the outer surface, and all the negative
fluid is already in the inner sphere, where, as Green has shown, it is in equili-
brium, and thus the fluids are in equilibrium throughout the sphere.

It may be remarked that this solution, according to which a certain portion
of matter becomes entirely deprived of both fluids, is inconsistent with the

362 Note 2: distribution of an attracting fluid

ordinary statements of the theory of two fluids, which usually assert that
bodies, under all circumstances, contain immense quantities of both fluids.

In the two-fluid theory, by depriving matter of both fluids, we get an in-
active substance which gives us no trouble, but in the one-fluid theory, matter
deprived of fluid exerts a strong attraction on the fluid, the consideration of
which would considerably complicate the mathematical problem.

[In connexion with this remark and with Note 3 a quotation from Green's
Memoir of 1833 (§ 6) is relevant.

" In order to explain the phenomena which electrified bodies present,
Philosophers have found it advantageous either to adopt the hypothesis of
two fluids, the vitreous and resinous of Dufay for example, or to suppose with
jEpinus and others, that the particles of matter when deprived of their natural
quantity of electric fluid, possess a mutual repulsive force. It is easy to per-
ceive that the mathematical laws of equilibrium deducible from these two
hypotheses ought not to differ, when the quantity of fluid or fluids (according
to the hypothesis we choose to adopt) which bodies in their natural state are
supposed to contain is so great, that a complete decomposition shall never be
effected by any forces to which they may be exposed, but that in every part
of them a farther decomposition shall always be possible by the application of
still greater forces. In fact the mathematical theory of electricity merely con-
sists in determining p the analytical value of the fluid's density, so that the
whole of the electrical actions exerted upon any point p, situated at will in the
interior of the conducting bodies, may exactly destroy each other, and conse-
quently p have no tendency to move in any direction. For the electric fluid
itself, the exponent n is equal to 2, and the resulting value of p is always such
as not to require that a complete decomposition should take place in the body
under consideration; but there are certain values of n for which the resulting
values of p will render $pdv greater than any assignable quantity; for some
portions of the body it is therefore evident that how great soever the quantity
of the fluid or fluids may be, which in a natural state this body is supposed to
possess, it will then become impossible strictly to realize the analytical value
of p, and therefore some modification at least will be rendered necessary, by the
limit fixed to the quantity of fluid or fluids originally contained in the body,
and as Dufay's hypothesis appears the more natural of the two, we shall keep
this principally in view, when in what follows it may become requisite to
introduce either."]

Infinite plate with plane parallel surfaces.

The distribution of the fluid in an infinite plate with plane parallel surfaces
is given in the general solution which we have obtained for a body bounded
by a quadric surface, namely, p —- Cpn~*.

In the case of the plate we must suppose it bounded by the planes x = + a,
and x — — a, and then p is defined by the equation

x2 = a2 (i - />»).

in disks and thin rods 363

If a is the quantity of fluid in a portion of the plate whose area is unity,

/•+ rt

= I pdx = Ca •

J -a

r /«-

\ 2

in disk.

The distribution in an infinitely thin disk may be deduced from that in an
ellipsoid by making one of the axes infinitely small. It is better however to
proceed by the method which we have already employed, only that instead of
supposing the line AtPA2 (Fig. p. 358) to be a double cone, we suppose it to
be a double sector cut from the disk. The breadth of this sector is proportional
to the distance from P, so that the condition of equilibrium of the repulsions
of two corresponding elements whose surface-densities are cr, and at is

,r-f)_P 3-n _ - n P 3-n

whence we find, as before, that if the equation of the edge of the disk is

then the surface-density at any point is

a = Cpn-\

The quantity of fluid in the disk is found by integrating over the surface
of the disk, and is 2 abC

<? = T=-T-

Hence if CTO is the mean surface-density, the surface-density at any point
is given by the equation

rt X n

-

Thin rod.

The distribution on an infinitely thin rod is found by considering A^
a rod of uniform section, which leads to the equation

where \ is the linear density, and if the length of the rod is 2a, and if x is the
distance from the middle, and x2 = a2 (i — p2), the distribution of the linear
density is given by A = 2

The charge of the whole rod is

Ca —Z- — = 2,

364 Note 2 : distribution of attracting ftma in thin rods
so that if A,, denotes the mean linear density,

2r +

when n = 2, A = A,,, or the density is uniform.

Since the fluid is in equilibrium in all these cases, the potential is uniform
throughout the body. We may therefore determine the value of the potential
at any point within the body by finding its value at any selected point, as for
instance at the centre. If de be an element of the fluid, and r its distance from
the given point, the corresponding element of the potential due to the force

whose value is er~n is erl~n.

n — i

We thus find for the potential of the sphere

n - i

When n becomes equal to 4, V becomes infinite.
When n is equal to 2, V= Qa~l.

For the plate bounded by parallel planes, V is infinite, except for values
of n between 3 and 4, for which

(n -i)(«- 3)

/T\

where <TO is the quantity of fluid in unit of area of the plate.
For a circular disk

in which n must be between i and 3.
When n = 2, V =- Oa~l.

2 *

For an infinitely narrow rod

Note 3: canals of incompressible Jiuid 365

NOTE 3, ART. 69.
On canals of incompressible fluid.

It appears from several passages (Arts. 40, 236, 273, 276, 278, 294, 348)
that Cavendish considered that the weakest point in his theory was the assump-
tion that the condition of electric equilibrium between two conductors connected
by a fine wire is the same as if, instead of the wire, there were a canal of in-
compressible fluid defined as in Art. 69.

It is true that the properties of the electric fluid, as defined by Cavendish
in Art. 3, are very different from those of an incompressible fluid. But it is
easy to show that the results deduced by Cavendish from the hypothesis of
a canal of incompressible fluid are applicable to the actual case in which the
bodies are connected by a fine wire.

In what follows, when we speak of the electrified body or bodies, the canal
or the wire is understood not to be included unless it is specially mentioned.

Cavendish supposes the canal to be everywhere exactly saturated with the
electric fluid, and that the only external force acting on the fluid in the canal
is that due to the electrification of the other bodies.

Since this resultant force is not in general zero at all points of the canal,
the fluid in the canal cannot be in equilibrium unless it is prevented from
moving by some other force. Now the condition of incompressibility excludes
any such displacement of the fluid as would alter the quantity of fluid in a
given volume, and the stress by which such a displacement is resisted is called
isotropic (or hydrostatic) pressure. In a hypothetical case like this it is best,
for the sake of continuity, to suppose that negative as well as positive values
of the pressure are admissible.

In the electrified bodies themselves the properties of the fluid are those
defined in Art. 3. The fluid is therefore incapable of sustaining pressure except
when its particles are close packed together, and as it cannot sustain a negative
pressure, the pressure must be zero in the electrified bodies, and therefore also
in the canal at the points where it meets these bodies.

The condition of equilibrium of the fluid in the canal is

dV dp

P -j- + j = °.
r ds ds

where V denotes the potential of the electric forces due to the electrified bodies,
p the density, and p the pressure of the fluid in the canal, and s the length of
the canal reckoned from a fixed origin to the point under consideration.

Since by the hypothesis of incompressibility, p is constant,

pV + p = C,

where C is a constant ; and if we distinguish by suffixes the symbols belonging
to the two ends of the canal where it meets the bodies Av and At,

366 Note 3: canals of incompressible jtuid

But we have seen that pl = p2 = o. Hence dividing by p we find for the
condition of equilibrium v v

or the electric potential of the two bodies must be equal.

We arrive at precisely the same condition if we suppose the bodies con-
nected by a fine wire which is made of a conducting substance.

Let V as before be the potential at any given point due to the electrified
bodies, and let V1 be its value in Alt and F2 its value in A2, and let V be the
potential due to the electrification of the wire at the given point, then the
condition of equilibrium of the electricity in the wire is that V + V must be
constant for all points within the substance of the wire. Hence at the two ends
of the wire F, + F.'-^* F.'.

Hence the actual potential due to the bodies and the wire together is the same
in A1 and A2.

The only difference, then, between the actual case of the wire and the
hypothetical case of the canal is that the surface of the wire is charged with
electricity in such a way as to make its potential everywhere constant, whereas
the canal is exactly saturated, and the effect of variation of potential is counter-
acted by variation of pressure.

Hence the canal produces no effect in altering the electrical state of the other
bodies, whereas the wire acts like any other body charged with electricity.

The charge of the wire, however, may be diminished without limit by
diminishing its diameter. It is approximately inversely proportional to the
logarithm of the ratio of a certain length to the diameter of the wire. Hence
by making the wire fine enough, the disturbance of the distribution of electricity
on the bodies may be made as small as we please.

[GREEN ON CAVENDISH'S THEORY.]

From the [beginning of the"] Preface [1828] to Green's "Essay on the Application
of Mathematical Analysis to the Theories of Electricity and Magnetism."

"After I had composed the following Essay, I naturally felt anxious to
become acquainted with what had been effected by former writers on the same
subject, and, had it been practicable, I should have been glad to have given, in
this place, an historical sketch of its progress ; my limited sources of informa-
tion, however, will by no means permit me to do so; but probably I may here
be allowed to make one or two observations on the few works which have fallen
in my way, more particularly as an opportunity will thus offer itself, of noticing
an excellent paper, presented to the Royal Society by one of the most illus-
trious members of that learned body, which appears to have attracted little
attention, but which, on examination, will be found not unworthy the man who
was able to lay the foundations of pneumatic chymistry, and to discover that
water, far from being according to the opinions then received, an elementary
substance, was a compound of two of the most important gases in nature.

Green on Cavendish's Electric Theory 367

"It is almost needless to say the author just alluded to is the celebrated
CAVENDISH, who having confined himself to such simple methods as may
readily be understood by any one possessed of an elementary knowledge of
geometry and fluxions, has rendered his paper accessible to a great number of
readers; and although, from subsequent remarks, he appears dissatisfied with
an hypothesis which enabled him to draw some important conclusions, it will
readily be perceived, on an attentive perusal of his paper, that a trifling altera-
tion will suffice to render the whole perfectly legitimate.

"Little appears to have been effected in the mathematical theory of elec-
tricity, except immediate deductions from known formulae, that first presented
themselves in researches on the figure of the earth, of which the principal are,
— the determination of the law of the electric density on the surfaces of con-
ducting bodies differing little from a sphere, and on those of ellipsoids, from
1771, the date of CAVENDISH'S paper, until about 1812, when M. POISSON pre-
sented to the French Institute two memoirs of singular elegance, relative to the
distribution of electricity on the surfaces of conducting spheres, previously
electrified and put in presence of each other.

[Footnote.] — "In order to make this quite clear, let us select one of Caven-
dish's propositions, the twentieth for instance [Art. 71], and examine with some
attention the method there employed. The object of this proposition is to show,
that when two similar conducting bodies communicate by means of a long
slender canal, and are charged with electricity, the respective quantities of
redundant fluid contained in them will be proportional to the n — i power of
their corresponding diameters ; supposing the electric repulsion to vary inversely
as the n power of the distance.

"This is proved by considering the canal as cylindrical, and filled with in-
compressible fluid of uniform density: then the quantities of electricity in the
interior of the two bodies are determined by a very simple geometrical con-
struction, so that the total action exerted on the whole canal by one of them
shall exactly balance that arising from the other; and from some remarks in
the 27'" proposition [Arts. 94, 95] it appears the results thus obtained agree
very well with experiments in which real canals are employed, whether they
are straight or crooked, provided, as has since been shown by Coulomb, n is
equal to two. The author, however, confesses he is by no means able to de-
monstrate this, although, as we shall see immediately, it may very easily be
deduced from the propositions contained in this paper.

"For this purpose let us conceive an incompressible fluid of uniform density,
whose particles do not act on each other, but which are subject to the same
actions from all the electricity in their vicinity, as real electric fluid of like
density would be; then supposing an infinitely thin canal of this hypothetical
fluid, whose perpendicular sections are all equal and similar, to pass from a
point « on the surface of one of the bodies through a portion of its mass, along
the interior of the real canal, and through a part of the other body, so as to
reach a point A on its surface, and then proceed from A to a in a right line,

368 Note 4: charges on two adjacent disks

forming thus a closed circuit, it is evident from the principles of hydrostatics,
and may be proved from our author's 23rd proposition [Art. 84], that the whole
of the hypothetical canal will be in equilibrium, and as every particle of the
portion contained within the system is necessarily so, the rectilinear portion aA
must therefore be in equilibrium.

"This simple consideration serves to complete Cavendish's demonstration,
whatever may be the form or thickness of the real canal, provided the quantity
of electricity in it is very small compared with that contained in the bodies.

"An analogous application of it will render the demonstration of the 22nd
proposition [Art. 74] complete, when the two coatings of the glass plate com-
municate with their respective conducting bodies by fine metallic wires of any
form."

NOTE 4, ART. 83.

On the charges of two equal parallel disks, the distance between them being
small compared with the radius.

The theory of two parallel disks, charged in any wa.y, may be deduced from
the consideration of two principal cases.

The first case is when the potentials of the two disks are equal. If the
distance between the disks is very small compared with their diameter, we may
consider the whole system as a single disk, the charge of which is approximately
the same as if it were infinitely thin. Hence if V be the potential, and if we
write A for the capacity of the first disk, and B for the coefficient of induction
between the two disks, the charge of the first disk is

and that of the second is

If we make V1 = V2 = V,

Q1 + Q,= 2(A-B) V.
Hence, by Note 2,

The second case is when the charges of the disks are equal and opposite.
The surface-density in this case is approximately uniform except near the
edges of the disks. I have not attempted to ascertain the amount of accumu-
lation near the edge except when n = 2. If we suppose the density uniform,
then for a charge of the first disk equal to na2, its potential, when b the distance
between the disks is small compared with a the radius, will be approximately

27r -

Note 5.- on zero of potential 369

Hence, since F2 = — Ft

A + B = £ (n - i) (3 - n) aa&"-3,

and we find

A = i (« - i) (3 ~ n)

When M = 2, . _ i «2 <

46 277 '

46 277 '

In this case, however, we can carry the approximation further, for it is
shown in Note 20 that

A - B=-(a + --. b log ~ )

TT\ 277 5 bJ

It is shown in "Electricity and Magnetism," Art. 202, that when two disks
are charged to equal and opposite potentials, the density near the edge of each
disk is greater than at a distance from it, and the whole charge is the same as

if a strip of breadth — had been added all round the disk.

277

Hence A + B = 1. ,(a + —}*

2b \ 277/

a2 a b

and ^=<L + Aa + _I_

40 477 477"

D «2 i i , /. a i\

B = -j- a = b [ log r — I .

40 477 4772 \ b 47

NOTE 5, ART. 90.
[On zero of Potential. See Note 7.]

This proposition seems intended to justify those experimental methods in
which the potential of the earth is assumed as the zero of potential.

Cavendish, by introducing the idea of degrees of electrification, as dis-
tinguished from the magnitudes of overcharge and undercharge, very nearly
attained to the position of those who are in possession of the idea of potential*.
But the very form of the phrases " positively or negatively electrified," which
Cavendish uses, confers an importance on the limiting condition of "no electrifi-
cation," which we hardly think of attributing to "zero potential." For we
know that all electrical phenomena depend on differences of potential, and that
the particular potential which we assume for our zero may be chosen arbitrarily,
because it does not involve any physical consequences.

[* See vol. n of this Edition, Preface.]

c. p. i. 24

37° Note 6: on the molecular constitution of air

It is true that the mathematicians define the zero of potential as the
potential at an infinite distance from the finite system which includes the
electric charges. This, however, is not a definition of which the experimentalist
can avail himself, so he takes the potential of the earth as a zero accessible to
all terrestrial electricians, and each electrician "makes his own earth."

The earth-connexion used by Cavendish is described in Art. 258. But when
the whole apparatus of an electrical experiment is contained in a moderate
space, such as a room, it is convenient to make an artificial "earth" by con-
necting by metal wires the case of the electrometer with all those parts of the
apparatus which are intended to be at the same potential, and calling this
potential zero.

It appears by observation, that in fine weather the electric potential at a
point in the air increases with the distance from the earth's surface up to the
greatest heights reached by observers, and in all parts of the earth. It is only
when there are considerable disturbances in the atmosphere that the potential
ever diminishes as the height increases. Hence the potential of the earth is
probably always less than that of the highest strata of the atmosphere.

If the earth and its atmosphere together contain just as much electricity
as will saturate them, and if there is no free electricity in the regions beyond,
then the potential of the outer stratum of the atmosphere will be the same as
that at an infinite distance, that is, it will be the zero of the mathematical
theory, and the potential of the earth will be negative.

NOTE 6, ART. 97.
On the Molecular Constitution of A ir.

The theory of Sir Isaac Newton here referred to is given in the Principia,
Lib. it, Prop. xxin.

Newton supposes a constant quantity of air enclosed in a cubical vessel
which is made to vary so as to become a cube of greater or smaller dimensions.
Then since by Boyle's law the product of the pressure of the air on unit of
surface into the volume of the cube is constant; and since the volume of the
cube is the product of the area of a face into the edge perpendicular to it, it
follows that the product of the total pressure on a face of the cube into the edge
of the cube is constant, or the total pressure on a face is inversely as the edge
of the cube.

Now if an imaginary plane be drawn through the cube parallel to one of
its faces, the mutual pressure between the portions of air on opposite sides of
this plane is equal to the pressure on a face of the cube. But the number of
particles is the same, and their configuration is geometrically similar whether
the cube is large or small. Hence the distance between any two given molecules
must vary as the edge of the cube, and the force between the two molecules
must vary as the total force between the sets of molecules separated by the

Historical survey 371

imaginary plane, and therefore the product of the repulsion between two given
molecules into the distance between them must be constant, in other words the
repulsion varies inversely as the distance.

In this demonstration the repulsion considered is that between two given
molecules, and it is shown that this must vary inversely as the distance between
them in order to account for Boyle's law of the elasticity of air.

If, however, we suppose the same law of repulsion to hold for every pair of
molecules, Newton shows in his Scholium that it would require a greater pressure
to produce the same density in a larger mass of air.

We must therefore suppose that the repulsion exists, not between every
pair of molecules, but only between each molecule and a certain definite number
of other molecules, which we may suppose to be denned as those nearest to the
given molecules. Newton gives as an example of such a kind of action the
attraction of a magnet, the field of which is contracted when a plate of iron is
interposed, so that the attractive power appears to be bounded by the nearest
body attracted.

If the repulsion were confined to those molecules which are within a certain
distance of each other, then, as Cavendish points out, the pressure arising from
this repulsion would vary nearly as the square of the density, provided a large
number of molecules are within this distance. Hence this hypothesis will not
explain the fact that the pressure varies as the density.

On the other hand, if the repulsion were limited to particular pairs of
particles, then since the particles are free to move, these pairs of particles
would move away from each other till only those particles were near each other
between which the repulsive force is supposed not to exist.

It would appear therefore that the hypothesis stated by Newton and adopted
by Cavendish is the only admissible one, namely, that the repulsive force is
inversely as the distance, but is exerted only between the nearest molecules.

Newton's own conclusion to his investigation of the properties of air on the
statical molecular hypothesis is as follows: — "An vero Fluida Elastica ex
particulis se mutuo fugantibus constent, Quastio Physica est. Nos proprie-
tatem Fluidorum ex ejusmodi particulis constantium mathematice demon-
stravimus, ut Philosophis ansam prabeamus Quaestionem illam tractandi."

The theory that the molecules of elastic fluids are in motion satisfies the
conditions of the question as pointed out by Newton in a much more natural
manner than any modification of the statical hypothesis.

According to the kinetic theory of gases, each molecule is in motion, and
this motion is during the greater part of its course undisturbed by the action
of other molecules, and is therefore uniform and in a straight line. When however
it comes very near another molecule, the two molecules act on each other for
a very short time, the courses of both are changed and they go on in the new
courses till they encounter other molecules.

24 — 2

372 Note j : idea of electric potential due to Cavendish

It would appear from the observed properties of gases that the mutual
action between two molecules is insensible at all sensible distances. As the
molecules approach, the action is at first attractive, but soon changes to a
repulsive force of far greater magnitude, so that the general character of the
encounter depends mainly on the repulsive force.

On this theory, the elasticity of the gas may still be said in a certain sense
to arise from the repulsive force between its molecules, only instead of this
repulsive force being in constant action, it is called into play only during the
encounters between two molecules. The intensity of the impulse is not the
same for all encounters, but as it does not depend on the interval between the
encounters, we may consider its -mean value as constant. The average value
of the force between two molecules is in this case the value of the impulse
divided by the time between two encounters. Hence we may say that the
force is inversely as the distance between the molecules, and that it acts between
those molecules only which encounter each other.

For an earlier investigation by Cavendish of the properties of an elastic
fluid, see Note 18.

NOTE 7, ART. 101.

[On the idea of Electric Potential, as introduced by Cavendish : see p. 18.]

Here Cavendish endeavours to fix a precise meaning to the terms "positively
and negatively electrified," terms which he found current among electricians,
but not well defined. The meaning which he here fixes to them, and which he
afterwards makes much use of, is equivalent to the meaning of the modern
term potential, as used by practical electricians. The idea of potential as used
by mathematicians is expressed by Cavendish in his theory of canals of in-
compressible fluid.

In the "Thoughts concerning Electricity," and in the unpublished papers,
degrees of electrification are spoken of. These degrees of electrification are
measured in the experimental researches by means of electrometers of different
kinds, and since he has compared the indications of his electrometers with the
degrees of electrification required to make a spark pass between the balls of
Lane's discharging electrometer, we may express all these measurements in
modern units, though Cavendish's original electrometers no longer exist.

I have not been able to trace the idea of electric potential in the work of
yEpinus, so that Cavendish seems the first to have made use of it. The relation
between the charge of a body and the degree of its electrification is the main
object of Cavendish's experimental researches, and the results of his work were
expressed in the material form of a collection of coated plates, each of which
had a capacity equal to that of a sphere of known diameter.

The leading idea in the great experimental work of Coulomb seems to be
the measurement of the charges of the different bodies of a system and of parts
of these bodies. Perhaps the most valuable of Coulomb's many contributions
to experimental physics was the measurement of the surface-density of the

Note 8.1 forces between influencing conductors 373

distribution of electricity on a conductor on different parts of its surface by
means of the proof plane. The numerical results obtained by Coulomb led
directly to the great mathematical work of Poisson. I have not been able,
however, to trace, even in those parts of Coulomb's papers where it would
greatly facilitate the exposition, any idea of potential as a quantity which has
the same value for all parts of a system of conductors communicating with
each other.

NOTE 8 [ART. 118].
Cases of Attraction and Repulsion.

The statements of Cavendish may be illustrated by the case of two spheres
A and B, whose radii are a and b, and the distance between their centres c.
If the charge of A is i, and that of B is o, the attraction is

b3 b6 W b9 + Ab«a3
2?+3?+4?+5 -- 3T - + &c-

an expression which shows that it depends chiefly on the value of b, the radius
of the sphere without charge.

If the sphere B, instead of being without charge, is at potential zero, that
is, if it is not insulated, the attraction is

b b3 a3b* +

+&c-

This expression exceeds the former by

b

—r + &c.
c c7

The number of times that the attraction of an uninsulated sphere exceeds
that of a sphere without charge is therefore approximately

which is greater as the sphere is smaller. This agrees with what Cavendish
says in Art. 108.

With respect to two bodies at the same potential, Cavendish remarks in
Art. 113, that it may be said that one of them may be rendered undercharged
in the part nearest to the other, and he shows that even in this case, the two
bodies must repel each other. But it may be shown that each of the bodies
must be overcharged in every part of its surface. For in the first place no part
can be undercharged, for the lines of force which terminate in an undercharged
surface must have come from an overcharged surface at which the potential
is higher than at the surface. But there is no body in the field at a higher
potential than the two bodies considered. Hence no part of their surface can
be undercharged.

Nor can any finite part of the surface be free from charge, for it may be
shown that if a finite portion of the surface of a conductor is free from charge,
every point which can be reached by continuous motion from that part of the

374 Note g: on electric leakage

surface without passing through an electrified surface must be at the same
potential. Hence no finite portion of a surface can be free from charge, unless
the whole surface is free from charge.

NOTE 9, ART. 124.
[On electric leakage.]

The rate at which electricity passes from a conductor to the surrounding
air or from the surrounding air to a conductor was believed to be much greater
by Cavendish and his contemporaries than is consistent with modern experi-
ments. Judging from the statements of the electricians of each generation, it
would seem as if this rate had been diminishing steadily during the last hundred
years in exact correspondence with the improvements which have been made
in the construction of solid insulating supports for electrified conductors.

Whenever the intensity of the electromotive force at the surface of a con-
ductor is sufficiently great, the air no doubt becomes charged*. This is the
case at a sharp point connected with the conductor even when the potential is
low, but when the curvature of the surface is continuous and gen tie, the conductor
must be raised to a high potential before any discharge to air begins to take place.

Thus in Thomson's portable electrometer, in which there are two disks
placed parallel to each other at different potentials, the percentage loss of
electricity from day to day is very small, and seems to depend principally on
the solid insulators, for when the disks are placed very near each other, less
loss is observed than when they are further apart, though the intensity of the
force urging the electricity through the intervening stratum of air is greater
the nearer the disks are to each other.

On the surface density of electricity near the vertex of a cone.

Green has given in a note to his Essay, section (12), the following results of
an investigation which, so far as I am aware, he never published f.

"Since this was written, I have obtained formulae serving to express,
generally, the law of the distribution of the electric fluid near the apex 0 of
a cone, which forms part of a conducting surface of revolution having the same
axis. From these formulae it results that, when the apex of the cone is directed
inwards, the density of the fluid at any point p, near to it, is proportional

* M. R. Nahrwold (Wiedemann's Annalen v. (1878), p. 440) finds that the dis-
charge from a sharp point communicates a charge to dusty air which can be
detected in the air for some time afterwards. This does not occur in air free from
dust. But the discharge from an incandescent platinum wire communicates a
lasting charge even to air free from dust. [Cf. the modern knowledge of leakage
as depending on the migrations of free electrons.]

f [The results of Green were at length demonstrated by Prof. H. M. Macdonald,
Cambridge Phil. Trans, vol. xvm, 1900 (Stokes Memorial Volume), pp. 292-8.]

Note io; disruptive discharge 375

to f""1; r being the distance Op, and the exponent n very nearly such as would

satisfy the simple equation

(4« + 2) 0 = 377,

where 2/J is the angle at the summit of the cone.

If 2jS exceeds TT, this summit is directed outwards, and when the excess is
not very considerable, n will be given as above: but 2/? still increasing, until
it becomes ZTT — 2y, the angle 2y at the summit of the cone, which is now
directed outwards, being very small, n will be given by

2
2n log - = i,

and in case the conducting body is a sphere whose radius is b, on which P
represents the mean density of the electric fluid; p, the value of the density
near the apex 0, will be determined by the formula

zPbn /r\"-1,
P = (a 4- b) y (a)
a being the length of the cone."

Professor F. G. Mehler* of Elbing has investigated the distribution of
electricity on a cone under the influence of a charged point on the axis, and the
inverse problem of the distribution on a spindle formed by the revolution of
the segment of a circle about its chord.

He finds that when the segment is a very small portion of the circle, so that
the conical points of the spindle are very acute, the surface-density at any
point is inversely proportional to the product of the distances of that point
from the two conical points.

NOTE 10 [ART. 139].
[Conditions for Disruptive Discharge^.]

Sir W. ThomsonJ has determined in absolute measure the electromotive
force required to produce a spark in air between two electrodes in the form of
disks, one of which was plane, and the other slightly convex, placed at different
distances from each other. Mr Macfarlane§ has recently made a more extensive
series of experiments on the disruptive discharge of electricity. He finds that
in air at the ordinary pressure and temperature the electromotive force required
to produce a spark between disks, 10 cm. diameter, and from i to 0-025 cm-
apart, is expressed by the empirical equation

V = 66-940 (s2 + -205035)*,
where s is the distance between the disks.

If we suppose that in the space between the disks the potential varies

* Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function, und
ihre Anwendung in der Theorie der Electricitatsvertheilung. (Elbing, 1870.)
t [See for modern knowledge Sir J. J. Thomson, Conduction... in Gases.]
I Proc. R. S. 1860, or Papers on Electrostatics, chap. xix.
§ Trans. R. S. Edin. vol. xxvm, Part n (1878), p. 633.

376

Note 10.- disruptive discharge

uniformly, as it does between two infinite planes, then the resultant electro-

y
motive intensity is R = — .

If, on the other hand, we suppose that the variation of the potential near
the surface of the disks is affected by unknown causes, we would get a better
estimate of the intensity by taking

R-dV
R~d^'

V dV
Both — and -^ diminish as the distance increases, approximating to the

limit 66-940.

This corresponds to a surface-density of 5-327 units of electricity per square
centimetre, and to a tension of 178-3 dynes per square centimetre. As the
ordinary pressure of the atmosphere is about a million dynes per square centi-
metre, the pressure with which the electricity tends to break through the air

is only about -^ — of the pressure of the atmosphere.

If the electrodes are convex surfaces, whose radii of curvature, a and b,
are large compared with the least distance c between the surfaces, then if

the greatest electric force at the surface whose radius is a will be equal to that
at either of two parallel plane surfaces at the same potentials whose distance
is s.

Note 1 1 : two disks far apart on the same axis 377

Hence the electromotive force required to produce a spark between convex
surfaces, as in Lane's electrometer, is less than if the surfaces had been plane
and at the same distance.

When the air-space is large, the path of the sparks, and therefore the electro-
motive force required to produce them, is exceedingly irregular. The accom-
panying figure is from a photograph of a succession of sparks taken between
the same electrodes from four Leyden jars charged by Holtz's machine.

A portion of the path near the positive electrode is nearly straight, there
is then a sharp turn, which, in all the sparks represented, is in the same direction.
Beyond this the course of the spark is very irregular, although its general
direction is deflected towards the same side as the first sharp turn.

NOTE ii, ART. 141.

Theory of two circular disks on the same axis, their radii being small
compared with the distance between them.

A circular disk may be considered as an ellipsoid, two of whose axes are
equal, while the third is zero, and we may apply the method of ellipsoidal
co-ordinates to the calculation of the potential*. In the case before us every-
thing is symmetrical about the axis, so that we have to consider only the zonal
harmonics, and of these only those of even order, unless we wish to distinguish
between the surface-density on opposite sides of the same element of the disk,
for this depends on the harmonics of odd orders.

Let a be the radius of the first disk, b that of the second, and c the distance
between them.

We shall use ellipsoidal co-ordinates confocal with the first disk. Let rt
and rz be the greatest and least distances respectively of a given point from the

edge of the disk, and let .

2 - ~ 2

...... (2)

then if z is the distance of the point from the plane of the disk, and r its distance

from the axis,

z = a\u>, ...... (3)

r* = a«(i - M2) (p* - I). ...... (4)

If the surface-density of the electricity on the disk is a function of the
distance from the axis, it may be expressed in the form

a = a0 + or2 + &c., ...... (5)

where an= --A^P^(^), ...... (6)

and P2n is the zonal harmonic of order 2,n. Only even orders are admissible,
for since every element of the disk corresponds to two values of fi, numerically

* See Ferrers' Spherical Harmonics, p. 135.

378 Note 1 1 : electrification of two disks

equal but of opposite signs, a term involving an harmonic of odd order would
give the surface-density everywhere zero.

The potential arising from this distribution at any point whose ellipsoidal
co-ordinates are <a = ap and 7? = av

is F=F0+F2 + &c. + Vn, ...... (7)

where F2n = A» r P* (M) <?'*« (")• ...... (8)

In this expression Q'2n (v) denotes a series, the terms of which are nu-
merically equal to those of QZn (v), the zonal harmonic of the second kind,
but with the second and all even terms negative. If we put i for V— I, we
may write

<?'*» = (-)"*•&(»') ...... (9)

&c

_
i . 3 • 5 4« + i 3 • 5 • 7 - (4» + 3)

This expression is an infinite series, the terms of which increase without
limit when v is diminished without limit.

It may, however, be expressed in the finite form *

<?'*, M = P\n (") tan-' - Z^ (v} , ...... (i i)

where P\nv = (-)- P^ (iv), ...... (12)

that is to say P'^ (v) is a zonal harmonic of the first kind with all its terms
positive, and Z^ (v) is a rational and integral function of v of 2n - i degrees,

which is such as to cancel all the terms of P'^ (v) tan-1 ( - j which do not vanish
when v becomes infinite.

The expression (n) is applicable to small as well as great values of v. Thus
we find when v is o, as it is at the surface of the disk,

Q'*> (°) = 22nM!n! 2 '

The potential at any point of the disk is therefore the sum of a series of
terms, the general form of which is

On the axis, p = i and av = z, and the potential is the sum of a series of
terms, the general form of which is

U*n = Atn±-_Q'2n(v). ...(15)

Since we have to determine the value of the potential arising from the first
disk at a point in the second disk for which z = c at a distance r from the axis,
and if we write r2 = j« (x _ p*)t ...... (16)

* See Heine, Handbuch der Kugelfunctionen, § 28, 20.

on the same axis far apart 379

where b is the radius of the second disk, and p is a quantity corresponding to /i
in the first disk, then the most convenient expression for the potential due to
the first disk at a point (p) in the second, is

. .

-*{l-p) + -- -(I- p) - &c

where U denotes the value of the potential at the axis, and where, after the
differentiations, va is to be made equal to c.

To investigate the mutual action of the two disks, let us assume that the
surface-density on the second disk is the sum of a number of terms of which
the general form is

-^W- ...... (18)

The potential at the surface of the second disk arising from this distribution
will be the sum of a series of terms of the form

The potential arising from the presence of the first disk is given in equa-
tion (17).

Having thus expressed the most general symmetrical distribution of elec-
tricity on the two disks and the potentials thence arising, we are able to calculate
the potential energy of the system in terms of the squares and products of the
two sets of coefficients A and B.

If W denotes the potential energy,

W-*ffoV4s, ...... (20)

when the integration is to be extended over every element of surface ds.
Confining our attention to the second disk, the part of W thence arising is

Trb* I aVpdp, ...(21)

./o

and the part arising from the term in the density whose coefficient is Btn is

f>toW4^ ...... (22)

The part of the value of V which arises from the electricity on the second
disk itself is the sum of a series of terms of the form (19). The surface-integral
of the product of any two of these of different orders is zero, so that in finding
the potential energy of the disk on itself we have to deal only with terms of
the form

™ 77 1 (an!)2 i . .

2" 4 b 24" (n !)4 4« + i '

The energy arising from the mutual action of the disks consists of terms

380 Note i i ; electrification of two disks

whose coefficients are products of A's and B's, and in calculating these we
meet with the integral *

I (i - p2)mPon (P) dp = (— i)n — — ...(24)

Jo 2tn + 2n + i ! m — n ! n ! n !

We have, therefore, for the harmonic of order zero. —

A i

Surface-density on the first disk, <TO = - , where A is the charge of the

2-n-a2 /j,

first disk.

Potential at the surface of the first disk Fn = — A .

2 a

Potential at the surface of the second disk, arising from this distribution
of electricity on the first,

I a* i a4 i a6
c\_* 3'2 5?

. i a6 ~|

= A -i »+--!- — f + &c.

7 c6 J

- A

•3-4-4- 5-6^ + &c.]

- &c.

Order 2.- ff£ = ^ __

Potential at the surface of first disk,

--^i^d/*1- *)•
2 a * 22 v'

Potential at the surface of the second disk,

. i«2r 2 4 a2 6 «4 n

"| = A.--K - &C.

2 c* L3 • 5 5 • 7 c 7 • 9 c J

i a*b* (i - />2) ra . 4 4 . 6 a2
" 7 '*

Potential at first disk,

T/ - Z. j l2 • 32 [35 4 _ 30 , 31
1 4 ~ 2a A* 22 . 4* L 8 M 8 ^ ' 8J '

Potential at second disk,

4 2 . 4 c s • 7 • 9 7 • 9 •

_A^aW±-J?)r2_±6_& -i
2.4 22c' L 7 • 9 J

and so on.

* I am indebted for the general value of this integral to Mr W. D. Niven, of
Trinity College. [See Sir W. Niven's memoir in Phil. Trans. 1879.]

on the same axis far apart 381

We have next to calculate the energy arising from this distribution on the
first disk, together with a corresponding distribution on the second disk, the
coefficients of the harmonics for the second disk being B, B2, B4, &c.

It will consist of three parts, the potential energy of the first disk on itself,
of the first and second on each other, and of the second on itself.

The first part will involve only terms having for coefficients the squares of
the coefficients A , for those involving products of harmonics of different orders
will vanish on integration.

The third part will, for the same reason, involve only squares of the coeffi-
cients B.

The second part will involve all products of the form AB.
Performing the integrations, putting a = ex and b = cy,

<4a

a 4 * a 4 22 . 5 * a 4 2"

+ R2 1 1L + B 2 - - * i- B 2 - - —
' b 4 4 ^ b 4 2* . 5 4 ^4 b 4 2«

+ £(*8 + V8

— ^ * * 2'3'5

*) • 0 I— / / /

- 4^« - 3 . 4««y« - 1^-5 ^y _ l^y + &c J

4-5
3 -ii

^5 %2>;2 _ &c J

3-5 -7 II

*V _L_ rx _ 4_7 ^2 _. 2 &c 1
c 3-5 -7\- "

c 5-7

In this expression for the energy of the system the coefficients A2, At, Ba, B4
are treated as independent of A and B. To determine the nearest approach
to equilibrium which can be obtained from a distribution defined by this limited
number of harmonics, we must make W a minimum with respect to At, Bt,
A 4 and B4'.

382 Note 1 2 : electric capacity

We thus find for the values of these coefficients

2 22 f" ^ 7 23^ ~I

A.= - B - - *3 i - ^^ x'' - 2v* + i*4 + ^ *2y2 + 3v4 - &c.

v 3 L 7 7 J

? - v3 [i - 2*2- i^y + 3*4 + — 3 - 5

Lv4-&c.]

We are now able to express the energy in the form

where A and B are the charges, and pu, p12, and pZ2 are the coefficients of
potential, the values of which we now find to be

77 i 2s 6» T a2 12 62 a4 a262 2 . 3 . 13 b*

Pu= - • -a 1 1 — 4 3 - --J+IO-J-+I2--+- — ^ -j - &c. .

2« TT 32 . 5 c6 L c2 7 c2 c4 c4 5 . 7 c4

(a2 + i2)
T~

i i a2+62 i a* + b* 2 «262 I fl6 + fc6
i ~ 3 —3- + 5 —jr- + 5 -p- - 7 C7

12 a2 62 2. 3. 13 a4

~

NOTE 12, ART. 151.
Ow <Ae electrical capacity of a long narrow cylinder.

The problem of the distribution of electricity on a finite cylinder is still,
so far as I know, in the state in which it was left by Cavendish. It is sometimes
assumed that the electric properties of a long narrow cylinder may be repre-
sented, to a sufficient degree of approximation, by those of the ellipsoid inscribed
in the cylinder. The electrical capacity of the cylinder must be greater than
that of the ellipsoid, because the electric capacity of any figure is greater than
that of any part of that figure.

It is easier to state the conditions of the problem than to obtain an exact
solution.

Let zl be the length of the cylinder, and let b be its radius.

Let the axis of the cylinder be the axis of x, and let the origin be taken at
the middle point of the axis. Let y be the distance of any point from the axis.

Let Xdx be the quantity of electricity on that part of the curved surface of
the cylinder for which x is between x and x + dx ; we may call A the linear
density of the electricity on the cylinder.

of a long narrow cylinder 383

Let a be the surface-density on the flat ends.

Let ^r be the potential at a point on the axis for which x = £.

* dx + /*27r<ry [(/ - £)* + v^dy
Jo

...... (i)

the first integral representing the part of the potential due to the curved surface,
and the other two the parts due to the positive and the negative flat ends
respectively.

The condition of equilibrium of the electricity is that t/t must be constant
for all points within the cylinder, and therefore for all points on the axis
between the two ends.

If, by giving proper values to A and a, we can make the value of <p constant
for any finite length along the axis, then, by Art. 144 of "Electricity and
Magnetism," 1(1 will be constant for all points within the surface of the cylinder.

It was shown in Note 2 that the distribution of electricity in equilibrium
on a straight line without breadth is a uniform one. We may expect, therefore,
that the distribution on a cylinder will approximate to uniformity as the radius
of the cylinder diminishes.

If we suppose A and a to be each of them constant,

£

where /j and /2 are the distances of the point (£) on the axis from the edges of
the curved surface at the + and — ends of the cylinder respectively.

Just within the positive flat end of the cylinder, where $ is just less than /,

/„

If the electricity were in equilibrium, this would be zero, and if the cylinder
is so long that we may neglect the reciprocal of /2, we find

A = 2-rrbcr, ...... (4)

or the surface-density on the end must be equal to the surface-density on the
curved surface.

The whole charge is therefore

E = X(2l+b). ...... (5)

The greatest value of the potential is at the middle of the axis, where £ = o.
Calling it ^r(0| and putting/ = I,

(6)

The potential at the end of the axis is

^(l, = A (log | + i . ...... (7)

384 Note 12: electric capacity

The potential at the curved edge is approximately

(8)

This is the smallest value of the potential for any point of the cylinder.
The capacity of the cylinder cannot therefore be less than

E 2.1 + b

0«»= 2l0gg-V'

E 2l + b
nor greater than -j— = . (10)

Cavendish does not take into account the flat ends of the cylinder, but in
other respects these limits are the same as those between which he shows that
the capacity must lie. The approximation, however, is by no means a close
one, for when the cylinder is very narrow the upper limit is nearly double the
lower. Indeed Cavendish, in Arts. 479, 682, has recourse to experiment to
determine the best form of the logarithmic expression.

We may obtain a much closer approximation by the following method,
which is applicable to many cases in which we cannot obtain a complete solution.

Let W be the potential energy of any arbitrary distribution of electricity
on a body of any form W= &(*{,), (11)

where e is the charge of any element of the body, and ifj the potential at that
element.

The charge is E = S (e). (12)

Let us now suppose the electricity to become moveable and to distribute
itself so as to be in equilibrium. The potential will then be uniform. Let its
value be ^0 , and since the charge remains the same the potential energy of the
electrification in the state of equilibrium will be

pp^ — IjA £. (13)

If K0 is the capacity of the conductor,

and K^

Since W, the potential energy due to any arbitrary distribution of the
charge, may be greater, but cannot be less than W0, the energy of the same
charge when in equilibrium, the capacity may be greater, but cannot be less, than

1 £2 (I, (e)]2

2 W °r I. '

This inferior limit of the capacity is greater than that derived from the
maximum value of the potential, and, as we shall see, sometimes gives a very
close approximation to the true capacity.

of a long narrow cylinder

385

In the case of the cylinder, if we suppose A to be uniform, and neglect the
electrification of the flat ends,

.4

E =

W =

(log f -

•(17)
.(18)

When the length of the cylinder is more than 100 times the diameter this
value of the capacity is sufficiently exact for all practical purposes. The capacity
of the inscribed ellipsoid is ,

To obtain a closer approximation let us suppose that the linear density A
is expressed in the form A,, + Ax + &c. + A,-, the general term being

A,,^nP,,g), (19)

where Pn is the zonal harmonic of order n.

If we consider a line of length 2,1 on which there is a distribution of electricity
according to this law, and if /j and /2 are the distances of a given point from
the ends of the line, and if we write

q - t
r

1/2 "/I

:>)

2 I ~2 I

then the potential, iftn, at the given point (a, |8), due to the distribution An, is

where Pn is the same zonal harmonic as in equation (19), and Qn is the corre-
sponding zonal harmonic of the second kind*, and is of the form

™ I T

n(a), (22)

a - I

where Rn (a) is a rational function of a of n — i degrees, and is such that Qn (a)
vanishes when « is infinite. The values of the first five harmonics of the second
kind are

<?o («) = log

« + I

<?, (a) - a log "— — - 2,

•(23)

Qy (a) - (fa3 - fa) log * - 5«2 + |.

Q4 (a) - (V-«« - V«2 + I) log "4l - ¥<* + *!«

In applying these results to the determination of the potential at any point
of the axis of the cylinder we must remember that a point on the axis is at the

* See Ferrers' Spherical Harmonics, chap. v.
c. P. i. 25

386

Note i 2 : electric capacity

distance b from any one of the generating lines of the cylinder, and therefore
the potential at any point on the axis is the same as if the whole charge had
been collected on one generating line.

Hence at the point on the axis for which x = £, if we write

L = log-^ — v — - + log- — T— - , (24)

the potential due to the distribution whose linear density is

is

™" " "WL 2.2 2.3.3 2.3.4.4

approximately, provided £ is between ± I.
Thus, if A,, = A0,

Al = y4l7'

*2_ *\

(27)

/3<5 x* is x2 3\

1 A I *J+J +J i •_* \

4 ~~~ ^^ 4 I O 74 i 72 ' O / >

\ o fr 4 i o/

then iji0 = ^40Z-,

I- 2),

? I\ ,r ,s

L~3)> (28)

I5|2+3\ (£_2B)

These values of the potential are calculated for the axis of the cyb'nder.
The potential at the curved surface may be found from that at the axis by
remembering that within the cylinder V2^ = o. At a distance b from the axis
the potential is therefore

, i i d^ us i d^ w

w, = w — is b -f- 2. ~+K O — utC.i (2Q)

where the values of t/j and its derivatives are those at the axis.
For a uniform distribution

d2Ji . (I — £ I + A

jf* = ~AO( JT + -JT) • (3°)

which is approximately - — p , when £ = o, and j , when £ = ± I. Hence,

I 2/

when the length of the cylinder is many times its diameter, the potential at

of a long narrow cylinder 387

the axis may be taken for that at the surface in approximations of the kind
here made.

We have next to find the integral of the product of the density into the
potential. We may consider the product of each pair of terms by itself. If we
write ^i for the value of L when £ = /, or approximately

(31)

,3,,

- - iAtAtl,

The charge is E = $Xdx = zAJ. (33)

Determining A 2 so as to make /(A,, + A-J (fa + fa) dx a minimum, we find

A x A n -*

^2 ' T"0 T 101 '

*• 3tr

and we obtain a second approximation to /f ,

I

(34)

36 t< - W-

This approximation is evidently of little use unless the length of the cylinder
considerably exceeds 7-245 times its diameter, for this ratio makes the second
term of trie denominator infinite. It shows, however, that when the ratio of
the length to the diameter is very great, the true capacity approximates to the
value of K0 given in (18).

We may proceed in the same way to determine A2 and A± so that

/(A,, + A2 + A4) (^TO + ift^ + ifit) dx

shall be a minimum, and we thus find a third approximation to the value of
the capacity, in which

u _ :'3 73 Q _ ill

^4 — £yj v -rsis~ ^4 _ ^9 ^

101\ lu _ «^«»9\ _ 45 ' "4 ' ^TT^'O /g __ 1 u II \ /y 8»89\ 45

so that when \i is very large the distribution approximates to

The value of the inferior limit of the capacity, as given by this approxi-
mation, is
K ,

5

~

__ __ _ _

~,f. <. 101 ^ru-i (.1 101\I7tt 101\/o «98»\ 461

3° * ~ -^TT 4°° U - TnrJ LI* TnrJ I* ntm TWJ

As « increases, /^ approaches to the value found by the first approximation.

25—2

388 Note 13: electric distribution on two cylinders

To indicate the degree of approximation, the value of f and of the successive
terms of the denominator are given below.

8 Denominator of (34) and (35)

b

ist term 2"d term 3r"l term

10 3-68888 2-68888 - 0-43151

20 4-38203 3-38203 - 0-13680

30 478749 378749 - 0-09775

50 5-29832 4-29832 - 0-07191

100 5-99146 4-99146 - 0-05291 - 0-13566

looo 8-29405 7-29405 - 0-02818 - 0-00892

The observed capacities of Cavendish's cylinders may be deduced from the
numbers given in Art. 281 by taking the capacity of the globe of 12-1 inches
diameter equal to 6-05, and their capacities as calculated by the formula of this
note are given in the following table.

Capacity by As measured by
Length Diameter formuia Cavendish

72 -185 5-668 5-669

54-2 -73 5-775 5754

35-9 2-53 5-907 6-044

The agreement of the calculated and measured values is remarkable.

NOTE 13, ARTS. 152, 280.
[Electric Distribution on] (wo cylinders.

In the case of two equal and parallel cylinders at distance c, _the linear
densities being uniform and equal to At and A2, the part of the potential energy
arising from their mutual action is

-i jX^dx = fafadx - AA (4! log r - 2f) ,

\ /

where r2 = 4/2 + c2.

If the two cylinders are in electric communication with each other A, — A2 ,
and the capacity of the two cylinders together is approximately

_ 2/ _
4/ r 2l r - c '

If a cylinder is placed at a distance d from a conducting plane surface and
parallel to it, then the electric image of the cylinder will be at a distance c = zd,
and its charge will be negative, so that the capacity of the cylinder will be
increased. The capacity of the cylinder in presence of a conducting plane at
distance \c, is ,

. 4/ . r + zl r - c

log J- -i- log — +-J-

Thus in Cavendish's experiment he used a brass wire 72 inches long and
0-185 i'1 diameter. Tin: capacity of this wire at a great distance from any other

On capacity of a condenser with curved plates 389

body would be 5-668 inches. Cavendish placed it horizontally 50 inches from
the floor. The inductive action of the floor would increase its capacity to
5-994 inches; Cavendish, by comparison with his globe, makes it 5-844.

To compare with this he had two wires each 36 inches long and o-i inch
diameter.

The capacity of one of these at a distance from any other body would be
2-8697 inches, or the two together would be 5-7394 inches.

The two wires were placed parallel and horizontal at 50 inches from the
floor. Each wire was therefore influenced by the other wire, and also by the
negative images of itself and the other wire.

The denominator of the fraction expressing the capacity is therefore

Wire Other Own Other

itself wire image image

18 6-2724 + 0-8256 — 0-1759 - 0-1754 = 6-7467

24 6-2724 + 0-6596 - 0-1759 - 0-1733 = 6-5828

36 6-2724 + 0-4672 - 0-1759 — 0-1678 = 6-3959

The numerator of the fraction which expresses the capacity of both wires
together is 36, so that the capacity of the two is

From Cavendish's
results

At 18 inches 5-334 4-967

24 5-469 5-026

36 5-629 5-277

Wire of 72 inches 5-994 5'844

NOTE 14, ART. 155.
Lemma XVI.

If we suppose the plate AB to be overcharged and the plate DF to be
equally undercharged, the redundant fluid in any element of AB being numeri-
cally equal to the deficient fluid in the corresponding element of DF, then
what Cavendish calls the repulsion on the column CE in opposite directions
becomes in modern language the excess of the potential at C over that at E.
Hence the object of the Lemma is to determine approximately the difference of
the potentials of two curved plates when their equal and opposite charges are
given, and to deduce their charges when the difference of their potentials is
given. [Compare Green's formula, Essay, § 8.]

NOTE 15, ART. 169.
On the Theory of Dielectrics.

Cavendish explains the fact discovered by him, that the charge of a coated
glass plate is much greater than that of a plate of air of the same dimensions,
by supposing that in certain portions of the glass the electric fluid is free to
move, while in the rest of the glass it is fixed.

390 Note 15: on the theory of dielectrics

Probably for the sake of being able to apply his mathematical theorems,
he takes the case in which the conducting parts of the glass are in the form of
strata parallel to the surfaces of the glass. He is perfectly aware that this is
not a true physical theory, for if such conducting strata existed in a plate of
glass, they would make it a good conductor for an electric current parallel to
its surfaces. As this is not the case, Cavendish is obliged to stipulate, as in
this proposition, that the conducting strata conduct freely perpendicularly to
their surfaces, but do not conduct in directions parallel to their surfaces.

The idea of some peculiar structure in plates of glass was not peculiar to
Cavendish. Franklin had shown that the surface of glass plates could be charged
with a large quantity of electricity, and therefore supposed that the electric
fluid was able to penetrate to a certain depth into the glass, though it was not
able to get through to the other side, or to effect a junction with the negative
charge on the other side of the plate.

The most obvious explanation of this was by supposing that there was a
stratum of a certain thickness on each side of the plate into which electricity
can penetrate, but that in the middle of the plate there was a stratum im-
pervious to electricity. Franklin endeavoured to test this hypothesis by grinding
away five-sixths of the thickness of the glass from the side of one of his vials,
but he found that the remaining sixth was just as impervious to electricity as
the rest of the glass*.

It was probably for reasons of this kind, as well as to ensure that his thin
plates were of the same material as his thick ones, that Cavendish prepared
his thin plate of crown glass by grinding equal portions off both sides of a
thicker plate. [Art. 378.]

It appears, however, from the experiments, that the proportion of the
thickness of the conducting to the non-conducting strata is the same for the
thin plates as the thick ones, so that the operation of grinding must have re-
moved non-conducting portions as well as conducting ones, and we cannot
suppose the plate to consist of one non-conducting stratum with a conducting
stratum on each side, but must suppose that the conducting portions of the
glass are very small, but so numerous that they form a considerable part of
the whole volume of the glass. If we suppose the conducting portions to be of
small dimensions in every direction, and to be completely separated from each
other by non-conducting matter, we can explain the phenomena without
introducing the possibility of conduction through finite portions of glass.

It was probably because Cavendish had made out the mathematical theory
of stratified condensers, but did not see his way to a complete mathematical
theory of insulating media, in which small conducting portions are disseminated,
that he here expounds the theory of strata which conduct electricity perpen-
dicularly to their surfaces but not parallel to them.

* Franklin's Works, 2nd Edition, vol. I, p. 301, Letter to Dr Lining, March 18,

Residual discharge 391

In forming a theory of the magnetization of iron, Poisson was led to the
hypothesis that the magnetic fluids are free to move within certain small portions
of the iron, which he calls magnetic molecules, but that they cannot pass from
one molecule to another, and he calculates the result orfthe supposition that
these molecules are spherical, and that their distances from each other are large
compared with their radii.

When Faraday had afterwards rediscovered the properties of dielectrics,
Mossotti, noticing the analogy between these properties and those of magnetic
substances, constructed a mathematical theory of dielectrics, by taking Poisson's
memoir and substituting electrical terms for magnetic, and Italian for French,
throughout.

A theory of this kind is capable of accounting for the specific inductive
capacity being greater than unity, without introducing conductivity through
portions of the substance of sensible size.

Another phenomenon which we have to account for is that of the residual
charge of condensers, and what Faraday called electric absorption. The only
notice which Cavendish has left us of a phenomenon of this kind is that recorded
in Arts. 522, 523, in which it appeared "that a Florence flask contained more
electricity when it continued charged a good while than when charged and dis-
charged immediately."

To illustrate this phenomenon, I gave in "Electricity and Magnetism," Art.
328, a theory of a dielectric composed of strata of different dielectric and con-
ducting properties*.

Professor Rowland has since shownf that phenomena of the same kind
would be observed if the medium consisted of small portions of different kinds
well mingled together, though the individual portions may be too small to be
observed separately.

It follows from the property of electric absorption that in experiments to
determine the specific inductive capacity of a substance, the result depends on
the time during which the substance is electrified. Hence most of those who
have attempted to determine the value of this quantity for glass have obtained
results so inconsistent with each other as to be of no use. It is absolutely
necessary, in working with glass, to perform the experiment as quickly as
possible.

Cavendish does not give the exact duration of one of his "trials," but each
trial probably took less than two or three seconds. His results are therefore
comparable with those recently obtained by HopkinsonJ, who effected the
different operations by hand.

* [See J. Hopkinson's collected Scientific Papers for theory and experiment.]
f American Journal of Mathematics, No. I, 1878, p. 53.

J Proceedings of the Royal Society, June 14, 1877; Phil. Trans. 1878, Part r, p. 17.
[Reprinted in collected Scientific Papers.}

39 2 Note 1 6.- mutual influences of condensers

The results obtained by Gordon*, who employed a break which gave 1200
interruptions per second, and those obtained by Schiller f by measuring the
period of electric oscillations, which were at the rate of about 14,000 per second,
are much smaller that those obtained by Cavendish and by Hopkinson.

Hopkinson finds that the quotient of the specific inductive capacity divided
by the specific gravity does not vary much in different kinds of flint glass. As
Cavendish always gives the specific gravity, I have compared his results with
those of Hop*kinson for glass of corresponding specific gravity.

Electrostatic capacity of glass.

Flint-glass ......... 3-279 7-93

Do., a thinner piece 3-284 7-65

Light flint ......... 3-2 6-85 3-013 2-96

Dense flint ......... 3-66 7-4 3'O54 3-66

Double extra-dense flint ... 4-5 10-1 3-i64

Very light flint ...... 2-87 6-57 5-83

Plate-glass ......... 2-8 8 6-10 6-43

Crown-glass ......... 2-53 8-6 3-108

NOTE 16, ART. 185.
Mutual Influence of two Condensers.

To find the effect on the capacity of a condenser arising from the presence
of another condenser at a distance which is large compared with the dimensions
of either condenser.

Let A and B be the electrodes of the first condenser, let L and N be the
capacities of A and B respectively, and M their coefficient of mutual induction,
then if the potential of A is I and that of B is o, the charge of A will be L and
that of B will be M , and if both A and B are at potential i the charge of the
whole will be L + zM + N, and this cannot be greater than half the greatest
diameter of the condenser.

Let a and b be the electrodes of the second condenser, let its coefficients be
I, m, n, and let its distance from the first condenser be R.

Let us first take the condenser AB by itself, and let us suppose that the
potentials of A and B are x and y respectively, then their charges will be
Lx + My and MX + Ny respectively.

At a distance R from the condenser the potential arising from these charges

Will \)(*

{Lx + M(x + y) + Ny} R-i = P,
* Proc. R. S. Dec. 12, 1878. f Pogg- Ann. 152 (1874), p. 535.

and conductors 393

and if the second condenser, whose capacity when its electrodes are in contact
is / + 2m + «, is placed at a distance R from the first and connected to earth,

its charge will be

- P (I + 2m + n) = Q.

This charge of the second condenser will produce a potential QR"1 at a
distance R, and will therefore alter the potentials of A and B by this quantity,
so that the potentials of A and B will be x + QR~l and y + QR~l respectively.

To find the capacity of A as altered by the presence of the second con-
denser, we must make the potential of A = i and that of B — o, which gives

x - {Lx + M (x + y) + Ny} (I + 2m + n) R-* = i,
y - {Lx + M (x + y) + Ny} (I + 2m + n) R~z = o.
Hence x = y + i,

and y = {L + M + (L + 2M + N) y} (I + 2m -| n) R-'2,

(L + M)(l+2m + n} R~*
i - (L + 2M + N) (1+ 2m + n) R~2 '
and the capacity of A is Lx + My or L + (L + M) y, or

(L + M)2 (I + 2m + n)

[AA] = L
of B is M

[AB] = M +
af a and b

[Aa] = -

2 - (L + 2M + N) (I + 2m + n) '
The charge of B is MX + Ny or M + (M + N) y, or

(Z. + M) (M + N) (I + 2tn + n)
R*-(L+2M + N) (l + 2m + n) '

The charges of a and b are — (I + m) P and — (m + n) P respectively, 01

R (L + M)(l + m)

[Ab] =

A'2 - (L + 2M + N) (I + 2m + n)
R (L + M) ( m + n)

R* - (L + 2M + N) (I + 2m + n) '

In these expressions we must remember that M is a negative quantity,
that L + M and M + N can neither of them be negative, and that their sum
L + zM + N cannot be greater than the largest semidiameter of the condenser.
Hence if R is large compared with the dimensions of the condensers, the second
terms of the values of [A A] and [AB] will be quite insensible, and even if the
condensers are placed very near together these terms will be small compared
with L, M, or N.

If a, instead of being part of a condenser, is a conductor at a considerable
distance from any other conductor, we may put m = n = o, and if A is also
a simple conductor, M = N = o, and we find

L2/
[AA] = L + ^5- Tl ,

RLl

~^'

by which the capacities and mutual induction of two simple conductors at a
distance R can be calculated when we know their capacities when at a great
distance from other conductors. See Note 24.

394 Note 17: theory of Cavendish s trial plate

NOTE 17, ART. 194.

Theory of the Experiment with the Trial Plate.
Let A and B be the inner, a and b the outer coatings of the Leyden jars.

Let C be the body tried and D the trial plate, M the wire connecting A
with C, and N the wire connecting b with D.

Let £ be the electrometer with its connecting wires.

Let the coefficients of induction be expressed by pairs of symbols within
square brackets, thus, let [(A + C) (C + D)] denote the sum of the charges of
A and C when C and D are both raised to potential i and all the other con-
ductors are at potential o.

First Operation. — The insides of the two jars are charged to potential P0,
the outsides and all other bodies being at potential o.

The charge of A is [A (A + B)] P0, and that of b is [b (A + B)] P0.

Second Operation. — The outside coating of b is insulated, the charging wire
is removed, and the inside of B is connected to earth. The charges of A and
of b remain as before.

Third Operation. — A is connected to C by the wire M, and b is connected
to D by the wire 2V.

The charge of A is communicated to A , C, and M , and the potential of this
system is Plt and the charge of b is communicated to b, D, and 2V, and the
potential of this system is Pg.

Hence we have the following equations to determine P1 and P2 in terms
of PC,

[(A + C + M) (A + C + M)] Pl + [(A + C + M) (b + D + 2V)] P2

= [A(A+B)]P0 (i)

[(A + C + M) (b + D + N)] Pl + [(b + D + 2V) (b + D + 2V)] P2

= [b(A+B)]P0 (2)

Fourth Operation. — The wires M and 2V are disconnected from C and D
respectively, and the jars A and b are discharged and kept connected to earth.

The charges of C and D remain the same as before.

Fifth Operation. — The bodies C and D are connected with each other and
with the electrometer E, and the final potential of the system CDE is observed
by the electrometer to be P3.

Equating the final charge of the system CDE to that of the system CD at
the end of the fourth equation,

[(C + D + E) (C + D + E)] P3 = [(C + D)(A + C + M)] Pl

+ [(C + D)(b+-D + N)]P, (3)

in terms of coefficients of induction 395

Eliminating P1 and P2 from equations (i), (2) and (3),

P3 [(C + D + E)2] {[(A + C + M)2] [(b + D + N)*]

- [(A + C + M) (b + D + N)]*}

(\A(A + B)} {[(C + D)(A + C + M)] [(b + D + N)*] \

-l(C + D)(b + D + N)]((A + C + M)(b + D + N)}} \
0 [b (A + B)] {[(C + D)(b + D + N)][(A + C + M)*}

-[(C + D)(A + C + M)] [(A+C + M)(b + D + N)]})

By means of his gauge electrometer, Art. 249, Cavendish made the value
of P0 the same in every trial, and altered the capacity of D, the trial plate,
so that P3 in one trial had a particular positive value, and in another an equal
negative value. He then wrote down the difference of the two values of D as
an indication to guide him in the choice of trial plates, and the sum of the two
values, by means of which he compared the charges of different bodies.

He then substituted for C a body, C', of nearly equal capacity, and repeated
the same operations, and finally deduced the ratio of C to C' from the equation

C : C' : : D, + Dt : £>/ + £>,_'.

The capacities of the two jars were very much greater than any of the
other capacities or coefficients of induction in the experiment, and of these
[b (B + b)] was less than half the greatest diameter of the second jar, and may
therefore be neglected in respect of [b2] or [Bb]. We may therefore put
[Bb] = - [ft2], and in equation (4) neglect all terms except those containing
the factors [A*] [b2] or [A2] [Bb].

We thus reduce equation (4) to the form
P3 [(C + D + E)2] = P0{[(C + D) (A + C + M)] - [(C + D) (b + D + N)]}

- [£>*] - [D (b + N)] + [D (A + M)]} ....... (5)

The bodies to be compared were either simple conductors, such as spheres,
disks, squares and cylinders, and those trial plates which consisted of two con-
ducting plates sliding on one another, or else coated plates or condensers.

Now the coefficient of induction between a coated plate and a simple con-
ductor is much less than that between two simple conductors of the same
capacity at the same distance, and the coefficient of induction between two
coated plates is still smaller. See Note 16.

Hence if both the bodies tried are coated plates, the equation (5) is reduced

^3 ([C2] + [Z>2J + [£2!) = P0 ([C2] - [fl2]), ...... (6)

so that the experiment is really a comparison of the capacities of the two
bodies C and D.

But if either of them is a simple conductor, we must add to its capacity its
coefficient of induction on the wire and jar with which it is connected, and
subtract from it its coefficient of induction on the other wire and jar. These
two coefficients of induction are both negative, but that belonging to its own

396 Note ij: theory of Cavendistis trial plate

wire and jar is probably greater than the other, so that the correction on the
whole is negative.

Hence in Cavendish's trials the capacity deduced from the experiment will
be less for a simple conductor than for a coated plate of equal real capacity.

This appears to be the reason why the capacities of the plates of air when
expressed in "globular inches," that is, when compared with the capacity of
the globe, are about a tenth part greater than their computed values. See
Art. 347.

It would have been an improvement if Cavendish, instead of charging the
inside of both jars positively and then discharging the outside of B, had charged
the inside of A and the outside of B from the same conductor, and then con-
nected the outside of both to earth, using the inside of B instead of the outside,
to charge the trial plate negatively. In this way the excess of the negative
electricity over the positive in B would have been much less than when the
outside was negative.

With a heterostatic electrometer, such as those of Bohnenberger or Thomson,
in which opposite deflections are produced by positive and negative electrifi-
cation, the determination of the zero electrification may be made more accu-
rately than any other, and with such an electrometer P3 should be adjusted
to zero. But the only electrometer which Cavendish possessed was the pith
ball electrometer, in which the repulsion between the balls when at any given
distance depends on the square of the electrification, and in which therefore
the indications are very feeble for low degrees or electrification. Cavendish
therefore first adjusted his trial plate so as to produce a given amount of separa-
tion of the balls by positive electrification, and then altered the trial plate so as
to produce an equal separation by negative electrification. In each case he has
recorded a number expressing the side of a square electrically equivalent to
the trial plate, together with the difference and the mean of the two values.

He seems to have adopted the arithmetical mean as a measure of the charge
of the body to be tried. It is easy to see, however, that the geometrical mean
would be a more accurate value. For, if we denote the values of the final
potential of the trial plate by accented letters in the second trial, we have

P,' ([C*] + [D*] + [£2]) - P0 ([C«] - [£"]) (7)

Since P3 + P,' = o, we find by (6) and (7)

[C*\ ([C«] + [£*]) - [D*] [D'"] + J [E*] ([/>*] + (D'*}).

If we neglect the capacity of the pith ball electrometer, which is much less
than that of the bodies usually tried, this equation becomes

[C2]8 = [£>2] [D'*},

or the capacity of the body tried is the geometrical mean of the capacities of
the trial plate in its positive and negative adjustments.

Note 1 8 : Cavendislis early views on electricity 397

NOTE 18, ART. 216.

On the " Thoughts Concerning Electricity," and on an early draft of
the Propositions in Electricity.

The theory of electricity sketched in the "Thoughts" is evidently an earlier
form of that developed in the published paper of 1771. We must therefore
consider the "Thoughts" as the first recorded form of Cavendish's theory, and
this for the following reasons.

(1) Nothing is said in the "Thoughts" of the forces exerted by ordinary
matter on itself and on the electric fluid. The only agent considered is the
electric fluid itself, the particles of which are supposed to repel each other. This
fluid is supposed to exist in all bodies whether apparently electrified or not, but
when the quantity of the fluid in any body is greater than a certain value,
called the natural quantity for the body, the body is said to be overcharged,
and when the quantity is less than the natural quantity the body is said to be
undercharged.

The forces exerted by undercharged bodies are ascribed, not, as in the later
theory, to the redundant matter in the body, but to the repulsion of the fluid
in other parts of space.

The theory is therefore simpler than in its final form, but it tacitly assumes
that the fluid could exist in stable equilibrium if spread with uniform density
over all space, whereas it appears from the investigations of Cavendish himself
that a fluid whose particles repel each other with a force inversely as any power
of the distance less than the cube would be in unstable equilibrium if its density
were uniform.

This objection does not apply to the later form of the theory, for in it the
equilibrium of the electric fluid in a saturated body is rendered stable by the
attraction exerted by the fixed particles of ordinary matter on those of the
electric fluid.

(2) The hypotheses are reduced in the later theory to one, and the third
and fourth hypotheses of the "Thoughts" are deduced from this.

(3) In the "Thoughts" Cavendish appears to be acquainted only with those
phenomena of electricity which can be observed without quantitative experi-
ments. Some of his remarks, especially those on the spark, he repeats in the
paper of 1771, but in that paper (Art. 95) he refers to certain quantitative
experiments, the particulars of which are now first published [Art. 265].

The "Thoughts," however, though Cavendish himself would have con-
sidered them entirely superseded by the paper of 1771, have a scientific interest
of their own, as showing the path by which Cavendish arrived at his final
theory.

He begins by getting rid of the electric atmospheres which were still clinging
to electrified bodies, and he appears to have done this so completely that he
does not think it worth while even to mention them in the paper of 1771.

398 Note 1 8: GaroenduKt early views on electricity

He then introduces the phrase "degree of electrification" and gives a
quantitative definition to it, so that this, the leading idea of his whole research,
was fully developed at the early date of the "Thoughts."

Several expressions which Cavendish freely used in his own notes and
journals, but which he avoided in his printed papers, occur in the "Thoughts."

Thus he speaks of the "compression" or pressure of the electric fluid.

Besides the "Thoughts," which may be considered as the original form of
the introduction to the paper of 1771, there is a mathematical paper corre-
sponding to the Propositions and Lemmata of the published paper, but following
the earlier form of the theory, in which the forces exerted by ordinary matter
are not considered, and referring directly to the " Hypotheses " of the " Thoughts. "

The first part of this paper is carefully written out, but it gradually becomes
more and more unfinished, and at last terminates abruptly, though, as this
occurs at the end of a page, we may suppose that the end of the paper has been
lost. I think it probable, however, that when Cavendish had advanced so far, he
was beginning to see his way to the form of the theory which he finally published,
and that he did not care to finish the manuscript of the imperfect theory.

The general theory of fluids repelling according to any inverse power of the
distance is given much more fully than in the paper of 1771, and the remarks
[at the beginning] on the constitution of air are very interesting.

I have therefore printed this paper, but in order to avoid interrupting the
reader with a repetition of much of what he has already seen, I have placed it
at the end of this Note.

CAVENDISH'S FIRST MATHEMATICAL THEORY FROM MS. BUNDLE 17.

Let a fluid whose particles mutually repel each other be spread uniformly
through infinite space. Let a be a particle of that fluid;
draw the cone baft continued infinitely, and draw the ,j

section bf$: if the repulsion of the particles is inversely
as any higher power of the distance than the cube, the
particle a will be repelled with infinitely more force from

the particles between a and b/3 than from all those situated beyond it, but if
their repulsion is inversely as any less power than the cube, then the repulsion
of the particles placed beyond bfi is infinitely greater than that of those between
a and b/3.

If the repulsion of the particles is inversely as the n power of the distance,
n being greater than 3, it would constitute an elastic fluid of the same nature
as air, except that its elasticity would be inversely as the n + 2 power of the

At I ^

distance of the particles, or directly as the - - power of the density of the
fluid.

But if n is equal to, or less than 3, it will form a fluid of a very different
kind from air, as will appear from what follows.

His first draft of a theory 399

COR. i. Let a fluid of the above-mentioned kind be spread uniformly through
infinite space except in the hollow globe BDE, and let
the sides of the globe be so thin that the force with which
a particle placed contiguous to the sides of the globe
would be repelled by so much of the fluid as might be
lodged within the space occupied by the sides of the
globe should be trifling in respect of the repulsion of the
whole quantity of fluid in the globe.

If the fluid within the globe was of the same density
as without, the particles of the fluid adjacent to either

the inside or outside surface of the globe would not press against those surfaces
with any sensible force, as they would be repelled with the same force by the
fluid on each side of them. But if the fluid within the globe is denser than
that without, then any particle adjacent to the inside surface of the globe will
be pressed against by the repulsion of so much of the fluid within the globe as
exceeds what would be contained in the same space if it was of the same
density as without, and consequently will be greater if the globe be large than
if it be small. Consequently the pressure against a given quantity (a square inch
for example) of the inside surface of the globe will be greater if the globe is
large than if it is small.

If the particles of the fluid repel each other with a force inversely as their
distance, the pressure against a given quantity of the inside surface would be
as the square of the diameter of the globe. So that it is plain that air cannot
consist of particles repelling each other in the above-mentioned manner.

If the repulsion of the particles was inversely as some higher power of the
distance than the cube, then any particle of the fluid would not be sensibly
affected except by the repulsion of those particles which were almost close to
it, so that the pressure of the fluid against a given quantity of the inside surface
would be the same whatever was the size of the globe, but then the elasticity
[would] be in a greater proportion than that of the £ power of the density.

If the repulsion of the particles is inversely as some less power than the cube
of the distance, and the density of the fluid within the globe is less than it is
without, then the particles on the outside of the globe will press against it, and
the force will be greater if the globe is large than if it be small.

If the density of the fluid within the globe be greater than without, then
the density will not be the same in all parts of the globe, but will be greater
near the surface and less near the middle, for if you suppose the density to be
everywhere the same, then any particle of the fluid, as d, would be pressed with
more force towards a, the nearest part of the surface of the sphere, than it would
[be] in the contrary direction.

If the repulsion of the particles is inversely as the square of the distance, I
think the inside of the sphere would be uniformly coated with the fluid to a
certain thickness, in which the density would be infinite, or the particles would

400 Note 1 8 : Cavendish's early views on electricity

be pressed close together, and in all the space within that, the density would
be the same as on the outside of the sphere.

The pressure of a particle adjacent to the inside surface against it is equal
to the repulsion of all the redundant matter in the sphere collected in the center,
and the force with which a particle is pressed towards the surface of the sphere
diminishes in arithmetical progression in going from the inside surface to that
point at which its density begins to be the same as without, therefore the whole
pressure against the inside of the sphere is equal to that of half the redundant
matter in the sphere pressed by the repulsion of all the redundant matter
collected in the center of the sphere.

Therefore, if the quantity of fluid in the sphere is such that its density, if
uniform, would be i + A, and the radius of the sphere be called r, the whole

dr3 dr3
pressure against the inside surface will be as — x — ^ , and the pressure against

a given space of the inside surface will be as d2 r2.

If this pressure be called P, d is as — — , and dr3 is as r-\/P. Consequently,

supposing the fluid to be pumped into different sized globes, the quantity of
fluid pumped in will be as the square root [of the force] with which it is pumped,
multiplied by the square of the diameter of the globe.

If the density within the sphere is less than without, then the density
within the sphere will not be uniform, but will be greater towards the middle
and less towards the outside, and if the repulsion of the particles is inversely
as the square of the distance, there would be a sphere concentric to the hollow
globe in which the density would be the same as on the outside of the globe,
and all between that and the inside surface of the globe would be a vacuum.

From these corollaries it follows that if the electric fluid is of the nature
here described, and is spread uniformly through bodies, except when they give
signs of electricity, that then if two similar bodies of different sizes be equally
electrified, the larger body will receive much less additional electricity in pro-
portion to its bulk than the smaller one, and moreover when a body is electrified,
the additional electricity will be lodged in greater quantity near the surface of
the body than near the middle.

Let us now suppose the fluid within the globe BDE to be denser than without,
and let us consider [in what manner] the fluid without will be affected thereby.

ist. There will be a certain space surrounding the globe, as ftSe, which will
be a perfect vacuum, for first let us suppose that the density without the globe
is uniform, then any particle would be repelled with more force from the globe
than in the contrary direction.

2ndly. Let us suppose that the space jSSe, BDE is not a vacuum, but rarer
than the rest of the fluid ; still a particle placed close to the surface of the globe
would be repelled from it with more force than in the contrary direction.

3rdly. Let us [suppose that] the density in the space between BDE and
/38e is greater than without, then according to some hypothesis of the law of

'Electric fluid communicating by canals 401

repulsion a particle placed at B might be in equilibrium, but one placed at /3
could by no means be so.

So that there is no way by which the particles can be in equilibrium, unless
there is a vacuum all round the globe to a certain distance. How the density
of the fluid will be affected beyond this vacuum I cannot exactly tell, except
in the following case: —

If the repulsion of the particles is inversely as the square of the distance,
there will be a perfect vacuum between BDE and /?8e, and beyond that the
density will be perfectly uniform, jSSe being a sphere concentric to BDE, and of
such a size, that if the matter in BDE was spread uniformly all over the sphere
/?§e, its density would be the same as beyond it.

For any quantity of matter spread uniformly over the globe /JSe or BDE
affects a particle of matter placed without that sphere just in the same manner
as if the whole fluid was collected in the center of the sphere, so that any
particle of matter placed without the sphere /J8e will be in perfect equilibrio.

In like manner if the fluid within BDE is rarer than without, there will be
a certain space surrounding the globe, as that between BDE and /JSe, in which
the density will be infinite, or in which the particles will be pressed close
together, and if the repulsion of the particles is inversely as the square of the
distance, the density of the fluid beyond that will be uniform: the diameter
of jSSe being such that if all the matter within it was spread uniformly, its density
would be the same as without.

Let a fluid of the above-mentioned kind be spread uniformly through
infinite space except in the canal acdef of any shape whatsoever, except that
the ends aghb and mden are straight canals of an equal diameter, and of such
a length that a particle placed at « or d shall not be sensibly affected by the
repulsion of the matter in the part gcmnfh, and let there be a greater quantity
of the fluid in this canal than in an equal space without.

Then the density of the fluid in different parts of the canal will be very
different, but I imagine the density will be just the same at a as at d. For
suppose ab and de to be joined, as in the figure, by a canal of an uniform
diameter and regular shape, nowhere approaching near enough to gcmnfh to
be affected by the repulsion of the particles within it. If the matter was not
of the same density [at a and .d] the matter therein could not be at rest, but there
would be a continual current through the canal, which seems highly improbable.

c. p. i. 26

402 Note 1 8: Cavendish's earliest theory

COR. Let C be a conductor of electricity of any shape, em and fn wires
extending from thence to a great distance. Let a and b be two equal bodies
placed on those wires at such a distance from C as not to be sensibly affected

C

by the electricity thereof, and let the conductor or wires be electrified by any
part: the quantity of electric fluid in the bodies a and b will not be sensibly
different, or they will appear equally electrified.

Case i. Let the parallel planes Aa, Bb, &c., be continued infinitely. Let
all infinite space except the space contained
between A a and Cc, and between Ee and Hh, A

be filled uniformly with particles repelling in- c

versely as the square of their distance; let the 3|

space between Ee and Hh be filled with fluid
of the same density, the particles of which can
move from one part to another; and let the

space between Aa and Cc be filled with matter o SL

whose density is to [that in] the rest of space h

as AD to AC.

Take EF = JCD, and GH such that the matter between Ee and Ff when
pressed close together, so that the particles touch each other, shall occupy the
space between Gg and Hh.

The space between Ee and Ff will be a vacuum, that between Ff and Gg
of the same density as the rest of space ; and between Gg and Hh the particles
will touch one another.

Case 2. Let everything be as in case the first, except that there is a canal
opening into the plane Hh, by which the matter in the space EH is at liberty
to escape; part of the matter will then run out, and the density therein will
be everywhere the same as without, except in the space EF, which will be
a vacuum, EF being equal to CD.

Case 3. Suppose now that a canal opens into the plane Aa by which the
fluid hi the space AC may escape. It will have no tendency to do so, for the
repulsion of the redundant fluid in A C on a particle at a will be exactly equal
to [the] want of repulsion of the space EH.

Case 4. Let now the space between Aa and Cc be filled with matter whose
density is to the rest of space as AB to AC.

Then the space between Hh and Gg will be a vacuum, GH being equal to
JBC. In the space EF the particles of matter will be pressed together so as
to touch each other, the quantity of matter therein exceeding what is naturally
contained in that space by as much as is driven out of the space GH ; and in
the space between Ff and Gg the matter will be of the same density as without.

of an electric fluid 403

Case 5. Suppose now that a canal opens into the plane Hh as in Case 2,
then will matter run into the space EH, and the density will be everywhere
the same as without, except in the space EF, where the particles will be pressed
close together, the quantity of matter therein exceeding the natural quantity
by as much as is naturally contained in the space EC.

Case 6. Suppose now that a canal opens into the plane Aa, the fluid will
have no tendency to run out thereat.

Case 7. Let us now consider what will be the result if the repulsion of the
particles is inversely as some other power of the distance between that of the
square and the cube; and first let us suppose matters as in the first case. There
will be a certain space, as EF, which will be a vacuum, and a certain space,
as FG, in which the particles will be pressed close together; for if the matter
is uniform in EH, all the particles will be repelled towards H if there is not a
vacuum at E, nor the particles pressed close together at G, but only the density
less at E than at H, then the repulsion of space EH at E will be less on [a]
particle at E and greater on a particle at H than if the density was uniform
therein, consequently on that account as well, as on account of the repulsion
of AC a particle at E or H will be repelled towards H, but if the space EF
is a vacuum and the particles in GH pressed close together, then if the spaces
EF and GH are of a proper size, a particle at F or G may be in equilibrio.

Case 8. If you now suppose a canal to open into the plane Hh as in the
3rd case, some of the matter will run out thereat, so that the whole quantity
of matter in the space EH will be less than natural. For if not, it has already
been shown that a particle at H will be repelled from A, but the quantity of
matter which runs out will not be so much as the redundant matter in AC,
for if there was, the want of repulsion of the space EH on a particle at h would
be greater than the excess of repulsion of the space AC.

Case 9. Suppose now that a canal opens into the plane A a as in Case 3;
a particle at « will be repelled from Dd, but not with so much force as if there
had been the natural quantity of fluid in the space EH, so that some of the
fluid will run out at the canal, but not with so much force, nor will so much
of the fluid run out as if there had been the natural quantity of fluid in EH.

Case 10. If you suppose matters to be as in the 4th case, then there must
be a certain space adjacent to Ee, in which the particles will be pressed close
together, and a certain space adjacent to Hh in which there must be a vacuum.

Case ii. If you suppose a canal to open into the plane Hh, some matter
will run into the space EH thereby, so that the whole quantity of matter therein
will be greater than natural.

The proof of these two cases is exactly similar to that of the two former.

Case 12. If you now suppose a canal to open into Aa, some fluid will run
into it, but not with so much force nor in so great quantity as if the natural
quantity of fluid had been contained in the space Hh.

26 — 2

404 Note 19: determination of law of electric attraction

I have supposed the planes Aa, &c. to be extended infinitely, because by
that means I was enabled to solve the question accurately in the cases where
the repulsion is supposed inversely as the square of the distance, which I could
not have done otherwise, but it is evident that the phenomena will be nearly
of the same kind if the planes are not infinitely extended.

For if the distance ag be small in respect of the length and breadth of the
plane A a, a particle placed at a will be repelled by the plane Aa with very
nearly the same force as if the plane was infinitely extended.

It is plain that these 6 last cases agree very exactly with the laws of elec-
tricity laid down in the 3rd and 4th hypotheses [Thoughts... Art. 202].

If the lines Bb and Dd touch one another so that

[Here the MS. ends. ED.]

NOTE 19, ART. 234.

[Determination of the Law of Electric Attraction.}
Cavendish's Experiment on the Charge of a Globe between two Hemispheres.

This experiment has recently been repeated * at the Cavendish Laboratory
in a somewhat different manner.

The hemispheres were fixed on an insulating stand, so as to form a spherical
shell concentric with the globe, which stood inside the shell upon a short piece
of a wide ebonite tube.

By this arrangement, since during the whole experiment the potentials of
the globe and sphere remained sensibly equal, the insulating support of the
globe was never exposed to the action of any sensible electromotive force, and
therefore had no tendency to become charged.

If the other end of the insulator supporting the globe had been connected
to earth, then, when the potential of the globe was high, electricity would have
crept from it along the insulator, and would have crept back again when, in
the second part of the experiment, the potential of the globe was sensibly zero.
In fact this was the chief source of disturbance in Cavendish's experiment.
See Art. 512.

Instead of removing the hemispheres before testing the potential of the
globe, they were left in their position, but discharged to earth. The effect on
the electrometer of a given charge of the globe was less than if the hemispheres
had been removed, but this disadvantage was more than compensated by the
perfect security from all external electric disturbances afforded by the con-
ducting shell.

The short wire which formed the communication between the shell and the
globe was fastened to a small metal disk hinged to the shell, and acting as a
lid to a small hole in it, so that when the lid and its wire were lifted up by

* [By Sir Donald M<=Alister in 1878.]

from charge on a globe enclosed within hemispheres 405

means of a silk string, the electrode of the electrometer could be made to dip
into the hole in the shell and rest on the globe within.

The electrometer was Thomson's Quadrant Electrometer.

The case of the electrometer, and one of the electrodes, were permanently
connected to earth, and the testing electrode was also kept connected to earth,
except when used to test the potential of the globe.

To estimate the original charge of the shell, a small brass ball was placed
on an insulating stand at a distance of about 60 cm. from the centre of the shell.

The operations were conducted as follows :—

The lid was closed, so that the shell communicated with the globe by the
short wire.

A Leyden jar was charged from a machine in another room, the shell was
charged from the jar, and the jar was taken out of the room again.

The small brass ball was then connected to earth for an instant, so as to
give it a negative charge by induction, and was then left insulated.

The lid was then lifted up by means of the silk string, so as to take away
the communication between the shell and the globe.

The shell was then discharged and kept connected to earth.

The testing electrode of the electrometer was then disconnected from earth,
and made to pass through the hole in the shell so as to touch the globe within
without touching the shell.

Not the slightest deflexion of the electrometer could be observed.

To test the sensitiveness of the apparatus, the shell was disconnected from
earth and connected to the electrometer. The small brass ball was then dis-
charged to earth.

This produced a large positive deflexion of the electrometer.

Now in the first part of the experiment, when the brass ball was connected
to earth, it became charged negatively, the charge being about ^ of the original
positive charge of the shell.

When the shell was afterwards connected to earth the small ball induced
on it a positive charge equal to about one-ninth of its own negative charge.
When at the end of the experiment the small ball was discharged to earth, this
charge remained on the shell, being about t|ff of its original charge.

Let us suppose that this produces a deflexion D of the electrometer, and
let d be the largest deflexion which could escape observation in the first part
of the experiment.

Then we know that the potential of the globe at the end of the first part
of the experiment cannot differ from zero by more than

±*v

fc 486 D
where V is the potential of the shell when first charged.

406 Note 19: determination of law of electric attraction

But it appears from the mathematical theory that if the law of repulsion
had been as r~(2+9)f the potential of the globe when tested would have been
by equation (25), p. 425, 0-1478 x ?F.

Hence q cannot differ from zero by more than ± — jr .

Now, even in a rough experiment, D was certainly more than 300^. In
fact no sensible value of d was ever observed. We may therefore conclude
that q, the excess of the true index above 2, must either be zero, or must differ
from zero by less than j

Theory of the Experiment.

Let the repulsion between two charges e and e' at a distance r be

f=ee'^(r), ...... (i)

where <f> (r) denotes any function of the distance which vanishes at an infinite
distance.

The potential at a distance r from a charge e is

V = er^>(r)df. ...... (2)

.'r

Let us write this in the form

V=cl-f(r), ...... (3)

where /*W-^p. ...... (4)

and/(r) is a function of r equal to if I I <f> (r) dr\ dr.

We have in the first place to find the potential at a given point B due to
an uniform spherical shell.

Let A be the centre of the shell, a its radius, a its whole charge, and a its

surface-density, then

a = 47r«2o-. ...... (5)

Take A for the centre of spherical co-ordinates and AB for axis, and let
AB = b.

Let P be a point on the sphere whose spherical co-ordinates are 6 and tf>,

and let BP = r, then

rz = a2 — lab cos 6 + bz. ...... (6)

The charge of an element of the shell at P is

aaasin8d8d<f>= - a
The potential at P due to this element is

aaasin8d8d<f>= - asm9d6d</>. ...... (7)

r

(8)

Theory of charge on an enclosed globe 407

and the potential due to the whole shell is therefore

Integrating with respect to (/> from o to 2ir,

...... (10)

Differentiating (6) with respect to 9,

rdr = absinOdO. (n)

Hence, V == £\ ±f (r)dr = \ ^ {/ (rz) -f (,,)} (12)

the upper limit r2 being always a + b, and the lower limit rl being a — b when
a > b, and b — a when a < b.

Hence, for a point inside the shell
for a point on the shell itself

and for a point outside the shell

-«)}- (15)

We have next to determine the potentials of two concentric spherical shells,
the radius of the outer shell being a and its charge a, and that of the inner
shell being b and its charge /?.

Calling the potential of the outer shell A, and that of the inner B, we find
by what precedes,

B = A/ (26) + JL {/(fl + b} _f(a _ b)} ....... (iy)

In the first part of the experiment the shells communicate by the short
wire and are both raised to the same potential, say V.

Putting A = B = V and solving equations (16), (17), we find for the charge
of the inner shell

B-2Vb - -- lflffl

t)f(2a)f(2b} - {/(«+'6) -f(a - b}}* '

In the original experiment of Cavendish the hemispheres forming the outer
shell were removed altogether from the globe and discharged. The potential
of the inner shell or globe would then be

Bl=^J(2b). ...... (19)

In the form of the experiment as repeated at the Cavendish Laboratory,
the outer shell was left in its place, but was connected to earth, so that A -= o.

40 8 Note 19: determination of law of electric attraction

In this case we find for the potential of the inner shell when tested by the
electrometer M.

"

.
}

Let us now assume with Cavendish, that the law of force is some inverse
power of the distance, not differing much from the inverse square, that is to

say>let #(r)-r-'^. ...... (21)

then /(,) = _£_,!-,. ...... (22)

If we suppose q to be a small numerical quantity, we may expand / (r) by
the exponential theorem in the form

~ q log r + (q log r)~ ~ •- ....... (23)

and if we neglect terms involving qz, equations (19) and (20) become
I a r [~a . a + b 4<z2

[~a .
\b

2 ^~b b a-b ~ «*-

« . « + & 4a2 "I

g log — g - logfl-^2J - ...... (25)

Laplace [Mec. Cel. I. 2] gave the first direct demonstration that no function
of the distance except the inverse square can satisfy the condition that a uniform

spherical shell exerts no force on a particle within it.

»

If we suppose that /3, the charge of the inner sphere, is always accurately
zero, or, what comes to the same thing, if we suppose B1 or B2 to be zero, then

bf (20) - of (a + b) - of (a - b) = o.
Differentiating twice with respect to b, a being constant, and dividing by a,

'*- = C' f"(c+2b)=f"(c),

which can be true only if f, (f) _ Q & ^^

Hence, /' (r) = C0r + Clf
and

whence, <f> (r) = Cl ^ .

We may notice, however, that though the assumption of Cavendish, that
the force varies as some inverse power of the distance, appears less general
than that of Laplace, who supposes it to be any function of the distance, it
is the most general assumption which makes the ratio of the force at two different
distances a function of the ratio of those distances.

If the law of force is not a power of the distance, the ratio of the forces at
two different distances is not a function of the ratio of the distances alone, but

Note 20: capacity of a thick disk 409

also of one or more linear parameters, the values of which if determined by
experiment* would be absolute physical constants, such as might be employed
to give us an invariable standard of length.

Now although absolute physical constants occur in relation to all the
properties of matter, it does not seem likely that we should be able to deduce
a linear constant from the properties of anything so little like ordinary matter
as electricity appears to be.

NOTE 20, ART. 272.
On the Electric Capacity of a Disk of sensible Thickness.

Consider two equal disks having the same axis, let the radius of either
disk be a, and the distance between them b, and let b be small compared with a.

Let us begin by supposing that the distribution on each disk is the same as
if the other were away, and let us calculate the potential energy of the system.

We shall use elliptical co-ordinates, such that the focal circle is the edge
of the lower disk. In other words we define the position of a given point by its
greatest and least distances from the edge of the lower disk, these distances

«(« + j8) and a (a - )8).
The distance of the given point from the axis is

r=aap, ...... (i)

and its distance from the plane of the lower disk is

z = a (a2 - i)* (I - p*)l. ...... (2)

If AI is the charge of the lower disk, the potential at the given point is

ifi = Aa~l cosec"1 a, ...... (3)

or, if we write a* = y2 + i, ...... (4)

...... (5)

If A 2 is the charge of the upper disk, the density at any point is

A

a =

(6)

where p* = «-2 (a2 - r2) = I - «2j32. (7)

Putting z = b in equation (2),

b2 = a2y2 (i - £2) or j8* = I - -£i • (8)

62 62

Hence p2 = -^- - y2 + —„ . (9)

«2y2 a?

* [This implies that such parameters are of sensible magnitude, and not deter-
mined by the dimensions of the electron.]

41 o Note 20: capacity of a thick disk

We have now to multiply the charge of an element of the upper disk into
the potential due to the lower disk, and integrate for the whole surface of the
upper disk,

i 2 Jo \2 /

= A1Ata-*(?- jT'tan-iy^) (10)

Between the limits of integration we may write with a sufficient degree of
approximation, , /h\l\ r h\i\~1

tan-1 y = y = - -ji + (-J I ]/'+(") I • (IJ)

At the centre of the disk p = i and
At the circumference,

•y = - , which agrees with (9).

p = o and y = (-) + o(-) by (9),
whereas the equation (n) gives

fb\* L b

rrU) +**

so that when b is very small compared with a, the value of y cannot differ greatly
from that given by equation (n). Hence we may write the expression (10)

12

The corresponding quantity for the action of the upper disk on itself is got
by putting A^ = A% and 6 = 0, and is

^22«-1f- (13)

In the actual case A± = Az = J£, where E is the whole charge, and the
capacity is

or, since in our approximation we have neglected f-J , our result may be ex-
pressed with sufficient accuracy in the form

(15)

showing that the capacity of two disks very near together is equal to that of
an infinitely thin disk of somewhat larger radius.

If the space between the two disks is filled up, so as to form a disk of
sensible thickness, there will be a certain charge on the curved surface, but at
the same time the charge on the inner sides of the disks will disappear, and that
on the outer sides near the edges will be diminished, so that the capacity of
a disk of sensible thickness is very little greater than that given by (15).

Note 2 1 : capacity of two circles on the same axis 4 1 1

We may apply this result to estimate the correction for the thickness of
the square plates used by Cavendish. The factor by which we must multiply
the thickness in order to obtain the correction for the diameter of an infinitely

thin plate of equal capacity is — log T .

27T O

a i a

Tin plate 600 1-017

Hollow plate n 0-381

Portland stone, &c 30 0-540

Slate 75 0-686

The correction is in every case much smaller than Cavendish supposed.

NOTE 21, ARTS. 277, 452, 473, 681.

Calculation of the Capacity of the Two Circles in Experiment VI.
The diameter of one of the circles was 9-3 inches, so that its capacity when
no other conductor is in the field is — = 2-060. The distance between their

7T

centres was 36, 24, and 18 inches, which we may call clf ca, and c3.

The height of the centres of the circles above the floor was about 45 inches,
so that the distance of the image of the circle would be about 90 inches and
that of the image of the other circle would be about

r = (90* + c«)* .
Hence, if P is the potential of the circles when the charge of each is i,

p _ TT i 2 a2 o _! _ _i

2a c 3 cs

where the first term is due to the circle itself, the second and third to the other
circle, as in Note 11, and the two last to the images of the two circles. We thus
find for the three distances

PI = 0-3438, P2 = 0-3567, P3 = 0-3689.

The capacity is 2P"1, and the number of "inches of electricity," according
to the definition of Cavendish, is 4P-1,

or 11-636, H-2I2, 10-844,

for the three cases.

The large circle was 18-5 inches in diameter and its centre was 41 inches
from the floor, so that its charge would be 12-69 inches of electricity.

Hence the relative charges are as follows:

Calculated

The large circle i-ooo i-ooo

The two small ones at 36 inches -917 -899

24 -884 -859

18 -855 -811

412 Note 22: capacity of a square plate

NOTE 22, ART. 283.
Electric Capacity of a Square.

I am not aware of any method by which the capacity of a square can be
found exactly. I have therefore endeavoured to find an approximate value
by dividing the square into 36 equal squares and calculating the charge of
each so as to make the potential at the middle of each square equal to unity.

The potential at the middle of a square whose side is i and whose charge
is i, distributed with uniform density, is

4 log (i + A/2) = 3-52549-

In calculating the potential at the middle of any of the small squares which
do not touch the sides of the great square I have used this formula, but for those
which touch a side I have supposed the value to be 3-1583, and for a corner
square 2-9247.

A B C C B A

B D E E D B
If the 30 squares are arranged as in the margin, and __,_,„„„

if the charges of the corner squares be taken for unity, __,_,_,,
the charges will be as follows : R n F F D R

A B C C B A
A B C D E F

I-OOO -599 -562 -265 -210 -2OI

and the capacity of a square whose side is i will be 0-3607.

The ratio of the capacity of a square to that of a globe whose diameter is
equal to a side of the square is therefore 0-7214.

In Art. 654 Cavendish deduces this ratio from the measures in Art. 478
and finds it 0-73, which is very near to our result. If, however, we take the
numbers given in Art. 478, we find the ratio 0-79. From Art. 281 we obtain
the ratio 0-747.

The ratio of the charge of a square to that of a circle whose diameter is
equal to a side of the square is by our calculation 1-133.

In Art. 648 Cavendish says that the ratio is that of 9 to 8 or 1-128, which
is very close to our result, but in Arts. 283 and 682 he makes it 1-153.

The numbers in Art. 281 from which Cavendish deduces this would make
it 1-1514.

The numbers given in Art. 478 would make it 1-176.

Cavendish supposes that the capacity of a rectangle is the same as that of
a square of equal area, and he deduces this from a comparison of the square
15-5 with the rectangle 17-9 x 13-4.

It is not easy to calculate the capacity of a rectangle in terms of its sides,
but we may be certain that it is greater than that of a square of equal area.

and of a cube 4 1 3

For if we suppose the electricity on the square rendered immoveable, and
if we cut off portions from two sides of the square and place them on the other
two sides so as to form a rectangle, we are carrying electricity from a place
of higher to a place of lower potential, and are therefore diminishing the energy
of the system.

If we now make the electricity moveable, it will re-arrange itself on the
rectangle and thereby still further diminish the energy. Hence the energy of
a given charge on the rectangle is less than that of the same charge on the
square, and therefore the capacity of the rectangle is greater than that of the
square*.

NOTE 23, ARTS. 288 AND 542.
On the Charge of the Middle Plate of Three Parallel Plates.

The plates used by Cavendish were square, but for the purpose of a rough
estimate of the distribution of electricity between the three plates we may
suppose them to be three circular disks.

First consider two equal disks on the same axis, at a distance small com-
pared with the radius of either.

If the disks were in contact, the distribution on each would be the same as
on each of the two surfaces of a single disk, and it would be entirely on the
outer surface.

If the distance between the disks is very small compared with their radii,
the force exerted by one of the disks at any point of the other will be nearly
but not quite normal to its surface. The component in the plane of the disk
will be directed outwards from the centre, so that the density will be greater
near the edge than in a single disk having the same charge, but as a first ap-
proximation we may assume that the sum of the surface-densities on both sides
of any element of the disk is the same as if the other disk were away.

But the density on the outer surface of the disk will be increased, and the
density on the inner surface diminished, by a quantity numerically equal to
the normal component of the repulsion of the other disk divided by 477, and the
whole charge of the outer surface will be increased, and the whole charge of the
inner surface diminished, by a quantity equal to the charge of that part of the
other disk, the lines of force from which cut the disk under consideration.

* [Approximate results may be readily obtained for such problems by the
principle that the potential energy of a system is stationary in the neighbourhood
of a position of equilibrium. Thus the energy of a given charge on a square plate
is very nearly the same as on a circular plate of equal area: therefore the capacities
of the two plates are nearly the same — according to Maxwell's result the capacity
is greater for the square plate, in the ratio 1-0027, in agreement with the final argu-
ment in the text. So also a cube may be reduced to a sphere of equal volume.
The degree of error may be elucidated by comparing the known results for elliptic
and circular plates of equal area, or for ellipsoidal and spherical bodies of equal
volume.

414 Note 23: charge of middle plate of three

Hence the charges of the inner and outer surfaces of the disk are

— w and — (a — o>)
a a v

respectively, where the value of the elliptic co-ordinate cu is that corresponding
to the edge of the other disk.

If a is the radius of either disk, and c the distance between them,

_

If we now place another equal disk on the same axis at a distance c from
one of them, the potential being the same for all three, the new disk will
greatly diminish the charge of the surface of the disk which is next to it, but
it will not have much effect on the charges of the other surfaces.

The result will therefore be that the charges of the two outer disks will
together be greater, but not much greater, than that of a single disk at the
same potential, but the charge of each of the surfaces of the middle disk will
be the same as that of one of the inner surfaces of a pair of disks at distance c.
Hence the charge of the middle disk will be to that of the two outer disks together
as o> to a.

If we substitute for the square plates of twelve inches in the side disks of
13-8 inches diameter which would have nearly the same capacity, then if the
distance between the outer disks is 1-15 inches, c = -575 and co = 1-936 and
a = 3-5 w, or the charge of the middle disk would be 3-5 times greater if the
outer disks had been removed.

If the distance between the outer disks is 1-65 inches, c = -875 and o> = 2-293,
whence « = 2-2 co, or the charge of the middle disk would have been 2-2 times
greater if the outer disks had been removed.

It is evident, however, that in the assumed distribution the potential is less
at the edges of the outer disks than at their centres. The electricity will therefore
flow more towards the edges of the outer disks, and, as this will raise the potential
near the edge of the middle disk, the charge of the middle disk will be less than
on our assumption. I have not attempted to estimate the distribution more
approximately.

Cavendish found the charge of the middle disk \ and J of what it would
have been without the outer disks. This is much less than the first approxi-
mation here given, but much greater than Cavendish's own estimate, founded
on the assumption that the distribution of electricity follows the same law in
the three plates.

Note 24: Cavendish's formula for disturbed capacity 415

NOTE 24, ARTS. 338, 652.

On the Capacity of a Conductor placed at a finite distance from
other Conductors.

Cavendish has not given any demonstration of the very remarkable formula
given in Art. 338 for the capacity of a conductor at a finite distance from other
conductors. We may obtain it, however, in the following manner.

If the distance of all other conductors is. considerable compared with the
dimensions of the positively charged conductor, C, whose capacity is to be
tried, the negative charge induced on any one of the other conductors will-
depend only on the charge of the conductor C and not on its shape. This induced
charge will produce a negative potential in all parts of the field; let us suppose

£•

that the potential thus produced at the centre of the conductor C is - — ,
where E is the charge of C and # is a quantity of the dimensions of a line.
If L is the capacity of C when no other conductor is in the field, then the

£•

potential due to the charge £ will be j , and the potential, which arises from

ft

E

the negative charge induced on other conductors, will be - — , so that the

x

actual potential will be E ( j - -) .

Dividing the charge by the potential we obtain for the actual capacity

" x-L'
or the capacity is increased in the ratio of x to x - L.

The idea of applying this result to determining the value of x by comparing
the charges of bodies, the ratio of whose capacities is known, is entirely peculiar
to Cavendish, and no one up to the present time seems to have attempted
anything of the kind.

The height of the centre of the circles above the floor seems to have been
about 45 inches. If we neglect the undercharge of other conductors and consider
only the floor, x would be about 90 inches in modern measure, but as a capacity
x is reckoned by Cavendish as zx "inches of electricity," the value of x in
"inches of electricity" would be 180.

If we could take into account the undercharged surfaces of the other con-
ductors, such as the walls and ceiling, the "machine," etc., the value of x would
be diminished, and it is probable that the value obtained from his experiments
by Cavendish, i66J, is not far from the truth.

4 1 6 Note 25: calculated capacities of cylinder and -wires

NOTE 25, ARTS. 360, 539, 666.
Capacities of the large tin Cylinder and Wires.

The dimensions of the cylinder are given more accurately in Art. 539. It
was 14 feet 8-7 inches long, and 17-1 inches circumference. Its capacity when
not near any conductor would be, by the formula in Note 12, 22-85 inches,
and when its axis was 47 inches from the floor it would be 31-3 inches, or in
Cavendish's language 62-6 inches of electricity. Cavendish makes its computed
charge 48-4, and its real charge 73-6. See Art. 666. Now the charge of either
of the plates D and E was, by Art. 671, 26-3 inches of electricity, so that

tin cylinder = 1-19 (D + E).

The capacities of the different wires mentioned in Arts. 360 and 539 are,
by calculation,

length diameter capacity

29 J 2-67

22 J 2-09

37 "IS 3-13

27-6 -15 2-46

20-8 -15 1-88

31 -15 2-71

24 -15 2-28

The ratio of the charge of the first of these wires to that of the second is 1-37.

NOTE 26, ART. 369.
Action of Heat on Dielectrics.

The effect of heat in rendering glass a conductor of electricity is described
in a letter from Kinnersley to Franklin* dated i2th March, 1761. He found
that when he put boiling water into a Florence flask he could not charge the
flask, and that the charge of a three pint bottle went freely through without
injuring the flask in the least.

Franklin in his reply describes some experiments of Canton's on thin
glass bulbs, charged and hermetically sealed and kept under water, showing
" that when the glass is cold, though extremely thin, the electric fluid is well
retained by it."

He then describes an experiment by Lord Charles Cavendish, showing that
a thick tube of glass required to be heated to 400° F. to render it permeable to
the common current.

A portion of a glass tube near the middle of its length was made solid, and
wires were thrust into the tube from each end reaching to the solid part. The
middle portion of the tube was bent, so that a portion, including the solid part ,
* Franklin's Works, edited by Sparks (1856), vol. v. p. 367.

Note 26: influence of temperature on glass 417

could be placed in an iron pot filled with iron-filings. A thermometer was put
into the filings; a lamp was placed under the pot; and the whole was supported
upon glass.

The wire which entered one end of the tube was electrified by a machine,
a cork ball electrometer was hung on the other, and a small wire, reaching to
the floor, was tied round the tube between the pot and the electrometer, in
order to carry off any electricity that might fun along upon the tube.

"Before the heat was applied, when the machine was worked, the cork
balls separated at first upon the principle of the Leyden phial. But after the
middle part of the tube was heated to 600, the corks continued to separate,
though you discharged the electricity by touching the wire, the electrical
machine continuing in motion. Upon letting the whole cool, the effect remained
till the thermometer was sunk to 400."

Experiments on the conductivity of glass at different temperatures have
been made by Buff*, Perryf, and Hopkinson J .

Hopkinson finds that if B is the specific conductivity divided by the specific
inductive capacity and multiplied by 477-, then for

glass N°. 2, log B = 1-35 + 0-04150,
glass N°. 7, log B = 4-17 + 0-02830,
where 6 is the temperature centigrade.

Glass N°. 2 is of a deep blue colour; it is composed of silica, soda, and lime.

Glass N°. 7 is "optical light flint," density 3-2, composed of silica, potash,
and lead; almost colourless, the surface neither "sweats" nor tarnishes in the
slightest degree. This glass at ordinary temperatures is sensibly a perfect
insulator.

The conductivity of glass when heated makes it very difficult to determine
its capacity as a dielectric. It appears from the experiments of Hopkinson on
glasses of known composition, that the glasses made with soda and lime conduct
more, and are also more subject to "electric polarization " and "residual charge "
than those made with potash and lead.

Both the conductivity and the susceptibility to residual charge increase as
the temperature rises, and this makes it very doubtful whether the apparent
increase of dielectric capacity, which was observed by Cavendish and also by
recent experimenters, is a real increase of the specific inductive capacity, or
merely an effect of increased conductivity.

The experiments of Messrs Ayrton and Perry § on wax at different tem-
peratures would seem to indicate a real increase of dielectric capacity, as well
as of conductivity, as the temperature rises up to the melting point. During
the process of melting the capacity decreases and at higher temperatures
begins to increase again, but the conductivity continues to increase as the
temperature rises.

* Annalen der Chemie und Pharmacie, xc. (1854), P- 257-

t Proc. R. S. 1875, p. 468. } Phil. Trans. 167 (1877), P- 599-

§ Phil. Mag. August, 1878.

c. p. i. 27

41 8 Note 27: dielectric capacities

NOTE 27, ART. 376.

Electrostatic capacity of different substances.

Cavendish Boltzmann Wiillner Gordon

Shellac* 4-47 2-95103-73 2-746

Rosin 2-55

Rosin and bees'-wax . . . 3-38

Dephlegmated becs'-wax 3-7

Plain bees'-wax 4

Sulphur SchiJto 3-84 2-88 to 3-21 2-579

Ebonite 2-21102-76 3-15 2-56 2-284

Paraffin 1-81102-47 2-32 1-96 1-994

Black caoutchouc 2-12

vulcanized 2-69 2-497

NOTE 28, ART. 383.
Capacity of a Cylindrical Condenser.

The rule by which Cavendish computed the charge of a condenser consisting
of two cylindrical surfaces having the same axis is given at Art. 313.

If R is the external and r the internal radius, and / the length of the cylinders,

T 7? -1 V

then Cavendish's expression for the "computed charge" is - R-_ -- /.

The true expression for the capacity is

i /

2 log R - log r
when the logarithms are Naperian.

We may express log R - log r in the form of the series
R - r 2 /R - A3 2 /R -

2

/R - A3 2 /R - n5 , „
U + ~r) + 5 \M + r) + *°"

R+~r 3
and we thus find as an approximate value of the capacity

r\«
f)

4 R -

4 R-r I - 3 \FTf ~ 45 T J'

The first term agrees with Cavendish's rule, for the "capacity" is half the
"inches of electricity," but the other terms show that Cavendish's rule gives
too large a value for the computed charge.

* [In Kaye and Laby, Physical and Chemical Constants, 191 1, the value for shellac
is given as 3 — 3-7 and for rosin as 1-8 — 2-6. The value for crown glass is given as 5 — 7
and for flint as 7 — 10, both well above shellac, as Cavendish found, but in a different
order. Cavendish's results are tabulated in Note 15, supra. It is found by Eguclii,
Proc. Phys. Math. Soc. of Japan, 1 920, that a mixture of resin and beeswax, solidified
under pressure, exhibits permanent polarization, which is absent in the separate
substances.]

i

Note 28: capacities of cylindrical condensers 419

The following table gives the charge as computed by Cavendish compared
with that given by the correct formula.

Flint jar
cylinder

Cavendish

85-9

87-1

True

72-55
73-^Q

Observed charge
by computed

9-88
8-83

Therm. I.
II

«.->/ i
II-O
II-I

/ j oy

8-37
7-84

9-58
IO"2Q

Green cyl. i

2

77'2
76-6

/ ^T1
65-92

6l-S4

11-15

11*22

3

40-8

JT-
•*4-2O

TO-2O

NOTE 29, ART. 437.
Electrical Fishes.

The fishes which are known to possess the power of giving electric shocks
belong to two genera of Teleostean Fishes and one of Elasmobranch Fishes,
and the position and relations of the electric organs are different in each.

In every instance, however, the electric organ may be roughly described
as being divided in the first place into parallel prisms or columns by septa,
which we may call (with reference to the organ, not the fish) longitudinal septa,
and in the second place each column is divided transversely by diaphragms,
the structure of which is different in the different families, but in every case
the terminations of the nerves lie on that surface of each diaphragm which
during the discharge becomes its negative surface.

In the large family of the Torpedos the electric organs are formed of a
large number of short columns, the columns running from the belly to the back
of the fish. The nerves terminate on the ventral surface of each diaphragm,
and the electric discharge is from belly to back through the organ, or in other
words, the back of the fish becomes positive with respect to the belly.

There seems to be but one species of Gymnotus. It is a long eel-like fish.
Its electric organs consist of a smaller number of very long columns running
from the tail to the head of the fish. The nerves terminate on the posterior
surface of the diaphragms, and the electric discharge is from tail to head through
the organ, or the head of the fish becomes positive with respect to the tail.

There are three species of Malapterurus which are known to be electrical.
In these the electric organs run longitudinally. Bilharz, observing that the
nerves appear to terminate in an expansion like the head of a nail on the posterior
surface of the diaphragms, concluded that the electric discharge must be from
tail to head through the organ, as in the Gymnotus. Ranzi* however, and
afterwards, independently of him, Du Bois Reymondf found that the discharge

* Nuovo Cimento, Tomo II, Dicembre 1856, p. 447, quoted by Du Bois Raymond
"Zur Geschichte der Entdeckungen am Zitterwelse," Archiv fur Anatomie u. Physio-
logic, &c. Leipzig, 1859, p. 210.

f Monatsbericht il. k. Akatl. Berlin, 1858.

27—2

4.20 Note 29: electrical fishes

is really from head to tail through the organ, so that the tail becomes positive
with respect to the head, and Schultze, who had been led to believe, from a
comparison of his own observations on the organs of pseudo-electric fishes with
the drawings of Bilharz, that the nerves might pass through the diaphragms
and terminate on their anterior surfaces, found, on examining the preparations
sent him by Du Bois Reymond, that this was really the case in Malapterurus,
so that we may now assert that in every known case the terminations of the
nerves are on that side of each diaphragm which during discharge becomes
negative.

The origin of the nerves which supply the electric organs is different in the
three families.

In the Torpedos the electric nerves are derived from the posterior division
of the brain. Irritation of this lobe produces an electric discharge of the organ,
but no muscular contraction. Irritation of other parts of the brain produces
muscular contractions, but not electric discharges, unless the disturbance pro-
duced affects the electric nerves.

In the Gymnotus the electric nerves arise from the whole length of the
spinal cord, and in Malapterurus the electric organs are supplied by the 2n<1
and 3rd pair of spinal nerves.

The electric nerves are so called because they govern the discharges of the
electric organ. No essential difference has been observed between the electric
phenomena in these nerves and those in other nerves. They must be classed,
with respect to origin as well as function, among the motor nerves. The only
difference is that their function is to govern the electric discharge of a peculiar
organ, instead of the contraction of a muscle.

The experiments of Dr Davy* and those of Matteuccif showed that the
discharge of the Torpedo produces all the known phenomena of an electric
discharge. Faraday J did the same for the Gymnotus, and Du Bois Reymond §
for the Malapterurus.

M. Marey[| has recently investigated some of the electrical phenomena of
the discharge of the Torpedo. He employed three methods of indicating the
discharge, the prepared leg of a frog, which is extremely sensitive to the feeblest
current, but has the disadvantage that the time required for the contraction
of the muscles, and still more the time required for their relaxation, is many
times the period of the recurrence of the electric discharges of the Torpedo, so
that the rapidly changing phases of the discharge cannot be distinguished by
this method.

The second indicator used by Marey was the electromagnetic signal of
M. Deprez, which can register 500 electric currents in a second by the motion
of a tracing point over the smoked surface of a revolving cylinder. The action

* Phil. Trans. 1834. f Comptes Rendus, 1836.

J London Medical Gazette, 1838. § Berlin Monatsb. 1858.

II Travaux du Laboratoire de M. Marey, in. (1877).

Experimental investigations 42 1

of this instrument was sufficiently prompt to register the number of the separate
currents of which the "continued discharge" of the Torpedo consists. It was
not, however, sufficiently sensitive to trace the curve of the intensity of the
current when the strength of the current was less than that required to work
the tracing point, and the trace therefore represents only the phases of greatest
strength of current in each separate discharge.

M. Marey calls each separate discharge of the Torpedo an electric flux.

The whole discharge consists of a rapid succession of these fluxes, at the
rate of from 60 to 140 per second, gradually decreasing in intensity, but re-
maining sensible sometimes for a second or a second and a half. In one of the
tracings 120 fluxes may be counted quite distinctly, with a somewhat irregular
continuation of feebler fluxes.

The electromagnetic signal, however, depending on the attraction of a soft
iron armature, is acted on by a force varying nearly as the square of the strength
of the current. It is therefore unable to respond to feeble currents, and it does
not indicate the direction of the currents, even when improved in certain par-
ticulars by M. Marey.

The third indicator used by M. Marey was the capillary electrometer of
M. Lippmann. In this instrument a capillary glass tube is filled in one part with
mercury and in the other with dilute sulphuric acid. The pressure of the mercury
is so adjusted that the division between the two liquids appears in the middle
of the field of a microscope. The electrodes of the instrument are connected
with the two liquids respectively, and when a small electromotive force acts
from one electrode to the other, the surface of separation of the two liquids
is seen to move in the same direction as the electromotive force, that is to say,
the mercury advances if the electromotive force is from the mercury to the acid,
and retreats if it is in the opposite direction.

This instrument, therefore, is admirably suited for the investigation of small
electromotive forces, and the mass of the moving parts is so small that it responds
most promptly to every variation of the electromotive force. Its only defect
is that its range is limited to the electromotive force required to decompose
the acid, and the electromotive force of the Torpedo, as we know, is of far
greater intensity than this. M. Marey therefore used a shunt, so as to diminish
the force acting on the electrometer to such a degree as to be within the working
limits of the instrument.

He thus ascertained that the back of the fish is positive with respect to the
belly, not only on the whole, but during every phase of each flux, and that it
does not sink to zero between the fluxes.

The modern researches on the electric fishes would seem to point to the
conclusion that the electric organ is not like a battery of Leyden jars in which
electricity is stored up ready to be discharged at the will of the animal, but
rather like a Voltaic battery, the metals of which are lifted out of the cells
containing the electrolyte, but are ready to be dipped into them.

422 Note 29: electrical Jishes

There seems to be no electric displacement in the organ till the electric nerve
acts on it. The energy of the electric discharge which then takes place is not
supplied to the organ by the nerve; the nerve only sets up an action which is
carried on by the expenditure of energy previously supplied to the organ by
the materials which nourish it.

During the discharge certain chemical changes take place in the organ.
These changes involve a loss of intrinsic energy, and the chemical products
found in the organ after repeated electric discharges are similar to the products
found in muscles after they have performed mechanical work.

The organ, by repeated discharges, becomes incapable of responding to
stimulation, and can only recover its power by the gradual process by which
it is nourished.

Faraday proposed to try whether sending an artificial current through the
Gymnotus would exhaust the organ, if sent in the direction of the natural
discharge, or would restore it more rapidly to vigour if sent in the opposite
direction. The only experiments on the effect of electricity on electric fishes
seem to be those of Dr Davy, who found that an artificial current did not excite
the electric organs of the Torpedo, though it had an effect on the muscles, but
less than on those of other fishes, and of Du Bois Reymond, who found that
Malapterurus was very slightly affected by induction currents passing through
the water of his tub, though they were strong enough to stun and even to kill
other fishes. When the induction currents were made very strong, the fish
swam about till he had placed his body transverse to the lines of discharge, but
did not appear to be much annoyed by them*.

The most valuable experiments hitherto made are probably those of Dr Carl
Sachs, who went out to Venezuela in 1876 for the express purpose of studying
the Gymnotus in its native rivers, with all the resources of Du Bois Reymond's
methods. Dr Sachs lost his life in an Alpine accident in 1878, and as he did
not himself publish his researches, it is to be feared that their results are lost
to science.

* A somewhat extensive account of the subject is given in a dissertation,
De' Pesci elettrici e pseudoelettrici, per Stefano St. Sihleanu (di Bucuresti, Romania),
Napoli, 1876.

[Much attention has more recently been given to the subject by physiologists.
It appears from microscopic observations (cf. Bayliss' I'hysiology, 1917, p. 661)
that in Malapterurus the electric organ consists of a large number of parallel plates
arranged along the fish, all innervated from a single neurone on each side: it gives a
discharge at about 450 volts, lasting about -005 sec. The manipulations of polari-
zation and arrangement of cells by which discharges of high tension were obtained
by Plant6 from his secondary batteries about thirty years ago may perhaps be
regarded as in analogy with the organic activities that go on in mutual correlation in
the electric organ of the fish.]

Note 30: inequality of opposed condensed charges 423

NOTE 30, ART. 560.

Excess of redundant fluid on positive side above deficient fluid on
negative side of a coated plate.

When two equal disks have the same axis, the first being at potential V
and the other connected to the earth, the algebraic sum of the charges of the
two disks is just half the charge of the two disks together if they were both
raised to potential V.

If the two disks are very near each other, the charge of the two together is
very little greater than that of one by itself at the same potential.

Hence the excess of the redundant fluid above the deficient, when one of
the disks is raised to potential V and the other connected with the earth, is
very little greater than Tr~laV , where a is the radius. (See Note 4.)

NOTE 31, ART. 573.
Intensity of the Sensation produced by an Electric Discharge.

Cavendish tried this and several other experiments (Arts. 406, 573, 597,
610, 613) to determine in what way the intensity of the sensation of an electric
shock is affected by the two quantities on which the physical properties of the
discharge depend, namely the quantity of redundant fluid discharged, and the
degree of electrification before it is discharged, the resistance of the discharging
circuit being supposed constant.

He seems to have expected (Art. 597) that the strength of the shock would
be "as the quantity of electricity into its velocity," or in modern language, as
the product of the quantity into the mean strength of the current of discharge.
Since the electromotive force acting on the body of the operator is measured
by the product of the strength of the current into the resistance of the body,
which we may suppose constant, Cavendish's hypothesis would make the in-
tensity of the shock proportional to the work done by the discharge within the
body.

According to this hypothesis, if a jar charged to a given degree produces
a shock of a certain intensity, then a charge equal to n times the charge of this
jar, communicated to n2 similar jars, and discharged through the same resistance,
would give a shock of equal intensity.

By the experiment recorded in Arts. 406 and 573, in which n = 2, it appeared
that the shock given by four jars charged with the electricity of two jars, was
rather greater than that of a single jar.

In the experiment in Art. 610 Cavendish compared the shock of jar I
electrified to 2j, with that of B + 2.A electrified to the same degree and com-
municated to the whole battery. Here the capacity of B + 2A was equal to
6 times jar i, and that of the whole battery was 154 times jar i, so that 6 times

424 Note 31: measures of sensation

the quantity of electricity communicated to 154 jars gave a shock of about
the same strength, though as Cavendish remarks, "as there is a good deal of
difference between the sensations of the two, it is not easy comparing them."

Here 154 is the 2g power of 6, so that the shock seems to depend rather
more on the quantity of electricity than on the degree of electrification. This
is the only experiment which Cavendish has worked out to a numerical result.

By the other experiments recorded in Art. 610, 34^ communicated to 7 rows,
gives a shock equal to 22 communicated to one row. This would make the
number of jars as the 4-3 power of the charges. By Art. 613 the number of jars
would be as the 3-3 power of the charge.

Cavendish had not the means of producing a steady current of electricity,
such as we now obtain by means of a Voltaic battery, so that he could not
discover the most important of the facts now known about the physiological
action of the current, namely, that the effects of the current, whether in pro-
ducing sensations, or in causing the contraction of muscles, depend far more
on the rapidity of the changes in the strength of the current, than on its absolute
strength. It is true that a steady current, if of sufficient strength, produces
effects of both kinds, but a current so weak that its effect, when steady, is
imperceptible, produces strong effects, both of sensation and contraction, at
the moments when the circuit is closed and broken.

But although this may be considered as established, I am not aware of any
researches having been made, from the results of which it would be possible
to determine, from the knowledge of the physical character of two electric
discharges, which would produce the greater physiological effect.

The kind of discharges most convenient for experiments of this kind is that
in which the current is a simple exponential function of the time, and of the form

_*
X" Ce"'' ,

where x is the strength of'the current at the time /, C its strength at the beginning
of the discharge, and r a small time, which we may call the time-modulus.

In this case the whole physical nature of the discharge is determined by
the values of the two constants C and r. The intensity of the sensation pro-
duced by the discharge through our nerves is, therefore, some function of these
two constants, and if we had any method of ascertaining the numerical ratio
of the intensities of two sensations, we might determine the form of this function
by experiments. We can hardly, however, expect much accuracy in the com-
parison of sensations, except in the case in which the two sensations are of the
same kind, and we have to judge which is the more intense.

According to Johannes Miiller, the sensation arising from a single nerve
can vary only in one way, so that, of two sensations arising from the same nerve,
if one remains constant, while the other is made to increase from a decidedly
less to a decidedly greater value, it must, at some intermediate value, be equal
in all respects to the first.

produced by various kinds of electric discharge 425

In the ordinary mode of taking shocks by passing them through the body
from one hand to the other, the sensations arise from disturbances in different
nerves, and these being affected in a different ratio by discharges of different
kinds, it becomes difficult to determine whether, on the whole, the sensation
of one discharge or the other is the more intense.

I find that when the hands are immersed in salt water the quality of the
sensation depends on the value of T.

When T is very small, say o-ooooi second, and C is large enough to produce
a shock of easily remembered intensity in the wrists and elbows, there is very
little skin sensation, whereas when T is comparatively large, say o-oi second, but
still far too small for the duration of discharge to be directly perceived, the
skin sensation becomes much more intense, especially in one place where the
skin may have been scratched, so that it becomes almost impossible so to con-
centrate attention on the sensation of the internal nerves as to determine
whether this part of the sensation is more or less intense than in the discharge
in which T is small.

There are two convenient methods of producing discharges of this type.

(i) If a condenser of capacity K is charged to the potential V, and dis-
charged through a circuit of total resistance R (including the body of the
victim), F

C-~, r=KK.

K

The whole quantity discharged is Q = CT = VK, and if r is the resistance
of the body of the victim, the work done by the discharge in the body is

(2) If the current through the primary circuit of an induction coil is y,
the coefficient of mutual induction of the primary and secondary coils M, that
of the secondary circuit on itself L, and the resistance of the secondary circuit R,
then for the discharge through the secondary circuit when the primary circuit
is broken,

-
* ~ R ' 2 L R-

I first tried the comparison of shocks by means of an induction coil, in which
M was about 0-78 and L about 52 earth quadrants, and in which the resistance
of the secondary coil was 2710 Ohms. By adding some German silver wire to
the primary coil, its resistance was made up to nearly I Ohm, and the primary
thus lengthened, another wire of the same resistance, and a variable resistance Q,
were made into a circuit. One electrode of the battery was connected to the
junction of the two equal resistances, and the other was connected alternately
to the two ends of the resistance Q, so that the current through the primary
was varied in the ratio of the primary P to P + Q, while the resistance of the
battery-circpit remained always the same. When the smaller primary current,

426 Note 31 : measures of sensation

y, was interrupted, I took the secondary discharge through my body directly,
but when the larger current, y', was interrupted, I made the secondary dis-
charge pass through a capillary tube filled with salt solution as well as my body.

The resistance between rny hands when both were immersed in salt water
was 1245 Ohms, making with the secondary coil a resistance of 3955 m the
secondary circuit, so that the time-modulus of the discharge was T = 1-3 x io~3
seconds.

The resistance of the first capillary tube was 370,000, so that when it was
introduced T — 1-4 x io~5.

By a rough estimate of the comparative intensity of the shocks I supposed
them to be of equal intensity when y' = 8-^y, and therefore if we suppose that
two shocks remain of equal intensity when C varies as TP, p = 0-468.

By another experiment in which a tube was used whose resistance was
450,000, p = 0-534.

When the shocks at breaking contact were nearly equal, that at making
contact was very much more intense with the small primary current and small
secondary resistance than with the large primary current and large secondary
resistance.

I then compared the discharges from two condensers of i and o-i micro-
farads capacity respectively, charging them with a battery of 25 Leclanche
cells, the electromotive force of which was about 36 Ohms.

The resistance of the discharging circuit for the microfarad was 11,200 Ohms,
including my body, so that

r = 1-12 x io~2 seconds.

The resistance of the discharging circuit of the tenth of a microfarad was
3600, so that T' = 3-6 x IQ-*.

The values of C were inversely as the resistances, so that if the two shocks
were, as I estimated them, nearly equal, the value of p would be 0-670.

This experiment was much more satisfactory and more easily managed than
that with the induction coil, and I thought it desirable to apply the same method
to the comparison of the contractions of a muscle when its nerve was acted on
by the discharge. I therefore availed myself of the kindness of Mr Dew-Smith,
who prepared for me the sciatic nerve and gastrocnemius muscle of a frog, and
attached the preparation to his myograph. The discharge was conducted through
about 0-4 cm. of the nerve by means of Du Bois Reymond's unpolarizable
electrodes, the resistance of the electrodes and nerve being 35,000 Ohms. When
the electrodes were in contact their resistance was 23,000, leaving about 12,000
as the resistance of the nerve itself.

I used two condensers, one o-i microfarad, and the other an air-condenser
of 270 centimetres capacity in electrostatic measure, or about 3 x io~4 micro-
farads.

The first was charged by one cell and the second by 25. The resistances
were arranged so that the contractions produced in the muscle we,re much less

produced by various kinds of electric discharge 427

than a third of a maximum contraction. The discharges were made alternately
every 15 seconds, and when the resistances were 35,000 and 140,000 respectively,
the alternate contractions as recorded on the myograph were as follows:

Small condenser Large condenser

144 146

147 148

147 147

146 146

147 145

Here the time-modulus was 1-05 x io~B seconds for the small condenser
and 1-4 x io~2 for the large one, and the values of C were as I to 100, so that
p = -640.

If we suppose that Cavendish took the shocks through pieces of metal held
in his hands, the resistance of the circuit would depend on the state of his skin.
He occasionally used a piece of apparatus, which he nowhere describes, but
which he names in three places* a shock-melter.

From Art. 585 it would appear that it was filled with salt water, even when
fresh water was the subject of the experiment, and from Art. 637 Cavendish
seems to have considered it his last resource as a method of receiving shocks.
I therefore think that it must have been an apparatus by which his hands were
well wetted with salt water, so that the resistance of his body would be between
1000 and 2000 Ohms.

The capacity of his battery of 49 jars was 321,000 glob, inc., which comes
to rather less than half a microfarad.

The discharges of this through 2000 Ohms would have a time-modulus of
about one-thousandth of a second.

The following table gives the different results obtained by Cavendish and
by myself, with the time-modulus of the discharges compared. The quantity p
is such that the ratio of the initial strength of the two discharges is inversely
as the p power of the ratio of the time-moduli when the shocks are equal in
intensity, or Q _ ^

'c, W <?2 W w2 W

The number of jars among which a quantity of electricity must be divided
in order to give a shock of a given intensity through a given resistance, varies

as the — power of the quantity of electricity.

Cavendish's experiments.

TI T2 P

Art. 573 0-0000065 0-000026 0-5 +

... 610 0-0000065 o-ooi 0-652

... do. 0-00014 o-ooi 0-767

... 613 0-00014 0-00042 0-697

* Arts. 585, 622, 637. See facsimile at p. 317.

428 Note 31: Cavendish's measures of electric shocks

Experiments by the Editor.

Induction coil 0-000014 0-0013 0-468

do. o-ooooii 0-0013 0-534

Condensers 0-00036 0-0112 0-670

Experiments on the prepared nerve and muscle of a frog,
o-ooooi 0-014 0-640

This value of p does not differ much from 0-652, the only result which
Cavendish has deduced in a numerical form from his experiments.

The most unaccountable of all the results arrived at by Cavendish is one
which seems to have perplexed him so much that he has left the account of the
experiments among which it occurs in a very impeffect state. He found (Arts.
639, 644) that the shock of a Ley den jar taken through a long thin copper wire
produced a more intense sensation than when it was taken from the jar directly.

As in some of the experiments the wire was wound on a reel, and therefore
the self-induction of the current might produce an oscillatory discharge, the
physiological effects of which might be different from those of the simple dis-
charge; I charged two Leyden jars to the same potential, using Thomson's
Portable Electrometer as a gauge electrometer, and took the discharge of one
through the secondary wire of an induction coil, the resistance of which was
about 1000 Ohms, and that of the other through an ordinary resistance coil
of 1000 Ohms.

In every trial I found that the sensation was more intense when taken
through the ordinary resistance coil than when taken through the induction
coil, and it is manifest that in the latter case the current begins and ends much
less abruptly, so that the result is quite in accordance with the modern theory,
that the sensation depends on the rapidity with which the strength of the current
changes. I am, therefore, quite unable to account for the opposite result obtained
by Cavendish. At the same time it is quite impossible that Cavendish could be
mistaken in this comparison of the intensity of his sensations, for he had more
practice than any other observer in comparing them, and he repeated this
experiment many times.

The only apparent objection to the experiment is that the resistance of the
copper wires was only 430 in one case and only 1000 in the other, whereas the
resistance of a man's body, from one hand to the other, varies from about
1000 when the hands are thoroughly wet, to about 12,000 when they are dry,
so that the resistance of the copper was small compared with the possible varia-
tions of the resistance of Cavendish's body.

The resistances of the tubes filled with solutions of salt, &c., were very
much greater, being from 20,000 to 900,000.

Note 32: resistances of iron wire and salt water compared 429

NOTE 32, ARTS. 398, 576, 687.
Comparison of the Resistance of Iron Wire and Salt Water.

Cavendish never published the method by which he made this comparison,
but the result given in Art. 398 seems to have been accepted by men of science
on Cavendish's bare word, without any question as to how it was obtained.

It appears fron Art. 576 that Cavendish made his body and the iron wire
the branches of a divided circuit, and then tried how many inches of salt water
must be put in the place of the iron wire, so that the shock might appear of
the same strength.

By Matthiessen's experiments on the resistance of metals, the resistance of
an iron wire of the dimensions given by Cavendish would be about 196 Ohms.
As this is much less than that of a man's body from hand to hand, it would
have made hardly any difference to the shock whether Cavendish took it through
his body alone, or through his body and the iron wire in series.

By using the iron wire as a shunt and increasing the discharge so as to
obtain a shock of easily remembered intensity, Cavendish was enabled to
compare the wire with a column 5-1 inches long of saturated solution of salt.

By this experiment the resistance of saturated solution of salt is 355,400
times that of iron.

By the statements in Art. 398, that the resistance of rain-water is 400,000,000
times that of iron wire, and 720 times that of a saturated solution of sea-salt,
the resistance of saturated solution would be 555,555 times that of iron wire.

It is true that this result given by Cavendish does not agree with the only
experiment he has recorded, but we must remember that it is the only result
which he published, and therefore he must have thought it the best he had.

By Kohlrausch's experiments on salt solutions combined with Matthiessen's
on metals, the resistance of saturated solution of salt is 451,390 times that of
annealed iron, when both are at 18° C. The ratio of the resistances would agree
with that given by Cavendish at a temperature of about n° C.

The coincidence with the best modern measurements is remarkable.

NOTE 33, ART. 619.

Conductivity of Solutions of Salt.

According to the measurements of Kohlrausch* the electric conductivity k,
of saturated solution of sodium chloride, the conductivity of mercury at o° C.
being taken as unity, is given by the equation

io8 k = 1259 (J + 0-0308^ + O-OOOI46/2).
* Wiedemann's Annalen, Bd. vi. (1879), p. 51.

43° Note 33: conductances of solutions of common salt

When the temperature is near 18° C., we may use the equation

= 2015 + 45-1 (/ - 18).

Saturated solution at 18° contains according to Kohlrausch 26-4 per cent,
of salt. Cavendish's saturated solution contained — ^ of salt, which is equivalent
to 26-45 per cent.

Kohlrausch finds that saturated solution of salt is one of the best standard
substances for the comparison of the resistance of other electrolytes. Its con-
ductivity seems to be sensibly the same, whether it is made with chemically
pure salt or with the ordinary salt of commerce. The temperature coefficient
is also smaller than that of many other electrolytes.

For other solutions of sodium chloride he finds that at 18°

IO*k •= 13650^) — 227OO/)2,

where p is the proportion, by weight, of the salt to the whole solution.
For the particular solutions examined by Cavendish we have

resistance in resistance found
p io*A terms of sat. sol. by Cavendish

3^ 2015 i i sat. sol.

t\ 980 2-56 1-91 salt in ii

•rV 430 4'69 3-97 salt in 29

7V 190 .10-58 8-8 salt in 69

TT« 94 21-44 15-75 salt in 142

TTTJ 9° 22-39 20-05 salt in 149

13-65 147-6 93-02 salt in 999

4-55 442-9 340-85 salt in 2999

1

NOTE 34, ART. 626.
Conductivity of other Solutions.

The substances mentioned by Cavendish are easily identified, with the
exception of "calc. S. S. A." and "f. alk. d." The weights of the quantities
furnish no indication, for they are so large as to show that a dilute solution
was used. The letters A and D probably indicate the bottles in which the
solutions were kept.

The expression f. alk. or fixed alkali occurs in several parts of Cavendish's
writings, especially in the manuscripts lithographed by Mr Vernon Harcourt
in the Report of the British Association for 1839. ^ certainly means pearl ashes
or carbonate of potash. The full title seems to have been alkali fixum vcgetabilc,
as distinguished from alkali fixum fossile, which is sodic carbonate, and other
writers seem to have used the expression fixed alkali for either of these, but
Cavendish always uses the expression as a synonym for pearl ashes, and dis-
tinguishes potassic hydrate by the name of "sope leys."

Note 34: conductances of other solutions 431

The conductivity as determined by Cavendish agrees much better with
potassic carbonate than with potassic hydrate, the conductivity of which is
much greater.

It seems likely that calc. S. S. was sodic carbonate, and the conductivity
would agree very well with this explanation, only it is difficult to find among
the names in use at the time any which could be written in this form. Mr [P. T.]
Main has suggested Calcined Salsola Soda. The burnt seaweed from the shores
of the Mediterranean, from which soda was often extracted, was, I believe,
called salsola, but I doubt whether the word soda was then in use.

The weights of the other substances are, when reduced to pennyweights, not
very far from the equivalent numbers now received, hydrogen being taken as
the unit.

The most remarkable exception is common salt itself, the solution of which
was one in 29, and therefore in 1116 there were 37-2 parts of salt. Now the
equivalent of NaCl is 58-5, which is very much greater.

Besides this the conductivity of a solution of salt in 29 of water would be
much less in comparison with that of the other solutions than would appear
from Cavendish's results, whereas if we assume that the molecular strength
of the salt solution was really the same as that of the other solutions, the numbers
do not differ much from those given by Kohlrausch.

The following table shows the results obtained by Cavendish and by
Kohlrausch.

Name given by
Cavendish

Sea Salt
Sal Sylvii
Sal Ammoniac
Calcined Glauber's

Salt

Quadrangular Nitre
Calc. S. S.
f. alk.

Oil of Vitriol
Spirit of Salt

Modern
symbol

Nad

KC1

NH4C1

£Na2SO4
NaNO3

!Na2CO3? + *H20
iK2CO3 + *H2O

AHC1 + arHjjO

Weight

used by
Cavendish

Modern

equivalent

Conductivity
found by
Cavendish
(Sea Salt - 1)

Conductivity
found by
Cavendish
(NaCl - 1)

37-2?

58-5

I-OO

I-OO

74

74-5

1-08

I-2I

5i

53'5

1-13

I-I7

69

71

0-696

o-95

89

85

0-887

0-91

346

83 + 18*

0-852

0-72

139

99 + i8x

0-819

0-96

48

49

0-783

1-23

130

36-6+18*

1-72

1-97

The theory of the electric resistance of electrolytes has been put on an
entirely new footing by F. Kohlrausch, who has not only measured the re-
sistance of a large number of solutions of different strengths and at different
temperatures, but has discovered that the conductivity of a dilute solution of
any electrolyte in water is the sum of two quantities, which we may call the
specific conductivities of the components of the electrolyte, multiplied by the
number of electro-chemical equivalents of the electrolyte in unit of volume of
the solution. (Since the components of an electrolyte are not themselves
electrolytes, it is manifest that they can have no actual conductivity, but the

432

Note 34: conductances of salt solutions

number to which we may give that name is such that when any two ions are
actually combined into an electrolyte, the conductivity of the electrolyte
depends on the sum of their respective numbers.)

Kohlrausch has also calculated the actual average velocity in millimetres
per second with which the components are carried through the solution under
an electromotive force of one volt per millimetre; and on the hypothesis that
the components are charged with the electricity which travels with them, he
has calculated the force in kilogrammes weight which must act on a milligramme
of the component in order to make its average velocity in the solution one
millimetre per second.

It appears to me that the simplest measure of the specific conductivity of
an ion is the time during which we must suppose the electric force to act upon
it so as to generate twice its actual average velocity. If we suppose that all the
molecules of the ion are acted on by the electromotive force, but that each
of them is brought to rest by a collision with a molecule of the opposite kind
n times in a second, then the average velocity will be half that which the force
can communicate to the molecule in the nth part of a second.

Salts with

Vnivalent
Metals with

univalent acids

bivalent acids

n x io-10

T x io18

n x io-10

T x io18

H

I594I

6273

H2

26732

3741

K

2354

42480

K2

2844

35160

XH4

5297

18880

(Nig,

6719

14883

Na

6131

16310

Na,

8730

"455

Li

30214

3310

Li2

55430

r&H

Ag

1030

97087

A ry

* o*

1275

78431

Cl

255i

39200

SO4

2305

43384

Br

1030

97087

CO3

4071

24564

I

637

156986

F

7848

12740

Bivalent Metals

CN

3433

29129

with SO4

N03

1569

63735

Kg

480

3776

C103

1324

75529

Zn

11281

8865

CjHjOg

3286

30432

Cu

11772

8496

iBa "

2207

453io

S04

42 1 S

23708

iSr
JCa

Pig
iZn
lCu

8681

16180

6817

4806

27925
11520
6180
14670
20807

According to the theory of Clausius, it is only a small proportion, sa\
of the molecules, which, at any given instant, are dissociated from molecules
of the other kind, so as to be free to move under the action of the electromotive
force, so that we must suppose each of the free molecules to continue free for

Note 35.- capacity of a circular disk 433

a time pT; but since the proportion of free molecules to combined ones is quite
unknown, the only definite result we can obtain from Kohlrausch's data is a
certain very small time T, such that if the electromotive force acted on the
molecules of the component during the time 7", it would impress on them a
velocity twice their actual average velocity.

Since the time T is very small, it is more convenient to speak of the molecule
being brought to rest « times in a second, and to calculate «•.

NOTE 35, ART. 654.
On the Ratio of the Charge of a Globe to that of a Circle of the same Diameter.

The true valuef of this ratio is Jir = 1-570796. . . ' : it had not been discovered
until much later .

Cavendish has given several different values as the results of his experi-
ments.

In the account of his experiments, which represents his most matured con-
clusions, he states this ratio is 1-57 (Art. 237).

All the other values, however, either as stated by Cavendish or as dedncible
from his experiments, are lower than this.

* [It is to be remembered that these remarks were published by Maxwell in 1879.
The hypothesis of free time T has been developed by J. J. Thomson, and later has
found application for the case of electrons, in a theory of electric conduction in metals
by Drnde and others.]

t [According to Lord Kelvin, writing in 1869 (Papers on Electrostatics and
Magnetism, p. 179) the expression for the distribution of electricity on a circular
disk, involving this value of its electric capacity, was first given by Green near the
conclusion of his paper "On the Laws of the Equilibrium of Fluids analogous to
the Electric Fluid " (Cambridge Transactions), so late as 1832, and comparison made
with the experiments of Coulomb on a copper plate 10 inches in diameter.

It is however the determination of capacity, a conception rendered possible by his
virtual introduction of the idea of potential, that is here original with Cavendish.
The law of density of the charge on a disk, here referred to, is an immediate inference
from Newton's theorem (Principia, Lib. I, Prop, xti, cor. 3) that a gravitating shell
bounded by similar ellipsoidal surfaces exerts no attraction throughout its interior.
Cf. Maxwell's Introduction, supra, pp. 10, 18.

In a footnote Lord Kelvin records * an entry which I find written in pencil in

an old memorandum book.'

Plymouth, Mon. July 2. 1849.

" Sir William Snow Harris has been showing me Cavendish's unpublished MSS-.
put in his ha»uis by Lend Burlington, and his work upon them : a most valuable mine
of results. I find already the capacity of a disc (circular; was determined experi-
mentally by Cavendish as 1/1-57 °f that of a sphere of the same radios...."

After due i niirmrai of surprise he proceeds " It is much to be desired that these
manuscripts of Cavendish gKnnlH be published complete; or, at all events, that their
safe keeping and accessibility should be secured to the world."]

c. P. i. 28

434 Note 35: capacity of a circular disk

In Art. 281 the charge of the globe of 12-1 inches diameter being i, that of
a circle 18-5 inches diameter is given as -992. The ratio of the charge of a globe
to that of a circle of equal diameter as deduced from this is 1-542.

In Art. 445 the charge of the globe is compared with that of a pasteboard
circle of 19-4 inches diameter. Cavendish gives the actual observations but does
not deduce any numerical result from them, which shows that he did not attach
much weight to them. As they seem to be the earliest measurements of the
kind, I have endeavoured to interpret the observations by assuming that the
positive and negative separations were equal when the observations are qualified
in the same words by Cavendish.

I thus find 14-2 or 14-3 for the charge of the globe, and 15-2 for that of
the circle, and from these we deduce for the ratio of the charge of a globe to
that of a circle of equal diameter 1-5054.

In Art. 456 the ratio as deduced by Cavendish from the observations on the
globe and the tin circle of 18-5 inches diameter is 1-56.

From the numerical data given in the same article, the ratio would be 1-554.

Cavendish evidently thought the result given here of some value, for he
quotes it in the footnote to Art. 473.

Another set of observations is recorded in Art. 478, from which we deduce
the ratio 1-561.

It appears by a comparison of Arts. 506 and 581 that Cavendish, at the date
of the latter article (which is doubtful), supposed the ratio to be 1-5. (See
footnote to Art. 581.)

At Art. 648 the ratio is stated as 1-54.

At Art. 654 measures are given from which we deduce 1-542 and 1-37.

The numbers in Art. 682 are the same as those in Art. 281.

[ 435 ]

LIFE OF CAVENDISH

BY THOMAS YOUNG, M.D., F.R.S.

(From the Supplement to the Encyclopaedia Britannica, 1816-1824.)

HENRY CAVENDISH, a great and justly celebrated Chemist, Natural Philosopher,
and Astronomer; son of Lord Charles Cavendish, and grandson of William,
second Duke of Devonshire; born the zoth of October, 1731, at Nice, where his
mother, Lady Anne Grey, daughter of Henry, Duke of Kent, had gone, though
ineffectually, for the recovery of her health.

Of a man, whose rank, among the benefactors of science and of mankind,
is so elevated as that of Mr Cavendish, we are anxious to learn all the details
both of intellectual cultivation and of moral character that the labours of a
biographer can discover and record. Little, however, is known respecting his
earliest education : he was for some time at Newcombe's school, an establishment
of considerable reputation at Hackney; and he afterwards went to Cambridge:
but it is probable that he acquired his taste for experimental investigation in
great measure from his father, who was in the habit of amusing himself with
meteorological observations and apparatus, and to whom we are indebted for
a very accurate determination of the depression of mercury in barometrical
tubes, which has been made the basis of some of the most refined investigations
of modern times. " It has been observed," says M. Cuvier, "that more persons
of rank enter seriously into science and literature in Great Britain than in other
countries : and this circumstance may naturally be explained from the constitu-
tion of the British Government, which renders it impossible for birth and fortune
alone to attain to distinction in the state, without high cultivation of the mind;
so that amidst the universal diffusion of solid learning, which is thus rendered
indispensable, some individuals are always found who are more disposed to
occupy themselves in the pursuit of the eternal truths of nature, and in the
contemplation of the finished productions of talent and genius, than in the
transitory interests of the politics of the day." Mr Cavendish was neither
influenced by the ordinary ambition of becoming a distinguished statesman,
nor by a taste for expensive luxuries or sensual gratifications : so that, enjoying
a moderate competence during his father's life, and being elevated by his birth
above all danger of being despised for want of greater influence, he felt himself
exempted from the necessity of applying to any professional studies, of courting
the approbation of the public either by the parade of literature or by the habits
of conviviality, or of ingratiating himself with mixed society by the display of
superficial accomplishments. It is difficult to refrain from imagining that his
mind had received some slight impression from the habitual recurrence to the
motto of his family: the words cavendo tutus must have occurred perpetually

28—2

436 Life of Cavendish

to his eye ; and all the operations of his intellectual powers exhibit a degree of
caution almost unparalleled in the annals of science, for there is scarcely a single
instance in which he had occasion to retrace his steps or to recall his opinions.
In 1760 he became a Fellow of the Royal Society, and continued for almost
fifty years to contribute to the Philosophical Transactions some of the most
interesting and important papers that have ever appeared in that collection,
expressed in language which affords a model of concise simplicity and unaffected
modesty, and exhibiting a precision of experimental demonstration com-
mensurate to the judicious selection of the methods of research and to the
accuracy of the argumentative induction; and which have been considered,
by some of the most enlightened historians, as having been no less instru-
mental in promoting the further progress of chemical discovery, by banishing
the vague manner of observing and reasoning that had too long prevailed,
than by immediately extending the bounds of human knowledge with respect
to the very important facts which are first made public in these communications.

i. Three Papers containing Experiments on Factitious Air. (Phil. Trans.
1766, p. 141.) It had been observed by Boyle, that some kinds of air were unfit
for respiration; and Hooke and Mayow had looked still further forwards into
futurity with prophetic glances, which seem to have been soon lost and for-
gotten by the inattention or want of candour of their successors. Hales had
made many experiments on gases, but without sufficiently distinguishing their
different kinds, or even being fully aware that fixed air was essentially different
from the common atmosphere. Sir James Lowther, in 1733, had sent to the
Royal Society some bladders filled with coal-damp, which remained inflammable
for many weeks — little imagining the extent of the advantages which were one
day to result to his posterity from the labours of that society by the prevention
of the fatal mischiefs which this substance so frequently occasioned. Dr Seip
had soon after suggested that the gas which stagnated in some caverns near
Pyrmont was the cause of the briskness of the water; Dr Brownrigg of White-
haven had confirmed this opinion by experiments in 1741 ; and Dr Black, in
1755, had explained the operation of this fluid in rendering the earths and
alkalis mild. Such was the state of pneumatic chemistry when Mr Cavendish
began these experimental researches. He first describes the apparatus now
commonly used in processes of this kind, a part of which .had been before
employed by Hales and others, but which he had rendered far more perfect
by the occasional employment of mercury. He next relates the experiments
by which he found the specific gravity of inflammable air to be about -,-\ of
that of common air] whether it was produced from zinc or otherwise: first
weighing a bladder filled with a known bulk of the gas, and then in a state of
collapse; and also examining the loss of weight during the solution of zinc in
an acid, having taken care to absorb all the superfluous moisture of the gas by
means of dry potass. He also observed that the gas obtained during the solu-
tion of copper in muriatic acid was rapidly absorbed by water, but he did not
inquire further into its nature. The second paper relates to fixed air, which was
found to undergo no alteration in its elasticity when kept a year over mercury;

by Dr Thomas Young 437

to be absorbed by an equal bulk of water or of olive-oil, and by less than half
its bulk of spirit of wine ; to exceed the atmospheric air in specific gravity by
more than one-half, and to render this fluid unfit for supporting combustion
even when added to it in the proportion of i to 9 only. Mr Cavendish ascer-
tained the quantity of this gas contained in marble and in the alkalis, but
his numbers fell somewhat short of those which have been determined by later
experiments ; he also observed the solubility of the supercarbonate of magnesia.
In the third part, the air produced by fermentation and putrefaction is examined.
Macbride had shown that a part of it was fixed air; and our author finds that
sugar and water, thrown into fermentation by yeast, emit this gas without
altering the. quantity or quality of the common air previously contained in the
vessel, which retains its power of exploding with hydrogen, exactly like common
air: he also shows that the gas thus emitted is identical with the fixed air
obtained from marble; and that the inflammable air, extricated during putre-
faction, resembles that which is procured from zinc, although it appeared to
be a little heavier.

2. Experiments on Rathbone Place Water. (Phil. Trans. 1767, p. 92.) In
this paper Mr Cavendish shows the solubility of the supercarbonate of lime,
which is found in several waters about London, and is decomposed by the pro-
cess of boiling, the simple carbonate being deposited in the form of a crust:
the addition of pure lime-water also causes a precipitation of a greater quantity
of lime than it contains. These conclusions are confirmed by synthetical experi-
ments, in which the supercarbonate is formed and remains in solution.

3. An Attempt to explain some of the principal Phenomena of Electricity by
means of an Elastic Fluid. (Phil. Trans. 1771, p. 584.) Our author's theory
of electricity agrees with that which had been published a few years before
by ^Epinus, but he has entered more minutely into the details of calculation,
showing the manner in which the supposed fluid must be distributed in a variety
of cases, and explaining the phenomena of electrified and charged substances
as they are actually observed. There is some degree of unnecessary complica-
tion from the great generality of the determinations: the law of electric
attraction and repulsion not having been at that time fully ascertained,
although Mr Cavendish inclines to the true supposition, of forces varying
inversely as the square of the distance: this deficiency he proposes to supply
by future experiments, and leaves it to more skilful mathematicians to render
some other parts of the theory still more complete. He probably found that
the necessity of the experiments, which he intended to pursue, was afterwards
superseded by those of Lord Stanhope and M. Coulomb; but he had carried
the mathematical investigation somewhat further at a later period of his life,
though he did not publish his papers * : an omission, however, which is the less
to be regretted, as M. Poisson, assisted by all the improvements of modern

* It is generally understood that Sir William Snow Harris, the eminent electrician,
is engaged in the publication of these important papers. — Note by the Editor [Dean
Peacock, in Young's Miscellaneous Works, vol. n, 1855. As regards the text, see
Maxwell's Introduction to this volume: also footnote, p. 433.]

438 Life of Cavendish

analysis, has lately treated the same subject in a very masterly manner. The
acknowledged imperfections, in some parts of Mr Cavendish's demonstrative
reasoning, have served to display the strength of a judgment and sagacity still
more admirable than the plodding labours of an automatical calculator. One
of the corollaries seems at first sight to lead to a mode of distinguishing positive
from negative electricity, which is not justified by experiment; but the fallacy
appears to be referable to the very comprehensive character of the author's
hypothesis, which requires some little modification to accommodate it to the
actual circumstances of the electric fluid, as it must be supposed to exist in
nature.

4. A Report of the Committee appointed by the Royal Society, to consider of
a Method for securing the Powder Magazine at Purfleet. (Phil. Trans. 1773,
p. 42. Additional Letter, p. 66.) Mr Cavendish, and most of his colleagues on
the committee, recommended the adoption of pointed conductors. Mr Wilson
protested, and preferred blunt conductors ; but the committee persisted in their
opinion. Later experiments, however, have shown that the point in dispute
between them was of little moment.

5. An Account of some Attempts to imitate the Effects of the Torpedo by
Electricity. (Phil. Trans. 1776, p. 196.) The peculiarity of these effects is
shown to depend in some measure on the proportional conducting powers of
the substances concerned, and on the quantity of electricity, as distinguished
from its intensity. Iron is found to conduct 400 million times as well as pure
water, and sea water 720 times as well; and the path chosen by the electric
fluid, depending on the nature of all the substances within its reach, an animal,
not immediately situated in the circuit, will often be affected on account of
the facility with which animal substances in general conduct the fluid. The
shock of a torpedo, producing a strong sensation, but incapable of being con-
veyed by a chain, was imitated by the effect of a weak charge of a very large
battery: and an artificial torpedo of wood being made a part of the circuit,
the shock diffused itself very perceptibly through the water in which it was
placed; but the experiment succeeded better when the instrument was made
of wet leather, which conducts rather better than wood, the battery being
more highly charged in proportion to the increase of conducting power.

6. An Account of the Meteorological Instruments used at the Royal Society's
House. (Phil. Trans. 1776, p. 375.) Of the thermometers it is observed, that
they are adjusted by surrounding the tubes with wet cloths or with steam,
and barely immersing the bulbs in the water, since a variation of two or three
degrees will often occur if these precautions are neglected. For the correction
of the heights of barometers we have Lord Charles Cavendish's table of the
depression arising from capillary action. The variation-compass was found to
exhibit a deviation from the meridian 15' greater in the house of the Royal
Society than in an open garden in Marlborough Street; there was also a mean
error of about 7' in the indications of the dipping-needle, but it was difficult
to ascertain the dip without being liable to an irregularity, which often amounted
to twice as much.

by Dr Thomas Young 439

7. Report of the Committee appointed to consider of the best Method of adjusting
Thermometers. (Phil. Trans. 1777, p. 816.) This paper is signed by Mr Cavendish
and six other members, but it is principally a continuation of the preceding.
It contains very accurate rules for the determination of the boiling point, and
tables for the correction of unavoidable deviations from them: establishing
29-8 inches as the proper height of the barometer for making the experiment,
if only steam be employed, and 29-5 if the ball be dipped in the water; but
with all precautions, occasional variations of half a degree were found in the
results.

8. An Account of a New Eudiometer. (Phil. Trans. 1783, p. 106.) Mr Cavendish
was aware of the great difference in the results of eudiometrical experiments
with nitrous gas, or nitric oxyd, according to the different modes of mixing the
elastic fluids; and he justly attributes them to the different degrees of oxy-
genization of the acid that is formed. But he found that when the method
employed was the same, the results were perfectly uniform; and he ascertained
in this manner that there was no sensible difference in the constituent parts of
the atmosphere under circumstances the most dissimilar: the air of London,
with all its fires burning in the winter, appearing equally pure with the freshest
breezes of the country. He also observed the utility of the sulphurets of potass
and of iron for procuring phlogisticated air; but he does not seem to have
employed them as tests of the quantity of this gas contained in a given mixture.

9. Observations on Mr Hutchins's Experiments for determining the degree of
Cold at which Quicksilver freezes. (Phil. Trans. 1783, p. 303.) In experiments
of this kind, many precautions are necessary, principally on account of the
contraction of the metal at the time of its congelation, which was found to
amount to about ^ of its bulk; and the results which had been obtained were
also found to require some corrections for the errors of the scales, which reduce
the degree of cold observed to 39° below the zero of Fahrenheit, or 71° below
the freezing point, answering to — 39-4° of the centesimal scale. In speaking
of the evolution of heat during congelation, he calls it "generated" by the sub-
stances, and observes, in a note, that Dr Black's hypothesis of capacities
depends "on the supposition that the heat of bodies is owing to their containing
more or less of a substance called the matter of heat; and as" he thinks "Sir
Isaac Newton's opinion, that heat consists in the internal motion of the particles
of bodies, much the most probable," he chooses "to use the expression heat is
generated," in order to avoid the appearance of adopting the more modern
hypothesis; and this persuasion, of the non-existence of elementary heat, he
repeats in his next paper*. It is remarkable that one of the first of Sir Humphry
Davy's objects, at the very beginning of his singularly brilliant career of refined
investigation and fortunate discovery, was the confirmation of this almost
forgotten opinion of Mr Cavendish; and for this purpose he devised the very
ingenious experiment of melting two pieces of ice by their mutual friction in
a room below the freezing temperature, which is certainly incompatible with

* [See the account of Cavendish's dynamical manuscripts, at the end of the second
volume of this edition.]

440 Life of Cavendish

the common doctrine of caloric, unless we admit that caloric could have existed
in the neighbouring bodies in the form of cold, or of something else that could
be converted into caloric by the operation ; and this transmutation would still
be nearly synonymous with generation, in the sense here intended. However
this may be, it is certain that, notwithstanding all the experiments of Count
Rumford, Dr Haldalt, and others, Sir Humphry has been less successful in
persuading his contemporaries of the truth of Mr Cavendish's doctrine of heat,
than in establishing the probability of his opinions respecting the muriatic acid.

10. Experiments on Air. (Phil. Trans. 1784, p. 119.) This paper contains
an account of two of the greatest discoveries in chemistry that have ever yet
been made public— the composition of water, and that of the nitric acid. The
author first establishes the radical difference of hydrogen from nitrogen or
azote ; he then proceeds to relate his experiments on the combustion of hydrogen
with oxygen, which had partly been suggested by a cursory observation of
Mr Warltire, a Lecturer on Natural Philosophy, and which prove that pure
water is the result of the process, provided that no nitrogen be present *. These
experiments were first made in 1781, and were then mentioned to Dr Priestley;
and when they were first communicated to Lavoisier, he found some difficulty
in believing them to be accurate. The second series of experiments demonstrates
that when phlogisticated air, or nitrogen, is present in the process, some nitric
acid is produced; and that this acid may be obtained from atmospheric air by
the repeated operation of the electrical spark.

It has been supposed by one of Mr Cavendish's biographers, that if
Mr Kirwan, instead of opposing, had adopted his chemical opinions, "he would
never have been obliged to yield to his French antagonists, and the anti-
phlogistic theory would never have gained ground." But in this supposition
there seems to be a little of national prejudice. Mr Cavendish by no means
dissented from the whole of the antiphlogistic theory ; and in this paper he has
quoted Lavoisier and Scheele in terms of approbation, as having suggested the
opinion "that dephlogisticated and phlogisticated air are quite distinct sub-
stances, and not differing only in their degree of phlogistication, and that
common air is a mixture of the two." He afterwards mentions several memoirs
of Lavoisier in which phlogiston is entirely discarded; and says that "not only
the foregoing experiments, but most other phenomena of nature, seem explicable
as well, or nearly as well, upon this as upon the commonly believed principle
of phlogiston"; and after stating a slight conjectural objection, derived from
the chemical constitution of vegetables, he proceeds finally to observe, that
"Lavoisier endeavours to prove that dephlogisticated air is the acidifying
principle": this is no more than saying, that acids lose their acidity by uniting
to phlogiston, which, with regard to the nitrous, vitriolic, phosphoric, and
arsenical acids, is certainly true, and probably with regard to the acid of sugar;

* M. Arago, in his liloge of Watt, attempted to transfer to that philosopher the
merit of this great discovery, and thus gave rise to a vehement controversy, which
has been finally and conclusively settled in favour of Cavendish by Dr Wilson, of-
Edinburgh. See his Life of Cavendish, 1 85 1 . — Note by the Editor [Dean Peacock, 1 855 .]

by Dr Thomas Young 441

"but as to the marine acid, and acid of tartar, it does not appear that they are
capable of losing their acidity by any union with phlogiston" and the acids of
sugar and tartar become even less acid by a further dephlogistication. It is
obvious that this argument amounts only to an exception, and not to a total
denial of the truth of the theory: M. Cuvier has even asserted that the anti-
phlogistic theory derived its first origin from one great discovery of Mr Cavendish,
that of the nature of hydrogen gas, and owed its complete establishment to
another, that of the composition of water: but it would be unjust to deny to
Lavoisier the merit of considerable originality in his doctrines respecting the
combinations of oxygen ; and however he may have been partly anticipated by
Hooke and Mayow, it was certainly from him that the modern English chemists
immediately derived the true knowledge of the constitution of the atmosphere,
which they did not admit without some hesitation, but which they did ultimately
admit when they found the evidence irresistible. On the other hand, it has
been sufficiently established, since Mr Cavendish's death, by the enlightened
researches of the most original of all chemists, that Lavoisier had carried his
generalization too far; and it must ever be remembered, to the honour of
Mr Cavendish, and to the credit of this country, that we had not all been seduced,
by the dazzling semblance of universal laws, to admit facts as demonstrated
which were only made plausible by a slight and imperfect analogy.

11. Answer to Mr Kirwan's Remarks upon the Experiments on Air. (Phil.
Trans. 1784, p. 170.) Mr Kirwan, relying on the results of some inaccurate
experiments, had objected to those conclusions which form the principal basis
of the antiphlogistic theory. Mr Cavendish repeated such of these experiments
as seemed to be the most ambiguous, and repelled the objections; showing, in
particular, that when fixed air was derived from the combustion of iron, it was
only to be referred to the plumbago, shown by Bergmann to exist in it, which
was well known to be capable, in common with other carbonaceous substances,
of affording fixed air.

12. Experiments on Air. (Phil. Trans. 1785, p. 372.) The discovery of the
composition of the nitric acid is here further established; and it is shown that
the whole, or very nearly * the whole of the irrespirable part of the atmosphere
is convertible into this acid, when mixed with oxygen, and subjected to the
operation of the electric spark: the fixed air, sometimes obtained during the
process, being wholly dependent on the presence of some organic substances.

13. An Account of Experiments made bv Mr John Macnab, at Henley House,
Hudson's Bay, relating to Freezing Mixtures. (Phil. Trans. 1786, p. 241.) From
these experiments Mr Cavendish infers the existence of two distinct species of
congelation in mixed liquids, which he calls the Aqueous and Spirituous Conge-
lations, and of several alternations of easy and difficult congelation when the
strength is varied, both in the case of the mineral acids and of spirit of wine.
The greatest degree of cold obtained was — y8J°.

[* That is, except the argon and other inert gases contained in Cavendish's
residue.]

28-5

4.42 Life of Cavendish

14. An Account of Experiments made by Mr John Macnab, at Albany Fort,
Hudson's Bay. (Phil. Trans. 1788, p. 166.) The points of easy congelation are
still further investigated, and illustrated by comparison with Mr Keir's experi-
ments on the sulphuric acid. It was found that the nitric acid was only liable
to the aqueous congelation, when it was strong enough to dissolve Jth of its
weight of marble; and that it had a point of easy congelation, when it was
capable of dissolving TVin5> the frozen part exhibiting, in other cases, a tendency
to approach to this standard. Mr Keir had found that sulphuric acid, of the
specific gravity 1-78, froze at 46°, and that it had another maximum when it
was very highly concentrated*.

15. On the Conversion of a Mixture of Dephlogisticated and Phlogisticated
Air into Nitric Acid, by the Electric Shock. (Phil. Trans. 1788, p. 261.) Some
difficulties having occurred to the Continental chemists in the repetition of
this experiment, it was exhibited with perfect success, by Mr Gilpin, to a number
of witnesses. This was an instance of condescension, which could scarcely have
been expected from the complete conviction, which the author of the discovery
must have felt, of his own accuracy, and of the necessity of the establishment
of his discovery, when time should have been afforded for its examination.

16. On the Height of the Luminous Arch, which was seen on Feb. 23, 1784.
(Phil. Trans. 1790, p. 101.) Mr Cavendish conjectures that the appearance of
such arches depends on a diffused light, resembling the aurora borealis, spread
into a flattened space, contained between two planes nearly vertical, and only
visible in the direction of its breadth : so that they are never seen at places far
remote from the direction of the surface; and hence it is difficult to procure
observations sufficiently accurate for determining their height, upon so short
a base: but in the present instance there is reason to believe that the height
must have been between 52 and 71 miles.

17. On the Civil Year of the Hindoos, and its Divisions, with an Account of
three Almanacs belonging to Charles Wilkins, Esq. (Phil. Trans. 1792, p. 383.)
The subject of this paper is more intricate than generally interesting; but it
may serve as a specimen of the diligence which the author employed in the
investigation of every point more or less immediately connected with his
favourite objects. The month of the Hindoos is lunar in its duration, but solar
in its commencement; and its periods are extremely complicated, and often
different for different geographical situations: the day is divided and sub-
divided sexagesimally. The date of the year, in the epoch of the Kalee Yug,
expresses the ordinal number of years elapsed, as it is usual with our astronomers
to reckon their days : so that the year 100 would be the beginning of the second
century, and not the tooth year, or the end of the first century, as in the
European calendar: in the same manner as, in astronomical language, 1817
December 3id. i8h. means six o'clock in the morning of the ist of January
1818.

* [Compare with these two papers the modern investigations of coexistent
chemical phases, and their applications to metallurgy and other sciences.]

by Dr Thomas Young 443

18. Experiments to determine the Density of the Earth. (Phil. Trans. 1798,
p. 469.) The apparatus, with which this highly important investigation was
conducted, had been invented and constructed many years before by the
Reverend John Michell, who did not live to perform the experiments for which
he intended it. Mr Cavendish, however, by the accuracy and perseverance with
which he carried on a course of observations of so delicate a nature, as well as
by the skill and judgment with which he obviated the many unforeseen diffi-
culties that occurred in its progress, and determined the corrections of various
kinds which it was necessary to apply to the results, has deserved no less
gratitude from the cultivators of astronomy and geography, than if the idea
had originally been his own. The method employed was to suspend, by a vertical
wire, a horizontal bar, having a leaden ball at each end; to determine the magni-
tude of the force of torsion by the time occupied in the lateral vibrations of the
bar; and to measure the extent of the change produced in its situation by the
attraction of two large masses of lead, placed on opposite sides of the case
containing the apparatus, so that this attraction might be compared with the
weight of the balls, or, in other words, with the attraction of the earth. In
this manner the mean density of the earth was found to be 5^ times as great as
that of water; and although this is considerably more than had been inferred
from Dr Maskelyne's observations on the attraction of Schehallion, yet the
experiments agree so well with each other, that we can scarcely suppose any
material error to have affected them. Mr MichelTs apparatus resembled that
which M. Coulomb had employed in his experiments on magnetism, but he
appears to have invented it before the publication of M. Coulomb's Memoirs.

19. On an Improved Method of Dividing Astronomical Instruments. (Phil.
Trans. 1809, p. 221.) The merits of this improvement have not been very
highly appreciated by those who are in the habit of executing the divisions of
circular arcs. It consists in a mode of employing a microscope, with its cross
wires, as a substitute for one of the points of a beam compass, while another
point draws a faint line on the face of the instrument in the usual manner. The
Duke de Chaulnes had before used microscopical sights for dividing circles ; but
his method more nearly resembled that which has been brought forwards in an
improved form by Captain Kater; and Mr Cavendish, by using a single micro-
scope only, seems to have sacrificed some advantages which the other methods
appear to possess : but none of them has been very fairly tried ; and our artists
have hitherto continued to adhere to the modes which they had previously
adopted, and which it would perhaps have been difficult for them to abandon,
even if they had been convinced of the advantages to be gained by some partial
improvements.

Such were the diversified labours of a philosopher, who possessed a clearness
of comprehension and an acuteness of reasoning which had been the lot of very
few of his predecessors since the days of Newton*. Maclaurin and Waring,
perhaps also Stirling and Landen, were incomparably greater mathematicians;

* [As regards Cavendish's dynamical manuscripts, see the end of the second
volume of this edition.]

444 1-tfe °f Cavendish

but none of them attempted to employ their powers of investigation in the pur-
suit of physical discovery: Euler and Lagrange, on the Continent, had carried
the improvements of analytical reasoning to an unparalleled extent, and they
both, as well as Daniel Bernoulli and d'Alembert, applied these powers with
marked success to the solution of a great variety of problems in mechanics and
in astronomy; but they made no experimental discoveries of importance: and
the splendid career of chemical investigation, which has since been pursued
with a degree of success so unprecedented in history, may be said to have been
first laid open to mankind by the labours of Mr Cavendish ; although the further
discoveries of Priestley, Scheele, and Lavoisier, soon furnished, in rapid suc-
cession, a superstructure commensurate to the extent of the foundations so
happily laid. "Whatever the sciences revealed to Mr Cavendish," says Cuvier,
"appeared always to exhibit something of the sublime and the marvellous; he
weighed the earth; he rendered the air navigable; he deprived water of the
quality of an element"; and he denied to fire the character of a substance.
"The clearness of the evidence on which he established his discoveries, so new
and so unexpected as they were, is still more astonishing than the facts them-
selves which he detected; and the works, in which he has made them public,
are so many master-pieces of sagacity and of methodical reasoning ; each perfect
as a whole and in its parts, and leaving nothing for any other hand to correct,
but rising in splendour with each successive year that passes over them, and
promising to carry down his name to a posterity far more remote than his rank
and connections could ever have enabled him to attain without them."

In his manners Mr Cavendish had the appearance of a quickness and
sensibility almost morbid, united to a slight hesitation in his speech, which
seems to have depended more on the constitution of his mind than on any
deficiency of his organic powers, and to an air of timidity and reserve, which
sometimes afforded a contrast, almost ludicrous, to the sentiments of profound
respect which were professed by those with whom he conversed. It is not
impossible that he may have been indebted to his love of severe study, not only
for the decided superiority of his faculties to those of the generality of man-
kind, but even for his exemption from absolute eccentricity of character. His
person was tall, and rather thin: his dress was singularly uniform, although
sometimes a little neglected. His pursuits were seldom interrupted by in-
disposition; but he suffered occasionally from calculous complaints. His retired
habits of life, and his disregard of popular opinion, appear to have lessened the
notoriety which might otherwise have attached to his multiplied successes in
science; but his merits were more generally understood on the Continent than
in this country; although it was not till he had passed the age of seventy, that
he was made one of the eight Foreign Associates of the Institute of France.

Mr Cavendish was no less remarkable in the latter part of his life, for the
immense accumulation of his pecuniary property, than for his intellectual and
scientific treasures. His father died in 1783, being at that time eighty years
old, and the senior member of the Royal Society: but he is said to have suc-
'ceeded at an earlier period to a considerable inheritance left him by one of his

by Dr Thomas Young 445

uncles. He principally resided at Clapham Common ; but his library was latterly
at his house in Bedford Square ; and his books were at the command of all men
of letters, either personally known to him, or recommended by his friends:
indeed the whole arrangement was so impartially methodical, that he never
took down a book for his own use, without entering it in the loan book; and
after the death of a German gentleman, who had been his librarian, he appointed
a day on which he attended in person every week for the accommodation of
the few, who thought themselves justified in applying to him for such books
as they wished to consult. He was constantly present at the meetings of the
Royal Society, as well as at the conversations held at the house of the President ;
and he dined every Thursday with the club composed of its members. He had
little intercourse with general society, or even with his own family, and saw
only once a year the person whom he had made his principal heir. He is said
to have assisted several young men, whose talents recommended them to his
notice, in obtaining establishments in life; but in his later years, such instances
were certainly very rare. His tastes and his pleasures do not seem to have
been in unison with those which are best adapted to the generality of mankind ;
and amidst the abundance of all the means of acquiring every earthly enjoy-
ment, he must have wanted that sympathy, which alone is capable of redoubling
our delights, by the consciousness that we share them in common with a
multitude of our friends, and of enhancing the beauties of all the bright prospects
that surround us, when they are still more highly embellished by reflection
"from looks that we love." He could have had no limitation either of comfort
or of luxury to stimulate him to exertion; even his riches must have deprived
him of the gratification of believing, that each new triumph in science might
promote the attainment of some great object in life that he earnestly desired;
a gratification generally indeed illusory, but which does not cease to beguile us
till we become callous as well to the pleasures as to the sorrows of existence.
But in the midst of this "painful pre-eminence," he must still have been capable
of extending his sensibility over a still wider field of time and space, and of
looking forwards to the approbation of the wise and the good of all countries
and of all ages: and he must have enjoyed the highest and purest of all intel-
lectual pleasures, arising from the consciousness of his own excellence, and from
the certainty that, sooner or later, all mankind must acknowledge his claim to
their profoundest respect and highest veneration.

"It was probably either the reserve of his manners," says Cuvier, "or the
modest tone of his writings, that procured him the uncommon distinction of
never having his repose disturbed either by jealousy or by criticism. Like his
great countryman Newton, whom he resembled in so many other respects, he
died full of years and honours, beloved even by his rivals, respected by the
age which he had enlightened, celebrated throughout the scientific world, and
exhibiting to mankind a perfect model of what a man of science ought to be,
and a splendid example of that success, which is so eagerly sought, but so seldom
obtained." The last words that he uttered were characteristic of his unalterable
love of method and subordination: he had ordered his servant to leave him,
and not to return till a certain hour, intending to pass his latest moments in

446 Life of Cavendish

the tranquillity of perfect solitude: but the servant's impatience to watch his
master diligently having induced him to infringe the order, he was severely
reproved for his indiscretion, and took care not to repeat the offence until the
scene was finally closed. Mr Cavendish died on the 24th of February, 1810;
and was buried in the family vault at Derby. He left a property in the funds
of about £700,000, which he divided into six equal parts, giving two to Lord
George Cavendish, the son of his first cousin, one to each of his sons, and one
to the Earl of^Besborough, whose mother was also his first cousin. Some other
personal property devolved to Lord George as residuary legatee; and a landed
estate of £6,000 a year descended to his only brother, Mr Frederic Cavendish,
of Market Street, Herts, a single man, and of habits of life so peculiarly retired,
that any further increase of income would have been still more useless to him
than it had been to the testator.

Much as Mr Cavendish effected for the promotion of physical science
throughout his life, it has not been unusual, even for his warmest admirers, to
express some regret that he did not attempt to do still more after his death, by
the appropriation of a small share of his immense and neglected wealth, to the
perpetual encouragement of those objects, which he had himself pursued with
so much ardour. But however we might be disposed to lament such an omission,
we have surely no reason to complain of his determination to follow more nearly
the ordinary course of distribution of his property, among those whose relation-
ship would have given them a legal claim to the succession, if he had not con-
cerned himself in directing it. We may observe on many other occasions, that
the most successful cultivators of science are not always the most strenuous
promoters of it in others; as we often see the most ignorant persons, having
been rendered sensible by experience of their own deficiencies, somewhat
disposed to overrate the value of education, and to bestow more on the improve-
ment of their children than men of profounder learning, who may possibly
have felt the insufficiency of their own accomplishments for insuring success
in the world. But even if Mr Cavendish had been inclined to devote a large
share of his property to the establishment of fellowships or professorships, for
the incitement of men of talents to a more complete devotion of their lives to
the pursuit of science, it is very doubtful whether he could have entertained a
reasonable hope of benefiting his country by such an institution: for the highest
motives that stimulate men to exertion are not those which are immediately
connected with their pecuniary interests: the senators and the statesmen of
Great Britain are only paid in glory; and where we seek to obtain the co-
operation of the best educated and the most enlightened individuals in any
pursuit or profession, we must hold out as incentives the possession of high
celebrity and public respect; assured that they will be incomparably more
effectual than any mercenary considerations, which are generally found to
determine a crowd of commercial speculators to enter into competition for the
proposed rewards, and to abandon all further concern with the objects intended
to be pursued, as soon as their avarice is gratified. To raise the rank of science
in civil life is therefore most essentially to promote its progress : and when we
compare the state, not only of the scientific associations, but also of the learned

by Dr Thomas Young 447

professions in this country and among our neighbours, we shall feel little reason
to regret the total want of pecuniary patronage that is remarkable in Great
Britain, with respect to every independent department of letters, while it is so
amply compensated by the greater degree of credit and respectability attached
to the possession of successful talent. It must not however be denied, that even
in this point of view there might be some improvement in the public spirit of
the country: Mr Cavendish was indeed neither fond of giving nor of receiving
praise ; and he was little disposed to enliven the intervals of his serious studies
by the promotion of social or convivial cheerfulness: but it would at all times
be very easy for an individual, possessed of high rank and ample fortune, of
correct taste and elegant manners, to confer so much dignity on science and
literature by showing personal testimonies of respect to acknowledged merit,
as greatly to excite the laborious student to the unremitting exertions of patient
application, and to rouse the man of brilliant talent to the noblest flights of
genius.

[ 449 ]

INDEX TO CAVENDISH MANUSCRIPTS

The references are to the Articles. [See also Table of Contents]

A, coated plate of glass so called, "First
got," 589, 592; Nairne's, 314, 593

A, Double, 333, 451, 455, 461, 478, 483, 487,

489, 491, 508, 509, 533, note 35

Absorption, electric, 523, note 15

Accuracy of measurements, 261

Adjustment of charges of coated plates, 316

/Epinus (Franz Ulrich Theodor, b. 1724,
d. 1802), i, 134, 340, 549

-Epinus' experiment, 134, 340, 549

Air between plates, not charged, 344, 345,
511, 516; communication of electricity
to, 118-125, 208, note 9; electric pro-
perties of, 99; electrified, 117, 256;
molecular constitution of, 97, and notes
6 and 18; electric phenomena illus-
trated by means of, 206 ; dielectric plate
of, 134, 34°. 457. 517. 560

Apparatus for trying charges, 240, 295

Assistant, 242, 560

Atmospheres, electric, 195—198

Attraction, 106-117, J97> 2O2- 2I°. n°te 8;
not caused by Torpedo, 408

B, coated plate, 593

B, Double, 455-457, 478, 483, 489

Baking varnished plates, 496

Barometer tubes as Leyden vials, 636

Basket for Torpedo, 615

Basket salt, 628

Battery of Florence flasks. 521; of 49 jars,

411, 432, 581; Nairne's, 585, 616
Beccaria, Giacomo Battista (1716—1781), 136
Bees'-wax as dielectric, 336, 371, 376
Breaking of electricity through plates, 520

Calc. S. S. A., 626, 694 and note 34

Calibration of tubes, 382, 383, 632-635

Calipers, 459

Canal for electric fluid, 40, 68, 69; bent, 48,
49, 84—95 and note 3

Canton, John, F.R.S. (1718—1772), 117, 205

Cement, 303, 484, 497

Chain battery, 433, 605, 613

Charge defined, 237; does not depend on
material, 68; of similar bodies as dia-
meters, 71; of thin plate independent
of thickness, 73; of condensers not
affected by other bodies, 317, 443, 555;
of coated plates greater than by theory,
332; 'intended,' 316; 'computed,' 311,
326, 377, 458; 'real,' 313, 377; with
strong electrification, 356, 357, 451,
539; with weak, 358, 463, 539; with
negative, 463; effect of temperature,
366; measurements of, see Tables; of
battery, 412; divided, 288

Charging jar, 223, 225

Circles, charges on, 273

Circuit, divided, 397, 417

Coated plates, 300, 314, 441; theory of, 74,

1 60, 169; lists of, see Tables
Coatings, electricity does not reside in, 133
Communication, 100, 219; of charge to bat-
tery, 414, 618
Comparison of charges, 236
Compound plate, 379—381, 560, 677-679
Computed charge, 311, 312
Condensation distinguished from compression,

200

Conduction by hot glass, 369
Conductivity, 469, 491 ; of straws. 565
Conductor defined, 98
Cone, attraction on particle at vertex, 7
Conical point, escape of electricity from, 124

and note 9
Contact, 306; never realized, 196 note; of

brass and glass, 541, 558
Copper wire, resistance of, 636—646
Cork balls, 116, 117, 441, 451
Crown glass, 301, 330, 378, 411, 430, 585, 595
Cylinder, 54, 148-151; charge of, 281, 285-

287 and note 12; two, 152 and note 13;

glass coated, 382, 454, 479; large tin,

358, 539 and note 25

D, coated plate, 483, 487
Deficient fluid, 67, note
DEFINITIONS:

Canal, 40

Charge, 237

Communication, 100

Compression, 199

Computed charge, 311

Condensation, 200

Conductor, 98

Deficient fluid, 67, note

Electrification, 102, 201

Immoveable fluid, 12

Inches of electricity, circular, 458, 648,
globular, 654, square, 648, 654

Incompressible fluid, 69

Insulation, 100

Non-conductors, 98

Observed charge, 325

Overcharge, 6, 201

Real charge, 313

Redundant fluid, 13

Saturated body, 6

Undercharge, 6
Degrees of electrification, 329, 356; of

electrometer, 560, note
Dephlegmated wax, 371, 375, 518
Discharge, divided, 397, 417, 576, 597, 613
Distance to which electricity spreads, 309,
323, 328

45°

Index to Cavendish Manuscripts

Dividing machine, 341, 459, 517, 591
Divisions of trial plate, 297
Double plates, 333

Earth connexion, 258, 271
Electricity an elastic fluid, 4, 195; limit to
density, 20; diffused through bodies not
electrified, 216; inches of, 647, 648
Electrification, degree of, 102, 201 and note 7
Electrodes, larpe, 258, 271
Electrometer :

Cavendish's discharging, 402, 405, 427,
43°. 434; gauge (paper cylinders), 224,
248, 295, 495, 511, 524, 542, 559; new
wood, 525, 563
Divisions of, 560, note
Henly's, 559, 568, 570, 571, 580; on rod,

5»9
Lane's, 263, 329, 559, 569, 570, 571, 580,

589, 603, 604
Paper cylinders, 486
Pith ball, 581
Straw, 249, 404, 559, 570, 571, 581; with

variable weights, 387; corks, 441, 451,

566

Testing, 244, 296, 358, 359
English plate glass, 301, 496
Equivalent thickness of compound plates,

379

Error, greater with coated plates than with
simple conductors, 299 ; probable of esti-
mation of capacity, 250, 261; in Exp. I,
234; due to unequal charging, 250

Excess of redundant fluid in coated plates,
560 and note 30

Experiment I, 218, 233, 291, 512, 562 and
note 19

II, 235, 292, 561

III, 265, 467

IV, 269, 293, 471, 480, 481 and note 20

V, 273, 447", 448, 452, 454, 472, 473, 474,
475, 681 and note 21

VI, 279, 453, 476, 477, 683

VII, 281, 448, 478, 682 and note 13

VIII, 288, 542 and note 23

f. alk., 627, 694

Floor, effect of, 335

Florence flask, 521; battery, 521

Fluid, electric, 195, 216, note i ; real, 91 ;
incompressible, 69, 94, 236, 273. 276,
278, 294, 348 and note 3

Force, near an electrified surface, 154; in-
versely as square of distance, 232, 512,
' 5J3. 5°2 and note 17

Fore and back room, 469

Frame placed below circles, 274

Frames, 221

Franklin, Benjamin, F.R.S. (1706-1790),
350 note, 363

Fringe of dirt on coated plates, 308, 326,
538

Garden, copper wire stretched round ,643

Gauge electrometer, 224, 248

General conclusions, 291

Gilt straws, 249, 394, 567

Glass, different electric qualities of, 301, 322

Glass house, 378

Glauber's salt, 626, 694

Globe, charge of compared with that of
circle, 237, 282, 445, 455, 450, 654, 681,
687, note 35

Globe, electrified, 20-27, 28°; capacity of,
281, 282; compared with double plate,

333, 334

Globe, charge of the terrestrial, 214
Globe of electrical machine, 248, 495, 563,

568, 569

Globe charged within hemispheres, 218, 512,

562, note 19

Globes, coated, 523, 542, 559, 563
Gradual spreading of electricity, 302
Guide for the eye, -249, 525, 571
Gum lac, 371, 374, 376
Gymnotus, 437, 601

Hamilton, Dr, Prof, of Philosophy, Dublin

(Priestley, p. 429), 126
Heat, effect on charge of glass, &c., 366, 368,

548, 549, 556, 680, note 26
Heat produced by current, 212
Height and size of room, 335
Hemispheres, hollow, 219
Henly (William, F.K.S., d. 1779, linen

draper in London), his electrometer,

559, 5"8, 569, 580
Hissing noise before spark, 213
Hot glass a conductor, 369, note 26; com-
pared with cold, 366, 368
Hunter (John, F.R.S. , b. 1728, d. 1793), 436,

601, 614
Hygrometer, corks, 459; Smeaton's, 468;

common, 468
Hypothesis, electric, 3, 202

Immoveable fluid, 12, 351
Inches of electricity, 458, 648, 654
Incompressible fluid, 40, 236, 273, 276, 278,

294, 348 and note 3
Increase of charge of globe due to induction,

339, °52 and note 24
Induction, 44-47, 175-194, 202 sq., 275, 277,

287, 288, 334, 335; calculation of, 338.

See Specific
Instantaneous spreading of electricity, 307,

310-323, 326
Insulation, 100
Iron, conductivity of, 398, 576, 687, note 32

Jar, 223; capacity of jars, 573, 581

Kinnerslev (Ebenezer, Physician in Phila-
delphia, b. 1712), 126, 136, 213; see
new experiments of electricity, Phil.
Trans., 1763, 1773

Knob for discharging, 511, 572

Lac, 371, 374, 376, 518, 520

Lac solution, 494

Lane, Timothy, F.R.S. (b. 1734, d. 1804),

136, 213, 601
Lane's electrometer, 263, 329, 540, 544, 559,

569, 57°. 571, 58°

Law of electric force from Exp. I, 291,

note 19

Leakage, electric, 260, 264, 393
Leather torpedo, 608
Leyden vial, 128, 206, 313, 363, 389
Light, Newton's fits, 354

Index to Cavendish Manuscripts

Light round the edge of coating, 307, 326,

532; brightest at first charging, 310
Linen thread, 244
Lines of discharge of torpedo, 400
Loops of chain battery, 43^, 605

Machine, electric, 242

Machine for trying coated plates, 295, 337,
340, 366, 495 ; new for measuring thick-
ness, 517

.Magazine of electricity, 207, 521, 565

Matter, electric fluid excluded, 4

Maximum density of electric fluid, 20 and
note i

Measurements of apparatus, 219, 255, 273,
275, 466, 472

Mechanism for Exp. I, 222

Mercury, 366

Metals, conducting power, 397, 398

Method of the work, 2

Method of trying charges, 241, note 17

Michell, Rev. John, F.R.S. (d. 1793), 354

Mineral water warehouse, 415

Moist wood, 392

Moment, statical, 388

Moveable electricity in glass, 350

Moveable fluid, 12, 350

Nairne, Edward, F.R.S. (d. 1806); Mr N.,
601; plates from, 482 (315); jar, 568;
electric machine, 559, 568; his own
large one, 580; his manner of lacquer-
ing, 496; his batteries, 585, 616

Needle discharger, 572

Negative electrification, 463

Newton, 18, 19, 97

Newton's fits, 354

Nuremberg glass. 301, 376, 497

Oblong, charge of, 284, 479; coatings, 320
Oil of vitriol, 626, 694
Overcharge, 6

p- ratio of charge spread uniformly on disk
to that collected in circumference, 140;
estimated value by experiment 276
281, 289

Penetration of electric fluid into glass 132
-169-174, 332, 339, 349, 355, 363

Pennsylvania, Phil. Soc. of, 437

Pith ball electrometer, 220, 240, 244, 358, 359

Plate of air, 134, 340; concave, 155 /circular,
55-65, 140; thin, 73

Plates, coated, lists of, 315, 324, 325, 370;
theory of, 129; separated circular, 74]
82, 141-144

Points, discharge of electricity by, 123, note 9

Positive electrification, 100, 101 ; defined to
be that of glass, 217; gives same pro-
portion of charges as negative, 364

Potential, 199 (note)

Priestley (Joseph, F.R.S., LL.D. Edin., b.
1733, d. 1804), 125, 126, 213, 354, 408,
60 1

Prime conductor, 241, 295, 359, 539

Prop, ix, 292, xvin, 269, xix, 140, xxn,
cor. 5, 140, xxiv, 144, 150, xxix, 282,
xxx, 289, xxxi, 285, xxxiv, 311, xxxv,
351, xxxvi, 365

Pulleys, 295

45

Quad, nitre, 626, 696

Rain water, 524

Real charge, 313

Real fluid, 91, 94

Reciprocity of induction, 334

Reduced charge, 270, 272

Redundant fluid, i ^

Reel, 636, 644

Repulsion, 106; of balls as square of re-
dundant fluid, 386, 525, 563

Resistance, electric, varies as length of con-
ductor, 131; what power of velocity
574. 575, 629, 686; effect of heat on,
619, 620, 690

Richard, his attendant, 511, 565

Ronayne, Thomas, 601

Rosin, 336, 371, 461, 464, 488

Rosin varnish, 497; experimental, 514, 520
548) plates, 518, 555, 560, 594

Roughness dissipates electricity 387

Rows of battery, 581

Rules for trial plates, 592; for strength of
salt water, 588; for measuring charge
of battery, 412, 441, 582

Sal Amm., 626, 694

Sal Sylvii, 626, 694

Salt water, resistance of, 398, note 33

Salted threads, 259; straws 394 zftc

Sand, wet, 608 "

Saturated solution s.s., 524, 617

Saturation, electric, 6

Scale of electrometer, 249, 560, 571

Sea water, 524

Sealing-wax, 219, 340, 511, 542

Sensitiveness of electrometer increases with

charge, 246
Shock, 207; increased by passing through

copper wire, 639 ; by points and knobs

compared, 572
Shock melter, 586, 622
Shock of torpedo, 397, 436; intensity, law

of, 573. 607, 610, note 31
Silk strings, 241, 266, 295, 358, 447, 45o, 472,

Similar bodies, charge of, 66, 72

Sliding coated plate, 488

Slit coatings, 321

Sound, before spark, 139 ; resistance tried by

637. 645
Spark, electric, 135-139, 212; none from

torpedo, 401 ; length does not depend

on number of jars, 402, 604, note 10
Specific gravity of salt water, 587, 588
Specific inductive capacity, 332 339 notes

15, 27

Spherical shell, force inside, 18, 19
Spirit of salt, 627, 694
Spirit of wine, 524, 631
Spreading of electricity, 299-367, 484, 485,

512; gradual, 494-500
Springing wire, 296
Square plate, charge of, 282, 283, 479 and

note 22 ; plates of various substances, 269
Steam, cause of explosion by lightning, 137
Stool, electric, 420, 612
Strata, conducting, in glass, 351, 354
Strength of electrification, 355; effect on

capacity, 356, 451, 463, 539

452

Index to Cavendish Manuscripts

System of coated plates, 316

Tables

Coated plates, 315, 324, 325, 370, 442, 462,

482, 500, 592, 593, 662, 663, 671
Cylinders, 383, 503, 596
Electrometers, 568, 570
Exp. Ill, 267; Exp. IV, 269, 270
Exp. V, 274, 275, 454, 473, 649, 681
Exp. VI, 279, 449; Exp. VII, 281, 682
Hot glass, 368
Jars, 573

Plates of air, 343, 519, 670
Plates of wax, &c., 371
Sliding plates, 589
Solutions of salt, &c., 689, 694, 695,

696

Specific gravity, 595
Trial plates, 465
Tubes, 575, 632, 633, 636
Thermometer tube, 383, 562
Thickness of plates, effect on charge, 269,
272 ; of coated plates, 314; of air plates,
341; measurement, 517, 594, 595
Three parallel plates, 288
Tinfoil, 222; discharger, 426
Torpedo, ist wooden, 409, 415, 596; 2nd
leather, 416, 600, 608, 611, 612, 615;
in basket, 421 ; in sand, 422 ; in net, 424.
See note 29
Touching, to compare charges, 413, 441,

582, 583

Trial plate, theory of, 153 and note 17; list
of, 590; description of, 238, 239, 296,
297, 298, 454, 457, 465, 592; charge as
square root of surface, 247, 251, 284;
sliding wire, 447; sliding cylinder, 547,

567

Trough, torpedo, 410, 587
Tubes, measures of, 632-635

Undercharge, 6

Usual degree of electrification, length of

spark ,i>j inch, 263, 329, 359, 520; why

so weak, 264

Vacuum, 99, 212, 213
Varnish, 304, 494
Vermilion, 494, 497
Vessel, conducting, 51-53
Vial, Leyden, 240
Vial, third made, 441
Vitriol, oil of, 626, 696

Walsh (John, F.R.S., M.P., d. 1795), 395,

396, 401, 415, 421, 424, 430
Wasting of electricity, 393, 394, 486, 487
Water, resistance of, 398; distilled, 617, 621,

688; rain, 617; purged of air, 624, 692;

impregnated with fixed air, 625, 693;

pump, 684; sea, 524, 684
Wax, 387
Waxed glass, 255, 271, 295, 447, 450, 476,

54'. 563

Weather, effect of on coated plates, 304
Weight of electric fluid, 5
White glass, 301, 460

Wilcke (Johann Karl, b. 1732, d. 1796), 134
Williamson, Hugh, M.D., 437
Wilson (Benjamin, F.K.S., b. 1721, d. 1788),

125

Wind, electric, 125

Wire, 219, 240; charge of, 279, 479, 683;
trials of, 447, 448; connecting, allow-
ance for, 337; in straw electrometer,

387. 388

Wires compared with canals of incompress-
ible fluid, 94, 278 and note 3

Woods, conductance of soaked, 561, 588,
609

"Work," MS. so called, 349

End of The Scientific Papers, Volume I

CAMBRIDGE: PRINTED BY j. B. PEACE, M.A., AT THE UNIVERSITY PRESS

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BINDING ps^T. JUL23 19731

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Physical &
Applied Sci.

Cavendish, Henry
Scientific papers