OS-

REESE LIBRARY

UNIVERSITY OF CALIFORNIA.

Received

Accessions No.

C^.

!. ^^k^^^

Shelf No.. ^

COURSE OF LECTURES

ON

NATURAL PHILOSOPHY

AND THE

MECHANICAL ARTS.

BY THOMAS VOUNG, M.D.

\*
FOR. SEC. K. S. F.L.S. MEMBER OF EMMANUEL COLLEGE, CAMBRIDGE,
AND LATE PROFESSOR OF NATURAL PHILOSOPHY IN THE
ROYAL INSTITUTION OF GREAT BRITAIN

IN TWO VOLUxMES.
VOLUME L

J,t)NIVElsj^ '

LONDON:

PRINTED FOR JOSEPH JOHNSON, ST. PAUL's CHURCH YARD,

BY WILLIAM SAVAGE, BEDFORD BURY.

1807.

^<:) 2^

*f7

J'

i\

UU'i

^

f7

a-**

'.t

TO THE RIGHT HONOURABLE THOMAS GRENVILLE

A MAN EQUALLY ESTEEMED FOR HIS PRIVATE VIRTUES

AND RESPECTED FOR HIS DISTINGUISHED TALENTS

WHO LATELY PRESIDED

AS FIRST LORD OF THE ADMIRALTY

OVER THAT DEPARTMENT OF THE PUBLIC SERVICE

TO WHICH THE PRINCIPLES OF MECHANICAL SCIENCE

MAY WITH THE GREATEST NATIONAL BENEFIT

BE PRACTICALLY APPLIED

THIS WORK IS DEDICATED

BY THE AUTHOR.

PREFACE.

Having undertaken to prepare a course of lectures on natural
philosophy, to be delivered in the theatre of the Ro3'.al Institution, I
thought that the plan of the Institution required something more than
a mere compilation from the elementary works at present existing; and
that it was my duty to collect from oi'iginal authors, to examine with
attention, and to digest into one system, every thing relating to the
principles of the mechanical sciences, that could tend to the improve- .
ment of the arts subservient to the conveniences of life. I found also,
in delivering the lectures, that it was most eligible to conmiit to writ-
ing, as nearly as possible, the whole that was required to be said on
each subject; and that, even when an experiment was to be performed,
it was best to describe that experiment uninterruptedly, and to repeat
the explanation during its exhibition. Hence it became necessary th^t
the Avritten lectures should be as clearly and copiously expressed, and
in a language as much adapted to the comprehension of a mixed audi-
ence, as the nature of the investigations would allow ; and that each
experiment, which was to be performed, should also be minutely de-
scribed in them. If therefore there was any novelty either in the mat-
ter or the arrangement of the lectures, as they were delivered for two
successive years, it is obvious that they must have possessed an equal
claim to the attention of a reader, had they been published as a book;
and upon resigning the situation of Professor of Natural Philosophy, I
immediately began to prepare them for pubUcation.

I had in some measure pledged myself, in the printed syllabus of the
lectures, to make a catalogue of the best works already published on

VI PREFACE.

the several subjects; with references to such passages as appeared to
be most important: it was therefore necessary, as well for this purpose,
as in order to procure all possible information that could tend to the
improvement of the work, to look over a select library of books en-
tirely with this view, making notes of the principal subjects discussed
in them, and examining carefully such parts as appeared to deserve
more than ordinary attention. Hence arose a catalogue of references ;
respecting which it is sufficient to say, that the labour of arranging
about twenty thousand articles, in a systematic form, was by no means
less considerable than that of collecting them. The transactions of
scientific societies, and the best and latest periodical publications,
which have so much multiplied the number of the sources of informa-
tion, constituted no small part of the collection, which was thus to be
reduced into one body of science.

' With the addition of the materials acquired in making this compi-
lation, and of the results of many original investigations, to which
they had given rise, it became almost indispensable to copy the
whole of the lectures once more, and to exchange some of them for
others, which were wholly new; at the same time all possible pains
were taken to discover and to correct every obscurity of expression or
of argument. Drawings were also to be made, for representing to the
reader the apparatus and experiments exhibited at the time of deliver-
ing the lectures, for showing the construction of a variety of machines
and instruments connected with the different subjects to be explained,
and for illustrating them in many other ways. These figures have been
extended to more than forty plates, very closely engraved, and the
execution of the engravings has been minutely superintended. But
the text of the lectures has been made so independent of the figures,
that the reader is never interrupted in the middle of a chain of reason-
ing, but is referred, at the end of a paragraph, to a plate, which has
always a sufficient explanation on the opposite page. . >:

PREFACE. VH

The bulk of this work is not so great, as to require, for its entire
perusal, any unreasonable portion of time or of labour. There may,
however, be some persons who would be satisfied with attending to
those parts in which it differs most from former publications, without
having leisure or inclination to study the whole. To such it may be
desirable to have those subjects pointed out, which appear to the au-
thor to be the most deserving of their notice.

The fundamental doctrines of motion have, in the first place, been
more immediately referred to axioms simply mathematical, than has
hitherto been usual; and the apphcation of these doctrines to practical
purposes has perhaps in some instances been facilitated. The passive
strength of materials of all kinds has been very fully investigated, and
many new conclusions have been formed respecting it, which are of
inunediate importance to the architect and to the engineer, and which
appear to contradict the results of some very elaborate calculations.

The theory of waves has been much simplified, and somewhat ex-
tended, and their motions have been illustrated by experiments of a
peculiar nature. A similar method of reasoning has been applied to the
circulation of the blood, to the propagation of sound, either in fluids
or in solids, and to the vibrations of musical chords; the general prin-
ciple of a velocity, corresponding to half the height of a certain modu-
lus, being shown to be applicable to all these cases: and a connexion
has been established between the sound to be obtained from a given
solid, and its strength in resisting a flexure of any kind ; or, in the case of
ice and water, between the sound in a solid and the compressibility in
a fluid state. ,The doctrine of sound and of sounding bodies in gene-
ral has also received some new illustrations, and the theory of music
and of musical intervals has been particularly discussed.

With respect to the mathematical part of optics, the curvature of

VIU PREFACE.

the images, formed by lenses and mirrors, has been correGtly investi-
gated, and thcs inaccuracy of some former Estimations has been de-
monstrated.

In the department of physical optics, the phenomena of halos and
parhelia have been explained, upon principles not entirely new, but
long forgotten : the functions of the eye have been minutely examined,
and the mode of its accommodation to the perception of objects at
different distances ascertained : the various phenomena of coloured
light have been copiously described, and accurately represented by
coloured plates; and some new cases of the production of colours
have been pointed out, and have been referred to the general law of
double lights, by which a great variety of the experiments of former
opticians have also been explained ; and this law has been applied to
the establishment of a theory of the nature of light, which satisfacto-
rily removes almost every difficulty that has hitherto attended the
subject.

I'he theory of the tides has been reduced into an extremely simple
form, which appears to agree better with, all the phenomena, than the
more intricate calculations which they have commonly been supposed
to require. With respect to the cohesion and capillary action of
liquids, I have had the good fortune to anticipate Mr. Laplace in
his late researches, and I have endeavoured to show, that my assump-
tions are more universally applicable to the facts, than those which
that justly celebrated mathematician has employed. I have also at-
tempted to throw some new light on the general properties of matter
in other forms : and on the doctrine of heat, which is materially con-
cerned in them ; and to deduce some useful conclusions from a com-
parison of various experiments on the elasticity of steam, on evapora-
tion, and on the indications of hygrometers. I have enumerated, in
a compendious and systematical form, the principal facts which have

PREPACEv IX

%een discovered with respect to galvanic electricity ,• and I have for-
tunately been able to profit by Mr. Davy's most important experi-
ments, which have lately been communicated to the Royal Society,
and which have already given to this branch of science a much
greater perfection, and a far greater extent, than it before possessed.
The historical part of the work can scarcely be called new, but several
of the circumstances, Avhich are related, have escaped the notice of
former writers on the history of the sciences.

Besides these improvements, if I may be allowed to give them that
name, there are others, perhaps of less importance, which may still be
interesting to those who are particularly engaged in those departments
of science, or of mechanical practice, to which they relate. Among these
may be ranked, in the division of mechanics, properly so called, a.
simple demonstration of the law of the force by which a body revolves
in an ellipsis ; another of the properties of cycloidal pendulums ; an
examination of the mechanism of animal motions ; a comparison of
the measures and weights of different countries ; and a convenient
-estimate of the effect of human labour : with respect to architecture, a
^simple method of drawing the outline of a column : an investigation of
the best forms for arches ; a determination of the curve which affords
the greatest space for turning ; considerations on the structure of the
joints employed in carpentry, and on the firmness of wedges ; and an
easy mode of forming a kirb roof: for the purposes of machinery of
different kinds, an arrangement of bars for obtaining rectilinear mo-
tion ; an inquiry into the most eligible proportions of wheels and
pinions ; remarks on the friction of wheel work, and of balances ; a
mode of finding the form of a tooth for impelling a pallet without fric-
tion ; a chronometer for measuring minute portions of time ; a clock
«capement ; a calculation of the effect of temperature on steel springs;
an easy determination of the best line of draught for a carriage ; a«
VOL. I. b

X PREFACE.

investigation of the resistance to be overcome by a wheel or roller ?
and an estimation of the ultimate pressure produced by a blow.

In the hydraulic and optical part, may be enumerated an over-
flowing lamp ; a simplification of the rules for finding the velocity of
running water ; remarks on the application of force to hydraulic ma-
chines ; a mode of letting out air from water pipes ; an analysis of
the human voice; and some arrangements for^olar microscopes, and
for other optical instruments of a similar nature.

In the astronomical and physical division of the work, will be found
a general rule for determining the correction on account of aberration ;
a comparison of observations on the figure of the earth ; a table of
the order of electrical excitation ; a chart of the variation of the com-
pass, and of the trade winds ; formulae for finding the heat of summer
and winter ; remarks on the theory of the winds ; and a comparative
table of all the mechanical properties of a variety of natural bodies.

A few of these subjects have been more fully discussed in the miscel-
laneous papers, which have already been published, in the Philosophi-
cal Transactions and elsewhere, and which are now reprinted with cor-
rections and additions ; others are summarily investigated in the ma-
thematical elements, which form a part of the second volume, or in
the remarks, which are inserted, in their proper places, iatlie catalogue
of references.

The arrangement of the whole work is probably dififerent in many
respects from any other that has yet been adopted ; the extent of the
subjects, which have been admitted, rendered it necessary to preserve
a very strict attention to a methodical and uniform system ; and it is
presumed, that this arrangement will be considered as in itself of some-

PREFACE. XI

value, especially in a work calculated to serve as a key, by means of
which, access may be obtained to all the widely scattered treasures of
science; and which will enable those, who are desirous of extending
their researches in any particular department, to obtain expeditiously
all the information that books can atford them.

It will not be thought surprising, that the execution of this plan,
allowino- for some professional engagements of a different kind, and for
a variety of accidental interruptions, should have occupied more than
three years, from the resignation of the professorship to the publica-
tion of the work. Some part of it is in its nature incapable of perma-
nent perfection, since the catalogue must require to be continually ex-
tended by the enumeration of new publications; and it might perhaps
be desirable that an appendix should be added to it at least every ten
years: but the lectures themselves may be expected to remain tolera-
bly commensurate to the state of the sciences for a much longer pe-
riod; since, in investigations so intimately connected with mathemati-
cal principles, the essential improvements will always bear a very
small proportion to the number of innovations. I do not, however,
mean to assert, that the catalogue is by any means complete, even with
regard to older works, but I believe that the references, which it con-
tains, are at least sufficient to lead those, who may consult the passages
quoted, to the works of every author of eminence that has treated of
the respective subjects. Nor do I profess to have excluded all refer-
ences that are of little importance; but I trust that the number, which
I have admitted, will be found inconsiderable; and it would have been
very difficult to have rejected any of them, without some chance of
omitting others of greater value.

Whatever the deficiencies of this work may be, I think it right to
observe, that my present pursuits will not allow me to look forwards to
any period, at which I shall be able to remove them, or even to attend
to the correction of the press, or the revision of the engravings, in case

Xii PREFACE.

of the necessity of a second edition. I have already begun to collect
materials for a work, in a form nearly similar, relating to every depart-
ment of medical knowledge: this work will not, however, be speedily
ready for publication ; it will be comparatively more concise than thesa
lectures, in proportion to what has been said and written respecting
physic, but, I hope, much more complete, with regard to all that is.
known with certainty, and can be applied with utility.

Wclbeck Street,
OOtb March, 180?.

CONTENTS.

PART THE FIRST. MECHANICS.

Lecture i. Introduction ; Page 1.

Objects of the Uoyal Institution; 1. Dissemina-
tion of eleraentary knowledge ; 2. Education of fe-
males ; Theory of practical mechanics, and of manu-
factures; 3. Simplicity of useful theory; 4. Diffi-
culty of making improvements; Repository of the In-
stitution; Library; Journals; 5. Nature of the lec-
tures; Merits of En<;lish philosophers; 6. Delivery
of the lectures; 7. General view; 8. Division of
the lectures; Synthetical metliod; 9.. 14. Induction;
Causatiop ; 15. Erroneous inductions ; 10. Newtonian
rules of philosophizing; Their insufficiency; 17.

Lectuhe II. On motion ; 18.

Definition of motion; 18. Absolute and relative
motion ; All motion relative ; 19. Quiescent space ;
Direction of motion; 20. Laws of motion; 21. Time;
■ 32. Composition of motion; Space in motion; 23.
Result of two motions ; 24. Resolution of motion;
25. General result of a number of motions; 2(5.

Lectuue hi. On accelerating forces;

2.7.

Definition of force; 27. Action of force; 38. Ac-
celeration and retardation; Velocity; 29. Uniform
force; Gravitation; Laws of falling bodits; Atwood's
machine; 30. Space described; Law of Galileo;
31. General law of velocities; Ascent; Velocity due
to a height; 32.

Lecture iv. On deflective forces;
33.

Centrifugal force; Sling; S.*?. Motion of a hoop;
Whirling table; 34. Laws of central forces; 35.
Keplerian laws; 36. Ellipsis; Projectiles; 37. Re-
solution of oblique motion; 38. Horizontal range;
Best elevation ; Parabolic path ; 39. Practice of gui>
Hery; Experiments of Robins; 40,41.
3

Lecture v. On confined motion;

42.

Motion limited by suspension, or by a smooth sur--
face; Effect of friction and of rotatory motion; In-
clined plane; 42. Descent in the chords of a circle ;.
Velocity of descent; 43. Ascending force; Energy;
Cycloidal pendulum; 44. Laws of pendulums; 45.
Swiftest descent; Circular pendulums, 40. Pendu-
lums with resistance; Revolving pendulums ; Corapo--
sition of vibrations; Regulator for steam engines; 47»
Circular road; Principle of the least action; 48,49.

Lecture vi. On the motions of sim-
ple masses ; 60.

Definition of a moveable body, without regard to its-
extension; 50. Inertia; Centre of inertia; Its pro-
perties; 51. Reciprocal forces; Quantity of motion;.
52. Momentum ; Centre of inertia of a system ; 53.
Motion of the centre of inertia ; 54. Action and re-
action; Newton's illustrations; 55. Magnitude of re-
ciprocal forces; 50. Fall of a feather and of a piece
of gold; Lucretius; Relation between forces and dis-
tances; 57. Displacement of the earth by the effect
of a machine; 58.

Lecture vii. On pressure and equi-
librium ; 59.

Pressure, a force couuteraoted ; Pressure and mo-
mentum incommensurable ; 59. Laws of pressure in-
cluded in those of motion; Opposition of pressures;
60. Equilibrium of meckanical po.wers ; Centre of
gravity; 61. Stability of equilibrium; 62. Stabihty
independent of equilibrium ; 63. Situation and mo-
tions of tlie centre of gravity of animals; 64. Levers
of two kinds; Fundamental property of the lever; 65..
Series of levers ; Bent levers ; Oblique levers ; 66,
^Ylle€l and axis; Wheels and pinion* ; Double axis;

XIV

COKTENTS.

^7. Pullies; 68. Blocks; Smeaton's pulUes; 69.
Oblique ropes ; Inclined plane ; 70. Wedges; Props, or
shores; 71. Screws; Nuts; Hunter's screw ; 72. De-
termination of mechanical power from virtual veloci-
ties ; 73, 74.

Lecture vlii. On collision ; 75.

Motions of various bodies acting reciprocally;
Elastic bodies; 75. Nature of repulsion; Experiment on
nn ivory ball ; Apparatus for experiments on collision;
76. Inelastic bodies; Energy; 78. Measure of force ;
llelation of labour to energy; 79. Preservation of
energy; or of ascending force; Effect of a blow; 30.
Rotation; Billiards; Reflection; 81,82.

Lecture ix. On the motions of con-
nected bodies ; 83,

Rotatory power ; 83. Consideration of the square of
the velocity ; Smeaton's apparatus ; Centre of gyration;
84. Centre of percussion and of oscillation ; Free ro-
tation ; 85. See corrections. Motion of a stick broken
by a blow; 86. Preponderance; Greatest effect of
machines ; Experiments ; 87, 88. Cautions with regard
to the construction of machines ; 89. Comparison of
animal with inanimate force; 90. Regulation of force ;
Small momentum of machines; Impossibility of a
perpetual motion ; 91,92.

Lecture x. On drawing, writing,
and measuring ; 93.

Subjects preliminary to the consideration of prac-
tical mechanics; Instrumental geometry; Statics; Pas-
sive strength ; Friction; 93. Drawing; Outline; Pen;
Pencil; Chalks; 94. Crayons; Indian ink; Water
colours; Body colours; 95. Miniatures; Distemper;
Fresco; Oil; 96. Encaustic paintings; Enamel; Mo-
saic work; Writing; 97. Materials for writing; 98.
Pens; Inks; Use of coloured inks for denoting num-
bers; 99. Polygraph; Telegraph; Geometrical in-
struments; Rulers; 100. Compasses; Flexible rul-
ers; 101. Squares; Triangular compas.ses; Parallel
rulers; Marquois's scales; 102. Pantograph; Pro-
portional compasses; 103. Sector; Measurement of
angles; 104. Theodolites ; Quadrants; Dividing engine;
Vernier; Levelling; 105. Sines of angles; 106. Gun-
ter's scale ; Nicholson's circle ; Dendrometer; Arith-
metical machines; Standard measures; Quotation
from Laplace; 107. New measures; Decimal divi-

sions; 108. Length of the pendulum, Mid of the tne-
ridian of the earth; 109. Measure^f time ; Objec-
tions; 110. Comparison of measures! Instruments for
measuring; 111. Micrometrical scales; Log lines; 11*.

Lecture xx. On modelling, per-
spective, engraving, and print-
ing; 113.

Copying a statue ; Modelling; Casting; 113. Per-
spective; Mechanical perspective ; 114. Geometri-
ci>l perspective; 115. Orthographical projection;
116; Projections of a sphere; 117. Invention of en-
graving; Woodcuts; 118. Mode of engraving; Rul-
ing; Mczzotinto; Etching; 119. Aqua tinta; 120.
Musical characters ; Printing; Copying letters ; Prmt-
ing from stones; 121. Letterpress ; Stereotype print-
ing; 122.

Lecture xii. On statics; 123.

Weighing; 123. English and French weights ; Ba-
lances; 124. False balances; 125. Weighing ma-
chines; Steelyards; Bent lever balances; 126. Spring
steelyard; Dynamometer; 127. Animal t actions ;
Strength of muscles; 128. Instances of strength;
Progressive motion ; 129. Running ; Pulling ; 130.
Sources of motion; Work of a labouring man; 131.
Temporary exertions; Horses; 132. Wind; Water;
Steam; 133. Gunpowder; Measurement of small
forces; 134.

Lecture xiii. On passive strength
and friction ; 135.

Immediate effects of force on a solid ; 135. Exten-
sion and compression; Rigidity; 136. Measure of
elasticity ; 137. Detrusion ; Lateral adhesion ; Flex-
ure; 138. Cause of irregularities; Stiffness; 139^
Stiffness of beams; Hollow beams; Torsion; 140.
Alteration; Ductility; 141. Temper of metals;
Toughness; Britileness; 142. Fracture; Strength;
Resilience; Effect of velocity ; 143. Limit of strength
or resilience ; 144. Qualities of natural bodies; Frac-
ture by simple compression ; 145. Strength of lateral
adhesion ; Transverse force ; 146. Fracture by flex-
ure; Comparative strength and resilience; 14T.
Uses of resistonces of different kinds; Coach springs;
148. Comparison of direct and transverse strength ;
Beam cut out of a tree ; Hollow masts; 149. Strong-
est forms of beams; 150. Machine for measuring

CONTENTS.

XV

jtrength ; Strengtk of different substances, 151. In-
convenience of bulk ; Friction ; Lateral adhesion ;
153. Uniformity of friction, 153. Usual magnitude of
friction; Best direction for draught; 154. Stability of
a wedge or nail ; 155. Resistance lo penetration ; 156.

Lecture xiv. On architecture and
carpentry ; 157.

Architecture; Form of a column; 157. Eddystone
lighthouse; 158. Wall; 159. Joints; Mortar; Arch;
160. Oblique pressure; of earth; 161. Bridge; 162.
Flat arch; Horizontal thrust; Piers; 163. Black-
friars bridge ; Dome ; 164. St. Paul's cathedral ; Pan-
theon; Orders of architecture; 165. Gothic architec-
ture ; Carpentry; Joints; 166. Scarfing ;16T. Jog-
gles; Tenons; Mortises; Straps; 168. Inconveni-
ence of transverse strains; Roofs; 169. Kirb roof ;
Height of a roof; 170. Wooden bridges; Centres of
bridges; Furniture; Parker's gates; 171.

Lecture xv. On machinerj'; 172.

Application of force; 172. Levers; Connected
rods; Hooke's joint ; Cranks; 173. Winches; Rec-
tification of circular motion; 174. Wlieelwork ;
175. Teeth of wheels ; 176. Kinds of wheels; 177.
Eccentric wheels ; Sun and planet wheels ; Construc-
tion of wheels; Weights and springs; 178. Fly
wheels; Air vessels; 179.

Lecture xvi. On the union of
flexible fibres j 180.

Chain ; Union by means of adhesion ; Friction of a
rope on a cylinder; 180. Twisting; Spinning; Rope-
making; 181. Materials of ropes; 182. Hemp; Flax;
183. Cotton; Silk; 184. Wool; Weaving; 185.
Crape ; Cloth ; Felts; 136. Hats; Paper; 187.

Lecture XVII. OnTimekeepers; 18S.

Clepsydrae; 188. Clocks; Fly clocks; 189. Ba-
lances; Chronometer with a revolving pendulum;
190. Measuremcntof minute intervals of time; Pen-
dulum; Balance spring; 191. Principal requisites of
a timekeeper; Sustaining force; 192. Equalisation of
the force; Intermediate spring or wheel; Scapemcnt;
Crank ; 193. Crutch scapement; Common, watch
scapement ; 194. Dead beat scapement and horizon-
tal watch; Friction of scapcments ; 195. See correc-
tions. Duplex scapement; Comma scapement;
Scapemcnts of Harrison, Mudge, Haley, Cumming,
and Nicholson; 196. Scapcments of Arnold and
Earnsliaw; Isoclironism of vibrations ; 197. Proper-

ties of springs, 198. Expansion of pendulums ; Com-
pensations for clocks; 199. Compensations for
watches; 200. Resistance of the air; Striking part ;
201. Supports of clocks ; Mutual influence of two
clocks ; 202.

Lecture xviii. On raising and re-
moving weights; 203.

Counteraction of gravitation ; Levers: 203. Per-
rault's lever; Axis with a winch; 204. Water whim-
sey; Gin; Capstan; 205. Double capstan; Wheel-
work; String of buckets; PuUies; 206. Inclined
plane; Duke of Bcidgwater's canal; 207. Screws;
Cranes ; 208. Walking wheels ; White's crane ; 209 ;
Weighing cranes ; Lewis; Counterpoise for a chain ;
Removing weights ; Porters; 210. Distribution of
weight ; 211. Simple dray ; Effect of agitation ; Oily
substances; 212. Rollers; Friction wheels ; 2 13. Per-
rault's ropes; Wheels of carriages; 214. Magnitude
of wheels; 215. Line ofdraught; Conical wheels ; 216 ;
Effect of springs ; 217. Attachment of horses ; Wheel
ways; 218; String of baskets or carts; 219.

Lecture xix. On modes of chang-
ing the forms of bodies ; 220.

Compression; Presses; Effect of momentum; 220.
Printing press; Sugar mill; 221. Oil mills; Ilam-
meiing; Ilydrostalic press; Extension; Laminat-
ing machine; Glazier's vice; 222. Wire drawing;
Pottery; Glassblowing; Percussion; 223. Forges;
Goldbeating ; Coining; Stamping; Penetration; 224;
Pile driving engine; 225. Sling; Bow and arrow ; 22S.
Whip; Division; Cutting instruments; Slitting milt ;
227. Lathes ; Boring ; 228. Agricultural instru-
ments; Mining; Sawing; 229. Stonecutting; Grind-
ing; 230. Polishing; 231. Trituration; Powder
mills; Agitation; Threshing machines ; 232. Corn
mills; 933. Kneading; Levigating; Demolition;
Bolt drawer ; 234. Burning ; -Blasting ; 235.

Lecture XX. On the history of me-
chanics ; 236,.

Origin of the Grecian learning ir» Egypt; Tliale? t
230. Ionian school ; Italiaivschool ; Pythagoras ; 237 ;
Demooritus ; Invention of the arch ; 238. See correc-
tions. Archytas and Eudoxus; Aristotle; Foundation
of Alexandria; 239. Epicurus; Archimedes; 240.
Siege of Syracuse ; 241. Athenaeus; Ctesibius; 249.
Vitruvius; Middle ages; 243. British manufactures ;
244. Anglonorman atid Gothic architecture; 245,

XVI

CONTENTS.

Roger Bacon; Clocks ; Engrnving and printing; 246.
Leonardo da Vinci; Bacon LordVerulam; Galileo;
Napier; 247. Laws of collision; Hooke; Barrow;
Newton; 248. FoUowen of Newton ; 249. Modern

matliematiclans and mechanics; 250. Timekeepers 4
Journals; Royal Institution ; 251. Future prospects;
Use of a. catalogue of references; 252. Table of the
chronology of mathematicians and mechanics; 253.

PART THE SECOND, HYDRODYNAMICS.

Lecture xxi. On hydrostatics ; 257.

Hydrodynamics more dependent on experiment than
mechanics; 257. Division of the subject into Hy-
draulics, Acustics and Optics; 258. Hydrostatics;
Definition of a fluid and a liquid; 259. Surface of a
gravitating fluid horizontal; 260. Surface of a re-
volving fluid; Pressure of a fluid; 261. Magnitude
of hydrostatic pressure ; 262. Hydrostatic paradox ;
J63. Blowing with the mouth and lungs; Pressure
on the bank of a river ; 264. Pressure on a concave
surface ; Pressure of diflferent fluids ; Equilibrium of
fluids with solids ; 265. Floating bodies ; 2C6. Sta-
biUty and oscillations of floating bodies; Buoyancy;
267. Bodies falling in fluids; Hooke's hemisphere;
Flexible vessels ; 268, 269.

Lecture xxii. On pneumatic equili-
brium; 270.

Properties of tlie air, and of gases ; Mercurial co-
lumn; 270. Steams and vapours; Weight of the air ;
STl.'. Experiments with the air pump; Constitution
of the atmosphere; 272. See Corrections. Measure-
ment of heights; Ascent of a balloon-; Pressure of
the atmosphere; 273. Magdeburg hemispheres ; Na-
ture of suction; 274. Barometers; 275. Compres-
sibility of liquids; 276.

Lecture xxiii. On the theory of

hydraulics; 277-

General principle of ascending force ; 277. Ber-
•nouUi's inferences; 278. ^'elocity of a jet of a fluid ;
Ajutages of different kinds; 279. Contraction of a
jet; Effect of a short pipe; 280. Diverging pipe;
Experiments of Bernoulli, Venturi, and Matthew
Young; 281. Discharge through large apertures;
Vessels emptying themselves ; 282. Lodss; Siphons;
983. Discharge through a vertical pipe; 284. Ex-
planation; Limit of velocity; Whirlpool; 285. In-
termitting springs; Ascending jets; 286. Oscilla-
tions of fluids ; Waves; 287. Reflection of waves ;
288; Height of waves; Experimental exhibition of
waves; 289. Divergence of waves; Combinations of
waves; Applications; 290. Elastic pipes; Circula-
tion of the blood; 29 L

Lecture xxiv. On tlic friction of
fluids; 292.

Experiments of Du Buat; Motions of rivers; 29*.
Friction and resist;mce; 293. Examples of the velo-
city of- rivers; Velocity at different depths; 294.
Weres; 295. Changes and flexures of rivers; Late-
ral friction; 290. Ven|uri's experiments; Ball sup-
ported by a jet; 297. Discharge of long pipes; Bent
pipes; 298. Dilatations of pipes ; Effect of tempera-
ture; 299.

Lecture xxv. On hydraulic pres-.
sure; 300.'

Pressure of fluids in motion; 300. Counterprcs-
sure ; Magnitude of the pressure and impulse of fluids;
301. Laws of hydraulic pressure; Particular case of
■water wheels; Oblique impulse; 302. Distribution
of pressure; 303. Elevation and depression produced
by the motion of a floating body; Form of a ship>
Body moving below the surface; 304. Convex sup-
faces; Hydraulic pressure of the air; 305. Concave
surfaces; Great effect of an increase of velocity;
S06. Reflection of a ball or stone ; 307.

Lecture xxvr. On hydrostatic in-
struments, and hydraulic archi-
tecture ; 308.

Statics and architecture of fluids; Hydrostatic ba-
lance; 308. Hydrometer; Glass globules; 309. Spe-
cific gravities of particular substances; Mixtures;
Spirit level; 310. Hydrostatic lamps; 3]1. Fjo-
bmikments; Dil^es: Rivers; 312. Reservoirs; Flood
gates; 313. . Strength of sluices and flood gates;
Friction; 314. Canals; Pirrs; Harbours; 315.

Lecture xxvir. On the regulation
of hydraulic forces; 316.

Machinery of fluids; Watcrpipes; Siphons; 310.
Stopcocks and valves; 317. Pitol's tube ; Hydromc"
trie fly; Captain Hamilton's hydraulic register; 318.
Motions of the air; Weight and impulse of Jluids;
Raising weights by the descent of water ; 319. Effect
4>{ velocity ; Overshot wheel ; 030. Undershot wheel ;

CONTENTS.

XVll

Mechanical power of a stream ; 321. Breast wheel ;
Second wheel; Oblique wheels and windmills ; 322,
SIS. Smoke jack; Kite; Parent's mill; Seamanship ;
Side wind; S'ii. Vovva and arrangement of a vessel;
325. Stability of a ship; 326.

Lecture xxviii. On hydraulic ma-
chines; 327.

Machines for raising water; Noria; Bucket wheel ;
Throwing wheel ; Rope pump : 32r. Venturi's drain ;
Spiral pipes; Screw of Archimedes; .'528. Water
screw ; Wirtz's spiral pump ; 329. Centrifugal pamp ;
330. Pumps ; Plunger pump ; 331. Forcing pump ;
Mixed pump ; Pistons ; Bramah's press ; Sucking
pump ; 332. Bag pump ; Lifting pump; Sucking and
forcing pnmp; Air vessel ; 333. Fire engine ; Roll-
er pumps and slider pumps ; 334. Arrangement of
pipes ; Bead pump ; Cellular pump ; Chain pump ;
Cranks ; 335. Wheels and rollers ; Chinese walking
■wheels ; Inverted pump ; Hydraulic air vessels ; 336.
Fountain of Hero ; Atmospheric machines ; Hydraulic
ram ; 337, 338.

Lecture XXIX. On pneumatic ma-
chines; 339-

Counteraction and application of pneumatic forces ;
Torricellian vacuum ; Air pump ; 339. Double barrel ;
Smeaton's pump; Experiments; 340. Gages ;Peargage';
S4J. Condensers ; Diving bells ; 342. Bellows ; Gas-
ometer! ; 343. Shower bellows ; Velocity of a blast ;
Ventilation; 344. Corn fan ; Chimnies ; 345. Fur-
naces ; Balloons ; Steam engines ; Saver/s engine ;
346. Newcomen's and Beighton's engine ; 347. Watt's
improvements ; 348. Power of Boulton and Watt's
machines ; Later alterations ; Gunpowder ; 349. Cal-
culations of Bernoulli and of Count Rumford ; pro-
perties of a gun ; 350. Bullets ; Shot ; Air gun ;
351.

Lecture xxx. On the history of hy-
drauHcs and pneumatics ; 352.

Discoveries of Archimedes ; 352. Ctesibius ; Hero ;
Viti'uvius ; 353. Canals ; Gunpowder ; Galileo; Tor-
ricelli ; 354. Castelli ; Mariotte ; Guglielmini ; Gue-
ricke; Hooke ; 355. Marquis of Worcester; 356.
Huygens ; Pardies ; Renaud ; James and John Ber-
noulli ; Newton ; Poleni ; 357. Bouguer ; D. Ber-
noulli ; 358. John Bernoulli ; Maclaurin ; 359.
VOL, I.

Robins ; Dalembert ; Kaestncr ; 360. Eolcr ; Smea.
ton ; Borda; Watt ; Specification of Mr. Watt's pa-
tent; 361, 362. Bossut ; Juan ; Prony ; 363. Chap_
man; Romme ; Hutton ; Rumford; Du Buat ; 364.
Black ; Montgolfier ; 365. Chronological table ; 366.

Lecture xxxi. On the propagation
of sound ; 367.

Importance of acustics; Division^f the subject; De-
finition of sound; 367. Propagation of sound ; Velocity
ofsound;368. Delineation of a sound; 369. Com-
pressibility of hard bodies; Transmission of sound hy
different mediums; 370. Correction on account of
heat; 371. Transmission in gases of different kinds;
In liquids ; 372. In solids ; Divergence of sound ;
373. Reflection of sound; 874. Illustration by
waves of water; Speaking trumpet ;Whispering gallery ;
375. Invisible girl ; Partial interception of sound ;
Decay of sound; 376, 377.

Lecture xxxii. On the sources and
effects of sound ; 378.

Origin of a simple sound ; Of a continued sound;
378. Musical sounds derived from vibrations; Open
pipes; Stopped pipes; 379. Harmonic sounds;
Effect of temperature ; Longitudinal sounds of solids;
Lateral vibrations ;. 380. Flexible chords and mem-
branes; 381. Harmonic sounds of chords; 382. Loaded
wire; Revolutions of chords; 383. Vibrations of
clastic rods; 384. Vibrations of plates, rings, and
vessels; Mixed vibrations of solids and fluids ; 385.
Sympathetic sounds; Hearing; 386. Description of
the ear; 387. Delicacy of the car ; 388.

Lecture xxxiii. On harmonics; 389.

Theory of harmonics; Combinations of sounds; 389.
Beats; 390. Grave harmonics; Concords; 391.
Melody ; Rhythm ; Simple compositions ; Diatonic
scale; 399. Half notes or semitones; 393. Minor
mode; Discords; Rules of accompaniment; 394. Tem-
perament ; 395. Distinction of the notes ; 396.

Lecture xxxiv. On musical instru-
ments; 397-

Division of musical instruments; Harp; Lyre; 397.
Harpsichord; Spinet; Pianoforte; Dulcimer; Clavi-
chord; Guitar; 398. Violins of different kinds;
Vielle; Trumpet Marigni; Aeolian harp ; 399.
C

XVlll

CONTENTS.

human voice'; 40{T. Drum ; Stacada ; Bell ; Harmo-
nica; Vox humana pipe ; 401. Simple wind instru-
ments; Mixed wind instruments; 402. History of
music; Lyre; Hermes ; Terpander; Pythagoras; Si-
raonides;403. Tibia; Aristotle; Ctesibius; Pope
Gregory; 404. Guido; Bacon ; Galileo ; Mersennc ;
Kircher ; Meibomius ; Wallis ; Newton ; Brook Tay-
lor ; Sauveur; 405. Lagrange; Euler; Bernoulli;
Dalembert; Sounds of rods; Grave harmonics of
Romieu and Tartini ; Sounds of pipes. Chladni ; 406 .
Laplace; Chronological table ; 407.

Lecture xxxv. On the theory of
optics ; 408.

Importance of optics ; Division of tlie subject ; De-
finition of light ; 408. Ray of light ; Motion of light .
Homogeneous mediums ; 409. Reflection ; 410. Re-
fraction ; 411. Polished surfaces ; Return of a ray ;
Refractive density ; 412. Index of refractive power ;
Intermediate refraction; Total reflection; 413. Di-
optrics and catoptrics ; Focus ; 414. Plane speculum ;
Principal focus; Convergence by reflection ; 415. Con-
cave and convex mirrors ; Prism; Multiplying glass;
Lens; 416. Effects of lenses ; Focus of a lens; 41T.
Joint focus; Image ; Optical centre ; 418. Curvature
of the image; 419.

Lecture xxxvi. On optical instru-
ments ; 420.

Divergence of light; Photometers ; 420. Measure-
ment of refractive densities; Instruments strictly
optical ; 421. Images formed by lenses and mirrors ;
Magnifiers ; Simple microscopes ; Globules ; 429. Il-
lumination of an image ; Burning Glasses ; Materials
of lenses and mirrors ; 423. Images visible in every
direction; Camera obscura; 424. Solar microscope ;
425. Lucernal microscope : Phantasmagoria ; 426.
Astronomical telescope ; Double microscope ; 427.
Galilean telescope : Common day telescope ; Dr.
Herschel's telescope; 428. Newtonian reflector;,
Gregorian telescope ; Cassegrain's telescope ; Smith's
microscope; Curvature of images in telescopes, 129;
Magnifying powers of telescopes ; Field glass ; 430.
Double magnifier; Aberration from colour; Achro-
matic glasses; 431. Achromatic eyepiece; Micro-
meters ; 432. Divided speculum ; 433.

Lecture xxxvi. On physical optics;
434.

Sources of light; Combustion ; Slow decomposition;
434. Electricity ; Friction ; Solar phosphori ; 435.
Emission'of light; Velocity of light ; Apparent aber-
ration ; 436. Oblique reflection ; Diffraction ; Dis-
persion ; Colour; 437. Division of the spectrum;
Light of diff'erent kinds; 438. Mixed lights ; Imita-
tion of white light ; Primitive colours ; 439. Mixture
of colours by rapid motion; Combinations ; 440. At-
mospherical refraction; Horizontal refraction; 441.
Rainbows ; 442. Halos and parhelia ; 443. Refrac-
tion of ice ; Complicated halos ; 444. Double refrac-
tion; Iceland spar; Second refraction ; Transparent
plates ; 445, 446.

Lecture xxxviii. On vision ; 447.

Description of the eye ; 447. Image on the retin* j
Advantages of the arrangement ; 448. Inversion of
the image ; Instinct ; 449. Sensibility of the retina ;
Focus of the eye ; Accommodation ; 450. Change in
the crystalline lens ; Uses of the iris ; 451. Optome-
ter ; Myopic and presbyopic sight ; 452. Single
vision ; Judgment of distance ; 453. Apparent mag-
nitudes of the sun and moon ; Aerial perspective ;
Painting; 454. Panorama; Duration of sensations;
Ocular spectra ; 455, 456.

Lecture xxxix. On the nature of
light and colours; 457.

Theories respecting the nature of light ; 457. Sim-
ple propagation ; Transparent mediums; 458. Uni-
formity of velocity ; 459. Reflection and refraction ;
Partial reflection ; 460. Total reflection; 461. Sources
of light ; Aberration ; Double refraction ; 462.
Dispersion ; Colours of thin plates; 463. Alternate
union and extinction of colours; Light admitted by
two holes ; 464. Supposed dimensions of undulations ;.
Correction ; Stripes in a shadow ; 465. Light passing
through a narrow aperture; Colours of striated sur-
faces; 466. Curved stripes.af colours; Fringes near
a shadow ; 467. Colours of thin plates ; 468. Co-
lours of natural bodies ; 469. Colours of mixed plates ;
supernumerary rainbows ; 470. Colours of concave
mirrors ; Agreement of the Iluygenian theory with
the phenomena ; 471.

Lecture xl. On the history of
optics ; 472.

Knowledge of the ancients ; Empedocles ; 472^

CONTENTS.

XIX

Aristotle ; Archimedes ; Euclid ; Ptolemy ; Alhazen j
Vitellio ; R. Bacon ; 473. Jansen ; Galileo ; Kepler;
Scheiner ; Rheita ; Maurolycus; DeDoniinis; Silel-
lius ; Descartes ; 474. Ferraat ; Leibnitz ; Barrow ;
Boyle ; Hooke ; 475. Newton ; Grimaldi ; 476-
Bartholin; Huygens; Roemcr , Bradley ; 477. Bou-

PART THE THIRD

Lecture xli. On the fixed stars;
487.

Division of the subjects of physics ;487. Astronomy ;
488. Empty S|;ace ; fixed stars ; 489. Light of the
stars; Figure; Twinkling; Number; Magnitudes;
490. Distances of the stars ; 491. Clusters or ne-
bulae ; 492. Arrangement of the stars in general ;
Milky way ; Proper motions of the ^stars ; 493. Dr.
Herschel's division of stars and nebulae ; Changes of
the stars ; 494. Constellations ; 495. Representa-
tions of the stars ; AUineations ; 496 . .498.

Lecture xLir. On the solar system ;
^99-

The sun a star; Progressive motion of the sun;
499. Orbit of the sun ; Rotation ; 500. Spots ;
Solar heat ; 501. Sun's attraction ; Solar atmosphere ;
502. Planets ; Ecliptics ; 503. Change of position
of the ecliptic ; Nodes ; Keplerian laws ; 504. Rota-
tion of the planets ; Precession of the equinoxes ; 505.
Nutation of the earth's axis ; Proportional distances
of the planets ; Mercury ; 506. Venus ; The earth ;
Mars; 507. Juno; Pallas; Ceres; Jupiter ; Saturn ;
608. Georgian planet ; Unknown planets; Satellites;
509. Moon ; 510. Satellites of Jupiter ; Ring of
Saturn ; 511. Comets ; 512. Number and orbits of
the comets; 513.

Lecture xliii. On the laws of gra-
vitation ;

Newton's great discovery ; Attraction of spherical
bodies; 515. Extent of tiie force ofgravity ; 5l6.
Sun's change of place ; Orbits of the planets ; Kep-
lerian laws ; 517. Universality of gravitation ; Mo-
tions of the apsides and nodes; Changes of the
•cliptic ; Forms of the planets ; 518. Precession ;
Nutation; Lunar motions; 519. Disturbing force of
the Run i 520. Acceleration of the moon's motion ;

guer ; Porterfield ; Jurin ; Smith ; Doliond ; Hall .
478. Euler ; 479. Lambert ; Mathematical opti-
cians; Mazeas; Dutour ; Comparetti ; Priestley;
480. Delaval ; R. Darwin ; Atmospherical refrac-
tion ; Wollaston; Ritter ; Herschcl ; 481. Laplace J
Attempts of the author ; 482. Chronological table ; 483'

.. PHYSICS ; 485.

Moon's rotation ; Orbits of comets; 521. Predictions
of Halley and Clairaut ; 522. Chronological table; 433.

Lecture xliv. On the appear-
ances of the celestial bodies; 523.

Apparent motions to be described after the real
ones; Motions of the stars and sun ; Motions of the
earth ; 523. Apparent revolution of the sun ; 524.
Sun's apparent diameter; Length of summer and win-
ter"; Day and night ; Sun's apparent path ; 525. Cen-
trifugal force ; Places of the stars ; Twilight , 526.
Relative positions and phases of the planets; 527.
Phases of the moon: Lunar eclipses ; 528. Eclipses
of the sun ; Series of eclipses ; 529. Harvest moon j
Eclipses of Jupiter's satellites ; 530. Comets; Light
of the heavenly bodies ; Planetary worlds ; 531. Fon-
tenelle ; Mercury ; Venus ; 532. Moon ; 533. Mars ;
Newly discovered planets ; Jupiter ; 534. Saturn ;
Georgian planet ; 535.

Lecture xlv. On practical astro-
nomy ; 536.

Real motions neglected ; Situation of a point in the
heavens ; Meridian ; 536. Astronomical instruments :
Time; Sidereal day; .Solar day; Equation of time'
537. Dialling; Chronology; 538. Calendar; 539.
Improvement suggested ; Republican calendar ; Me-
tonic cycle ; Golden number ; 540. Epact ; Moon's
age; Julian period; Astronomical time ; Quadrants;
Transit instruments ; 541. Iladley's quadrant ; De-
clinations ; Refraction and parallax ; 542. Latitudes:
Longitudes ; 543. Lunar observations ; Distance of
the sun ; Transits ; 544. Densities of the sun add
planets; Artificial globe ; " 565". Planispheres ;;566-
Orreries ; 567.

Lecture xlvi. On Geography; 568.

Particular account of the earth; Curvature of its
surface; Direction of the plumb line; 568. Ellipti-

XX

CONTENTS,

city ; Mcasuremtnts of degrees ; 569. Zones ; 570.
Climates; Sea and land; Continents; 571. Rivers;
Elevations; 572. Mountains; 573. DifFcrent orders
of mountains; Internal parts of the earth; 574. Den-
sity of the earth ; 575.

Lecture xLvii. On the tides;
576.

Tides noticed by the ancients ; Daily changes ; 570.
Monthly changes; Yearly clianges; Connexion with
the moon; Effect of gravitation on a fluid sphere;
577. Primitive lunar tides; Comparison with a pen-
dulum ; 578. Direct and inverted tides ; Tides of a
lake; 579. Resistance; Tides of the Atlantic ; 580.
Particular modifications ; 58 1. Tides of t'.ie Channels,
and of rivers; 582. Inferior and superior tides ; Laws
of elevation and of depression; 583. Mode of ob-
serving the tides; Solar tides; Combination of tides;
584. Retardation of spring and neap tides; 585.
Increased height in converging channels; Combina-
tions in particular ports; 586. Currents; Tides of the
atmosphere ; 587, 588. See corrections.

Lecture xlviii. On the history
of astronomy ; 589.

Earliest astronomy ; Signs of the zodiac; 589. Baby-
lonian observations; Chaldeans; Hermes; Egyptians;
Chinese; 590. Indians; Greeks; 591. Thales; Py-
thagoras; Meto; Alexandrian school ; 592. Erato-
sthenes; Hipparchus; 593. Ptolemy; 594. Arabians;
Persians; 595. Copernicus; Tycho Brahe; 596.
Kepler; 59T. Napier; Huygeus; Cassini; Gravita-
iJon; 598. Newton's discoveries; Extract from Pem-
berton; 599,600. British astronomers ; Observatory
at Greenwich; 001. Determination of the longitude ;
Late discoveries; 602, 603. See corrections. Chrono-
logical table ; 004.

Lecture xlix. On the essential
properties of matter ; 605.

Importance of minute objects; 605. Definition of
mater; Place of the investigation; 006. Essential
and accidental properties of matter; Extension; Di-
visibility; 607. Actual division of matter; 608.
Impenetrability; 609. Permeability; Orders of sub-
stances; 610. Repulsion; Apparent contact; 611.
Laws of repulsion; 612. Dalton's hypothesis; Re-

pulsion of liquids and solids; Reciprocality of repul-
sion; 613. Inertia; Gravitation; Cause of gravita-
tion; 614. Mathematical conceptions; Newton's
opinion; 615. Constitution of a medium capable of
producing gravitation; 616. Difficulties; 617.

Lecture l. On cohesion ; 618.

Accidental properties of matter; Laws of cohesion ;
618. Modification of cohesion by heat; Liquidity; 619i
Superficial cohesion; 620. Bubbles; Form of the sur-
face of a fluid ; 021. See corrections. Magnitude of the
force of cohesion; Ascent between two plates; 622.
Capillary tubes ; Horizontal surface ; 623. Detached
portion of a liquid ; Lycopodium ; Attractions and re-
pulsions of floating bodies; 024. Apparent cohesion
of plates ; Drop between plates; Oil spreading on
water; Sponge; 025. Long column supported by
cohesion; Cohesion of solids; More perfect union;
026. Solidity; 627. Cause of solidity ; Elasticity;.
028. Stiffness; Strength; Softness; Ductility; 629.
Primary cause of cohesion; 630.

Lecture li. On the sources and
effects of heat; 631.

Division of the subject of heat ; Definition of heat
and cold; 631. Excitement of heat; Condensation;
Friction ; Count Rumford's experiments ; 632. Ef-
fect of velocity ; 633. Pictet's experiments ; Heat
from combustion ; 634. Communication of heat i
Conducting powers; Fluids; 635. Radiation of heat;
Mr. Leslie's discoveries ; 636. Differences of solar
and culinary heat ; Invisible heat ; Equilibrium of ra-
diant heat ; 637. Apparent reflection of cold ; Re-
frangibility of heat ; 638. Blackening rays ; Effects
of heat; Tejnporary effects; 639. Expansion of
gases; Condensation; 640. Expansion of fluids;
Diminution of cohesive powers; Boiling; Slow eva-
poration; 041. Contraction; Freezing; Expansion
of solids; 042. Liquefaction; Cracks from heat;
043. Permanent effects of heat; Glass drops; Tem-
pering of metals ; 644, 645.

Lecture lii. On the measures
and the nature of heat ; 646.

Measures of expansion; Pyrometer; Scale of heat;
646. Mixtures; Sun's rays; Expansion of solids and
fluids; Tiiermometers ; 647. Wedgwood's thermo-

CONTENTS.

XXI

meter j Different scales ; 648. Temporary change of
a thermometer; Air thermometers; 649. Capacities
for heat; Natural zero ; 650. Theory of capacities ;
651. Chemical effects; Latent heat; C52. Mr.
Davy's experiments; Intimate nature of heat; Theory
of caloric; Confutation; 653. Heat a quality;
Newton's opinion ; Vibrations ; 654. Mechanical ef-
fects of vibrations ; Chemical effects ; Comparison
with sound; 655. General inferences ; 656,657.

Lecture liii. Ou electricity in
equilibrium ; 6o8.

Utility of electrical hypotheses; Division of the
subject; 658. Supposed electric fluid; Its attrac-
tions and repulsions ; 659. Conductors and noncon-
ductors ; 660. Positive and negative electricity ; Lo-
cal electricity; Distribution of electricity; 661.
Electricity of a sphere; Connected spheres; 662.
Difference of hydrostatic and electrical pressure;
Attractions and repulsions ; 663. Induced electri-
city ; Neutral point ; Effects of attraction and repul-
sion; 664. Currents of air; Bodies electrified in dif-
ferent degrees; Charge; 665. Discharge; Shock;
Coated jar; Battery; Comparison of conducting
powers; 666, 667.

Lecture liv. On electricity in
motion ; 668.

Effects and causes of electrical motions, and elec-
trical apparatus; Velocity; 668. Spark; Perfora-
tion of a jar; Direction of the motion; 669. Opini-
ons respecting positive and negative electricity ; Ef-
fects of electricity ; Accumulation ; Simple current ;
Electric light ; 670. Heat; Mechanical effects ; 671.
Chemical effects; Sensible effects; 672. Excitation
of electricity ; Electrics; 673. Vapours; Tourmalin;
Galvanic electricity; Chemical chanws; 674. G:»l-
vanic combinations ; General laws ; 675. Particular
facts; Pile of Volta; 676. Troughs; Animal elec-
tricity ; 677. Mr. Davy's discoveries ; Electrical na-
ture of chemical attractions ; Theory of the pile ; 678.
Efficacy of decomposable substances; 679. Electrical
machines ; Teylenan machine ; Electrophorus ; 680.
Condenser; 681. Multiplier; Doublers ; Electrical
balance; Quadrant electrometer; 682. Gold kaf elec-
trometer ; Lane's electrometer ; 683. General obser-
Tations; 684.

Lecture lv. On magnetism; 6SS.

Resemblance of magnetism and electricity ; Theory ;

685. Conducting powers ; Magnetical substances ;

686. Aurora borealis; North and South poles ; At-
tractions and repulsions; 687. Polarity; Arrange-
ment of filings; Directive force; 688. Terrestrial
magnetism; Compass; Dipping needle; Illustra-
tion ; 689. Temporary magnetism : Natural magnet ;
Magnetic poles of the earth ; 690. Diurnal changes j
Variation of the declination; Line of no declination;
691. Dip; Artificial magnets; 692. Double touch ;
Magnetic paste ; Division of a magnet ; 693. Strik-
ing and ringing a magnet ; Hammering brass; Solu-
tion in an acid ; 694. Resemblance of polarity to
crystallization ; 695.

Lecture lvi. On climates and
winds; 696.

Meteorology; Division of the subject ; Climates;
Meteorological thermometers ; 696. Immediate effects
of the sun ; 697. Prevost's calculations ; Variations
of temperature ; Slow changes ; 698. Heat of the
sea ; Effect of freezing and thawing ; Heat of the at-
mosphere ; 699. Sunnner and winter ; Temperatures
of different places ; Local variations ; 700. Winds ;
Periodical winds ; Trade winds; Had ley ; 701. Hal-
ley's theory ; Atmosphere of Jupiter; Greater heat of
the northern hemisphere ; 702. Westerly winds ;
Local modifications; Monsoons; 703; Land and sea
breezes; Hurricanes; Variations of the barometer;
704, 705.

Lecture lvii. On aqueous and
igneous meteors ; 7O6.

Evaporation, and its effects; Theory of Deluc and
Dallon; 700. Quantity of water evaporating; Preci-"
pitation ; 707. ^Moisture; Mediterranean; Currents
at the Straights; Attraction of moisture; 708. B.
Provost; Hygrometers; 709. Natural hygrometer;
Water contained in air; 710. Visible vapour; Dew;
Mists; 711. Ruin; Indications of the barometer;
Effects of mountains; 712. Periodical rains; Thun-
der and lightning; 713. Atniospheiical electricity;
Thunderstorms; 714. Conductors; Sudden conden-
sations; 715. Wall rspouts;- Aurora borealis; Earth-
quakes and Volcaiius; 716. Volcanic countries;
Earthquakes of Calabria; 717. Eruptions of Vesu-

XXll

CONTENTS.

viiis; 718, 719. Geological changes ; Reality of va-
rious clianges ; 720. Effects of rivers and of the sea ;
Shouting stars; 721. Falling stones ; 722.

Lectuhe lviii. On vegetation;
723.

Sketchof natural history ; Minerals; Vegetables ; 723.
Animals ; 724. Distinctions of animals and vegetables;
725. Description of a vegetable: Germination j
Parts of plants; 726. Vessels; 727. Motion of the
sap; 728. Mr. Knight's experiments ; Grafting; 729.
Diseases of plants; Exposure to the air; Linnean
system; 730, 731. System of Jussieu; 732.

Lecture lix. On animal life;
733.

Classification of aninuils, according to Linn^ ; 733.
Mammalia; Birds; 734. Amphibia; Fishes; 735.
Insects; 736. Vermes; 737. Senses; Nutrition; 738.
Nervous system; 739. Nature of the nerves; Dis-
*asesj 740. Natural cures; 741.

Lecture lx. On the history of
terrestrial physics ; 742.

General retrospect ; Knowledge of the ancients ;
742. Chinese; Numa; Tliales; Anaximander; Anaxi-
menes; 743. Pyth.igoras; Anaxagoras; Democritus;
Heraclitus; Plato; 744. Aristotle; Epicurus; 745. R.
Bacon; Discovery of tlie compass; Gesner; Aldro-
vandus ; Gilbert of Colchester ; 746. Variation of
the compass; F.Bacon; Opinions of heat; Drebel ;
747. Harvey ; Circulation of the blood ; Barometer ;
Bauhins; Ray; Willughby ; 748. Philosophical so-
cieties; Variation charts; 749. Electricity; Lin-
nean system ; Discoveries respecting heat ; 750.
Theory of magnetism and electricity; Boscovich;
Hygrometry; 751. Galvanism; Pile of Volta ; 752.
Mr. Davy's experiments; Dalton; Rumford; 753.
Herschel ; Leslie ; Capillary tubes ; Laplace ; 754.
Advantages to be expected from modern institutions ;
755. Chronological table; 756.

EXPLANATION OF THE PLATES; 757-

ADDITIONS AND CORRECTIONS.

p. 40. L. 5 from the bottom; for "therefore,"
read, afterwards.

P. ri.- L. 5 from the bottom; for " IV," read, V.
P. 72. L. 2, for " IV," read, V.
P. 87. After 1. 4, insert.

When an insulated body revolves round an axis in
any direction, the state of revolution cannot be per-
manent, unless the axis be so situated, that the cen-
trifugal forces on each side of it balance each other.
It is obvious that this must happen in a homogeneous
sphere, whatever may be the situation of the axis ;
and it has been demonstrated, that when the body is of
an irregular form, there are at least three rlifterent
axes, situated at right angles to each other, round
which the body may revolve in an equilibrium either
stable or tottering. It may also be shown that if a
body, revolving round any axis, receive at the same
time an impulse which would cause it to revolve round
a second axis in another direction, the two revcrfutions
will be combined, and will form a single revolution
round a third axis, in an intermediate position, which
will remain at rest until it be displaced by some new
force, provided that it be one of the axes of perma-
nent revolution: so that no body can revolve round a
moveable axis without a continual disturbing force.
And when an irregular body begins to move on an
axis incapable of equilibrium, its revolution will be
gradually altered, so as to approach continually to a
revolution round one of the natural axes; bnt it will
never pass beyond the state of equilibrium, as in many
other cases of deviation from such a state ; since the
momentum, produced by the excess of centrifugal
force in one part of the revolution, is destroyed irf
another. For a similar reason, if a stick be thrown in a,
horizontal position, with a rotatory motion, it will fall
in the same position much more certainly than if it
were thrown without any rotation; for any small dis-
turbing force, which might be sufficient to turn it into
a vertical position during the course of its path, will
only produce, when combined with the rotatory mo-
tion, a slight change of the direction of the rotation,
which will confine the deviation of the stick from a
horizontal position within narrow limits.

P. 138. L. 9, after " concerned," insert, it has in-
deed been asserted that the specific gravity of elastic
gum is even diminished by tension, so that the actual
distances of the particles cannot, in this cas«, be sup-
posed to be materially increased.

P. 146. L. 3, after " 124," insert, 125.

L. 8 from the bottom, for « IX," read, X.
P. 169. L. 7, for "XIV, read, XIII.
P. 176. L. 19, for " the circle," read, a second
circle.

P. 196. L. 5 . . 2, from the bottom, for " If the fric-
tion. . to obviate this," read, Since friction is always
increased by an increase of pressure, the effect of any
addition to the sustaining force must tend, in some de-
gree, to retard the vibrations, even if the friction be
somewhat less increased than the force propelling the
balance. In order to obviate this retardation.

P. 238. L. 5 from the bottom, after " arches," in-
sert, since they must have left too small a space for
the passage of the water. If, however, we may be-
lieve Herodotus, whom Mr. King has quoted, this was
in reality a kind of drawbridge. According to thi»
author, it was built by Nitocris, the immediate Suc-
cessor of Serairamis: the stones were united by iron
and lead, and beams were laid across them, which
viere removed at night, in order to prevent the mutual
depredations of the inhabitants of difterent parts of
the city.

P. 261. L. 19, for "XX," read, XIX.
P. 267. L. 18, for " heel," read, pitch.
P. 273. L. 3 from the bottom, omit " logarithm of."
L. 2 from the bottom, for " numbers,"
read, corresponding logarithms.
P. 292. L. 9, for " de," read, du.
P. 420. L. *, for "more," read, most.
P. 424, after line 5, insert.

Dr. Wollaston has/ very ingeniously applied the-
effect of the reflection of two plane surfaces, inclined
to each other, to the construction of an instrument for
drawing, which he calls a camera lucida. He usually^
employs the internal reflection of a prism of glass, of
which the four surfaces are ground so as to form pro-
per angles with each other. The image formed by-,
the first surface is inverted, and the second reflection
restores it to its original position, but places it in a
direction which is at right angles with the direction of
the object ; so that when we look down through the
prism on a sheet of paper, we see a perfect picture of
the objects immediately before us, while at the same
time the aperture, through which we look, is only partly
occupied by the edge of the prism, the remaining part
being left open, or simply covered with a lens, for the
adraissjon of the direct rays of light, by which we may

•xs.iv

Acr>rTro?rs and coruections.

see, at the same time, the paper aud the pencil to be
employed, for making a diawiug or a copy of any ob-
ject placed before us.

P. 425. L. 1^, for " XXVn," read, XXVIII.

P. 464. L. 15, for " other points at," read, at other
points.

P. 477. Last lino but one, after " telescopes,'' in-
sert, but with respect to the theory of halos and par-
helia, he was less successful than Mariotte had been
some years before.

P. 335. L. 7 from the bottom, for " ecipses," read,
species.

P. .545 . . . Running title. The numbers of all the
pages are too great by 20.

P. 587. L. 15. . 17, for " the attraction . . is pro-
duced," read, a current is observed iu its most ex-
posed parts.

P. 588. L. 14, 15, for " on account . . moon" read.
These currents, as well as the general current of the
sea, have been attributed by some astronomers to the
immediate attraction of the sun and moon, and of the
satellites of Jupiter, which they have supposed to
act in the same manner as the attraction of the sun
operates in retarding the lunar motions ; but the fact
is, that, according to Mr. Laplace, the disturbing force
of the sun produces this effect on the moon only iu pro-
portion as it increases her distance from the earth ;
consequently no such retardation can possibly be pro-
duced by the force of gravitation in the rotation of the
sea or of the atmospliere, and the whole effect must be
attributed to the operation of meteorological causes,
producing first the trade winds, and secondly occa-
sionmg, by means of the friction of these winds, a simi-
lar motion in the sea. In the case of the atmosphere
of Jupiter, the effects of heat can indeed scarcely be
supposed to be very perceptible, and the rotation of
this planet being extremely rapid, it is not at all im-
possible that the satellites may exert an action on the
atmosphere somewhat analogous to the retardation of
the moon's motion by the disturbing force of the sun.

P. 565, L. 12, for " Almamoun, was the son", read,
Almamoun, the son.

P. 003. L. 2. for " The observations of the transit of
Venus were twice made in the South Seas", read. Ob-
servations of the transit of Venus were made with
great care in the South Seas.

At the end, insert. For tlie latest improvement
that has been made in astronomy, we are also indebted
to the zeal and ingenuity of Dr>01bers,who, in pursuit

of an opinion which be had formed, respecting the ori-
gin of the three small planets from the separation of
a larger one into frngments, has been in the habit of
of examining monthly that part of the heavens, io
which he supposes the event to have taken place, and
through whicli each of the bodies must necessarily pass.
He has had the good fortune to discover, in this man-
ner, a fburth planet, which nearly resembles the
throe otiiers in its appearance, except that it seem*
to be considerably larger.

P. C21. L. 22, after " descriptions,'' insert.

We may form some idea of the effects of this mutual
action, by neglecting the force of repulsion, as Clairaut
has done, and attending only to that of cohesion.

P. 622. L. 5 . . 13, for " It may also . . densities,"
read. This mode of re.isoniiig is however by no means
sufficient to explain all the phenoini nu ; for it may be
inferred from it that when the attractive power of tlie
solid is greater or less than half that of the liquid, the
surface of the liquid must, at its origin, be in the
same direction with that of the solid, instetvd of form-
ing an angle with it, as it often does in reality. But
the difficulty may be removed by reverting to the ge-
neral principle of superficial cohesion, and by com-
paring the common surface of the liquid and solid
with the surface of a single liquid, of which the attrac-
tive powfer is equal only to the difference of the re-
spective powers of the substances concerned. In this
manner it may be shown, that if the attractive power
of the solid be equal to that of the liquid, or still
greater, it will be wetted by the liquid, which will
rise until its surface acquires the same direction with
that of the solid ; and that iu other cases, the angle of
contact will be greater, in proportion as the solid is less
attractive. A similar comparison is also equally ap-
plicable to the contact of two liquids of different den-
sities.

P. 630. L. 11, for " one," read, we.

P. 678. L. 7. for " when in contact," read, cither
during their contact, or after separation.

P. 702. L. 9 . . 28. For " Astronomers . . years,''
read, " nor can any sufficient cause be found, in the
attractions of the celestial bodies, either for the
general easterly trade winds, or for the current of the sea
in a similar direction, which appears to be the imme-
diate effect of their friction on the surface of the water."

P. 770. Fig. 172, add. The strap itself must how-
ever be made stronger when in the situation B.

COURSE OF LECTURES

ON

NATURAL PHILOSOPHY

AND THE

MECHANICAL ARTS

PART I.

MECHANICS.

COURSE OF LECTURES

ON

NATURAL PHILOSOPHY

AND THE

MECHANICAL ARTS.

LECTURE I.

INTRODUCTION.

It is to be presumed, that most of those who honour the theatre of the
Royal Institution with their attendance, are already acquainted with the na-
ture of the objects which its founders and promoters have been endeavouring
to attain; yet it appears to be by no means superfluous, that I should define
with accuracy my own views of the utility that is likely to be derived from
it, and of the most effectual means of accomplishing its purposes; in order
tlaat we may be able to distinguish, without difficulty, the most eligible track
for our common progress through the regions of science; and that those who
are desirous of accompanying me in the journey, may know precisely what
route we are to follow, and what departments will more particularly arrest
our attention.

Societies, which are merely literary and philosqphical, have in general
prmcipally proposed to themselves, to enlighten the understanding by the
discovery of unknown phenomena, and to exercise the reasoning powers, by

VOL. r.

B

2 tECTURE I.

opening new fields for speculation. Other associations have been more par-
ticularly intended for the encouragement of the arts, of manufactures, and
of commerce. The primary and peculiar object of the Royal Institution of
Great Britain is professedly of an humbler, but not of a less interesting na-
ture. It is, to apply to domestic convenience the improvements which have
been made in science, and to introduce into general practice such mechanical
inventions as are of decided utility. But while it is chiefly engaged in this
pursuit, it extends its views, in some measure, to the promotion of the same
ends which belong to the particular provinces of other literary societies; and
it is the more impossible that such objects should be wholly excluded, as it
is upon the advancement of these that the specific objects of the Institution
must ultimately depend. Hence the dissemination of the knowledge of
natural philosophy and chemistry becomes a very essential part of the design
of the Royal Institution: and this department must, in the natural order
of arrangement, be anterior to the application of the sciences to practical
uses. To exclude all knowledge but that which has already been applied to
immediate utility, would be to reduce our faculties to a state of servitude,
and to frustrate the very purposes which we are labouring to accomplish.
No discovery, however remote in its nature from the subjects of daily ob-
servation, can with reason be declared wholly inapplicable to the benefit
of mankind.

It has therefore always appeared to me, to be not only the best beginning,
but also an object of high and permanent importance in the plan of the In-
stitution, to direct the public attention to the cultivation of the elementary
doctrines of natural philosophy, as well speculative as practical. Those who
possess the genuine spirit of scientific investigation, and who have tasted the
pure satisfaction arising from an advancement in intellectual acquirements,
are contented to proceed in their researches, without inquiring at every step^
what they gain by their newly discovered lights, and to what practical pur-
poses they are applicable: they receive a sufficient gratification from the en-
largement of their views of the constitution of the universe, and experience,
in the immediate pursuit of knowledge, that pleasure which others wish to
obtain more circuitously. by its means. And it is one of the principal advan-
tages of a liberal education, that it creates a susceptibility of an enjoyment
so elegant and so rational.

INTRODUCTION. S

A considerable portion of my audience, to whose information it will be
my particular ambition to accommodate my lectures, consists of that sex,
which, by the custom of civilised society, is in some measure exempted from
the more laborious duties that occupy the time and attention of the other
sex. The many leisure hours, which are at the command of females in the
superior orders of society, may surely be appropriated, with greater satis-
faction, to the improvement of the mind, and to the acquisition of know*
ledge, than to such amusements as are only designed for facilitating the in-
sipid consumption of superfluous time. The hours thus spent will unquestion-
ably become, by means of a little habit, as much more agreeable at the mo-
ment, as they must be more capable of affording self approbation upon re-
flection. And besides, like the seasoning which reconciled the Spartans to
their uninviting diet, they will even heighten the relish for those pursuits
which they interrupt: for mental exercise is as necessary to mental enjoy-
ment, as corporal labour to corporal health and vigour. In this point of
view, the Royal Institution may in some degree supply the place of a sub-
ordinate university, to those whose sex or situation in life has denied them
the advantage of an academical education in the national seminaries of
learning.

But notwithstanding the necessity of introducing very copiously specu-
lations of a more general nature, we must not lose sight of the original ob-
jects of the Royal Institution; and Ave must therefore direct our attention
more particularly to the theory of practical mechanics, and of manufactures.
In these departments we shall find some deficiencies which may without much
difficulty be supplied from scientific principles; and by an ample collection
and display of models, illustrative of machines, and of inventions of all kinds,
we may proceed in the most direct manner to contribute to the dissemination
of that kind of knowledge which is most particularly our object. So that we
must be more practical than academies of sciences, and more theoretical than
societies for the improvement of arts; while we endeavour at the same time
to give stability to our proceedings, by an annual recurrence to the element-
ary knowledge which is subservient to the purposes of both; and, as far as
we are able, to apply to practice the newest lights, which may from time to
time be thrown on particular branches of mechanical science. It is thus that,
we may most effectually perform, what the idolized sophists of antiquity but

4 LECTURE I.

verbally professed, to bring down philosophy from the heavens, and to make
her an inhabitant of the earth.

To those who are engaged in the practical cultivation of various arts, sub-
servient to the conveniences of life, these lectures may be of some utility, by
furnishing them with well established principles, applicable to a variety of
cases, which may occasionally occur to them, where a little deviation from the
ordinary routine of their profession may be necessary. Unfortunately, the
hands that execute are too often inadequately supported by the head that dir
rects ; and much labour is lost for want of a little previous application tp the
fundamental doctrines of the mechanical sciences. Npr is any exorbitant
portion of time or industry necessary for this purpose; for it happens singu-
larly enough, that almost all practical applications of science depend on prin-
ciples easily learnt; and, except in astronomy only, it has seldom been fbund
that very abstruse investigations have been of great importance to society.
Our most refined analytical calculations are by far too imperfect to apply 1;o
all possible cases of mechanical actions that caabe proposed; ai^d those pro-
blems which most frequently occur, may in general be solved by metliods
sufficiently obvious ; although, from a want of proper order and perspicuity
in the treatment of first principles, it has often happened that the most ele-
mentary propositions have been considered as requiring great study and ap-
plication.

We may also be able to rendex.an miportant service to society, and to con-
fer, a still more essential benefit on individuals, by repressing the premature
zeal of unskilful inventors^ , Weuepd g}}\y read over the monthly accounts of pa-
tents, intended fo;?. securing the pecuniajiy advantages of useful discoveries, in
order to be convinced what expense of time and fortune is continually lavishr
ed on the feeblest attempts to innovate and improve. If we can be successful
in convincing siich inconsiderate enthusiasts of their r^al ignorance, or if we
can show them, that even their own fairy ground has been preoccupied, we
may save.thep} from impending ruin, and may relie,v.e the public from the
distraction of having its attention perpetually excited by unworthy objects.
The ridicule attendant on the name of a projector has been in general but too
well deserved ; for few, very few, who have aspired at improvement, have ever
had the patience to submit their inventions to sujch experimental tests as cominou

INTRODUCTION. 5

sense would suggest to an impartial observer. We may venture to affirm that
out of every hundred of fancied improvements in arts or in machines, ninety
at least, if not ninety nine, are either old or useless ; the object of our re-
gearches is, to enable ourselves to distinguish and to adopt the hundredth.
But while we prune the luxuriant shoots of youthful invention, we must re-
member to perform our task with leniency, and to show that we wish only
to give additional vigour to the healthful branches, and not to extirpate the
parent plant.

The Repository of the Royal Institution, as soon as it can be properly fur-
nished, will be considered as a supplementary room for apparatus, in which
the most interesting models, exhibited and described in the lectures, will be
placed for more frequent inspection, and where a few other articles may per-
haps deserve admission, which will not require so particular an explanation.
To those who have profited by the lectures, or who are already too far ad-
vanced to stand in need of them, our rooms for reading and for literary con-
versation may be a source of mutual instruction. Our Library in time nuist
contain all those works of importance which are too expensive for the private
collections of the generality of individuals; which are necessary to complete
the knowledge of particular sciences, and to which references will occasion-
ally be given in the lectures on those sciences. Our Journals, free from com-
mercial shackles, will present the public, from time to time, with concise ac-
counts of the most interesting novelties in science and in the useful arts ; and
they will furnish a perpetual incitement to their editors to appropriate, as muck
as possible, to their own improvement, whatever is valuable in the jxiblications
of their cotemporaries. When all the advantages, which may reasonably be
expected from this Institution, shall be fully understood and impartially con-
sidered, it is to be hoped that few persons of liberal minds will be indifi'ercnt
to its success, or unwilling to contribute to it and to participate in it.

To that regulation, which forbids the intFoduction of any discussions con-
nected with the learned professions, I shall always most willingly submit, and
most punctually attend. It requires the study of a considerable portion of a
man's life to qualify hirh to be of use to mankind in any of them ; and nothing-
can be more pernicious to individuals or to society, tlian the attempting to
proceed practically upon an imperfect conception of a few iirst principles only.

6 LECTURE I. ,

In physic, the wisest can do but little, and the ignorant can only do worse
than nothing: and anxiously as we are disposed to seek whatever relief the
learned and experienced may be able to afford us, so cautiously ought we
to avoid the mischievous interference of the half studied empiric : in politics
and in religion, we need but to look back on the history of kingdoms and
republics, in order to be aware of the mischiefs which ensue, when " fools
rush in where angels fear to tread- "

Deeply impressed with the importance of mathematical investigations, both
foi- the advancement of science and for the improvement of the mind, I thought
it in the first place an indispensable duty to present the Royal Institution, in
my Syllabus, with a connected system of natural philosophy, on a plan seldom,
if ever, before executed in the most copious treatises. Proceeding from the
simplest axioms of abstract mathematics, the syllabus contains a strict demon-
stration of eveiy proposition which I have found it necessary to employ through,
out the whole extent of natural philosophy. In the astronomical part only,
some observations occur, unsupported by mathematical evidence: here, how-
ever, it was as impracticable, as it would have been useless, to attempt to enter
into investigations, which in many instances have been extended far beyond
the limits even of Newton's researches. But for the sake of those who are
not disposed to undertake the labour of following, with mathematical ac-
curacy, all the steps of the demonstrations on which the doctrines of the me-
chanical sciences are founded, I shall endeavour to avoid, in the whole of this
course of lectures, every intricacy which might be perplexing to a beginner,
and every argument which is fitter for the closet than for a public theatre. Here
I propose to support the same propositions by experimental proofs : not that I
consider such proofs as the most conclusive, or as more interesting to a truly
philosophic mind than a deduction from general principles ; but because there
is a satisfaction in discovering the coincidence of theories with visible effects,
and because objects of sense are of advantage in assisting the imagination to
comprehend, and the memory to retain, what in a more abstracted form
anight fail to excite sufficient attention.

This combination of experimental with analogical arguments, constitute^
the principal merit of modern philosophy. And here let the citizen of the
world excuse the partiality of an Englishman, if I pride myself, and congra-

INTRODUCTION. 7

tulate my audience, on the decided superiority of our own country, in the first
establishment, and in the subsequent cultivation, of the true philosophy of the
operations of nature. I grant that we have at times been culpably negligent
of the labours of others ; tliat we have of late suffered our neighbours to ex-
cel us in abstract mathematics, and perhaps, in some instances, in patient
and persevering observation of naked phenomena. We have not at this mo-
ment a Lagrange or a Laplace : what we have, I do not think it necessary
to enumerate: but there is a certain combination of theoretical reasonins: with
experimental inquiry, in which Great Britain, from the time of the reforma-
tion of philosophy, has never been inferior to any nation existing. I need
only refer to the Transactions of the Royal Society, for abundant instances- of
the mode of investigation to which I allude; and I will venture to affirm,
that their late publications are equal in importance to any that have preceded;
It was in England that a Bacon first^taught the world the true method of the-
study of nature, and rescued science from that barbarism in which the fol-
lowers of Aristotle, by a too servile imitation of their master, had involved
it ; and with which, even of late, a mad spirit of innovation, under the name
of the critical philosophy, has, in a considerable part of Europe, again been
threatening it. It was in this country that Newton advanced, with one gi-
gantic stride, from the regions of twilight into the noon day of science. A
Boyle and a Hooke, w^ho would otherwise have been deservedly the boast of
their century, served but as obscure forerunners of Newton's glories. After
these, a crowd of eminent men succeeded, each of great individual merit; but,
absorbed in the prosecution of the Newtonian discoveries, they chose rather
to be useful by their humble industry, than to wander in search of the brilli-
ancy of novelty. It is difficult to judge of our cotemporaries ; but we appear
at present to be in possession of more than one philosopher, whose names-
posterity will be eager to rank in the same class with the few that have been
enumerated. But it is not our present business to enter into the history of
science; respecting what is supposed to bd wholly unknown, we can have
little curiosity : a short sketch of the progress of each branch of natural
philosophy will be more properly introduced, after we have finished our inves-
tigation of the principal doctrines belonging to it.

With regard to the mode of delivering these lectures, I shall in general in-
treat my audience to pardon the formality of a written discourse, in favour of

8 LECTURE r.

the advantage of a superior degree of order and perspicuity. It would un-
questionably be desirable that every syllable advanced should be rendered per-
fectly easy and comprehensible even to the most uninformed ; that the most
inattentive might find sufficient variety and entertainment in what is submit-
ted to them, to excite their curiosity, and that in all cases the pleasing, and
sometimes even the surprising, should be united with the instructive and the
important. But whenever there appears to be a real impossibility of recon-
ciling these various objects, I shall esteem it better to seek for substantial
utility tlian temporary amusement ; for if we fail of being useful for want of
being sufficiently popular, we remain at least respectable: but if we are
imsuccessful in our attempts to amuse, we immediately appear trifling and con-
temptible. It shall however at all times be my endeavour to avoid each ex-
treme ; and I trust, that I shall then only be condemned, when I am found ab-
struse from ostentation, or uninteresting from supineness. The most difficult
thing for a teacher is, to recollect how much it cost himself to learn, and to
accommodate his instruction to the apprehension of the uninformed: by bear-
ing in mind this observation, I hope to be. able to render my lectures more
and more intelligible and familiar; not by passing over difficulties, but by
endeavouring to facilitate th£ task of overcoming them ; and if at any time I
appear to have failed in this attempt, I shall think myself honoured by any
subsequent inquiries, that rriy audience may be disposed to make.

We have to extend our views over the whole circle of natural and artificial
knowledge, to consider in detail the principles and application of the philoso-
phy of nature and of art We are to discuss a great number of subjects, to
each of which a separate title and rank among the sciences has sometimes
been assigned; and it is necessar}"^, in order to obtain a distinct conception
ot the foundation and relation of each subdivision, to pay particular attention
to the order in which the sciences are to be treated, and to the connexion
which subsists between them, as well as to the degree of importance, which
each of them claims, with regard either to theory or to practice. To insist
on the propriety of a distinct and logical order is unnecessary; for however
superfluous we may deem the scholastic forms of rhetoric, it is confessedly
advantageous to the judgment as well as to the memory, to unite those things
which are naturally connected, and to separate those which are essentially dis-
tinct. When a traveller is desirous of becoming acquainted with a city or

INTncDUCTIOX. <^

country, before unknown to him, he naturally begins by taking, from some
elevated situation, a distant view of the distribution of its parts ; and in the
same manner, before we enter on the particular consideration of the subjects
of our researches, it may be of use to form to ourselves a general idea of the
sciences and arts which are to be placed among them.

Upon the advantages of mathematical and philosophical investigation in
general, it is unnecessary to enlai'ge, because no liberal mind can require any
arguments to be convinced how much the judgment is strengthened, and the
invention assisted, by habits of reasoning with caution and accuracy. The
public opinion is rather, on the contrary, in danger, at least in some paits of
the world, of being too exclusively biassed in favour of natural philosophy j
and has sometimes been mclined to a devotion too much limited to science,
without a sufficient attention to such literature as an elegant mind always de-
sires to see united with it. As to the practical importance of philosophical
tlieories of the arts, it may have been overrated by some, but no person is
authorised to atTirm, rhat.it has been too highly estimated, unless he has made
himself master of every thing that theory is capable of doing; such a one,
although he may in some cases be obliged to confess the insufficiency of our
calculations, Avill never have reason to complain of their fallacy.

The division of the whole course of lectures into three parts, was originally
suggested by the periodical succession in which the appointed hours recur: but
it appears to be more convenient than any other for the regular classification
of the subjects. The general doctrines of motion, and their application to all
purposes variable at pleasure, supply the materials of the first two parts, of
which the one treats of the motions of solid bodies, and the other of those of
fluids, inclftding the theory of light The third part relates to the particular
history of the phenomena of nature, and of the affections of bodies actually
existing in the universe, independently of the art of man; comprehending
astronomy, geography, and the doctrine of the properties of matter, and of
the most general and powerful agents that influence it t^'

4.1 j-i

■ The synthetical order of proceeding, from simple and general principles,
to their more intricate combinations in particular cases, is by far the most
compendious for conveying information, with regard to sciences that are at all

VOL. I. c

10 LECTURE I.

referable to certain fundamental laws. For these laws being once established,
each fact, as soon as it is known, assumes its place in the system, and is re-
tained in the memory by its relation to the rest as a connecting link. In the
analytical mode, on the contrary, which is absolutely necessary for the first
investigation of truth, we are obliged to begin by collecting a number of in-
sulated circumstances, which lead us back by degrees to the knowledge of
original principles, but which, until we arrive at those principles, are merely
a burden to the memory. For the phenomena of nature resemble the scatter-
ed leaves of the Sibylline prophecies; a Avord only, or a single syllable, is
written on each leaf, which, when separately considered, conveys no in-
struction to the mind; but when, by the labour of patient investigation,
every fragment is replaced in its appropriate connexion, the whole begins at
once to speak a perspicuous and a hai-monious language.

Proceeding therefore in the synthetical order, we set out from the abstract
doctrines of mathematics, relating to quantity, space, and number, which we
pass over, as supposed to be previously understood, or as sufficiently explained
in the mathematical elements, and go on to their immediate application to
mechanics and hydrodynamics, or to such eases of the motions of solids and
fluids as are dependent on arbitrary assumptions, that is, where we do not
confine our inquiries to any particular cases of existing phenomena. By
means of principles which are deducible in a satisfactory manner from mathe-
matical axioms, with the assistance only of the general logic of induction,
we shall be able to draw such conclusions, as are capable of giving us
very important information respecting the operations of nature and of art, and
to lay down such laws, as, to an uninformed person, it would appear to be be-
yond the powers of reason to determine, without the assistance of experiment.
The affections of falling bodies, and of projectiles, the phenomen*^ of bodies
revolving round a centre, the motions of pendulums, the properties of the centre
of gravity, the equilibrium of forces in machines of diflferent kinds, the laws
of preponderance, and the efi'ects of collision ; all these are wholly referable to
axiomatical evidence, and are frequently applicable to important uses in prac-
tice. Upon these foundations, we shall proceed to the general principles of
machinery, and the application of forces of different kinds : we shall inquire
what are the principle sources of motion that we can subject to our command,
and what advantages are peculiar to each of them ; and then, according to

INTRODUCTION*. H

the purposes for which they are employed, we shall separately examine the
principal machines and manufactures in which those forces are applied to the
service of mankind.

Such instruments and machines as are more or less immediately suhservient
to mathematical purposes, will be the first in order, including- all the meclian-
ism of literature, the arts of writing, engraving, and- printing, in their various
branches, and the comparison of measures, with each other and with differ-
ent standards ; the principles of perspective will also form a useful appendage
to the description of geometrical instruments. The determination of weights,
and of the magnitude of moving forces of various kinds, constituting the sci-
ence of statics, will be the next subject, and will be followed by the con-
sideration of the retarding force of friction, and of the passive strength of
the various materials, that are employed in building and in machinery.

All these subjects are in part preparatory to the immediate examination of
the mechanical arts and manufactures, which are so numerous and complicated
as not to admit of regular arrangement without some difficulty: they may
however be divided into such as are principally employed for resisting, for
modifying, or for counteracting, any motion or force ; thus architecture and
carpentry are chiefly intended to resist the force of gravitation : these compre-
hend the employments of the mason, the bricklayer, the joiner, the cabinet
maker, and the locksmith. In these departments it is often of the utmost im-
portance to the mechanic, to recur, especially in works of magnitude, to philoso-
phical principles ; and in many other cases, where there is no need of much
calculation, we may still be of service, by collecting such inventions of in-
genious artists, as are convenient and elegant, and which, although simple in
their principles, are not obvious in their arrangements; and in the same man-
ner we may be able, in taking a general view of other arts and manufactures,
to explain their principles, where theory is concerned, and to exhibit practical
precedents, where the nature of the subject requires no refined investigation.

The modification of motion and force includes its communication and alter-
ation, by joints of various kinds, by wheelwork, and by cordage, and its
equalisation by means of timekeepers. The subject of wheehvork gives con-
siderable scope for mathematical research, and requires the more notice, as it

H N LECTURE I.

has often been inaccurately treated: the consideration of cordage leads us to-
that of union by twisting, and by intermixture of fibres; including the im-
portant arts of carding, combing, spinning, ropemaking, weaving, fulling,
felting, and papermaking; which constitute the employment of many mil-
lions of manufacturers, of all ages and sexes, in every part of the world, and
by which the animal and vegetable productions of a large portion of the sur-
face of the globe, are made to contiibute, as well to. the power and riches of
the individuals wlio supply them, as to the health and comfort of the public
that consumes them. The admirable art of the watch and clock maker is a pe-
culiarly interesting department of practical mechanics, it affords employment
for mathematical investigation, for experimental inquiry, and for ingeni6us in-
vention; and the perfection, wliich it has derived from a combination of these
means, does honour as well to the nations who have encouraged it, as. to the
individuals who have been engaged in it..

To counteract the powers of gravitation and of friction, is the object of
such machines as are vised for raising and removing weights : cranes, friction
wheels, and carriages of all kinds, are referable to this head, and some of
them have been the subjects of much speculation and experiment. Lastly, to
overcome and to modify the corpuscular forces of cohesion and repulsion, and
to change the external forms of bodies, is the object of machinery intended for
compression, extension, penetration, attrition, trituration, agitation, and de-
molition. For these purposes we employ presses, forges, rolling, stamping,
coining, and milling machines;, the processes of digging, ploughing, and
many other agricultural arts; boring, mining, grinding, polishing, and turn-
ing; mills of various kinds, threshing mills, corn, mills, oil mills, and powder
mills; besides the chemical agents concerned in blasting rocks, and in the opei*^
ations of artillery. All these arts are comprehended in the department of me-
chanics, which constitutes the first division of this course. Not that we shall
be able to enter at large into the detail of each; but having formed a general
outline, we may fill up its particular parts with more or less minuteness, as
we may find more or less matter of importance to insert in each ; and those
who wish to pursue the subjects further, will every where be able to derive
great assistance from the authors whose works will be mentioned.

The doctrines of hydrodvnamics relate to the motions and affections of

INTRODUCTION. Iti

fluids, in which we no longer consider each distinct particTe that is capable of
separate motion, but where we attend to the effect of an infinite number of
particles, constituting a liquid or aeriform aggregate. The general theory of
such motions will be premised, under the heads hydrostatics, or the affections
of liquids at rest, pneumatostatics, or the properties of clastic fluids at rest;
and hydraulics, or the theory of fluids in motion. The practical application
of this theory to hydraulic and pneumatic machines is of very considerable
importance, and is as interesting to the philosopher as it is necessary to the
engineer. The employment of the force of water and wind to the best ad-
vantage, the draining of lands and mhies, the supply of water for domestic
convenience, the manoeuvres of seamanship, the construction of the steam
engine, are all dependent upon hydrodynamical principles, and are often con-
sidered as comprehended in the science of hydraulics. Harmonies and optics,
the remaining parts of this division, are more insulated : the doctrine of
sound, the theory of music,, and the construction of musical instruments, are
as pleasing to the intellect in theory, as they are gratifying to the senses in
practice; but the science of optics is not less interesting, and at the same
time far more useful; the instruments which it furnishes are of almost indis-
pensable necessity to the navigator, to tire naturalist, to the physiologist, and
evert to the man of business or pleasure. It is perhaps in this science that
many persons of the greatest genius have been the most happily employed.
The reasons for which it is classed as a division of hydrodynamics will be ex-
plained hereafter.

The contemplation of the particular phenomena of nature, as they are dis-
played in the universe at large, contributes perhaps less to the perfection of
any of the arts, which are immediately subservient to profit or convenience,,
than the study of mechanics and hydrodynamics. But the dignity and mag'^
niiicence of some of these phenomena, and the beauty and variety of others,
render them highly interesting to the philosophical mind, at the same tinle
that some of them are of the utmost importance in their application to the
purposes of life. In ail these respects the science of astronomy holds the first
rank ; its uses in assisting navigation, and in regulating chronology, are be-
yond all calculation. Geography, and hydrography, or the particular histories
of the earth and sea, are immediately connected with astronomy. The discus-
iion of the properties of matter in general, and of the alterations of tempera--

,14 LECTURE I.

tuie to which all bodies are hable, has not hitherto received a distinct appel-
lation as a science ; but both these subjects require a separate consideration, and
afford a vast scope for speculation and for observation. Electricity and magne-
tism are partly referable to the affections of matter, and partly to the agency of
substances which appear to agree with common matter in some properties, and
to differ from it in others. The phenomena produced by these agents are
often such as excite a high degree of curiosity to inquire into their causes,
although the inquiry too often terminates only in astonishment; but we have
reason to expect considerable advancement in these sciences from the singular
discoveries of modern chemists. The utihty of the philosophy of electricity
is sufKciently exemplified in the general introduction of conductors for secur-
ing us against lightning, to say nothing of the occasional employment of
electricity in medicine; and since the important discovery of the compass, we
have only to lament that the changeable nature of magnetic effects so much
limits the utility of that instrument for nautical and geographical purposes.
Of meteorology, and of geology, our knowledge is hitherto very imperfect;
notwithstanding many difltuse treatises which relate to them, we cannot boast
of having reduced them to any determinate laws ; and yet there are some me-
teorological facts which well deserve our attention. Natural history is the last
of the sciences that it will be necessary for us to notice ; some may think it
superfluous to attempt to give so superficial a sketch of this most extensive
subject, as our plan will allow; but it is still possible to select some general
observations respecting the methods of classification, as well as the philo-
sophy of natural history, which, although very concise, may yet be in some
measure instructive. This third division of the course would properly include,
together with the general properties of matter, and the particular actions of
its particles, the whole science of chemistry, but the variety and importance
of chemical researches, demand a separate and minute discussion; and the
novelty and beauty of many of the experiments with which the labours of our
cotemporaries have presented us, and which will be exhibited in the theatre
of the Royal Institution by the Professor of Chemistry, are sufhcient to
make this department of natural philosophy the most entertaining of all the
sciences.

Such is the whole outline of our plan, and such are the practical uses, to
which the arts ana sciences, comprehended in it, are principally applicable.

INTRODUCTION. 15

Before we proceed to the examination of its several parts, we must pause to
consider the mode of reasoning which is the most generally to be adopted.
It depends on the axiom which has always been essentially concerned in every
improvement of natural philosophy, but which has been more and more em-
ployed, ever since the revival of letters, under the name induction, and which
has been sufficiently discussed by modern metaphysicians. That like causes
produce like effects, or, that in similar circumstances similar consequences en-
sue, is the most general and most important law of nature; it is the founda-
tion of all analogical reasoning, and is collected from constant experience, by
an indispensable and unavoidable propensity of the human mind.

It does not appear that we can have any other accurate conception of cau-
sation, or of the connexion of a cause with its effect, than a strong impression
of the observation, from uniform experience, that the one has constantly fol-
lowed the other. We do not know the intimate nature of the connexion by
which gravity causes a stone to fall, or how the string of a bow urges the
arrow forwards ; nor is there any original absurdity in supposing it possible
that the stone might have remained suspended in the air, or that the bow-
string might have passed through the arrow as light passes through glass.
But it is obvious that we cannot help concluding the stone's, weight to be the
cause of its fall, and that every heavy body will fall unless supported; and
the pressure of the string to be the cause of the arrow's motion, and, that if
we shoot, the arrow will fly ; if we hesitated to make these conclusions, "we
should often pay de:ir for our scepticism. This explanation is sufficient to
show the identity of the two expressions, that like causes produce like effects,
and, that in similar circumscances similar consequences ensue. And such is
the ground of argument from experience, the simplest principle of reasoning,
after pure nK! them atical truths; which appear to be so far prior to experi-
ence, as their contradiction always implies an absurdity repugnant to the
imaginatioco

In the application of induction, the greatest caution and circmnspection
are necessary ; for it is obvious that, before we can infer with certainty the
complete similarity of two ^ents, we must be perfectly well assured that we
are acquainted with every circumstance which can have any relation to their
causes. The error of some of the ancient schools consisted principally in the

]() LECTURE I.

want of sufficient precaution in this respect; for although Bacon is, with
great justice, consiclered as the author of the most correct method of induc-
tion, yet, according to his own statement, it was chiefly the guarded and gra-
dual application of the mode of argument, that he laboured to introduce. He
remarks, that the Aristotelians, from a hasty observation of a few concurring
facts, proceeded immediately to deduce universal principles of science, and
fimdamental laws of nature, and then derived from these, by their syllogisms,
all the particular cases, which ought to have been made intermediate steps in
the inquiry. Of such an error we may easily find a familiar instance. Wd
observe, that, in general, heavy bodies fall to the ground unless tliey are Sjup-
ported; it was therefore concluded that all heavy bodies tend downwards:
and since flame was most frequently seen to rise upwards, it was inferred that
flame was naturally and absolutely light. Had sufficient precaution been em-
ployed in observing the effects of fluids on falling and on floating bodies, in
examining the relations of flame to the circumambient atmosphere, and in as-
certaining the specific gravity of the air at different temperatures, it would
readily have been discovered, that the greater weight of the colder air was the
cause of the ascent of the flame ; flame being less heavy than air, but yet
having no positive tendency to ascend. And accordingly the Epicureans,
whose arguments, as far as they related to matter and motion, were often,
more accurate than those of their cotemporaries, had corrected this error; for
we find in the second book of Lucretius a very just explanation of the pheno-
menon. ,

■" See with what force yon river's crystal stream

Resists the weight of many a massy beam.

To sink the wood the more we vainly toil,

The higher it rebounds, with swift recoil.

Yet that the beam would of itself ascend

No man will rashly venture to contend.

Thus too the flame has weight, though highly rare,

Nor mounts but when compelled by heavier air."

It may be proper to notice here those axioms which are denominated by
Newton rules of philosophizing; although it must be confessed that they
render us very little immediate assistance in our investigations. The first is,

INTRODUCTION. - 17

that " no more causes are to be admitted as existing in nature, than are true,
and sufficient for explaining the phenomena to be considered:" the second,
" therefore effects of the same kind are to be attributed, as far as is possible,
to the same causes:" thirdly, " those qualities of bodies which cannot be in-
creased nor diminished, and which are found in all bodies within the reach of
our experiments, are to be considered as general qualities of all bodies exist-
ing:" fourthly, "in experimental philosophy, propositions collected by induc-
tion from phenomena, are to be esteemed cither accurately or veiy nearly true,
notwithstanding any contrary hypotheses, until other phenomena occur, by
which they may either be corrected or confuted."

As an illustration of the remark, that these axioms, though strictly true
are of little real utility in assisting our investigations, I shall give an instance
from the subject of electricity. Supposing that we wish to determine, whe-
ther or no the electric fluid has weight ; we are to inquire whether or no gra-
vitation is one of those properties which are described in the third rule, and
whether that rule will authorise us to apply it to the electric fluid, as one of
those qualities of bodies, which cannot be increased nor diminished, which
are found in all bodies within the reach of our experiments, and which are
therefore to be considered as general qualities of all bodies existing. Now
it appears to be in the first place uncertain whether or no the increase and di-
minution of gravity, from a change of distance, is strictly compatible with the
terms of the definition ; and in the second place, we are equally at a loss to
decide, whether or no the electric fluid can with propriety be called a body,
for it appears in some respects to be wholly different from tangible matter,
while it has other qualities in common with it. Such are the difficulties of
laying down general laws on so comprehensive a scale, that we shall find it
more secure to be contented to proceed gradually by closer inductions in par-
ticular cases. We shall however seldom be much embarrassed in the choice
of a mode of argumentation. The laws of motion, Avhich will be the first
immediate subjects of discussion, have indeed sometimes been referred to
experimental evidence ; but we shall be able to deduce them all in a satis-
factory manner, by means of our general axiom, from reasonings purely ma-
thematical, which, wherever they are applicable, are unquestionably prefer-
able to the imperfect evidence of the senses, employed in experimental inves-
tigations.

VOL. I. D

18

LECTURE ir.

ON MOTION.

TL HE whole science of mechanics depends on the laws of motion, either ac-
tually existing, or suppressed by the opposition of the forces which tend to
produce it. The nature of motion requires therefore to be particularly ex-
amined at the entrance of the science of mechanical philosophy ; and although
the subject is so abstract as to demand some effort of the attention, being
ijeldom capable of receiving much immediate illustration from the objects of
sense, yet we shall find it indispensable to our progress in the investigation of
many particular problems of importance, to obtain, in the first place, a clear
conception of the properties and affections of motions of all kinds.

One of the ancient philosophers, on being asked for a definition of motion,
i?. said to have walked across the room, and to have answered, you see it, but
what it is, 1 cannot tell you. It does not, however, appear absolutely necessary
to appeal to the senses for the idea of motion: for a definition is the resoliition
of a complex idea int,o the more simple elements which compose it; and, in the
present instance, these elements are, the existence of two points at a certain
^stance^ and after a certain interval of time, the existence of the same points
at.a different distance; the difterence of the distances being supposed to be as-
certained according to that postulate of geometry, which has in general been
tacitly understood, but which I have expressly inserted iri the geometrical part
of my syllabus ; requiring that the length of a line be capable of being identi-
fied, whether by the effect of any object on the senses, or merely in ima-
gination.

Motion, therefore, is the change of rectilinear distance between two points.
Allowing the accuracy of this definition, it appears that two points are ne-

\

ox MOTION. \Q

cessary to constitute motion; that in all cases when we are inquiring whether
or no any body or point is in motion, we must recur to some other point
which we can compare with it, and that if a single atom existed alone in the
universe, it could neither be said to be in motion nor at rest. This may seem
in some measure paradoxical, but it is the necessary consequence of our de-
finition, and the paradox is only owing to the difficulty of imagining the ex-
istence of a single atom, unsurrounded by innumerable points of a space which
we represent to ourselves as immoveable.

It has been for want of a precise definition of the term motion, that many
authors have fallen into confusion with respect to absolute and relative mo-
tion. For the definition of motion, as the change of rectilinear distance be-
tween two points, appears to be the definition of what is commonly called re-
lative motion ; but, on a strict examination, we shall find, that what we usu-
ally call absolute motion is merely relative to some space, which we imagine
to be without motion, but which is so in imagination only. The space which
we call quiescent, is in general the earth's surface; yet we well know, from
astronomical considerations, that every point of the earth's surface is perpe-
tually in motion, and that in very various directions : nor are any material
objects accessible to our senses, which we can consider as absolutely motion-
less, or even as motionless with regard to each other; since the continual va-
riation of temperature to which all bodies are liable, and the minute agitations
arising from the motions of other bodies with which they are connected, will
always tend to produce some imperceptible change of their distances.

When therefore we assert, that a body is absolutely at rest, we only mean to
compare it with some large space in which it is contained : for that there ex-
ists a body absolutely at rest, in as strict a sense as an absolutely straight line
may be conceived to exist, we cannot positively affinn; and if such a quies-
cent body did exist, we have no criterion by which it coidd be distinguished.
Supposing a ship to move at the rate of three miles in an hour, and a person
on board to walk or to be drawn towards the stern at the same rate, he would
be relatively in motion, with respect to the ship, yet we might very properly
consider him as absolutely at rest: but he would, on a more extended view,
be at rest only in relation to the earth's surface ; for he would still be revolv-
ing round the axis of the earth, and with the earth round the sun; and with

20 LECTURE II.

the sun and the whole solar system, he would be slowly movmg among the
starry worlds which surround them. Now with respect to any ettects within
the ship, all the subsequent relations are of no consequence, and the change
of his rectilinear distance from the various parts of the ship, is all that needs
to be considered in determining those effects. In the same manner, if the ship
appear, by comparison with the water only, to be moving through it with the
velocity of three miles an hour, ami the water be moving at the same time in
a contrary direction at the same rate, in consequence of a tide or current, the
ship will be at rest with respect to the shore, but the mutual actions of the ship
and the water will be the same as if the water were actually at rest, and the
ship in motion.

It is not sTifficient to observe the increase or decrease of distance of a mov-
ing point from another single point only: we must compare its successive si-
tuations with many other points surrounding it; and for this purpose these
points must be at rest among themselves, in order to be considered as belong-
ing to a quiescent space or surface ; which may be defined as a space or sur-
face, of which all the points remain always at equal distances from each other,
without any external influence. In this sense we must call the deck of the
ship a quiescent surface, whether the ship be at anchor or under sail : but we
must not consider a surface revolving round a centre as a quiescent surface ;
for it will appear hereafter that no such motion can exist without the influ-
ence of a centripetal force, which"renders it improper for determining the af-
fections of a moving body.

When a point is in motion with respect to a quiescent space, it is often
simply denominated a moving point, and the right line joining any two of its
places, immediately contiguous to each other, is called its direction. If it re-
mains continually in one right line drawn in the quiescent space, that line is
always the line of its direction; if it describes several right lines, each line is
the line of its direction as long as it continues in it ; but if its path becomes
curved, we can no longer consider it as perfectly coinciding at any time with
a right line, and we must recur to the letter of the definition, by supposing a
right line to be drawn through two successive points in which it is found, and
then if these points be conceived to approach each other without limit, we
shall have the line of its direction. Now such a line is called in geometry a

ON MOTIOK. 21

tangent: for it meets the curve, but does not cut it, provided that the curva-
ture be continued. (Plate I. Fig. 1 ... 3.)

Having formed an accurate idea of the nature of motion, and of the im-
port of the terms employed in speaking of its properties, we may proceed to
consider the mechanical laws to which it is subjected, and which are derivable
from the essence of the definitions that have been premised. The first is, that
a moving point never quits the line of its direction without a disturbing cause :
-for a right line being the same witb respect to all sides, no reason can be
imagined why the point should incline to one side more than another; and
the general law of induction requires, that the moving point should preserve
the same relations towards the points similarly situated on every side of the
line; This argument appears to be sufficiently satisfactory to give us ground
for asserting, that the law of motion here laid down may be considered as in-
dependent of experimental proof. It was once proposed as a prize question
by the academy of sciences at Berlin, to determine whether the law& of mo-
tion were necessary or accidental; that is, whether they were to be consider-
ed as mathematical or as physical truths. Maupertuis, then president of the
academy, wrote an elaborate dissertation, in which he endeavoured to deduce
them from a complicated principle of the prodtiction of every eifect in the
manner which requires the least possible action^ a principle which he sup-
poses to be most consistent with the wise economy of nature. But this prin-
ciple has itself been shown to be capable of accommodation to any other
imaginable laws of motion, and the intricacy of the theory tends only to en-
velope the subject in unnecessary obscurity; the laws of motion appear to be
easily demonstrable from the simplest mathematical truths, granting only the
homogeneity or similarity of matter with respect to motion, and allowing the
general axiom, that like causes produce like effects. If, however, any person
thinks differently, he is at liberty to call these laws experimental axioms, col-
lected from a comparison of various phenomena; for we cannot easily reduce
them to direct experiments, since we can never remove from our experiments
the action of all disturbing causes; for either gravitation, or the contact of
surrounding bodies, will interfere with, all. the motions which we can ex-
amine.

Having established the rectilinear direction of undisturbed motion, we

22 LFXTURE ir.

come to consider its uniformity. Here the idea of time enters into our sub-
ject. To define time in general is neither easy nor necessary; but we must
have some measure of equal times. Our abstract idea of time depends on the
memory of past sensations ; but it is obvious that the results of an intellectual
measure of the duration of time would be liable to the greatest uncertainty.
We may observe, that, on a journey, the perpetual succession of various ob-
jects will often make a week appear, upon retrospection, as long as a month
spent in a continuation of such employments as are uniform, without being la-
borious ; the multitude of new impressions not only serving to increase the ap-
parent magnitude of the interval, by filling up its vacuities, but tending also
to diminish the vivacity of the ideas which they have superseded, and to give
them the character of the fainter recollections of an earlier date. We are
therefore obliged to estimate the lapse of time by the changes in external ob-
jects: of these changes, the simplest and most convenient is the apparent mo-
tion of the sun, or rather of the stars, derived from the actual rotation of the
earth on its axis, which is not indeed an undisturbed rectilinear motion, but
which is equally applicable to every practical purpose. Hence we obtain, by
astronomical observations, the well known measures of the duration of time,
implied by the terms day, hour, minute, and second.

Now the equality of times being thus estimated from any one motion, all
other bodies moving without disturbance, will describe equal successive parts
of their lines of direction in equal times. And this is the second law of mo-
tion, which, with the former law, constitutes Newton's first axiom or law of
motiort: " that every body perseveres in its state of rest or uniform rectilineaf
motion, except so far as it is compelled by some force to change it." It ap-
pears that this second law is strictly deducible from the axioms and definitions
which have been premised, and principally from the consideration of the re-
lative nature of motion, and the total deficiency of a criterion of absolute mo-
tion. For, since the velocity of a body, moving without resistance or disturb-
ance, is only a relation to another body, if the second body has no mechanical
connexion with the first, its state with respect to motion can have no efi^ect
on the velocity of the first body, however great its comparative magnitude
may be : and if a body is at rest, there is nothing to determine it to begin to
move either to the right hand or to the left; if it is at rest with respect to
any other bodies, it will remain in the same condition, whatever the relative

oil UOTlOVt. ^3

motions of those bodies may be, when compared with the surrounding objects;
and these relations can only be preserved by its continuance in uniform recti-
linear motion. Tills law is also confirmed by its perfect agreement with all
experimental observations, although it is too simple to admit of an immediate
proof. For we can never place any body in such circumstances as to be to-
tally exempt from the operation of all accelerating or retarding causes; and
the deductions from such experiments as we can make, would require in ge-
neral, for the accurate determination of the necessary corrections, a previous
knowledge of the law which we wish to demonstrate.

When, indeed, we consider the motion of a projectile, we have only to allow
forthedisturbingforceof gravitation, which so modifies the effect, tliat the bo-
dy deviates from a right line, but remains in the same vertical plane ; whence
we may infer, that, in the absence of the force of gravitation, the body would
continue to move in every other plane in which its motion began, as well as
in the vertical plane, since in that case all these planes would be indifferent
to it; it must therefore remain in their common intersection, which could only
be a straight line: so that by thus combining arguments Avith observation, we
may obtain a confirmation of the law of the rectilinear direction of undisturb-
ed motion, partly founded on direct experiments 'Its uniformity is however
still less subjected to immediate examination; ytf, from a consideration of the
natiue of friction and resistance, combined with the laws of gravitation, we
thay ultimately show the perfect Coincidence of the flieory with experiment.
The tendency of matter to persevere in this manner' in the state of rest or
of uniform rej^tilinear motion, is called its inertia.

In all thicse cases it is of importahcfe to attend to the composition of motion,
or the joint effieCt of more than one motion existing at the same time. The
existence of two or more motions, at the sAme time, in the same body, is not
at first comprehended without some difficulty. It is in fact only a combina-
tion or separation of relations that is considered: in the same manner as by
Combining the relation of son to father, and brother to brother, we obtain,
the relation of 'nephew to uncle, so by combining the motion of a man walk-
ing in a ship, with the motion of the ship, we determine the relative velocity
of the man with respect to the earth's surface. It is, however, necessary, for
ascertaining these relations, to consider the affections of a space or surface in

24 JLECTURE H,

motion, and to examine how it may mov£ in tlie most simple manner with
respect to another space.

If any number of points move in parallel lines, describing equal spaces in
equal times, they are at rest with respect to each other; for it may easily be
demonstrated that the rectiUnear distance of each, from each of the rest, re-
mains unchanged: and if all the points of a plane move in this manner on
another plane, either plane may be said to be in rectilinear motion with re-
spect to the other. This is easily exemphfied by causing one plane to move
on another, so that two or more of its points shall always remain in a given
right line in the second plane : as when a square is made to slide along the
straight edge' of a board, the surface of the square is in rectilinear motion
Avith respect to the board. (Plate L ¥ig. 4.)

If, besides this general motion of the plane, any point be supposed to have a
particular motion in it, the point will have two motions with respect to the
other plane, the one in common with its plane, and the other peculiar to it-
self; and the joint effect of these motions with respect to the second plane is
called the result of the two motions. Thus, when a carriage moves on a per-
fectly level road, all its points describe parallel lines, and it is in rectilinear
motion with respect to the road: its wheels partake of this motion, but have
also a rotatory motion of their own ; and the result of the two motions of each
point of the wheels is the cycloid or trochoid that it describes in a quiescent
vertical plane. (Plate I. Fig. 5.)

When an arm is made to slide upon a bar, and a thread, fixed to the bar,
is made to pass, over a pulley at the end of the arm next the bar, to a slider
which is moveable along the arm, the slider moves on the arm with the same
velocity as the arm on the bar; but if the thread, instead of being fixed to the
slider, be passed again over a pulley attached to it, and then brought back to
be fixed to the arm, the motion of the slider will be only half that of the arm ;
and this will be true in whatever position the arm be fixed. Here we have
two motions in the slider, one in common with the arm, and the other pecu-
liar to itself, which may be either equal or unequal to the first; and by trac-
ing a line on a fixed plane, with a point attached to the slide/, we may easily
examine the joint result of both the motions. (Plate I. Fig. 6.)

ON MOTION. . 25

The joint result of any two motions is the diagonal of the parallelogram, of
which the sides would be described, in the same time, by the separate motions ;
that is, if we have two lines representing the directions and velocities of the
separate motions, and from the remoter extremity of each draw a line parallel
to the other, the intersection of these lines will be the place of the moving
body at the end of the given time. This is the necessary consequence of the
coexistence of two motions in the sense that has been defined; it is also ca-
pable of a complete illustration by means of the apparatus that has been de-
scribed. (Plate I. Fig. 7.) ,

Any given motion may be considered as the result of any two or more
motions capable of composing it in this manner. Thus the line described by
the tracing point of our apparatus will be precisely the same, whether it be
simply drawn along in the given direction, or made to move on the arm
with a. velocity equal to that of the arm, or, when the arm is in a different
position, with only half that velocity. (Plate I. Fig. 8.)

This principle constitutes the important doctrine of the resolution of mo-
tion. There is some difficulty in imagining a slower motion to contain, as
it were, within itself, two more rapid motions opposing each other: but in
fact we have only to suppose ourselves adding or subtracting mathematical
quantities, and we must relinquish the prejudice; derived from our own feel-
ings, which associates the idea of effort with that of motion. When we
conceive a state of rest as the result of equal and contrary motions, we use
the same mode of representation, as when we say that a cipher is the sum of
two equal quantities with opposite signs; for instance, plus ten and minus
ten make nothing.

«\>

The law of motion here established differs but little in its enunciation
from the original words of Aristotle, in his mcclianical problems. He says,
that if a moving body has two motions, bearing a constant proportion to
each other, it must necessarily describe the diameter of a parallelogram, of
which the sides are in the ratio of the two motions. It is obvious that this
proposition includes the consideration not only of uniform motions, but also
of motions which are similarly accelerated or retarded: and weshould scarce-
ly have expected, that, from the time at which the subject began to be so clcar-

VOJL. I. E

q6 lecture II.

ly understood, two thousand years would have elapsed, before this law began
to be applied to the determination of the velocity of bodies actuated by de-
flecting forces, which Newton has so simply and elegantly deduced from it.

In the laws of motion, which are the chief foundation of the Principia,
their great author introduces at once the consideration of forces; and the first
corollary stands thus ; " a body describes the diagonal of a parallelogram by
two forces acting conjointly, in the same time in which it would describe its
sides by the same forces acting separately." It appears, however, to be more
natural and perspicuous to defer the consideration of force, until the simpler
doctrine of motion has been separately examined.

We may easily proceed to the composition'of any number of different motions,
by combining them successively in pairs. Hence any equable motions, repre-
sented by the sides of a polygon, that is, of a figure consisting of any number
of straight sides, being supposed to take place in the same moveable body, in
directions parallel to those sides, and in the order of going round the figure,
destroy each other, and the body remains at rest. We may understand the
truth of this proposition by imagining each motion to take place in succession
for an equal small interval of time; then the point would describe a small
polygon similar to the original one, and would be found, at the end of every
such interval, in its original situation.

When the motions to be combined are numerous and diversified, it is often
convenient to resolve each motion into three parts, reduced to the directions
of three given lines perpendicular to each other. It is easy to find in this
manner by addition and subtraction only, the general result of any number
of motions. We may describe the flight of a bird, ascending in an oblique
direction, by estimating its progress northwards or southwards, eastwards or
westwards, and at the same time upwards, and we may thus determine its
place as accurately, as by ascertaining the immediate bearing and angular ele-
vation of its path, and its velocity in the direction of its motion.

27

LECTURE III.

ON ACCELERATING FORCES.

l^E have hitherto only considered motion as ah-eady existing, without any
regard to its origin or alteration;' We have seen that all undisturbed motions
are equable and rectilinear; and that two motions represented by the sides of
a parallelogram, cause a body to describe its diagonal by their joint effect.
We are now to examine the causes which produce or destroy motion. Any
cause of a change of the motion of a body, with respect to a' quiescent space, is
called a force; that is, any catise which pr6duc'es motion in a body at res't, or
which increases, diminishes, oi* modifies it in a body which -tvas before in mo-
tion. Thus the power of gravitation, which causes a stone to fall to the
ground, is called a force ; but when the stone, after descending down a hill,
rolls along a horizontal plane, it is no longer impelled by any force, and its
relative motion continues unaltered, until it is gradually destroyed by the re-
tarding force of friction. Its perseverance in the state of motion or rest in
consequence of the inertia of matter, has sometimes been expressed by the
term vis inertiae, Or force of inertia; but it appears to be somewhat inaccurate
to apply the term force to a property, which is never the cause of a change of
motion in the body to which it belongs.

It is a necessary condition in the definition of force, that it be the cause of
a change of motion with respect to a quiescent space. For if the change were
only in the relative motion of two points, it might happen without the opera-
tion of any force: thus, if a body be moving Without disturbance, its motion
with respect to another body, not in thehneofits direction, will be perpetually
changed ; and this change, considered alone, would indicate the existence of
a repulsive force: and, on the other hand, two bodies may be subjected to the
action of an attractive force, while their distance remains unaltered, in con-
sequence of the centrifugal effect of a rotatojy motion. (Plate I. Fig. 9->

iJ8 LECTURE III.

The exertion of an animal, the unbending of a bow, and the commun?Ca-
tion of motion by impulse, are familiar instances of the actions of forces. Wc
must not imagine that the idea of force is naturally connected with that of la-
bour or difficulty; this association is only derived from habit, since our vo-
luntary actions are in general attended with a certain effort, which leaves an
impression almost inseparable from that of the force that it calls into action.

It is natural to inquire in what immediate manner any force acts, so as ta
produce motion; for instance, by what means the earth causes a stone to gra-
vitate towards it. In some cases, indeed, we are disposed to imagine that we
understand better the nature of the action of a force, as, when a body in mo-
tion strikes another, we conceive that the impenetrability of matter is a suffi-
cient cause for the communication of motion, since the first body cannot con-
tinue its course without displacing the second; and it has been supposed that
if we could discover any similar impulse that might be the cause of gravita-
tion, we should have a perfect idea of its operation. But the fact is, that
even in cases of apparent impulse, the bodies impelling each othcF are not ac-
tually in contact; and if any analogy between gravitation and impulse be ever
established, it will not be by referring them both to the impenetrability of
matter, but to the intervention of some common agent, perhaps imponderable.
It was observed by Newton, that a considerable force was necessary to bring
two pieces of glass into a degree of contact, which still was not quite perfect;
and Professor Robison has estimated this force at a thousand pounds for every
square inch. These extremely minute intervalsiiave been ascertained by ob-
servations on the colours of the thin plate of air included between the glasses ;
and when an image of these colours is exhibited by means of the solar mi-
croscope, it is very easily shown that the glasses are separated from each
other, by the operation of this repulsive force, as soon as the pressure of the
screws which confine them is diminished; the rings of colours dependent on
their distance contracting their dimensions accordingly. Hence it is obvious,
that whenever two pieces of glass strike each other,, without exerting a pres-
sure equal to a thousand pounds on a square inch, they may affect each other's
motion without actually coming into contact. Some persons might perhaps
be disposed to attribute this repulsion to the elasticity of particles of air
adhering to the glass, but I have found that the experiment succeeds equally
well in the vacuum of the air pump. We must therefore be contented to ac-

i

ON ACCZLERATIXG FOUCES. <>9

knowledge our total ignorance of the intimate nature of forces of every kind;
and we are first to examine the eftect offerees, considering only their magni-
tude and direction, without any regard to their origin.

It was truly asserted by Descartes, that the state of motion is equally na-
tural with that of rest. When a body is once in motion, it requires no fo
reign power to sustain its velocity. If therefore a moving body is subjected
to the influence of any force, which acts upon it in the line of its direction, its
motion will be either accelerated or retarded, accordingly as the direction of
the force coincides with that of the motion, or is opposed to it. A ston*, for
instance, beginning to fall, or projected downwards, by uo means retains the
same velocity throughout its. descent, but acquires more and more motion every
instant. We well know,, that the greater the height from which a body falls,
the more danger there is of its destroying whatever opposes its progress. In
the same manner, when a ball is thrown upwards, it gradually loses its motion
by the operation of gravitation, which is now a retarding force, and at last
begins again to descend.

It may here be proper to inquire what is the precise meaning of the term ve-
locity; we appear indeed to understand sufficiently the common, use of the
word, but it is not easy to give a correct definition of it. The velocity of a
body may be said to be the (juantity or degree of its motion, independently of
any consideration of its mass or magnitude ; and it might always be measured
by the space described in a certain portion of time; for instance a second, if
there were no other motions than undisturbed or uniform motions : but the ve-
locity may vary very considerably within the second, and we must therefore
have some other measure of it than the space actually described in any finite
interval of time. If however the times be supposed infinitely short, the ele-
ments of space described may be considered as the true measures of velocities.
These elements, although smaller than any assignable quantity, may yet be
accurately compared with each other ;. and the reason that they afford a true
criterion of the velocity, is this, that the change produced in the velocity,
tluring so short an interval of time, must be absolutely inconsiderable in com-
parison with the whole velocity, and the element of space becomes a true mea-
sure of the temporary velocity, in the same manner as any larger portion of
space may be the measure of a uniform velocity.

30 LECTURE nr.

Wlieu the increase or diminution of the velocity of a moving body is uni-
form, its cause is called a uniform force: the spaces which would be described
in any given time, with the actual velocity uniformly continued, being always
equally increased or diminished by the action of such a force. For example, if
the velocities, at the beginning of any two separate seconds, be such, that the
1)ody Avould describe one foot and ten feet in the respective seconds, if undis-
turbed, and the spaces actually described become two feet and eleven feet, each
being increased one foot, the accelerating force must be denominated uniform.

• The power of gravitation, acting at or near the earth's surface, may, with-
out sensible error, be considered as such a force. Thus, if a body begins to
fall from a state of rest, it describes about 16 feet, or more correctly l6-fV,
in tile first second ; if it begins a second with a velocity of SSI feet, it describes
.'32 and] 6, or 4 H feet, in this second. The decrease of the force of gravitation
in proportion to the squares of the distances from the earth's centre, is barely
fj^iteptible, iit any heights within our reach, by the nicest tests that we can
employ. .

The velocit}' produced by any uniformly accelerating force, is proportional
to the magnitude of the force, and the time of its operation conjointly. When
tlie forces are the same, a little consideration will convince us that, since every
equal portion of time adds equally to the velocity, the whole velocity produced
or destroyed must be in proportion to the whole time; and when the forces
diifer, the velocities differ in the same ratio; for the forces are only measured
by the velocities which they generate. Thus a double force, in a double time,
produces a quadruple velocity. That a force producing a double velocity is
properly called a double force, may be shown from the laws of the composition
of motion; for when the equal sides of a parallelogram representing two se-
parate forces or motions, approach to each other, and at last coincide in direc-
tion, the diagonal of the parallelogram, representing their joint effect, becomes

equal to the sum of the sides, (Plate I. Fig. 10.)

./<:'• DV -Mi n't -: ^

The machine invented by Mr. Atwood furnishes us with a very convenient
mode of making experiments on accelerating forces. The velocity, produced
by the undiminished force of gravity, is much too great to be conveniently sub-
mitted to experimental examination; but by means of this apparatus, we can

2

ON ACCELERATING FORCE?. JJ

diminish it in any degree that is required. Two boxes, which are attached to a
thre 1(1 passing over a pulley, may be filled with different vveights, wliich coun-
terbalance each other, and constitute, together with the pulley, an inert mass,
which is put into motion by a small weight added to one of them. The time
of descent is measured by a second or lialf second pendulum, the space de-
scribed being ascertained by the place of a moveable stage, against which the
bottom of the descending box strijses: and when we wish to determine imme-
diately the velocity acquired at any point, by measuring the space uniforndy
described in a given time, the accelerating force is removed, by means of a ring,
which intercepts the preponderating weight, and the box proceeds with a uni-
form velocity, except so far as the friction of the machine retards: it. By
changing the proportion of the preponderating weight to the whole weight of
the boxes, it is obvious that we may change the velocity of the descent, and
thus exhibit the effects of forces of different magnitudes. The most conveni-
ent mode of letting the weights go, without danger of disturbance from their
vibrations, is to hold the lowest weight only, and to allow it to ascend at the
instant of a beat of the pendulum. (Plate I. Fig. 11.)

That the velocity generated is proportional to the time of the action of the
force, or that the force of gravitation, thus modified, is properly called a uni-
form accelerating force, .may be shown by placing the moveable ring so as to
intercept the same bar successively at two different points: thus the spact; uni-
formly described in a second, by the box alone, is twice as great, when the force
is withdrawn after a descent of ten half seconds, as it is after a descent of five..
And if we chose to vary the weight of the bar, we might show in a similar
manner, that the velocity gcDcrated in a given time is proportional to the force
employed.

We are neJit to determine the magnitude of the whole space described in a
given time with a velocity thus uniformly increasing. The la;W discovered by
Galileo, that the space described is as the square of the time of descent, and
that it is also equal to half the space which would be described in the same time
with the final velocity, is one of the most useful and interesting propositions
in the whole science of mechanics. Its truth is easily shown from mathema-
tical considerations, by comparing the time with the base, and the velocity
with the perpendicular of a triangle gradually increasing, of which the area

St LECTURE IV.

Standing its weiglit, to the sling which is above it, in consequence of the ex-
cess of the centrifugal force abo\e the force of gravitation.

It is also a centrifugal force that is thp foundation of the amusement of a boy-
driving a hoop. A hoop at rest, placed on its edge, would very quickly fall
to the ground; but Avhcn it is moving forwards, a slight inclination towards
either side causes the parts to acquire amotion towards that side, those which
are uj)permost being most affected Iry it; and this lateral motion, assisted
sometimes by the curvature of the surface of the hoop, causes its path to de-
viate from a rectilinear direction, so that instead of moving straight forwards,
it turns to that side, towards which it began to incline; and in this po-
sition, its tendency to fall still further is counteracted by the centrifugal force,
and it generally makes several complete revolutions before it falls. The mo-
tion of a bowl, with its bias, is of a similar nature; the centrifiigal force
counteracting the tendency to curvilinear motion, so as to diminish it very con-
siderably, until the velocity is so much reduced, as to suifer it to describe a path
evidently curs'ed, and becoming more and more so as the motion is slower.

When a body is retained in a circular orbit, by a force directed to its centre^
its velocity is every where equal to tliat which it would acquire, in falling, by
means of the same force, if uniform, through half the radius, tliat is, through
one fourth of the diameter. This proposition affords a very Convenient me-
thod of comparing the effects of central forces with those of simple accele-
rating forces, and deserves to be retained in memory. We may in some mea-
sure demonstrate its truth by means of the whirling table: an apparatus which
is arranged on purpose for exhibiting the properties of central forces, although
it is more calculated for showing their comparative thati their absolute magni-
tude; for accordingly as we place the string on the pullies,, the two horizontal
arms may be made to revolve either with equal velocities, or one twice as fast
as the other. The sliding stages, which may be placed at different distances
from the centres, and which are made to move along the arms with as little
friction as possible, are in a certain proportion to the weights, which are to be
raised, by means of threads passing over pvdlies in the centres, as soon as the
centrifugal forces of the stages with their weights are sufficiently great; and
the experiment is to be so arranged, that when the velocity, having been gra-
dually increased, produces a sufiicient centrifugal force, both stages may raise

2

ox DEFLECTIVE FORCES. 35

their weights, and fly off at the same instant. But, for the present purpose, one
of the stages only is required, and the time of revolution may be measured
by a half second pendulum. We may make the force, or the weight to be
raised, equal to the weight of the revolving body, and we shall find that this
body will fly off when its velocity becomes equal to that which would be ac-
quired by any heavy body in falling through a height equal to half the dis-
tance from the centre, and as much greater as is sufficient for overcoming the
friction of the machine. (Plate I, Pig. 13.)

. From this proposition we may easily calculate the velocity, with which a
sling of a given length must revolve, in order to retain a stone in its place in
all positions ; supposing the motion to be in a vertical plane, it is obvious
that the stone will have a tendency to fall when it is at the uppermost point
of the orbit, unless the centrifugal force be at least equal to the force of gra-
vity. Thus if the length of the sling be two feet, we must find the velocity
acquired by a heavy body in falling through a height of one foot, which will
he eight feet in a second, since eight times the square root of 1 is eight; and
this must be its velocity at the highest ])oint; with this velocity it would per-
form each revolution in about a second and a half, but its motion in other
parts of its orbit will be greatly accelerated by the gravitation of the stone.

It may also be demonstrated, that when bodies revolve in equal circles,
their centrifugal forces are proportional to the squares of their velocities.
Thus, in the whirling table, the two stages being equally loaded, one of
them, which is made to revolve with twice the velocity of the other, will
lift four equal weights at the same instant that the other raises a single one;
But when two bodies revolve with equal velocities at different distances, the
forces are inversely as the distances ; consequently the forces are, in all cases,
directly as the squares of the velocities, and inversely as the distances.

If two bodies revolve in equal times at different distances, the forces by
which they are retained in their orbits are simply as the distances. If one of
the stages of the whirling table be placed at twice the distance of the other,
it will raise twice as great a weight, when the revolutions are performed in
the sajne time.

3Q i^EcruRE IV.

In general, the forces are a& tlie distances directly, and as the squares of
the times of revolution inversely. Thus the same weight revolving in a
double time, at the same distance, will have its effect reduced to one fourth,
but at a double distance the effect will again be iucceased to, half of its ori-
ginal magnitude.

From these principles we may deduce the law which was discovered by
Kepler in the motions of the planetary bodies, but which was first demon
strated by Newton from mechanical considerations. Where the forces vary
inversely as the squares of the distances, as in the case of gravitation, the
squares of the times of revohition are proportional to the cubes of the dis-
tances. Thus if the distance of one body be four times as- great as that of
another, the cube of 4 being G4, which is the scjuai^e o-f 8, the time^of its
revolution will be 8 times as great as that of the first body. It would be
easy to show the truth of this proposition experimentally by means of the
whirling table, but the proof would be less striking than those of the simples
laws which have already been laid down.

Hitherto we have supposed the orbit of a revolving body to be a perfect
circle; but it ol ten happens in nature, as, for instance, in all the planetary
motions, that the orbit deviates more or less from a circular form; and in
such cases we may apply another very important law which was also disco-
vered by Kepler; that the right line joining a revolving body and its centre
of attraction, always describes equal aieas in Cfjual- times, and the velocity of
the body is therefore always inversely as the peri>endicular drawn from the
centre to the tangent. (Plate I. Fig. 14.}

The demonstration of this law, invented by Newton, was one of the most
elegant applications of the geometry of infinites or indivisibles; a branch of
mathematics of which Archimedes laid the foundations, which Cavalleri and
Wallis greatly advanced, and which Newton brought near to perfection. Its
truth may be in some measure shown by an experiment on tlie revolution of
a ball suspended Ijy a long thread, and drawn towards a point immediately
under the point of suspension by another thread, which may either be held
in the hand, or have a weight attached to it. The ball being made to re-
volve, its motion becomes evidently more rapid when it is drawn by the ho-

ON DEFLECTIVE FORCES. 37

rizontal thread nearer to the fixed point, and slower when it is suffered to fly
off to a greater distance. (Plate II. Fig. 15.)

It was also discovered by Kepler that each of the planets revolves in an
ellipsis, of which the sun occupies one of the foci. It is well known that an
ellipsis is an oval figure, which maybe described by fixing the ends of a thread
to two points, and moving a tracing point so that it may always be at the
point of tbe angle formed by the thread ; and that the two fixed points are
called its foci. The inference respecting the force by which a body may be
made to revolve in an ellipsis, was first made by Newton ; that is, that the
force directed to its focus must be inversely as the square of the distance.
We have no other expcrimentul proof of this theorem than astronomical ob-
servations, which are indeed perfectly decisive, but do not require to be here
anticipated. (Plate II. Fig. 16.)

There is another general proposition which is sometimes of use in the com-
parison of rectilinear and curvilinear motions. Two bodies being attracted in
the same manner towards a given centre, that is, with equal forces at equal
distances, if their velocities be once equal at equal distances, they will re-
main always equal at equal distances, whatever be their directions. For in-
stance, if one cannon ball be slxot oblitjuely upwards, and anotlier perpendi-
cularly upwards, with the same velocity, the one will describe a curve, and
the other a straight line, but their velocities will always remain equal, not
at the same instants of time, but at equal distances from the earth's centre,
or after having ascended through equal vertical heights, although in different
directions. This proposition lias usually been made a step in tbe demonstra-
tion of the law of the force by which a body is made to revolve in an ellipsis;
but there is a much simpler method of demonstrating that law, by means of
some properties of the curvature of the ellipsis..

In treating of the motion of projectiles, the force of gravitation may^
without sensible error, be considered as an equable force, acting in parallel
lines perpendicular to the horizon. In reality, if we ascend a mile fuom the
earth's surface, the actual weight of a body is diminished about a. two thour
sandth part, or three grains and a half for every pound, and w.e may discover
this inequality by means of the vibrations of pendulutns, which become a lit-

38 LFXTURE IV.

tic slower when they are placed on the summits of very high mountains. On
the other hand, a body not specifically heavier thau water, gains more in
apparent weight on account of the diminished density of the atmosphere at
great elevations, than it loses by the increase of its distance from the earth,
liut both these differences ma}-, in all common calculations, be wholly disre-
garded. The direction of gravity is always exactly perpendicular to the ho-
rizon, that is, to the surface of the earth, which is somewhat curved, on ac-
count of the earth's spheroidical figure ; but any Small portion of this surface
may be practically considered as a plane, and the vertical lines perpendicular
to it, as parallel to each other.

The oblique motion of a prqjectile may be the most easily understood by
resolving its velocity into two parts, the one in a horizontal, the other in a
vertical direction. It appears from the doctrine of tilie composition of motion,
that the horizontal velocity will not be aflPected by the force of gravitation
acting in a direction perpendicular to it, and that it will therefore continue
uniform ; and that the vertical motion will also be the same as if the body had
no horizontal motion. Thus if we let fall from the head of the mast of a ship a
weight, which partakes of its progressive motion, the weight will descend by
the side of the mast in the same manner, and with the same relative velocity,
as if neither the ship nor the weight had any horizontal motion.

We may therefore always determine the greatest height to which a projectile
will rise, by finding the height from Avhich a body must fall, in order to gain
a velocity equal to its vertical velocity, or its velocity of ascent, that is, by
squaring one eighth of the number of feet that it would rise in the first second
if it were not retarded. For example, suppose a musket to be so elevated that
the muzzle is higher than the but-end by half of the length, that is, at an
angle of 30° ; and let the ball be discharged with a velocity of 1000 feet in a
second; then its vertical velocity will be half as great, or 500 feet in a second :
now the square of one eighth of 500 is 3906, consequently the height to which
the ball would rise, if unresisted by the air, is 3906" feet, or three quarters of a
mile. But in fact, a musket ball, actually shot upwards, with a velocity of 1670
feet in a second, which would rise six or seven miles in a vacuum, is so re-
tarded by the air, that it docs not attain the height of a single mile.

ON DEFLECTIVE FORCES. S^

Wc may easily find the time of the body's ascent from its initial velocity ;
for the time of ascent is directly proportional to the velofcity, and may be found
in seconds by dividing the vertical velocity in feet by 32; or if we divide by
16 only, we sllall have the time of ascent and descent; and then the horizontal
rano-e mavl>e: found, by calculating the distance described in this time, with the
imiform horizontal velocity. Thus, in the example that wc have assumed, di-
vidino- 500 by 16, we have 31 seconds for the whole time of the range ; but the
hypotenuse of our triangle being 1000, and the perpendicular 500, the base
will be 886 feet; consequently the horizontal range is 31 times 886, that is,
nearly 28000 feet, or above 5 miles. Biit the resistance of the air will reduce
this distance also to less than one mile.

It may be demonstrated that the horizontal rat>ge of a body, projected with a
given velocity, is always proportional to the sine of twice the angle of elevation r
that is, to the elevation of the muzzle of the piece in a situation twice as remote
from a horizontal position as its actual situation. Hence it follows, that the
greatest horizontal range will be when the elevation is half a right angle; sup-
posing thebody to move in a vacuum. But the resistance of the air increases
with the length of the path, and the same cause also makes the angle of descent
much greater than the angle of ascent, as we may obseive in the track of a
bomb. ' For both these reasons, the best elevation is somewhat less than 45°,
andsometijnes, when the velocity is very great, as little as 30°. But it usually
happens in the operations of natural causes, that neAr the point where any
quantity is greatest or least, its 'variation is slower than elsewhere*! a small
difference, therefore, in the angle of elevation, is of little consequence to the ex-
tent of the range, provided that it contiftu'e between the limits of 45" and 35°;
and for theisanve reason^ the angular adjtistmettt requires, less accuracy in this-
position than in any other, "Which besides the economy of powder, makes it
the best elevation for practice. (PlatC' 11. Fig. I7, 18.)

Tlie path of a projectile, supposetl to move without resistance, is always a:
parabola. This interesting proposition was first discovered by Galileo; it fol-
lows very readily from the doctrine of the composition of motion, combined
with the' laws which that philosopher established concerning the fall of heavy
bodies. If from any points of a given right liTie, as many lines be drawn,
parallel to each other, and proportional to the squares of tlie corresponding

40 LECTURE IV.

segments of the fiist line, the curve in wliich all their extremities arc found,
is a parabola. ' Now supposing the first line to be placed in the direction of
the initial motion of a projectile, and parallel vertical lines to be drawn
through any points of it, proportional to the squares of the segments which
they cut off, these lines will represent the eft'ect of gravitation, during the
times in which the same segments would have been described, by the motion
of projection alone; consequently the projectile will always be found at the ex-
tremity of the vertical line corresponding to the time elapsed, and will there-
fore describe a parabola. (Plate II. Fig. 17, ^9-)

It is easy to show by experiment, that the path of a projectile is a parabola :
if we only let a ball descend from a certain point, along a groove, so as to ac-
quire a known velocity, we may trace on a board the parabola which it will
afterwards describe, during its free descent ; and by placing rings at different
parts of the curve, we 'may observe that it will pass through them all without
striking them. (Plate II. Fig. 19-)

In practical cases, on a large scale, wliere the velocity of a projectile is
considerable, the resistance of the atmosphere, is so great as to render the Ga-
lilean propositions of little or no use ; and a complete determination of the
path, mcluding all the circumstances which may influence it, is attended
with difficulties almost insuperable. It appears from Robins's experiments,
that the resistance of the air to an iron ball of 4-4: inches in diameter, moving
at the rate of 800 feet in a secqnd, is equal to four times its weight, and that
where the velocity is much greater, the resistance increases far more rapidly.
I3ut what must very much diminish the probability of our deriving any great
practical advantage from the theory of gunnery, is an observation, made also
by J^Ir. Robins, that a ball sometimes deviates three or four hundred yards
laterally, without any apparent reason; bo that we cannot be absolutely cer-
tain to come within this distance of our mark in any direction. The circum-
stance is probably owing to an accidental rotatory motion communicated to
the ball in its passage through the piece, causing therefore a greater friction
from the air on one side than on the other; and it may in some measure be re-
medied by employing a rifle barrel, which determines the rotation of the ball in
such a manner that its axis coincides at first with the path of the ball, so that
the same face of tlie ball is turned in succession every way. For the ordinary

ON DEFLECTIVE FORCES. 41

purposes of gunnery, an estimation governed by experience is found to be
the best guide; at the same time there is no doubt but that some assistance
may be obtained from theory and from experiment. Those who are desirous
of pursuing the subject, may find much information relating to it, collected by
Professor Robison, in the article Projectile of the Encyclopaedia Britannica.

VOL. I.

LECTURE V.

ON CONFINED MOTION.

\VE have hitherto considered the princiijal cases of motion, either undisturb-
ed, or simply subjected to the action of an accelerating, retarding, or deflec-
tive force. We now proceed to examine the effects of an additional modifica-
tion, which is introduced, when the motion is limited to a given line or surface
of any kind; the body either being supposed to slide on the surface of a solid
actually extended, or being confined to an imaginary surface by its attach-
ment to a thread, or still more narrowly restricted, by means of two threads,
which allow it to move only in a given line. Suspension is the most conveni-
ent mode of making experiments on confined motion ; but it is not always easy
to cause the body to remain in the surface that is required ; and to confine it in
this manner to a perfectly plane surfiice, is impossible. When we suffer a body
to slide along any surface, there is a loss of force from friction, from the pro-
duction of rotatory motion, or from both these causes combined. The effect
of friction is obvious and well known ; and we may be convinced of the re-
tardation attendant on the production of rotatory motion, by allowing two cy-
linders, of equal dimensions, to roll down an inclined plane ; the one being co-
vered with sheet lead, the other having an equal weight of lead in its axis,
<^nd being covered with paper; and both having similar projecting surfaces at
the ends, which come into contact with the plane : we may easily observe that
in the first cylinder, much more of the force is consumed in producing rotatory
motion, than in the second, and that it therefore descends much more slowly.
(Plate 11. Fig. 20.)

When a body is placed on an inclined plane, the force urging it to de-
scend, in the direction of the plane, is to the whole force of gravity, as the
height of the plane is to its length. This is demonstrable from the principles
pf the composition of motion, and may also be shown experimentally with

ON CONFINED MOTION. 4$

great accuracy, when we consider the doctrine of" the cquihbrium of forces.
But the interference of friction will only allow us to observe, with respect to the
velocities, produced, that they nearly approach to those which the calculation
indicates. Thus if a plane be inclined one inch in 32, a ball will descend ou
it in two seconds, instead of 64 feet, somewhat less, than two feet.

It may be deduced from the laws of acccleraiting forces, that when bodies
descend on any inclined planes, of equal heights, but of different inclinations,
the times of descent are as the lengths of the planes, and the final velocities
are equal. Thus a body will acquire a velocity of 32 feet in a second, after
having descended 16 feet, either in a vertical line ov in an oblique direction;
but tlie time of descent will be as much greater than a second, as the oblique
length of the path is greater than 16 feet. This may be sliown by experi-
ment, as nearly as the obstacles already mentioned will permit, the times be-
ing measured by a pendulum, or by a stop watch. (Plate H.. Fig. 21.)

There is an elegant proposition, of a similar nature, which is still more capable
of experimental confirmation; that is, that the times of falling through all
chords drawn to the lowest point of a circle are equaL If two or more bodies
are placed at different points of a circle, and suffered to descend at the same
instant along as many planes, which meet in the lowest point of the circle,
they will arrive there at the same time. (Plate II. Fig. 32.)

The velocity of a body, descending along a given surface, is the same as that
of a body falling freely through an equal height, not only Avhen the surface
is a plane, but also when it is a continued curve, in which the body is retain-
ed by its attachment to a thread, or is supported by any regular surface, sup-
posed to be free from friction. We may easily sliow, by an experiment on a
suspended ball, that its velocity is the same when it descends from the same
height, whatever may be the form of its path, by observing the height to
which it rises on the opposite side of the lowest point. We may alter the
fonn of the path in which it descends, by placing pins at different points, so
as to interfere with the thread that supports the ball, and to form in succes-
sion temporary centres of motion; and we shall find, in all cases, that the body
ascends to a height equal to that from which it descendetl, with a small de-
duction on account of friction, (Plate II. Fig. 23.)

44 LECTURE V.

Hence is derived the idea conveyed by the term living or ascending force;
for since the height, to which a body will rise perpendicularly, is as the square
of its velocity, it will preserve a tendency to rise to a height which is as the
square of its velocity, whatever may be the path into which it is directed,
provided that it meet with no abrupt angle, or that it rebound at each angle
in a new direction, without losing any velocity. The same idea is somewhat
more concisely expressed by the term energy, which indicates the tendency
of a body to ascend or to penetrate to a certain distance, in opposition to a
retarding force.

The most important cases of the motion of bodies, confined to given sur-
fiices, are those which relate to the properties of pendulums. Of these the
simplest is the motion of a body in a cycloidal path. The cycloid is a curve
which has many peculiarities; we have already seen that it is described by
marking the path of a given point in the circumference of a circle which rolls
on a right line. Galileo was the first that considered it with attention, but
he failed in his attempts to investigate its properties. It is singular enough,
that the principal cause of his want of success was an inaccurate experiment:
in order to obtain some previous information respecting the area included by
it, he cut a board into a cycloidal form, and weighed it, and he inferred from
the experiment, that the area bore some irrational proportion to that of the
describing circle, while in fact it is exactly triple. In the same manner it has
happened in later times, that Newton, in his closet, determined the figure of
the earth more accurately, than Cassini from actual measurement. It was
Huygcns that first demonstrated the properties of the cycloidal pendulum,
which are of still more importance in the solution of various mechanical pro-
blems, than for the immediate purposes of timekeepers, to which that emi-
nent philosopher intended to apply them. (Plate I. Fig 5.)

If a body be suspended by a thread playing between two cycloidal cheeks,
it will describe another equal cycloid by the evolution of the thread, and the
time of vibration will be the same, in whatever part of the curve it may begin
to descend. Hence the vibrations of a body moving in a cycloid are denomi-
nated isochronous, or of equal duration. This equality may be shown by let-
ting go two pendulous balls at tlie same instant, at different points of the curve,
and observing that they meet at the lowest point. (Plate II. Fig. 24.)

ON CONFIXED MOTION. 45

The absolute time of the descent or ascent of a pendulum, in a cycloid, is to
the time in which any heavy body would fall through one half of the length
of the thread, as half the circumference of a circle to its diameter. It ia
therefore nearly equal to the time required for the descent of a body through
^ of the length of the thread; and if we suffer the pendulum to descend, at
the same moment that a body falls, from a point elevated one fourth of the
length of the thread above the point of suspension, this body will meet the
pendulum at the lowest point of its vibration. (Plate II. Fig. Sil4.)

Hence it may readily be inferred, that since the times of falling through any
spaces, are as the square roots of those spaces, the times of vibration of differ-
ent pendulums are as the square roots of their lengths. Thus, the times of
vibration of pendulums of 1 foot and 4 foot in length, will be as 1 to 2 : the
time of vibration of a pendulum 39 '4v inches in length is one second; the
length of a pendulum vibrating in two seconds must be four times as great.

The velocity, with which a pendulous body moves, at each point of a cy-
cloidal curve, may be represented, by supposing another pendulum to revolve
imiformly in a circle, setting out from the lowest point, at the same time
that the first pendulum begins to move, and completing its revolution in the
time of two vibrations; then the height, acquired by the pendulum revolving
equably, will always be equal to the space described by the pendulum vibrat-
ing in the cycloid. (Plate II. Fig. 24.)

It may also be shown, that if the pendulum vibrate through the whole curve,
it will everywhere move with the same velocity as the point of the circle
which is supposed to have originally described the cycloid, provided that the
circle roll onwards with an equable motion.

All these properties depend on this circumstance, that the relative force,
urging the body to descend along the curve, is always proportional to the dis-
tance from the lowest point; and it happens in many other instances of the
action of various forces, that a similar law prevails: in all such cases, the vi-
brations are isochronous, and the space described corresponds to the versed
sine of a circular are increasing uniformly, that is to tlie height of any point

A6 ^ECTUUE V.

* of a wheel revolving uniformly on its axis, or rolling uniformly on a horizontal .
l^laue.

The cycloid is the curve in which a body may descend, in the shortest
possible time, from a given point, to another obliquely below it. It mav
easily be shown that a body descends more rapidly in a cycloid than in the
right line joining the two points. This property is of little practical uti-
lity; the proposition was formerly considered as somewhat difficult to be
demonstrated, but of late, from the invention of new modes of calculation,
theorems of a similar nature have been much extended with great facility. The
experiment 'naturally suggests a familiar proverb, which cautions us against
being led away too precipitately by an appearance of brevity and facility.
(Plate II. Fig. '25.)

It has been found that the inconveniences, resulting from the complicated
apparatus necessary to introduce a cycloidal motion, for the pendulums of
clocks, are more than equivalent to the advantage of perfect isochronism' in
theory. For since, in small cycloidal arcs, the curvature is nearly constant, the
time of vibration of a simple circular pendulum must be ultimately the same/
as tliat of a cycloidal pendulum of the same length; but in larger arcs, the time
must be somewhat greater, because the circular arc falls without the cycloidal,
and is less inclined to the horizon at e(}ual distances from the lowest point. •
This may be shown by a comparison of two equal pendulums, vibrating in arcs
of different extent : if may also be observed, by an experiment with two simple
pendulums of different lengths, that their times of vibration, like those of cy-
cloidal pendulums, are proportional to the square roots of their lengths; a
half second pendulum being only one fourth as long as a pendulum vibrating
seconds.

We have been obliged to suppose the weight, as well as the inertia, of a pen-
dulum, to be referred to one point, since we are not at present prepared to ex-
amine the effect of tlie slight difference between the situations, and the velocities
of the different parts of the substances, employed in our experiments. The na-
ture of rotatory motion requires to be more fully understood, before we can
attend to the determination of the centres of oscillation of bodies of various

ON CONFINED MOTION. ' 4f

figures, that is, of the points in which their whole weight may be supposed to
be concentrated, with regard to its effect on the times of their vibrations.

It is remarkable that the isochronism of pendulums, which is a property so
important in its application, may still be preserved, notwithstanding the in-
terference of a constant retarding force, such as the force of friction is in
many cases found to be. It has been shown by Newton, that each complete
vibration of a cycloidal pendulum, retarded by a resistance of this nature, will
be shorter than the preceding one by a certain constant space, but that it
will be performed in the same time.

There is a great analogy between the vibrations of pendulums, and the re-
volution of balls suspended from a fixed point. If a body, suspended by <l
-thread, revolve freely in a horizontal circle, the time of revolution will be the
same, whenever the height of the point of suspension, above the plane of rcvo>-
lution is the same, whatever be the length of the thread. Thus, if a number
of balls are fixed to threads, or rather wires, connected to the same point of
an axis, which is made to revolve by means of the whirling table, they will so
arrange themselves, as to remain very nearly in the same horizontal plane.
(Plate II. lig. 26".) lUifjiq

The time of each revolution of the balls is equal to the time occupied by a
double vibration of a pendulum, of which the length is equal to the height of
the point of suspension above the plane in which they revolve ; consequently
all the revolutions will be nearly isochronous, while the threqds or wires
deviate but little from a vertical situation. In fact, we may imagine such a
revolution to be composed of two vibrations of a simple pendulum, existing
at the same time, in directions at right angles to each other; for while a pen-
dulum is vibrating from north to south, it is liable to the impression of any
force, capable of causing a vibration from east to west; and the joint result of"
both vibrations will be a uniform revolution in a circle, if the vibrations are
equal and properly combined; but if they are unequal, the joint vibration will
be ultimately an ellipsis, the joint force being directed to its centre, and al-
ways proportional to the distance fiom that centre. (Plate II. Fig. 27.)

The near .approach of these revolutions to isochronism has sometimes been

48 LECTUEE V.

applied to the measurement of time, but more frequently, and more successfully,
to the regulation of the motions of machines. Thus in Mr. Watt's steam
engines, two balls are fixed at the ends of rods in continual revolution, and
as soon as the motion becomes a little too rapid, the balls rise considerably,
and turn a cock, which diminishes the quantity of steam admitted. (Plate II,
Fig. 28.)

The same laws are applicable to many other cases of rotatory motion ; for
instance, if we wish to determine the height, at which a ball, revolving with a
given velocity, will be retained in a spherical bowl ; or the inclination of a
circular road, capable of counteracting the centrifugal force of a horse, running
round it : for the horse, like the ball of the revolving pendulum, has a cen-
trifugal tendency, which is greater as his velocity is greater : this centrifugal
force, combined with the force of gravity, composes a result, which, in the
case of the pendulum, is completely counteracted by the force of the thread or
wire, and must therefore be in the direction of the thread, and which obliges
the horse to place his legs in a similar direction, proceeding from an imaginary
point of suspension above; since he would otherwise be liable to fall out-
wards, if his velocity were sufficiently great. But in order to withstand the
pressure of the horse's legs, the road must be in a direction perpendicular to
them; otherwise its materials will naturally be forced outwards, until they pro-
duce an elevation sufficient to give the road the required form. Thus, if the
diameter of the ring were 40 feet, and the horse moved at the rate of 12 miles
an hour, he would perform about 500 revolutions in an hour, and half a revo-
lution in 3 seconds and a half. Now the length of a pendulum vibrating in
34- seconds, must be 39 inches multiplied by the square of 34^, or a little more
than 80 feet : the road must therefore be perpendicular to the direction of a
line drawn to it from a point 80 feet above the centre of the ring; and its ex-
ternal circumference must be higher than its internal circumference by one
fourth of its breadth. It would however be improper to have a road of this
form in a manege, since the horse must be taught to perform all his evolutions
on a perfect plane.

There is a general principle of curvihnear motion, which is in itself of lit-
tle importance or practical utility, but which so far deserves to be noticed, as
it has been magnified by some philosophers into a fundamental law of nature.

ON CONFINED MOTION. 49

Among all the curves that a body can describe, in moving from one point to
another, it always selects that, in which, if its velocity be supposed to be every
where multiplied by the distance that it describes, the sum of the infinitely
small products will be a minimum, that is, less than in any other path that the
body could take. For example, if a body move freely, and therefore with a
uniform velocitj^, in any regular curved surface, it will pass from one part of
the surface to another by the shortest possible path. This has been called the
principle of the least possible action ; it is however merely a mathematical in-
ference from the simpler laws of motion, and if those laws were even dilFerent
from what they are, the principle would be true in another form, and in ano-
ther sense of the word action.

VOL. I. H

50

LECTURE VI.

ON THE MOTIONS OF SIMPLE MASSES.

JfXlTHERTO we have considered the motions of one or more single points
or atoms only, without any regard to the bulk or mass of a moveable body :
but it now becomes necessary to attend also to the difference of the masses of
bodies in motion. This may however be done, without considering the actual
magnitude or extent of the body. We may easily conceive different masses
or bulks to be concentrated in a mathematical point ; and it is most conveni-
ent to define a moveable body, as a moveable point or particle, composed of
other elementary particles, differing only in number, and thus constituting the
proportionally different mass or bulk of the body.

Although, in our experiments on motion, Ave are obliged to have recourse to
material bodies, and although such bodies differ considerably from this defini-
tion of a single moveable body, yet they serve sufficiently well to represent
such bodies, especially when they are small, and regularly formed ; and we
are here considering the doctrine of motion rather in a mathematical than in a
physical sense, so that we are able to neglect all such properties of matter as
are not immediately necessary to our purpose. Indeed though the general
properties of matter are usually placed at the entrance of elementary works on
mechanics, it has yet been found necessary to omit the consideration ^f their
effects, in examining the laws and affections of motion. The forces of cohe-
sion and repulsion, for example, act, in general, in a very complicated manner, in
almost all cases of the communication of motion; but to consider these opera-
tions minutely in treating of collision, would be to involve the subject in very
great and veiy unnecessary difficulties ; and the complete investigation of
these properties of matter would require the employment of various branches
of mechanical and hydrodynamical science. We may therefore take a much
simpler course, by deferring entirely all theoretical consideration of actual

ON THE MOTIONS OP SIMPLE MASSES. 51

matter ; but in the mean time we must have, for our experimental illustrations,
some measure of the mass or bulk as here defined. We might employ spheri-
cal bodies, composed only of homogeneous substances, that is, of substances of
the same kind, and we might estimate the mass by the comparative magnitude,
imagining all the particles of each sphere to be united in its centre. But it is
more convenient to anticipate, from the gravitation of matter, a measure of
the mass derived from the weight : since it can be proved that the weight of
a body is proportional to its absolute quantity of matter, supposing all matter
to be alike in its affections relative to motion. So that instead of numberino-
the particles of each body, the same purpose is answered by determining their
comparative weight.

?••
Inertia, -or a tendency to persevere in a state of rest, or of uniform rectilinear
motion, is a property attached to all matter, and may be considered as propor-
tional to the mass or weight of a body. When the motions of a system of bo-
dies are considered, their inertia may in some respects be referred to a single
point, which is called the centre of inertia. The centre of inertia of two bo-
dies is that point, in the right line joining them, M'hich divides it into two such
portions, that the one is to the other, as the mass of the remoter body to that
of the adjacent body. For instance, if one body weighs a pound, and another
two pounds, and their distance is a yard, then the centre of inertia is at the
distance of two feet from the smaller body, and one foot ftom the larger : and
the distance of each is to the whole distance, as the weight of the other to the
whole weight. Also the products obtained by multiplying each weight by its
distance are equal : thus two multiplied by one, is equal to one multiplied by
two. (Plate II. Fig. 39.)

This point is most commonly called the centre of gravity ; it has also some-
times been denominated the centre of position. Since it has many properties
independent of the consideration of gravity, it ought not to derive its nam<5
from gravitation, and the term centre of inertia begins now, with great propri-
ety, to be generally adopted.

The centre of inertia of any two bodies initially at rest, remain's at rest, not-
withstanding any reciprocal action of the bodies ; that is, notwithstanding any
action which aftccts the single particles of both equally, in increasing or diniif-

52 LECTURE vr.

iiishing their distance. For it may be shown, from the principles of the compo-
sition of motion, that any force, acting in this manner, will cause each of the
two bodies to describe a space proportional to the magnitude of the other
body : thus a body of one pound will move through a space twice as great as
a body of two pounds weight, and the remaining parts of the original distance
will still be divided in the same proportion, by the original centre of inertia,
Avhich therefore still remains the centre of inertia, and is at rest. And it fol-
lows also, that if the centre of inertia is at first in motion, its motion will not
be aftected by any reciprocal action of the bodies.

This important property is very capable of experimental illustration ; first
observing, that all kr^^wn forces are reciprocal, and among the rest the action
of a spring: we place two unequal bodies so as to be separated when a spring-
is set at liberty, and we find that they describe, in any given interval of time,
distances which are inversely as their weights ; and that consequently the
place of the centre of inertia remains unaltered. They may either be made to
float on water, or may be suspended by long threads ; the spring may be de-
tached by burning a thread that confines it, and it may be observed whe-
ther or no they strike at the same instant two obstacles, placed at such dis-
tances as the theory requires ; or if they are suspended as pendulums, the arcs
■\^'hich they describe may be measured, the velocities being always nearly pro-
portional to these arcs, and accurately so to their chords. (Plate II. Fig. 30.)

The same might also be shown of attractive as well as of repulsive forces.
For instance, if we placedourselves in a small boat, and pulled a rope tied to a
much larger one, we should draw ourselves towards the large boat with a mo-
tion as much more rapid than that of the large boat, as its weight is greater
than that of our own boat; arid the two boats would meet in their common
centre of inertia, supposing the resistance of the water inconsiderable.

Having established this property of the centre of inertia, as a law of motion,
we may derive from it the true estimate of the quantity of motion in differ-
ent bodies, in a much more satisfactory manner, than it has usually been ex-
plained. For since the same reciprocal action produces, in a body weighing
two pounds, only half the velocity that it produces in a body weighing one
pound, the cause being the same, the effects must be considered as equal, and

2

ON THE MOTIONS OF SIxAIPLE MASSES, 53

the quantity of motion naust always be measured by the joint ratio of mass to
mass, and velocity to velocity ; that is, by the ratio of the products, obtained
by multiplying the weight of each body by the number expressing its velo-
city ; and these products are called the momenta of the bodies. \Vc appear to
have deduced this measure of motion from the most unexceptionable argu-
ments , and we shall have occasion to apply the momentum thus estimated as
a true measure of force ; at the same time that we allow the practical import-
ance of considering, in many cases, the efficacy of forces, according to another
criterion, when we multiply the mass by the square of the velocity, in order
to determine the energy : yet the true quantity of motion, or momentum, of
any body, is always to be understood, as the product of its mass into its velo-
city. Thus a body weighing one pound, moving with a velocity of a hundred
feet in a second, has the same momentum, and the same (juantity of motion,
as a body of ten pounds, moving at the rate of ten feet in a second.

We may also demonstrate experimentally, by means of !^fr. Atwood's ma-
chine, that the same momentum is generated, in a given time, by the same
preponderating force, whatever may be the quantity of matter moved. Thus
if the preponderating weight be one sixteenth of the whole weight of the
boxes, it will fall one foot in a second, instead of 16, and a velocity of two
feet will be acquired by the whole mass, instead of a velocity of 32 feet, which
the preponderating weight alone would have acquired. And when we com-
pare the centrifugal forces of bodies revolving in the same time, at diflerent
distances from the centre of motion, we find that a greater quantity of matter
compensates for a smaller force ; so that two balls connected by a wire, with
liberty to slide either way, will retain each other in their respective situations,
when their common centre of inertia coincides with the centre of motion ; the
centrifugal force of each particle of the one being as much greater than that
of an equal particle of the other, as its weight, or the number of the particles,"
is smaller. ,

But it is not enough to determine the centre of inertia of two bodies only,
considered as single points ; since in general a much greater number of points
is concerned : we must therefore define the sense in which the term is in this
case to be applied. We proceed by considering the first and second of three or
more bodies, as a single body, equal to both of them, and placed in their com-

54 LECTURE VI.

mon centre of inertia ; determining the centre of inertia of this iniaginarj
body and tlie tliird body, and continuing a similar process for all the bodies
of the system. And it matters not with which of the bodies we begin the
operation, for it may be demonstrated, that the point thus found will be the
same by whatever steps it be determined. When we come to consider the
properties of the same point as the centre of gravity, we shall be able to pro-
duce an experimental proof of this assertion, since it will be found that there
is only one point in any system of bodies which possesses these properties.
(Plate III. Fig. 31.)

We may always represent the motion of the centre of inertia of a system,
of moving bodies, by supposing their masses to be united into one body, and
tliis body to receive at once a momentum equal to that of each body of the
system, in a direction parallel to its motion. This may often be the most
conveniently done, by referring all the motions of this imaginary body to
three given directions, and collecting all the results, into three sums, which
will represent the motion .of the centre of inertia of the s-ystenu

We have already presupposed this proposition, when we have employed ma-
terial bodies of finite magnitude, that is, systems of material atoms, to represent
imaginary bodies of the same weight, condensed into their centres ; and it
now appears, that the velocity and direction of the motions of such bodies as
we have employed, agree precisely with thoseof our imaginary material points.
We cannot attempt to confirm this law by experiment, because the deductions
from the sensible consequences of an experiment would require nearly the
same processes as the mathematical demonstration.

It is'obvious that the result of any number of uniform and rectilinear mo-
tions, thus collected, must also be a uniform and rectilinear motion. The
centre of inertia of a system of bodies moving without disturbance, is, there-
fore, either at rest, or moving equably in a right line.

The mass, or weight, of each of any number of bodies, being multiplied by its
distance from a given plane, the products, collected into one sum, will be
equal to the whole weight of the system, multiplied by the distance of the
common centre of inertia from the same plane. And the proposition will be

ON THE MOTIONS OF SIMPLE MASSES. 55

equally true, if instead of the shortest distances, we substitute the distances
from the same plane, measured obliquely, in any directions always parallel to
each other. This property is peculiarly applicable to the consideration of the
centre of gravity, and affords also the readiest means of determining its place
in bodies of complicated forms. (Plate III. Fig. 32.)

We have already seen that the place of the centre of inertia of two bodies
is not affected by any reciprocal action between tliem ; and the same is true
of the actions of a system of three or more bodies. We might easily apply
our experiment on the reciprocal action of two bodies to a greater number,
but we should throw no further light on the subject, and the mode of obtain-
ing the conclusion would be somewhat complicated.

All the forces in nature, with which we are acquainted^ act reciprocally be-
tween different masses of matter, so that any two bodies repelling or attracting
each otlier, are made to recede or approach with equal momenta. This cir-
cumstance is generally expressed by the third law of motion, that action and
reaction are equal. There would be something peculiar, and almost incon-
ceivable, in a force which could affect unequally the similar particles of mat-
ter ; or in the particles themselves, if they could be possessed of such differ-
ent degrees of mobility, as to be equally moveable with respect to one force,
and unequally with respect to another. For instance, a magnet and a piece
of iron, each weighing a pound, will remain in equilibrium when their weights
are opposed to each other by means of a balance ; they will be separated with
equal velocities, if impelled by the unbending of a spring placed between thenij
and it is difficult to conceive that they should approach each other with une-
qual velocities in consequence of magnetic attraction, or of anj' other natural
force. The reciprocality of force is therefore a necessary law in the mathe-
matical consideration of mechanics, and it is also perfectly warranted by ex-
perience. The contrary supposition is so highly improbable, that the princi-.
pie may almost as justly be termed a necessary axiom, as a phenomenon col-
lected from observation.

Sir Isaac Newton observes, in his third law of motion, that " reaction is
always contrary and equal to action, or, that the mutual actions of two bodies
are always equal, and directed contraiy ways." He proceeds, " if any body

56 LECTURE VI.

draws or presses another, it is itself as much drawn or pressed. If any one
presses a stone with his finger, his finger is also pressed by the stone. If a
horse is drawing n M'eight tied to a rope, the horse is also equally drawn back-
wards towards the weight : for the rope, being distended throughout, will iu
the same endeavour to contract, urge the horse towards the weight, and the
weight towards the horse, and will impede the progress of the one as much as
it promotes the advance of the other." Now although Newton has always
applied this law in the most unexceptionable manner, yet it must be confessed
that the illustrations here quoted are clothed in such language as to have too
much the appearance of paradox. When we say that a thing presses another,
we commonly mean, that the thing pressing has a tendency to move forwards,
^ into the place of the tiling pressed, but the stone would not sensibly advance
into the place of the finger, if it were removed ; and in the same manner we
imderstand, that a thing pulling another has a tendency to recede further from
the thing pulled, and to draw this after it; but it is obvious that the weight
which the horse is drawing would not return towards its first situation, with
the horse in its train, although the exertion of the horse should intirely cease;
in these senses, therefore, we cannot say, that the stone presses, or,tliat the weight
pulls, and we have no reason to ofi^end the just prejudices of a beginner, by
introducing paradoxical expressions without necessity. Yet it is true in both
cases, that if all friction, and all connexion with the surrounding bodies, could
be instantaneously destroyed, the point of the finger and the stone would re-
cede from each other, and the horse and the weight would approach each
other, with equal quantities of motion. And this is what we mean by the re-
ciprocality of forces, or the equality of action and reaction.

The quantity of action of two attractive or lepulsive bodies on each other
is partly dependent on their magnitude. When the bodies are of the same
kind, their mvitual action is in the compound ratio of their bulks; that is, in
the ratio of the products of the numbers expressing their bulks. For instance,
if two bodies, each containing a cubic inch of matter, attract or repel each
other with a force of a grain, and there be two other bodies, the one contain-
ing two inches, the other ten, of the same matter, then the mutual attraction
or repulsion of these will be expressed by 20 grains ; for each of the 10 inches
is attracted by each of the two with a force of a grain. And the mutual ac-
tion of 3 and 10 will be 30, of 4 and 10, 40; so that when one of the bodies

ON THE MOTIONS OF SIMPLE MASSES. 57

remains the same, the attraction will be simply as the bulk of the other.
Hence the quantity of matter, in every body surrounding us, is considered as
proportional to its weight; for it is inferred from experiment, that all material
bodies are equally subject to the power of gravitation towards the earth, and
are, in respect to this force, of the same kind. For the apparent difference
in the velocity, Avith which different substances fall through the atmosphere,
is only owing to the resistance of the air, as is sometimes shown by an ex-
periment on a feather and a piece of gold, falling in the vacuum of an air
pump; but the true cause was known long before the invention of this ma-
chine, and it is distinctly explained in the second book of Lucretius:

" In water or in air when weights descend.
The heavier weights more swiftly downwards tend.
The limpid waves, the gales that gently play,
Yield to the weightier mass a readier way,
But if the weights in empty space sliould fall.
One common swiftness we should find in all."

We are therefore to suppose, that the different weights of equal bulks of
different substances, depend merely on the greater or less number of particles
contained in a given space, independently of any other characters that may
constitute the specific diff^erences of those substances.

In some cases it is necessary to consider the sum of the masses of two bo-
dies, in order to estimate their mutual action, that is, when we wish to know
the whole relative motion of two bodies with respect to each other; for here
we must add together their single motions with respect to the ceutre of iner-
tia, which are inversely in the same ratio. This consideration is sometimes
of use in determining the action of the sun on the seveial planets.

If two bodies act on each other with forces proportional to any power of
their distance, for instance to the square or the cube of the distance, the forces
will also be proportional to the same power of either of their distances from
their common centre of inertia. Thus, in the planetarj' motions, when one
body performs a revolution by means of the attractive force of another, this
other cannot remain absolutely at rest; but because it is more convenient to

VOL. I. I

58 LECTURE VI.

detenuine the effect of the attraction as directed to a fixed point, \vc consider
the force as residing in the common centre of inertia of the two bodies, whicli
remains at rest, as far as the mutual actions of those bodies only are concerned,
and it may be shown, that the force diminishes, as the square of the distance
of the bodies, either from this point or from each other, increases. The reci-
procal forces of two bodies may therefore be considered as tending to or from
their common centre of inertia, as a fixed point; but it often happens that, the
dift'erence of magnitude being very great, the motion of one of the bodies may
be disregarded. Thus we usually neglect the motion of the sun, in treating of
the planetary motions produced by bis attraction, although, by means of very
nice observations, this motion becomes sensible. But it is utterly beyond the
power of our senses to discover the reciprocal motion of the earth produced
by any terrestrial cause, even by the most copious eruption of a volcano,
although, speaking mathematically, we cannot deny that, whenever a cannon
ball is fired upwards, the whole globe must suffer a minute depression in its
course. The boast of Archimedes was therefore accompanied by an unneces-
sary condition: " give me," said he, " but a firm support, and I will move the
earth;" but granting him his support, he could only have displaced the earth
insensibly by the properties of his machines; and without any such sup-
port, when he threw rocks upon the ships of Marcellus, he actually caused
the walls of Syracuse and theisland of Sicily to move northwards, with as much
momentum, as carried his projectiles southwards against the Roman arma-
ments.

■"fO

LECTURE VIl.

ON PRESSURE AND EQUILIBRIUM.

We have now examined the principal cases in whicli a simple force is em-
ployed in the production of motion; it is pf equal consequence to attend to
the opposition of forces, where they prevent each other's action. A force
counteracted by another force, so that no motion is produced, becomes a
pressure: thus we continually exert a pressure, by means of our weight, up-
on the ground on which we stand, the seat on which we sit, and the bed on
which we sleep; but at the instant when we are falling or leaping, we neither
exert nor experience a pressure on any part.

It was very truly asserted by the antients, that pressure and motion are ab-
solutely incommensurable as effects; for according to' the definition of pres-
sure, the force appears to he what is called in logic a potential cause, M'hich
is not in a state of activity: and since an interval of time must elapse after
the removal of the opposite force, before the first force can have caused any
actual motion, this effect of a finite time cannot with justice be conceived to
bear any proportion to the pressure, which is as it were a nascent effect only.
It is true that a large weight, pressing on a spring, may keep it bent, in ex-
actly the same place, into which a smaller weight, falling on it with a certain
velocity, would inflect it: but, to retain a spring in a certain position, and to
bend it into that position, are effects absolutely incommensurable; the one
being a measure of the constant repulsive force of the spring, bent to a certain
point, the other of the sum of the effects of the same spring, in various degrees
of flexure, for a certain time. Plencc the smallest possible momentum is said
to be more than equivalent to the greatest possible pressure: a very light
weight, falling from a very minute distance, will force back a very strong
spring, although often through an imperceptible space only. But the impulse
of a stream of infinitely small particles, like those of which a fluid is supposed

60 LECTURE VII.

to consist, striking an obstacle in a constant succession, may be counteracted
by a certain pressure, without producing any finite motion.

Nothing however forbids us to compare two pressures, by considering the
initial motions which they would produce, if the opposition were removed ;
nor is there any dilficulty in extending the laws of the composition of motioa
to the composition of pressure. For since we measure forces by the motions,
which they produce, it is obvious that the composition of forces is included
in the doctrine of the composition of motions; and Avhen we combine three
fprces according to the laws of motion, there can be no question but that the
resulting motion is truly determined in a:Il cases, whatever may be its magni-
tude; nor can any reason be given* why it should be otherwise, when this mo-
tion is evanescent, and the force becomes a pres^re. The case is similar to
that of a fraction, which may still retain a real valud, when both its numerator
and denominator become less than any assignable quantity. Some authors
on mechanics, and indeed the most eminent, Bernoulli, Dalembert, and La-
place, have deduced the laws of pressure, more immediately, from the principle
of the equality of the eifects of equal causes ; and the demonstration may be
found, in an improved form, in the article Dynamics of the Supplement of the
Encyclopaedia Britannica ; but its steps are still tedious and intricate.

We are therefore to consider the momentum, or quantity of motion, which
would be produced by any force in action, as the measure of the pressure
occasioned by it, when opposed; and to understand by e()ual or proportion-
ate pressures, such as are produced by forces which would generate equal or
proportionate momenta in a given time. And it may be inferred, that two con-
trary pressures will balance each other, when the momenta, which the forces
would separately produce, in contrary directions, are equal ; and that any
one pressure will counterbalance two otl>ers, when it would produce a mo-
mentum, ccjual and contrary to the momentum which would be derived from
the joint result of the other forces. For, supposing each of two forces op-
posed to each other to act for an instant, and to remain inactive for the next
equal instant, while the other force is exerted, it is obvious that these effects
will neutralise each other, so that the body, on which they are supposed to
operate, will retain its situation ; but such an action is precisely half of the con-
tinuedactionof each force ; consequently, since the halves completely counteract

2

ON PRESSUBE AND EQUILIBRIUM. 61

each other, the 'vholes will do the same. And a similar mode of reasoning
may be extended to any number of forces opposed to each other.

It follows from the laws of the composition of motion, that the result of
two pressures, expressed by the sides of a parallelogram, will be represented by
its diagonal, and that, if a body remain at rest by means of three pressures,
they must be related to each other in magnitude as the sides of a triangle
parallel to their directions. ,This may be very completely shown by experi-
ment. We attach three weights to as many threads, united in one point, and
passing ovev three; pulliies ; then by drawing any triangle, of which the sides
are in the directions of ■ the threads, or in parallel directions, we may always
express the magnitude lof each weight, by the length of the side of the triangle
corresponding to its thread. (.P.late III. Fig. 33.)

The most important of the problems relating to equilibrium are such as con-
cern the machines which are usually called mechanical povj^ers. We are not,
however, to enter at present into all the properties and uses of these machines;
we have at first only to examine them in a state of rest, since the determination
of theirmotion requires additional Considerations, and their application to prac-
tice belongs to another subdivision of our subject.

There is a general law of mechanical ecjuilibrium, which includes tlie prin-
cipal properties of most of these machines. If two or more bodies, con-
nected together,' be suspended from a given point, they will be at rest when
their centre of inertia is in the vertical line passing through the point of suS"
pension. The truth of this proposition may easily be illustrated, by the actual
suspension of any body, or systenl of bodies, from or upon a fixed point ; the
whole remaining in equilibrium, when the centre of inertia is either vertically
below the point of suspension, or above the point of support, or when the
fixed point coincides with the centre of inertia. And whatever may be the -
form of a Compound body, it may be considjered.as a system of bodies cour
nected together, the situation of the common centre of the inertia determining
the quiescent position of the body. (Plate III. Fig. S^-.JS.)
♦

Hence the centpe of inertia is called the centre of gravity ;, and it may be
practically found, by determining the intersection of two lines which bccohie

6S . LECTURE Vir,

vertical in any two positions in which the body is at rest. Thus, if we sus-
pend a board of an irregular form from any two points successively, and mark
the situation of the vertical line in each position, we may find by the inter-
section the place of the centre of gravity: and it will appear that this in-
tersection will be the game, whatever positions we employ, (Plate III.
Fig. 39.)

The consideration of the degree of stability of equilibrium is of material
importance in many mechanical operations. Like other variable quantities,
the stability may be positive, negative, or evanescent. ''jTbe^ Equilibrium is
positively more or less stable, when the centre of gravity would be obliged to
ascend more or less rapidly, if it quitted the vertical lirte: the equilibrium is
tottering, and the stability is negative, when the centre of gravity would
descend if it were displaced; but when the centre of gravity coincides with
the centre of motion, or when its path would be a hoiizontal right line, the
equilibrium has been called insensible, but may more properly be termed neu-
tral, and the body will rest in any position, without tending either to tall, or
to return to its original situation. It is obvious that the centre of gravity
cannot move, without descending, when it is vertically over the fixed point,
nor without ascending, when it is immediately below it ; so that in the one
case the equilibrium is tottering, and in the other stable. Hence we may
Understand the reason of fixing the moveable handles of a vessel of any kind
at its upper part, in order that the centre of suspension may be always above
the centre of gravity. If they be fixed too low; the vessel will be liable to
overset, unless there be sufficient friction to retain it in its proper situation.
(Plate III. Fig. 40.)

An oval surface, placed on a horizontal plane, is capable of a stable equili-
brium, when it rests on its side, or on the extremity of its lesser axis, and of
a tottering equilibrium, when it stands on the extremity of its greater axis.
13ut the equilibrium of a circle or a sphere is always neutral, foi', when dis-
turbed, it neither recovers its first position, nor deviates further from it. A flat
body, resting ort a'sphere, will have its equilibrium tottering or stable, accord-
ingly as its centre of gravity is more or less than the semidiamcter of the
sphere above the point of Contact. (Plate III. Fig. 41, 42.)

ON PRESSURE AND EQUILIBRIUM. 63

The stability of a body supported on a flat basis, of a given extent, is of a
different kind, and is independent of equilibrium. For here, if the centre of
gravity niove either way, it -must begin its motion in an inclined direction,
instead of describing- a curve which is initially horizontal. The stability of
such a body becomes less and less, as it is more and more inclined, till, when
the centre of gravity is vertically over the margin of the basis, there is a tot-
tering equilibrium ; and if the inclination be still further continued, the body
will tall. (Plate III. Fig. 43.)

The broader the basis, and the lower the centre of gravity, the steeper must
the path of that centre be, and consequently the greater the stability. Thus
the disposition of the weight in a carriage may considerably aft'ect its stability,
by altering the place of the centre of gravity. A waggon loaded with iron is
much less easily overturned, than when it is loaded with an equal M-eight of
hay; supposing the inequality of the road, of any accidental obstacle, to ele-
vate one side of the waggon, it will always recover its position, provided that
the centre of gravity remain within the vertical line, passing tlirough the point
of contact of the lower wheel and the ground ; and it is obvious that the
higher the centre of gravity is situated, the sooner it passes this line. If
the velocity of the motion' were very great, the wheel which is elevated
might be lifted off the ground by the momentum, and the centre of gravity
might thus be carried beyond the vertical line, by means of an obstacle which
would not have overset the waggon, if it had been moving slowly. (Plate III.
Fig. 44.)

If a person be sitting or standing in a carriage, the part of the carriage on
which he sits or stands may be considered as representing the place of his
weight, provided that his situation be always perpendicular; but if the motion
be rapid, he will not be able to remain constantly in a posture perfectly erect,
and the centre of gravity of the carriage, with its pas.sengers, Avill be some-
what more elevated, than it would be on this supposition.

The direction of the initial motion of the centre of gravity readily explains
the suspension of a weight, or a bucket of water, on a rod resting, on the end of
a table, when another rod is employed, to keep the bucket at such a distance
from the end of the first, that the centre of gravity may be under the table ;

-Ci LECTURE VXl.

for although the bucket seems suspended by its handle, yet if the handle be-
gan to descend, the centre of gravity would be obliged to rise ; consequently
the whole will retain its position, and remain at rest. (Plate III, Tig. 45.)

The apparent ascent of a loaded cylinder on an inclined plane, and tjie mo-
tion of a roller composed of two united cones, with a coynnpu axis, resting on
the edge of a triangle which is inclined to the horizon, may bq easily under-
stood from the same consideration. (Plate III. Fig. 46.)

We may also observe, in tJie equilibrium of animals, many circumstances il-
lustrative of the properties of the centre of gravity. W hen a person stands on
one foot, and leans forwards, in the attitude which is usually exhibited in the
statues of Mercury, the other foot is elevated behind, in order to bring back
the centre of gravity, so as to be vertically over some part of the foot on which
he stands. But on account of the convex, and irregular form of the foot, the
basis that it affords is really very narrow; hence when we attempt to stand on
one foot, we find it often necessary to use a muscular exertion, in order to bring
the point of support to that side towards which we are beginning to fall ; and
when the basis is still more contracted, the body never remains at rest, but, by
a succession of actions of this kind, sometimes too minute to be visible, it is
Jcept in a state of perpetual vibration, without ever attaining such a position as
would give it any degree of positive stabiUty; and thus it! may be, conceived to
be supported even on a single point, recovering its position, from time to time,
by means of a slight degree of rotatory motion, which is produced by its flex-
ure, and by the changes of the position of the extremities : hence, b}' habit, the
arts of ropedancers and balancers are acquired. Sometimes, however, the po-
sition of the balancer ^is not so dilhcult to be preserved as it appears, the cur-
vature of the wire in contact with the foot tending materially to assist him.

When we attempt to rise from a scat, we generally draw our feet inwards,
in order to bring the point of support into, or near, the vertical line passing-
through the centre of gravity, and to create a tottering equilibrium, which is
favourable for the beginning of motion. And before we rise, we bend the
upper part of the body forwards, in order to procure a momentum, capable of
carrying the centre of gravity beyond the vertical line, passing through the
point of support.

ON PRESSURE AND EQUILIBRIUM. 65

When a horse is walking, the centre of gravity is sometimes supported
only by two feet of the same side, yet for a time so short, that its declension
towards the other side is easily recovered, after the legs on that side have re-
sumed their activity. Some authors have thought it impossible that a qua-
druped should stand for an instant with both feet of the same side raised from
the earth ; but when a horse is walking fast, it may very often be observed,
that the print of the hind foot is considerably more advanced than that of the
fore foot, which has been raised to make way for it.

From the general law of the equilibrium of the centre of gravity, we may
deduce the properties of levers of all kinds. It follows from the definition of
this point, that if two bodies be attached to a straight rod of inconsiderable
weight, they may be sustained in equilibrium, by a fixed point, or fulcrum,
which divides their distance into portions which are inversely as their weights.
And it is obvious that if any other equivalent forces be substituted for weights,
acting at the same distance from the fulcrum, and with the same inclination
to the rod or lever, the conditions of equilibrium will be precisely the same.
Also if either of the forces be transferred to an equal distance on the other
side of the fulcrum, and act there in a contrary direction, the equilibrium
will still remain. Hence we have two principal kinds of levers; the first, in
which the fixed point, or fulcrum, is between the points at which the forces or
weights are applied ; the second, where the forces aie applied, in contrary di-
rections, on the same side of the fulcrum. (Plate III. Fig. 47.)

The demonstrations of the fundamental property of the lever have been
very various. Archimedes himself has given us two. Huygens, Newton,
Maclaurin, Dr. Hamilton, and Mr. Vince, have elucidated the same subject
by different methods of considering it. The demonstration of Archimedes,
as improved by Mr. Vince, is ingenious and elegant, but it is neither so ge-
neral antl natural as one of Dr, Hamilton's, nor so simple and convincing as "
Maclaurin's, which it may be worth our while to notice. Supposing two
equal weights, of an ounce each, to be fixed at the ends of the ecpial arms of
a lever of the first kind; in this case it is obvious that there will be an equi-
librmm, since there is no reason why either weight should preponderate. It
is also evident that the fulcrum supports the whole weight of two ounces,
neglecting that of the lever ; consequently we may substitute for the fulcrum

VOL. I. K

()6 LECTURE VII.

a force equivalent to two ounces, drawing the lever upwards ; and instead of
one of the weights, we may place the end of the lever under a firm obstacle,
and the equilibrium will still remain, the lever being now of the second kind.
Here therefore, the weight remaining at the other end of the lever counter-
balances a force of two ounces, acting at half the distance from the new ful-
crum ; and we may substitute for this force a weight of two ounces, acting at
an equal distance on the other side of that fulcrum, supposing the lever to be
suihciently lengthened, and there will still be an equilibrium. In this case the
fulcrum will sustain a weight of three ounces; and we may substitute for it a
force of three ounces acting upwards, and proceed as before. In a similar
manner the demonstration may be extended to any commensurable proportion
of the arms, that is, any proportion that can be expressed by numbers ; and
it -is easy to show that the same law must be true of all ratios whatever, even
if they happen to be incommensurable, such as the side of a square, compared
to it§ diagonal, which cannot be accurately expressed by any numbers what-
ever; the forces remaining always in equilibrium, when they are to each other
inversely as the distances at which they are applied.

It is sometimes more convenient to have a series of levers acting on each
otlier, with a moderate increase of power in each, than to have a single lever
equivalent in its effect. We may also bend either arm of a lever in any man-
ner that we please, without altering its power, provided that the direction of
the force be perpendicular to the line drawn to the fulcrum; or if the force be
applied obliquely, it may always be imagined to act at the end of a lever equal
in length to the perpendicular let fall from the fulcrum on the direction of the
force. Thus, if two levers are connected by a rope or bar, when the direction
of one of them nearly coincides with that of the rope, a forc'G applied trans-
versely to the lever acts with a great mechanical advantage against the rope ;
but as the inclination increases, the advantage gradually diminishes, and
changes, at last, to an ecpial advantage on the side of the rope and the other
lever to which it is attached. When therefore a great force is required in the
beginning of the motion, and afterwards a much smaller force with a greater
velocity, this apparatus may be extremely convenient: thus, in opening a
steam valve, the pressure of the steam is at first to be overcome, and after this,
little or no additional force is required ; and j\Ir. Watt has very ingeniously
applied this arrangement of levers to the purpose in his steam engines. In the

ON PRESSURE AND EQUILIBRIUM. 67

same manner, it is necessary that tlie platten of a printing press, or the part
which presses the pap^^i'- on the types, should descend from a considerable
height, blrt'jft is Only at; the imtant of taking off the impression that a great
force is required; and both these' ca'ds are obtained by similar means in a press
lately invented by Lord Stanhope. (Plate III. Fig. 48,. 49.)

The wheel and axis bear a very strong resemblance to the lever. . i|",.twd
threads, or perfectly flexible and inextensible lines, be wound- in contrary di-
rections round two cylinders, drums, or rollers, moveable tog-ether on ".the
$ame axis, there will be an eciuilibrium, when the weights attached to thft
threads, or- the forces operating on tlienij- are inversely as the radii of the cy-
linders, or as the diameters of which they are the halves. It may easily be
understood, that the weights have the same power in turning round the cy-
linders, as if they were immediately attached to the arms of a lever, equal in
length to their semidiameter, and that the conditions of equilibrium will be
the same. The demonstration may also be more immediately deduced from
the position of the centre of gravity, immediately below the axis of the cy-
linders, which requires the weights to be inversely as the radii. With respect
to stability, the equilibrium is neutral, and the cylinders will remain at rest
in any situation. A single cylinder is also often combined with a levea- or
winch, and in this case the radius of tire cy.linder is to be compared with the
Jeagth-of the lever ipr;wi<ieh. (Plate III. Fig. 50.)

Systems of wheels and pinions, of various kinds, resemble, in their mecha-
nical properties, either a series of levers, or the combination of cylinders,
which constitutes the wheel and axis; but the form of the teeth may produce
a difference in their action, which will be mentioned when the practical con-
struction of wheelwork is discussed.

Sometimes the axis connected with a winch is composed of two cylinders,
one end of the rope being uncoiled from the smaller, while the other end
winds round the larger ; the weight being supported by a pulley rimning in
its angle. Here the conditions of equilibrium are easily determined from the
place of the centre of gravity, and the effect of the machine is the same, as if
the weight* were attached to a rope coiled round a simple cylinder, of a dia-
meter equal to half the difference of the diameters of the double axis. The

68 LECTURE VII.

machine is, however, much stronger than such a cyhnder would be, and does
not require so great a curvature in the ropes employed. (Plate IV". Fig. 51.)

The laws of the efjuilibrium of puUies have been referred, by some writers
on mechanics, to those of the lever ; but the comparison is both unnecessary
and imperfect; in the simple case of two equal weights attached to a thread
passing over a single pulley, which is the only one that allows us to recur to
the properties of the lever, the conditions of equilibrium are axioraatically
evident, without any further reasoning; and in more complicated cases, the cal-
culations proceed on perfectly different grounds. We are, therefore, to con-
sider a pulley as a cylinder, moving on an axis, merely in order to change
the direction of a thread, without friction ; for whatever is demonstrable of
pullies or their combinations, would be equally true of as many perfectly smooth
grooves, which do not bear the most distant analogy to the lever.

Now when the direction of a thread is altered, by passing over any perfectly
smooth surface, it communicates the whole force acting on it; for the resist-
ance of a surface, without friction, can only be in a direction perpendicular
to itself and to the thread, and the operation of any force remains undisturbed
by a resistance which is always in a direction perpendicular to it,

A fixed pulley, therefore, has no effect in gaining a mechanical advantage ;
but by means of a moveable pulley, it is obvious that a weight may be sup-
ported by two forces, each equivalent to half the weight, applied in a vertical
direction to the extremities of the thread; and these forces may be derived
from two weights, if the thread be made to pass over two fixed pullies in a
proper position ; and if one of the ends be attached to a fixed point, and the
other remain connected to its weight, the equilibrium will continue unimpair-
ed, each portion of the thread still supporting one half of tlie original weight; '
so that, by means of a single moveable pulley, one body may retain in equili-
brium another of double its weight. (Plate IV. Fig 52, 53.)

The modes of arranging pullies are very various, but the advantage which
they procure may always be estimated, from the consideration that every part
of the same thread must be equally stretched; and where there is only one
thread, the weight will be divided equally among all the portions which help

OJf PRESSURE AND EQUILIBRIUM. GQ

to support the moveable block, each of them bearing a weight equivalent to
the force \yhich is applied at the end of the thread. In the common ship's
blocks, the pullies or shieves are equal in magnitude, and placed side by side ;
here their number cannot conveniently exceed two or three, without causing
an obliquity in the block, when the force is applied to the rope. Mr. Smeaton,
for this reason, imeuted a system of pullies, arranged in two rows in each
block, one larger, and the other smaller : the force being applied in the mid-
dle, the rope passes on the larger pullies, till it arrives at the last, then re-
turns through the whole of the smaller series, to the opposite side, and comes
back again on the larger, to be finally attached in the middle. (Plate IV.
Fig. 54: .. 56.)

If the diameters of all the pullies, in both blocks, be taken in the ratio of
the number of portions of the thread intervening between them and the fixed
extremity, their angular velocity will be equal, each of them turning on its
axis in the same time. They may therefore be fixed to a single axis in each
block ; and in this case the axis being longer, there will be less accidental
friction from its want of steadiness, and even the necessary friction may, per-
haps, be somewhat diminished. (Plate IV. Fig. 57. )

If one end of a thread} supporting a moveable pulley, be fixed, and the other
attached to another moveable pulley, and tlic threads of this pulley be similarly
arranged, the weight will be counterpoised by a power, which is found by
halving it as many times as there are moveable pullies; for it is obvious that
each of the&e pullies doubles the efilxt of the power. (Plate IV. Fig. 58.)

There are also other arrangements, by which the eflfect of pullies may be in-
creased or diversified : for instance, where one end of each rope is attached
to the weight to be moved; or where two of the pullies are connected by a
rope passing over a third; but these methods are of little practical utility.
(Plate IV. Fig. 59, 60.)

We have hitherto supposed the ropes, passing over the pullies, to be either
perfectly or very nearly parallel to each other ; but when their directions are
oblique, the forces applied to them require to be modified accordingly. Thus,
if two threads be attached to a weight, and passed over two pullies, fixed at a

70 tECTonE vii»

distance from each other, so that two equal weights may be attached to their
extremities, the depression of the first weight below either pulley, will be to
its distance from the pulley, in tlie same proportion as half of the weight to
either of the other weights ; and if, instead of having a weight attached to it,
one end of the thread be fixed to a firm obstacle, the effect will be precisely
the same. A machine of this kind is sometimes called a swig, perhaps by
corruption from swing. (Plate IV. Fig. 61.)

If all the weights are unequal, we must draw a triangle, of which the three
sides are in the same proportions as the weights ; and we may determine the
directions of the threads, by placing such a triangle, with the side, representing
the middle weight, in a vertical position.

A force may also be applied obliquely to a wheel and axis. Supposing a
rope to be coiled obli(}uely round the axis, it will require, in order to preserve
the equilibrium, a force as much greater than would be sufficient, if it were
simply applied in the direction of the motion, as the length of any part of
the rope uncoiled is greater than the perpendicular distance of its extremity
from the axis. So that when the rope becomes very oblique, a great force is
required in order to counteract a much smaller one acting perpendicidarly.
This remark may be in some measure illustrated by considering the method
used by joiners and stonecutters for keeping a saw straight: two ropes or
braces are twisted together by means of a pin or lever passing between them,
and serve each other in place of an axis, round which they are coiled obliquely,
so that they act with great force, when they are sufficiently tight, and not too
much twisted. (Plate IV. Fig. 62.) .

It appears from the laws which have already been laid down, respecting the
motions of bodies on inclined surfaces, that a weight, acting vertically, will
hold in equilibrium another weight, resting on an inclined plane, without
friction, when the first is to the second as the height of the plane to its ob-
lique length. The pressure on the plane is in this case to the weight resting
on it, as the horizontal length of the plane is to its oblique length. This
pressure rnay be measured experimentally, by substituting for the resistance
of the plane, that of a thread perpendicular to it. (Plate IV. Fig. 63.)

ON PRESSURE AND EQUILIBUIUM. 7r

The same principles are applicable to the ecpiilibrium of the wedge. A
we<ige is a solid which has . tla-ee plane faces inclined to each other, and
two triangular ends ; and we suppose the faces perfectly polislied, so as to
be free from friction, and that no force can act on them otherwise than in a
perpendicular direction. Now in order that three forces, acting on the faces
or sides of a wedge, may hold each other in equilibrium, each of them must
be in proportion to the length of the side on which it acts : they must also be
applied at such parts that their directions may meet in one point ; for other-
wise they will not be completely opposed to each other, and a rotatory mo-
tion will be produced. (Plate IV. Tig. 64.)

If each face of the wedge were conceived to be capable of receiving a pres-
sure, not only in a perpendicular direction, but in any other direction at plea-
sure, as some authors have supposed, the instrument wowld lose its essential
character as a wedge ; but in such cases, the proportion of the forces required
for the state of ecjuilibrium, may always be determined by drawing a triangle
with its sides parallel to their directions.

It happens, however, not uncommonly, that the force actually operating
on the wedge is derived from another foice, acting in a direction more qr less
ohli(]ue, as when a heavy body rests on one of the faces of tlie wedge which is
inclined to the horizon, the body being retained in its situation, by an obstacle or
a thread which confines it to a vertical line, and the sliding away of tlie wedge
being prevented by a horizontal force. A wedge so situated, and supposed to
be capable of sliding without friction on a horizontal surface, is sometimes
called a moveable inclined plane, and it will support the weight resting on it,
if the horizontal force be to the weight, as the height of the plane is to its
horizontal length. If the thread, or the obstacle helping to support the weight,
be placed in any other direction, tlie magnitude of the forces must be determined
from the general law of the composition of three pressures. (Plate I V.Fig 65.)

If a prop or bar, leaning against a smooth vertical surface or wall, be em-
ployed to support or to raise a weight, by means of a force which draws its
base along a smooth horizontal surface, the horizontal force must be to the
weight as the distance of the bottom of the prop from the wall to its perpcn-

72 LECTURE VII.

dicular height. And from similar principles, the conditions of the equilibrium
of arches, domes, and roofs may be determined. (Plate IV. Fig. 66, 67.)

The action of a screw depends on the same principles as that of an inclined
plane; for by rolling a thin and flexible wedge, for instance, a triangular
piece of card, round a cylinder, we form a screw. We may consider the force
tending to turn the screw round its axis, as applied horizontally to the base of
the wedge, and the weight which is to be raised as acting vertically on its in-
clined surfice: the circumference of the cylinder will represent the horizontal
length of the wedge, and the distance between the threads, measured in the
direction of the axis, will be its height, provided that the threads be single;
consequently, the forces required for the equilibrium are to each other, as the
height of one spire to the circumference of the screw. But besides these
forces, it is necessary that some obstacle be present, which may prevent the
body, on which the screw acts, from following it in its motion round its axis,
otherwise there can be no equilibrium. (Plate V. Fig. 68.)

The cylinder, which is the foundation of a screw, may be either convex or
concave, making a cylindrical or a tubular screw, and these, when fitted to-
gether, are sometimes called a screw and a nut. The nut acts on the screw
with the same mechanical power as a single point would do, since it only di-
vides the pressure among the different parts of the spire. In general the
screw is applied in combination with a lever, in order to procure an advantage
in overcoming the friction, which is always considerable in the simple screw
and nut, and which would resist a force applied immediately at the circum-
ference, without any diminution of its power. Sometimes the spires of a
?crew are made to act on the teeth of a wheel, when a very slow motion of
the wbeel, or a very rapid motion of the screw, is required for the purposes of
the machine. (Plate V. Fig. 69, 70. )

The power of screws may be increased, in a great proportion, by means of an
arrangement invented by Mr. Hunter; which is somewhat similar, in its opera-
tion, to the double axis already described. A cylindrical screw is bored, and
made at the same time a tubular screw, with a little difference in the distances
of the threads, so that when it is turned within a fixed nut, it rises or sinks a

ON PRESSURE AND EQUltlBUIUM. 7J

little more or less than the internal screw which perforates it would rise or
sink by the action of its own threads, and a weight attached to this internal
screw ascends, in each revolution, only through a space ecjual to the difference
of the height of the two coils. Here the machine is analogous to a very thip
wedge, of which the thickness is only equal to the difference of the distances
of the threads, and which of course acts with a great mechanical a<lvantage.
It might in some cases he more convenient to make two cylindrical screws, of
different kinds, at different parts of the same axis, rather than to perforate it.
The friction of such machines is, however, a gi«at impediment to their opera-
tion. (Plate V. Fig. 71.)

In all the kinds of equilihrium that we have considered, and in all other
cases that can be imagined, it will be found that the forces, or rather weights,
opposed to each other, are so arranged, that if they were put in motion, their
momenta in the direction of f gravity would, in the first instance, be equal and
contrary, the velocity being as much greater as the magnitude of the weight
is smaller. Thus, if an ounce weight, placed on a lever, at the distance of four
feet from the fulcrum, counterpoise a weight of four ounces at the distance of
one foot, the velocity with which the ounce would descend, if the lever were
moved, would be four times as great as that with which the weight of four
ounces would descend. A single moveable pulley ascends with half the ve-
locity of the end of the rope which is drawn upwards, and acts with a force
twice as great ; a block of three shieves enables a weight to sustain another
six times as great ; but the velocity, with which this weight ascends, is only
one sixth of that with which the smaller weight must descend. When a
weight rests, on an inclined plane, of which the height is one half of the
length, it may be retained by the action of a weight of half its magnitude,
drawing it up the plane by means of a thread passing over a pulley; here if
the weight ascended or descended along the oblique surface, its velocity, re-
duced to a vertical direction, would be half as great as that of the smaller ■
weight which balances it.

Some authors have considered this law as affordins: a fundamental demon-

o

stration of the conditions of equilibrium in all possible cases. For since,
wherever two weights are in equilibrium, if one of them descended, the other

VOL. I. T

74 LECTURE VII.

must ascend Avith an equal quantity of motion, it appears absurd to suppose
that the force of gravitation could produce these two equal and contrary effects
at the same time. But it is more satisfactory to trace, in every case, the steps
by which the immediate actions of the different weights are enabled to oppose
each other; and the general law may then be inferred, by induction, from the
agreement of the particular results, in confirmation of the general reasoning
which tends tp establish its trutk

75

LECTURE VIII.

ON COLLISION. X

Having inquired into the laws and properties of tlie motions and rest of
single bodies, under the operation of one or more forces, and into the equili-
brium of these forces, in different circumstances, we are next to examine
some simple cases of the motions of various moveable bodies acting recipro-
cally on each other. In all problems of this kind, it is of importance to re-
collect the general principle already laid down, respecting the centre of in-
ertia, that its place is not affected by any reciprocal or mutual action of the
bodies constituting the system.

Whenever two bodies act on each other, so as to change the direction of
their relative motions, by means of any forces which preserve their activity
undiminished at equal distances on every side, the relative velocities with
which the bodies approach to, or recede from each other, will always be
equal at equal distances. For example, the velocity of a comet, when it
passes near the eajth in its descent towards the sun, is the same as its velocity
of ascent in its return, although, at different distances, its velocity has under-
gone considerable changes. In this case, the force acts continually, and at-
tracts the bodies towards eacli other; but the force concerned in collision,
when a body strikes or impels another, acts only during the time of more or
less intimate contact, and tends to separate the bodies from each other. '
When this force exerts itself as powerfully in causing the bodies to separate,
as in destroying the velocity with which they meet each other, the bodies
are called perfectly elastic : when the bodies meet each other without a re-
action of this kind, they are called more or less inelastic. Ivory, metals,
and elastic gum, are highly, and almost perfectly elastic : clay, wax, mixed
with a little oil, and other soft bodies, are almost inelastic : and tlie effects

76 LECTURE VI I r.

of inelastic bodies may be imitated by elastic ones, if we cause them to unite
or adhere after an impulse, so as to destroy the effect of the repulsive force
which tends to separate them.

When two bodies approach to each other, their form is in some degree
changed, and the more as the velocity is greater. In general, the repulsive
force exerted is exactly proportional to the degree in which a body is com-
pressed ; and when a body strikes another, this force continues to be increased
until the relative motion has been destroyed, and the bodies are for an instant
at rest with respect to each other ; the repulsive action then proceeds with an
intensity which is gradually diminished, and if the bodies are perfectly elastic,
they reassume their primitive form, and separate with a velocity equal to that
with which they before approached each other. Strictly speaking, the repul-
sion commences a little before the moment of actual contact, but only at a
distance which in common cases is imperceptible. The change of form of an
elastic substance, during collision, is easily shown by throwing a ball of ivory
on a slab of marble, or a piece of smooth iron, coloured witli black lead, or
printing ink ; or by suffering it to fall from various heights : the degree of
compression will then be indicated by the magnitude of the black spot which
appears on the ball. It may be shown, from the laws of pendulums, that, on
the supposition that the force is proportional to the degree of compression, its
greatest exertion is to the weight of a striking body, as the height from
which the body must have fallen, in order to acquire its velocity, to half the
depth of the impression.

For making experiments on the phenomena of collision, it is most conveni-
ent to suspend the bodies employed, by threads, in the manner, of pendulums;
their velocities may then be easily measured, by observing the chords of the
arcs through which they descend or ascend, since the velocities acquired in
descending through circular arcs are always proportional to their chords; and
for this purpose, the apparatus is provided with a graduated arc, which is com-
monly divided into equal parts, although it would l^e a little more correct to
place the divisions at the ends of arcs, of which the chords are expressed by
the corresponding numbers. (Plate V. Fig. 72.)

The simplest case of the collision of elastic bodies is when two equal balls

ON COLLISION. 77

descend through equal arcs, so as to meet each other with equal velocities.
They recede from each other after collision with the same velocities, and rise
to the points from which they before descended, with a small deduction for
the resistance of the surrounding bodies.

"When a ball at vest is struck by another equal ball, it receives a velocity-
equal to that of the ball which strikes it, and this ball remains at rest. And
if two equal balls meet or overtake each other with any unequal velocities,
their motions will be exchanged, each rising to a height equal to that from
which the other descended.

The effect of collision takes place so rapidly, that if several equal balls be
disposed in a right line, in apparent contact with each other, and another
ball strike the first of them, they will all receive in succession the whole velo-
city of the moving ball before they begin to act on the succeeding ones; they
will then transmit tlie whole velocity to the succeeding balls, and remaui en-
tirely at rest, so that the last ball only will fly off.

In the same manner, if two or more equal balls, in apparent contact, be in
motion, and strike against any number of others placed in a line, the first of
the moving balls will first drive off the most remote, and then the second the
last but one, of the row of balls which Avere at rest: so that the same number
of balls will fly off together on one side, as descended to strike the rcw of
balls on the other side ; the others remaining at rest.

If the line of balls, instead of being loosely in contact, had been firmly
united, they would have been impelled with a smaller velocity, and the ball
striking them would have been reflected. For when a smaller elastic body
strikes a larger, it rebounds with a velocity less than its first velocity, and the
larger body proceeds also with a less velocity than that of the body striking it.
But if a larger body strikes a smaller, it still proceeds with a smaller velocity,
and the smaller body advances with a greater.

The momentum communicated by a smaller elastic body to a larger one is
greater than its own, and when the first body is of a magnitude comparatively
inconsiderable, it rebounds with a velocity nearly as great as the velocity of

"76 LECTURE Vllt.

of inelastic bodies may be imitated by elastic ones, if we cause them to unite
or adhere after an impulse, so as to destroy the effect of the repulsive force
which tends to separate them.

When two bodies approach to each other, their form is in some degree
changed, and the more as the velocity is greater. In general, the repulsive
force exerted is exactly proportional to the degree in which a body is com-
pressed ; and when a body strikes another, this force continues to be increased
until the relative motion has been destroyed, and the bodies are for an instant
at rest with respect to each other ; the repulsive action then proceeds with an
intensity which is gradually diminished, and if tlie bodies are perfectly elastic,
they reassume their primitive form, and separate with a velocity equal to that
with which they before approached each other. Strictly speaking, the repul-
sion commences a little before the moment of actual contact, but only at a
distance which in common cases is imperceptible. The change of form of an
elastic substance, during collision, is easily shown by throwing a ball of ivory
on a slab of marble, or a piece of smooth iron, coloured with black lead, or
printing ink ; or by suffering it to fall from various heights : the degree of
compression will then be indicated by the magnitude of the black spot which
appears on the ball. It may be shown, from the laws of pendulums, that, on
the supposition that the force is proportional to the degree of compression, its
greatest exertion is to the weight of a striking body, as the height from
which the body must have fallen, in order to acquire its velocity, to half the
depth of the impression.

For making experiments on the phenomena of collision, it is most conveni-
ent to suspend the bodies employed, by threads, in the manner'of pendulums ;
their velocities may then be easily measured, by observing the chords of the
arcs through which they descend or ascend, since the velocities acquired in
descending through circular arcs are always proportional to their chords; and
for this purpose, the apparatus is provided with a graduated arc, which is com-
monly divided into equal parts, although it would \)e a little more correct to
place the divisions at the ends of arcs, of which the chords are expressed by
the corresponding numbers. (Plate V. Fig. 72. )

The simplest case of the collision of elastic bodies is when tsvo equal balk

ov coLLisiaN. 77

descend through equal arcs, so as to meet each other with equal velocities.
They recede from each other after collision with the same velocities, and rise
to the points from which they before descended, with a small deduction for
the resistance of the surrounding bodies.

"When a ball at rest is struck by another eqnal ball, it receives a velocity
equal to that of the ball which strikes it, and this ball remains at rest. And
if two equal balls meet or overtake each other with any unequal velocities,
their motions will be exchanged, each rising to a height equal to that from
which the other descended.

The effect of collision takes place so rapidly, that if several equal balls be
disposed in a right line, in apparent contact with each other, and another
ball strike the first of them, they will all receive in succession the whole velo-
city of the moving ball before they begin to act on the succeeding ones ; they
will then transmit tlie whole velocity to the succeeding balls, and remain en-
tirely at rest, so that the last ball only will fly off.

In the same manner, if two or more equal balls, in apparent contact, be in
motion, and strike against any number of others placed in a line, the first of
the moving balls will first drive off the most remote, and then the second the
last but one, of the row of balls which Avere at rest: so that the same number
of balls will fly off together on one side, as descended to strike the row of
balls on the other side ; the others remaining at rest.

If the line of balls, instead of being loosely in contact, had been firmly
united, they would have been impelled with a smaller velocity, and the ball
striking them would have been reflected. For when a smaller elastic body
strikes a larger, it rebounds with a velocity less than its first velocity, and the
larger body proceeds also with a less velocity than that of the body striking it.
But if a larger body strikes a smaller, it still proceeds with a smaller velocity,
and the smaller body advances with a greater.

The momentum communicated by a smaller elastic body to a larger one is
greater than its own, and when the first body is of a magnitude comparatively
inconsiderable, it rebounds with a velocity nearly as great as the velocity of

78 LECTURE vrri.

its impulse, and tlie second body acquires a momentum nearly twice as great
as that of the first. When a larger body strikes a smaller one, it communi-
cates to it only as much momentum as it loses.

In the communication of motion between inelastic bodies, the want of a
repulsive force, capable of separating them with an equal relative velocity, is
probably owing to a permanent cliange of form ; such bodies receiving and
retaining a depression at the point of contact When the velocity is too
Mnall to produce this change of form, the bodies, however inelastic^ may
usually be observed to rebound a little.

Bodies, which ai-e perfectly inelastic, remain in contact after collision; they
must therefore proceed with tlie same velocity as the centre of inertia had
before •colHsion. Thus, if two equal balls meet, with equal velocities, they
remain at rest; if one is at rest, and the other strikes it^ they proceed with
half the velocity of the ball which was first in motion. If they are of un-
equal dimensions, the joint velocity is as much smaller than that of the strik-
ing ball, as the weight of this ball is smaller than the sum of the weights of
both balls. And in a similar manner, the effects of any given velocities in
either ball may be determined,

It follows immediately from the properties of the centre of inertia, that
in all cases of collision, whether of elastic or inelastic bodies, the sum of the
momenta of all the bodies of the system, that is, of their masses or weights
multiplied by the numbers expressing their velocities, is the same, when re-
duced to the same direction, after their mutual collision, as it was before
their collision. When the bodies are perfectly elastic, it may also be shown
that the sum of their energies or ascending forces, in their respective direc-
tions, remains also unaltered.

The tenn energy may be applied, with great propriety, to the product of the
mass or weight of a body, into the square of the number expressing its ve-
locity. Thus, if a weight of one ounce moves Avith a velocity of a foot in a
second, we may call its energy 1 ; if a second body of two ounces have a ve-
locity of three feet in a second, its energy will be twice the square of three,
or 18. This product has been denominated the living or ascending force,

ON COLLISION. 7g

since the height of the body's vertical ascent is in proportion to it; and some
liave considered it as the true measure of the quantity of motion ; but although
this opinion has been very universally rejected, yet the force thus estimated
well deserves a distinct denomination. After the considerations and demon-
strations which have been premised on the subject of forces, there can be no
reasonable doubt with respect to the true measure of motion ; nor can there
be much hesitation in alloAving at once that since the same force, continued
for a double time, is known to produce a double velocity, a double force
must also produce a double velocity in the same time. Notwithstanding the
simplicity of this view of the subject, Leibnitz, Smeaton, antl many others,
have chosen to estimate the force of a moving body, by the product of its
mass into the square of its velocity; and though we cannot admit that this
estimation of force is just, yet it may be allowed that many of the sensible
eft'ects of motion, and even the advantage of any mechanical power, however
it may be employed, are usually proportional to this product, or to the
weight of the moving body, multiplied by the height from which it must
have fallen, in order to acquire the given velocity. Thus a bullet, moving
with a double velocity, will penetrate to a quadruple depth in clay or tallow:
a ball of etjual size, but of one fourth of the weight, moving with a double
velocity, will penetrate to an equal depth: and, with a smaller quantity of
motion, will make an equal excavation in a shorter time. This appears at
first sight somewhat paradoxical : but, on the other hand, we are to consider
the resistance of the clay or tallow as a uniformly retarding force, and it will
be obvious, that the motion, which it can destroy in a short time, must be
less than that which requires a longer time for its destruction. Thus also "
when the resistance, opposed by any body to a force tending to break it, is to
be overcome, the space through which it may be bent, before it breaks, being-
given, Jis well, as: the force exerted aticvery point of that space, the power of
any body to break it is proportional to the energy of its motion, or to its
weight multiplied by the square of its velocity.

In almost all cases of the forces employed in practical mechanics, the labour
expended in producing any motion, is proportional, not to the momentum, but
to the energy which is obtained ; since these forces are seldom to be considered
as uniformly accelerating forces, but generally act at some disadvantage,
when the velocity is already considerable. For. instance, if it be necessary to

go LECTURE VIII.

obtain a certain velocit}', by means of tbe descent of a beavy body fiom a
beigbt, to wliicb we carry it by a fligbt of steps, we must ascend, if we wish
to double the velocity, a quadruple number of steps, and this will cost us
nearly four times as much labour. In the same manuer, if we press with a
g-iven force on the shorter end of a lever, in order to move a weight at a
greater distance on the other side of the fulcrum, a certain portion of the
force is expended i.n the pressure which is supported by tlie fulcrum, and we
by no means produce the same momentum, as would have been obtained, by
the immediate action of an equal force, on the body to be moved.

An elastic ball, of 2 ounces weight, moving with a velocity of 3 feet in a
second, possesses an energy, as we have already seen, which ma}- be ex-
pressed by 18. If it strike a ball of 1 ounce which is at rest, its velocity
will be reduced to 1 foot in a second, and the smaller ball will receive a
velocity of 4 feet: the energy of the first ball Avill then be expressed by 2,
and that of the second by 16, making together 18, as before. The momentum
of the larger ball after collision is 2, that of the smaller 4, and the sum of
these is equal to the original momentum of the first ball.

Supposing the magnitude of an elastic body, which is at rest, to be infinite,
it will receive twice the momentum of a small body that strikes it ; but its
velocity, and consequently its energy, will be inconsiderable, since the
energy is expressed by the product of the momentum into the velocity. And
if the larger body be of a finite magnitude, but still much greater than the
smaller, its energy will be very small ; that of the smaller, which rebounds
with a velocity not much less than its original velocity, being but little di-
minished. It is for this reason, that a man, having a heavy anvil placed on
his chest, can bear, without much inconvenience, the blow of a large hammer
striking on the anvil, while a much slighter blow of the hammer, acting im-
mediately on his body, would have fractured his ribs, and destroyed his life.
The anvil receives a momentum nearly twice as great as that of the hammer;
but its tendency to overcome the strength of the bones, and to crush the man,
is only proportional to its energy, which is nearly as much less than that of
the hammer, as four times the weight of the hammer is less than the weight
of the anvil. Thus, if the weight of the hammer were 5 pounds, and that of
the anvil 100, the energy of the anvil would be less than one fifth as great as

ox COLLISION'. , 81

tliat of the hammer, besides some further dimmution, on accoiiut of the want
of perfect elasticity, and from the effect of the larger surface of the anvil, in
dividing the pressure occasioned hy the blow, so as to enable a greater por-
tion of the chest to cooperate in resisting it.

When a body strikes another, in a direction which does not pass through
its centre of gravity, the effect produced involves the consideration of rotatory
motion, since in this case the body is made to revolve on an axis. But this
can never happen when the borly is spherical, and its surface perfectly polish-
ed; since every impulse must then be perpendicular to the surface, and must
consequently be directed to the centre of the body. If the motion of a ball,
which strikes another, is not directed to its centre, the surface of contact must
be oblique with respect to its motion, and the second ball will only receive an
imptdse in a direction perpendicular to this surface, while the first receives,
from its reaction, an equal impulse in a contrary direction, which is com-
bined with its primitive motion. The magnitude of this impulse may be de-
termined by resolving the motion of the first ball into two parts, the one pa-
rallel to the surface of contact, and the other perpendicular; the first part re-
maining always unaltered, the second being modified by the collision. If, for
example, the balls were equal, this second part of the motion would be de-
stroyed, and the remaining motion would be in the direction of the surface
of contact, and perpendicular to that of the ball impelled.

Hence it follows, that if we wish to impel a billiard ball in a given direc-
tion, by the stroke of another ball, we have only to imagine a third ball to
be placed in contact Avith the first, immediately behind it in the line of the
required motion, and to aim at the centre of this imaginary ball: the first
ball will then be impelled in the required direction, and the second will also
continue to move in a direction perpendicular to it.

By a similar resolution of the motion of an elastic ball, we may determine
its path, when it is refiected from a fixed obstacle. That part of the motion,
which is in a direction parallel to the surface of the obstacle, remains undi-
minished: the motion perpendicular to it is changed for an equal motion
in a contrary direction, and the joint result of these constitutes a motion,
in a direction, which is equally inclined to the surface, with the first motion,

VOL. I. M

S2 LECTURE VIII.

but on the opposite side of the perpendicular. Of this we have also a familiar
instance in the motions of billiard balls ; for we may observe, that a ball re-
bounds from the cushion, in an angle equal to that in which it arrives at it;
and if we wish that our ball, after reflection, should strike another, placed in
a given situation, we may suppose a third ball to be situated at an equal
distance, on the other side of the cushion, and aim at this imaginary ball:
our ball will then strike the second ball, after reflection, with a direct im-
pulse. We here suppose the reflection to take place when the centre of the
ball arrives at the cushion, while in fact the surface only comes into contact
with it; if we wish to be more accurate, we may place the imaginary ball, at
an equal distance beyond the centre of a ball, lying in contact with the
nearest part of the cushion, instead of measuring the distance from the
cushion itself. (Plate V. Fig. 73.)

When the number of bodies, which meet each other, is greater, and their
magnitudes and motions are diversified, the calculation of the effects of col-
lision becomes very intricate, and the problem is scarcely applicable to any
practical purpose. Those who are desirous of pursuing the investigation as a
mathematical amusement, will find all the assistance that they rec[uire in the
profound and elegant works of Maclaurin.

S3

LECTURE IX.

ON THE MOTIONS OF CONNECTED BODIES.

The motions of single bodies, acting in any manner on each other, which
we have been considering, as far as they belong to the effects of coUision, are
of less importance to practical mechanics, than the affections of such bodies
as are united, so as either to revolve round a common centre, or to participate
in each other's motions, by any kind of machinery.

It is only within half a century, that the phenomena and effects of rotatory
motion have been sufficiently investigated. Newton committed a mistake,
which is now universally acknowledged, in his computation of the precession
of the equinoxes, for want of attending sufficiently to the subject; and it is of
importance in the calculation of many of the effects of mechanical arrange^
ments, that it should be treated in an accurate manner.

•

The effect of a moving body, in producing motion in any other bodies, so
connected as to be capable of turning freely round a given centre, is jointly
proportional to its distance from that centre, and to its momentum in the
direction of the motion to be produced. Thus a body, of one pound weight,
moving with a velocity of one foot in a second, Avill have three times as great
an effect on a system of bodies, to which its whole force is communicated, at
the distance of one yard from the centre of their motion, as if it acted only
at the distance of a foot, on the same system of bodies : a double weight, or
a double velocity, would also produce a double effect. For, supposing two
unequal bodies to be connected by an inflexible line, and to move with
equal velocities, in a direction perpendicular to that of the line, it is demon-
strable, from the principles of the composition of motion, that they may be
wholly stopped by an obstacle applied to the centre of gravity, consequently
their effects, in turning the line round this point, are equal; here the mo-

84 LECTURE IX.

menta are proportional to the weights, but the products obtained by multiply-
ing them by the distances from the centre, at which they act, are equal r
these products therefore represent the rotatory power of the respective bodies.
Hence in a connected system of bodies, revolving round a given point, with
equal angvdar velocities, the effect produced by the rotatory motion of each
body, as well as the force which is employed in producing it, is expressed by
the product of the mass multiphed by the square of the velocity, since the
velocity is in tWs case proportional to tli€ distance from the centre ;- and this
product is the same that I have denominated the energy of a moving body.

These propositions are of great use in all inquiries respecting the operations-
of machines; and it is of importance to bear in mind, that although the equi-
librium of a system of bodies is determined by the equality of the products
of their weights, into their effective distances on each side of the centre,
yet that the estimation of the mechanical power of each body, when once
in motion, requires the mass to be mvdtiplied by the square of the distance,,
or of the velocity. For this reason, together with some others, which have
been already mentioned, some have considered the square of the velocity as
affording the true measure of force; but the properties of motion, concerned
in the determination of rotatory power, are in reality no more than necessary
consequences of the .simpler laws, oa which the whole theory pf mechanics
is founded. _ ,

The effects of rotatory motion may be very conveniently examined, by
means of an apparatus, similar to that which was employed for the same pur-
pose by Mr. Smeaton. A vertical axis is turned by a thread passing
over a pulley, and supporting a scale with weights ; the thread may be applied
at different parts of the axis, having different diameters, and the axis supports
two arms, 'on which two leaden weights are fixed, at distances which may be
varied at pleasure. The same force will then produce, in the same time, but
half the velocity, in the same situation of the weights, when the thread is ap-
plied to a part of the axis of half the diameter: and if the weights are removed
to a double distance from the axis, a quadruple force will be required, in order
to produce an equal angular velocity in a given time. (Plate V. Fig. 74.)

When a number of connected bodies, or a single body of considerable mag-

OS THE MOTIONS OF CONNECTED BODIES. 85

nitude, is made to revolve round a centre, it is sometimes necessary to in-
quire, into what point their masses might be supposed to be concentrated, so
as to preserve the same rotatory power, with the same angular velocity. This
point is called the centre of gyration* In a circle, or any portion of a circle,
turning round its centre, the square of the distance of this point, from the
centre, is half the square of the semidiameter ; and the whole eftect of the mo-
mentum of the circle, upon an obstacle at its circumference, is exactly half
as. great as that of an equal quantity of matter, striking the obstacle with the
velocity of tlie circumference.-

There is another point, of which the determination is of considerable utility
in manv meclianical problems: this is the centre of percussion ; or the point
at which an obstacle nuist be applied, in order to receive the whole eftect of a
stroke of a body, which is revolving round a given centre, without producing
any pressure,, or strain, on the centre, or axis of motion. In a straight line,
or a slender, rod, iixed at one extremity, the distance of this point, from the
centre of motion, is two thirds of the whole length.

The same point is also the centre of oscillation, the distance of which de-
termines the time of oscillation, or vibration, of the body, suspended as a
pendulum, upon the given centre, of motion. It may easily be shown, that
a rod a yard long, and of equable thickness, suspended at one extremity, vi-
brates in the same time as a ball suspended by a ducd< , of which the length
is two feet. But if the rod were suspended on a centre, at some point
within its extremities, the time of its vibration would be prolonged, so as to •
become equal to that of a simple pendulum of much greater length. This
may be illustrated by two balls, fixed at the end of a rod, with a centre of
suspension moveable to any part of the rod, for as the centre approaches the
middle of the rod, the vibrations are rendered extremely slow. -(Plate V.
Fig 75.)

The rotatory motion of bodies, not fixed on an axis, might be considereol
in, this place, but the subject involves in its whole extent some intricacy of
calculation, and, except in astronomy, the investigation is scarcely applicable
to any problems which occur in practice. We may, however, examine a few
of the simplest cases. If two bodies be supposed to be connected by an in-

86 LECTURE IX.

flexible line, and to be moving with equal velocities in parallel directions; if
an immoveable obstacle be applied, so as to form a fulcrum, at the common
centre of gravity, they will, as we have already seen, be wholly stopped: but
if the fulcrum be applied to any othcf part of the line, one of the bodies
will move forwards, and the other backwards, with a velocity which may
easily be determined by calculating their rotatory power with respect to the
fulcrum. If the fulcrum be applied at a point of the line continued beyond
the bodies, the one will lose and tlie other gain velocity, since the quantity
of rotatory power will always remain unaltered: that point only which "is de-
nominated the centre of oscillation retaining its original velocity. Now the
same inequality in the motion of the bodies, and consequently the same an-
;giilar velocity of rotation will be produced, if the connected bodies be ini-
tially at rest, and tlie fulcrum be applied to them with the same relative velo-
city. For example, if a straight rod or wire receive an impulse at one end in
a transverse direction, the centre of oscillation, Avhich is at the distance of
two thirds of the length from the end struck, will at the first instant remain
at rest, conseciuently the centre will move with on^ fourth of the velocity of
the impulse, and this must be the velocity of the progressive motion of the
rod, since the centre of gravity of any body, which is at liberty, moves al-
ways with an equable velocity in a right line, while the whole rod Avill also
revolve equably roimd its centre, except such retardations as may arise from
foreign causes. In a similar manner the computation may be extended to
bodies of a more complicated form. Thus it has been calculated at what ,
point of each planet an impulse must have operated, in order to communicate
to it at one bloM' its rotation and its progressive motion in its orbit.

Those who have asserted that the motion of the centre of gravity of a body
can only be produced by an impulse, which is either wholly or partly.directcd
towards it, have obviously been mistaken. The centre of oscillation is the
only point which remains at rest with regard to the first eflPcct of the stroke,
and the centre of gravity, which nev^r coincides with the centre of oscilla-
tion, moves in the direction of the impulse, while the parts beyond the cen-
tre of oscillation begin to move in a contrary direction. Hence it is, that
a thin stick may be broken, by a blow on the middle, without injuring the
glasses on which it is supported: for the ends of the stick, instead of being
depressed by the stroke, would rise Avith half the velocity of the body wtich

ON THE MOTIONS OF CONNECTED BODIES. 87

strikes them, if the two portions were separated without tlie loss of any force.
But unless some art has been previously employed in producing a partial se-
paration, it will fre(juently be found, that the stick has strength enough to
break the glasses before it gives way.

The subject of preponderance, or of the action of "weights or forces coun-
teracted by other forces, and incumbered with foreign matter to be put in
motion, requires for its discussion a previous knowledge of the simple opera-
tion of forces, of the conditions of equilibrium, and of the estimation of rota-
tory power. The consideration of the effects of preponderance enables us to
determine, in some circumstances, the best possible proportions of the powers
of machines, for producing the required effects in the most advantage-
ous manner. For, in order that motion may be produced, it is not sufficient
that there be an equilibrium, in procuring which a part only of the power is
expended, but there must be an excess of force above that which would be
necessary for the equilibrium; and it is often of consequence to know what
portion of the power must be employed in each way, in order that the great-
est effect, may be produced in a given time. We are sometimes told, that
what we gain in power, we lose in time. In one sense indeed the remark is
true; thus one man can do no more by a powerful machine in ten hours,
than ten men can do by a weaker machine in one hour; but in other senses
the assertion is often erroneous; for by increasing the mechanical advantage
to a given degree, we may in some cases considerably increase the perform-
ance of a machine, without adding to the force.

According to the nature of the force employed, and to the construction
of the machine, a different calculation may be required for finding the best
proportions of the forces to be employed ; but a few simple instances will
serve to show the nature of the determination. Thus, in order that a smaller
weight may raise a greater to a given vertical height, in the shortest time
possible, by means of an inclined plane, the length of the plane must be to
its height, as twice the greater weight to the smaller, so that the acting force
may be twice as great as that which is simply required for the equilibrium.
This may be shown experimentally, by causing three equal weights, sup-
ported on wheels, to ascend at the same time as many inclined planes of the
same height, but of different lengths, by means of the descent of three other

S8 LECTURE I?C.

equal weights, connected with the former three, by threads passing over pul-
lies. The length of one of the planes is twice its height, that of anothei
considerably more, and that of a third less: if the M'eights begin to rise at
the same time, the first A\ill arrive at the top, before cither of the others.
(Plate V. Fig. 76.)

If a given weight, or any equivalent force, be employed to raise another
equal weight, by means of levers, wheels, puUies, or any similar powers, the
greatest eftect will be produced, if the acting weight be capable of sustaining,
in equilibrium, a weight about twice and a half as great as itself. This pro-
position may be very satisfactorily illustrated by an experiment. Three double;
puUies being placed, independently of each other, on an axis, round which
they move freely, the diameters of the two cylindrical portions, which com-
pose the iirst, being in the ratio of 3 to 2, those of the second as 5 to 2, and
those of the third as 4 to 1, six equal weig-hts arc attaclicd to them in pairs,
so that three may be raised by the descent of the other three, on the principle
' of the wheel and axis. If then Ave hold the lower weights, by means of
threads, or otherwise, and let them go, so that they may begin to rise at the
same instant, it will appear evidently that the middle pulley raises its weight
the fastest ; and consequently, tliat in this case, the ratio of 5 to 2 is more
advantageous, than either a much less, or a much greater ratio. If the weight
to be raised were very great in proportion to the descending weight, the ar-
rangement ought to be such, that this weight might retain, in equilibrium, a
weight about twice as great as that which is actually to be raised. If the
descending weight were a hundred times as great as the ascending weight,
the greatest velocity would be ohtaijied in this case, by making tlie descend-
ing weight capable of holding in equilibrium a M'cight one ninth as great as
itself. (Plate Vf. Fig. 77.) ^

The proportion required for the greatest effect is somewhat different, when
the heights, through which Ijoth the weights are to move, arc limited, as they
usually must be in practical cases. Here, if we suppose the operation to be
continually repeated, the cfi'ect will be greatest in a given time, when the
ascending weight is between two thirds arul one half, of the exact countci-
poise to the descending Aveiglit. If, however, the force were accunudated
daring the action of the machine, there would be no limit to the advantage of

ON THE MOTIONS OF CONNECTED BODIES. 89

a slow motion. Thus, if we have a stream of water, fiUing a single reservoir,
which is to raise a weight by means of its descent, the proportion here as-
signed will be the best for performing the most work in a given time; but if
we chose to double our machine, so that'one reservoir should be filled during
the descent of another, it would be proper to proportion the weights in such a
manner, that the whole time required for filling one of the reservoirs should
be occupied in the descent and the reascent of the other.

In all these cases, if great accuracy were required, it would be necessaiy
in the calculation to add to the mass to be moved, the quantity of moveable
matter in the machine, reduced to a mean distance from the fulcrum or centre,
according to its rotatory power, in the same manner as the centre of gjTation
is determined. But there is seldom occasion for such a degree of precision.
The magnitude of the pressure which is exerted on the fulcrum, during the
motion of the connected bodies, may always be determined, by comparing
the actual velocity of the centre of gravity with that of a body descending
without resistance.

These propositions and experiments must be allowed to require an attentive
consideration from those who are engaged in practical mechanics ; and it is
natural to suppose that the proportions laid down may be adopted w^th safety,
and employed with success, and that we may sometimes derive important ad-
vantages from their application. But on more mature consideration, we shall
find some practical reasons for caution in admitting them without material
alterations.

If a machine were constructed for raising a solid weight, and so arranged
as to perform its office in the shortest possible time with a given expense of
power, the weight would still possess, when it arrived at the place of its
destination, a considerable and still increasing velocity: in order that it might
retain its situation, it would be necessary that this velocity should be destroy-
ed; if it were suddenly destroyed, the machinery would undergo a strain which
might be very injurious to it: and if the velocity were gradually diminished,
the time would no longer be the same as is supposed in the calculation. In
the second place, the forces generally employed arc by no means uniformly
accelerating forces, like that of gravitation, to which the propositions which

VOL. I. N

go LECTURE IX.

we have been considering are adapted : they are not only less active when a
certain velocity has once been att:uned, but they are often capable of a tem-
porary increase or diminution of intensity at pleasure. We have seen the in-
convenience of producing a great final velocity, on account of its endanger-
ing the structure of the machine : if therefore our permanent force be calcu-
lated according to the common rule, so as to be able to maintain the equili-
brium, and overcome the friction, the niomentum or inertia of the weights,
when once set in motion, will be able to sustain that motion equably; and it
will not be dithcult to give them a sufficient momentum, by a greater exer-
tion of the moving force, for a short space of time, at the beginning: and
this is in fact the true mode of operation of many machines where animal
strength is employed. Other forces, for instance those of wind and water,
regulate themselves in some measure, at least with respect to the relative ve-
locity of the sails and the wind, or the floatboards and the water ; for we may
easily increase the resistance, until the most advantageous effect is produced.
Many authors, considering the pressure of a stream of water as analogous to
the impulse of a number of unconnected particles, striking the floatboards»
and then ceasing to produce any further effect, have inferred, that the force
obtained by such an impulse must be as the square of the relative velocity^
and that the effect of an undershot wheel must be the mo&t advantageous,
when its velocity is one third of that of the stream : but it will hereafter ap-
pear, that this estimation of hydraulic force is by no means accurate. If we
compare the greatest velocity with which a man or a horse can run or walk
without fatigue, to the velocity of the stream, and the actual velocity of that
part of the machine to which the force is applied, to the velocity of the float-
boards of a water wheel, the strength which can be exerted may be repre-
sented, according to the experiments of some authors, by the impulse of the
stream, as supposed to be proportional to the square of the relative velocity ;
consequently the same velocity would be most advantageous in both cases,
and the man or horse ought, according to these experiments, to move, when
his force is applied to a machine, with one third of the velocity with which
he could walk or run when at liberty. This, for a man, would be about a
mile and a half an hour ; for a horse, two or three miles : but in general both
men and horses appear to work most advantageously with a velocity some-
what greater than this.

ON THE MOTION'S 01' CONNECTED BODIES. 91

Where a uniformly accelerating force, like that of gravitation, is employed
in machines, it might often be of advantage to regulate its operation, so that
it might act nearly in the same manner as the forces that we have been con-
sidering ; at first with greater intensity, and afterwards with sufficient power
to'sustain the equilibrium, and overcome the friction only. This might be done,
by means of a spiral barrel, like the fusee of a watch ; and a similar modifica-
tion has sometimes been applied, by causing the ascending weight, when it
-arrives near the place of its destination, to act on a counterpoise, which resists
it with a force continually increasing, by the operation of a barrel of the same
kind, so as to prevent the effect of the shock which too rapid a motion would
occasion.

On the whole, we may conclude, that on account of the limited velocity
which is usually admissible in the operation of machines, a very small por-
tion of the moving force is expended in producing momentum ; the velocity
of 3 miles an hour, would be generated in a heavy body, descending by its
own weight, in one seventh of a second, and a very short time is generally
sufficient for obtaining as rapid a motion as the machine or the nature of the
force will allow; and when this has been effected, the whole force is employed
in maintaining the equilibrium, and overcoming the resistance : so that the
common opinion, which has probably been formed without entering minutely
into the consideration of the subject, and which appears, when first we examine
its foundation with accuracy, to lead to material errors, is in great measure jus-
tified by a more profound investigation.

To seek for a source of motion in the construction of a machine, betrays a
gross ignorance of the principles on which all machines operate. The only
interest that we can take in the projects which have been tried for procuring a
perpetual motion, must arise from the opportunity that they afford us to ob-
serve the weakness of human reason; to see a man spending whole years in the
pursuit of an object, which a week's application to sober philosophy might have
convinced him was unattainable. The most satisfactory confutation of the
notion of the possibility of a perpetual motion, is derived from the considera-
tion of the properties of the centre of gravity: we have only to examine whe-
ther it will begin to descend or to ascend, when the machine moves, or whe-
ther it will remain at rest. If it be so placed, that it must either remain at

p2 LECTURE IX.

rest or ascend, it is clear, from the laws of equilibrium, that no motion derived
from gravitation can take place: if it may descend, it must either continue
to descend for ever, with a finite velocity, which is impossible, or it must first
descend and then ascend, with a vibratory motion, and then the case will be
reducible to that of a pendulum, where it is obvious that no new motion is
generated, and that the friction and resistance of the air must soon destroy
the original motion. One of the most common fallacies, by which the super-
ficial projectors of machines for obtaining a perpetual motion have been de-
luded, has arisen from imagining, that any number of weights ascending by
a certain path, on one side of the centre of motion, and descending in the
other, at a greater distance, must cause a constant preponderance on the side
of the descent : for this purpose, the weights have either been fixed on hinges
which allow them to fall over at a certain point, so as to become more distant
from the centre, or made to slide or roll along grooves or planes, which lead
them to a more remote part of the wheel, from whence they return as they
ascend: but it will appear on the inspection of such a machine, that although
some of the weights are more distant from the centre than others,^ yet there is,
always a proportionally smaller number of them on that side on which they
have the greatest power; so that these circumstances precisely couuterbalancci
each other. (Plate VI. Fig. 78.)

95

LECTURE X.

ON DRAWING, WRITING, AND MEASURING.

JEXAVING investigated all the general principles and laws of motion, and
of mechanical power, we may now proceed to the consideration of particular
departments of practical mechanics. But before we can satisfactorily compare
the various- forces, which we are to employ or to oppose, we must have some
mode of determining their magnitude; and we must begin by examining the
spaces which are measures of their action : a knowledge of the instruments
employed for delineation, and of the rules of perspective projection, is also
necessarily required, as a previous step in the study of practical mechanics. We
have therefore to consider, as preliminary subjects, first the arts which may be
expressed by the terms instrumental geometry, or the geometry of mechanics;
secondly, statics, or the mode of ascertaining the magnitude of weights, and
of other active forces; and thirdly, the examination of the passive strength of
materials of various kinds, and of the negative force of friction.

The art of drawing can scarcely be distinguished by any correct definitioa"
from painting. In its simplest state, when we merely imitate an original laid
before us, it is called copying; and in writing, we only copy the letters of the
alphabet. If we proceed in a mathematical manner in the operation of draw-
ing, we require a number of geometrical instruments, whicli are still more
necessary for the first construction of diagrams or figures. In modelling and
sculpture, a solid is simply imitated ; but when a solid is represented on a
plane, the principles of perspective are employed in determining the positioa
of the lines which are to form the picture. The productions of the arts of
drawing and writing are multiplied and perpetuated by means of engraving
and printing; inventions which have been the sources of inestimable advantage
in the instruction and civilisation of mankind.

§♦ , LECTURE X.

In drawing, we may employ the pen, the pencil, chalks, crayons, inks,
water colours, or body colours ; we may paint in miniature, in distemper, in
fresco, in oils, in varnish, in wax, or in enamel; and we may imitate the
effects' of painting, by mosaic work, or by tapestry.

The first step in copying a drawing, or in painting, is to procure a correct
outline : a master of the art can do this with sufficient accuracy, by such an
estimate of the proportions of the figures, as the eye alone enables him to
form ; especially if he be assisted by lines, which divide the original into a
number of squares, and enable him to transfer their contents to the corre-
sponding squares of the copy, which may in this manner be reduced, or en-
larged, when it is required. But a copy may sometimes be more expeditiously
made, by tracing immediately from the original, when the materials employed
are sufficiently transparent to admit the outlines to be seen through them ; or,
where the original is of no value, by pricking a number of points through it, so
as to mark the copy, either at once, or by means of charcoal powder inibbed
through the holes, which is called stenciling: and for this purpose, an inter-
mediate copy may be fonned on semitransparent paper. Another method is
to put a thin paper, rubbed with the powder of black lead, or of red chalk,
between the original and the paper intended for the copy, and to pass a blunt
point over all the lines to be traced, which produces correspondent lines on
the paper; this is called calking. Where the work is large, it may be cover-
ed with a thin gauze, and its outlines traced on the gauze with chalk, which
is then to be placed on the blank surface, and the chalk shaken off it, in the
way that a carpenter marks a board with his line.

The pen was formerly much used for making rough sketches, and it is still
sometimes employed for the same purpose, as well as for assisting the efiect of
the pencil. The appearances of uniform lights and shades must necessarily
be imitated in drawings with the pen, as well as engravings, by a mixture of
the whiteness of the paper, with the blackness or colour of the ink, the eye
being too remote to distinguish minutely the separate lines, by which the
effect is produced, although they do not entirely escape its observation. In
this respect, drawings in pencils and chalks have an advantage over engrav-
ings ; these substances, after being laid on in lines, are spread, by means of
rubbers, or stumps, of paper, leather, or linen, so as to produce a greater

ON DRAWING, WRITING, AND MJ^AStJRINS. f)5

uniformity of tint. Some, indeed, are of opinion, that engravings derive
a great brilliancy from the hatches that are employed in shading them, and
that minute inequalities of colour make every tint more pleasing. In draw-
ings with chalk, however, the advantage of rubbers is unquestionable. The
lines of a drawing may be made to have an appearance of greater freedom
than those of an engraving; they should be parallel, and when they are
crossed, moderately oblique to each other; their direction should be governed
by that of the outline. Engravings in mezzotinto exhibit no lines: but they
are deficient in spirit and precision: the effect of aqua tinta approaches much
nearer to that of drawing, and it has a similar advantage in the mode of pro-
ducing its liglits and shades. (Plate VI. Fig. 79.)

It is well known, that the best pencils are made of English black lead, or
plumbago. Of black chalks, the Italian is harder and more generally useful
than the French : red chalk has the disadvantage of not being easily removed,
either by bread or by Indian rubber, without leaving a brownish mark. All
these chalks are of the nature of a soft schistus or slate: they may be made
to adhere firmly to the paper, by dipping the drawings in milk freed from
cream, or even in water only, which dissolves the size or gum of the paper.
Sometimes a grey paper is used, which serves for a middle tint, and lessens
the labour, the lights and shades only being added in white and black chalks.

Crayons consist of colours mixed up with gum water, or other adhesive
substances, and usually also with some chalk, plaster, or pipe clay, so as to
be of a proper consistence for working in the manner of chalks. The prin-
cipal inconvenience attending them is their want of adhesion to the paper:
the paper must therefore not be too smooth.

For drawings washed in light and shade only, the materials employed are
Indian ink, the black liquor of the cuttle fish, or bistre, which is extracted
from soot: both these last produce a browner and richer tint than the Indian
ink. In using these washes, as well as water colours, there is a great diversity in
the methods of different artists: some work with a dry pencil, others with a
full one : some begin all their coloured drawings in black only, others use
colours from the beginning. When a full pencil is used, care must be taken
that no part of the same tint dry sooner or later than the rest. When body

56 ^ LECTURE X.

colours are employed, there is less difficulty in producing a uniformity of tint
than with water colours, each coat of the colour being laid on in sufficient
quantity to cover all that is below it without mixing: hence it becomes easier
to make any alterations that may be required. For water colours of all
descriptions, a certain quantity of gum is used, and sometimes a size made of
isinglass, with a little sugarcandy. Body colours contain less gum than other
water colours. Besides paper, wood, silk, and cotton velvet, are sometimes
used for drawings in water colours.

In miniatures, the most delicate tints are laid on in points, with simple water
colours ; but for the draperies, body colours are sometimes used. They are
commonly executed on ivory.

For painting in distemper, the colours are mixed with a size made by boil-
ing shreds of untanned leather, or of parchment, for several hours : this me-
thod is chiefly employed for colouring walls or paper, but sometimes for paint-
ing on cloth. For delicate purposes, the size may be made with isinglass.

When a wall or cieling is painted in fresco, the rough coat of the plaster
is covered with a coat of fine sand and lime, as far as it can be painted before
it is dry, the colours being partly imbibed by this coat, and thus becoming
durable. When they have been once laid on, no alteration can be made,
without taking off the last coat of plaster, and each part must be completed
at once ; it is therefore always necessary to have a finished drawing for a
copy ; this is visually executed on paper, and is called a cartoon. The colours
can be only of earths or metallic oxids ; they are prepared as for painting in
distemper. The only paintings of the antients, which have been preserved,
were executed in fresco.

The art of painting in oil was first discovered by Van Eyck of Bruges, to-
wards the end of the 14th century: it has now become almost the only man-
ner in which paintings of magnitude are performed. The colours are mixed
with linseed or nut oil, and sometimes with oil of poppy seed, together with
a small portion of oil of turpentine, to assist in drying them; and with the
occasianal addition of other oily and resinous substances. The work may be
fjxecuted on wood, cloth, silk, paper, marble, or metals: these substances

ON DRAWING, WRITING, AND MEASURING. 97

l>eing first washed with size, and then primed with an oil colour, which is usu-
ally white, but sometimes dark. Some painters have, however, preferred a
ground of distemper. The glare of the oil colours, or of tlie varnish, which
is added in order to give them brilliancy, is considered as an inconvenience
attending oil paintings; and some of the colours are too liable to fade or to
blacken by the effect of time.

The encaustic paintings of the ancients were imperfect approximations to
the art of painting in oil. Wax or resins were employed for retaining the
colours in their places ; and they were api)lied by means of a moderate heat.
An effect nearly similar is produced by dissolving the resins in spirits of wine,
as is done in painting in varnish. A much greater degree of heat is required
for paintings in enamel: for this purpose the colours are mixed with a glass
of easy fusion, and, when finely powdered, they are usually ap])lied with oil of
turpentine, or sometimes oil of lavender, to a ground of metal or porcelain; '
they are afterwards fixed and vitrified by exposure to the heat of a furnace.

Mosaic work is performed by putting together small pieces of stone, or
baked clay, of various colours, so as to imitate the effects of painting: in tapes-
try, and in embroidery, the same is done by weaving, or working in, threads of
different kinds.

The art of writing is of great antiquity, but it is probably in all countries,
and certainly in some, of a later date than that of drawing representations of
nature. The Mexicans, at the first arrival of the Spaniards in South America,
are said to have employed drawings as a mode of conveying intelligence;
some of them simply resembling the objects to which they related, others in-
tended as hieroglyphics ; that is, like the antient Egyptian characters, of a
nature intermediate between drawing and writing. The Chinese have always
used arbitrary marks to represent whole words, or the names of external ob-
jects, not resembling the objects to which they relate, nor composed of letters
appropriated to constituent parts of the sound, although they are said to be
combined froni a few hundred radical characters expressive of the most simple
ideas. The art of writing with alphabetical letters must have been suffici-
ently understood, in the age of Moses, to serve the purpose of the promulga-
tion of laws and of religion : it is generally supposed to have been invented

VOL. I. o

gS LECTURE X.

by the Phenicians. Among the Greeks it was in a very imperfect state until
the time of the siege of Troy, or about 3000 years ago. The Chinese write
from above downwards, beginning on the riglit side; the other eastern na-
tions have always written from right to left. The most ancient Greek in-
scriptions are turned alternately backwards and forwards, the letters being re-
versed in the lines which begin on the right side; but the Greeks soon con-
fined themselves to that mode, which has been since adopted by all European
nations, and which appears to be in itself the most natural, at least for writ-
ing with a pen, and with the right hand.

The earliest methods of writing were probably such as rather deserve the
name of engraving; the letters being cut in stone, in wood, on sheets of lead,
on bark, or on leaves. For temporary purposes, they were formed on tablets
of wax, with a point called a stile, and this practice was long continued for
epistolary correspondence, and was not wholly out of use in the fourteenth
century. The stile was made of metal or of bone; its upper extremity was
flattened, for the purpose of erasing what had been written. The Egyptian
papyius is said by Varro to have been first used for. writing, at the time of
the foundation of Alexandria; the leaves of palms, the inner bark of trees,'
or sometimes linen cloth, having been before employed. The exportation of
the papyrus was forbidden by Ptolemy, and in consequence of this prohibition,
skins of parchment, or of vellum, were first applied to the purpose of writing
at Pergamus, for the library of king Eumenes, whence they were called mem-
brana pergamena. To make the best paper, the widest and finest leaves of the
papyrus were matted together, united b}' a vegetable glue, and pressed till
they became sufficiently smooth; the coarser kinds were not used for writing,
but for commercial purposes. In China, paper is sometimes made of a thin
and almost transparent membrane taken from the bark of a tree. Paper of
cotton was introduced into Europe from the east in the middle ages : it has
been since superseded by that which is made of linen rags, and which is also
an eastern invention ; but for coarse and strong paper, old ropes of hemp are
also used ; and sometimes many other vegetable substances have been employed.
The strength and consistence of paper is owing to the lateral adhesion derived
from the intermixture of the fibres, assisted by the glutinous size, which is
also of use in obviating the bibulous cpiality of the paper, by filling up its
pores.

2

ON DRAWING, WRITING, AND MEASURING. 99

Ivory, and prepared ass's skin, are sometimes employed for writing with a
black lead pencil; for slates, a pencil of a softer kind of slate is used. The
ancient mathematicians usually constructed their diagrams on sand for the in-
struction of their pupils.

Pens of 'goose quills, swan's quills, or crow quills, were known as early as
the seventh century : in Europe they have generally superseded the reeds,
which were employed for Avriting by the ancients: but in India, reeds, canes,
and bamboos, are still in use. In China a hair pencil is used instead of a pen.

The inks of the ancients arc said to have been made of a carbonaceous sul)-
stance, and the modern Indian ink owes its blackness to similar materials.
Common writing ink consists of a gallate of iron, suspended by means of a
little gum; the sulfuric acid, which remains mixed with it, is probably of no
consequence to its blackness. It has been observed, that an abundance of
the gallic acid produces a much blacker colour, than is obtained where this acid
is used in a smaller proportion. Mr. Kibaucourt's method of making ink, is
to boil eight ounces of galls, and four of logwood, in twelve pounds of water,
until the quantity is reduced to one half; and, having strained the decoction,
to add to it four ounces of sulfate of iron, one of sulfate of copper, three of
gum arable, and one of sugar candy. But for ordinary purposes, it is sufficient to
infuse three ounces of galls for a day or two in a pint of water, and to add to
it an ounce of gum arable, half an ounce of green sulfate of iron, or cop-
peras, and a drachm of sulfate of copper, or blue vitriol, or even a much
smaller quantity of gvim and of copperas, if a very fluid ink is required. The
sulfate of copper produces a durable stain, but it does not immediately add
to the blackness of the ink: its principal use is to counteract the tendency of
the ink to become mouldy. Sometimes a mercurial salt is employed for the
same purpose, and a little cotton, if the inkstand is too open, is also useful in
preserving the ink ; but the addition of spirits is often insufficient, and is liable
to make the ink run.

It has been proposed to use inks of diffiL'rent colours for indicating different
lumibcrs; so that by ten kinds of ink applied in different ways, any numbers
at pleasure might be expressed. Thus, in making an index of the words of an
author, each page might be readily covered with lines of different colours

100 LECTURE X.

drawn in clIfFerent directions, so that each Avord, when cut out, might indicate
the page to which it belongs.

An ingenious instrument has lately been constructed, by means of which
copies may be multiplied with great facility ; it is called the polygraph, and
consists of two or more pens, so connected by frames and springs, as to move
always in parallel directions, each having an inkstand and a sheet of paper for
itself. In this manner five copies may be made at once with tolerable facility,
and themethod may perhaps hereafter be extended to a much greater number.

A mode of Avriting, perfectly different from any of those which have been
mentioned, is performed by means of the telegrapli, which is justly consider-
ed as the invention of the ingenious Dr. Hooke. The ancients had attempted
something similar, by the exhibition of torches on elevated situations; but Dr.
Hooke observes, that the addition of the telescope is absolutely necessary for
the practical success of the process ; and the directions which he gives for its
performance differ very little from the plan which has since been generally-
adopted, first in France, and afterwards, with some variations, in this coun«
try. Dr. Hooke proposed the employment of alphabetical and other arbitrary-
characters ; at present it is usual to have six boards, each turning on its axis
■so as to appear or disappear at pleasure: these admit of sixty four combina-
tions, which, are sufficient, besides indicating the letters of the alphabet, for
every other purpose that can be required. (Plate VI. Fig. 80, 81.) .

Pens for drawing lines and figures differ sometimes from those which are
used for writing; they are made of two plates of steel inclined to each other
and adjusted by a screw; or sometimes of a plate of tin folded up, so as ta
include a receptacle for the ink ; or of a glass tube drawn to a very fine point,
and still remaining perforated. In all these pens, as well as in common,
pens, the ink is retained by its cohesion, and by the capillary attraction of the.
pen ; and it attaches itself to the paper by the operation of similar powers.

It is by no means easy to comply strictly with that postulate of geometry,
which requires us to draw a straight line from one point to another. The
edge of a ruler is made straight by the instrument called a plane, which is.
worked with a considerable velocity, and therefore naturally tends to move in

ON DRAWING, WRITING, AND MEASURING. 101

a right line, besides that it is guided by the flatness of its lower surface. We
judge of the straightness of a line, by means of the well known property
of light, which moves only in right lines, so that if we look along the edge
of a ruler, we easily discover its irregularities ; and this may be done with
still greater accuracy,, if we look through a small hole made with a pin in a
card. Rulers of silver, bniss) or ivory, have a material advantage over those
of wood, as they are not liable to be spoilt by warping, A pen filled with
ink cannot be applied close to the edge of a ruler without inconvenience ; it
is therefore best, for diagrams which require great accuracy, to draAV the
lines first with a steel point, or a very hard black lead pencil, and to finish
them with ink if necessary. The paper should also be fixed on a drawing
board; and plates of lead or copper may be employed, instead of paper, for
very delicate purposes. The carpenter's chalk line is a useful instrument for
supplying the place of a very long ruler; it becomes straight when it is
stretched, because a right line is the shortest distance between any twa-
points.^

For drawing a circle of a gfven radius, we use compasses, with one pofnt
generally of metal, the other of various descriptions. Compasses are some-
times made with a spring, instead of a joint, and opened or shut by a screw:
sometimes a graduated arc is fixed in one leg, and passes through the other;
and when great accuracy is required, hair compasses may be employed, having
ajoint with a spring in one of the legs, which is bent a little by means of a
fine screw. Beam compasses are useful for drawing circles of larger radii :
they have also the advantage of being steadier than the common compasses,,"
and of admitting readily the application of a graduated scale, so as to indi-
cate the measure of the radius of the circle which is described. Sometimes,
for drawing portions of very large circles, two wheels, differing a little in dia-
meter, are fixed on a common axis, and thus made to revolve round a point,
which is more or less distant, accordingly as the wheels are set at a greater or
less distance on the axis, the surface of the wheels tracing the circles on the
paper; or two rulers joined together, so as to form an angle, are made tojslide
against two points, or edges, projecting from a third ruler, so that the angular
point remains always in the arc of a circle. The same effect may be produced,
somewhat more commodiously, by means of a thin piece of elastic wood,
which is made to assume any required curvature, by the action of screws, appli^

102 LECTURE X.

ed to difterent parts of its concavitj' : it would, however, be more simple and
accurate to employ only one screw, in the middle of the arc, and to make
the flexible ruler, or bow, every where of such a thickness, as to assume a cir-
cular form in its utmost state of flexure: it would then retain the circular
form, without a sensible error, in every other position. (Plate VI. Fig.
82 . . 85.)

For drawing a line perpendicular to another, we often employ a square ;
and if we use a rectangular drawing board, there is an additional convenience
in making the square to slide on its margin. Rulers also, of various descrip-
tions, are commonly made rectangular, in order to answer occasionally the
same purpose.

Triangular compasses are sometimes used, for laying down a triangle equal
to a given triangle; and by repeating the operation, any figure, which can be
divided into triangles, may be copied without the intersection of arcs: but the
same end is more commonly obtained, by pricking off the figure with a steel
point. (Plate VI. Fig. 86.)

Various properties of parallel lines are employed in constructing parallel
rulers: a parallelogram with jointed angles is the most commonly used; two
equal rulers being united by equal cross bars placed in an oblique position,
and turning on pins fixed in the rulers: the instrument is much improved by
adding a third ruler, similarly united to the second, for then the oblifjuity of
one of the two motions may be made to correct that of the other. A simple
cyhnder, or a round ruler, answers the purpose in a rough manner, and two,
small rollers, fixed on the same axis, are also sometimes attached to a flat
ruler, and cause it to move so as to be always in parallel positions. A very
useful instrument for drawing parallel lines, at any given distances, is now
generally known by the name of Marquois's scales, although it is by no means
of late invention ; by sliding a triangle along a graduated ruler, we read off
the divisions on an amplified scale with great accuracy; but where the dis-
tances of the lines are great, the obliquity of this motion is a considerable
inconvenience. The ruler or square of the drawing board affords us lines
parallel to each other, in a certain position; and if it be made with a joint,
,or as the workmen call it, bevilledj it may be employed for the same purpose,

ON DRAWING, WRITING, AND MEASURING. 103

in all other directions. The systems of lines, on which music is written, are
drawn at one stroke by a pen with five orifices, usually made of brass. It
was long since proposed to rule a whole page at once, with a more complicat-
ed pen of the same kind, and the greatest part of the paper, on which music
is written in this country, is actually ruled by such a machine, for which a
patent has been taken out. (Plate VI, Fig. 87, 88.)

The pantograph is used for copying figures, and at the same time reducing
or enlarging them; it consists of four rulers, two of them united by a joint at
the extremities, and receiving at the middle the other two, which are but
half as long, and are also united together, so as to form with the others a
jointed parallelogram, of which {wo of the sides are produced beyond the
angles ; if holes be made in these, and in one of the shorter rulers, so situated
as to be in the same right line in any position of the instrument, they will
remain in a right line in any other position, and they will always divide this
line in the same proportion : so that if one of the holes be placed on a fixed
axis or pin, a tracing point inserted in another, and a pencil in the third,
any figure delineated b\ the pencil will be similar to that which is described
by the tracing point. And instead of holes in the rulers, they may be fur-
nished with sliding sockets, to receive the axis, the point, and the pencil,
(Plate VI. Fig. 89.) .:' '

Proportional compasses are also of great use, in reducing lines and figures to . "' *^ '
a difterent scale. This instrument consists of two legs, pointed at each end,
and turning on a centre, which slides in a groove common to both legs, and is
furnished with an index. The divisions of the scale are so laid down, that
the centre may divide the length of the legs from point to point in a given
proportion; hence, by the properties of similar triangles, when the legs are
opened to any extent, the intervals between each pair of points must be to
each other in the same ratio as the portions of the legs. Sometimes a screw
is added, for the sake of adjusting the centre with greater accuracy; and it is
usual to lay down scales for dividing the circumference of a circle into a
given number of parts, and for some other purposes; but the irrstrument
might be much improved by inserting, in the common scale, fractional or de-
cimal divisions, between the whole numbers, so that the legs might be di-

^-

104 LECTURE X.

vided,for example, in the ratio of 2 to 3, 3 to 4, or 4 to 5, or of 10 to 1 1, !S
oris, at pleasure. (Plate VI. Fig. 90.)

The use of the sector depends also on the properties of similar triangles. The
scale of equal parts, which is laid down on each leg, beginning from the cen-
tre, serves to determine the length of the legs of two equilateral triangles,
in any required proportion to each other, according to the division which we
mark, and the transverse distances from the corresponding points are neces-
sarily in the same proportion. Thus, if we have any line in a figure which we
wish to call three feet, or three inches, we may take the interval with a pair
of common compasses, and open the sector to such an angle, that it may ex-
tend from the third division of one leg to that of the other ; then all the other
divisions of the scale will furnish us with the lengths corresponding to any
distances that we may wish to lay down. The other scales usually engraved
on the sector are principally intended for trigonometrical calculations on
similar principles. (Plate VII. Fig. 91.)

The mag-nitude of angles admits an easy determination and description, by
the comparison of the respective arcs with a circle, or with a right angle.
We may divide an angle geometrically, by continual bisection, into parts as
small as may be required, and by numbering these parts, we may define any
angle, with an error smaller than any assignable quantity. Bisections of
this kind are sometimes actually employed in the construction of instruments;
for instance, in one of the arcs of the mural quadrant of the observatory at
Greenwich, the right angle is divided into 96 parts, by the continual bisec-
tion of one sixth of the circle. There arc also some practical methods of di-
viding angles into three or more equal parts, which are sufliciently accurate
for many purposes, although it is well known that in theory the perfect tri-
section of an angle is beyond the reach of plain geometry. This trisection is,
necessary in the common division of tlie circle into 360 degrees, a number
which was probably chosen because it admits a great variety of divisors, and
because it nearly represents the diurnal and annual motion of the sun among
the stars. The circle being^ divided into 6 parts, the chord of each of which
is equal to the radius, these parts are divided into 60 degrees, each degree
into 60 minutes, and each minute into 60 seconds : further than this we can-

Oy DRAWING, WETTING, AND MEASURING. 105

not easily carry the accuracy of our determination, although, in calculations,
we sometimes descend as far as tenths or even hundredths of a second. The
decimal division of a right angle, which has been lately adopted in France,
appears to have very little advantage for the purposes'^ of calculation, beyond
the common method, and its execution in practice must be much more
ditHcult.

Whole circles, or theodolites, divided into degrees and their parts, quadrants
and sextants, are usually employed in measuring angles; and protractors, se-
micircles, and lines of chords, in laying them off. The most convenient of
quadrants for general use is Hadley's reflecting instrument, which is in fact
an octant or a sextant, but in which, for reasons depending on optical prin-
ciples, each degree of the arc is reckoned for twc

For the graduation of all instruments of this kind, of moderate dimensionSy
Mr. Ramsden's dividing engine is of great utility ; the instrument being fixed
on the revolving plate of the engine, its arc is made to advance under the
cutting tool by very minute steps, regulated by the turns of a screw, of which
each revolution is divided into a considerable number of equal parts. The
largest and finest instruments are, however, still usually divided by hand,
that is, by means of compasses. Some artists have first divided a straight
plate, and then made a hoop of it, which has served as a standard for further
processes. An arc of J° 10', of which the chord is one eighth of the radius,
may be employed as a test of the accuracy of the work. A micrometer screw .
is often used in large instruments as a substitute for the minutest divisions; a
moveable part of the index being brought to coincide with the nearest point
marked in the arc, by turning the screw through a part of its revolution,
which is measured by means of a graduated circle. But a simpler method of
reading off divisions with accuracy in common instruments, is the application
of a vernier, an apparatus so called from its inventor. The space occupied
by eleven divisions of the scale being divided into ten parts on the index, the
coincidence of any of the divisions of the index with those of the scale,,
shows, by its distance from the end, the number of tenths that arc to be added
to that of the intire divisions. (Plate VII. Fig, 92.)

There are several ways of measuring the angular elevation of an object

YOL. I. B

106 LECTURE X.

above the horizon; at sea, the apparent horizon, formed by the surfiice of the
water, affords the most convenient determination ; but since the spectator is
somewhat elevated above the convex surface of the sea, the apparent horizon
is necessarily lower than the true horizon, and a correction is therefore re-
quired according to the height. In the open sea this correction may be de-
termined by measuring the whole angle above and below the apparent horizon,
and taking one fourth of the difference for the dip or depression. On shore,
a plumb line is the simplest instrument for determining the situation of the
horizon, and its accidental vibrations may be prevented by suspending the
weight in water or in oil. For small instruments, a spirit level, of which the
operation depends on hydrostatical principles, is capable of greater delicacy
than a plumb line. It readily indicates, when well made, an error of a single
second, but it requires some attention to avoid inequalities of temperature,
which would, tend to disturb its figure. Well rectified ether is found, on ac-
count of its perfect fluidity, to be the best liquid for a spirit level. An arti-
ficial horizon is a reflecting surface, employed for obtaining an image, as much
below the horizon, as the object is above it, and for measuring the angular dis-
tance of this image from the object : sometimes a plane speculum of glass or
metal is used for this purpose, being previously adjusted by a spirit level ; and
sometimes the surface of mercury, treacle, or tar, protected from the wind by
a vessel with holes in it, or by a glass cover, either detached, or simply
floating on the mercury, when this liquid is employed.

It is in many cases simpler and more convenient to estimate angles, not by
the arcs subtending, them, but by their sines, or the perpendiculars falling
from one leg on the other. Thus, it is usual among miners, to say that the
ground rises or falls one foot, or one yard, in ten, when the sine of the angle
of its inclination to the horizon is one tenth of the radius. Angles of different
magnitudes are indeed proportional to the arcs, and not to the sines, so that
in this sense the sine is not a true measure of the comparative magnitude of
the angle; but in making calculations, we are more frequently obliged to em-
ploy the sine or cosine of an angle than the angle or arc itself. It is, how-
ever, easy to pass from one of these elements to the others by means either of
trigonometrical tables, or of the scales engraved on the sector.

The sines, tangents, and secants laid down on the sector, may be employed

ON DRAWITffO, WRITING, AND MEASURING. lOT

according to the properties of similar triangles, in the computation of propor-
tions. The same purpose is answered by Gunter's scale, by the sliding rule,
and by the logarithmic circles of Clairaut and of Nicholson, which are cm-
ployed mechanically in the same manner as a table of logarithms is used arith-
metically, the proportion of any two numbers to each other being determined
by the distance of the corresponding divisions on the scale; so that if we wish
to double or to halve a number, we have only to find the distance from 1 to 2,
and to lay it off from the given number either way. (Plate VII. Fig. 93, 94.)

The measurement of angles is at once applied to the estimation of distances
in the dendrometer or engymeter; a part of the instrument forms a base of
known dimensions, and the angle at each extremity of this base being mea-
sured with great accuracy, the distance of the object may be inferred from an
easy calculation, or from a table. The most complete instruments of this
kind have two speculums for measuring the difference of the angles at once,
in the manner of Hadley's quadrant. Telescopic scales or micrometers are
also sometimes used for measuring angles subtended by distant objects, of^
which the magnitude is known or may be estimated, for example, by the
height of a rank of soldiers, and inferring at once the distance at which they
stand. '

Arithmetical and even algebraical machines, of a much more complicated na-
ture, have been invented and constructed with great labour and ingenuity; but
they are rather to be considered as mathematical toys, than as instruments
capable of any useful application.

An angle, when once measured, can be verbally and numerically described,
by reference to the whole circle as a unit : but for the identification of the
measure of a right line, we have no natural unit of this kind, and it is there-
fore necessary to establisli some arbitrary standard with which any given
lengths and surfaces may be compared. It might be of advantage in the com-
munication between different countries to fix one single standard to be em-
ployed throughout the world, but this does not appear to be practically pos-
sible, even if it were determined what the standard ought to be. " The ob-
servation of the isochronism of the small vibrations of a pendulum, and the
ease and certainty with which the length of a pendulum vibrating secomls-

108 LECTURE X.

may be ascertained, have suggested," says Mr. Laplace, in his account of
the system of the world, " the idea of employing this length as a universal
measure. We cannot reflect on the prodigious number of measures in use,
not only among different nations, but even in the same country, their ca-
pricious and inconvenient divisions, the difficulty of determining and com-
paring them, the embarrassment and the frauds which they occasion ,in com-
merce, without regarding, as one of the greatest benefits, that the improve-
ments of the sciences and the ordinances of civil governments can render to
humanity, the adoption of a system of measures, of which the divisions, being
uniform, may be easily employed in calculations, and which may be derived,
in a manner the least arbitrary, from a fundamental magnitude indicated by
nature itself. A nation that would introtluce such a system of measures,
would unite to the advantage of reaping the first fruits of the improvement,
the pleasure of seeing its example followed by other countries, of which it
would thus become. the benefactor: for the slow but irresistible empire of
reason must at length prevail over national jealousies, and over all other ob-
stacles that are opposed to a measure, of which the convenience is universally
felt, -Such were the motives that determined the constituent assembly to in-
trust tlifi Academy of Sciences with this important charge. The new system
of 'weights and measures is the result of the labours of the Committee, seconded
by the zeal and information of several members of the national representa-
tion.

" The ideiitity of the calculation of decimal fractions and of whole num-
bers, leaves no doubt with respect to the advantage of the division of mea-
sures of all kinds into decimal parts: it is sufficient^ in order to be convinced
of this, to compare the difficulty of compound multiplication and division,
with the facility of the same operations where whole numbers only are con-
cerned, a facility that becomes still greater by means of logarithms, of which
the use may also be rendered extremely popular by simple and cheap instru-
ments. The decimal division was therefore adopted without hesitation; and
in order to preserve the uniformity of the whole system, it was resohed to
deduce every thing from the same linear measure, and its decimal divisions.
The question was then reduced to the choice of this universal measure, to
v/liich the name of metre was to be given.

ox DRAWING, WRITING, AND MEASURING. IOl>

" The length of the pendulum, and that of a meridian of the earth, are the
two principal standards thdt nature affords us, for fixing the unit of linear
measures. Both of these being independent of moral revolutions, they can-
not experience a sensible alteration without very great changes in the physical
constitution of the earth. The first method, which is of easy execution, li?,s
the inconvenience of making the measure of length depend on two elements,
heterogeneous with respect to itself and to each other, gravitation, and time ;
besides that the division of time into small portions is wholly arbitrary. ' It
was resolved, therefore, to employ the second method, which, " says Mr. La-
place, " appears to be of very high antiquity; it is so natural to man to refer
measures of distance to the dimensions of the globe which he inhabits, in
order that, in transporting himself from place to place, he may know, by the
denomination of the space passed through alone, the relation of this sj)ace to
the entire circumference of the earth. This method has also the advantage of
making nautical measures correspond at once with celestial ones. The navi-
gator has often occasion to compare with each other the distance that he has
passed over, and the arc of the heavens corresponding to that distance; it is
therefore of consequence that these measures should be readily obtained from
each other, by altering only the place of the units. But, for this purpose,
the fundamental unit of linear measures must be an aliquot, part of the ter-
restrial meridian, which must correspond to one of the divisions of the circum-
ference of a circle. Thus the choice of the metre was reduced to that of the
xmit of angular measure, and the right angle, as constituting the limit of the
inchnation of two lines to each other, was considered as entitled to the pre-
ference.

" The arc, Mdiich was measured in 1740, from Dunkirk to the Pyrenees,
might have served for finding the magnitude of the quadrant of the meridian ;
but a new and more accurate measurement of a larger arc was more likely to
excite an interest in favour of the new measures. Delambre and M^chain
were therefore intrusted with the direction of the operations for measuring
an arc from Dunkirk to Barcelona, and after making a proper correction for
the ellipticity of the earth, according to the measurement of the arc in Peru,
the quadrant was determined to be equal to 5130740 of the iron tojse used at
the equator, its temperature being 6] ■^° of Fahrenheit: the ten millionth part

110 LECTURE X.

of this quadrant was taken for the unit or metre. A standard was deposited
in the custody of the legislative body, adjusted at the temperature of melting
ice. In order to be able always to identify this length, without recurring to
an actual measurement of the arc, it was of importance to compare it very
accurately with that of the pendulum vibrating seconds, and this has been
done with great care by Borda, at the observatory of Paris. The unit of mea-
sures of land is the are, or 1 00 square metres : a cubic metre of wood is called
a stere, and a cubic decimetre, or a cube of which the side is one tenth of a
metre, is a litre, or measure of fluids.

" Uniformity appeared to require that the day should be divided into ten
liours, the hour into a hundred minutes, and the minute into a hundred se-
conds. This division, useful as it will be to astronomers, is of less advantage
in civil life, where arithmetical operations are seldom performed on the parts
of time ; and the difficulty of adapting it to clocks and watches, together
with our commercial relations with foreign countries, have suspended its in-
troduction for the present. We may, however, expect that it will ultimately
be brQught into general use."

Such is Mr. Laplace's account of the new system of measures, the result of
the joint labours of many of the ablest mathematicians on the continent.
There is not at present any great probability that it will ever be employed in
this country. It is of little consequence from what the original unit has been
derived, unless we can with ease and accuracy recur to its origin: and whe-
ther a standard has been first adjusted according to the circumference of tiie
globe, or to the foot of an individual hero, the facility of comparing other
measures with it is the same. It is confessed that the pendulum affords the
readiest method of recovering the standard when lost; and if it was necessary
for the Committee of the French Academy to determine a unit absolutely
new, it would perhaps have been more eligible to fix on one which was inde-
pendent of any ulterior comparison, than to seek for an ideal perfection in at-
tempting- to copy from a more magnificent original : to say nothing of the un-
certainty with regard to the ellipticity of the earth, and the probable irregu-
larity of its form in various respects. On the other hand, it must be allowed,
that the correct determination of the length of the pendulum has sometimes

ox DRAWING, WRITING, AND MEASURING. Ill

been found more difficult than Mr. Laplace's statement would lead us to sup-
pose it, and we cannot depend on any measurement of it as totally exempt
from an error of the ten thousandth part of the whole.

• The metre, as definitively established by the government of France, is equal
to 39',i^^ English inches, measured, as it has been usual in this country,
on a standard scale of brass, at the temperature of 62° of Fahrenheit; while
the French, on the contrary, reduce the length of their measures to that
which they would acquire at the'freezing point. Hence ten thousand inches
are nearly 254 metres, a thousand feet 305 metres. The length of the pen-
dulum vibrating seconds in London, was found by George Graham, from a
mean of several experiments, all agreeing very nearly together, to be 39-r^
inches. This is also nearly a mean between the length which may be de-
duced, with proper corrections, from Borda's experiments at Paris, and Mr.
Whitehurst's experiments made in London, with the apparatus invented by
Mr. Hatton, where the length ascertained is the diiference between the lengths
of two pendulums vibrating in different times. Mr. Whitehurst's measures,
however, require some corrections, which Mr. Nicholson has pointed out.
The fall of a heavy body in the first second appears, from this determination
of the length of the pendulum, to be sixteen feet one inch and a tenth.

Of the old French measure, 15 inches made nearly 16 English, and 76,
very exactly, 81 ; the toise was 76 -,^0^ inches. In Germany the Rhinland
foot is generally used ; 100 of these feet make 103 English.

A wine gallon contains 231 cubic inches; an ale gallon is the content of
10 yards of a cylindrical inch pipe.

A variety of instruments are used for the immediate comparison of the
standard measure, or its parts, with other lengths or distances. Such arc
scales, simple and diagonal, verniers, micrometer screws, beam compasses,
rods, lines, chains, and measuring wheels. The greatest accuracy has ge-
nerally been supposed to be obtained, in large distances, by means of rods,
made of glass or of platina, in order to be less susceptible of such changes as
are produced by variations of temperature; General Roy, however, found
that a steel chain was as little liable to error, as any mode that he could em- ,

112 LECTURE X.

ploy; and those whq have continued the extensive survey which he began,
even prefer it to every other. For the comparison of standards, and for de-
termining small distances with great precision, beam compasses, or scales
with sliding indices, furnished with microscopes and cross wires, have been
constructed by the artists of this country : in France, a lever has sometimes
been introduced, its longer arm having an ample range of motion, corres-
ponding to a very minute difference in the length of the substance which
acts on the shorter arm. But for common purposes the diagonal scale is suf-
ficiently accurate, and may be applied without the error of the thousandth
of an inch: in cases where a very delicate vernier, or a micrometer screw is
applied, a magnifier is usually required. Mr. Coventry has, however, suc-
ceeded in making simple scales, which are accurate enough to measure the ten
thousandth of an inch. lie draws parallel lines on glass, at this distance,
which are in some parts sufficiently regular, although they can only be seen
by the help of a powerful microscope : but those which are at the distance of
the five thousandth of an inch are much more correct and distinct. For di-
viding rectilinear scales of all kinds, ]\Ir. Ramsden constructed a machine
which acts by the turns of a screw: others have employed an apparatus re-
sembling Marquois's parallel rulers. (Plate VII. Fig. 95 . . 97')

The motion of a ship at sea is measured by a log line, or a rope divided by
knots into ecjual parts, and attached to a log, which is retained nearly at rest
by the resistance of the water. Attempts have also been made to cause a
little waterwheel to turn by the motion of the ship, and to measure both the
rate and the distance run ; and an instrument has been invented for doing
the same upon hydraulical principles; raising the water of a gage to different
heights, by means of the pressure occasioned by the relative motion of the
jship and the water, and discharging at the same time a small stream into a
reservoir, with a velocity proportional to that of the sliip.

rn

LECTURE XL

ON MODELLING, PERSPECTIVE, ENGRAVING, Aljijy

PRINTING.

\y E have examined die principal instrupicnts and materials employed for
<lra>yingand for measuring; we ^ve now to consider, fust, the methods of co-
pying solids, and of projecting their images on a plane surface ; 5ind secondly,
the arts of perpetuating the works of the pen and of the pencil by engraving
and printing.

When it is required to make a copy of a solid >of an irregular form, as, for
.^xample, of a sta.tue, we jnust xletexmine the situation of a sufficient number
of points to guide uS in our work with accuracy, by means of an instrument
■capable of being fixed in any required situation, so that the extremity of a
sliding bar, or pin, may be in contact with each point in the original, and
then removed to a similar pait of another frame, on which the copy is placed,
a perforation being made, by degrees, in the block, so as to suffer the pin to
arrive at its proper place, at which it stops. (Plate VII. Fig. 98.)

The model of a statue is generally first made of clay, and a cast of this
taken immediately in nlaster of Paris, since the clay would crack and change
its form in drying. This mode of copying, by means of plaster, is exceed-
ingly useful in various departments of the mechanical arts: the original is
well oiled and placed in a proper vessel ; a mixture of prepared plaster and
water, of the consistence of cream, is then poured on it; this in a short time
hardens, and is divided into several parts, in such a manner as not to injure
the original figure in its removal. These pieces, being again united, fornv a
mould for the ultimate cast. Sometimes a small figure is first modelled in a
mixture of wax, turpentine, and oil; and a mould being formed on this,
VOL. r. ■ Q,

!I4 LECTURE XI.

the ultimate cast is made either of plaster, or of a composition pf wax with
white lead and a little oil, which serves as an imitation of marble.

We have, however, much less frequent occasion to make an exact copy of
a solid of an}' kind, than to represent its appearance by means of perspective
delineation. Supposing ourselves provided with proper materials for drawing,
we may easily imitate, with the assistance of a correct eye, and a hand well
exercised, the figures and relative positions of objects actually before us, by
delineating them in the same form as they would appear to be projected on a
transparent surface placed before the eye. Considering the simplicity of this
process, it is almost surprising that the doctrine of perspective should have
been supposed to require a very serious study, and that material errors should
have been committed with respect to it, by men whose general merits -in
other departments of painting is by no means contemptible. But it must be
confessed, that when, instead of imitating objects immediately before us, the
pencil is employed in embodying imaginary forms, calculated either for beauty
or for utility, a great degree of care and attention may be necessary, in order"
to produce a true representation of objects, which are either absent, or have
no existence: and here memory and fancy only will scarcely ever be suffi-
cient, without a recurrence to mathematical principles. To architects there-
fore, and to mechanics in general, a knowledge of perspective is almost in-
dispensable, whenever they Avish to convey, by a drawing, an accurate idea of
their projected works.

If any assistance be required for the delineation of an object actually before
MS, it may easily be obtained in a mechanical manner, by means of a frame
with cross threads or wires, interposed between the eye and the object. The
eye is applied to an aperture, which must be fixed, in order to preserve the
proportions of the picture; and which must be small, in order that the threads
and the more distant objects may be viewed at the same time, with suffici-
■ ent distinctness. The paper being furnished with corresponding lines, we
may observe in what division of the frame any conspicuous point of the ob-
ject appears, and may then represent its image by a point similarly situated
among the lines drawn on our paper; and having obtained, in this manner,
a suflicient number of points, we may complete the figures by the addition of

ON MODELLING, PERSPECTIVE, EKGUAVING, AND PRINTING. 115

proper outlines. Sometimes, for the delineation of large objects requiring
close inspection, it has been found useful to employ two similar frames, the
one a little smaller than the other, and placed at a certain distance from it, so
that every part of the object, when seen through the corresponding divisions
of both frames, appears in the same manner as if the eye were situated at a
very remote point. It was in this manner that the elegant anatomical figures
of Albinus were executed. (Plate VII. Fig. 99.)

But if it be required to lay down, in the plane of a picture, the projection
of an object, of which the actual dimensions and situation are given, we may
obtain the requisite measures from the properties of similar triangles, and the
consideration of the rectilinear motion of light. We may consider our picture
as a reduced copy of a projection formed on an imaginary plane, which, a.»
well as the picture, is generally supposed to be in a vertical situation, and
which stands on the horizontal plane, at the point where the objects to be
represented begin. In order to find the position of the image of a given
right line, we must determine the point in which a line parallel to it, passing
through the place of the eye, cuts the plane of the picture; this is called the
vanishing point of the given line, and of all other lines parallel to it, since
the image of any such line, continued without limit, will be a right line di-
rected to this point, but never passing it. When the lines to be represented
are parallel to the picture, the distance of their vanishing point becomes in-
finite, and their images are also parallel to the lines and to each other. The
centre of the picture, or that point v/hich is nearest to the eye, is the vanish^
ing point of all lines perpendicular to the picture; through this point it is
usual to draw a horizontal and a vertical line: we may then lay off downwards
on the vertical line the distance of the eye from the picture, in order to find
the point of distance, which serves to determine the position of any oblique
lines on a horizontal plane: for if we draw a ground plan of any object, cou-
siderijig the picture as a horizontal surface, we may find the vanishing point
of each of it s lines, by drawing a line parallel to it through the point
of distance, until it meets the horizontal vanishing line. (Plate VII.
rig. 100, 101.) ,

In order to find the position of the image of a given point of a line, wc
must divide the whole image in such a manner, that its parts may be to each

Il6 LECTURE Xr.

other, in tlie same proportion as the distance of the given point, and of tl)e
eye, from the plarie of projection. This may be readily done, when a ground
plan has been first made, by drawing a line from any point in the plan, to
the point of distance, which will cut the whole image of the line in the poitit
required. (Plate VII. Fig. 102.)

When it is required to determine a point in a line parallel to the picture,
we may suppose a line to be drawn through it perpendicular to the picture,
and, by finding the image of this line, we may intersect the former image in
the point required. It is thus that the height of any number of columns, or
'figures, at different distances, may be readily determined. (Plate VIIL
rig. 103.)

The projection of curvilinear figures is most conveniently effected, by draw-
ing across them parallel lines, which form small squares or rectangles, throwing
these divisions into perspective, and tracing a curve through the correspond-
ing points. There are also methods of determining mathematically, or of
drawing mechanically the ellipsis, which results from the projection of a circle,
in a given position, but they are considerably intricate, and a steady hand is
seldom in want of them. (Plate VIII. Fig. 104.)

This system of perspective must necessarily be employed when we wish to
represent objects, which appear to us under angles of considerable magnitude,
and to give them as much as possible the appearance of an imitation of nature.
But for almost all purposes of science, and of mechanical practice, the most
convenient representation is the orthographical projection, where the distance
of the eye, from the plane, is supposed to be increased without limit, and the
rays of light passing to the eye to be parallel to each other. In order to re-
present any object in this manner, we must assume one line for the direction
of the centre of the picture, to which the images of all lines perpendicular to
the plane of projection must be parallel, and another for that of the point of
tlistance, by means of which we may measure the first lines, as if that point
were actually within reach; and in this manner we may determine the place
of any number of points of the object to be delineated. (Plate VIII.
Fig. 105.)

ON MODELLING, PERSPECTIVE, ENGRAVING, AND PRINTING. 117

If we wish to apply the mechanical method of drawing by the assistance
of a frame to this mode of representation, instead of a fixed aperture for a
sight, or a second frame of smaller dimensions, we must employ a second ,
frame of the same magnitude with the first, in the manner which has already
been 'described. Professor Camper has censured Albinus for not adopting
this method in his figures: but subjects so large as those which he has re-
presented would have had less of tlie appearance of nature, if they had been
projected orthographically, nor Avould such projections have been materially
more instructive.

It frequently happens, that in geographical and astronomical drawings, we
have occasion to represent, on a plane, the whole, or a part of a spherical surface.
Here, if we employ the orthographical projection, the distortion will be such,
that the parts near the apparent circumference will be so much contracted,
as to render it impossible to exhibit them with distinctness. It is, therefore,
more convenient, in this case, to employ the stereographical projection, where
the eye is supposed to be at a moderate distance from the object. The place
of the eye may be assumed either within or without the sphere, at pleasure,
and according to the magnitude of the portion which we wish to represent,
the point, from which the sphere may be viewed with the least distortion,
may be determined by calculation. But in these cases all circles obliquely si-
tuated on the sphere must be represented by ellipses: there is, however, one
point in which the eye may be placed, which has the peculiar and im-
portant advantage, that the image of every circle, greater or lesser, still re-
mains a circle. This point is in the surface itself, at the extremity of the di-
ameter perpendicular to the plane of projection ; and this is the point usually
employed in the stereographical projection of the sphere, which serves for the
geometrical construction of problems in spherical trigonometry. The pro-
jection of the whole surface of the sphere would occupy an infinite space, but
within the limits of the hemisphere, the utmost distortion of the linear mea-
sure is only in the proportion of 2 to 1, each degree at the circumference of
the figure occupying a space twice as great as at the centre. The angles,
which the circles form in crossing each other, are also correctly represented.
(Plate VIII. rig. 106.) • •

For projecting figures on curved or irregular surfaces, the readiest methotl

lis LECTURE xr.

is to trace cross lines on them, with the assistance of such a frame as lias been
described for drawing in perspective, representing the appearance of uniform
squares or rectangles, and to delineate in each of these the corresponding
parts of the object, or of the drawing which serves as a copy.

The arts of writing and drawing, in all their varieties, are extended in
their performance, and perpetuated in their duration, by means of engraving
and printing. If there is any one circumstance to which we can peculiarly at-
tribute the more rapid progress of general civilisation in modern than in ancient
times, it is the facility of qiultiplying copies of literary productions of all
kinds, by the assistance of these arts. The distinguishing character of print-
ing consists in the employment of moveable types: the art of engraving is
more simple, and in some of its forms, more ancient. The Romans were in
the habit of using seals and stamps, for marking letters and words on wax and
on pottery; it was usual in the middle ages to employ perforated plates of
metal as patterns for guiding a brush, by means of which the capital letters
Avere inserted in some manuscripts, and the Chinese are said" to have been long
in possession of the art of printing books from wooden blocks. It was in this
form that printing was first introduced into Europe, in the beginning of the
fifteenth century. There seems to have been formerly a method of engraving
on wood with greater ease and accuracy than is now practised; the hatches
may be observed in old wooden cuts to cross each other more frequently, and
with greater freedom, than in modern \vorks, although some have conjectured,
with considerable appearance of probability, that these old engravings were
in reality etched in relief on metal. The art of engraving on wood is, how-
ever, at present in a high degree of perfection in this country, and blocks are
still frequently used for mathematical diagrams andother simple figures; for
, although they are somewhat more expensive than copper plates, they wear
much longer, and they have the advantage of being printed off at the same
time with the letter press, and of being included in the same page with the
text to which they belong, since the ink is applied to the projecting parts
only, both of these cuts and of the common printing types.

The method of engraving on plates of pewter or of copper, and of taking
impressions, by means of the portion of ink retained in the furrows cut by
the graver, was also introduced in the fifteenth century. For dry engraving,

ON MODELLI^'G, PERSPECTIVE, ENGRAVING, AND PRINTING. IIQ

the chawing, if it is not executed in black lead, is generally prepared by
passing a pencil over its principal features, and the outline is transferred to
the plate, which has a thin coat of white wax laid on it, by placing the draw-
ing on it, and rubbing it with a burnisher ; sometimes a drawing in Indian ink,
especially if freed from a part of its gum, may be transferred in this manner
without the application of a pencil. When written characters are to be en-
graved, the plate is laid on a cushion, so as to be readily turned under the
graver, which is a great convenience in forming curved lines.

In laying on equable shades of considerable extent, much labour is saved
by the use of a ruling machine, which enables us to draw lines, at any re-
quired distance, very accurately parallel, and either straight, or following
each other's gentle undulations, in order to avoid the appearance of stiffness.
This machine, like the dividing engine, is sometimes adjusted by the revolu-
tions of a screw, and sometimes by the oblique motion of a triangular slider.
Besides the cutting graver, which is of a prismatic form, terminated by an
oblique surface, other instruments are occasionally employed; the dry needle
makes a very fine line, and leaves the metal that it has displaced, to be rub-
bed off by anothei- tool. Sometimes a number of detached excavations are
formed by a pointed instrument, and the projections are afterwards removed;
this is called stippling. A burnisher and some charcoal are required for
erasing the strokes of the graver, when it is necessary, and for polishing the
surface. It is seldom, however, that a plate is begun and completed by dry
engraving only.

For engraving in mezzotinto, the plate is roughened, by scraping it in
every direction with a tool made for the purpose, so that an impression from
it, in this state, would be Avholly dark ; the lights are then inserted, by re-
moving the inequalities of the surface, in particular parts, by means of a
smooth scraper, and a burnisher. As the plate wears in printing, some of
these parts are liable to have the grain a little raised again, so that the lights
are less clear in the later impressions than in the proofs. It is well known,
that in common engravings the proofs are usually the darkest throughout.

The most expeditious and most generally useful mode of working on cop-
per, is the process of etching. The plate, being covered with a proper var-

ISO l.i:G.TUiB;E .XI.

iiisli, is usually blackened with smoke, giitltlie drawing is placed on it, with the
interposition of a paper nibbed over with red chalk, which, when the drawing
is traced with a wooden point, adheres to the varnish, in the form of the out-
line: or if it is re(iuired that the ultimate impression be turned the same way
as the drawing, an intermediate outline must be procured in the same man-
ner on a separate paper, and then transferred to the plate. All the outlines
thus marked are traced with needles, which make as inany furrows in the
varnish, and leave the copper bare: tjie shades are inserted with the assist-
ance of the ruling machine, wherever parallel lines can be employed. The
plate tlms prepared, and furnished with an elevated border of a proper con-
sistence, is subjected to the action of the diluted nitric acid, until all the
parts arc sufficiently eorroded, care being taken in the mean time to sweep
off the air bubbles as they collect, and to stop out, oi; cover with a new ya,r-
nish, the lighter parts, which aje soonest completed. When the varnish is re-
moved, the finishing touches are added with the graver: and if the plate re-
quires further corrosion, the varnish jnay sometimes be replaced, without fill-
ing up the lines, by applying it on a ball or cushion, taking care to avoid
any oblique motion. It is said that the acid sometimes operates so as to un-
dermine the metal on each aide, adad to render the furrows wider as they be-
come deeper, and that for this reason in etchings, as well as in mezzotintos,
the later impressions are sometimes darker than the proofs; but this is by no
means universally true. It is well known to chemists, that glass may be cor-
roded in a similar rjaanner by means of the fluoric acid.

An etching may also be expeditiously executed by using a varnish mixed
with mutton fat, and drawing upon a paper laid on the plate ; the varnish
then adheres to the back of the paper, under the lines which are drawn, and
is immediately removed when the paper is taken off, without the use of
needles. Sometimes the outlines only are etched, and the plate is finished in
mezzotinto.

In the mode of engraving called aqua tinta, the outline having been first
etched, the shades are also produced by corrosion, the parts being prepared
by various methods, so as to be partially protected from the action of the
iicid. Sometimes a little resin, very finely powdered, is sifted on the plate,
•whioh is:then sufficiently warmed to make the particles adhere to it; some-

ON MODELLING, PERSPECTIVE, ENGRAVING, AND PRINTING. 121

times it is varnished with a spirituous solution of resin, which cracks through-
out in drying ; and if a strong hue be any where required, it may be traced
with a mixture of whiting with some adhesive substance, before the varnish
is laid on; this Avill cause it to break up at that part; or the varnish may be
partially removed, by rubbing it with spirits, or with an essential oil. The
lighter parts may be covered, during the corrosion, with a second varnish,
which defends tliem from the acid. This mode of engraving succeeds very
well in imitating the effect of drawings, but the plates are soon worn out. In
order to judge of the state of the work, an impression of any part of the
plate may be taken off", by pouring on it a little plaster of Paris mixed with
water.

Musical characters are usually stamped with punches ; in this country, on
plates of pewter, but in France generally on copper. Mr. Rochon has in-
vented a machine for stamping letters on copper, instead of printing, but the
method does not appear to have been practically employed.

In whatever way the plate may have been engraved, when an impression
is to be taken from it, it is covered with printing ink of the finest kind, by
means of stuffed balls, and then wiped, chiefly with the hand, so that the ink
is wholly removed from the polished surface; it is then placed, with the
moistened paper, on a board, between ffannels, and strongly pressed in pass-
ing between two wooden rollers. By frequent use the plate loses its sliarpness,
and sometimes requires to be retouched; hence arises the greater value of first
impressions; but by proper precautions in cleaning the plate, its delicacy may
be preserved for a long time.

An impression, while it is moist, may be reversed, by passing it through
the press with another paper. And by writing with a peculiar ink, e\cn
common letters may be thus copied on thin paper, and the impression will be
legible on the opposite side. Mr. Montbret proposes to put some sugar candy
into the ink, and to take a copy on unsized paper by means of a hot iron.

A simple and elegant method of multiplying drawings has been lately in-
troduced by Mr. Andr^. The drawings are made with an unctuous compo-
sition, in the form of a crayon or of an ink, on a soft stone of 4 calcarious

VOL. I. li

122 LECTURE XI,

nature, somewhat like a stone maiie. When the drawing is finished, the
stone is moistened, and imbibes so much water, that the printing ink will
not adhere to it, except at tlie parts where the crayon or the ink has been
applied; and in this manner an impression is procured, which has much of
the freedom and spirit of an original drawing. When tlie ink is used, a little
' acid is afterwards applied to the stone, in order to corrode its intermediate
parts ; and the bold stile of the impression much resembles that of the old
wooden cuts.

The art of printing with separate types was invented soon after the in-
troduction of wooden blocks into Europe. Tlie improvement was great and
important. The year 144'3, or 1444, is considered as the date of the oldest
printed book ; but the precise time and place of the invention remain some-
what doubtful: the art, however, advanced towards perfection by very rapid
steps. The letters are first cut, in a reversed form, on steel punches; with
these a matrix of copper is starhped, and the matrix forms the lower part of
the mould in which the types are cast; the metal is a composition of lead
and antimony, which is easily fusible. Thus the printed sheet is the
fourth form of the letter, reckoning from the original engraving on the punch:
in the stereotype printing, lately invented, or rather improved and revived,
it is the sixth. In this method, when a form for the side of a sheet has been
composed, made up, corrected, and locked up by wedges in the chase or
iron frame, which confines it, a mould of the whole is formed in fine plaster,
and as many repetitions of it may be cast very thin, in type metal, as will serve
to print for the use of a century, without the expense of keeping a large
quantity of types made up, or of providing paper for a numerous impression
at once.

The modes of arrajiging the types in boxes or cases, of composing the
separate lines on the stick, and making them up by degrees into pages and
forms, of correcting the press, of applying the ink, and taking oflf the im-
pression, are entirely calculated for the simplicity and convenience of the
manual operations concerned, and require little or no detailed explanation..

123

LECTURE XII.

ON STATICS.

f

The examination of the magnitude of the various forces, employed in prac-
tical mechanics, constitutes the doctrine of statics. The term statics, in a
strict sense, implies the determination of weights only; but it may without
impropriety be extended to the estimation of forces of all kinds, especially
active forces, that can be compared with weights, in the same manner as the
term hydrostatics comprehends every thing that relates to the equilibrium of
fluids. The measurement of the passive strength of the materials employed,
the changes produced in them by the forces which they resist, and the laws
of the negative force of friction, are also subjects immediately introductory to
the particular constructions and uses of machinery, and nearly coimected
with the department of statics.

The art of weighing is peculiarly important, as it furnishes us with the
only practical mode of determining the quantity of matter in a given body.
We might indeed cause two bodies to meet each other with known velocities,
and from the effects of their collision, we might determine their comparative
momenta, and the proportion of their masses; but it is obvious that this pro-
cess would be exceedingly troublesome, and incapable of great accuracy; we
therefore recur to the well known law of gravitation, that the weight of
every body is proportional to the quantity of matter that it contains, and we
judge of its mass from its weight. If all bodies were of equal density, we
might determine their masses from their external dimensions ; but we seldom
find even a single body which is of uniform density throughout; and even if
we had such a body, it would in general be much easier to weigh it correctly
than to measure it.

The weight of a body is commonly ascertained, by comparing it immediately

124 LECTURE XII.

«

Avith otlier weights of known dimensions: but sometimes the flexure of a.
spring is employed for the comparison. Standard weights hav" generally been
deduced from a certain measure of a known substance, and in particular of
water. According to the most accurate experiments, when the barometer is
at 30 inches, and Fahrenheit's thermometer at 62°, 12 wine gallons of distilled
water weigh exactly 100 pounds avoirdupois, each containing 7000 grains
troy; and a cubic inch weighs 2524- grains. A hogshead of water, wine
measure, weighs, therefore, 525 pounds, and a tun 2100 pounds, which is
nearly equal to a ton weight. i\Ir. Barlow supposes that the tun measure of
water contained originally S2 cubic feet, and weighed 2000 pounds, which
was also called a ton weight, the gallon being somewhat smaller than it is at
present, and the cubic foot weighing exactly 1000 ounces, or 624- pounds.
A quarter of wheat weighed about a quarter of a ton, and a bushel as much
as a cubic foot of water. A chaldron of coals was also considered as equiva-
lent to a ton, although it now weighs nearly half as much more. But at the
mean temperature of this climate, or 52°, a cubic foot of distilled Mater
weighs only 9.9S ounces. The avoirdupois ounce appears to agree very nearly
with the ancient Roman ounce. Of the old French weight, 100 pounds
made 108 English pounds avoirdupois. The gramme of the'new weights is a
cubic centimetre of pure water at its greatest density, that is, about the
temperature of 39° of Fahrenheit; it is equal to 1 5^ English grains : hence
tlie chiliogramme is 2-j- pounds, and five myriogrammes are nearly a hundred
weight. Five grammes of silver, including one tenth of alloy, make a franc,
Avhich is one eightictli better than the old franc or livre, _^«tl is intrinsically
worth nearly ninepen^e three farthings English.

The instruments usually employed for the comparison of weights are either
balances, or steelyards. In the common balance, the weights of the substances
compared are equal ; in a compound weighing machine, we use weights \vhich
are smaller, in a certain proportion, than those which they represent : in the
steelyard, a single weight acquires different values at different parts of tlie
arm, and in the bent lever balance, the position of the arms determines the
magnitude of the counterpoise. The spring steelyard measures the weight,
by the degree of flexure that it produces in a spring.

The beam of a common balance must have its arms precisely equal. The

ON STATICS. 12,5

scales, being freely suspended from fixed points in the beam, act on them al-
ways in the direction of gravity ; and the effect is the same as if the whole
weight were concentrated in those points. The beam supports the scales, and
is itself supported, by means of line edges of hard steel, working on steel, agate,
or garnet, in order that the motion may be free, and the distances of the
points precisely defined. The best beams are made of two hollow cones of
brass, united at their bases ; they are lifted off their supports when the ba-
lance is not used, in order to avoid accidental injuries; the scales also are
supported, so as not to hang from the beam, until they have received their
weights. According to the position of the fulcrum, with respect to the points
of suspension of the scales, the equilibrium of the balance may be either stable,
neutral, or tottering; or if the beam be too flexible, it may pass from one
of these states to the other by the effect of the weights. The stable equili-
brium is the most usual and the best, because it gives us an opportunity of
determining the degree of inequality of the weights, by the position in which
the centre of gravity rests, or by the middle point of the vibrations of the
beam, which are sometimes measured by an index, pointing to a graduated
arc. If, however, the fulcrum be too much elevated above the centre of
gravity, the equilibrium may be too stable, and may retjuire too great an in-
equality, in order to produce a sensible preponderance. If, on the contrary,
by the elevation of the points of suspension of the scales, the equilibrium be
rendered tottering, the lower scale will not rise, even if it be somewhat less
loaded than the upper; and sieelyards of this construction have scmietimes
been employed, in order to impose on the purchaser by the appearance of an
ample weight. It is necessary, where great accuracy is desired, to bring the"
equilibrium very near the state of neutrality, and to make the vibrations of
the beam slow and extensive, whether the scales have weights in them or
not: for this purpose a small weight is sometimes inclosed within the beam,
which is raised or depressed at pleasure, by a screw, so as to bring the
centre of gravity of the whole moveable apparatus, as near to the fulcrum as
may be required for the occasion. IVfr. llamsden's balance, made for the
Royal Society, is capable of weighing ten pounds, and turns with one ten
millionth part of the weight. (Plate VIII. Fig. 107 . • IO9.)

The arms of a balance have sometimes been made imequal for fraudulent
purposes, the weight being placed nearer to the fulcrum than the substance

1^6 .Z.ECTURE xri.

to be weighed. It is obvious that the fraud may be detected, by changing^
the places of the contents of the two scales. In such a case, if a counterpoise
to the same weight be determined in each situation, the sum of both will be
greater than twice the weight; and the purchaser would be sure of having
even more than his due, by requesting the seller to weigh half in the one scale
and half in the other. For example, if one arm of the beam were only three
fourths as long as the other, the counterpoise, to a weight of twelve ounces,
would be nine ounces in one scale, and sixteen in the other, making together
twenty five instead of twenty four ounces. (Plate VIII. Fig. 110.)

Supposing the beams of a balance to be accidentally unequal, either in
length or in weight, we may still weigh in it with accuracy, by making a
perfect counterpoise of any kind to a weight, and then removing the weight
and putting in its place as much of the substance to be weighed, as is suffi-
cient to restore the equilibrium.

The weights may also be reduced, or increased, in proportion to the length
of the arms, if they differ from each other, care being taken to put the weights
always into the same scale. This is actually performed in weighing machines,
where a composition of levers is employed, in order to enable us to determine
the weight of large masses by means of weights of moderate dimensions.
(Plate IX. Fig. 111.)

When the effective lengths of one or both arms of the beam are capable of
being varied, by changing the points of suspension according to the divisions
of a scale, the instrument is called a steelyard. Where one weight only is used,
it is not necessary that the two arms should exactly balance each other, since
the divisions may be so placed as to make the necessary adjustment; but it is
sometimes convenient to have two or three weights, of different magnitudes,
and fcH" this purpose the instrument should be in equilibrium without any
weight. In such cases, great accuracy may be obtained by applying a small
weight at the end, in the form of a micrometer screw. (Plate IX. Fig. 1 12.)

The arms of a balance, though constant in length, may vary in effect with-
out limit, if they can sufficiently alter their inclination to the horizon ; for
no weight, however great, acting on the arm of a bent lever, can make it per-

ON STATICS. 127

fectly vertical, since, in this position, the weight may be overpowered by
the minutest counterpoise acting on the other arm. The centre of gravity
being, in the common balance, very nearly in a right line between the weights,
in order that it may be immediately below the fulcrum, the arm must have a
very considerable angular motion for a slight inequality of the weights ; but
in the bent lever balance, the centre of gravity is at such a distance from the
fulcrum, that a moderate motion of the arms may bring it into the vertical
line. This motion is measured by an index on a graduated arc, which gives
the instrument a considerable range; and where expedition is particularly
desired, it may often be used with advantage; but if the weights to be de-
termined are large, tiie scale becomes very much contracted, and the instru-
ment requires to be levelled with great accuracy. A counterjioise acting on
a spiral or conical barrel, has also been applied to a similar purpose ; it is ca-
pable of a scale somewhat more extended than a bent lever balance, but it is
less simple, and scarcely more accurate. (Plate IX. Fig. 113.)

A spring, which is usually of a spiral form, being made to support a hook
by the intervention of a graduated bar, the divisions of this bar, which are
drawn out beyond the fixed point, indicate the weight supported by the hook.
This instrument is called a spring steelyard. Mr. Ilanin's spring steelyard
has a long index, which revolves on a centre, and shows at once the weight
according to the standards of different countries. The divisions of the scales
in moderate flexures of the spring are nearly equal: hence it may be inferred,
that the space through which a spring is bent, and consequently its curva-
ture, or change of curvature, is simply proportional to the force which acts
on it, and that the vibrations of a weight supported by a spring, must, like
those of a cycloidal pendulum, be performed in ecpial times, whatever may be
their magnitude. The strength of all springs is somewhat diminished by
heat, and for each degree of Fahrenheit that the temperature is raised, we
must deduct abcmt one part in five thousand from the apparent weight in-
dicated by the spring steelyard. (Plate IX. Fig. 114.)

The spring steelyard affords us the most convenient method of measunng
the immediate intensity of the forces exerted by animals of different kinds,
in the labour which they perform. When it is adapted for this purpose, it is
■sometimes called the dynamometer. We may also estimate the force of an

128 LECTURE XII. ' .

animal, which is employed in drawing a distant boat or carriage, by the in-
clination of the rope or chain to the horizon, compared with the weight of
that portion of it which the animal supports, that is, of the part which extend*
to the point where the curve becomes horizontal.

All animal actions, or, at least, all the external actions of animals, are ulti-
mately dependent on the contractions and relaxations of the flesliy parts, -
which are called muscles. The operation of the particular muscles belongs
properly to the Iscience of physiology ; but their mechanism may in general
be understood from the properties of the lever and of the centre of gravity.
^\\t bones are the levers, the joints the fulcrums, and the force is applied by
the muscles, which are usually attached to the bones by the intervention of
tendinous cords. When a muscle contracts in the direction of its fibres, it
becomes at the same time thicker, and its total bulk is little if at all diminish-
ed: when it relaxes itself, it is merely passive, for the fibres, being extremely
flexible, can have little or no effect in separating the parts to which they are
attached; this separation is generally performed by the action of other mus-
cles, which are called the antagonists of the first, but sometimes by clastic
ligaments, or by other means. The bone forms a lever of the second kind,
where the two forces opposing each other are on the same side of the fulcrum.
In general the insertion of a muscle is much nearer to the fulcrum than the
point of action, and the obliquity of its direction gives it a still greater me-
chanical disadvantage with regard to rotatory power; but it is more conve-
nient in the animal economy to produce a great contractile force, than 'a great
extent in the original motion. For instance, when the arm is raised by the
exertion of the deltoid muscle of the shoulder, a very strong contraction takes
place in the muscle, but the action is only continued through a short ^pace ;
had the contractile power been weaker and more extensive, the shoulder must
have been made higher, in order to give it sufficient purchase, and the pro-
jection would have been inconvenient.

Borelli has calculated that the immediate force of the biceps, or double-
headed muscle which bends the arm, is equivalent to about 300 pounds, and
that of the muscles which raise the lower jaw, above 500 in man, but in beasts
of prey far greater. It is obvious that in muscles of the same kind, the
strength must be as the number of fibres, or as the extent of the surface which

2

ON STATICS. 129

would be formed by cutting the muscle across; and it i* not improbable that
the contractile force of the muscles of a healthy man is equivalent to about
500 pounds for each s(}uare inch of their section. The Avcakcst man can lift
with his hands about 1125 pounds, a strong man 400. Topham, a carpenter,
mentioned by Desaguliers, could lift 800 pounds. lie rolled up a strong
pewter dish with his fingers; he lifted with his teeth and knees a table six
feet long, with a half hundred weight at the end. He bent a poker, three
inches in circumference, to a right angle, by striking it upon his left fore
arm: another he bent and unbent about bis neck ; and snapped a liempen rope
two inches in circumference. A few years ago there was a person at Oxford
who could hold his arm extended for half a minute, with half a hundred weight
hanging on his little finger. A young gentleman, who has distinguished
liimself as a pedestrian by going gO miles in IQ hours, has also lifted two
hundred weights, one in each hand, and made them meet over his head.

Sometimes feats of strength apparently extraordinary have been exhibited
by men who have not really been possessed of any material superiority. De-
saguliers relates, that one of them used to withstand the force of two horses
drawing at a girdle passed round his middle, while his feet acted on a firm
obstacle. By falling suddenly backwards, in an oblique position, he broke a
rope which was fixed a little before his feet. He supported one or two men
by forming his body into an arch ; and by a harness fitted to his hips, he sus-
tained a cannon, weighing two or three thousand pounds. In all these cases
the muscles principally employed are the extensors of the legs and thighs, but
tliQ^ passive strength of the bones is more concerned than the active force of
the muscles. In the instance, mentioned by Lahirc, of a young man who
raised an ass from the ground, by cords tied to the hair of his head, the sensi-
bility of the nerves of the skin must have been diminished by habit, so as to
allow the hair to be thus forcibly extended, without immoderate pain.

The application of animal force is usually performed by means of a pro-
gressive motion. The muscles 'employed in this process are in general, if not
always, the strongest of the body, both by nature, and by habit; so that
when force alone is required, it is n)Ost ad\ antageously obtained from their
exertions. In walking, the centre of gravity is moved forwards Avith a ve-
locity nearly uniform. If the legs were perfectly inflexible, the centre of

VOL. I. s

130 J^ECTUBE XII.

gravity would describe, in succession, portions of circles, of which each leg
would alternately be the radius: but if the velocity were great enough to
create a centrifugal force more than equivalent to the force of gravity, the ,
pressure would be removed from each leg after the first instant of its touching
the ground; the path would become parabolic instead of circular, and the
walking would be converted into running: for the difference between walk-
ing and running is this, that in running, one foot is removed from the
ground before the other touches it ; while in walking, the hindmost foot is
only raised after the foremost has touched the ground. Now supposing the
length of the inflexible leg three feet, the centrifugal force would become
equal to the weight, with a velocity which would be acquired by a heavy
body in falling through a foot and a half, that is, near 10 feet in a second,
or 7 miles an hour; and this is the utmost velocity with which it would be
mechanically possible to walk with inflexible legs. But the flexibility of the
iegs makes the progressive motion much more uniform, by softening the
angles of the path, which the centre of gravity describes, and rendering it
either more or less curved at pleasure; so that it becomes mechanically if not
physically possible, to walk with a velocity somewhat greater than 7 miles an
hour, and to run or dance with as small a velocity as we please, since we
may make the path of the centre of gravity somewhat less, or much more
curved, than a circle described on the point of the foot as a centre. (Plate
IX. Fig. 115, 116.)

The flexions and extensions of the legs are also almost the only means
by which an impulse is given to the body; if the legs were perfectly inflexible,
it would be extremely difficult, although not absolutely impossible, to obtain
a progressive motion. The centre of gravity is principally impelled forwards
in the beginning of the ascending part of the curve which it describes, in
walking, by the action of the leg which is left behind, but in running or
hopping, by that of the only foot ^yhich touches the ground at any one time.
When we thrust against any obstacle, or draw a rope in a horizontal, or in a
descending direction, the* body is inclined forwards, and in some cases its
action is limited by the effect of the weight of the body reduced to the direc-
tion of the line of draught: but we much more usually draw or \n\\l in an as-
cending direction, so that our whole muscular force may be exerted Avithout
any limit of this kind.

ON STATICS. 131

It happens, however, very frequerttly, that we have occasion foi' motions of
such a nature as to be more conveniently performed by the hands and arms
than by the action of walking or running; and where delicacy is required
rather than strength, the form of the hantl and lingers gi\'es the human spe-
cies a great superiority overall other auinmls, although by no means, as some
authors have supposed, an advantage equivalent to that of the higher perfec-
tion of the intellectual powers. It is true, as we may observe in the manu-
factories of this country, that machinery has been invented by which a jjower
of any kind may be converted to purposes seemingly the most intricate and
refined ; and after all that has been done by a Watt and an Arkwright, it is diffi-
cult to determine a positive limit to the ingenuity of mechanical invention.

It is necessary to consider, in examining the different sources of motion,
not only the immediate magnitude of the forces which they produce, but also
the velocity with whieh they are capable of acting, and the time for which
that action can be continued. The daily work of a labouring man, of middle
age, and in good health, will serve as a consenient unit for the comparison
of moving powers of all kinds. It may be most easily rememl)ered in this
form: a man can raise a weight of 10 pounds to the height of 10 feet in a
second, and can continue this labour for 10 hours a da\-. The actual velocity
of the man's motion must vary according to the mode in which his force is ap-
plied ; but we suppose that velocity to be such as to give the greatest effect
under the circumstances of the machine. This is a moderate estimate of the
work of a labourer, without any deduction for friction. Desaguliers states
the performance of a man working at a winch, with the assistance of a fly, as
considerably greater, but he does not allege any correct experiments in sup-
port of his estimate. Professor Robison, however, mentions a hydraulic ma-
chine in which the effect was actually more than one tenth greater, without
making any allowance for friction; so that it is probable, considering the loss
both from friction and from the momentum with wliich the water nuist have
been disengaged, that the immediate performance was at least one third more
than this unit: the machine was worked by a light'man carrying a weight, and
walking backwards and forwards on a lever. According to ]\fr. Buchanan's ex-.
perinients,an action like that of ringing bells produced an effect about one third
greater than turning a winch, and the actir)n of rowing, an effect four ninths
greater; but it does not appear that these experiments were continued for a

19S LECTURE XII.

whole day ; and the greatest number of observations make the daily per-
formance of workmen considerably less. It is indeed seldom that the
muscles employed in progressive motion arc so much exerted as in the ar-
rangement described by Professor Robison. A Chinese, in the operation call-
ed sculling, is said to beat a European at his oar.

For a sliort time a much greater effect than this may be produced by a great
exertion: thus a man weighing above 160 pounds can ascend by means of
steps, at the rate of more than three feet in a second, for a quarter, or per-
haps half a minute; and this is an effort five times as great as that which can
be continued for a day. Usually, however, where the hands are chiefly em-
ployed, whether in turning a winch, or in pumping, it is only possible to exert
a double, or at most a triple action, for a minute or two : thus, although a
machine may only enable a man to raise a hogshead of water in a minute to the
height of ten feet for a whole day, yet it is easy to work it so rapidly for a
single minute as to raise double the quantity, or to raise a single hogshead to
a height of twenty feet. The whole exertion of force must be a little greater
than that which is thus estimated, because a certain degree of superfluous
momentum must be generated in removing weights from one situation to
another: but this loss is usually inconsiderable.

The action of carryijig a load horizontally requires an exertion of a differ-
ent kind, and admits of no direct comparison with the application of a
constant force to overcome the gravitation of a weight, or any other im-
mediate resistance. The work of a labourer thus employed is however
confined within moderate limits. A strong porter can carry §00 pounds at
■the rate of three miles an hour; and, for a short distance, even 300 pounds:
a chairman carries 150 pounds, and walks four miles an hour; and in Turkey
it is said that there are porters, who, by stooping forwards, and placing the
weight very low on their backs, are enabled to carry from 700 to 900 pounds.
The subjects of Mr. Coulomb's experiments appear to have been either weaker,
or more inactive, than the generality of porters in this country: he calculates
that the most advantageous load for a man of common strength is about a
hundred weight; or, if he is to return without a burden, 135 pounds.

The daily work of a horse is equal to that of five or six men: its immediate

ON STATICS. . 133

force is something greater, but it cannot support the labour of more thati 8
hours a day, when drawing with a force of 200 pounds, or of 6 hours when
with a force of 240, Avalking two miles and a half an hour. It is generally
supposed, that in drawing up a steep ascent a horse is only equivalent to 3 or
4 men, and the employment of horses in walking wheels, where the action
is similar to that of ascending a hill, has for this reason been condemned.
For men, on the contrary, an ascent of any kind appears to afford a favourable
mode of exertion. But, perhaps, the weight of the carriage, and of the horse
itself, has not always been sufficiently considered in the comparison. The
strength of a mule is equal to that of three or four men. The expense of
keeping a horse is in general about twice or three times as great as the hire of
a day labourer ; so that the force of horses may be reckoned about half as ex-
pensive as that of men. The horse Childers is said, although, perhaps, with-
out sufficient authority, to have run an English mile in a single minute ; his
velocity must in this case have been 88 feet in a second, which would have
been sufficient to carry him on an inclined plane witliout friction, or in a
very long sling, to the perpendicular height of 1 20 feet.

A large windmill, on which Mr. Coulomb made many experiments, was
capable, on an average, of working eight hours a day; its whole performance
was equivalent to our estimate of the daily labour of 34 men ; 25 square feet
of the sails doing the work of one labourer. The expense of the machinery,
with its repairs, would probably amount to less than half the expense of a
number of horses capable of exerting the same force. Where a stream of
water can be procured, its force is generally more convenient, because more
regular, than that of the wind.

A steam engine of the best construction, with a. thirty inch cylin<ler has
the force of 40 horses ; and, since it acts without intermission, will perforin
the work of 120 horses, or of 600 men, each square inch of the piston being
nearly equivalent to a labourer. According to IVIr. Boulton, the consumption
of a bushel, or 84 pounds of coals, will raise 48000 cubic feet of water 10 feet
high, which is ecjuivalent to the daily labour of 8 4- nien, or perhaps more :
the value of tliis quantity of coals is seldom more than that of the work of a
single labourer for a day; but the expense of the machinery generally
renders a steam engine spmewhat more than half as expensive as the number
of horses for which it is substituted. According to other accounts, a 24 inch

1J4 LECTURE Xir.

cylinder, being equivalent to about 1% horses, requires ouly a chaldron of
coals in a day, each bushel doing the w6rk of ten men.

The force of gunpowder is employed with advantage where a very powerful
action is required for a short space, as in dividing rocks, or in generating a
great velocity in a projectile. As a source of momentum or energy only, this
power is by no means economical, the daily labour of a man being equivalent
to the effect of about 40 pounds of powder ; but the advantage of artillery
consists in having the force communicated by means of an elastic fluid ex-
tremely rare, which is capable of generating a very great velocity in the ball
only, without any waste of power in producing a useless momentum in any
other substance.

The comparative force of different kinds of gunpowder is determined by an
eprouvette, or powder proof: the effect is measured by the angular motion of
a little wheel, a projecting part of which is impelled by the explosion of a
small quantity of the powder, while the friction of a spring or a weight
creates a resistance which may be varied if it be required. The absolute
force of a given quantity of powder may be ascertained either by suspending a
cannon as a pendulum, and measuring its angular recoil ; or l>y shooting into
a large block, and finding the velocity which is imparted to it by the ball.

For measuring very small attractive or repulsive forces, with great ac-
curacy, the most convenient test is furnished by the effects of twisting. An
arm or beam is suspended horizontally by a long wire, and the force re-
quired to cause the beam to make one or more revolutions being ascertained^
we may divide the circle described by its extremities into as many parts as
we think proper, and the force required to bring the beam into any position
will always be proportional-, without a sensible error, to the magnitude of
the part of the circle intercepted between the given position, and that in
which the arm would naturally rest. When the force is of such a nature as
to be capable of producing a vibration, the body on which it acts being sus-
pended by the thread of a silkworm, or of a spider, we may compare its
magnitude Avith that of gravitation, by observing the time required for each
. vibration, and determining the operation of the force according to the laws
of pendulums. It is in this manner that the forces concerned in the effects
of electricity and of magnetism have been measured by Mr. Coulomb.

135

LECTURE XIII.

ON PASSIVE STRENGTH AND FRICTION.

XriE passive strength of the materials employed in the mechanical arts de-
pends on the cohesive and repulsive forces of their particles, and on the
rigidity of their .structure. The consideration of the intimate nature of these
forces belongs to the discussion of the physical properties of matter; but the
estimation of their magnitude, and of their relative value in various circum-
stances, is of undeniable importance to practical mechanics, and requires to
be examined as a continuation of the subject of statics. The retarding force
of friction is very nearly allied to some kinds of passive strength, and may be
in great measure explained from similar considerations.

The principal effects of any force, acting on a solid body, may be reduced to
Seven denominations; extension, compression, detrusion, flexure, torsion,
alteration, and fracture. When a Aveight is suspended below a fixed point,
the suspending substance is extended, or stretched, and retains its form by
its cohesion, assisted by its rigidity: when the weight is supported by a
block, or pillar, placed below it, the block is compressed, and resists pri-
marily by a repulsive force, bvit secondarily also by its rigidity. The eflfect
here called detrusion, is produced when a transverse force is applied close to
a fixed point, in the same manner as the blades of a pair of scissors act on
the pin, and the force which resists this operation is principally the rigidity,
or lateral adhesion of the strata of the substance, but it could scarcely be
effectual without some degree of cohesive and repulsive force. When three
or more forces are applied to different parts of any substance, they produce
flexure, that is, they bend it, some of its parts being extended, and others
compressed. In torsion, or twisting, the central particles remain in their
natural state, while those which are in opposite parts of the circumference

156 LECTURE XIII.

are detruded, or displaced, in opposite directions. The operation of forces
applied in any of these ways may produce a permanent alteration, or change
of figure, in substances sufficiently soft, and perhaps, in a certain degree, in
all substances : this change is sometimes called by workmen settling, or tak-
ing a set. But the limit of all these effects is fracture, which is the conse-
quence of the application of any force capable of overcoming the strength of
the substance, and to which the generality of writers on mechanics have
hitherto confined their attention.

The forces, by which the form of any substance is changed, may also be di-
vided into two kinds, simple pressure, and impulse ; but it is only with re-
gard to fracture that it will be necessary to Lake the force of impulse into
consideration.

Extension and compression follow so nearly the same laws, that they may
be best understood by comparison with each other. The cohesive and re-
pulsive forces, which resist these effects, depend almost as mucli on the
solidity, or rigidity of the substances, as on the attractions and repulsions
which are their immediate causes : for a substance perfectly liquid, although
its particles are in full possession of their attractive and repidsive powers,
may be extended or compressed by the smallest force that can be applied to
it. It is not indeed certain that the actual distances of the particles of all
bodies are increased when they are extended, or diminished when they are
compressed : for these changes are generally accompanied by contrary changes
in other parts of the same substance, although probably in a smaller degree.
We may easily observe, that if we compress a piece of elastic gum in any
direction, it extends itself in other directions; and if we extend it in length,
its breadth and thickness are diminished.

If the rigidity of a body were infinite, and all lateral motions of its par-
ticles were prevented, the direct cohesion alone would be the measure of the
force required to produce extension, and the direct repulsion of the force
required to produce compression; in this respect indeed, the actual rigidity of
some substances may be considered as infinite, wherever the exten^jion or
compression is moderate, and no permanent alteration of form is produced;
and within these limits these substances may be called perfectly elastic. If

2

ON PASSIVE STRENGTH AND FRICTION. 137

the cohesion and repulsion were infinite, and the rigidity limited, the only
effect of force would be to produce alteration of fonn : and such bodies would
be perfectly inelastic, but they would be harder or softer according to the de-
gree of rigidity.

It is found by experiment, that the measure of the extension and compres-
sion of uniform elastic bodies is simply proportional to the force which oc-
casions it; at least when the forces are comparatively small. Thus if a weight
of 100 pounds lengthened a rod of steel one hundredth of an inch, a weight
of 200 would lengthen it very nearly two hundredths, and a weight of 300
pounds three hundredths. The same weights acting in a contrary direction
would also shorten it one, two, or three hundredths respectively. The former
part of this law was discovered by Dr. Hooke, and the effects appear to be
perfectly analogous to those which are more easily observable in elastic
fluids.

According to this analogy, we may express the elasticity of any substance
by the weight of a certain column of the same substance, which may be de-
nominated the modulus of its elasticity, and of which the weight is such,
that any addition to it would increase it in the same proportion, as the weight
added would shorten, by its pressure, a portion of the substance of equal dia-
meter. Thus if a rod of any kind, 100 inches long, were compressed 1 inch
by a weight of 1000 pounds, the weight of the modulus of its elasticity would
be 100 thousand pounds, or more accurately 99000, which is to 100000 in
the same proportion as 99 to 100. In the same manner, we must suppose
that the subtraction of any weight from that of the modulus will also di-
minish it, in the same ratio that the equivalent force Avould extend any por-
tion of the substance. The heigJit of the modulus is the same, for the same
substance, whatever its breadth and thickness may be : for atmospheric air,
it is about 5 miles, and for steel nearly 1500. This supposition is sufficiently
confirmed by experiments, to be considered at least as a good approximation:
it follows that the weight of the • modulus must always exceed the utmost
cohesive strength of the substance, and that the compression produced by
such a weight must reduce its dimensions to one half: and I have found that
a force capable of compressing a piece of elastic gum to half its length will
usually extend it to many times that length, and then break or tear it; and
VOL. I. T

'138 LECTURE XIII.

also that a force capable of extending it to twice its length will only com-
press it to two thirds. In this substance, and others of a similar nature, the
resistance appears to be much diminished by the faciUty by which a contrary
change is produced in a different direction; so that the cohesion and repul-
sion thus estimated appears to be very weak, unless when the rigidity is in-
creased by a great degree of cold. It would be easy to ascertain the specific
gravity of such a substance in different states of tension and compression,
and some light might be thrown, by the comparison, on the nature and oper-
ation of the forces which are concerned.

It is difficult to compare the lateral adhesion, or the force which resists the
detrusion of the parts of a solid, with any form of direct cohesion. This force
constitutes the rigidity or hardness of a solid body, and is wholly absent from
liquids, although their immediate cohesion appears to be nearly equal to that
of solids. Some experiments have been made on the fracture of bodies by
means of detrusion, but it does not appear that the force necessary to pro-
duce a temporary derangement of this kind has ever been examined : it may
be inferred, however, from the properties of twisted substances, that tl>e
force varies in the simple ratio of the distance of the particles from their
natural position, and it must also be simply proportional to the magnitude of
the surface to which it is applied.

The most usual, as well as the most important effect, produced by the ap-
plication of force, is flexure. When a force acts on a straight column in the
direction of its axis, it can only compress or extend it equally through its
.whole substance; but if the direction of the force be only parallel to the axis,
and applied to some point more or less remote from it, the compression or ex-
tension will obviously be partial: it may be shown that in a rectangular
column, when the compressing force is applied to a point more distant from
the axis than one sixth of the depth, the remoter surface will no longer be
compressed but extended, and it may be demonstrated that the distance of
the neutral point from the axis is inversely as that of the point to which the
force is applied. From the effect of this partial compression, the column
must necessarily become curved ; and the curvature of the axis at any point
will always be proportional to its distance from the line of direction of the
force, not only while the column remains nearly straight, but also when it i*

ON PASSIVE STREKCTII ANT) FRICTION. 129

bent in any degree that the nature of tlie substance will allow. If the co?
lumn was originally bent, any force, however small, applied to the extre-
mities of the axis, will increase the curvature according to the same law, but
if the column was originally straight, it cannot be kept in a state of flexure
by any longitudinal force acting precisely on the axis, unless it be greater
than a certain determinate force, which varies according to the dimensions of
the column. It is not however true, as some authors have asserted, that
every column pressed by such a force must necessarily be bent; its state
when it is straight, and submitted to the operation of such a force, will re-
semble a tottering equilibrium, in which a body may remain at rest until
some external cause disturbs it. The figure of a column naturally straight,
but bent a little by a longitudinal force, will coincide with that of the har-
monic curve, in which the curvature is as the distance from the basis. (Plate
IX. Fig. 117. . 121.)

Considerable irregularities may be observed in all the experiments which
have been made on the flexure of columns and rafters exposed to longitudinal
foi ces ; and there is no doubt but that some of them were occasioned by the
difKculty of applying the force precisely at the extremities of the axis, and
others by the accidental inequalities of the substances, of which the fibres must
often have been in such directions as to constitute originally rather bent than
straight columns. '

When a rod, not very flexible, is fixed at one end in a horizontal position,
the curvature produced by its own weight is every where as the square of the
distance from the other end: and if a rod be simply supported at each end,
its curvature at any point will be proportional to the product of the two parts
into which that point divides it. But when the weights are supposed to be
applied to any given points of the rod only, the curvature always decreases
uniformly between these points and the points of support. (Plate IX. Fig.
122, 123.)

The stiffness of any substance is measured by the force required to cause it
to recede through a given small space in the direction of the force. It is only
necessary to consider this property with regard to forces applied transversely;
In such cases the stiffness is directly as the breadth and the cube of the depth

140 lECTURE XIII.

of the beam, and Inversely as the cube of its length. Thus if we have &
beam which is twice as long as another, we must make it, in order to ob-
tain an equal stiffness, either twice as deep, or eight times as broad. The
property of stiffness is fully as useful in many works of art as the ultimate
strength with which a body resists fracture: thus for a shelf, a lintel, or a
chimney piece, a great degree of flexure would be almost as inconvenient as
a rupture of the substance.

When a beam is supported at both ends, its stiffness is twice as great as
that of a beam of half the length firndy fixed at one end ; and if both ends
are firmly fixed, the stiffness is again quadrupled. For if the whole beam
were inverted and supported by a fulcrum in the middle, each half would re-
semble a separate beam fixed at one end, and the fulcrum would bear the
sum of two equal weights placed at the extremities, disregarding that of the
beam ; and consequently the same flexure will be produced by placing a
double weight on the middle of the beam in an inverted position. If both
ends were firmly fixed, the curvature would be every where as the distance
from the middle of each half, the whole being in the same state as four se-
parate beams fixed at their extremitii^s : each of these beams would be eight
times as stiff as beams of -twice the length, and the whole beam, in this state,
would be eight times as stiff' as if the ends were simply supported. It is,
however, difficult to fix the ends of a beam so firmly as to increase its resistance
in this proportion, unless it be continued both ways considerably beyond the
supports.

It is evident that a tube, or hollow beam, of any kind, must be much
stiffer than the same quantity of matter in a solid form: the stiffness is indeed
increased nearly in proportion to the square of the diameter, since the cohe-
sion and repulsion are equally exerted with a smaller curvature, and act also
on a longer lever.

Torsion, or twisting, consists in the lateral displacement, or detrnsion, of
the opposite parts of a solid, in opposite directions, the central particles only
remaining in their natural state. We might consider a wire as composed of
a great number of minute threads, extending through its length, and closely
connected together; if we twisted such a wire, the external threads would

ON PASSIVE STRENGTH AND FRICTION, 141

be extended, and, in order to preserve the equilibrium, the internal ones would
be contracted ; and it may be shown that the whole wire would be shortened
one fourth as much as the external fibres would be extended if the length re-
mained undiminished; and that the force would vary as the cube of the angle
through which the wire is twisted. But the force of torsion, as it is de-
termined by experiment, varies simply as the angle of torsion; it cannot,
therefore, be explained by the action of longitudinal fibres only; but it ap-
pears rather to depend principally, if not intirely, on the rigidity, or lateral
adhesion, which resists the detrusion of the particles. If a wire be twice as
thick as another of the same length, it will require sixteen times as much force
to twist it once round; the stiffness varying as the fourth power of the dia-
meter, that is, as the square of its square. But if the length vary, it is
obvious that the resistance to the force of torsion will be inversely as the
length.

A permanent alteration of form is most perceptible in such substances as
are most destitute of rigidity, and approach most to the nature of fluids. It
limits the strength , of materials with regard to practical purposes, al-
most as much as fracture, since in general the force which is capable of
producing this effect, is sufficient, with a small addition, to increase it till
fracture takes place. A smaller force than that which has first produced an
alteration of form, is seldom capable either of increasing, or of removing it,
a circumstance which gives such materials, as are susceptible of an alteration
of this kind, a great advantage for many purposes of convenience and of art.
The more capable a body is of a permanent alteration of form, the more
ductile it is said to be; pure gold and silvei', lead, annealed iron and copper,
wax Avhen warm, glass when red hot, and clay when moist, possess consider-
able ductility. Wood admits of little permanent change of form, except in
a green state, although it sometimes settles a little, when it has been exposed
to pressure. Even stone will become permanently bent in the course
of years, as we may observe in old marble chimney pieces. But the most
ductile of all solid substances appears to be a spider's web. Mr. Bennet
twisted a thread of this kind many thousand times, and shortened it more
than a fourth of its length, yet it showed no disposition to untwist.

A ductile substance acquires the same cohesive and repulsive powers with

142 tECTURE Xirf.

regard to its new form, as it possessed in its original state; and when the
alteration of form has once commenced, those powers are neither increased
nor diminished by continuing the operation : the degree of flexure or torsion,
required for producing a further alteration, appears also to be little varied:
thus if the spider's web could at first be twisted only one half round, so as to
retain the jjower of returning to its original state, without any permanent
alteration of form, it would never acquire the power of returning more than
half a revolution, however it might be twisted. From a want of attention to
this consideration, a late respectable author has called in question, without
sufficient reason, tlie accuracy of Mr. Bennet's experiments.

A variation of ductility, in any substance, does not appear to depend on
any change in the magnitude of the ultimate powers of cohesion and repul-
sion. Steel, whether perfectly hard, or of the softest tem])er, resists flexure
with equal force, when the deviations from the natural state are small: but
at a eeitain point the steel, if soft, begins to undergo an alteration of form ;
at another point it breaks if much hardened; but when the hardness is mo-
derate, it is capable of a much greater curvature without either permanent
alteration or fracture ; and this quality, which is valuable for the purposes of
springs, is called toughness, and is opposed to rigidity and brittleness on the
one side, and to ductility on the other. There may, however, be an ap-
parent difference in the stiffness of some substances in different states, arising
from the greater facility with which their dimensions are extended in one di-
rection while they are contracted in another: thus elastic gum appears to
possess a much greater degree of stiffness when its hardness is increased by
cold than when it is at a more elevated temperature ; but the change pro-
duced in this case by heat is not an increase of that ductility which facilitates
a permanent alteration of form, but rather of the toughness which allows a
temporary change of figure, continuing only while the force is applied. The
effect of forging and of wiredrawing tends to lessen the ductility of metals,
and to render them tough, and even rigid: so that in hammering copper and
brass, and in drawing wire, it is necessary to anneal the metals more than
once by fire, in order to restore their ductility, Avhich is lessened by the opera-
tion. The corrosion of the surface of a metal by an acid is also said to
render it brittle ; but it is not impossible that this apparent brittleness may
be occasioned by some irregularity in the action of. the acid.

ON PASSIVE STREKGTH AND FRICTION. H3

The last effect of force on solid materials is their fracture, which, as well as
the former changes, may be produced either by impulse, or by pressure alone.
The action which resists pressure is called strength, and that which resists
impulse may properly be termed resilience. The strength of every body is in
the joint ratio of its immediate cohesion and repulsion, or elasticity, and of
its toughness, or the degree in which it may be extended, compressed, or
otherwise deranged, without a separation of its parts. 'I he resilience is
jointly proportional to its strength and its toughness, and is measured by the
product of the mass and the square of the velocity of a body capable of break-
ing it, or of the mass and the height from which it must fall in order to ac-
quire that velocity ; while the strength is merely measured by the greatest
pressure that it can support in a state of rest.

The simplest way in which a body can be broken, is by tearing it asunder.
The cohesive force continues to be increased as long as the tenacity of the
substance allows the particles to be separated from each other Avithout a per-
manent alteration of form; when this has been produced, the same force, if its
action is continued, is generally capable of causing a total solution of conr
tinuity; and sometimes a separation takes place without any previous altera-
tion of this kind that can be observed.

It follows from the nature of resilience, that a body of a pound weight,
falling from the height of a yard, Avill produce the same effect in breaking
any substance, as a body of three pounds falling from the height of a foot ;
so that here, as well as in the estimation of mechanical power, it is the energy,-
and not the momentum, that is to be considered as the measure of the effect.
If we know the strength of any substance, and the degree in which it is ca-
pable of extension, we may easily determine its resilience from a consideration
of the laws of pendulums. For the same weight which would break it by
pressure, will acquire a sufficient impulse for breaking it, if it fall from a
height equal to half the space through which the substance may be extended,
supposing the direction of the stroke to be horizontal, so that its effect may
not be increased by the force of gravity. Thus if the pressure of a weight of
100 pounds broke a given substance, after extending it through the space of
an inch, the same weight would break it by striking it with the velocity that
•would be acquired by the fall of a heavy body from the height of half an

144 LECTURE XIII.

inch, and a weight of one pound would break it by falling from a height of
50 inches.

It is obvious that the cohesive strength, as well as the resilience, of any sub-
stance must be simply proportional to the magnitude of its transverse section,
that is, of the surface of fracture. Some experiments appear to show that it
increases in a greater proportion than this surface, others that it increases in
a smaller proportion; but it is probable that in both cases some accidental ir-
regularities must have interfered, and that a, wire two inches in diameter is
exactly four times as strong as a wire one inch in diameter. The length has
no effect cither in increasing or in diminishing the cohesive strength; but the
resilience is proportional to the length, since a similar extension of a longer
fibre produces a greater elongation.

There is however a limit beyond which the velocity of a body striking
another cannot be increased without overcoming its resilience, and breaking
it, however small the bulk of the first body may be, and this limit depends
on the inertia of the parts of the second bod}^, which must not be disregarded
•when they are impelled with a considerable velocity. For it is demonstrable
that there is a certain velocity, dependent on the nature of a substance, with
which the effect of any impulse or pressure is transmitted through it; a cer-
tain portion of time, which is shorter accordingly as the body is more
elastic, being required for the propagation of the force through any part of
it; and if the actual velocity of any impulse be in a greater proportion to this
velocity than the extension or compression, of which the substance is capable,
is to its whole length, it is obvious that a separation must be produced, since
no parts can be extended or compressed which are not yet affected by the im-
pulse, and the length of the portion affected at any instant is not sufficient to
allow the required extension or compression. Thus if the velocity with
which an impression is transmitted by a certain kind of wood be 15000 feet in
a second, and it be susceptible of compression to the extent of -^-l-g- <*f its
length, the greatest velocity that it can resist will be 75 feet in a second,
which is equal to that of a body faliing from a height of about 90 feet. And
by a similar comparison we may determine the velocity which will be suffici-
ent to penetrate or to break oft' a substance in any other manner; if we calcu-
late the velocity required to convey the impulse frOm one part of the substance

ON PASSIVE STRENGTH AXD FUICTIOV. lAS

to the other, and ascertain the degree in which it can have its dimensions
altered without fracture.

It is easy to understand, from this statement, the different qualities of na-
tural bodies with respect to hardness, softness, toughness, and brittleness.
A column of chalk, capable of supporting only a pound, will perhaps be com-
pressed by it only a thousandth part of its length ; a column of elastic gum,
capable of suspending a pound, may be extended to more than twice its length,
the elastic gum will therefore resist the energy of an impulse incomparably
greater than the chalk. A diamond, so hard as to resist an enormous pres-
sure, may be broken, by a moderate blow, with a small hammer. A weight
of 1000 pounds, moving with a velocity of one foot in a second, and acting
on a small surface of a board, may possess sufficient energy to break or to
penetrate it; with a velocity of 100 feet in a second, a weight of .rV of ^
pound will possess the same energy, and produce the same effect, if it act on
a similar surface; but if the wood be so constituted, as to be wholly incapable
of resisting a velocity of 100 feet in a second, it may be penetrated by a
weight of -r4-5- of a pound as well as by one tenth, and by a moderately soft
body as well as by a harder one. The whole board, however, if at liberty,
would receive a much greater momentum from the impulse of the large
weight, than from that of the small one, its action being continued for a
much longer time. And it is for this reason that a ball shot by a pistol will
perforate a sheet of paper standing upright on a table, without overturning it.

The strength, or rather hardness, of a substance, exposed to the action of a
force that tends to compress it, must not be confounded with its resistance to
a force applied longitudinally and tending to produce flexure. A slender rod
of wood, when it yields to a longitudinal pressure, commonly bends before it
breaks, and gives way at last to the force by a transverse fracture ; but a
column of stone or brick, and even a thick pillar of wood, is crushed without
bending, and generally by a smaller force than that which would produce or
continue a flexure. In this case the parts slide away laterally, and in a rect-
angular pillar; if the texture of the substance is uniform, and not fibrous,
the surfaces of fracture will make nearly a right angle with each other, sup-
posing the resistance arising from the lateral adhesion, in the direction of any
surface or section, to be simply proportional to that section : but if this force,

VOL. I. U

146 LECTURE XIII.

like that of friction, is increased by a pressure which tends to bring the parts
into closer contact, the angle left after fracture must be more acute. (Plate
X. Fig. 124.)

The power of the force of lateral adhesion, in resisting fracture, is consider-
ed by Mr. Coulomb as nearly equal to that of the direct cohesion of the same
substance, or a little greater; while Professor Robison makes it twice as
great. If, however, this force be supposed to be simply equal to the direct
cohesion, it may be inferred that the strength of a square bar in resisting
compression is twice as great as its cohesive strength, allowing that the frac-
ture takes place in the surface of least resistance. It is, however, seldom
that the strength, with which a body resists compression, is in so great a pro-
portion as this to its cohesive strength; and where the substance is in any
degree composed of fibres, they must naturally produce great irregularities by
their flexure. The strength in resisting compression, must, according to
this statement, be simply proportional to the magnitude of the section of the
substance, although some experiments on freestone appear to indicate that
when the section is increased, the strength is increased in a greater proportion;
jind there is no reason to suppose that it can be influenced either way by the
length. A cylindrical or prismatic form is therefore the best that can be
given to materials of a given bulk, in order to enable them to resist a force
which tends to crush them, except tliat the additional pressure of their own
weight on the lower parts, requires that those parts should be a little stronger
than the upper parts. It appears also that something is gained by making
the outline a little convex externally: for it may be demonstrated, that for a
column or upright beam, to be cut out of a slab of equable thickness, supposing
the strength to be independent of pressure, the strongest form is a circle.
(Plate IX. Fig. 126, 127.)

When a body is broken by a transverse force applied very near to a fixed
point, its lateral adhesion is overpowered by the effect which we have called
detrusion, and its strength in this case is therefore generally somewhat greater
than its direct cohesive strength. But when the part to which the force is
Immediately applied is at a distance from the fixed point greater than about
one sixth of the depth, the fracture is no longer the immediate consequence
of detrusion, but of flexure.

2

ON PASSIVE STRENGTH AND FRICTION. 147

Flexure is the most usual manner in Avhich fracture is produced ; tlie super-
ficial parts on the convex side are most extended, and usually give way fiist;
except in soft fibrous substances, such as moist or green wood, which is more
easily crushed than torn; and in this case the concave side fails first, and be-
comes crippled, and the piece still remains suspended by the cohesion of the
fibres. After the convex surface has been cracked, the whole substance is
usually separated, but not always; for example, a triangular beam, with one
of the edges uppermost, may be charged with such a weight that the upper
edge may be divided and the lower part may remain intire.

When a column or rafteris broken by the operation of a longitudinal pres-
sure, the stiffness of the column being once overcome, a small addition of force is
usually sufficient to produce fracture, unless the pressure has been applied to a
part more or less distant from the axis ; for in this case a moderate force may
produce a moderate flexure, and a much greater force may be required to
break the column. But in general, the stiffness of columns is of more con-
sequence, than their strength in resisting transverse fracture.

The strength of beams of the same kind, and fixed in the same manner, in
resisting a transverse force, is simply as their breadth, as the square of their
depth, and inversely as their length. Thus if a beam be twice as broad as
another, it will also be twice as strong, 'but if it be twice as deep, it will be
four times as strong: for the increase of depth not only doubles the number
of the resisting particles, but also gives each of them a double power, by in-
creasing the length of the levers on which they act. The increase of the
length of a beam must also obviously weaken it, by giving a mechanical ad-
vantage to the power which tends to break it: and some experiments appear
"to show, that the strength is diminished in a proportion somewhat greater than
that in which the leno;th is increased.

's'

The strength of a beam supported at both ends, like its stiffness, is twice
as great as that of a single beam of half the length, which is fixed at one end ;
and the strength of the whole beam is agiiin doubled if both the ends are
firmly fixed.

The resilience of a prismatic beam, resisting a transverse impulse, follows

i48 LECTURE XIII,

. a law very different from that which determines its strength, for it is simply
proportional to the bulk or weight of the beam, whether it be shorter or
longer, narrower or wider, shallower or deeper, solid or hollow. Tims a beam
ten feet long will support but half as great a pressure, without breaking, as
a beam of the same breadth and depth, which is only five feet in length; but
it will bear the impulse of a double weight striking against it with a given
velocity, and will require that a given body should fall from a double height
in order to break it.

It is therefore of great consequence in the determination of the form and
quantity of the materials to be employed for any mechanical purpose, that
we should consider the nature as well as the magnitude of the forces which
are to be resisted. Stiffness, strength, or resilience, may be separately or
jointly required in various degrees. For a cicling, stiffness would be princi-
pally desirable ; for a door, strength; for the floor of a ball room, resilience;
for a coach spring, resilience and flexibility, that is, resilience witliout stift-
pess. An observatory should be as stiff' as possible, a ship as strong as pos-
fsible, a cable as resilient as possible.

It is a common remark that a floor which shakes is the strongest ; and, im-
probable as it appears at first sight, it may perhaps be founded in truth: for
if the absolute strength of a stiff' and a shaking floor were equal, the shaking-
floor would bear the effiects of motion with the least injury. It is possible
that a stiff" floor, which "would support a numerous assembly, might give way
at a ball; while a more resilient one, which would be suited for dancing,
might be destroyed by a crowded concert.

A coach spring, divided into plates, has the same power of resisting, with-
out being broken, the momentum of the carriage, arising from sudden eleva-
tions and depressions, as. it would possess if it formed one entire mass,
' while its greater flexibility allows it to regulate these motions in a much more
gradual and gentle manner. A single piece of timber may perhaps sometimes
have too much of the flexibility of a coach spring, its strata sliding in some
degree on each other: in such a case its stiff'ness and strength may be in-
creased by binding it very firmly with hoops. .

ON PASSIVE STRENGTH AXD FRICTION. liQ

The transverse strength of a perfectly elastic substance, fixed at one end,
is to its direct cohesive strength as the depth of the substance to six times its
length. This proportion is equally applicable to such substances as resist
compression more strongly than extension: for their immediate repulsive
force is probably not greater than their cohesive force, when their dimensions
are equally changed, so that the middle of the beam is always in its natural state;
and when the curvature is sufficient to overcome the cohesive force, the
whole beam must give way. When, however, the substance is less capable
of resisting compression than extension, the concave surface gives way first,
and the strength depends immediately on the repulsive strength of the sub-
stance. This is perhaps the reason, that, in experiments on beams of oak,
the transverse strength has seldom been tbund in a greater ratio to the whole
cohesive strength than that of the depth to nine times the length.

It may be inferred from the consideration of the nature of the different
kinds of resistance which have been explained, that if we have a cylindrical
tree a foot in diameter, which is-to be formed into a prismatic beam by flat-
tening its sides, we shall gain the greatest stiflPness by making the breadth or
thickness 6 inches, and the depth 104^, the greatest strength by making the
breadth 7 inches and the depth 9-1, and the greatest resilience by making the '
beam square. The stiffness and the strength of the beam may be much in-
creased by cutting the tree into, four pieces, turning their edges outwards,
and uniting them so as to make a hollow beam: but it will require great
strength of union, to make the whole act as one piece, and the resilience of
the bean> will be rather diminished than increased by the operation.

The adoption of the hollow masts and beams which an ingenious mechanic
has lately introduced, requires, therefore, some caution. For where an im-
pulse is to be resisted, such a mast is no stronger than a solid mast of the
same weight, and much weaker than a solid mast of the same diameter. The
force of the wind is, however, rather to be considered as constituting a pres-
sure than a finite impulse, except when a sudden scpiall carries a loose sail
before it with considerable velocity. A similar caution may also be extended
to some other attempts to make improvements in naval architecture: it is a
common opinion, and perhaps a well founded one, that flexibility is of great

150 ■ LECTURE XIII.

ad^'antag•e to a ship's sailing; if therefore we sacrifice too much resilience to
strength, and too much of both to stiffness, we may perhaps create greater
evils than those which we wish to avoid.

We have hitherto supposed the beams, of which the strength has been com-
pared, to be prismatic, that is, of equal breadth and thickness throughout,
which is not only the simplest form in theory, but the most generally useful in
practice. If however we have the power of giving any form that we please to
materials of a certain weight, which may often be done where several smaller
pieces are to be cut out of a larger one, or a larger one to be composed of
several smaller ones, or where the materials are either ductile or fusible, it is
frequently possible to determine a more advantageous form than that of an
equable beam or column. For since the extension which the parts of the
substance admit, without giving way, is the limit of their strength, if the
depth of a beam be everywhere equal, and the curvature unequal, the frac-
ture will first take place where the curvature is greatest, and the superfluous
strength of the other parts will be lost; so that, in order to have the greatest
strength that a given quantity of materials is capable of affording in a beam of
given length, the form must be such that the strength may be everywhere
equal, the tension of the surface being equal throughout; and the depth
must be as much smaller as the curvature is greater. It is also necessaiy to
consider whether the substance is likely to be crushed, and whether it is li-
able to be broken by detrusion, rather than by flexure. Sometimes the depth
of the beam may be limited, and sometimes its breadth; or it may be required
that the breadth and depth may be always equal or proportional to each other,
and the force may be either applied at one end of the beam, or it may be
equally divided throughout its length ; it may also principally depend on the
weight of the substance itself; and the strongest form will be different, accord-
ing to the different conditions of its application. In the most common cases,
the outline must be either triangular, or parabolic, as if the point of the tri-
angle were rounded off" ; but the curves required are sometimes of much more
difficult investigation. (Plate X. Fig. 128. . 147.)

The strength of bodies is sometimes employed in resisting torsion, as in the
case of the axles of wheels and pinions, rudders of ships, and screws of all

ON PASSIVE STRENGTH AND FRICTION. 151

kinds: but there is seldom occasion to determine their absolute strength in
resisting a force thus applied : if they are sufficiently stiif, their parts arc not
often separated by any violent efforts.

In Older to investigate the strength of the various substances employed for
the purposes of the mechanical arts, it is most convenient to use a ma-
chine furnished with proper supports, and gripes, or vices, for holding the ma-
terials, and with steelyards for ascertaining the magnitude of the force ap-
plied, while the extension or compression is produced by a screw or a winch,
with the intervention of a wire, a chain, or a cord : provision ought also to
be made for varying the cHrection of the force, when the flexure of the ma-
terials renders such a change necessary, (Plate XI. Fig. 148.)

According to the experiments of various -authors, the cohesive strength of
a square inch of razor steel is about 150 thousand pounds, of soft steel 120,
of wrought iron 80, of cast iron 50, of good rope 20, of oak, beech, and
willow wood, in the direction of their fibres 12, of fir 8, and of lead about
3 thousand pounds : the cohesive strength of a square inch of brick 300, and
of freestone 200. Teak wood, the tectona grandis, is said to be still stronger
than oak.

The weight of the modulus of the elasticity of a square inch of steel, or
that weight which would be capable of compressing it to half its dimensions,
is about 3 million pounds; hence it follows, that when a square inch of steel
is torn asunder by a weight of 150000 pounds, its length is first increa.sed to-
one twentieth more than its natural dimensions.

The strength of different materials, in resisting compression, is liable to
great variation. In steel, and in willow wood, the cohesive and repidsive
strength appear to be nearly equal. Oak will suspend much more than fir;
but fir will support twice as much as oak; probably on account of the.cuiva-
ture of the fibres of oak. Freestone has been found to support about 2000
pounds for each square inch, oak in some practical cases more than 4000.

The strongest wood of each tree is neither at the centre nor at the circum-
ference, but in the middle between both; and in Europe it is generally thicker

152 tECTURE XIIX.

and firmer on the south east side of the tree. Although iron is much stronger
than wood, yet it is more liable to accidental imperfections; and when it
fails, itgives no warning of its approaching fracture. The equable quality of
steel may be ascertained by corrosion in an acid; but there is no easy mode
of detecting internal flaws in a bar of iron, and we can only rely on the ho-
nesty of the workman for its soundness. Wood, when it is crippled, com-
plains, or emits a sound, and after this, although it is much weakened, it
may still retain strength enough to be of service. Stone sometimes throws
off small splinters when it is beginning to give way: it is said to be capable
of supporting by much the greatest weight when it is placed in that position,
with respect to the horizon, in which it has been found in the quarry.

It is obvious that when the bulk of the substance employed becomes
very considerable, its weight may bear so great a proportion to its strength
as to add materially to the load to be supported. In most cases the weight
increases more rapidly than the strength, and causes a practical limitation
of the magnitude of our machines and edifices. We see also a similar limit
in nature: a tree never grows to the height of 100 yards; an animal is never
strong enough to overset a mountain. It has been observed that whales are
often larger than any land animals, because their weight is more supported by
the pressure of the medium in which they swim.

The force of friction, which resists the sliding of different bodies on each
other, seems to be intimately connected with that lateral adhesion, or rigidity,
which is opposed to the internal displacement of the parts of a single body, by
the effect which we have denominated detrusion : and when the friction is con-
sidered as resisting pressure rather than motion, it approaches still more nearly
to the same force. It is probably derived in great measure from the strength of
the protuberant particles, which must be broken, bent, or compressed by the
motion of the bodies on each other: but it is not always that the existence
of such particles can be asserted, much less can they be made perceptible to
the senses, and we can only examine the effects which they may be supposed
to produce, by immediate experiments on the forces required to counteract
them. Such experiments have been made on a very extensive scale by
Musschenbroek and Coulomb, and many of their results have been confirmed
by Mr. Vince, in a simple and elegant manner.

OK TASSIVZ STRENGTH AND FRICTION. 15*

With a few exceptions, the friction of all solid bodies is, either perfectly, or
Very nearly, a uniformly retarding force, neither increasing nor diminishing
when the relative velocity of the bodies concerned is changed. The friction
of some rough substances is a little increased with the velocity, but, as they
become more polished, this variation disappears. When, however, the mo-
tion is wholly extinct, and the bodies remain in contact with each other,
their adhesion is usually greater than the friction, and by a continuation of
the contact, it may become twice or even thrice as great, especiidly where the
surfaces are large, and the substances but moderately hard.

The truth of tlie assertion, that friction is a uniformly retarding force, may
be shown very conveniently by means of Atwood's machine for experiments
on accelerated motion. By suffering the axis of the pulley to rest on the
surface of any fixed substance, we may subject it to a friction of which the
magnitude may be varied by diflerent methods; and we shall find that the
motions of the boxes still indicate the action of a uniformlv acceleratinir
force,' the spaces described being always proportional to the squares of the
times of descent; it follows, therefore, that since the operation of gravity is
uniform, th^t of friction which is deducted from it at each instant, must
also be uniform, in order that the remaining acceleration may follow the
same law.

The uniformity of the force of friction may also be shown by the descent
of a flat substance on an inclined plane: if the body be caused to begin its
descent with a certain velocity, it will be retarded, when the resistance is-
greater than the relative force of gravity : in this case the retardation will
continue until it is wholly stopped, the resistance not diminishing with the
velocity. If, on the contrary, the relative weight overpowers the resistance
at first, the motion will be continually accelerated, the resistance not being
increased by the increase of the velocity. But since every experiment of
this kind must be performed in the presence of the air, the resistance of this
fluid, which follows another law, will in the end prevent the acceleration.

It may in general be asserted, with some exceptions, that the force of
friction is simply proportional to the weight or pressure that brings the sub-
stances concerned into contact, independently of the magnitude of their sur-

VOL. I. X

154 LECTURE XIII-

faces : but Mr. Coulomb has observed that in many cases there is, besides
this force, another resistance, amounting to several pounds for each square
foot of the surface, which is independent of the pressure; and by calculatina:
these forces separately, we may probably always ascertain the whole resist-
iince with sufficient accuracy. This constant portion is usually much smaller
than that which varies with the weight, and in all common cases it may be
safely neglected, and the friction of stone on stone may be called equal to
one half of the pressure, that of wood on wood one third, and that of metal
on metal one fourth; and this may serve as an estimate sufficiently accurate
for calculating the effiscts of machines; although, if their parts were, perfectly
adjusted to each other, and all the surfaces well polished, the friction would
not in general exceed one eighth of the pressure, whatever might be the na-
ture of the materials. The application of unctuous substances lessens the
friction in the first instance; but unless they are frequently renewed, they
sometimes tend rather to increase it.

The simplest mode of ascertaining the magnitude of the friction of two
bodies, is to incline their common surface to the horizon until the one begins
to slide on the other: this point determines the magnitude of their adhesion;
but in order to find that of their friction when they are in motion, they must
be first separated, and then allowed to move on each other, while the vhole
apparatus is gently agitated. The friction will then be to the pressure, as the
height of the inclined plane to its horizontal length, Avhcn the inclination is
barely such as to allow the continuance of any motion which is imparted to
the substance placed on the plane.

It follows from the doctrine of the resolution of force, that when any body
is to be drawn along a horizontal surface, which produces a resistance propor-
tionate to the pressure, a part of the force may be advantageously employed
in diminishing the pressure produced by the weight of the body ; hence, in
order for the most advantageous application of the force, its direction must
be inclined to the horizon, and it may be demonstrated, that the inclination
must be the same with that of a plane on which the relative weight of the
body is precisely equal to the friction. Thus if we can determine the incli-
nation of a road which is barely sufficient for a carriage to descend on it by
its own weight, tlie same inclination will be the best possible for the appli-

ON PASSIVE STRENGTH AND FRICTION. 155

cation of any force by Avhich the can'iage is to be drawn along a horizontal
road of the same materials.

It is obvious that an inclined plane, on which a weight rests by means of
an adhesion proportionate to the pressure, can never be forced backwards by
any increase of that pressure, since the resistance increases in the same pro-
portion, and continues always sufticient to prevent the relative motion of the
weight and the inclined plane. Two such planes, put together, would con-
stitute a wedge, which would be equally incapable of giving way to a pressure
applied to its opposite surfaces, each of them possessing similar properties
with respect to friction. Thus, if the friction or adhesion were exactly one
eighth of the pressure, the height of the inclined plane would be one eighth of
its length, and the back of the wedge one fourtli. Such a wedge Avould
therefore possess a perfect stability with respect to any forces acting on its
inclined surfaces. But the effects of agitation, and the minute tremors pro-
duced by percussion, have a great tendency to diminish the force of adhesion,
by interrupting the intimacy of contact; and where a pin, a nail, or a screw
is required to retain its situation with firmness, the inclination of the surfaces
must be smaller than the angle of such a wedge as is barely capable of afford-
ing a sufficient resistance in theory.

It appears, therefore, that the force of lateral adhesion, acting between two
bodies in contact, is of great importance in all mechanical arts; the firmness
of architecture and of carpentry depends in great measure on it. This kind of
resistance being equally powerful, when the force is applied in the direction of
the surface, to whatever part of the surface it may tend, it follows that any
body which is subjected to friction on all sides, will retain its situation with
the same force, that was used in overcoming the friction, in order to bring it
into that situation, or rather with a greater force, since the lateral adhesion is
generally a little greater than the friction: so that a cylindrical wire cannot
be withdrawn from a perforation in a board, by any direct force less than that
which was employed in introducing it; and this kind of stability, together
with that of a wedge or nail resisting a lateral pressure, constitutes the se-
curity of the lighter structures of carpentry, while those of architecture re-
ceive a great part of their firmness from the accumulation of weight, which

156 . • LECTURE XIII.

makes the resistance of their lower parts to any lateral motion almost in-
superable.

When a hard body penetrates another, or when a substance is ground away
by the attrition of another, the force, which opposes the motion, is to be con-
sidered, like the force of friction, as a uniformly retarding force. There is no
reason for imagining the stiffness of a bar, whether longer or shorter, to de-
pend on the velocity of the body that bends it, and the space through which
it may be bent, without breaking, is also limited only by the toughness of
the materials. In the same manner, when the internal parts of a solid are
broken and displaced by the penetration of another, or its external parts
abraded by its attrition, the resistance is the same, whatever the velocity
may be, and the space described by the body, before its velocity is destroyed,
is always proportional to the square of that velocity, or to the energy which
' results from a combination of the proportions of the velocity and the mo-
mentum.

157

LECTURE XIV.

ON ARCHITECTURE AND CARPENTRY.

X HE subjects, which we have lately examined, are to be considered as pre-
liminary to the particular departments of practical mechanics. The first di-
vision of these is to consist of such as are employed in resisting forces of various
kinds, but they may almost all be referred, without inconvenience, to the ge-
neral heads of architecture and carpentry, of which the principal business is, to
resist the force of gravitation. Architecture, in its most extensive sense, mav
be understood as comprehending carpentry, but the term is more usually ap-
plied to the employment of those materials, which are only required to resist
the effects of a force tending principally to produce compression, while the
materials used by carpenters are frequently subjected to the operation of a
force which tends to extend or to bend them: the works of architects beins
commonly executed in stone or brick, and those of carpenters in wood, besides
the occasional use of iron and other metals,- in both cases.

The simplest problem in mechanical architecture appears to be, to deter-
mine the most eligible form for a column. The length and weight being sup-
posed to be given, it is of importance to investigate the form which affords
the greatest possible strength ; but it is somewhat difficult tQ^. ascertain the
precise nature and direction of all the forces which are to be resisted. If we
considered the column as a beam fixed in the ground, and impelled by a
transverse force, it ought to be much tapered, and reduced almost to a point
at its extremity; but it is seldom that any force of this kind can be power-
ful enough to do more than overcome tlie weight alone of the column,
and it is only necessary to regard the load which presses vertically on it;
and whether we consider the force as tending to bend or to crush it, the
forms commonly employed will appeat to be sufficiently eligible. ]\Ir. La-

158 LECTURE XIV.

grange seems to have been misled by some intricacies of mathematical investi-
gation, too remote from physical accuracy, when he calculated that a cylinder
was the strongest form for resisting flexure; that form approaches in reality
much more nearly to-an oblong spheroid, of which the outline is elliptical.
The consideration of the flexure of a column is, however, of little practical
importance in architecture, for upon a rough estimate of the properties of
the materials usually employed, it may be computed that a column of stone
must be about forty times as high as it is thick, in order to be capable of
being bent by any weight which will not crush it ; although a bar of wood
or of iron may be bent by a longitudinal force, if its length exceed about
twelve times its thickness. The force may therefore be considered as tend-
ing only to crush the column ; and since the inferior parts must support
the Aveight of the superior parts, in addition to the load which presses on
the whole column, their thickness ought to be somewhat increased ; and it
appears from a consideration of the direction in which the fracture is most
easily effected, that the outline ought to be made a little convex externally,
and more curved above than below, which is the usual, althougli not the
universal practice ; an elliptic arc is perhaps the most eligible outline, or a
curve formed by bending a ruler fixed at the summit of the column ; some-
times the form is made to differ little from a cone, but such a figure is very
inelegant. The diminution of the thickness amounts in general to about one
sixth or one seventh of the whole, and sometimes to one fourth. (Plate XI.
Fig. 149.)

For a light house, where a great force of wind and water was to be resist-
ed, Mr. Smeaton chose a curve with its concavity turned outwards. If we
calculated what would be the best form for a wooden pillar, intended to re-
main always ipimersed >n the water to a certain depth, we should find that a
cone or pyramid would possess the greatest possible strength for supporting
the motion of the water; and a cone more acute than this would be equally
capable of resisting the force of the wind, supposing it to be less active than
that of the water ; the part below the water might, therefore, be widened so
as to become a portion of a more obtuse cone, the upper part remaining
more slender; and the greatest agitation of the sea being near its surface,
the basis of the pillar might be a little contracted, so as to have the outline
of the lower part a little convex outwards, if the depth of the water were

2

ON ARCHITECTURE AND CARPENTRV. 159

considerable. But in the case of a building of stone, the strength often de-
pends as much on the weight of the materials as on their cohesive power :
and the lateral adhesion, which is materially influenced by the weight,
constitutes a very important part of the strength. For resisting a force
which tends to overset the building, the form in which the weight gives
the greatest strength is that of a conoid, or a solid of whicli the outline is a
parabola, concave towards the axis: and for procuring, by means of the
weight, a lateral adhesion which is every where proportional to the force, the
form must be cylindrical. So that in a building circumstanced as we have sup-
posed the pillar to be, there appears to be no reason for making either portion
of the outline taken separately, convex towards the axis, although the angu-
lar junction of the two portions of cones might very properly be rounded off;
and the upper parts might be a little enlarged if it were desirable to reduce
the thickness of the walls. But the Eddystone light house is completely
above the level of the sea, although in stormy weather every part of it is ex-
posed to the action of the waves, fhe water being sometimes thrown up to a
much greater height than that of the light house: so that it may be consider-
ed as exposed to the force of a fluid more and more powerful as it is nearer to
the foundation; and in this point of view its form differs but little from that
which the most accurate theory would point out; but it is probably a little
weaker about the middle of its height, or somewhat lower, than in any other
part. (Plate XI. Fig. 150.)

A wall must be reduced in thickness as it rises, for the same reason as a
column is diminishecl; and if the wall is a part of a house, it must be reduced-
in a still greater degree, since the load, which is to be supported by it at dif-
ferent parts of its height, is usually much varied, by the weight of the floors,
and of the contents of the apartments. But sometimes the obliquity of the
surface of the wall may become inconvenient, by promoting the growth of moss
and weeds. In building a wall, the first precaution that is required, is to
dig deep enough to ascertain the nature of the ground; the next, to lay a
sufficiently extensive and firm foundation ; and it has been very properly re-
commended that where a well is wanted, it should be dug before the founda-
tions of the house are laid, in order to examine the qualities of the different
strata which are to support them. The disposition of the stones, or bricks, is
not a matter of indifference ; the strength is obviously greatest when all the

160 tECTURE XIV.

surfaces are either horizontal or vertical; for if they are oblique, thej' must
have a tendency to slide away laterally, and the wall must be very liable to
crack: hence the reticulated walls, sometimes employed by the ancients, of
which all the joints were oblique, possessed but little durability. If the ma-
terials are thrown together without order, they press on the parts in contact
with them ; but occasionally, as in the case of piers, or quays, this circum-
stance may be of some advantage in opposing external pressure; or at least
the effect of such a pressure may remove the inconvenience which would
otherwise arise from the irregularity of the structure.

In some cases it is necessary to unite the stones of a building mechanically,
either by cramps of iron, fixed by means of melted lead, or by other methods,
similar to those which are more usually employed in carpentry. Mr. Smeaton ■•
was obliged to fix the stones of his light house to the rock and to each other,
by dovetail joints, and to connect each horizontal tier with the tier below it,
by pins of wood passing through the stones, with wedges driven in at each end,
to make them expand, and tie the stones fast together. But, in general, it is
sufficient to employ mortar, made of lime or terras, and sand, of which the
ufility depends principally on the firmness and cohesive strength that it ac-
quires in consequence of its chemical properties. Sometimes the whole
structure is composed of a mass which is at first soft, but hardens as it dries;
in this manner mud walls are built; and the materials called pis6 are of a si-
milar nature. (Plate XL Fig. 151.)

The wall or column, when raised, must in general help to support a single
lintel or beam, an arch, a dome, or a roof of carpentry. The strength of the
lintel depends more on the nature of the substance, than on any art employed
in forming it, excepting the precaution to give it as much depth as is con-
venient, especially towards the middle, if the depth be any where unequal ;
but the construction of an arch affords considerable scope for the exertion of
mechanical science.

The simplest theory of the arch, supporting itself in equilibrium, is that of
Dr. Hooke, the greatest of all philosophical mechanics. The arch, when it
has only its own weight to bear, may be considered as the inversion of a chain
suspended at each end ; for the chain hangs in such a form, that the weight of

ON ARCHITECTURE AND CARPENTRY. l6l

each link is held in equilibrium by the result of the two forces acting at its ex-
tremities ; and these forces or tensions are produced, the one by the weight of
the portion of the chain below the link, the other by ^:he same weight increased
by that of the link ; both of them acting originally in a vertical direction. Now
supposing the chain inverted, so as to constitute an arch of the same form
and weight, the relative situations of all the lines, indicating the directions of
the forces, will remain the same, the forces acting only in contrary directions,
so that they are compounded in a similar manner, and balance each other on
the same conditions, but with this difference, that the equilibrium of the
chain is stable, and that of the arch tottering. This property of the equili-
brium renders an ;iccurate experimental proof of the proposition somewhat
difficult ; but it may be shown that a slight degree of friction is sufficient for
retaining in equilibrium an arch formed by the inversion of a chain of beads.
The figure is called a catenaria,when the links are supposed to be infinitely small,
and the curvature is greatest at the middle of the chain. It is not at all necessary
to the experiment that the links of the chain be ecjual; the same method may
be applied to the determination of the form requisite for an equilibrium, what-
ever may be the length or weight of the constituent parts of the arch ; and when
the arch is to be loaded unequally in different parts, we may introduce this cir-
cumstance into the experiment, by suspending proportional weights from
different parts of the chain. Thus we may employ Avires or other chains to
represent the pressure, and adjusting them by degrees, till their extremities
hang in a given line, we may find the form which will best support the weight
of the materials, the upper surface,or extrados,of the arch being represented by
the same line in an inverted position, while the original chain shows the forni
of the intrados, or of the. curve required for the arch stones themselves. In
common cases, the form thus determined will differ little from a circular arc,
of the extent of about one third of a whole circle, rising from the abutments
with an inclination of 30° to the vertical line, and it never acquires a direction
much more nearly perpendicular to the horizon. It usually becomes more
curved at some distance below the summit, and then again less curved. (Plate
XL Fig. 152 . . 154.)

But the supposition of an arch resisting a weight, which acts only in a ver-
tical direction, is by no means perfectly applicable to cases which generally
occur in practice. The pressure of loose stones and earth, moistened as they

VOL. I. y

15S LECTURE XIV.

frequently are by rain, is exerted very nearly in the same manner as the pres-
sure of fluids, which act equally in all directions: and even if they were united
into a mass, they would constitute a kind of wedge, and would tlms produce
a pressure of a similar nature, notwithstanding the precaution recommended
by some authors, of making the surfaces of the arch stones vertical and hori-
zontal only. This precaution is, however, in all respects unnecessary, because
the effect which it is intended to obviate, is productive of no inconvenience,
except that of exercising the skill of the architect. The effect of such a pres-
sure only requires a greater curvature near the abutments, reducing the form
nearly to that of an ellipsis, and allowing the arch to rise at first in a vertical
direction.

A bridge must also be so calculated as to support itself without being in
danger of falling by the defect of the lateral adhesion of its parts, and in order
that it may in this respect be of equal strength throughout, its depth at
each point must be proportional to the weight of the parts beyond it. This
property belongs to the curve denominated logarithmic, the length cor-
responding to the logarithm of the depth. If the strength were afforded
by the arch stones only, this condition might be fulfilled by giving them the
requisite thickness, independently of the general form of the arch : but the
whole of the materials employed in the construction of the bridge, must be
considered as adding to the strength, and the magnitude of the adhesion as
depending in great measure on the general outline.

We must examine in the next place what is the most advantageous form
for supporting any weight which may occasionally be placed on the bridge,
in particular at its weakest part, which is usually the middle. Supposing
the depth at the summit of the arch and at the abutments to be given, it may
be reduced considerably in the intermediate parts, without impairing the
strength, and the outline maybe composed of parabolic arcs, having their
convexity turned towards each other. This remark also would be only ap-
plicable to the arch stones, if they afforded the whole strength of the
bridge, but it must be extended in some measure to tlie whole of the
materials forming it.

If therefore we combine together the curve best calculated for resisting the

2

ON ARCHITECTURE AND CARPENTRY. 163""

pressure of a fluid, which is nearly elliptical, the logarithmic, and the pa-'
rabolic curves, allowing to each its due proportion of influence, we may
estimate, from the comparison, which is the fittest form for an arch intended
to support a road. And in general, whether the road be horizontal, or a
little inclined, Ave may infer that an ellipsis, not diff'ering much from a
circle, is the best calculated to comply as much as possible with all the con-
ditions. (Plate XL Fig. 155.)

The tier of bricks cut obliquely, which is usually placed over a window
or a door, is a real arch, but so flat as to allow the apparent outline to be
horizontal. Mr. Coulomb observes, that the greatest strength is obtained
by causing all the joints to tend to a single point: but little dependence can
be placed on so flat an arch, since it produces a lateral thrust which may easily
overpower the resistance of the wall. For the horizontal force, required to
support each end of any arch, is equal to the weight of a quantity of the
materials which are supported by its siimmit, supposed to be continued, of
their actual depth, to the length of a semidiameter of the circle of which the
summit of the arch is a portion. This simple calculation will enable an ar-
chitect to avoid such accidents, as have too often happened to bridges for want
of sufficient firmness in the abutments. The equilibrium of a bridge, so far
as it depends only on the form of the arch, is naturally tottering, and the
smallest force which is capable of deranging it, may completely destroy the
structure; but when the stones or blocks composing it have flat surfaces in
contact with each other, it is necessary that the line expressing the direc-
tion of the pressure be so much disturbed, as to exceed at some part the li-
mits of these surfaces, before the blocks can be displaced. When this curve,
indicating the general pressure which results from the efiect of a disturb-
ing force, combined with the original thrust, becomes more remote from
the centre of the blocks than one sixth of their depth, the joints will begin
to open on the convex side, but the arch may still stand, while the curve
remains within the limits of the blocks.

It is desirable that the piers of bridges should be so firm, as to be able not
only to support the weight of half of each adjoining arch, but also to sustain,
in case of the failure of one of those arches, the horizontal thrust of the other;
and the same condition is obviously necessary for the stability of walls of any

164 LECTURE XIV.

kind which support an arched or vaulted roof, wherever there is no oppor-
tunity of assisting the strength by ties or chains of any kind. There are two
ways in which such a pier or wall may give way: it may either be overset, or
caused to slide away horizontally; but since the friction or adhesion which
resists the horizontal motion is usually greater than one third of the pressure,
it seldom happens that the whole thrust of the arch is so oblique as not to
produce a sufficient vertical pressure for securing the stabiUty in this respect;
and it is only necessary to make the pier heavy enough to resist the force
which tends to overset it. It is not, however, the weight of the pier only, but
that of the half of the arch which rests on it, that resists any etfort to over-
set it, and in order that the pier may stand, the sum of these weights, act-
ing on the end of a lever equal to half the thickness of the pier, must be
more than equivalent to the horizontal thrust, acting on the whole height of
the pier. The pier may also be simply considered as forming a continuation
of the arch, and the stability will be preserved as long as the curve, indicat-
ing the direction of the pressure, remains within its substance.

The arches of Black Friars bridge are of an oval form, composed of cir-
cular arcs, and differing but little from ellipses ; the arch stones are so large that
the pressure in any direction might be very greatly increased without caus-
ing the general result to exceed the limits of their magnitude, or even to
approach very near to their surfaces. (Plate XII. Fig. 156.)

The construction of a dome is less difficult than that of an arch, since the
tendency of each part to fall is counteracted, not only by the pressure of the
parts above and below, but also by the resistance of those which are situ-
ated on each side. A dome may therefore be erected witliout any tempo-
rary support, like the centre which is required for the construction of an
arch, and it may at last be left open at the summit, without standing in
need of a keystone, since the pressure of the lower parts is sufficiently re-
sisted, by the collateral parts of the same horizontal tier, to prevent the pos-
sibility of their falling in, or of their forcing out the upper parts. The weight
of the dome may however force out its lower parts, if it rises in a direction
too nearly vertical ; and supposing its form spherical, and its thickness
equable, it will require to be confined by a hoop or chain as soon as the span
becomes eleven fourteenths of the whole diameter. But if the thickness of

ON ARCHITECTURE AND CARPENTRY. l€^

the dome be diminislied as it rises, it will not require to be bound so high:
thus, if the increase of thickness in descending begin at about 30 degrees
from the summit, and be continued until, at about 60 degrees, the dome be-
comes a little more than twice as thick as at first, the equilibrium will be
so far secure; and at this distance it would be proper to employ either a
chain, or some external pressure, to preserve the stability, since the weight
itself would require to be increased without limit, if it were the only source
of pressure on the lower parts. (Plate XII. Fig. 157.)

The dome of St. Paul's cathedral is elliptical, and is built of wood, and
confined by strong chains, consisting of iron bars; that of the Pantheon at
Rome is nearly circular, and its lower parts are so much thicker than its
upper parts, as to aflPord sufficient resistance to their pressure : they are sup-
ported by walls of gVeat thickness, and furnished with many projections
which answer the purpose of abutments and buttresses. (Plate XII. Fig.
158, 159.)

A knowledge of the parts and proportions usually assigned to columns, and
to buildings in general, and of their technical names and divisions, belongs
rather to the subject of ornamental than to that of useful architecture; and
the consideration of symmetry and elegance is in great measure foreign to
that of the mechanical properties of bodies, which it is our present busi-
ness to investigate. The five orders of ancient architecture are found to
differ considerably in their proportions, in the different remains of Greek
and Roman edifices ; but there always remain some characteristic distinctions :"
the Tuscan is known by its strength and simplicity, Avithout any peculiar
ornament; the Doric by its triglyphs, or triangular grooves, above each
column, imagined to represent the ends of beams; the Ionic by the large
volutes, and the Corinthian by the foliage, respectively enveloping their
capitals; and the Composite usually by the combination of both these
characters; each order being lighter than the preceding, and being sometimes
employed with it in the upper parts of the same building. In general, tlie
length of the Tuscan column, with its capital, is equal to about seven
diameters of the base, that of the Doric eight, of the Ionic nine,
and of the Corinthian and Composite ten diameters. (Plate XII. Fig.
160 . . 164.)

\Q6 LECTURE XIV.

The Gothic architects appear to have been superior to tlie Greeks
in the mechanical arrangement of the parts of their edifices, so as to
produce the most advantageous effect in preserving the general equi-
librium. They made every essential member of their buildings a constituent
part of their system of ornament, and even those embellishments, which, by a
superficial observer, might be deemed useless or prejudicial, are frequently cal-
culated, either by their strength, or by their weight, to serve some beneficial
purposes. The pointed arch is not in all cases well calculated for equilibrium,
but when it has a pillar resting on its summit, it is exceedingly strong.
The most celebrated of modern architects have sometimes been less successful
than those of the middle ages ; and for want of paying sufficient attention to
mechanical principles, have conunitted such errors in their attempts to pro-
cure an equilibrium, as have been followed by the most mischievous conse-
quences. Examples of this might be pointed out in the bridges of our own
country, and the churches of others; but if we are masters of the true theory
of pressure, we shall be able to avoid similar errors, without examining the
particular circumstances which have occasioned these accidents. (Plate XII.
Fig. 165.)

The principles of equilibrium, which are employed in architecture, are
equally applicable to many cases in carpentry; and where the work is princi-
pally calculated to Avithstand a thrust, there is little difference in the operation
of the forces concerned; but where a tie is introduced, that is, a piece which
resists principally by its cohesive strength, the parts often require to be ar-
ranged in a different manner. The general principle, that three forces, in
order to retain each other in equilibrium, must be proportional to the sides
of a triangle corresponding to their directions, is sufficient for determining
the distribution of pressure in almost all cases that can occur. The conclu-
sions which have been drawn from this principle, and from other similar con-
siderations, respecting the strength of materials, will also be of great use in
directing us how to determine the best forms for beams, rafters, and timbers
of all kinds, and how to arrange and connect them in the best manner with
each other.

The employment of the cohesive strength of materials in carpentry intro-
duces a difficulty which scarcely exists in architecture. Tavo blocks, placed

ON ARCHITECTURE AND GARPENTRT. - 1^7

on each other, resist the force of a weight compressing them, as effectually as if
they formed hat one piece: biit they have no sensible cohesion to enable them
to withstand a force tending to separate them, and if they are required to co-
operate by tlieir cohesive strength, some mode of uniting them must be found.
For this purpose, it is generally necessary to sacriiice a considerable portion
of the strength of the materials employed. The most usual mode is to place
the ends of the pieces side by side, first reducing their dimensions, where a
regular outline is required ; and to jjrocure a firm adhesion between them by
means of external pressure, or to employ the natural adhesion of some parts
which are made to project beyond the rest in each piece, and receive in their
interstices the corresponding projections of the other piece.

Where the adhesion is produced by external pressure only, it is of advan-
tage to subdivide the joints into a considerable number of parts, as is usually
done in the masts of ships, and to make the junction of any two pieces, fol-
lowing each other in the same line, as distant as possible from any other
junction; for in this manner, the loss of strength may be diminished almost
without limit, provided that the distance between the joints be great enough
to afford a firm adhesion to each part. The junction may also be formed by
an oblique line ; but the obliquity must be so great that any lateral pressure
may increase the stability of the wedge, the length being in a greater pro-
portion to the depth than the pressure to the adhesion that it occasions; and
the pieces must be pressed together very forcibly by means of hoops or bolts.
(Plate XIII. Fig. 166 . . 168.)

Where the natural adhesion of some projecting parts in each piece is em-
ployed, the projections must be sufficiently long to secure their strength,,
and they must be as Httle. prominent as possible, partly because the contigu-
ous piece nuist be excavated for their reception, and partly because their
strength is diminished when they project more than one sixth of their length.
A beam united to another in this manner is said to be scarfed. (Plate XIII.
Fig. 169.)

In order to preserve the strength of a compound beam, intended to resist a
transverse action in a particular direction, it is necessary to avoid, as much
as possible, reducing the depth of the beam in that direction, and to secure

16>8 ■ LECTURE XIV.

the union with the greatest care on the convex side of the beam, which is
stretched by the operation of the force. Where no inconvenience can re-
sult from the projection of a piece on one side, it is easy to preserve the
strength unimpaired, by splicing or fishing it on the convex side ; and if the
depth of the piece added be only half as great as that of the original beam,
the strength will be somewhat increased by the operation, supposing the two
ends to meet each other without any connexion. Such pieces require, how-
ever, to be firmly united, either by pins passing through them, or by blocks
or joggles let in to a certain depth, in order to prevent their sliding on each
other; and this mode of union is stronger than scarfing them, because it does
not diminish the depth. (Plate XIII. Fig. 170, 171.)

Where the pieces to be connected together are in different directions, the
end of one of them is usually reduced in its size, and becomes a tenon, while
a mortise is cut in the other for its reception, and the joint is also often se-
cured still more firmly by a stiap of iron. If a joist be let into a beam, at its
upper edge, and made very tight by wedges, the strength of the beam will
not be materially diminished ; but the vicissitudes of moisture and dryness
may very much impair the firmness of the union, and the end of the joist
may fail in dry weather to afford sufficient resistance to the flexure of the
beam: so that in some cases it might be more adviseable to cut the mortise
near the middle of the depth of the beam. If two pieces meet obliquely, and
one of them exerts a thrust against the other, the simplest mode of opposing
this thrust is to bind them together by a strap of iron fixed to the second
piece; this strap renders it impossible for the first to advance without having
its extremity crushed ; it is also common to make a mortise in the second
piece, a part of which serves as an abutment for the first : and for this pur-
pose the piece must be continued far enough beyond the abutment to give the
projection sufficient force of adhesion, a condition which is the more easily
fulfilled when the action of the strap produces a pressure on it. The assist-
ance of a strap is still more indispensable where the pieces are perpendicular to
each other, and the force tends to draw one of them away from the other: in
this case the mortise may be made a little wider at the remoter part, and the
end of the tenon may be made to fit it by driving in wedges, in the same
manner as Mr. Smeaton united his blocks of stone; but a large mortise would
weaken the beam too much, and a strong strap or hoop is usually required for

ON ARCHITECTURE AND CARPENTRY. 16«>

additional security. Such a strap ought always to be as straight as possible,
so as to act only in the direction of the force to be resisted: it has been too
customary to accommodate the strap to the form of the beams, or to make it
deviate in other ways from a right line: but wherever a strap is bent in any di-
rection, to a distance from a right line equal only to its depth in that direction,
its strength is so reduced, as not to exceed one seventh of what it would have
been, if it had remained straight. (Plate XtV. Fig. 172 . . 174.)

It is equally necessary in all other cases which occur in carpentry, to avoid
as much as possible a transverse strain, the disadvantage of which is obvious
from the great inferiority of the strength of any substance, resisting a trans-
verse force, to its primitive cohesive or rcpulsive strength.. For similar
reasons, it is proper to avoid employing a very open angle at a point where a
load is supported, the great obliquity of the two pieces forming the angle re-
quiring them to exert a great force in order to oppose a much smaller one.
Allowance must also be made for the contraction of the timber, and care
must be taken that it do not so alter the arrangement of the parts, as to bring
a disproportionate strain on a point not calculated to support it. If the two
pieces forming an obtuse angle consisted, either wholly or partly, of woodcut
across the grain, and the piece joining their extremities were cut in the usual
manner, the oblique pieces would contract considerably more as they became
drier, and the angle would become more obtuse, so that the strain, produced
by a given weight, would be greater than in the original state of the triangle.
Sometimes the work is liable to be deranged by the operation of a lateral force,
which may have appeared too trifling to produce any considerable effect, bat
which may still destroy the greater part of the strength, by causing the re-
sistances to deviate from the plane of the forces which they are intended to
oppose.

The framing of a roof is one of the most common and most important sub-
jects for the employment of the theory of carpentry. If the rafters were
simply to abut on the walls, they would force them outwards; a tie beam is
therefore necessary, to counteract the thrust. In order to enable the tie
beam to support a weight, a king post is suspended from the rafters; and
frequently braces arc again erected from the bottom of the king post, to sup-

VOL. I. z

170 LECTURE XIV.

port the middle of the rafters. Somethnes a flat or less inclined portion is
placed in the middle, forming a kirb or mansard roof, somewhat resembling ai*.
arch ; this form has the advantage, when it is properly proportioned, of lessening
the transverse strain on the rafters, by making them shorter; but this pur-
pose is answered equally well by the addition of the braces which have been
already mentioned. A kirb roof aftbrds, however, a greater space within,
than a plain roof of the same height, and produces also somewhat less strain
on the tie beam or on the abutments: the tie beam may be suspended from it
by a king post and two queen posts, descending perpendicularly from the
joints ; and the place of the king post may be supplied by a cross beam unitr
ing the heads of the queen posts and keeping them at a proper distance; this
beam may also be suspended by a shorter kingpost from the summit. Such a
roof appears to be more advantageous than it has been commonly supposed,
(Plate XIII. Fig. 175.. 177.)

The angle of inclination of a roof to the horizon usually varies in diiferenf
climates: in Italy the height is generally less than one fourth of the breadth;
in England it was formerly three fourths, but it now commonly approaches
much more to the Italian proportion. In northern climates, a steep roof is
required on account of falls of snow, which greatly increase the lateral thrust
of the rafters; for the horizontal force exerted by a roof is always pro-
portional to the length of a line perpendicular to the rafter, descending from
its extremity till it meets another similar line drawn from the opposite rafter;
and this perpendicular is obviously much increased when the roof becomes very
flat. But for bearing the transverse strain, which tends to break the rafters
themselves, a low roof is stronger than a high one, supposing the number of
braces and queen posts equal on both : for if we have to support a given weight
by a beam or rafter, whether it be placed in the middle, or equally divided through-
out the length, we neither gain nor lose force by lengthening the beam and rais-
ing it higher, while the horizontal span continues the same, since the obli-
quity lessens the effect of tlie weight precisely in the same ratio that the
length of the beam diminishes its strength ; but by lengthening the beam we
also add to the weight which is to be supported, and we thus diminish the
strength of the roof. It must be observed, in calculating the strength of a
<rafter, that the slight flexure, produced by the transverse strain, has a material

ON ARCHITECTURE AND CARPENTRV. • l/I

effect in diminishing its strength in resisting a longitudinal force; and this
diminution must be determined according to the principles that have been laid
down respecting the equilibrium of elastic substances.

Wooden bridges, and the temporary centres on which arches of stone arc
supported during their construction, depend nearly on the same principles as
roofs: the external parts usually support a thrust, and the internal act as
ties; but the abutments are generally capable of withstanding a horizontal
thrust without inconvenience, so that by their assistance the strain on the
ties is considerably diminished. Great strength may also be obtained, where
it is practicable to support each part of the centre by two beams, in the di-
rection of chords, bearing immediately on the abutments. (Plate XIV.
Fig. 178, 179.)

The various articles of household furniture belong to subordinate branches
of carpentry, but their form is in general more accommodated to conveni-
ence and elegance than to strength and durability. Yet even in making a
chair, there is room for error and for improvement ; the same principles that
direct us in framing a roof, are capable of application here; but if they were
implicitly followed, they would lead us to the employment of bars crossing
each other in an inelegant manner. Doors, gates, locks, and hinges, are
either parts of the carpenter's employment, or appendages to his works; and
it is possible that^by attentive consideration, improvements might be made in
all of them. Mr. Parker has devoted much time and labour to the subject of
gates, with their hinges and fastenings, and has presented to the Royal In-
stitution a very useful collection of models, which show the result of his in-
vestigations.

172

LECTURE XV.

ON MACHINERY.

Having taken a general view of those branches of practical mechanics
in which forces are to be resisted, we are next to consider the modifications
of forces and of motions ; and in the first place the modes of applyinor
forces, of changing their direction and intensity, and of communicating
them to different parts of our machines by the intervention of rods, joints,
cranks, wheelwork, ropes, or other flexible substances ; in the second place,
the structure of these substances, and the metliods by which the union of
flexible fibres in general may be effected ; and ir^ the third place, the regula-
lation and equalisation of motion, by means of clocks and watches.

The modes of applying mechanical forces are almost as various as the
machines that are constructed, and the purposes for which they are employ-
ed: but in general, the strength of men is applied by means of levers, or
winches, or by walking wheels, which slide beneath them as they attempt to
ascend ; and that of other animals, by a horizontal arm projecting from a ver-
tical axis, to which they are harnessed, and sometimes also by causing them
to walk on or in a moveable wheel. Many of these arrangements may how-
ever be very conveniently considered as belonging to the particular objects
for which each machine is constructed, especially to the modes of raising
weights by cranes, and of grinding substances by mills.

When nlotion is simply communicated to a substance placed before the
moving body, such materials must be employed as are capable of exerting
a repulsive force, or a thrust; and these are generally of the same kind as
are sometimes concerned in the operations of architecture, but more com-
monly in those of carpentry, particularly metal and wood. But when the
body to be moved is behind the moving power, and is pulled along by it,

ON MACHINERY. 17S

chains or ropes are sometimes more convenient. In the union of wood for
moveable machinery, it is generally advisable to avoid employing pins or
bolts of metal ; for these, by their superior weight and hardness, sometimes
injure the wood iu contact with them, and become loose.

When the direction of the motion communicated is also to be changed, levers
or cranks may be employed, united by joints or hinges of various kinds.
Sometimes a long series of connected rods is suspended by other rods or
chains, so as to convey the ettect of the force to a considerable distance ; in
this case the motion is generally alternate, when, for example, pumps are
worked by means of a waterwheel at a distance from the shaft in which the
pumps are placed. In this arrangement, there is no necessary loss on ac-
count of the alternation of the motion of the rods ; for if they are suspend-
ed at equal distances from a number of fixed points, they will move back-
wards and forwards,, in the manner of a single pendulum:; but the magnitude
of the friction is the principal inconvenience produced by the weight of
the series. Where a lever is employed for changiug the direction of a great
force, its strength may be increased by the addition of a frame projecting in
the direction of its depth; and if the lever is bent, a cross piece uniting its
arms is still more requisite. (Plate XIV. Fig. 180 . . 182.)

For the communication of a rotatory motion, Dr. Hookc's universal joint is
sometimes of use, especially when the inclination is not required to be ma-
terially changed ; but if the obli(juity is great, the rotation is not commu-
nicated equably to the new axis at all points of its revolution. This joint
is formed by a cross, making the diameters of two semicircles, one of
Ayhich is fixed at the end of each axis. (Plate XIV. Fig. 183.)

The best mode of connecting a rotatory motion with an alternate one, is, in
all common cases, to employ a crank, acting on one end of a long rod,
which has a joint at the other. If the rotatory motion of the crank be
equable, the progressive motion of the rod will be gradually accelerated
and retarded, and for a considerable part of the revolution the force exert-
ed will be nearly uniform : but if we attempted to communicate at once
to the rod its whole velocity in each direction, as has sometimes been done
by inclined planes, or by wheelwork, the motion would become extremely

174 LECTURE XV.

irregular, and the machinery would be destroyed by the strain. (Plate XIV.
Fig. 184.)

On the other hand it must be observed, that the force applied to a ma-
chine may, in general, be divided into two portions; the one employed in op-
posing another force, so as to produce equilibrium only, the other in generat-
ing momentum. With respect to the first portion, a single crank has the
inconvenience of changing continually the mechanical advantage of the ma-
chine; with respect to the second, its motion in the second quarter of its re-
volution is accelerated, instead of being retarded, by the inertia which this
portion of the force is intended to overcome: and from a combination of both
these causes, the motion must necessarily be rendered very irregular. They
may, however, be completely removed by employing always cranks in pairs,
one of them being fixed so as to make a right angle with the other, which
is also the best position for two winches to be turned by two labourers ; since
the point of the circle, in which a man can exert his greatest strength, is
nearly at the distance of a right angle, or a little more, from the point at
which his force is smallest.

An alternate motion may be comunicated to a rod, so that the force may
be either uniformly exerted, or varied according to any given law, by means
of an inclined surface, formed into a proper curve, and acting on a friction
wheel fixed to the rod ; and a single plane surface, placed obliquely, would
answer sufiiciently well for this purpose. But in such cases, as well as when
a crank is used, it is necessary to employ other means for supporting the
rod in its proper situation; this may either be done by additional friction
wheels, or in a more elegant manner, by such an arrangement of jointed
rods, as will cause the extremity of one of them to move in a curve Avhich
does not sensibly differ from a right line. If we fix two pins in a beam, so
as to connect to it two equal rods, of which the extremities are joined by a
third, and the end of this third rod which is nearest to the centre of the
beam be connected to a second beam of a proper length, the oj^osite end of
the rod will initially describe a right line; and for this purpose the length of
the second beam must be to the distance of the nearest pin from the centre
as that distance is to the distance of the pins from each other. The same
effect may also be produced by means^ of a frame, made of two pieces, each a

2

ON MACHINERY. ' 173

yard long, united by joints to each other, and to two other pieces of a foot
each; one of the first pieces being fixed, if the shorter piece opposite to it
be produced to the length of four feet, its extremity will move at first in a
right line. The proportions of the rods may also be made more convenient
than these, and others may be added to them, if it be required, which may
make a line move so as to remain always in parallel directions, (Plate XIV.
Fig. 185 . . 188.)

But of all the modes of communicating motion, the most extensively use-
ful is the employment of wheelwork, which is capable of varying its direc-
tion and its velocity without any limit.

Wheels are sometimes turned by simple contact with each other; some-
times by the intervention of cords, straps, or chains, passing over them; and
in these cases the minute protuberances of the surfaces, or whatever else may
be the cause of friction, prevents their sliding on each other. Where a
broad strap runs on a wheel, it is usually confined to its situation, not by
causing the margin of the wheel to project, but, on the contrary, by mak-
ing the middle prominent: the reason of this may be understood by ex-
amining the manner in which a tiglit strap running on a cone would tend to
run towards its thickest part. Sometimes also pins are fixed in the wheels, and
admitted into perforations in the straps; a mode only practicable where
the motion is slow and steady. A smooth motion may also be obtained, with
considerable force, by forming the surfaces of the wheels into brushes of hair.
(Plate XV. rig. 189.)

More commonly, however, the circumferences of the contiguous wheels
are formed into teeth, impelling each other, as with the extremities of so many
levers, either exactly or nearly in the common direction of the circum-
ferences; and sometimes»i.an endless screw is substituted for one of the
wheels. Informing the teeth of wheels, it is of consequence to determine
the curvature which will procure an equable communication of motion, with
the least possible friction. For the e(juable communication of motion, two
methods have been recommended ; one, that the lower part of the face of
each tooth should be a straight line in the direction of the radius, and the
upper a portion of an epicycloid, tliat is, of a curve described by a point of a

176 LECTURE XV.

circle rolling on the wheel, of which the diameter must be half that of the
opposite wheel; and in this case it is demonstrable that the plane surface of
each tooth will act on the curved surface- of the opposite tooth so as to pro-
duce an equable angular motion in both wheels : the other method is, to
form all the surfaces into portions of the involutes of circles, or the curves
described by a point of a thread which has been wound round the wheel,
while it is uncoiled; and this method appears to answer the purpose in an
easier and simpler manner than the former. It may be experimentally de-
monstrated, that an equable motion is produced by the action of these curves
on each other: if we cut two boards into forms terminated by them, divide
the surfaces by lines into equal or proportional angular portions, and fix
them on any two centres, we shall find that as they revolve, whatever parts
of the surfaces may be in contact, the corresponding lines will always meet
each other. (Plate XV. Fig. 190 . . 192.)

Both of these methods may be derived from the general principle, that the
teeth of the one wheel must be of such a form, that their outline may be
described by the revolution of a curve upon a given circle, while the outline
of the teeth of the other wheel is described by the same curve revolving
within the circle. It has been supposed by some of the best authors that the
epicycloidal tooth has also the advantage of completely avoiding friction;
this is however by no means true, and it is even impracticable to invent any
form for the teeth of a wheel, which will enable them to act on other teeth
without friction. In order to diminish it as much as possible, the teeth
must be as small and as numerous as is consistent with strength and dura-
bility ; for the 'effect of friction always increases with the distance of the
point of contact from the line joining the centres of the wheels. In calcu-
lating the quantity of the friction, the velocity with which the parts slide
over each other has generally been taken for its measure: this is a slight
inaccuracy of conception, for, as we have already seen, the actual resist-
ance is not at all increased by increasing the relative velocity; but the
cflect of that resistance, in retarding the motion of the wheels, may be shown,
from the general laws of mechanics, to be proportional to the relative ve-
locity thus ascertained. When it is possible to make one wheel act on
teeth fixed in the concave surface of another, the friction may be thus dimi-
nished in the proportion of the difference of the diameters to their sum. If

on MACHINERY. 177

the face of the teetli, where they are in contact, is too much inchned to the
radius, their mutual friction is not much affected, but a great pressure on their
axes is produced ; and this occasions a strain on the machinery, as well as a4»
increase of the friction on the axes.

If it is desired to produce a great angular Velocity with the smallest possible
quantity of wheel work, the diameter of each wheel must be between three
and four times as great as that of the pinion on which it acts. Where the
pinion imj)els the wheel, it is sometimes made with three or four teeth only;
but it is much better in general to have at least six or eight; and considering
the additional labour of increasing the number of wheels, it may be advisable
to allot more teeth to each of them than the number resulting from the calcu-
lation ; so that we may allow 30 or 40 teeth to a wheel acting on a pinion of 6
or 8. In works which do not require a great degree of strength, the wheels
have sometimes a much greater number of teeth than this ; and on the other hand,
an endless screw or a spiral acts as apinion of one tooth,since it propels the wheel
through the breadth of one tooth only in each revolution. For a piiiion of
six teeth, it would be better to have a wheel of 35 or 37 than 36; for each
tooth of the wheel would thus act in turn upon each tooth of the pinion, and
the work would be more equally worn than if the same teeth continued to
meet in each revolution. The teeth of the pinion should also be somewhat
stronger than those of the wheel, in order to support the more frequent recur-
rence of friction. It has been proposed, for the coarser kinds of wheelwork,
to divide the distance between the middle points of two adjoining teeth into
30 parts, and to allot 16 to the tooth of the pinion, and 13 to that of the
wheel, allowing 1 for freedom of motion.

The wheel and pinion may either be situated in the same plane, both being
commonly of the kind denominated spur wheels, or their planes may form an
angle: in this case one of them may be a crown or contrate wheel, or both of
them may be bevilled, the teeth being cut obliquely. According to the rela-
tive magnitude of the wheels, the angle of the bevil must be different, so
that the velocities of the wheels may be in the same proportion at both ends
of their oblique faces: for this purpose, the faces of all the teeth must be di-
rected to the point where the axes would meet. (Plate XV. Tig. 193, 194.)

VOL. I. A a

178 LECTURE XV.

In cases where a motion not quite equable is required, as it sometimes hap-
pens in the construction of clocks, but more frequently in orreries, the wheels
may either be divided a little unequally, or the axis may be placed a little out
of the centre ; and these eccentric wheels may either act on other eccentric
wheels, or, if they are made as contrate wheels, upon a lengthened pinion.
(Plate XV. Fig. 195, 196.)

An arrangement is sometimes made for separating wheels which are in-
tended to turn each other, and for replacing them at pleasure; the wheels are
said to be thrown by these operations out of gear and into gear again.

When a wheel revolves round another, and is so fixed as to remain nearly in a
parallel direction, and to cause the central wheel to turn round its axis, the
apparatus is called a sun and planet wheel. In this case, tlie circumference
of the central wheel moves as fast as that of the revolving wheel, each point
of which describes a circle equal in diameter to the distance of the centres of
the two wheels: consequently, when the wheels are equal, the central wheel
makes two revolutions, every time that the exterior wheel travels round it.
If the central wheel be fixed, and the exterior wheel be caused to turn on its
own centre during its revolution, by the effect of the contact of the teeth, it
will make in every revolution one turn more with respect to the surrounding-
objects, than it would make, if its centre were at rest, during one turn of the
wheel which is fixed: and this circumstance must be recollected when such
wheels are employed in planetariums.

Wheels are usually made of wood, of iron, either cast or wrought, of steel,
or of brass. The teeth of wheels of metal are generally cut by means of a ma-
chine; the wheel is fixed on an axis, which also carries a plate furnished with
a variety of .circles, divided into different numbers of equal parts, marked
by small excavations ; these are brought in succession under the point of a
spring, which holds the axis firm,' while the intervals between the teeth are
expeditiously cut out by a revolving saw of steel. The teeth are afterwards
finished by a file; and a machine has also been invented for holding and
working the file. (Plate XV. Fig. 197.)

It is frequently necessary in machinery to protract the time of application

1 , ON MACHINERY. l/y

of a given force, or to reserve a part of it for future use. Tiiis is generally
effected by suffering a weight to descend, which has been previously raised,
or a spring to unbend itself from a state of forcible flexure, as is exemplified
in the weights and springs of clocks and watches. The common kitchen
jack is also employed for protracting and equalising-the operation of a weight:
in the patent jack the same effect is produced by an alternate motion, the
axis being impelled backwards and forwards, as in clocks and watches, by
means of an escapement, and the place of a balance spring being supplied by
the twisting and untwisting of a cord.

In these machines, as well as in many others of greater magnitude, the fly
wheel is a very important part, its velocity being increased by the operation
of any part of the force which happens to be superfluous, and its rotatory
power serving to'continue the motion when the force is diminished or with-
drawn. Thus, when a man turns a winch, he can exert twice as nxiich force
in some positions as in others, and a fly enables him in some cases to do
nearly one third more work. In the pile engine, also, without the help of
the fly, the horses would fall for want of a counterpoise, as soon as the
weight is disengaged. Such a fly ought to be heavy, and its motion must
not be too rapid, otherwise the resistance of the air will destroy too much of
the motion ; but in the kitchen jack, as well as in the striking part of a clock,
where the superfluous force is purposely destroyed, the fly is made light, and
strikes the air with a broad surface. An effect similar to that of a fly and a
spring is sometimes produced in hydraulic machines by the introduction of an
air vessel, the air contained in which is compressed more or less according to-
the intensity of the force, and exerts a more uniform pressure in expelling the
fluid which is forced irregularly into it.

180

LECTURE XVI.

ON THE UNION OF FLEXIBLE FIBRES.

JLlIE strength of cordage, and of other substances which ai"e employed in
the communication of motion, where flexiblHty is required, as well as the
utility of other flexible materials which serve for furniture or for clothing,
depends principally upon the lateral adhesion produced by twisting, or by the
intermixture of fibres. The union of flexible fibres, therefore, being fre-
quently subservient to the communication of motion, and the machinery, usually
employed for producing it, belonging immediately to the subject of the mo-
dification of motion, we may with propriety consider at present, as far as
our plan will allow us, those important branches of the mechanical arts, of
which the object is to effect a union of this kind.

When a chain is made of wire, each link is separately bent, and remains
united with the neighbouring links in virtue of its rigidity: but the fibres of
vegetable and of animal substances must be united by other means. For
this purpose we have recourse to the force of friction, or rather of lateral ad-
hesion, and the fibres are so disposed, that besides the mutual pressure
which their own elasticity causes them to exert, any additional force applied
in the direction of the length of the aggregate, tends to bring the parts into
closer contact, and to augment the adhesion, in the same manner as we have
already seen that a wedge and a screw may be retained in their situations. The
simple art of tying a knot, and the more complicated processes of spinning,
ropemaking, weaving, and felting, derive their utility from this principle.

When a line is coiled round a cylinder, for ' instance, in letting down
a weight, by means of a rope which slides on a post, or on such a
grooved cylinder as is sometimes employed to enable a person to lower him-
self from a window in cases of fire, the pressure on the whole circumference

1

ON THE UNION OP FLEXIBLE FIBRES. 181

is to the weight, as twice the circumference to the diameter; supposing, for
example, that the friction of rope on metal were one tenth of the pressure,
then a single coil of rope round a cylinder of metal would support about two
thirds of the weight; or if the weights acting on the different ends are dif-
ferent, the adhesion may be a little greater or less than in this proportion,
according to the manner in ■'.vhich the rope is applied. If such a rope
made two or three coils, it would be impossible to apply a force sufficient
to cause it to slide in the grooves. *

From considering the effect of a force which is counteracted by otker forces
acting obliquely, we may understand both the effect of twisting, in binding
the parts of a rope together, and its inconvenience, in causing the strength
of the fibres to act with a mechanical disadvantage. The greater the obli-
quity of the fibres, the greater will be their adhesion, but the greater
also will be their immediate tension, in consequence of the action of a
given force in the directioii of the rope: so that after employing as much ob-
liquity and as much tension, as is sutBcient to connect the fibres firmly, in
all cases of relaxation and of flexure, and to prevent in some measure the
penetration of moisture, all that is superfluously added tends to overpower
the primitive cohesion of the fibres in the direction of their length.

The mechanism of simple spinning is easily understood; care is taken,
where the hand is employed, to intermix the fibres sufficiently, and to en-
gage their extremities as much as possible in the centre; for it is obvious
that if any fibre were Avholly external to the rest, it could not be retained in
the yarn; in general, however, the materials are previously in such a state of
intermixture as to render this precaution unnecessary. Where we have a
number of single continuous fibres, as in reeled silk, they are sufficiently con-
nected by twisting, and we have no need of spinning. In both cases such
machinery has been invented for performing the necessary operations, as is
both honourable and lucrative to the British nation.

A single thread or yarn, consisting of fibres twisted together, has a ten-
dency to untwist itself; the external ptrts are the most strained in the opera-
tion, and at first shorten the thread, until the internal parts have no lonj?;er
roam for spreading out laterally, as, they must necessarily do when their

182 LECTURE XVI.

length is diminished; the elasticity of all the parts, therefore, resists, and tends
to restore the thread to its natural state. But if two such threads are retained
in contact at a given point of the circumference of each, this point is rendered
stationary hy the opposition of the equal forces acting in contrary directions,
and becomes the centre, round which both threads are carried by the remain-
ing forces, so that they continue to twist round each other till the new com-
bination causes a tension, capable of counterbalancing the remaining tension
of the original threads. Three, four, or more threads may be united nearly
in the same manner: a strand consists of a considerable number of yarns thus
twisted together, generally from sixteen to twenty five, a hawser of three
strands, a shroud of four, and a cable of three hawsers or shrouds. Shroud
laid cordage has the disadvantage of being hollow in the centre, or of re-
quiring a greater change of form in the strands to fill up the vacuity, and in
undergoing this change, the cordage stretches, and is unequally strained.
The relative position and the comparative tension of all the fibres in these com-
plicated combinations are not v^ry easily determined by calculation ; but it is
found by experience to be most advantageous to the strength of the ropes to
twist the strands, when they are to be compounded, in such a direction as to
untwist the yarns of which they are formed; that is, to increase the twist of
the strands themselves: and probably the greatest strength is obtained when
the ultimate obliquity of. the constituent fibres is the least, and the most
equable. This advantage is obtained in a considerable degree by Mr. Hud-
dart's method of adjusting the length of the strand to its position in the
rope, and his registered cordage appears to derive a decided superiority from
this arrangement of the strands. A very strong rope may also be made by
twisting five or six strands round a seventh as an axis: the central strand, or
heart, is found after much use to be chafed to oakum ; it should be more
twisted than the rest, in order to allow it to extend a little ; such ropes are,
however, unfit for running rigging, or for any use in which they are liable to
be frequently bent.

Ropes are most commonly made of hemp, but various other vegetables are
occasionally employed; the Chinese even use woody fibres, and the barks of
trees furnish cordage to other nations; we have indeed in this country an ex-
ample of the use of the bark of the lime tree, which is employed for garden
matting. The finest hemp is imported from Riga and St. Petersburg. The

2

ON THE UNION OF FLEXIBLE FIBRES. 183

male and female flowers of liemp are on different plants ; the male plants are
soonest ripe, and require to be first pulled. They are prepared for dressing by
being exposed to the air, and the fibrous part is separated from the dry pulp
by beating and hackling. In spinning the yarn, the hemp is fastened round
the waist; the wheel is turned by an assistant, and the spinner, walking back-
wai-ds, draws out the fibres with his hands. When one length of the walk
lias been spun, it is immediately reeled, to prevent its untwisting. The ma-
chines employed in continuing the process of ropemaking are of simple con-
struction, but both skill and attention are required in applying them so as to
produce an equable texture in every part of the rope. The tendency of two
strands to twist, in consequence of the tension arising from the original twist
of the yarns, is not sufficient to procure an equilibrium, because of the friction
and rigidity to be overcome; hence it is necessary to employ force in order to
assist this tendency, and the strands or ropes afterwards retain spontaneously
the form which has thus been given them: the largest ropes even require ex-
ternal force in order to make them twist at alL

The constituent ropes of a common cable, when separate, are stronger than
the cable, in the proportion of about 4 to 3 ; and a rope worked up from yarns
180 yards in length to 135 yards, has been found to be stronger than when
reduced to lao yards, in the ratio of 6 to 5. The difference is owing partly
to the obliquity of the fibres, and partly to the unecjual tension produced by
twisting. Mr. Huddart's ropes of 100 yarns lose but about one eighth of the
whole strength of the yarns ; and his experiments appear to show that similar
ropes made in the common manner retain only one half of their original strength.
The tarring of ropes, although sometimes necessary for their preservation from
decay, is found to lessen their strength, probably because it produces partial ad-
hesions between some of the fibres, which cause them to be disproportionully
strained. A rope is also said to be weaker when wet than when dry, perhaps
because the water enables the fibres to slide more readily on each other, or be-
cause the presence of water is in general favourable to separation of any kind.
A good hempen rope will support, without danger, one fifth as many tons as
the square of its circumference contains inches.

Flax is weaker than hemp, but not less extensively useful. Its growth
considerably exhausts the strength of the soil which produces it; its cultiva-

184 LECTURE XVt.

tion is encouraged in this country by a bounty from government, and a large
quantity is also imported from the north of Europe. The plant, while green,
is laid in water for ten days, and undergoes a chemical cliange, Avhich softens
the pulpy part, without injuring the strength of the fibres, and renders it
more easy, when it has been dried and exposed to the air for a fortnight, to
separate the two substances in the process of dressing it. This is performed
by beating it with the edge of a flat piece of wood, the stroke being oblique,
and nearly in the direction of the fibres, and afterwards combing it, in order
to reduce the fibres into regular order, and to prepare them for spinning. The
refuse, consisting of the shorter fibres, is tow.

Cotton is a fine fibrous substance, that envelopes the seeds of a plant. The
best is brought from the isle of Bourbon ; but by far the greatest quantity
from the West Indies, although the Turkish dominions as well as the East
Indies furnish us with a considerable supply. It is usually white, but there
is a yellow kind, which is used for nankeens. It is separated from the seeds
by means of rollers, between which it passes, and leaves the seeds behind. It
is then beaten, on a flake, or a stool covered with a texture of cord. Next, it
is carded, either by hand, the fibres being drawn into regular order by cards,
that is, by brushes of fine pointed wire ; or, more commonly, by machinery,
the cards being disposed in cylinders which revolve nearly in contact with
each other. The drawing or roving machine then draws it into long flakes,
a state preparatory to its being spun by Sir Richard Arkwright's machines or
jennies, which form at once forty thteads by the labour of one person.

. The silkworm is bred in the greatest abundance in Italy and in Asia; it has

lately been introduced very successfully into the British possessions in the

East Indies. The principal food of the caterpillar is the white mulberry tree,

which is too delicate to thrive well in northern climates : in Italy the trees

are planted in beds, like willows, and the foliage is cut as it is wanted. The

room in which the Avorms are fed, is kept at the temperature of 80 degrees of

Fahrenheit. The eggs of a former year are hatched either by animal heat, or

by that of the sun ; at the age of six weeks, the caterpillars begin to spin,

first a light external texture, which is carded and spun for coarse silk, and

afterwards a compact oval pod or cocoon, of one continued thread. The

threads of several cocoons are reeled off at the same time ; for this purpose

ON THE UNION OF FLEXIBLE FIBUES, ] 85

they are generally put into warm water, which kills the chrysalis; but when it
is preserved, it soon turns to a moth, which lives but a few days, taking no
food, and dies after producing eggs for the next season.

The silk is either yellow or white, but the white is an accidental variety
only. By repeated washings, the yellow silk is bleached, and that which is
originally white, acquires a more perfect whiteness. Soap is also used for re-
moving a gummy substance that accompanies the silk of the cocoons.

Wool is distinguished into two principal varieties, long and short wool.
The longest is from Lincolnshire; it is combed, by means of instruments
furnished with a double row of long and sharp teeth of iron or steel; it is re-
peatedly drawn from one comb to the other, heat being used in the process,
and also a little oil. The fleeces of long wool are generally heavier than those
of short wool, but less valuable, on account of their coarseness ; they are
used for worsteds, and for cloths in which the separate threads remain visible,
as stuifs, shalloons, serges, and tammies. Short wool, on the contrary, is
carded, and is used for cloths in which the individual threads are concealed
by the projecting fibres.

The principal use of thread and yarn, when spun, is for the purpose of
weaving. The same force of lateral adhesion that retains the twisted fibres
of each thread in their situations, is here also employed in giving firmness to
the cloth ; and this adhesion is generally increased by the action of any external
force, tending to strain the whole texture.

The first step in weaving is to form a warp, which consists of threads
placed side by side, continued through the length of the piece, and sufficient
in number to constitute its breadth. This being wound on a beam or roller,
in the loom, the threads are drawn through a harness, consisting of loops
formed by twine fixed to bars or frames, which elevates and depresses the
threads in succession by means of treadles, moved by the feet, in an order
which is d liferent, according to the different nature of the intended work;
the cross thread or woof, being thrown between them at each alternation, by
means of a shuttle, and forced into its place by a batten or comb, made of

VOL. I. B b

1^6 LECTURE XVI.

wire or reeds, while the piece, in proportion as it is completed, is rolled up-
on a second beam, opposite to the first.

Crape is composed of threads which are so strongly twisted, as to have a dis-
position to curl, and in weaving it, moisture is sometimes employed, in order
to obviate this tendency during the process. Woollen cloth, when woven, is
rendered stronger and more compact by means of the fulling mill, in which it
is beaten by heavy hammers of wood, at the same time that fullers' earth, or
alcaline substances of animal origin, are applied in order to cleanse it. In
this operation, both its length and breadth are diminished, and it is reduced
to a texture approaching to that of felt. The reason of the contraction is pro-
. bably this, that all the fibres are bent by the operation of the hammer, but not
all equally, and those which have been the most bent are prevented by their
adhesion to the neighbouring fibres from returning to their original length.
After fulling, the cloth is roughened by means of teasels, which are cultivated
for the purpose; and the most projecting fibres are cut away by the operation
of shearing. /

The lateral adhesion of fibres of various kinds gives strength also to felted
substances, assisted, as some assert, by minute barbs, with which the fibres of
furs are said to be furnished. The whole strength is, however, much inferior
to that of cloth ; partly because the fibres are in general nmch shorter, and
partly because their arrangement is less accurately adjusted.

The materials commonly used for felting, are the furs of rabbits and beavers>
mixed with each other, and with sheep's wool, in various proportions, according
to the quality required. A very fine fur has lately been discovered on the
skin of a species of seal, mixed with its hair, and it has been employed not
only for felting, but also for spinning and weaving into a cloth resembling the
shawls of the East Indies. The fur of the rabbit is also mixed with a coarser
hair, which is separated from it, by being first pulled off from the skins, with
a sharper knife. 'The materials to be felted are intimately mixed by the opera-
tion of bowing, which depends on the vibrations of an elastic string; the
rapid alternations of its motion being peculiarly well adapted to remove all
irregular knots and adhesions among the fibres, and to dispose them in a very

ON THE UNION OF FLEXIBLE flBRES. 187

light and uniform arrangement. This texture, when pressed under cloths and
leather, readily unites into a mass of some firmness ; this mass is dipped into
a liquor containing a little sulfuric acid, and when intended for a hat, is
moulded into a large conical figure, which is reduced in its dimensions by
working it with the hands, and is formed into a flat surface, with several con-
centric folds, which are still more compacted in order to make the brim, and
the circular part of the crown, and forced on a block, which serves as a mould
for the cylindrical part. The black dye is composed of logwood, sulfate of
iron, and a little acetite of copper, or verdigris; and the stiftening is a thiu <
glue. , ,

The texture of paper is scarcely different from that of felt, except that its
fibres are less visible to the naked eye. To make white paper, linen rags are
ground with warm water in a mill, into a paste of the consistence of cream: a
portion of the paste is taken up in a wire sieve, which is' passed obliquely
through it, and this, being a little shaken, subsides into a sheet, which is
turned out on a piece of flannel ; a number of sheets being thus formed, they
are then pressed, first with the interposition of flannel, and afterwards alone,
while they are still moist. For thick paper, two or more sheets are laid on
each other before the first pressing. To fill up the pores of the paper, and to
increase its strength,, a size is employed, which is generally made by boiling-
shreds of parchment or untanned leather. Sometimes the size is added after
printing on the paper, but this is only done in works of inferior elegance,
and in this country not at all.

Such are the principal cases of the union of flexible fibres, for the different
purposes of strength or of convenience. Their importance is such that they
might be esteemed worthy of a more detailed consideration ; but we are not
likely to make any material improvements in these departments of mechanical
art by the application of theoretical refinements.

1S8

T.ECTURE XVII.

ON TIMEKEEPERS.

X HE measurement of time by clocks and watches is a very important and in-
teresting department of practical mechanics. The subject is intimately con-
nected with the consideration of astronomical instruments, but it is not essen-
tially dependent on astronomical principles.

Time is measured by motion ; but in order that motion may be a true
measure of time, it must be equable. Now a motion perfectly free and un-
disturbed, and consequently uniform, is rendered unattainable by the resist-
ances inseparable from the actual constitution of material substances. It
becomes therefore necessary to inquire for some mode of approximating to such
a motion. Astronomical determinations of time, which are the most accurate,
can only be made under particular circumstances, and even then they as-
sist us but little in dividing time into small portions.

The first timekeepers somewhat resembled the hour glasses which are still
occasionally employed ; they measured the escape of a certain quantity, not of
sand, but of water, through a small aperture. In these clepsydrae, it ap-
pears from Vitruvius's account that wheelwork was employed, and the hour
was shown on a graduated scale; the graduations were also probably so ad-
justed as to correct the error arising from the inequality of the velocity oc-
casioned by the variation of the height of the water in the reservoir. This
inconvenience was however sometimes wholly avoided, by means of a con-
stant steam, which kept the vessel full, or still more elegantly, by the siphon
of Hero, which was a bent tube supported by a float, so that its lower orifice,
at which the water was discharged, was always at a certain distance below the
surface. Dr. Hooke proposed to keep the reservoir full, by means of a

2

ON TIMEKEEPERS. 189

semicylindrical counterpoise, so that the time might be determined either
from the measure or weight of the quantity of water discharged, or from the
position of the counterpoise. Various other modes might also be devised for
making cheap and simple timekeepers on similar principles, dependent on the
motion of various liquids or elastic fluids; but great accuracy could scarcely
be expected from them. A candle sometimes serves as a coarse measure of
time; and by burning a thread whicli passes through it, it may easily be
made to answer the purpose of an alarm.

Clocks and watches are machines in which wheelwork is employed for the
measurement of time, being driven by a weight or by a spring, and regulat-
ed by a pendulum or a balance. Watches differ from clocks, in being port-
able, and this condition excludes the pendulum and the weight from their
construction.

It is conjectured that the Saracens*: had clocks which' were - moved by
weights, as early as the eleventh century. Trithemius mentions an orrery,
moved by a weight, and keeping time, which was sent, in 1232, by the
Sultan of Egypt, as a present to the Emperor Frederic II. Wallingford, in
1326, had made a clock which was regulated by a fly. The use of such a fly
in equalising motion depends on the resistance of the air^ which increases ra-
pidly when the velocity is increased, and therefore prevents any great ine-
quality in the motion, as long as the moving power varies but little; and if
the action of the weight were transmitted with perfect regularity by the
wheels, and the specific gravity of the air remained unaltered by pressure or
by temperature, a fly clock might be a perfect machine, the weight being
always exactly counterbalanced by the resistance of the air, attending a certain
velocity of the fly ; and it might even be possible to regulate the inequalities
of the action of the weight, by causing the fly to open and shut, or to turn on
an axis, by means of a spring, according to the magnitude of the resistance.
The unequal density of the air would however still remain uncompensated";
and in this respect a liquid would be a better medium than an elastic fluid.
For experiments which are but of short duration, and which require great
precision, a chronometer regulated by a simple fly is still a useful instru-
ment. Mr. Whitehurst's apparatus for measuring the time occupied in the
descent of heavy bodies, is governed by a fly ; the index is stopped by the

igO LECTURE XVII.

machinery, and points out the time elapsed without an error of the hundredth
part of a second.

The alternate motion of a balance, thrown backwards and forwards by the
successive actions of a wheel impelling its pallets, is also capable of produc-
ing a degree of uniformity in the motion of the wheel; for the force operat-
ing on the pallet is consumed in destroying a velocity in one direction, and
in generating a velocity in the contrary direction ; and the space in which it
acts being nearly the same in all cases, the velocity generated will also be
nearly the same at all times, as long as the force remains the same. The ad-
dition of a balance to a clock was made soon after the year 1400, for Ar-
nault, who died in 1465, describes a planisphere, constructed by his master De
Fondeur, which had a balance with a scapement like that of a common watch,
but without a spring. Such a balance vibrates much more slowly than a ba-
lance provided with a spring; if the balance spring of a common watch be re-
moved, the hands will pass over the space of about twenty eight minutes in
an hour.

It i| said that before the pendulum was used, a balance wheel was some-
times suspended in a horizontal position by a thread passing through its axis,
which coiled round it, and caused it to rise and fall as it oscillated^backwards
and forwards. This mode of regulation differed but little in principle from
the modern pendulums, but it was more complicated and less accurate.
Huygens, in somewhat later times, constructed a clock with a revolving
weight, wliich rose higher, and increased the resistance, whenever an aug-
mentation of the force increased the velocity; and he caused the thread,
which supported the weight, to bend round a curve of such a form as to pre-
serve the equality of the revolutions.

A chronometer maybe constructed on this principle for measuring small por-
tions of time, which appears to be capable of greater accuracy than Mr.
Whitehurst's apparatus, and by means of which an interval of a thousandth
part of a second may possibly be rendered sensible. If two revolving pendu-
lums be connected with a vertical axis, in such a manner, as to move two
weights backwards and forwards accordingly as they fly off to a greater or
smaller distance, the weights sliding, during their revolution, on a fixed sur-

ON TIMEKEEPEnS. 191

face, a small increase of velocity will considerably increase the distance of
the weights from the axis, and consequently the effect of their friction, so
that the machine will be immediately retarded, and its motion may thus be
made extremely regular. It may be turned by a string coiled round the up-
per part, and this string may serve as a support to a barrel, sliding on a
square part of the axis, which will consequently descend as it revolves. Its
surface, being smooth, may be covered either with paper or with wax, and a
pencil or a point of metal may be pressed against it by a fine spring, so as to
describe always a spiral line on the barrel, except when the spring is forced a
little on one side by touching it slightly, either with the hand, or by means
of any body of which the motion is to be examined, whether it be a falling
weight, a vibrating chord or rod, or any other moving substance- In this
manner, supposing a barrel a foot in circumference to revolve in two se-
conds, each hundredth of an inch would correspond to the six hundredth
part of a second; and the scale might be still further enlarged if it were ne-
cessary. (Plate XV. Fig. 198.)

By means of tliis instrument we may measure, without difficulty, the
frequency of the vibrations of sounding bodies, by connecting them with a
point, which will describe an undulated path on the roller. These vibrations
may also serve in a very simple manner for the measurement of the minutest
intervals of time; for if a body, of which the vibrations are of a certain
degree of fiequency, be caused to vibrate during the revolution of an axis,
and to mark its vibrations on a roller, the traces will serve as a correct index
of the time occupied by any part of a revolution, and the motion of any other
body may be very accurately compared with the number of alternations
marked, in the same time, by the vibrating body. For many purposes, the
machine, if heavy enough, might be turned by a handle only, care being-
taken to keep the balls in a proper position, and it would be convenient to
have the descent of the barrel regulated by the action of a screw, and
capable of being suspended at pleasure.

But for the general purposes of timekeepers, all other inventions have

•been almost universally superseded by the pendulum and the balance

spring, or pendulum spring. About the year 1000, Ibn Junis, and the

other Arabian astronomers were in the habit of measuring time, during their

192 LECTURE XVII.

obsert^ations, by the vibrations of pendulums; but they never connected
them with machinery. The equaUty of the times occupied by these vibra-
tions, whether larger or smaller, was known to Galileo in 1600, and some
time before 1633, he proposed that they should be applied to the regulation
of clocks. But Sanctorius, in his commentary on Avicenna, describes an in-
strument to which he had himself applied the pendulum in 1612. Huygens
made the same application only in 1658, which is the date of his work on
the subject. In the same year, Hooke applied a spring to the balance of a
watch; and soon after, he conceived the idea of improving timekeepers suffi-
ciently for ascertaining the longitude at sea, but he was interrupted in the
pursuit of his plan. Hooke was also probably the first that employed for a
clock a heavy weight vibrating in a small arc; an arrangement from which
the peculiar advantages of a pendulum are principally derived.

The objects which require the greatest attention in the construction of
timekeepers, are these; to preserve the moving power, or sustaining force,
as equable as possible, to apply this force to the pendulum or balance in the
most eligible manner, and to employ a pendulum or balance of which the vi-
brations are in their nature as nearly isochronous as possible. In clocks, the
sustaining force, being generally derived from a weight, is already sufficiently
equable, provided that care be taken that the line by which it is suspended may
be of equal thickness throughout, and may act on a perfect cylinder. But
in some clocks, and in all watches, the moving power is a spring. One of the
first clock springs is said to have been an old sword blade; a clock with such
a spring was lately preserved at Brussels: the spring which is at present used,
is a thin elastic plate of steel, coiled into a spiral form. Every spring exerts
the more force as it is more bent; in order to correct this inequality, the
chain or cord by which it acts on the work is wound on a spiral fusee; so
that, in proportion as the force is lessened, it is applied to a larger cylinder,
or a longer lever. The general outline of the fusee must be nearly such,
that its thickness at any part may diminish in the same proportion as it
becomes more distant from the point at which the force would cease alto-
gether, the curve being that which is denominated a hyperbola; but the
workmen have in general no other rule than a habitual estimation. (Plate
XV. Fig. 199.)

ON TIMEKEEPERS. 193

Notwithstanding all possible precautions in the immediate application of the
weight or spring, the irregular action of the teeth of the wheels, the in-
creasing tenacity of the oil usually employed, and other accidental disturb-
ances, make it still desirable to procure a further equalisation of the force,
which is sometimes obtained in clocks, by raising the loaded arm of a lever
to a given height, whence it may descend; and in watches, by bending a
spring into a given position,' from which it may return, so as to limit with
great precision the propelling force employed in each vibration. The ne-
cessity of applying oil is sometimes in great measure removed by jewelling
the holes in which the axes or verges run; a perforation being made in a
plate of ruby, and a diamond applied upon this, in contact with the end of the
axis; the hardness and high polish of these stones tending very considerably
to diminish the friction.

There are also different methods of continuing the action of the force,
while the clock or watch is wound up : a spring is interposed between the
fusee and the wheel impelled by it, a little inferior in force to the original
weight or spring, so as to remain always bent, until, when the pressure of
the main spring is removed, it begins to act upon a fixed point on one side,
and upon the wheel of the fusee on the other, so that it propels the work
for a short time with a force nearly equal to that of the main spring. Some-
times also the spring is wound up by causing a small wheel to revolve round
the centre of the fusee,having its teeth engaged on one side in those of a wheel
which makes a part of the fusee, and on the other side with the internal teeth
of a hoop connected with the work , so that the same pressure which winds
up the spring tends also to turn the hoop round, and to continue the motion.
(PlateXVI. Jig. 200.)

The scapement, by which the sustaining force is communicated to the pen-
dniiim or balance, demands a greater exertion of skill and accuracy than any
other part of a timekeeper. Sometimes the alternate motion of the pendu-
lum has been produced by the action of a crank, but this construction sub-
jects it too much to the irregularities of the Vvdieelwork, and is liable to se-
veral other objections. A crank cannot properly be called a scapement, for
according to the etymology of the term, the pendulum must escape for a
time from the action of the wheelwork, and in general, the more indcpen-

VOL. I. c c

194- LECTURE XVII.

dent its motion is rendered, the better is the effect of the machine. The
simplest forms in common use are the crutch scapement for a clock, and the
pallets with a vertical wheel, for a watch; the dead beat scapement, and
the cylinder with a horizontal wheel, are improvements on these ; and the
detached scapement is a still further refinement.

The crutch scapement, called by the French the anchor scapement, is an
arch in the plane of the scape wheel, and parallel to that in which the pen-
dulum vibrates, supporting at each extremity a pallet, of which the face is
a plane, and which is impelled in its turn by the teeth of the scape wheel.
The faces are so inclined, that the pallets are alternately forced, by the ac-
tion of the teeth, to retire from the centre of the wheel : and great care i&
taken in making the teeth exactly at equal distances, so that they may fall
regularly on the pallet, immediately after the disengagement of the teeth on
the other side from the opposite pallet. (Plate XVI. Fig. £01.)

In the common watch, the axis of the balance is parallel to the plane of
the scape wheel, which is a contrate or crown wheel, and the flat pallets are
fixed on the axis of the balance, at the opposite parts of the circumference of
the scape wheel. (Plate XVI. Fig. 202.)

In both these cases, the impulse given to one pallet carries the opposite
pallet with some force against the approaching tooth, and drives the wheel a
little backwards, with a visible recoil. Here the sustaining power, being ap-
plied principally at the extremities of the vibrations, disturbs their isochronism,
or the equality of the times in which they are performed, by partially in-
creasing the force. We may recollect that, in order that all vibrations, of
whatever magnitude, may be performed in equal times, the force must be
exactly proportional to the distance from a given point, consequently, if an
additional force be applied near the extremities of the vibration only, the
longer vibrations will occupy less time than the shorter ; and we may observe
that, by adding to the force of the spring of a common watch with the key,
we may accelerate its motion, at the same time that the angular magnitude
of the vibration is increased. The motion of the balance also, being slowest
at the extremities of its vibration, where the sustaining force is applied, is
more affected by the inequalities of this force than if it were subjectetl to its

9

ox TIMEKEEPERS. IQS

action through an equal space in the middle of the vibration. Yet a good
clock on this construction may keep time without an error of the ten
thousandth part of the whole, and a watch within a two thousandth. In the
common watch scapement, there is little friction, for the force acts almost
perpendicularly on the pallet; it appears to have been the oldest scapement,
and was employed before the application of springs to balances: it requires a
considerable extent of^ motion in the balance, and cannot therefore well be
applied to clocks with such pendulums as vibrate in small arcs. The crutch
scapement, on the contrary, cannot be applied immediately to a vibration in
a very large arc; but by the interposition of a lever with a roller, or of a part
of a wheel with a pinion, it may be adapted to the balance of a watch; and
some watches thus constructed by Emery, Letherland, and others, appear to
have succeeded very well. ,

To avoid the inconveniences of the recoiling scapements, Mr. Graham in-
vented or introduced the dead beat for the clock, and the cylinder for the
watch. In both of these, the tooth of the scape wheel rests, during the
greater part of the vibration, on a cylindrical surface, and acts on the in-
clined plane for a short time only, in the middle of each vibration; so that a
change of the sustaining power scarcely produces a sensible derangement of
the isochronism ; for which ever way we turn the key of a horizontal watch,
as long as it continues to go, the frequency of its vibrations is scarcely
affected. A good horizontal watch will keep time within about a ten
thousandth part, especially if a little oil be frequently applied to it, or if the
cylinder be made of a ruby: and the timekeeper in the observatory at Green-
wich, with a dead beat scapement, made by Graham, varies from true time
only two parts in a million. (Plate XVI. Fig. 203, 204.)

Still, however, the friction of the teeth of the scape wheel on the cylinder
or pallet, and the tenacity of the oil, where it is employed, may interfere in
a slight degree with the time of vibration, especially by the irregularities to
which they are liable. If the friction were perfectly uniform, it would
scarcely disturb the isochronism, but friction is always increased by an in-
crease of pressure ; hence, therefore, the effect of any addition to the sus-
taining force must tend in some degree to retard the vibrations ; and to ob-
viate this, the surfaces, on which the teeth rest, have sometimes been so

196' LECTURE XVII.

»

formed as to create a slight recoil; but this construction docs not appear to
have been very successful in practice. The friction may, however, be con-
siderably diminished by the duplex scapement, apparently so called from the
double series of teeth employed. The teeth of the more prominent series are
detained on a cylinder so small as to be unfit for receiving an impulse from
them, the balance is therefore impelled by the other series of teeth, acting on
a pallet at a greater distance from its axis. Tlie French have sometimes em-
ployed a construction somewhat similar, which they call the comma scapement,
the teeth first resting on a small arch of repose, and then impelling the curved
jsurface of a pallet extending to a considerable distance beyond it. In both
these cases the single pallet, which is impelled by a tooth of a simple form,
requires less labour in the execution than a number of a larger teeth, each of
which is to be finished with great accuracy : but watches on these construc-
tions, especially those with the comma scapement, are too liable to be stopped
by any sudden motion, although the duplex scapement begins to be fre-
quently employed for pocket timekeepers. (Plate XVI. Fig. 205.)

Mr. Harrison avoided all friction on the pallet, by connecting it with the
pendulum by means of a slender spring, so flexible as to follow the motion of
the scape wheel to a sufficient extent without sliding on its teeth. But the
construction which is most usually employed where the greatest accuracy is
required, is the detached scapement; in which the teeth of the scape wheel
always rest on a detent, exce])ting a short interval, when it is unlocked in
order to impel the pallets. Mr. Mudge employed a detached scapement, ac-
tuated by a subsidiary spring, of which the force is scarcely liable to any va-
riation; the detent being unlocked by the motion of the balance. Mr. Haley
has refined still further on this construction, by causing the subsidiary spring-
to unlock the wheel in its return, so that the balance is relieved from this ac-
tion, which may sometimes produce a slight irregularity. These construc-
tions are, however, much too delicate for common ppcket watches. In a
clock, Mr. Gumming has employed a detached scapement, in which a lever is
raised to a certain height by each tooth of the scape wheel, and acts immedi-
ately on the pendulum in its descent in the middle of the vibration. The
scape wheel is unlocked by the pendulum during its ascent, and a variation
of the pressure may, therefore, produce a very slight inequality in the motion
of the pendulum. Mr. Nicholson has attempted to remove this cause of

ON TIMEKEEPERS. 197

error, by a construction in which the scape wheel only assists the pendulum in
raising the lever; but it depends on the degree of force applied, to determine
what part of the weight the scape wheel shall sustain; this scapement cannot,
therefore, by any means be considered as detached. It is, however, easy to
remove the defect of Mr. Cumming's scapement, if it can be called a defect,
by a method similar to that which Mr. Haley has applied to watches; each
tooth of the wheel being unlocked by the descent of the lever on the opposite
side, at the moment that It ceases to act on the pendulum, and remaining in-
active until the pendulum meets it. (Plate XVI. Fig. 206, 207.)

The detents of the scapements of Mudge and Gumming are parts of the
pallet, but in the timekeepers now commonly made by Arnold, Earnshaw,
and others, the tooth is detained by a pallet or pin projecting from a lever,
the point of which is forced back by the balance, at the moment that the
pallet presents itself to another of the teeth. Mr. Arnold employs an
epicycloidal tooth, acting on a single point of the pallet; Mr. Earnshaw
makes .ji flat surface of the tooth first act on the point of the pallet, and then
the; point of the tooth on a flat surface of the pallet. In other respects there
is littledifFerence in these scapements ; and both the artists have been judged
worthy of a public reward for their success. (Plate XVI. Fig. 208, 209.)

The last of the three principal objects which require the attention of the
watchmaker, is to employ a pendulum or balance of which the vibrations
are in their nature perfectly isochronous. For this purpose the weight of
the pendulum ought to move in a cycloidal arc, but the difficulty of pro-
ducing svich a motion in practice is much greater than the advantage deriv-
ed from it, and a circular vibration, confined to a small arc, is sufficiently
isochronous for all practical purposes. The error of such a vibration is nearly
proportional to the square of the arc described by the pendulum, and
amounts to a second and a half, in a day of 24 hours, for a single degree on
each side the point of rest; so that a pendulum keeping true time in an Sic
of three degrees, would gain 13^ seconds if the arc were very much con-
tracted or made cycloidal, and would lose 104^ seconds by having the vibra-
tion extended to an arc of four degrees. In order to avoid the friction
which would be occasioned by the motion of the pendulum on an axis, it is
usually suspended by a flexible spring, which is wholly free from friction.

198 LECTURE xvir.

The elasticity of this spring adds a minute force to the power of gravitation,
which acts o*\ the pendulum, and this force mxist be considered when the
length of a simple pendulum is compared with the frequency of its vibra-
tions. It does not, however, interfere with the equality of the vibrations
among each other ; for in all springs, Dr. Hooke's general law, that the force
increases as the degree of flexure, is found for moderate oscillations to be per-
fectly accurate; such a force, therefore, accelerates the larger and the smaller
vibrations precisely in the same degree. But in balances, it is desirable to
have the velocity, and the extent of the Vibration, as great as possible, in
order that the motion may be the less influenced by the inequalities of the
sustaining power; and in large excursions. Dr. Hooke's law is not so pre-
cisely true; there must also necessarily be some inaccuracy from the loss of a
certain portion of the force in generating the momentum of the spring itself,
which, when the form is spiral, introduces great intricacy into the calcula-
tion of the properties of the vibration. Yet it has been found by experiment
that a certain length may be determined for almost every spring, which will
afford vibrations cither perfectly or very nearly isochronous. In orcler that
the weight or inertia of the spring may interfere the less with the regularity
of its motion, it is sometimes tapered, and made thinner at the extremity :
it is now also usual in th.e best watches to employ a spring coiled into a
cylindrical form, like that of the spring of a bell, of which the motion ap-
pears to be somewhat more regular than that of a flat spiral. This was in-
deed the original construction, but was probably laid aside on account of the
space which it required. The balance springs are made of the finest steel,
. and the best are manufactured in this country, although the French are said
to have the art of making their main springs of .a better temper than ours.
Sometimes the balance spring is made of an alloy of gold and copper; these
springs are very elastic, but they are too liable to break, Mr. Earnshaw ob-
serves, that the strength of a spring always diminishes a little as it wears; and
endeavours to derive a compensation for this diminution of strength, by em-
ploying a spring of such a form, that the vibrations in small arcs may be a
little more frequent than in larger ones, in order that when the presence of
dust and the tenacity of the oil contract the extent of the vibrations, this
contraction may tend to produce an acceleration which compensates for the
diminished force of the spring. But it is perhaps more eligible to make every
compensation, as far as possible, independent of circumstances foreign to

ON TIMEKEEPERS. 199

the cause of the error. The strength of the spring is found to be less im-
paired by use when it is hardened than when the steel is softer. It some-
times happens, that from a sudden motion, or from some other accidental
circumstance, the balance of a timekeeper may be thrown beyond the point
at which the pallets are impelled by the scape wheels, and the whole motion
may from this cause be interrupted. To prevent this accident, a small bar
or pin is usually fixed on the balance spring, which is carried outwards
when the vibration begins to be extended too far, and stops the further pro-
gress of the balance, by intercepting a pin which projects from it. This ar-
rangement is called banking the balance.

We have already seen that the squares of the times of vibration of two pen-
dulums are proportional to their lengths ; so that if we add to a pendulum
one hundredth part of its length, we increase the time of its vibration very
nearly one two hundredth. But since all bodies are expanded by heat, the
variable temperature of the atmosphere must necessarily produce changes
of this kind in the motions of pendulums, and it may be observed that a
clock goes somewhat more slowly in summer than in winter. The same ex-
pansion has a similar elFcct in the motion of a balance, and the increase of
temperature produces also a diminution of the elastic force of the spring it-
self. There is, however, a great ditt'erencc in the expansibilities of various
substances; dry deal is one of the least expansible, and is therefne often
used for the rods of pendulums. Brass expands one part in a hundred
thousand for every degxee of Fahrenheit, or a little more or less tloan this,
accordingly as it contains more or less zinc. Glass and platina are less than
half as expansible as brass, iron about two thirds, and mercury three times
as much. A pendulum of brass would therefore make one vibration in ten
thousand less at 70° than at 50°, and would lose 84- seconds in a day; a ba-
lance regulated by a spring would lose much more; for I have observed that
vibrations governed by the elasticity of steel have lost in frequency as much
as one ten thousandth part for a single degree of Fahrenheit; and Bertlioud
informs us, that where a clock, probably with a pendulum of steel, loses 20
seconds by heat, a watch loses eight minutes.

Mr. Graham appears to have been the first tliat attempted to compensate
for the effects of temperature by the different expansibilities of various sub^

200 LECTURE XVir.

Stances. He employed, for a pendulum, a tube partly filled with mercury ;
when the tube expanded by the effect of heat, the mercury expanded much
more; so that its surface rose ai. little more than the end of the pendulum was
depressed, and the centre of oscillation remained stationary. This mode of
compensation is still sometimes practised with success; but the gridiron pen-
dulum is more commonly used: it was the invention of Harrison, who com-
bined seven bars, of iron or steel, and of brass, in such a manner, that tlie bars of
brass raised the weight as much as the bars of iron depressed it. At present
five bars only are usually employed, two of them being of a mixture of zinc
and silver, and three of steel. Mr. Ellicott suspended a pendulum at the ex-
tremity of a lever, which was supported by a pillar of brass, much nearer
to the fulcrum ; as the pendulum expanded, the end of the lever was raised
in the same degree, and the weight remained at its original distance from
the point of suspension, which was determined by a fixed plate, transmitting
the slender spring, as usual, between two opposite edges. The same efl'ect is
produced more simply by suspending the pendulum from the summit of a bar
nearly parallel to it, and of the same substance with itself, resting on a fix-
ed support, and either of the same length with the pendulum, or a little
longer, accordingly as the distance of the fixed plate from the point of sup-
port of the bar, is determined by materials which may be considered as
nearly of an invariable length, or as liable to a certain degree of expansion.
(Plate XVI. Fig. 210.)

All these methods of compensation are peculiar to clocks ; for watches, it
is usual to unite together two metals which differ in. expansibility, so, as to
form a compound plate; one side of the plate is commonly of steel, the other
of brass, and it is obvious that any increase of temperature, by causing the
brass to expand more than the steel, must bend the Avhole plate. Such a
plate is variously applied ; the most accurate method, which is employed by
Arnold and other modern artists, is to make it a part of the balance itselfj
fixing a weight on its extremity, which is brought nearer to the centre, by
the increase of curvature of the plate, whenever the expansion of the arms of
the balance tends to remove it further off. The best way of making the
plate appears to be to turn a ring of steel, and to immerse it in melted brass,
and then to turn away what is superfluous of the brass. The magnitude of the
weight, and the length of the plate, may easily be so regulated, as to com-

ON TIMEKEEPERS. 201

pensate not only for the expansion produced by heat, but also for the dimi-
"nution of the elasticity of the spring. Sometimes also a plate has been ap-
plied in such a way as to shorten the spring when the temperature is increased,
by an operation similar to that which serves to regulate a common watch,
the clip, that determines the effective length of the spring, being moved
backwards and forwards; and a similar effect has also been produced by
dividing this chp into two parts, one of which is fixed to a compound
plate, and is made to approach the other so as to confine the spring more
narrowly, and thus diminish its length, upon an increase of temperature.
(Plate XVI. Fig. 211.)

Tlie flexure of a compound plate has also been applied in a simple and ele-
gant manner by Mr. Nicholson to the pendulum of a clock, by causing it to
support the upper extremity of the pendulum. The plate is placed horizon-
tally, the brass being uppermost, and carries the pendulum in the middle,
while the ends rest on two fixed points, of which the distance may be ad-
justed with great accuracy, so that when the temperature is increased, the
curvature of the plate may raise the rod of the pendulum, enough to keep
the weight or bob at a constant distance below the fixed point, which deter-
mines its upper extremity. (Plate XVI. Fig. 212.)

The resistance, opposed to the motion of a pendulum by the air, affects in
some degree its velocity, and the variation of the density of the atmosphere
must therefore also produce some irregularities in timekeepers: they are,how-
ever, too small to be sensible. Derham found that the resistance of the air
accelerated the motion of a half second pendulum about four vibrations in
an hour, by diminishing the arc in which it vibrated: and when the vibra-
tions were restored to their original magnitude, the resistance of the air pro-
duced a retardation of eight vibrations in the same time. But a heavy pen-
dulum, vibrating in a small arc, is very little affected by this resistance.
i

Besides these more essential parts of the watchmaker's art, there are se^
veral subordinate considerations which require his attention ; the striking part
in particular occupies, in clocks, and in repeating watches, no inconsiderable
portion of the bulk of the machine. But the apparatus employed on these oc-
casions requires neither refinement of invention nor delicacy of execution.

VOL. I. D d

go* LECTURE XVir.

In old clocks, the number of hours struck is usually determined by the revo-
lution of a certain portion of a wheel, which supports an arm, and allows the
hammer to strike, until at a proper time it falls into a notch. In watches,
and in more modern clocks, the same effect is produced by means of a spiral
of 12 teeth, revolving once in 12 hours.

It is of considerable importance to the accurate performance of a good
clock, that it should be firmly fixed to a solid support. Any unsteadiness in
the support causes the point of suspension to follow the motion of the pen-
dulum, and enlarges the diameter of the circle of which the pendulum de-
scribes an arc; it must, therefore, tend in general to retard the motion of the
clock. Sometimes, however, an unsteady support may he of such a nature as
to accelerate the motion; and an observation of this kind, made by
Berthoud, has suggested to Bernoulli a theory of compound vibrations,
which may perhaps be true in some cases, but is by no means universally
applicable to every case. On account of some circumstances of this
kind, it happens that when two clocks are placed near each other, and rest
in some degree on the same support, they have often a remarkable etfect on
each other's vibrations, so as to continue going for several days, without va-
rying a single second, even when they would have differed considerably if
otherwise situated: and it sometimes happens that the clock which goes the
more slowly of the two will set the other in motion, and then stop itself; a
circumstance which has been explained from the greater frequency of the vi-
brations of a circular pendulum when confined to a smaller arc, the tendency
of the pendulums to vibrate in the same time causing the shorter to describe
an arc continually larger and larger, and the longer to contract its vibrations,
until at last its motion entirely ceases. This sympathy has some resemblance
to the alternate vibrations of two scales hanging on the same beam, one of
which may often be observed to stop its vibrations when the other begins to
move, and to resume its motion when its companion is at rest ; but it is still
more analogous to the mutual Influence of two strings, or even two organ
pipes, which, though not separately tuned to a perfect unison, still influenx-e
each other's vibrations in such a manner as to produce exactly the same note
when they sound together.

fUV

203

LECTURE XVIII.

ON RAISING AND REMOVING WEIGHTS,

The methodical arrangement of our subject leads us, after having consi-
dered the modifications of force, to those machines which are intended for
counteracting it, or for producing motion in opposition to an existing force.
The simplest of the forces to be counteracted, is gravitation, and it is one of
the most common employments of mechanical powers to raise a weight from a
lower to a higher situation. This operation is also intimately connected with
the modes of overcoming the corpuscular force of friction"^r adhesion, which
constitutes the principal difficulty in removing bodies horizontally from place
to place; for if we had only to produce motion in an unresisting mass of mat-
ter, a loaded waggon might in time be drawn along by a silk worm's thread.
The raising and removing of weights, therefore, together with the modes of
avoiding friction in general, constitute the first part of the subject of the
counteraction of forces, and the remaining part relates to the machinery in-
tended'ifor overcoming the other corpuscular powers of bodies, by such opera-
tions as are calculated to change their external forms.

Machines for raising Aveights, which involve only the mechanics of solid
bodies, are principally levers, capstans, wheels, puUies, inclined planes, screws,
and their various combinations, in the form of cranes.

A lever is a very simple instrument, but of most extensive utility in raising-
weights to a small height. We may recollect that levers are distinguished
into two principal kinds, accordingly as the power and weight are on differ-
ent sides, or on the same side of the fulcrum ; the forces counteracting each
other being in the one case in the same direction, in the other, in opposite
directions. Thus, when a man lifts a stone by means of a lever of the first
kind, resting on a fulcrum between himself and the stone, he presses down

204 LECTURE XVIII.

the end of the lever, and the utmost force that he can apply is equal to the
whole weight of his body: but when he thrusts the lever under the stone, so
that its extremity bears on the ground, it becomes a lever of the second kind,
and in order to raise the stone, he must now draw the end of the lever up-
wards. In this direction, a strong man can exert a force equivalent to twice
his weight; consequently the second kind of lever possesses here a temporary
advantage over the first; although, if the operation were continued, the
workman would be more fatigued by raising even the same weight by this
method, than if he could conveniently apply his weight to a lever of the first
kind ; and for this purpose, cross bars have sometimes been added to levers, in
order to enable several workmen to stand on them with advantage at once.
A bent lever operates precisely with the same power as a straight one, provid-
ed that the forces be applied in a similar manner with respect to its arms:
and in all cases, the forces capable of balancing each other are inversely as
the distances of the points of action from the fulcrum. Some addition of force
is necessary for overcoming the equilibrium, and producing motion, but the
velocity of the motion being seldom of much consequence, a small preponder-
ance is usually sufficient.

The principal inconvenience of the lever is the short extent of its action : this
may, however, be obviated by means of the invention of Perrault, in which two
pins are fixed in the lever, at a short distance from each other, sliding in two
pairs of vertical grooves, provided with ratchets, so that when the long arm of
the lever is pulled by means of a rope, the nearer pin serves as a fulcrum, and the
more distant one is elevated at the same time with the weight, and is detain-
ed in its place by the click; but when the rope is slackened, the weight sinks
a little, and raises the pin, which first served as a fulcrum, to a higher place
in its groove. The same effects may also be produced by catches or clicks rest-
ing upon ratchets on the opposite sides of a single upright bar, which passes
through a perforation in the lever. There must, however, be a considerable
loss of force, from the continual intermission of the motion. (Plate XVII.
Fig. £13.)

An axis with a winch, that is, a lever bent at the end, is known from the
common machine for raising a bucket out of a well. A vertical or upright
axis, with two or more levers inserted into it, becomes a capstan. In these

' ON RAISING AND REMOVING M'EIGHTS. 205

cases, if we wish to estimate the force with accuracy, we must add to the
radius of the axis half the thickness of the rope, when we compare it with the
a,rm of the lever.

Sometimes the weight of a reservoir or bucket of water is employed for rais-
ing another bucket, filled with coals or other mateiials, by means of a rope or
chain, coiled round a cylinder or drum, or two drums of different sizes. This
machine is called a water whimsey : when the bucket of water has reached the
bottom, a valve is opened by striking against a pin, and lets out the water.
In a machine of this kind, employed in the Duke of Bridgwater's coal works,
the water descends thirty yards, and raises a smaller quantity of coals from a
depth of sixty. In such cases, supposing the action to be single, and the
stream of water to be unemployed during the descent of the reservoir,a consi-
derablepreponderance may be advantageously employed in giving velocity to the
weights, provided that the machinery be not liable to injury from their impulse.

An erect axis or drum, turned by the force of horses walking in a circle, is
used for raising coals and other weights, and is called a gin, probably by cor-
ruption from engine: the buckets being attached to the opposite ends of a rope
which passes round the drum, and which is drawn by means of its adhesion to
the drum. One of the buckets descends empty, while the other is drawn up
full, and when the motions of the buckets are to be changed, the horses are
turned, or the wheels are made to impel the axis in a contrary direction, when
any other moving power is employed.

When a ship's anchor is weighed, the cable itself would be too large to be
bent round the capstan ; it is therefore connected with it by means of an end-
less rope, called the messenger. As the messenger is coiled round the lower
part of the capstan, it quits the upper part; so that its place becomes lower and
lower, till at last it has no longer room on the capstan; it is therefore neces-
sary to force it up from time to time: this is called surging the messenger;
it is commonly done by beating it, and to facilitate the operation, the
capstan is made somewhat conical. It has been proposed to employ lifters in
different parts of the circumference, which are raised once in each revolution,
by passing over an inclined plane, with the interposition of friction wheels ;
a patent has been taken out for the invention, and it has already been intro-

206" ^ LECTURE XVIII. \

duced in the navy. Some experienced judges, however, are of opinion, that
it would be better and more simple to employ a capstan so much tapered, that
the tension of the rope itself, guided only by a pulley, might always be suffi-
cient to bring the messenger into its place.

The capstan, which consists of two cylinders of different sizes on the same
axis, with a rope passing from the smaller one over a pulley, which is con-
nected with the weight, and returning to be wound up by the larger one, is
very powerful in its operation ; but it requires a great length of rope for a
small extent of motion. (Plate IV. Fig. 51.)

Wheel work is employed in avariety of ways for raising weights: its powers
are in all cases derived from the same principles as the actions of levers, each
wheel and pinion being considered as composed of a series of bent levers, of
which the axis is the common fulcrum, and which act in succession on the
teeth of the next wheel. The simplest combination of wheelwork used for
this purpose constitutes a jack ; a bar which is furnished with teeth on one
side, being raised by the last pinion. Such instruments were not unknown even
to the ancients; the barulcus described by Hero was a machine of this nature.

(fif A series of buckets connected by ropes, and passing over a wheel, is often
employed for raising water to a small height; and sometimes even for solid
substances in the state of powder, in particular for raising flour, in a corn mill;
and in this case the flour must be brought within reach of the buckets by means
of a revolving spiral, which pushes it gradually forwards. When a weight of
^ any kind is raised in buckets distributed through the circumference of a wheel,
the force, required for retaining the weight in equilibrium, is as much less
than the weight, as the diameter of a circle is less than half the circumference,
the remainder of the weight being supported by the axis of the wheel.

PuUies, and their combinations in blocks, are universally employed on
hoard of ships. They are very convenient where only a moderate increase of
power is required ; but in order to procure a very gxeat advantage, the number
of separate pullies or sheaves must be very much multiplied; a, great length
of rope must also be employed; and it is said that in a pair of blocks with
five pullies in each, two thirds of the force are lost by the friction and the

ON RAISING AND REMOVING WEIGHTS. 207

ligidity of the ropes. The inconvenience resulting from a large number of
puUies, may, however, as we have already seen, be considerably lessened
when they are arranged in Mr. Smeaton's manner, the acting rope being in-
troduced in the middle, so as to cause no obliquity in the block. Tackles,
or combinations of pullies for raising weights, are most conveniently sup-
ported on shore by means of shears, which consist of three rods, or poles,
resting on the ground, and meeting each other in the point of suspension.
For raising stones in building, two poles are employed, with a rope fixed to
their summit, which keeps them in a proper position ; their lower ends are
usually connected by a third pole, which serves as an axis. (Plate IV. Fig. 56.
Plate XVII. Fig. 214.)

Sometimes a pulley is drawn horizontally along a frame, setting out from
the point where the rope is fixed, so that while the bucket is raised, it is
also transferred diagonally to the opposite end of the scaffolding. This ap-
paratus is used in some of the Cornish stream works, in which the earth of a
whole valley is raised, in order to be washed for the separation of tin ore.
(Plate XVII. Fig. 215.)

A fixed inclined plane is often of use in assisting the elevation of great
weights, by means of other machinery. It is supposed that in all the edifices
of remote antiquity, where great masses of stone were employed, as in the
pyramids of Egypt, and the druidical temples of this country, these vast
blocks were elevated on inclined planes of earth, or of scaffolding, with the
assistance also of levers and rollers. Inclined planes are frequently used for
drawing boats out of one canal into another; and sometimes the local cir-
cumstances are such that this may be done with great convenience, merely
by allowing a loaded boat to descend, and to turn the axis which raises an
empty one. An example of this may be seen, on a large scale, in the Duke
cf Bridgwater's canal. This canal is extended, above ground, for forty
miles on one level; an underground navigation twelve miles long joins it at
Worsiey, leading to the coal mines under VValkden moor. At a height of
354- yards above this, is another subterraneous portion, nearly six miles in
length. The connection between these levels is formed by an inclined plane:
the boats are let down loaded, and proceed three miles along the tunnel into
the open cani;il. The inclined plane is fixed in a stratum of stone, which

208 LECTURE xviir.

fortunately has the most eligible inclination of 1 in 4, and is 33 yards in
thickness, affording the most advantageous means of fixing every part of the
machinery with perfect security. The whole length of the plane is 151 yards,
besides a lock of 18 yards at the upper end, (Plate XVII. Fig. 216.)

Inclined planes are also universally employed for facilitating the ascent of
heights, by men or by animals; they may either be uniform, as roads, or the
general inclination of the surface may be superseded by the formation of
separate steps or stairs. The inclination of the surface may be governed by
the proportion of the strength of the animal to its weight, the force required
to support any weight on a plane being to the whole weight as the height of
the plane to its length ; and if the plane be a little less inclined than the
exact equilibrium would require, the animal will be able to acquire a sufficient
velocity at first to carry it easily up the ascent with a motion nearly equable.
The strength of a labourer may be advantageously employed in ascending a
given height by a flight of steps, and placing himself on a stage which may
raise a weight by its descent; but it appears that the force of other animals
is less calculated for exertions of this kind.

The screw is not often immediately applied to the elevation of weights ;
although sometimes a number of screws has been used for raising by
slow degrees a large and unmanageable weight, for instance, that of an
obelise : and a perpetual screw is frequently employed in giving motion to
Avheelwork. Such machines possess a considerable mechanical advantage,
but they are subject to much friction, and are deficient in durability. Mr.
Hunter's double screw might be applied with advantage, if the extent of the
motion re(juired were extremely small ; but this limitation confines its utility
within very narrow bounds.

A crane is a machine for raising weights by means of a rope or chain,
descending from an arm, which is capable of horizontal motion, and passing
over a pulley to be wound up on an axis. The axis is turned, either im-
mediately, or with the interposition of wheelwork, by a winch, by the hori-
zontal bars of a windlass, or by a walking wheel, and sometimes by the force
of wind, of water, or of steam. A walking wheel is an advantageous mode
of employing the str.ength of a labourer, but the bulk of the machine is

ON RAISING AN» REMOVING WEIGHTS. 20i)

sometimes inconvenient and detrimental: when, however, the man walks
upon the wheel, and not within it, this objection is in great measure obvi-
ated. A walking wheel requires to be provided with some method of pre-
venting the dangerous consequences of the rapid descent of the weight, in
case of an accidental fall of the labourer : for this purpose, a catch is usually
employed, to prevent any retrograde motion; a bar has also sometimes been
suspended from the axis of the wheel, on which tlic man may support him-
self with his hands, and other similar precautions have been adopted. Some-
times the plane of a walking wheel is but little inclined to tlie horizon, and
the man walks on its flat surface. In either case the labour of horses, asses,
or oxen, may be substituted for that of men : but for cranes this substitution
would be very disadvantageous, sinae nmch force would be lost in stopping
frequently so bulky a machine as would be required. The employment of a
turnspit dog is an humble example of the same operation, and even goats
appear to have been sometimes made to climb in a similar manner. In a
walking wheel used for raising water at Carisbrook Castle, in the Isle of
Wight, the work was performed by the same individual ass for the wliole of
forty five years preceding 1771. Walking wheels have also been invented, on
which horses were to act externally with their fore feet or hind feet only;
but they have seldom, if ever, been applied to practical purposes. In general
it is advisable that walking wheels for quadrupeds should present to them a
path as little elevated as possible; and it might probably be of advantage to
harness them either to a fixed point, or to a spring or weight, which would
enable them to exert a considerable force even in a horizontal direction; but
probably after all they might be more advantageo\isly employed in a circular
mill walk. (Plate XVII. Fig. 217.)

Mr. White's crane affords a good specimen of an oblique walking wheel;
the force may be varied accordingly as the labourer stands at a point mcfie or
less distant from the centre; and in order to avoid accidents, a break is
always acting on the axis of the wheel by its friction, except when it is re-
moved by the pressure of the man's hand on a lever, upon which he leans as he
■walks. The force is also varied in some cranes by changing the pinion, which
acts on the principal wheel, and an expanding drum has been contrived for
the same purpose, consisting of a number of bars moveable in spiral grooves,

VOL. I. EC

glO tECTUR£ XVIII.

SO as to form a greater or smaller cylinder at pleasure. In order to place the
weight in any situation that may be required, the pulley may be made to slide
horizontally on the gib or arm. (Plate XVII. Fig. 218.)

A model of a crane was exhibited some years ago to the Royal Society, in
which a large wheel fixed to a short axis was made to roll round on a plane,
while the lower end of its axis was connected by a joint with another axis in
a vertical position: then the wheel, having to describe a circumference some-
what larger than its own, was turned slowly, and therefore powerfully, round
its axis, and the motion was communicated to the fixed axis. The machine,
however, appears to be more curious than useful.

•

Sometimes a steelyard has been combined with a crane, for weighing goods
at the same time that they are raised by it. A small crane, fixed in a carriage,
is convenient for loading and unloading goods. In France, the carts used on
the wharfs are generally so long as to reach the ground behind when depressed,
and to furnish an inclined plane, along which the goods are raised by a lever
and axis, or a kind of capstan, fixed in front.

For taking hold of stones which are to be raised by means of a rope, a hole
is sometimes formed in them, wider within than at its opening, and in this
a lewis is inserted, consisting of two inverted wedges, separated by a plug, to
which they are fastened by a pin. (Plate XVII. Fig. 219.)

When a rope or chain, which is to raise a weight, is so long as to require a
counterpoise, the effect of this may be varied according to the length of the
rope, which is unbent, by hanging it on a second rope or chain, which acts on
a spiral fusee, slowly turned by a wheel and pinion.

The use of cranes is so extensive and so indispensable, that their forms
have been often multiplied on account of local circumstances, or even from
caprice; but the constructions which have been described appear to be of the
most general utility, and from them it will be easy to judge of others.

When weights of any kind are simply to be removed from one situation to

OV RAISING AND RJEMOVING WEIGHTS. 1211

another, the most natural and obvious method, if they are portable, is to
carry them. There is, however, some scope for theory even in this common
operation, and we have seen that calculations have been made in order to de-
termine the most advantageous burden for a porter to carry, but the experi-
ence of a few trials would in general be a better guide. Some carry weights
on their heads, others on their shoulders, others low down on their backs: and
according to the situation of the burden, they bend forwards or backwards, so
that the common centre of gravity of the weight and the body comes immedi-
ately or very nearly over some part of the ground between their feet. The
difiiculty of carrying a weight at the extremity of a long rod is easily under-
stood from the properties of the lever, and the same principles will enable us
to deteruMne the distribution of a load between two porters, in Avhatever way
they may carry it. Supposing the weight to be placed on a porter's horse, or
hand barrow, and at equal distances from both extremities, each of the men
will support an equal portion of it; but if it be nearer to the one than
to the other, the load will be distributed in the same proportion as the poles
are divided by the centre of the burden. For instance, if the weight were
300 pounds, and it were one foot distant from the one, and two from the
other, the first would have to carry 200 pounds, and the second 100. If the
porters ascend a hill, or a flight of steps, the distribution of the load will re-
main the same, provided that the centre of the weight lie in the plane of the
poles. But if the weight consists of a large body placed on that plane,
the centre of gravity being above it, the effect of an inclinatiou to
the horizon may materially change the distribution of the load, since
the pressure will always be determined by the distance of the ends of the poles
from the line passing perpendicularly through the centre of gravity; so that,
if the elevation were sufficient, the whole burden might rest on the lower
porter. And in the same manner, if the weight were suspended below the
poles, the inclination would cause a greater proportion of the load to be borne
by the upper porter. The force is, however, only thus distributed as long as
the arms of the porters continue parallel to each other; but the inequality
wovdd naturally be lessened by a change of the directions in which they would
act; it would only be necessary that those directions should meet in some part
of the vertical line passing through the centre of gravity ; the magnitude
of each force would then be determined by the length of the side of a triangle
corresponding to its direction, and the load might be either equally or un-

312 LECTURE XVIII.

equally divided, according to the positions of the arms. (Plate XVII. Fig.
220, 221.)

A man can carry in general a weight four or five times as great as that
•which he can raise continually in a vertical direction witli the same velocity:
so that we may consider the resistance to be overcome as a kind of friction
which amounts to about a fourth or a fifth of the weight. If we attempted to
draw a weight along a horizontal surface, the resistance of the surface would
often not only impede the motion, but also injure the texture of the substance
to be moved. This injury may, however, be avoided by the interposition of a
simple frame or dray, and the dray may be armed with a substance subject to
little friction, as with -iron: the friction may also be somewhat further dimi-
nished by making the outline of the dray a little convex below so that a slight
agitation may be continually produced during its motion. Sometimes the
simple expedient of placing a load on two poles of elastic wood, the thickest
ends of which are supported by the horse, and the thinner drag on the
ground, is of use both in diminishing the friction, by confining it to a smaller
and smoother surface, and in equalising the motion, by the flexibility of the
poles.

It often happens that agitation of any kind enables us to lessen consider-
ably the friction between two bodies, especially when they are elastic. If
we wish, for instance, to draw a ring along an iron rod, by a thread which is
nearly perpendicular to it, we may exert all our strength in vain if we apply
it by slow degrees, since the increase of force continues to increase the ad-
hesion. But if we pull the ring suddenly, and then slacken the thread, it
rebounds from the rod by its elasticity, and in this manner it slides readily
along, by a continuance of alternations. In such a case, however, it would
be more natural, if the thread were sufficiently heavy, to give it a serpentine
motion, which would draw the ring in a more oblique direction. It is said
that when a screw is fixed very firmly in a piece of iron, it may be extricated
much more easily while the iron is filed in some neighbouring part. The
agitation thus produced probably operates in a manner somewhat similar to
tliat of the rod.

Friction may in general be considerably diminished by the interposition of

ON RAISING AND REMOVING WJEIGHTS, 213

oily substances, where the surfaces are of such a nature as to admit of their
application. Thus common oil, tallow, or tar, are usually interposed between
metals which work on each other. It is necessary to attend to the chemical
properties of the oil, and to take care that it be not of such a nature as to
corrode the metals employed, especially where the work requires great ac-
curacy. Tallow is liable to lose its lubricating quality, unless it be frequently
renewed. Between surfaces of wood, soap is sometimes applied, but more
commonly black lead, which becomes highly polished. The advantages of
canals, and of navigation in general, are principally derived from the facility
with which the particles of fluids make way for the motion of bodies floating
on them.

The interposition of rollers or of balls bears some resemblance to tlie appli-
cation of fluids. Supposing the surfaces to be flat and parallel, a roller
moves between them without any friction: but it has still to overcome the
resistance occasioned by the depression which it produces in the substance
on which it moves, and which is greater or less according to the softness and
want of elasticity of the substance. If the substance were perfectly elastic,
the temporary depression would produce no resistance, because the tendency to
rise behind the roller would be exactly equivalent to the force opposing its
progress before; and the actual resistance only arises from a greater or
smaller Avant of elasticity in the materials concerned. The continued change
of place of the rollers is often a material objection to their employment; their
action may in some cases be prolonged by fixing wheels on their extremities,
as well as by some other arrangements; but thcKse methods are too compli-
cated to afford much practical utility. Rollers may also be placed betwceu
two cylinders, the one convex and the other concave, and the friction may
in this manner be wholly removed, whatever may be the magnitude of the
rollers. (Plate XVII. Fig. 222, 223.)

The effect of friction in any machine being always diminished, in propor-
tion as the velocity of the parts sliding on each other is diminished, it is ob-
vious that by reducing £lie dimensions of the axis of a wheel as much as possi-
ble, we also reduce the friction. When the pressure on the axis is derived
principally from the weight of the wheel itself, the friction may be lessened
by placing the wheel in a horizontal position, and making the axis vertical;

•14 LECTURE XVIII.

for in this manner tlie weight may be supported on an axis ending in
a very small surface, and the effect of the friction on this surface will be
about one third less than if it acted at the circumference. The velocity of
the parts sliding on each other may be still more reduced, by placing each
extremity of the axis on another wheel, or between two wheels, on which
the axis rolls as they turn, round, so that the friction is transferred to the
axis of these wheels, of which the motion is very slow. But when a
great weight is to be supported, ft is necessary that the friction wheels be
very strong, and very accurately formed; for if their surface were irregu-
lar, they might stand still, and their use would be destroyed. (Plate
XVIII. Fig. 224.)

Perrault attempted to avoid all friction by supporting the axis of a wheel
in the coil of a rope, which allowed it to turn while the whole wheel ascended
and descended; but the stiffness of a rope occasions in general even a greater
resistance than the friction for which it is substituted.

The wheels.of carriages oweagreat part of their utility to the diminution of
friction, which is as much less in a carriage than in a dray, as the diameter
of the axle is less than that of the wheel, even supposing the dray to slide on
a greased surface of iron. The wheels also assist us in drawing the carriage
over an obstacle, for the path which the axis of the wheel describes, is always
smoother and less abrupt than the surface of a rough road on which the wheel
rolls. It is obvious that both these advantages are more completely attained
by large wheels than by smaller ones ; the dimensions of the axis not being in-
creased in the same proportion with those of the wheel, and the path of the axis,
to which that of the centre of gravity is similar, consisting of portions of larger
circles, and consequently being less curved; and if the wheels are elastic, and
rebound from an obstacle, the difference is still increased. It is, however, barely
possible, that the cui"vature of the obstacle to be overcome may be intermediate
between those of a larger and of a smaller wheel; and in this case the higher
wheel will touch a remoter part of the obstacle, so that the path of the axis
will form an abrupt angle, while the smaller wheel follows the curve, and
produces a more equable motion; this, however, is a case of rare occurrence, and
an advantage of little importance. (Plate XVIlt. Fig. 225, 226.)

ON RAISING AKD REMOVING WEIGHTS. 215

Tiie greater part of the resistance to the motion of a carriage very frequently
arises from the continual displacement of a portion of the materials of the road,
which do not react on the wheels with perfect elasticity, but undergo a per-
manent change of form proportional to the loss of force. Hence, in a soft
sand, although the axles of the wheels may move in a direction perfect'ly hori-
zontal, the draught becomes extremely heavy. The more the wheel sinks,
the greater is the resistance, and if we suppose the degree of elasticity of the
materials, and their immediate resistance, at different depths to be known, we
may calculate the effect of their reaction in retarding the motion of the car-
riage. Thus, if the materials were perfectly inelastic, acting only on the pre-
ceding half of the immersed portion of the wheel, and their immediate pres-
sure or resistance were simply proportional to the depth, like thatof fluids, or of
elastic substances, the horizontal resistance would be to the weight nearly as the
depth of the part immersed to two thirds of its length; but if the pressure in-
creased as the square of the depth, which is a more probable supposition, the re-
sistance would be to the weight as the depth to about four fifths of the
length; the pressure may even vary still more rapidly, and we may
consider the proportion of the resistance to the weight as no greater than that
of the depth of the part immersed to its length, or of half this length to the
diameter of the wheel; and if the materials arc in any degree elastic, the resist-
ance will be lessened accordingly. But on any of these suppositions, it may be
shown that the resistance may be reduced to one half, either by making a wheel
a little lessi than three times as high, or about eight times as broad as the given
wheel. This consideration is of particular consequence in soft and boggy soils,
as well as in sandy countries ; thus, in moving timber in a moist situation, it be-
comes extremely advantageous to employ very high wheels, and they have the
additional convenience that the timber may be suspended from the axles by
chains, without the labour of raising it so high as would be necessary for
placing it upon a carriage of any kind. (Plate XVIII. Tig. 227.)

But the magnitude of wheels is practically limited, by the strength or the
weight of the materials of which they are made, by the danger of overturn-
ing when the centre of gravity is raised too high, and in the case of the first
pair of wheels of a four wheeled carriage, by the inconvenience that would
arise, in turning a corner, with a Avheel which might interfere with the body
of the carriage. It is also of advantage that the draught of a horse should be in

216 LECTURE xvnr.

a direction somewhat ascending, partly on account of the shape of the horse's
shoulder, and partly because the principal force that he exerts is in the direci-
tion of a line passing through tlie point of contact of his hind feet with the
groiind. But a reason equally strong, for having the draught in this direc-
tion, is, that a part of the force nicay always be advantageously employed in
lessening the pressure on the ground; and to answer this purpose the most
effectually, the inclination of the traces or shafts ought to be the same with
that of a road on which the carriage would begin or continue to descend by
its own weight only. In Order to apply the force in thi.'? manner to both
pairs of wheels, where there are four, the line of draught ought to be
directed to a point half way between them, or rather to a point immediately
under the centre of gravity of the carriage; and such a line would always
pass above the axis of the fore wheels. If the line of draught pass immedi-
ately through this axis, the pressure on the hind wheels will remain un-
altered; and if the traces or shafts be fixed still lower, the pressure
on the hind wheels will even be somewhat increased by the draught.
It is evident, therefore, that this advantage cannot be obtained if the fore
wheels are very high; we may also understand that in some cases the com-
mon opinion of the eligibility of placing a load over the fore wheels, rather
than the hind wheels, may have some foundation in truth. When several
horses are employed, the draught of all but the last must be nearly horizontal;
in this case the flexure of the chain brings it into a position somewhat more
favourable for the action of the horses; but the same cause makes, the direc-
tion of its attachment to the waggon unfavourable; further than this there is
no absolute loss of force, but it appears to be advisable to cause the shaft
horse to draw in a direction as much elevated as possible; and on the whole
it is probable that horses drawing singly have a material advantage, when
they do not require additional attendance from the drivers.

The practice of making broad wheels conical has obviously the disadvan-
tageous effect of producing a friction at each edge of the wheel, when the
carriage is moving in a straight line ; for such a wheel, if it moved alone,
would always describe a circle round the vertex of the cone to which it be-
longs. When the wheels are narrow,a slight inclination of the spokes appears
to be of use in keeping them more steady on the axles than if they were
exactly vertical; and when, by an in clination of the body of the carriage, a

OV EAISING AND REMOVING WEIGHTS. Sl/

g-reater proportion of the load is thrown on the lower wheel, its spokes, being
then in a vertical position, are able to exert all their strength with advantage.
The axles being a little conical, in order that they may not become loose, or
may easily be tightened as they wear, it is necessary that they should be bent
down, so that their lower surfaces may be horizontal, otherwise the wheels
would press too much on the linch pin. For this reason, the distance between
the wheels should be a little greater above than below, and their surfaces of
course slightly conical. (Plate XVIII. Fig. 2Q8.)

It has been proposed to fix the wheels to their respective axles, to continue
the axles as far as the middle of the carriage only, and to cause them to turn oa'
friction wheels or rollers; a plan which may succeed if the apparatus is not
too complicated for use; but in fact the immediate friction on the axles is not
great enough to render this refinement necessary. If both opposite wheels
were fixed to a single axis, one of them would be dragged backwards and the
other forv/ards, whenever the motion deviated from a straight line; and a -si-
milar effect actually takes place in those carriages which are supported on a
single roller.

The effect of the suspension of a carriage on springs is to equalise its motion,
b]^ causing every change to be more gradually communicated to it, by means
of the flexibility of the springs, and by consuming a certain portion of every
sudden impulse in generating a'degree of rotatory motion. This rotatory mo-
tion depends on the oblique position of the straps suspending the carriage,
which prevents its swinging in a parallel direction; such a vibration as would
take place if the straps were parallel, would be too extensive, unless they
were very short, and then the motion would be somewhat rougher. The ob-
liquity of the straps tends also in some measure to retain the carriage in a ho^
rizontal position : for if they were parallel, both being vertical, the lower
one would have to support the greater portion of the weight, at least accord-
ing to the common mode of fixing them to the bottom of the carriage, the
spring, therefore, being flexible, it would be still further depressed. But
when the straps are oblique, the upper one assumes always the more vertical
position, and consequently bears more of the load ; for when a body of any
kind is supported by two oblique forces, their horizontal thrusts must be
equal,, otherwise the body would move laterally; and in order that the hori-

VOL. I. F f

S18 LECTURE xviir.

zontal portions of the fcirces may be equal, the more inclined to the horizon
must be the greater: the upper spring will, therefore, be a httle depressed,
and the carriage will remain more nearly horizontal than if the springs were
parallel. The reason for dividing the springs into separate plates has already
been explained: the beam of the carriage, that unites the whee Is, supplies the
strength necessary for forming the communication between the axles: if the
body of the carriage itself were to perform this office, the springs would re-
quire to be so strong that they could have little or no effect in equalising the
motion, and we should have a waggon instead of a coach. The ease with
which a carriage moves, depends not only on the elasticity of the springs,
but also on the small degree of stability of the equilibrium, of which we
may judge in some measure, by tracing the path which the centre of gravity
must describe, when the carriage swings. (Plate XVIII. Fig. 229.)

The modes of attaching horses and oxen to carriages are different in different
countries, nor is it easy to determine the most eligible method. When horses
are harnessed to draw side by side, they are usually attached to the opposite
ends of a bar or lever; and if their strength is very unequal, the bar is some-
times unequally divided by the fulcrum, the weaker horse being made to act
on the longer bar, and being thus enabled to counteract the greater force of
his companion. But even without this inequality, a compensation takes
place, for the centre on which the bar moves is always considerably behind
the points of attachment of the horses; and when one of them falls back a
little, the effective arm of the lever becomes more perpendicular to the direc-
tion of his force, and gives him a greater power, while the opposite arm be-
comes more oblique, and causes the other horse to act at a disadvantage: so
that there is a kind of stability in the equilibrium. If the fulcrum were
further forwards than the extremity of the bar, the two horses could never
draw together with convenience. (Plate XVIII. Fig. 230.)

In mining countries, and in collieries, it is usual, for facilitating the mo-
tion of the carriages employed in moving the ore or the coals, to lay wheel-
ways of wood or iron along the road on wliich they are to pass; and this
practice has of late been extended in some cases as a substitute for the con-
struction of navigable canals. Where there is a turning, the carriages are
usually received on a frame, supported by a pivot, which allows them to be

ON RAISING AND REMOVING WEIGHTS, 210

turned with great ease. In particular situations, these waggons are
loaded by little carts, rolling without direction down inclined planes, and
emptying themselves; they are also provided with similar coutrivcnces for
being readily unloaded, when they arrive at the place of their destination.
The carriages used for drawing loaded boats over inclined planes, where they
have to ascend and again to descend, are made to preserve their level by
having at one end four wheels instead of two, on the same transverse line;
the outer ones as much higher than the pair at the other end, as the inner
ones are lower; and the wheelway being so laid, that either the largest or tlie
smallest act on it, accordingly as the corresponding part of the plane is lower
or higher than the opposite end. It is possible that roads paved with iron
may hereafter be employed for the purpose of expeditious travelling, since
there is scarcely any resistance to be overcome, except that of the air, and
such roads would allow the velocity to be increased almost without limit

For removing earth from one situation to another, a series of baskets has
sometimes been hung on two endless ropes, moving on pullics of such a form,
as to suffer the bars supporting the baskets to pass freely over them ; the
baskets being moved by means of a winch, acting on the rope by a wheel
like one of the pullies. Sometimes also a series of httle carts has been con-
nected by ropes, and drawn in a circle or oval up and down an inclined plane.
These methods may be adopted in making roads, where a hill is to be levelled,
and the materials are to be employed in filling up the valley below: but in
such cases two carts, connected by a cylinder or windlass, are generally
sufficient; and they may be arranged in the same manner as the carriages for
removing boats on an inclined plane.

220

LECTURE XIX.

ON M01>ES OF CHANGING THE FORMS OF BODIES.

I HE corpuscular forces by which bodies retain their peculiar forms of aggre-
gation, require in many cases to be counteracted or modified by mechanical
processes : thus we have frequent occasion to compress bodies into a smaller
space, to aug-ment their dimensions in a particular direction, to divide their
substance, either partially or totally, in given lines or surfaces, or to destroy
their general form, by reducing them into more minute portions; and we may
consider these subjects as principally referable to the effects of compression,
extension, penetration, division, attrition, digging, boring, agitation, tritura-
tion and demolition. The two first of these articles depend on such a change
as we have examined, in considering the strength of materials, under the name
of alteration, the remainder on fracture.

The instruments peculiarly intended for compression are in general of
the description of presses; and the most common act by means of a screw.
The friction on the screw interferes considerably with the power of the ma-
chine; but it isof usein keeping the press fixed in a situation into which it has
been brought by force. The screw is^ always turned by a lever ; for without
this assistance, however powerful it might be, the friction would render it al-
most useless. When great force is required, the screw is made as close as is
consistent with the strength of its spires. Mr. Hunter's double screw may
also be used with advantage, where only a, small extent of motion is required.
The screw of a printing press, or of a stamping press, is, on the contrary, open,
and it is caused to descend with considerable momentum, the handle being-
loaded with. a weight. Wherever a force is so employed as to produce an im-
pulse which acts on any b.ody, the momentum, which is the result of the
action of the force for a certain- time, is usually much more powerful than the

ON MODES OF CHANGING THE FORMS OF BODIES. 221

simple pressure; the degree of its efficacy depends, however, on the degree of
compressibility of the substance. Thus, if a heavy body fall from a certain
height, so as to acquire a momentum, in consequence of the force of gravity,
it will ultimately exert on the substance upon which it falls, a force about as
much greater than its weight, as the space, through which the surface of the
substance struck is depressed, by means of the impulse, is less than twice the
height from which the body has fallen; and unless either the substance is
very compressible, or the height very small, this force must be incomparably
greater than the pressure of the weight only.

For a printing press, a single heavy toller is sometimes made to pass over,
the paper, when it has been laid on the types; and since the whole action of;.'
such a roller is confined to a small part, at any one time, it is said to .exert
sufficient force, and to perform its work more equably than a common press;
but its operation must be comparatively slow. A common mangle for linen
acts nearly in a similar manner. In calendering mills, the force of a spring is
employed, for exerting a pressure on the block, with w.hich the materials arc
glazed.

The copper plate printing press, and the m-achi«e for copying letters, are com-
posed of two rollers, parallel to each other, pressing on the substance which
is interposed, and which is brought into its situation partly by the friction of
the surface of the roLer, and partly by external force.

The rollers, by which sugav canes are- pressed, are in general situated verti-
cally, the middle one of three being turned by horses, by mules, or by water,
and the canes being made to return round it, so as to pass through both in-
terstices in succession. It appears to be of some advantage in presses of this
kind, that all the rollers should be turned independently of their action on the
materials interposed, since the friction of two rollers may tend to draw the
materials into the space between them, with more regularity and greater force,
than the action of a single roller would do. For this reason, it may be ad-
visable to retain the toothed wheels turning the rollers, even when their axes >
are not firmly fixed, but held together by an elastic hoop. (Plate XVIII..,
Bg. 231.)

222 , LECTURE XIX.

' In oil mills, a still greater momentum is applied to the purpose of compres-
sion than in the printing press: hammers, or long wooden beams, placed ver-
tically, are raised by a water wheel, and suffered to fall on wedges, which act
very forcibly on the materials contained in bags on each side.

Compression is also sometimes performed by the operation of hammering:
thus, cast brass is generally hammered before it is used, in order to increase its
strength; the hammer renders it so much stiffer, that if it is necessary to pre-
serve its ductility, it must be frequently annealed by exposure to heat. Anvils
and vices are necessary appendages to the hammer; their use depends princi-
pally on their firmness, which is chiefly derived from weight in the one case,
and from strength in the other; and pincers may be considered as portable
vices.

For the purpose of producing a continued pressure on such substances as
have'^a tendency to contract their dimensions, under the operation of a press,
a spring has been interposed between the press and the materials, which is
capable of pursuing them with a certain degree of force: the utility of such
an arrangement must, however, be extremely limited. Mr. Bramah has ap-
plied a well known law of hydrostatics to the construction of a very useful press,
which is simple, powerful, and portable.

Extension is seldom performed by forces that tend immediately to increase
the dimensions of the substance only : it is generally procured by reducing
the magnitude of the substance in another direction, sometimes by means of
pressure, but more effectually by percussion. The rollers of the press em-
ployed for laminating metals are turned by machinery, and are capable of being
moved backwards and forwards, in order to repeat the operation on the same
^ substance; their distance is adjusted by screws, which are turned at once by
pinions fixed on the same axis, in order that they may be always parallel. In
this manner lead, copper, and silver, are rolled into plates, and a thin plate
of silver being soldered to a thicker one of copper, the compound plate is sub
mitted again to the Action of the press, and made so thin as to be afforded at
a qioderate expense. The glazier's vice U a machine of the same nature, for
forming window lead: the softness of the lead enables it to assume the re-

ON MODES or CHANeiNG THE FORMS OF BODIES. 223

quired shape, in consequence of the pressure of the rollers or wheels; and the
circumference of these wheels is indented, in order to draw the lead along
by the corresponding elevations. (Plate XVIIL Fig. 232.) ,

In drawing wire, the force is originally applied in the direction of the ex-
tension, but it produces a much stronger lateral compression, by means of
the conical apertures through which the wire is successively drawn. For
holding the large wire, pincers are at first used, which embrace it strongly
while they pull, and open when they advance to a new position, the inter-
ruption being perhaps of use, by enabling the pincers to acquire a certain mo-
mentum before they begin to extend the wire; but afterwards, when the
wire is finer, it is simply drawn through the aperture from one wheel or
drum to another. During the operation, it requires frequent annealing,
which causes a scale to form on its surface; and this must be removed by
rolling it in a barrel with proper materials; for the application of an acid is
said to injure the temper of the metal. Copper is sometimes drawn into wire
so large as to serve for the bolts used in shipbuilding, especially for sheathing
ship's bottoms. Silver wire, thinly covered with gold, is rendered extremely
fine, and then flattened, in order to be fit for making gold thread : the thick-
ness of the gold is inconceivably small, much less than the millionth part of
an inch, and sometimes only a ten millionth.

In order to form the handles of vessels of earthenware, the clay is forced
through a hole of a proper shape in an iron box. The operation of the pot-
ter's wheel consists in great measure of compression and extension, performed
by the hands; the vessels are finished, when they are partly dry, in a lathe,
or by other instruments; some kinds of earthenware are formed in a mould
only.

When a thread or a plate of glass is extended in a semifluid state, it has a
tendency to preserve an equable thickness throughout: this is derived from
the effect of the air in cooling it, the thinnest parts becoming immediately a
little colder than the rest, and consequently harder, so that they retain their
thickness, until the neighbouring parts are brought into a similar state.

Extension is performed by means of percussion, in forges, and in the com-

f24 ' LECTURB XIX.

mon operation of the Bmith's hammer. In forges, the hammers are raised by
macliinery, and thrown forcibly against a spring, so as to recoil with great
velocity. With the help of this spring, the hammer sometimes makes 500
strokes in a minute, its force being many times greater than the weight of
the hLimmer, Such forges are used in making malleable iron, in forming-
copper plates, a:id in manufacturing steel. (Plate XVIII. Fig. 233.)

Gold is beaten between the intestines of animals, on a marble anvil; for
tliis purpose it is alloyed with copper or silver. It is reduced to the thick-
ness of little more than the three hundred thousandth of an inch. Silver
leaf is about the hundred and sixty thousandths it is made of silver without
alloy.

The operation of coining depends also principally on an extension of the
metal into the recesses of the die ; it is performed by a strong pressure, united
with a considerable impulse, communicated by a screw like that of a printing
press; and sometimes the impression is formed by the repeated blows of a
hammer only.

Thin plates of silvered copper are moulded into any figure that may be re-
quired, by being placed between two corresponding stamps, of which the
one is fixed, and the other attached to the bottom of a heavy hammer. The
hammer is raised and suffered to fall in a right line, by means of pincers,
which open when they have acquired a certain height. Sometimes the con-
tact, produced by the forcible impulse of a die, is sufficiently intimate to cause
a thin plate of silver to cohere permanently with a surface of iron ; and this
anode of uniting metals is actually employed in some manufactures.

The operations of perforating, cutting, turning, boring, digging, sawing,
grinding, and polishing, resemble each other, in great measure, with respect
to the minute actions of the particles of bodies which they have to overcome.
Penetration is generally performed in the first instance by the effect which we
have called detrusion, where the magnitude of the penetrating substance is
considerable: but when a fine point or edge is employed, it probably first
tears the surface where it is most depressed, and then acts like a wedge on
the portions of the substance left on each side, with a force so much the

ON MODES OF CHANGING THE FORM% OF BODIES. 225

greater as the edge is thinner. The resistance opposed by a solid, or even
by a soft substance, to the motion of a body tending to penetrate it, appears
to resemble in some measure the force of friction, Avhich is nearly uniform,
whether the motion be slow or rapid, destroying a certain quantity of
momentum in a certain time, whatever the whole velocity may be, or what-
ever may be the space described. Hence arises the advantage of giving a
great velocity to a body which is to penetrate another, the distance to which
a body penetrates being as the square of its velocity, or as its energy ; and a
certain degree of energ-y being required in order to make it even penetrate at
all. It is true that when we exchange a slow motion for a more rapid one, by
the immediate action of any mechanical power, we can only obtain the same
energy from the same power, for we must diminish the mass in the same pro-
portion as the square of the velocity is increased ; but a very small part of the
force, which is consumed in the operation of a machine of any kind, is em-
ployed in generating momentum ; by much the greatest part is spent in over-
coming resistances which vary but little with the velocity ; a small portion
only of the resistance increasing in proportion to the square of the velocity;
so that by applying a triple force, we may obtain more than a double velocity,
and more than a quadruple effect: and besides it has already been observed
that when the velocity begins to exceed a certain limit, the effect is increased
in a much greater proportion than that of its square. The same work is also
performed with less pressure, and less strain on the machinery, where a great
velocity is employed. It is on account of the efficacy of velocity, in facilitat-
ing penetration, that soft substances, moving very swiftly, will readily per-
forate much harder ones ; and for the same reason a gunshot wound, and
even the loss of a limb, takes place with so little disturbance of the neigh-
bouring parts, that it is sometimes scarcely felt. The advantage of an impulse,
however inconsiderable, above a pressure, however great, may be easily under-
stood from the ease with which a moderate blow of a hammer causes a nail
to penetrate a substance, into which the whole force of the arm could not
have thrust it.

In the engine for driving the piles, or upright beams, used for the founda-
tions of buildings in water, or in soft ground, the weight is raised slowly to
a considerable height, in order that, in falling, it may acquire suthcient
energy to propel the pile with efficacy. The same force, if applied by very
powerful machinery immediately to the pile, would perhaps produce an equal

VOL. I. G g

Q26 * LECTURE XIX.

fFect in d riving it, but it would be absolutely impossible in practice to con-
struct macbiuery strong enougb for tbe purpose, and if it were possible, tbere
would be an immense loss of force from tbe friction. For example, supposing-
a weight of 500 pounds, falling from a beigbt of 50 feet, to drive the pile
2 inches at each stroke; then, if the resistance be considered as nearly uni-
form, its magnitude must be about 150 thousand pounds, and the same mov-
ing power, with a mechanical advantage of 300 to 1, would perform the work
in the same time. But for this purpose some parts of the machinery must be
able to support a strain equivalent to the draught of 600 horses. In the pile
driving engine, the forceps, or tongs, sometimes called the monkey, or fol-
lower, is opened as soon as the weight arrives at its greatest height; and at
the same time a lever detaches the drum, employed for raising the weight,
from the axis or windlass, at which the horses are drawing; the follower
then descends after the weight, uncoiling the rope from the drum, and
the force of the horses is employed in turning a fly wheel, until the con-
nexion with the weight is again restored. (Plate XVIII. Fig 234.)

When we throw a stone, or a missile weapon of any kind, with the hand,
the stone can acquUe no greater velocity than the hand itself, accompanied
by the neighbouring part of the arm: so that the whole velocity must be pro-
duced in a mass of matter comparatively very large. A sling enables us to
throw a stone or a ball much further; for here the stone may be moved with
a velocity far greater than the hand that impels it, although the action of the
force on the stone is indirect, and the resistance of the air consider-
able. An elastic bow, furnished Avith a strong and light string, enables
us to apply to an arrow or to a ball the whole force of our arms, unencum-
bered with any considerable portion of matter, that requires to be moved with
the arrow; hence a very great velocity may be obtained in this maflner. An
air gun possesses the same advantage in a still greater degree, and the force
of fired gunpowder excels perhaps all others, from its concentrating an im-
mense force in the form of an inconceivably hght elastic fluid; of course a ball
impelled by this force, becomes a most effectual instrument in penetrating the
most refractory substances. We may easily calculate the velocity of an arrow,
by comparing its motion with that of a pendulum, if we know the proportion
of its weight to the force that bends the bow; including in the weight a small
addition for the inertia of the bow and bowstring; the height to which the
arrow will rise, being about as much greater than the space through which

ON MODES OF CHANGING THE FORMS OF BODIES. 227

the bowstring acts on it, as the greatest force applied in drawing the bow is
greater thantwice the weight to be moved.

The action of a whip, either on the air, or on a solid body, depends on
the int;rease of velocity, occasioned by the successive transmission of the mo-
tion from a thicker to a thinner portion of its flexible substance, so that at
last, the energy of the lash, and of its knots, gives it a sufficient capability of
exciting sound, or of inflicting pain.

The instruments generally employed for the division of solid bodies, are
wedges, chisels, knives, and scissors; they sometimes act by pressure only,
but they are more powerful when impulse is added to it. Hatchets, planes,
saws, and files, always act with some rapidity. Cutting instruments are in
general very thin wedges, but the edge itself is usually much more obtuse;
Mr. Nicholson has estimated the angle, formed ultimately by the surfaces
constituting the finest edge, at about 56 degrees. Knives are sometimes fixed~-
on wheels, so as to revolve in a direction oblique to their edges, as in some
machines for cutting chaff, where the straw is also drawn forwards, through
a space variable at pleasure, during each revolution of the knife. An instru-
ment of a similar nature has also been invented for the purpose of cutting
weeds under water.

For the edges of all cutting instruments, steel is principally employed.
After being hardened, by plunging it when red hot into cold water, it is
tempered, by laying it on a heated iron, or more accurately, by Mr. Stodart's
method, of immersing it in a metallic composition in the state of fusion.
When its surface has acquired a yellow tinge, it is fit for edge tools, and the
degree of heat proper for watch springs is indicated by a blue colour. The
backs of knives are often made of iron, which is less brittle than steel: these
substances are generally welded together, by hammering them when red hot;
but sometimes, in large instruments, a back of iron is only rivetted on.

The iron employed for making nails, and other small articles, is first rolled
into flat bars, and then cut into narrow rods, by causing it to pass between
the cylinders of the slitting mill, the surfaces of which are formed into rect"-

228 LECTURE XIX.

angular grooves, and which are placed close to each other, so that the pro-
minent parts of the one are opposed to the depressions of the other, and the
bars are divided by the pressure of the opposite forces, acting transversely at
the same points, so as to separate them by the effect which we have already
considered under the name detrusion. The same machinery also generally
works a pair of large shears, for cutting bars of any kind. (Plate XVIII.
Fig. 235.)

The lathe is an elegant instrument, in which a considerable relative velocity
is produced between the tool and the substance to be cut, by the revolution
of this substance on an axis, while the tool is supported by a rest. Orna-
mental lathes admit of a great variety of mechanical contrivance, but they are
of little practical use, except for amusement. Picture frames are,' however,
sometimes turned in oval lathes; and in the manufacture of buttons, machines
of a similar nature are occasionally employed. The effect of every lathe of a
complicated construction depends on a certain degree of motion of which its
axis is capable: if this motion be governed by a screw, a screw of any dia-
meter may be turned by its assistance; if by a frame producing an elliptic
curve, any number of ovals, having the same centre, may be described at
once; and if a moveable point connected with the work, be pressed by a
strong spring against a pattern of any kind, placed at one end of the axis, a
copy, of the same form, may be made at the other end of the axis.

The process of boring is a combination of penetration and division, and
sometimes of attrition. Awls, gimlets, screws, augers, and centrebits, are
various forms of borers. The drill has the advantage of a rapid motion, com-
municated by the drill bow, which turns it round by means of a little wheel
or pulley. In boring cannon, the tool is at rest, while the cannon revolves,
and by this arrangement the bore of the cannon is formed with much more
accuracy than according to the old method of putting the borer in motion ;
perhaps because the inertia of so large a mass of matter, as constitutes the can-
non, assists in defining the axis of revolution with more accuracy. The borer
is pressed against the cannon by a weight, hung on the arm of a bent spring

»'

and during the operation, the outsid^ is also turned into its intended shape by
the application of proper instruments. Cylinders for steam engines are cast

>

ON MODES OF CHANGING THE FORMS OF BODIES, £29

hollow, and afterwards bored; but in this case the borer revolves, and the
cylinder remains at rest.

Ploughs, spades, pickaxes, mattocks, harrows, and other agricultural in-
struments, resemble in their operation the chisel and the wedge : the numer-
ous diversities in their form and the complications of their structure, are de-
termined more by the various modifications of their action, required for par-
ticular purposes, than by any material difference in the mode of application
of the principles on which they depend. (Plate XVIII. Fig. 236.)

The process of mining is a combination of boring and digging. Shafts are
sunk, levels are driven, and drains are carried off, by the help of picks or
pickaxes, wedges, and hammers, the rocks being also sometimes loosened by
blasting with gunpowder. In searching for coal, ashaft is sunk through the up-
permost soft strata, and the rock is then bored, by striking it continually with
an iron borer, terminating in an edge of steel, which is in the mean time turned
partly round; and at proper intervals a scoop is let down, to draw up the
loose fragments. In this manner a perforation is sometimes made for more
than a hundred fathoms, the borer being lengthened by pieces screwed on
to it; it is then partly supported by a counterpoise, and is worked by ma-
chinery; if it happens to break, the piece is raised by a rod furnished with a
hollow cone, like an extinguisher, which is driven down on it. Sometimes
the borer is furnished with knives, which are made to act on any part at
pleasure, and to scrape off a portion of the surrounding substance, which is
collected in a proper receptacle.

• For sawing Avood on a large scale, sawing mills are very advantageously
employed, being usually driven by water. Several saws are generally fixed
in a frame, parallel to each other; they are worked up and down by a crank,
and at every alternation a wheel is drawn round a little, by a catch, or click, and
moves forwards the frame which supports the timber. When the machine is
employed for cutting the fellies which form the circumference of wheels, the
frame supporting the timber is made to turn round a centre. A circular saw is
used in the construction of blocks and pullies; and in order to make the motion
more secure from the effect of accidental irregularities, the wheels are made,
to turn each other by contact only, without teeth. The machinery for mak-

^

230 LECTURE XIX.

ing blocks, in the Royal dock yard at Portsmouth, has been lately much im-
proved and enlarged; it is worked by a steam engine, the action of which is
applied to a great variety of purposes. The advantage of a saw which re-
volves continually, appears to be very considerable, since a much greater velo-
city may be given to it than can be obtained when the motion is alternate.
Such a saw has also sometimes been applied to cutting off piles under
water.

In mills for sawing marble into slabs, tlie saws are drawn backwards and
forwards horizontally: they are made of soft iron, without teeth; and sand
being applied to them, with water, during the operation, the sand is partly
imbedded in the iron, and grinds away the marble.

'Granite is worked by driving a number of thin wedges very gradually into
it, at various parts of the section desired ; and sometimes wedges of wood are
employed, which being moistened by water, their expansion separates the parts
from each other. It is also said that many stones may be divided by drawing-
lines on them with oil, and then exposing them to heat. Perhaps some pro-
cesses of this kind might be performed Avith advantage under water; it is well
known that glass maybe cut in a rough manner under water, without much
difficulty, by a common pair of scissors.

For reducing the magnitude of a substance in a particular part, instruments
of attrition are used; rasps, files, grindstones, and hones; and of all these
the immediate actions appear to resemble those of chisels and saws. The
hatches of files are cut with a hard chisel while the steel is soft, and the files
arc afterwards hardened. In using the grindstone,- water is applied, in order to
avoid the inconvenience produced by too much heat; and sometimes tallow is
substituted for water with equal advantage: but oil is not found to answer the
same purpose; audit has been conjectured that the cold continually occasion-
ed by the melting of the tallow at the point of friction, serves as a substitute
for the cooling effect of the evaporation of the water. For grinding and po-
lishingsteel, the grindstones are made to revolve, either vertically or horizontally,
with a velocity so great as to describe sometimes as much as 60 feet in a
second. The steel is also in some cases drawn backwards and forwards hori-
zontally on a circular surface, and in order that the action may be equally di-

ON MODES OF CHANGiyG THE FORMS OF BODIES. 231

vided throughout the surface, it is allowed to revolve on an axis hy means
of the friction; its motion being confined to one direction by the action of a
catch.

Various substances, chiefly of mineral origin, are also used, on account of
their hardness, as intermediate materials, for grinding and poHshing others.
These are diamond dust, corundum, emery, tripoli, putty, glass, sand, flint,
red oxid of iron, or crocus martis, and prepared chalk; they are sometimes
applied in loose powder, and sometimes fixed on leather, wood, or paper.
Cuttle fish bone, and seal skin, are furnished by the animal kingdom, and
Dutch rushes by the vegetable; these are employed chiefly in polishing wood
or ivory.

Marble is made smooth by rubbing one piece on another, with the interposi-
tion of sand; the polishing blocks are sometimes caused to revolve by machi-
nery in a trough, in which the marble is placed under water, and are drawn
at the same time gradually to and from the centre ; or the slab itself, with the
frame on which it rests, is drawn slowly backwards and forwards, while the
blocks are working on it. Granite is polished with iron rubbers, by means of
sand, emery, and putty; it is necessary to take care during the operation
that the water, which trickles down from the rubbers, and carries with
it some of the iron, may not collect below the columns, and stain them;
but this inconvenience may be wholly avoided by employing rubbers of
glass.

Optical lenses are fixed on blocks by means of a cement, and ground with
emery, by a tool of proper convexity or concavity: if they are small, a large
number is fixed on the blocks at the same time. Tlie tool is sometimes first
turned round its axis by machinery, and when the lenses are to be finished, a
compound motion is given to it by means of a crank; and in order to make
it more smooth, the wheels turn each other by brushes instead of cogs. The
point of the lens where its two surfaces are parallel, is determined by looking
through it at a minute object, while it is fixed on a wheel with a tubular axis,
and shifting it, until the object no longer appears to move; a circle is then
described, as it revolves, in order to mark its outline.

4

232 LECTURE XIX.

Machines for trituration, by means of which the larger niasses-of matter are
crushed, broken, or ground, into smaller parts, are in general comprehended
under the denomination of mills. After the pestle and mortar, the simplest
machine of this kind appears to be the stamping mill; the stampers resemble
the hammers of the mill employed in the extraction of oils from seeds, and
the machine is used for reducing to powder the ores of metals, and sometimes
also barks, and linseed ; the surface of the stampers being armed with iron
or steel. But barks and seeds are more usually ground by the repeated pres-
sure of two wheels of stone, rolling on an axis which is forced in a hori-
zontal direction round a fixed point. A nobleman of distinguished rank and
talents has lately employed for a moj^ar mill, a wheel of cast iron, formed of
two portions of . cones, joined at their bases: after thirty revolutions, the
mortar being sufficiently ground, a bell rings, and the horse stops.

The materials for making gunpowder are also ground by a wheel revolving
in a trough: in order to corn them, they are moistened, and put into boxes
with a number of holes in their bottoms, and these boxes being placed side
by side, in a circular frame, suspended by cords, the frame is agitated by a
crank revolving horizontally, and the paste shaken through the holes : the
corns are polished by causing them to revolve rapidly within a barrel.

A revolving barrel is used for forming and polishing small round bodies of
different kinds, and it is often employed in agriculture as a churn for making
butter. The purpose of agitation is perhaps more effectually answered by an
alternate motion, which has sometimes been produced in a barrel churn, by
means of a cord attached to a heavy pendulum.

Threshing machines are of two kinds ; the one consists of a number of flails,
beating the corn nearly in the same manner as they are used by labourers ;
in the other, which is more commonly employed in this countr}', the corn is
drawn along by two revolving rollers, and caused to pass between a cylinder,
and its concave cover, while a number of blocks, projecting from the surface
of the cylinder, beat or rub out the grains very effectually from the ears ; the corn
falls out at the lower part, and is winnowed by a fan which the machine turns
at the same time. In this manner it is said that a horse will thresh about 100

ON MODES OF CHANGING THE FORMS OF BODIES. 233

bushels of corn in a day. It is commonly reckoned the work of a labourer to
thresh about six bushels in a day. (Plate XVIII. Fig. 237.)

Some kinds of grain are occasionally ground in mills of iron or steel, which
consist of a solid cylinder or cone turning within a hollow one, both the
surfaces being cut obliquely into teeth. But the common mill for grinding
corn is composed of two circular stones of silicious grit, placed horizontally ;
the upper one revolves with considerable velocity, and is supported by an axis
passing through the lower one, at a distance variable at pleasure: When the
diameter is five feet, the stone usually makes about 90 revolutions in a minute;
if the velocity were greater, the flour would be too much heated. The corn
is shaken out of a funnel, or hopper, by means of projections from the revolv-
ing axis, which strike against the orifice ; it passes through the middle of the
upper millstone, and is readily admitted between the stones; the lower stone
is slightly convex, and the upper one somewhat more concave, so that the
corn passes over more than half the radius of the stone before it begins to be
ground: after being reduced to powder, it is discharged at the circum-
ference, its escape being favoured by the convexity of the lower stone, as well
as by the centrifugal force. The surface of the stones is cut into grooves,
in order to make them act more readily and eft'ectually on the corn. The re-
sistance, in grinding wheat, has been estimated at about a thirty fifth of the
weight of the millstone. The stones have sometimes been placed vertically,
and the axis supported on friction wheels : but the common position appears
to be more eligible for mills on a large scale. It is said that a man and a
boy can grind by a hand mill a bushel of wheat in an hour; in a watermill,
the grinding and dressing of a bushel of wheat is equivalent to the effect of
20160 pounds of water falling through a height of 10 feet, which is
about as much as the work of a labourer for a little more than half an hour.
In a windmill, when the velocity is increased by the irregular action of the
wind, tlie corn is sometimes forced rapidly through the mill, without being
sufficiently ground. There is an elegant method of preventing this, by means
of the centrifugal force of two balls, which fly out as soon as the velocity is
augmented, and as they rise in the arc of a circle, allow the end of a lever to
rise with them, while the opposite end of the lever descends with the upper
millstone, and brings it a little nearer to the lower one. The bran or husk
is separated from the flour, by sifting it in the bolting mill, which consists of a

VOL. 1. H h ,

334 LECTURE XIX.

cylindrical sieve, placed in an inclined position, and turned by machinery.
(Plate XVIII. Fig 238.)

When the flour is made into bread, the dough requires to be kneaded : for
this purpose a machine is sometimes used, in which four or more bars, parallel
to the axis of motion, are turned round, by means of a walking wheel. The
dough is placed in a circular trough, in which the bars revolve not quite in the
middle, so as to approach in each revolution to one of its sides, and thus the
dough is perpetually compelled to change its form.

A machine of nearly the same construction is employed for levigating flints,
after they have first been made red hot, and plunged into cold water, in order
to render them friable. They are mixed, when it is necessary, with other
large stones, and the water, in which the process is performed, carries oft" the
powder, and deposits its coarser parts in a short time, while the finer remain
much longer suspended, and are thus separated from the rest.

When a mechanical structure is to be demolished, or a natural substance to
be broken into smaller parts, we have often occasion to employ the collected
force of men, the powers of machinery, or the expansive force of chemical
agents. Battering rams, or wooden beams, suspended by ropes, and armed
with iron, which were used by the warriors of antiquity in besieging a town,
are now generally superseded by the introduction of artillery, although
they may perhaps still aftbrd, in some cases, a more economical and
equally powerful mode of operation. The same momentum, and the same
energy, may be given to a battering ram at a less expense tlian to a cannon
ball; but it is probable that the efficacy of a cannon ball is chiefly owing
to the augmentation of its velocity beyond that limit, which is the utmost
that the substance to be destroyed can sustain without giving way, inde-
pendently of the mass of the body which strikes it.

For demolishing smaller aggregates, pincers, hammers, and crows, are
generally sufficient ; to these sometimes more complicated instruments are
added. Thus, for example, several machines have been invented for draw-
ing out ship's bolts. A hook which grapples like the common instrument
for drawing teeth, has been applied for holding them fi«mly, and sometimes

ON MODES OF CHANGING THE TORMS OF BODIES. 235

a screw, turned by means of wheelwork, has been used for gaining a force
sufficient to overcome their adhesion. In all such cases, however, the effect
of percussion has a considerable advantage ; and even if other means are em-
ployed, it is of use to begin with lessening the firmness of the adhesion by the
blows of a hammer; and in this manner a screw may be extracted, which is
so firmly attached by its rust, as to be immoveable by other means.

The expansive force of heat is frequently of great service in dividing rocks,
or in destroying old buildings. This is sometimes done simply by the appli-
cation of fire, as in the mine of Ramraelsberg, in the Hartz, where the stra-
tum containing the ore is of such a nature, partly, perhaps, on account of the
combustible matter which enters into its composition, that, by the effect of
a large quantity of fuel, which is burntin the vast excavation,of which it forms
the side, it is rendered so friable as to be worked with ease. More commonly,
however, the force of gunpowder is employed, and rocks are generally blasted
with great convenience by an explosion of this powerful agent. A hole being
bored to the depth of three or four feet, the powder is placed at the bottom,
and a wire being introduced, small stones and sand are rammed round it,
and the wire is withdrawn, leaving a communication for firing the powder, by
means of a train of sufficient length to insure the safety of the workman.
It is said that the explosion is more efficacious when the powder does not fill
the whole of the cavity; this, however, appears to require confirmation. The
chemical powers, which are the ultimate causes of the operation of gunpow-
der, belong to a department of philosophy which it is not our business to in-
vestigate: but the elasticity of the gases and vapours which are extricated, as
modified by the heat which accompanies their production, will be considered"
and explained in the subsequent divisions of this Course of Lectures.

236

LECTURE XX.

ON THE HISTORY OF MECHANICS.

J- HE order which we have pursued, in considering the various departments
of mechanical science, has been in great measure synthetical, dictated by
the plan of proceeding logically from the most simple principles to their more
complicated combinations, so as to build at every step on foundations which
had been firmly laid before: and this method is unquestionably the best
adapted for the expeditious progress of a student in sciences with which he
is unacquainted. But having once acquired a certain degree of knowledge,
he is anxious to be informed by what steps that knowledge w.is originally
obtained, and to what individuals mankind is indebted for each improvement
that has been successively made. Hence, although we cannot attempt to
enter into a complete history of mechanics, it may still be satisfactory to
take a short retrospect of a few of the most remarkable eras in mechanical
philosophy, and in those parts of mathematics on which it immediately
depends.

It is universally allowed that the Greeks derived the elements of mathema-
tical, mechanical, and astronpmical learning from Egypt and from the East.
Diogenes Laertius, who appears to be very desirous of claiming, for his
countrymen, the merit of originality, does not deny that Thales and Pytha-
goras acquired much of their knowledge in their travels. Thales of Miletus
is the first that can be supposed to have introduced these studies into Greece.
Moeris, who was probably a king of Egypt, and Theuth or Thoth, a native
of the same country, are mentioned as having laid the foundations of geome-
try; but the science could scarcely have extended, in those ages, further than
was barely necessary for the measurement of land: since Thales, or even a
later philosopher, is said to have first discovered that two lines drawn from

ON THE HISrORY OF MECHAlTlCS. 23T

the extremities of* the diameter of a circle, and meeting in any other part of
its circumference form with each other a right angle. Thales was one of the
seven whom antiquity distinguished by the appellation of wise men ; he
flourished about 600 years before the Christian era, and he was the father of
the Ionian school, the members of which, in subsequent times, devoted them-
selves more particularly to the study of moral than of natural philosophy.

The Italian school, on the contrary, which was founded by Pythagoras,
appears to have been more inclined to the study of nature and of its laws; al-
though none of the departments of human knowledge were excluded from
the pursuits of either of these principal divisions of the Grecian sages, until
Socrates introduced, into the Ionian school, a taste for metaphysical speculations,
which excluded almost all disposition to reason coolly and clearly on natural
causes and effects. To Pythagoras, philosophy is indebted for the name
which it bears; his predecessors had been in the habit of calling themselves
wise; he chose to be denominated a lover of wisdom only. He had studied
under Pherecydes, and Pherecydes under Pittacus: but with respect to mathe-
matical and mechanical researches, it does not appear that either of his teach-
ers had made any improvements. On his return from his travels in Egypt and
th'fe East, in the time of the last Tarquin, about 500 years before Christ, he
found his native country Samos under the dominion of the tyrant Polycrates,
and went as a voluntary exile to seek a tranquil retreat in a corner of Italy.
At Croto, says Ovid, he studied and taught the laws of nature.

" From human view what erst had lain concealed
His piercing mind to open light revealed ;
To patient toil his ardent soul constrained.
Of Nature's richest stores possession gained :
And thence, with glowing heart and liberal hand,
He dealt her treasures o'er the listening land.
The wondering crowd the laws of nature hears.
And each great truth in silent awe reveres. "

However erroneous the opinion may be, that Pythagoras was acquainted
with the laws of gravitation, it is certain that he made considerable improve-

g38 LECTURE XX.

ments both in mathematics and in mechanics, and in particular that he dis-
covered the well known relation between the hypotenuse and the sides of a
right angled triangle, and demonstrated that the square of the hypotenuse is
always equal to the sum of the squares of the sides. This theorem is more
essential to the perfection of geometry than any other proposition that can be
named: and if we may judge by the story of his having sacrificed a hecatomb
to the Muses, on occasion of the discovery, beseems to have had a foresight of
the magnificence of the edifice, that was in subsequent times to be built on this
foundation.

Democritus of Abdera lived about a century after Pythagoras, whose works
he studied, and whose principles he adopted. He appears to have been possess-
ed of very extensive knowledge and profound learning; but little remains of
his works, excepting their titles. Some have attributed to him the invention
of the method of arranging stones so as to form an arch. Seneca thinks that
so simple an invention must have been practised in earlier ages: but Mr. King
has endeavoured to show that its general introduction in building was of much
later date. Architecture, and other mechanical arts had however been con-
siderably advanced some time before this period, if it is true that Ctesiphon
or Chersiphron, who built the temple of Ephesus, was cotemporary with
Croesus and Thales. It is uncertain at what time bridges of stone were first
built; and it is doubtful whether the art of building bridges of wood was very
well understood in those ages : for according to Herodotus, it was commonly
believed, that Thales avoided the necessity of procuring a passage over the
Halys for the army of Croesus, by encamping them on its banks, and cutting
a channel for the river in their rear, although the historian himself is of opi-
nion, that they passed over bridges which already existed. Curtius speaks of a
bridge of stone over the F.uphrates at Babylon, which appears to have been
built long before the time of Alexander, whose expedition he relates; and it
is scarcely probable that a stone bridge could have withstood the impulse of
so rapid a river, if it had been supported by columns only, without arches.
We are informed by Pliny that Ctesiphon lowered his large blocks of stone by
placing them on ])eaps of sand bags, and letting out the sand by degrees; it
does not appear how he raised them, but the inclined plane seems to afford
the simplest and most obvious method.

ON THE HISTORY OF MECHANICS. 239

Archytasof Tarentum, and Eiicloxus of Cnidus were also Pythagoreans. They
were the first that attempted to make the mathematical sciences familiar by
popular illustrations; and Archytas is said by some to have invented the pul-
ley and the screw. They lived nearly 150 years after Pythagoras, and geo-
metry had made in the mean time very rapid advances, for the properties of
the conic sections were well known to these philosophers. " The first per-
sons," says Plutarch, "that cultivated the method of organic geometry, were of
the school of Eudoxus and Archytas. These philosophers introduced elegance
and variety into science, by illustrations derived from sensible objects, and
made use of mechanical contrivances for expediting and familiarising the solu-
tions of problems, which, if more mathematically treated, are complicated
and difficult: each of them invented a method of determining in this manner
the magnitude of two mean proportionals between two given lines, by the as-
sistance of certain curves and sections. Plato by no means approved of their
mode of proceeding, and reprehended them severely, as giving up and pervert-
ing the most essential advantages of geometry, and causing the science to
revert from pure and incorporeal forms to the qualities of sensible bodies,
subjected to narrow and servile restraints. It was for this reason that practi-
cal mechanics were separated from geometry, and were long neglected by
philosophers, being considered as a department only of the art of war."

Aristotle, who was almost the last of the Ionian school, flourished a little
less than lulf a century after Archytas; he was perhaps the author of no ori-
ginal discoveries relating to the principles of mechanics, but we find, in his
treatise on this science, the law of the composition of motion very distinctly
laid down ; he makes, however, some mistakes respecting the properties of
levers. His general merit in elegant literature, as well as in natural history
and natural philosophy, is too well known to require encomium.

The foundation of Alexandria commences a period memorable for science
in general, but more particularly for mathematics and astronomy. Dino-
crates was the architect whom Alexander employed in laying out and in
building this celebrated city. Among those who studied in this school, the
sciences are indebted to none more than to Euclid, who lived about 300
years before our era. It is uncertain how much of his Elements may have
been derived from his own investigations ; but the masterly manner in which

3.40 LECTUUE XX.

this well known work is arranged, and the precision and accuracy which reign
in every part of it, demand ahnost as great a share of praise as is due to ori-
ginal discovery.

Epicurus was a cotemporary of Euclid, and is considered as the last of the
Pythagorean or Italian philosophers. The penetration that he discovered in
assigning the true causes to many mechanical phenomena, his explanations of
which are copied by Lucretius, is sufficient to induce us to look forwards
with impatience to the publication of such of his works, as have lately been
discovered amongthe manuscripts of Ilerculaneum. Apollonius of Perga lived
about half a century later ; the elegance and extent of his investigations of
the most abstruse properties of the conic sections left but little to be added
to them by more modern geometricians. The architect Philo appears to have
been more ancient than Apollonius: but he is not the Philo whose essay on
warHke engines is published in the collection of the Ancient mathematicians;
since this author was a pupil of Ctesibius.

For the demonstration of the fundamental properties of the lever and of
the centre of gravity; for the discovery of the laws of h3'drostatics, and of the
modes of determining the specific gravities of bodies; for the construction of
the first cranes, and of the first planetarium; and for those improvements of
the methods of mathematical investigation which have been the basis of every
modern refinement in analytical calculation; for all these additions to our
knowledge and our powers, we are indebted to Archimedes. On a character
so conspicuous, we can with pleasure dwell long enough to attend to some
particulars of his history, which are related by Plutarch, in his account of the
siege of Syracuse; omitting, however, such details as are evidently
fabulous. " Archimedes," says Plutarch, " armed with his own inven-
tions only, made light of the splendour of the Roman preparations, and of
the glory of the name of Marcellus. And these were inventions that he even
considered as of subordinate value, as geometrical playthings, which had been
the amusements of his leisure hours. It was king Hiero that first induced
him to transfer a portion of his science from intellectual to materinl objects,
and to condescend in some degree to the comprehension of the multitude, by
giving a sensible form to those truths, which in their abstract state are disco-
verable only to the reasoning faculty. Archimedes, who was a friend and a

ox THE HISTORY OF MKCHANICS. 241

relation of Hiero, had asserted that any weight wliatever might be moved by
any given power: and depending on tlie vahdity of his arguments, had given
scope to his imagination, and boasted that if he had another earth to which
he could step over, he would draw the whole of the present globe out of its
place. Hiero, surprised at the boldness of his assertion, requested him to
give some substantial proof of its truth, by moving a great weight with a
small power: up.on this Archimedes procured a ship, which was with great
labour drawn up on the shore, and having completely manned and freighted
lier, he seated himself at a distance, and by lightly touching the first move-
ment of a machine, he drew her along as smoothly and as safely as if she had
been sailing in the deepest water. Hiero, full of astonishment, and admiring-
tlie powers of mechanical art, prevailed on Archimedes to construct such en-
gines both of defpnce and of offence, as might be of use to him in case of a
siege: for these, however, Hiero, who lived a life of peace and prosperity, was
not so unfortunate as to have occasion; but they now became highly. valua-
ble to the Syracusans, and they were of the more advantage, as their inventor was
present, to direct their use. And in fact the whole people of Syracuse con-
stituted but a part of Archimedes's corporeal macliinery, and he was the soul
that moved and governed the whole. All other arms were deserted, and they
employed his engines alone, both for their own defence, and for the annoy-
ance of the enemy. In short, the Romans soon became so terrified, that if
they saw a stick or a rope upon the walls, they cried out that it was some
macliine of Archimedes, and immediately fled; so that Marcellus at last deter-
mined to desist from attempting to take the place by assault, and resolved to
blockade it only.

"Archimedes, however, had such depth of intellect, and such sublimity
of mind, that notwithstanding he had obtained, by these inventions, the
credit and glory of an intelligence rather divine than human, he thought it
unworthy of him to leave any written treatise on the subject, considering
practical mechanics, and every art that is concerned in satisfying the wants
of life, as ignoble and sordid; and resting all his hopes of fame on those
works, in which the magnificent and the elegant are exhibited, un conta-
minated by the imperfections of the material world: works that are comparable
to nothing else that the mind of man has produced ; in which the subject only
contends with the mode of treating it, the magnitude and beauty of the o»€

VOL. I. J i

242 LECTURE XX.

being rivalled by the accuracy and vigour of the other. It is impossible that
propositions more difficult and important should be deduced from simpler and
purer elements. Some attribute this excellence to his natural genius, others to
his indefatigable application, which has given to every thing that he has
attempted the appearance of having been performed'wlth ease. For we might
ourselves search in vain for a demonstration of his propositions; but so smooth
and direct is the way by which he leads us, that when we have once passed
it, we fancy that we could readily have found it without assistance. We may,
therefore, easily give credit to what is said of him, that being as it were fas-
cinated by this domestic syren, that bore him company, he often neglected his
food and his clothing; that when sometimes brought by compulsion to the
baths, he used to draw his figures in the ashes of the fire places, and to make
his calculations upon the cosmetics that were employed by the attendants; de-
riving, like a true votary of the muses, every pleasure from an intellectual
origin. Among all his beautiful discoveries, he is said to have chosen that
of the proportion of the sphere and cylinder for his sepulchral honours; re-
questing of his friends that they would place on his tomb a cylinder contain-
ing a sphere, and inscribe on it the ratio which he had first determined.

" By artifice, and through the thoughtlessness and security of a day of
festivity, the Romans at length obtained possession of Syracuse, and in the
pillage, although orders had been issued that the life of Archimedes should
be spared, he was killed by a private soldier. His death is variously related,
but all accounts agree, that Marcellus was deeply concerned for his loss, that
he held his assassin in abhorrence, and conferred distinguished favours on his
surviving relations." This event is supposed to have happened about 212
years before the birth of Christ: and the cultivation of mechanical philosophy,
which had been continued for four hundred years with increasing success, was
almost wholly interrupted for eighteen centuries.

There lived, however, in the mean time, some mathematicians and mechanics
of considerable merit. A work on warlike machines, addressed to Marcellus
by Athenaeus, is still extant, and may be found in the splendid collection
of writers on military mechanics entitled Mathematicl Veteres. Ctesibius of
Alexandria was about a century later than Archimedes; he enriched hydrau-
lics with several valuable machines; although he contributed little to the ad-

/ ON THK HISTORY OP MECHANICS. 243

vancement of theoretical investigation. Hero was of the same school, and his pur-
suits were similar ; some of his treatises on hydraulics, pneumatics, and mechanics,
are published in the collection of Ancient mathematicians, and some others are
still extant in manuscript. We are informed by Pappus, that Hero and Philo
liad referred the properties of the lever, the wheel and axis, the pulley, the
wedge, and the screw, to the same fundamental principle ; so that (he theory
of the mechanical powers began at that time to be extremely well understood.
The treatises of Hero on pneumatics and on automatons contain many very
ingenious inventions, but they are rather calculated for amusement than for
utility; among them is a cupping instrument, which operates nearly in the
manner of an air pump. A work of Bito, on warlike machinery, addressed
to king Attains, is included in the same collection.

Vitruvius was an author of great general knowledge: he lived under one of
the earliest of the Caesars, and the greatest part of our information respecting
the mechanics of antiquity has been derived from his works. ApoUodorus was
employed by Trajan, in building a bridge over the Danube, in the year 102;
he has left a treatise on besieging a town, which is to be found among the
Ancient mathematicians. Diophantus, Pappus, and Proclus, were mathematicians
of eminence; Diophantus confined himself in great measure to arithmetic
and pure geometry ; but the last book of Pappus's collections is devoted
to mechanics, and Proclus wrote a treatise on motion, which is stilj extant.
The rudiments of algebraical notation and calculation may be found in the work*
of Diophantus ; but the Arabians appear to have first practised the method of
denoting quantities in general by literal characters ; they made, however, no
considerable advances, and mathematics in general remained nearly stationary
until the time of the revival of letters.

During the long interval, in which learning and science were involved in
the darkness of the middle ages, the arts subservient to the convenience of
life were also in great measure neglected. It is evident from many remains
of antiquity, that various manufactures had attained, in Greece and at Rome,a
high degree of perfection; but the irruptions of the barbarians were as effectual
in suppressing the refinements of civilisation, as in checking the pursuit of li-
terary acquirements: our own country was not the earliest in recovering the
arts which had been lost, but it has always received with open arms those

244 LECTURE XX.

wlio have excelled in them ; and the improvements which have been made,
within a few centuries, in the British manufactures, liave obtained for them a
celebrity unrivalled by those of any other nation. The ancient Britons are sup-
posed to have made, in common with the other Celtic nations, coarse cloths and
felts of wool, and perhaps some articles of linen; their chariots of war, which
are mentioned by Caesar, could not have been executed without some skill in
the arts of the carpenter and the smith. The Romans introduced a certain degree
of civilisation into England, but it appears to have been in great measure
forgotten soon after they left the country. In the seventh century, several
architects and workmen were brought from the continent by Wilfrid and
Biscopj they restored the practice of building with stone, which had been
generally superseded by wood, and laid the foundation for other improve-
ments. In the time of king Alfred, the English goldsmiths began to excel,
and before the conquest, the woollen manufactures had acquired a consider-
able degree of perfection. The paper now in use vras introduced about the
year 1100; it was probably imported from the continent, since the linen
manvifacture was little advanced in England till 150 years later; but em-
broidery was much practised, although in the 12th century silks were princi-
pally woven in Sicily, The manufactory of cloth was considerably improved,
in the 14th century, by the establishment of Kempe and other Flemish weavers
in England: and many of the arts were benefited, about the same time, by the
inventioli of the method of drawing wire, which was first introduced at Nu-
remberg. In the succeeding century, the increasing number of hands em-
ployed in various manufactures, suggested to some mind of superior penetra-
tion the great principle of the division of labour, by which each individual is
enabled to acquire so high a degree of perfection in a very limited branch of
each manufacture, that the whole work is performed much more perfectly, as
well as more expeditiously, than if it had been begun and completed by any
one person, even of greater abilities and experience. The invention of the
modern spinning wheel is attributed to Jiirgen of Brunswick, and the year
1530 is assigned as its date: England soon profited by the improvement;
many manufacturers took refuge in this country from the Duke of Alva's per-
secutions in Flanders, and before the end of the century a new modification
of the art of weaving was introduced by Lee of Cambridge, who invented
the stocking loom, imitating the texture of the knit stockings, which were
first manufactured in Spain about the year 1550. Mills for drawing wire and

. - ox THE HISTORY OF MECHANICS. 245

for slitting iron were also first erected in the sixteenth century ; Birming-
ham and Sheifield were even at that time, according to Camden, celebrated
for their manufactures; and the machinery which has been since introduced
at different periods in those places, affords a facility and expedition which
astonisli every unexperienced spectator. The names of Watt and of Boulton
have acquired a just celebrity from their refined improvements, but many
other mechanics of inferior rank have exhibited a degree of ingenuity which
would have done honour to the most distinguished talents. The manufactures
of Manchester are also of considerable antiquity ; but they are very greatly
indebted to the inventions of Arkwright and his followers, which have also
been introduced in many other parts of the united kingdom. The import-
ance of these improvements may be estimated from the quantity of cotton
which is annually imported into Great Britain; in 1787, it amounted to 23
million pounds, and gave employment to 420 thousand manufacturers ; in
1791, it was increased to 32 millions: about one half is consumed in Avhite
goods, one fourth in fustians, and the remainder in hosiery, mixtures, and
candle wicks. But the woollen manufactory affords a subsistence to above a
million persons, who receive annually for their work about nine millions,
sterling, and employ as much wool as is worth about three.

In architecture, the Anglonorman stile prevailed in this country from the
conquest to the beginning of the thirteenth century; the arch was frequently
employed, and its form was semicircular. The Gothic architecture, dis-"
tinguished by its pointed arches, which is said to have originated from the
Saracens, was first introduced into England about the year 1170, and was
more and more generally adopted fo^ about three centuries. Of the architects
of this school, two of the most celebrated were William of Sens, and Walter
of Coventry: the most elegant specimen of its performances is, perhaps, King's
College Chapel at Cambridge, which was founded by Henry the Sixth, and
begun in the year 1441. The Cathedral of Lincoln appears to have been one
of the earliest Gothic edifices; Westminster Abbey was finished about 1285,
the Minster of York was begun a few years afterwards; and it is difficult to
determine which of these three buildings most deserves the attention of the
antiquary and the architect, or whether the Cathedral at Canterbury may-
Hot be equal to either of them.

246 LECTURE XX.

In the midst of an age of darkness, an insulated individual arrests our at-
tention by merits of no ordinary kind. Roger Bacon was burn at Ilchester,
in the year 1214; it is well known that his experiments had led him to a
discovery of the properties of gunpowder, although he humanely concealed
the nature of its composition from the public, and described it only in au
enigma: the extent of his optical knowledge has been variously estimated^
but it was unquestionably much greater than that of the ancient philosophers.
He appears, however, to have had some companions in his mechanical pur-
suits; he declares that he had seen chariots which could move with incredible
rapidity, without the helpof animals ; he describes a diving bell; and he says
that he had been informed, on good authority, that machines had been made,
by tlie assistance of which men might fly through the air, Cimabue, who
first began to revive the long neglected art of painting, was cotemporary with
Bacon. The use of oil in painting is commonly supposed to have been in-
troduced by Van Eyck, but there are traces, in the records of this country, of
its employment as early as the year 1235.

The clepsydrae, or water timekeepers of the ancients appear to have been
gradually transformed, in the middle ages, into the clocks of the Saracens
and of the Arabians; and these were introduced into Europe in the thirteenth
century. About the year 1290, turret clocks were erected at Westminster and
at Canterbury. The first clock, of which we know the construction, is that
which was made by Wallingford in 1326, and which was regulated by a fly ;
and the second that of Defondeur, or Fusorius, with a simple balance, made
about 1400. But it appears that some portable watches had been constructed
in the beginning of the fourteenth century; and about the year 1460, several
clock makers are said to have come to England from Flanders.

The art of engraving on metal, and of printing with the rolling press, is sup-
posed to have been invented in the year 1423. Some attribute the art of
printing with types, to Laurentius Coster of Haerleni, who, as they say, in
1430, employed for the purpose separate blocks of wood, tied together with
thread. Gensfleich, one of his workmen, went to Mentz, and was there as-
sisted by Gutenberg, who invented types of metal. But the best authors ap-
pear to disbelieve this story ; and Gutenberg, in partnership with Fust antl

ojc THE HisToar OF iiEcnAjfics. S-J-T

Schaeffer, is the first that is universally allowed to have practised the art. It
was introduced into this country by William Caxton.

«

Leonardo da Vinci, the most accomplished man of his age, was born about
the year 1443, and cKcelled not only in painting and poetry, but also in ar-
chitecture, mathematics, and mechanics. The state of practical mechanics
in this and the subsequent centuries may be estimated from Ramelli's collec-
tion of machines, which contains several curious and useful inventions; some
of them long since forgotten, and even lately proposed again as new.

The works of Bacon, Lord Verulam, although not immediately tending to
the advancement of mathematics or of mechanics, are universally allowed to
have conduced very materially to the improvement of every branch of science,
by the introduction of a correct and conclusive method of philosophical ar-
gument and inquiry. Guido Ubaldi published, in 1577, a treatise on me-
chanics, not wholly exempt from inaccuracies, and in the following year a
valuable commentary on the works of Archimedes : some of the properties
of projectiles were about the same time rather imagined than demonstrated
by Tartalea: Benedetti soon after began to reason correctly respecting the
principles of mechanics; but it was reserved for Galileo to lay the founda-
tions of the discoveries, which have succeeded each other with increasing ra-
pidity for more than two centuries. He investigated, in the year 1589, the
laws of accelerating forces, and showed the nature of the curve which is
described by a projectile : he inferred from observation the isochronism of
the vibrations of a pendulum, and the principle was soon after applied by
Sanctorius to the regulation of timekeepers. Stevinus, a Dutchman, was
the first that clearly stated the important law by which the equilibrium of any
three forces is determined : and the properties of the centre of gravity were
successively investigated by Lucas Valerius, Lafaille, and Guldinus, who
made some additions to the elegant propositions of Archimedes which relate
to it.

The application of the more intricate parts of the mathematics, to practical
purposes of all kinds, has become incomparably easier and more convenient
since the invention of logarithms. This important improvement was made by
Baron Napier; his tables were published in 1614: and they were reduced to

24S LECTURE XX.

a still more useful form by the labours of Briggs and of Gunter, Descartes,
about the same time, was makiug considerable additions to the science of
algebra, and the mathematics were soon after enriched by Cavalleri's inven-
tion of the method of indivisibles. This method was founded on the prin-
ciples introduced by Archimedes, it was further improved by Wallis, and it
led to the still more valuable invention of the fluxional analysis.

The laws of collision were investigated nearly at the same time in England
by Wren and Wallis, and in France by Iluygens. After the discoveries of
Archimedes and of Galileo, those of Huygens hold the third place, in the
order of time, among the greatest benefits that have been conferred on sci-
ence. His theory of cycloidal pendulums, and his doctrine of central forces
were the immediate foundations of Newton's improvements.

Hooke was as great in mechanical practice, and in ingenious contrivance,
as Huygens was in more philosophical theory ; he was the first that applied
the balance spring to watches, and he improved the mode of employing pen-
dulums in clocks; the quadrant, the telescope, and the microscope, were ma-
terially indebted to him ; he had the earliest suspicions of the true nature of
the cause that retains the planets in their orbits ; and the multitude of his
inventions is far too great to be enumerated in a brief history of the progress
of science.

The composition of motion, and several other mechanical and optical sub-
jects, are elegantly treated in the lectures published by the learned Dr. Bar-
row. He was professor of mathematics at Cambridge, and voluntarily re-
signed his chair to make way for his successor, the pride of his country, and
the ornament of mankind. Sir Isaac Newton was born at Woolsthorpe in
Lincolnshire, on Christmas day in l642, the year of Galileo's death: At the
age of 12 he was sent to school at Grantham, and at 18 to Cambridge. He
made some important improvements in algebraical analysis, and laid the
foundation of his admirable method of fluxions, before he was 24 years old;
but his modesty prevented him from immediately publishing any work on
these subjects. His first optical experiments were also made in the year 1666,
and they were communicated to the Royal Society, then in its infancy, on his
admission as a member, in 1672. The theory of gravitation, and the mecha-

ON THE HISTORY OF MECHANICS, 249

nics of the universe, are developed in his Mathematical Principles of Natural
Philosophy, first published in 1687- The following year he was chosen
representative of the university of Cambridge, in parlia*ment, and in I6g6", he
was placed, upon the recommendation of the Earl of Halifax, in a lucrative situa-
tion in the Mint. From 1703 until his death in 1727, he continued president
of the Royal Society, and enjoyed, to the age of 80, an uninterrupted state of
good health. He was knighted by Queen Anne, in 1705, and died possessed
of a considerable fortune. " He had the singular happiness," says Mr^ Fon-
tenelle, ' ' of obtaining, during his life, all the credit and consideration to which
his sublime researches and his fortunate discoveries entitled him. All men of
science, in a country which produces so many, placed Newton, by a kind of
acclamation, at their head ; they acknowledged him for their chief and their
master; no opponent, nor even a cool admirer, dared to appear. His philosophy
was adopted throughout England, and it is supported in the Royal Society, and
iuall the excellent productions of the members of that Society, with as much
confidence, as if it had been consecrated by the respect of a long course of
ages." A remarkable instance of the extent and refinement of Newton's ma-
thematical acquirements may be found in a paper of a celebrated modern
mathematician, on the subject of atmospherical refraction; Mr. Kramp observes,
with a mixture of surprise and doubt, that Newton appears to have been ac-
quainted with those methods of algebraical calculation which he had himself
pursued; at the same time he says that this is almost incredible, since " he
must have discovered certain improvements in the higher analysis which were
unknown even to Euler, and to every other mathematician before Laplace."

Although Newton was unquestionably the first inventor of the method' of
fiuxions, yet Leibnitz, whether he had received any hints of Newton's ideas,
as there is some reason to suspect, or whether his investigations were wholly
independent of those of Newton, was the first that published any work on the-
subject ; and he extended its application to many important problems,
earlier, perhaps, than any English mathematician. James and John Bernoulli
also pursued the same studies with considerable success, and the general law*
of mechanics were very elegantly investigated, and successfully applied by
these three contemporary philosophers on the continent, while Machin, Gotes,
Halley, and Demoivre, were applying themselves to similar pursuits in this
country. Perrault, Lahire, Amontons, and Parent, members of the Parisian;

VOL. I. • Kk

I

250 LECTURE XX,

academy of sciences, were the authors of many useful investigations relating
to practical mechanics; but few of them were made public till after the year
1700; some of tlieir inventions made their appearance much later^ in the va-
luable collection of machines approved by the academy, and some of them
liave been inserted in the useful work published by Leupold, at Leipzig, under
the title of a Theatrum Machinaruni. Throughout the last century, the
transactions of various societies, established for the promotion of science, be-
came every year more numerous, and the publication of the literary journals of.
Leipzig and of Paris formed a mode of communication, which was extremely
serviceable in facihtating the dissemination of all new discoveries.

The philosophy of Newton assumed also a more popular and attractive form
in the writings of Clarke, Pemberton, Maclaurin, and Musschenbroek, and
the lectures of S'Gravesande and Desaguliers; at the same time that its
more refined investigations were pursued with success in this country by Mac-
laurin and Simpson, and on the continent by Hermann, Daniel Bernoulli,
Leonard Euler, and Clairaut. Maclaurin, Bernoulli, and Euler, had the
honour of sharing with each other the prize, proposed by the academy of
sciences at Paris, for the best essay on the intricate subject of the tides; but a
premature death prevented Maclaurin from long pursuing the career which he
began so successfully. Bernoulli and Euler continued for many years to vie
with each other, for the elegance and extent of their researches: Euler appears
to have been the more profound mathematician, and Bernoulli the more ac-
curate philosopher.

The latter half of the eighteenth century was in many respects extremely
auspicious to the progress of the sciences; the names of Dalembert, Lan-
den, Waring, Frisi, Robisoa, Lagrange, and Laplace, deserve to be enume-
rated in the first class of mathematicians and theoretical mechanics; those of
Smeaton, Wedgwood, and Watt are no less distinguished for their success in
improving the practice of the useful arts and manufactures. The union of all
these objects, into one system of knowledge, was effected, on a magnificent
.scale, in the Encyclopedic, a work which does as much honour to the lai^our and
genius of some of its authors, as it reflects disgrace on the principles and poli-
tics of others. The Society for the encouragement of arts, manufactures, and
commerce, was established in London about the same time that the Ency-

» ON THE HISTORY OF MECHANICS. HSl

clopedie began to appear at Paris, and its premiums and publications have,
witliout doubt, excited a degree of attention to the subjects of practical me-
chanics, and agricultural, as well as commercial improvements, which must
have been beneficial both to individuals and to the public. The academy
of Paris began to print, in 17<52, a collection of the descriptions of arts and
trades of all kinds, on a still more extended scale than had been attempted
in the Encyclopedic; the work was carried to a very considerable length,
but it by no means comprehends all the articles which were intended to
compose it.

The construction of watches has been so much improved, by the artists both
of this country and of France, that they have been rendered capable of afford-
ing very essential service to navigation, especially since the astronomical
methods of determining a ship's place have been brought to such a degree
of perfection, as greatly to facilitate the frequent correction of the accidental
errors of the timekeeper. The first artist that constructed watches, suffici-
ently accurate for the determination of the longitude, was William Harrison,
who was indebted to himself alone for his education and his inventions; in
1765 he received for his labours, from the Board of Longitude, the promised-
reward often thousand pounds.

There has scarcely been a period, in any age of the world, in which the
sciences, and literature in general, have been so rapidly promoted, and so uni-
versally disseminated, as within the last forty years. This advancement has
partly been the cause, and partly the effect, of the great multiplication of scien-
tific journals, cyclopaedias, and encyclopaedias, which have been annually in-
creasing since the beginning of the Journal de Physique in 1773; supported by
the interest which they have derived, in great measure, from the new and amus-
ing discoveries and improvements, which have been made in chemistry and na-
tural history: some of the most copious of these works have had a sale, un-
precedented even for books of more moderate extent.

The charter of the Royal Institution is dated in 1799; its foundation Avill
not perhaps make an era in the history of the refinements of science; but if
it be hereafter found to have given notoriety to what is useful, and popularity
to what is elegant, the purposes of those who established it will not have been
frustrated.,

252 LECTURE XX.

After all that lias been effected by the united labours and talents of the
philosophers who have been mentioned, and of many more, who, though less
fortunate, have yet been highly meritorious, there is still ample opportunity
for the employment of genius and industry in following their steps. To sup-
pose that little or nothing remains to be done, betrays a want either of know-
ledge, or of courage. The experimental researches of some of the greatest philo-
sophers have been very imperfectly conducted, and the most interesting results
may be expected from repeating and diversifying them. Whatever advances
Our neighbours may have made beyond us, in intricate calculations and com-
binations, \ve are still able to vie with them, and shall probably long-
remain so, in the accuracy of our instruments, and in the art of using them
with precaution and with success.

When, however, we contemplate the astonishing magnitude to which a
collection of books in any department of science may even at present be ex-
tended, and the miscellaneous nature of the works in which many of the most va-
hiable disquisitions have been communicated to the public, together with the
natural disposition to indolence, which a high degree of civilisation too fre-
quently encourages, there is the greatest reason to apprehend, that from the
continual multiplication of new essays, which are merely repetitions of others
that have been forgotten, the sciences will shortly be overwhelmed by their
own unwieldy bulk, that the pile will begin to totter under its own weight,
and that all the additional matter that we heap on it, will only tend to add to
the extent of the basis, without increasing the elevation and dignity of the fabric.
Having been impressed, from continued experience,with the truth of this observa-
tion, I have employed no small portion of time and labour, in order to obtain an
effectual remedy for the evil; and I trust that, in future, everyone who is de-
sirous of enlarging the sphere of our knowledge, with respect to any branch
of science, connected with the subject of these Lectures, will find it easy, by
consulting the authors who will be quoted in my catalogue of references, to
collect that previous knowledge of all that has been already done with the
same view, which, in justice to himself, he ought to acquire before he enters
on the pursuit, or at any rate, in justice to the public, before he calls on the
syoiid at large to participate in his improvements and discoveries.

ON THE HISTORY OF MECHANMCS.

259 ~

CHRONOLOGY OV MATHEMATICIANS AND MECHANICS.

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The points show the time of the birth and death of each

(lerson, where they have been ascertained.

.W R E

N.

COURSE OF LECTURES

ON

NATURAL PHILOSOPHY

AND THE

MECHANICAL ARTS.

PART IT.

HYDRODYNAMICS.

COURSE OF LECTURES

ON

NATURAL PHILOSOPHY

AND THE

MECHANICAL ARTS.

LECTURE XXI.

ON HYDROSTATICS.

I HE mechanical properties and affections of fluids, and the laws and pheno-
mena of their motions, are to be the subjects of the second division, of this
Course of Lectures. Although these properties are in reality derived from the
same fundamental principles as the doctrines of pure mechanics, they are yet in
great measure incapable of being referred, in a demonstrative and accurate-
manner, to the operation of simple and general causes. We are therefore fre-
quently under the necessity of calling in the assistance of experimental deter-
minations; and for this reason, as well as others, the science of hydrod3'na-
mics may with propriety hold a middle rank, between mathematical mechanics
and descriptive physics. In treating of the mechanics of solid bodies, we are
able to begin with axioms, or self evident truths, almost inseparable from the
constitution of the human mind ; to deduce from them the general laws of
motion, and to apply these laws, with little chance of error, to every combi-
nation of circumstances in which we have occasion to exarnine their conse-
<|uences; and it requires only a certain degree of attention and of mathema'
vol.. I. L 1

258 LECTUBE XXI.

tical knowledge, to be perfectly convinced of the justice of all our conclusions,
without any reference to experimental proof. But here our abstract reason-
ings begin to fail; and whether from the imperfection of our modes of consi-
dering the mechanical actions of the particles of fluids on each other, or from
the deficiencies of our analytical calculations, or, as there is more reason to
suppose, from a combination of both these causes, all attempts to reduce the
affections of fluids to a perfect mechanical theory have been hitherto unsuc-
cessful. At the same time it will appear, that by a proper mixture of calcu-
lation with experiment, we may obtain sufficient foundations for all such de-
terminations as are likely to be of any practical utility.

The whole of the subjects, which will be classed under the denomination
Hydrodynamics, may be divided into three general heads; Hydraulics,
Acustics, and Optics; terms which are sufficiently understood, as relating
to the common properties of fluids, to sound, and to light; but which do
not allow of a very strict definition, without a still further division. The
first subdivision which we shall consider, will relate to the laws of the
eqivilibrium of fluids, or of the opposition of forces acting on them, without
producing actual motion, comprehending hydrostatics, or the doctrine of
the equilibrium of liquids, either within themselves, or with moveable bodies ;
and pneumatostatics,or the equilibrium of elastic fluids. The actual motions of
fluids will be considered in the second subdivision: and the third will
relate to the instruments and machines in which the principles of hydrostatics,
hydraulics, and pneumatics, are applied to the purposes of the arts or of
domestic convenience. The science of hydraulics must be allowed to be of as
great importance to civil life, and especially to a maritime nation, as any de-
partment of practical mechanics. Let us only reflect for a moment to what
the metropolis of England would be reduced, if deprived of pipes for the con-
veyance of water, of pumps, and of fire engines; and how much the commerce
of the whole kingdom has been facilitated by the formation of navigable canals,
and we shall soon be convinced of the obligations that we owe to the art of
modifying the motion of water, and to the principles of hydraulics, on which
that art depends.

The facts concerned in acustics and harmonics, or the doctrine of sound, and
the science of music, are not exclusively dependent on the characteristic pro-

ON HYDROSTATICS. Q^g

^erties of fluids. la these departments, although we eftn by no means ex-
plain with precision the manner in which every appearance is produced, we
shall still find a variety of very beautiful phenomena, which have indeed been
too generally neglected, and supposed to be of the most abstruse and unin-
telligible nature; but which, when carefully examined, will appear to be
much more within the reach of calculation, than the simplest doctrines of
hydraulics. We may also apply some of these phenomena to a very complete
explanation of an extensive class of facts in optics, which, in whatever
other way they are considered, are inextricably obscure. Whether this ex-
planation may or may not be admitted as satisfactory, it deserves at least a
fair examination; it would, therefore, be impossible to assign to the science
of optics an earlier place in the order of the system, even if we agree with
those, who imagine that all the phenomena of light depend on causes wholly
deducible from the mechanics of solid bodies.

We must commence the subject of hydfostaties, or the doctrine of the equili-
brium of liquids, With a definition of the essential characteristics of a fiui^i
substance. The most eligible definition appears to be, that a fluid is a
collection of material particles, which may be considered as infinitely small,
and as moving freely on each other in every direction, witliout friction.
Some have defined a fluid as a substance which communicates pressure equally
in all directions; but this appears to be a description of a property derivable
from the former assumption, which is certainly more simple; and although it
may be somewhat difficult to deduce it mathematically, in a manner strictly
demonstrative, yet we may obtain from mathematical considerations a suffi-
cient conviction of its truth, without assuming it as a fundamental or
axiomatic character. A fluid which has no immediate tendency to expand
when at liberty, is commonly considered as a liquid : thus water, oil, and
mercury, are liquids; air and steam are fluids, but not liquids.

W6 shall for the present consider a liquid as without either compressibility
or expansibility: and we must neglect some other physical properties essen-
tial to liquids, such as cohesion and capillary attraction; although, in reality
the particles of liquids are found, by very nice experiments, to be subject to the
same laws of elasticity which we have already examined with regard to solids,

260 lECTURE XKI.

and are possessed also of cohesive powers, which essentially distinguish them
from elastic fluids, and which resist any force tending directly to separate the
particles from each other, while they admit any lateral motion with perfect
facility. In treating of hydrostatics, therefore, we suppose the fluids con-
cerned to be of uniform density throughout; and as far as elastic fluids agree
with this description, they are subject to the same laws with liquids; on the
other hand, all fluids, as far as they are compressible, possess properties simi-
lar to those which will hereafter be examined, when we investigate the subject
of pneumatic equilibrium.

The first law of hydrostatics which arrests our attention, is this, that the sur-
face of every homogeneous gravitating fluid, when at rest, is horizontal. If any
part of the surface were inclined to the horizon, the superficial particles would
necessarily tend towards its lowest part, in the same manner as if they moved
without friction on the inclined surface of a solid. And if any two portions of
the surface of the fluid are separated, as in two branches of a tube or pipe, how-
ever they may be situated, the fluid cannot remain at rest, unless the surfaces be
in the same level plane: for if we imagine such a tube, containing water, to be
made of ice, and to be immersed in a large reservoir of water, and then
thawed, the water will make a part of the general contents of the reservoir, and
consequently -will remain at rest, if its surfaces are level with that of the re-
servoir: and it is obvious that the tube has acquired no new power of sup-
porting it from being tliawed: consequently, the water would have remained
in equilibrium at the same height in the original state of the solid tube. The
experimental proof of this proposition is easy and obvious, and the property
affords one of the most usual modes of determining a horizontal surface. But
when we compare the heights of fluids occupying tubes of different magni-
tudes, it is necessary, if the tubes are small, to apply a slight correction on
account of the actions of the tubes on the fluids which they contain,
which are more apparent, as their diameters are smaller. The same cause
produces also a curvature in each separate surface, which, is always visible
at the point of contact with the tube or vesseL (Plate XIX. Fig Q,39-)

If several separate fluids of different kinds be contained in the same vessel^
they 'vill never remain at rest unless all the surfaces intervening between

ON HTDROSTATICS. fS.6l

them be horizontal; and this is in fact the state of the surface of common li-
quids, which is exposed to the pressure of the atmosphere.

The power of gravitation, strictly speaking, does not act precisely in paral-
lel lines, so that the surface of lakes, instead of being perfectly plane,
becomes, like that of the earth, a little convex. It is obvious that the surface
of a fluid must always be perpendicular to the direction of the joint results
of all the forces which act on it; and since the earth turns round on its axis,
the centrifugal force resulting from its motion is combined with that of
gravity, in determining the position of the general surface of the ocean.

A similar combination of a centrifugal force with gravitation may be ob-
served when a bucket is suspended by a rope, and caused to turn round on
its axis by twisting the rope: the direction of the joint forces is such that
the surface, iu order to be perpendicular to it, must assume a parabolic form.
When also any number of different fluids are made to revolve in the same
manner, or when they are inclosed in a glass globe and turned by means of
the whirling table, the surfaces which separate them acquire always the forms
of parabolic conoids, when the axis remains in a vertical position : but if the
axis be in any other position, the situation of the surface will be of more diffi-
cult determination. (Plate XX. Fig. 240.)

In all these cases the equilibrium is stable ; for if any part of the fluid be
raised above the surface, it will immediately tend to return to its level.
But if a heavier fluid were contained in a bent tube or siphon, with its legs
or branches opening downwards, and immersed in a lighter fluid, the equili^
brium would be tottering, since, if it were once disturbed, it would never be
restored. (Plate XIX. Fig 241.)

From these principles, we may infer, that the pressure of a fluid on every
particle of the vessel containing it, or of any other surface, real or imaginaryf
in contact with it, is equal to the weight of a column of the fluid, of which
the base is equal to that particle, and the height to its depth below the sur-
foce of the fluid. Thus, if we have a vessel of water one foot deep, each
•quare foot of the bottom will sustain the pressure of a cubic foot of water,

2(53 tECTUBE XXT.

or nearly 1000 ounces; if we have a vessel of mercury an inch in depth, each
square foot will sustain a pressure of one twelfth part of a cubic foot of mer-
cury, or 11 30 ounces; the atmosphere presses on each square foot of the earth's
surface with a force of about 34000 ounces, which is equivalent to the pressure
of a column of mercury 30 inches high. The pressure of the water on a small
portion of the lowest part of the side of the vessel containing it, is also equal
to the weight supported by an equal portion of the bottom; but we cannot esti-
mate the force sustained by any large portion of the side, without considering
the difl'erent depths below the surface, at which its difierent parts are si-
tuated.

It is obvious that if wc conceive a fluid to be divided by an imaginary
sorface of any kind, the particles contiguous to it are urged on either side by
equal forces, the fluid below resisting them, and pressing them upwards,
with as much force as the fluid above presses them downwards, their own
weight being comparatively inconsiderable, for without this equality of
pressures, they could not possibly remain at rest. And if we employ a
vessel of such a form as to occupy the place of any superior portion of the
fluid, the pressure against that part of the vessel which is thus substituted
will be the same that before supported the weight of the fluid removed; and
in order that all may remain in equilibrium, the vessel must itself exert an
equal pressure on the fluid below it; so that the pressure on the bottom will
be the same as if the vessel had remained in its original state, and were filled
to the same height with^the fluid. (Plate XIX. Fig. 242.)

In order to understand this the more readily, we may suppose the portion
of the fluid, instead of being removed, to have been congealed into a solid
mass of equal density; it is obvious that this congelation of the fluid would
not have altered the quantity of its pressure ; it would, therefore, have re-
mained in equilibrium with the water below; the mass might also be united
with the sides of the vessel, so as to form a part of it, without increasing or
diminishing any of the pressures concerned : and we should thus obtain a
vessel similar to that which was the subject of our investigation, the pres-
sure on the bottom being always the same, as if the mass, supposed to be
congealed, had remained fluid. Thus, the pressure on the base of a conical

ON HYDROSTATICS. v 263

or pyramidical vessel, full of water, is three times as great as the weight of
the water, since its content is one third of that of a column of the same
height, and standing on the same base. (Plate XIX. Fig. 243.)

In this manner the smallest given quantity of any fluid contained in a pipe
may be made to produce a pressure equivalent to any given weight, however
large, which rests on the cover of a close vessel communicating with the
pipe, and this may be done either by diminishing the diameter of the pipe,
and increasing its height, while the weight is supported by 'a surface of
a certain extent, or by increasing the magnitude of this surface, without
adding to the height of the pipe; for in either case the ultimate force of the
fluid, in supporting the weight, will be equal to the weight of a column of
the same height, standing on the whole surface which is subjected to its action.
And if the effect of the column be increased by any additional pressure, in-
dependent of its weight, that pressure may be represented by supposing the
height of the column to be augmented ; and the effect of the additional pres-
sure will also be increased in proportion to the magnitude of the surface
which supports the weight. It is on this principle that the pressure of water
has been applied, by Mr. Bramah, to the construction of a very convenient
press. (Plate XIX. Fig. 244.)

Although this property of fluids is the cause of some results which would
scarcely be expected by a person not accustomed to reflect on the subject,
and has, therefore, not improperly, been called the hydrostatic paradox, yet
it depends wholly on the general and acknowledged principles of mechanical
forces; nor can we agree with those authors, who have asserted, that a very
small quantity of a fluid may, " without acting at any mechanical advantage"
whatever, be made to balance a weight of any assignable magnitude : for
the immediate operation of the force very much resembles, in the most com-
mon cases, the effect of a wedge, or^of a moveable inclined plane ; thus, a
wedge remains in equilibrium, when the forces acting on each side are in pro-
portion to its length, like the hydrostatic pressure on a vessel of a similar form.
The conditions of the equilibrium of fluids may also be determined, in all cases,,
from the general law of the descent of the centre of gravity to the lowest point.
Thus, it is easy to show that even when two branches of a tube are of

264 LECTURE XXI.

unequal diameter, a fluid must stand at tlie same height in both of them, ia
order to remain in equiUbrium : for if any portion be supposed to stand, in
either leg, above the surface of the fluid in the other leg, it is obvious that
its centre of gravity may be lowered, by removing so much of it as will raise
the fluid in the opposite leg to its own level, the situation of the fluid belo%T
remaining unaltered : consequently the centre of gravity of the whole fluid can
never acquire its lowest situation, unless both the surfaces are in the same level.

The air, and all other elastic fluids, are equally subject with liquids to this
general law. Thus, a much greater force is required, in order to produce a
blast of a given intensity, with a large pair of bellows, than with a smaller
pair; and for the same reason, it is much easier to a glassblower, when he
uses a blowpipe, to employ the muscles of his mouth and lips, than those of
his chest, although these are much more powerful. If we estimate the sec-
tion of,the chest at a foot square, it will require a force of seventy pounds to
raise a column of mercury an inch high, by means of the muscles of respira-
tion, but the section of the mouth is scarcely more than eight or nine square
inches, and a pressure of the same intensity may here be produced by a force
of about four pounds. The glassblower obtains, besides, the advantage of
being able to continue to breathe during the operation, the communication
of the chest with the nostrils remaining open, w^hile the root of the tongue is
pressed against the palate.

It is obvious that the pressure on each square inch of the side of a vessel,
or on each square foot of the bank of a river, continually increases in de-
scending towards the bottom. If we wish to know the sum of the pressures
on all the parts of the side or bank, we must take some mean depth by which
we can estimate it; and this must be the depth of the point which would be
the centre of gravity of the surface, if it were possessed of weight. I'hus, if
we had a hollow cube filled with water, the centre of gravity of each side
, being in its middle point, the pressure on each of the upright sides would be
half as great as the pressure on the bottom, that is, it would be equal to half
the weight of the water contained in the cube.

If, however, we wished to su])port the side of the cube externally by a
force applied at a single point* that point must be at tl\e distance of one

ON HYDaOSTATlCS. 265

third of the height only from the bottom. For the pressure at each point
may be represented by a line equal in length to its depth below the surface,
and a series of such lines may be supposed to constitute a triangle, of which
the centre of gravity will indicate the place of the centre of pressure of the
surface ; and the height of the cerftre of gravity will always be one third of
that of the triangle. It is easily inferred, from this representation, that the
whole pressure on the side of a vessel, or on a bank, of a given length, is pro-
portional to the square of the depth, below the water, to which it extends.
(Plate XIX. Fig. 245.)

The magnitude of the whole pressure on a concave or convex surface may
also be determined by the position of its centre of gravity ; but such a de-
termination is of no practical utility, since the portions of the forces, which
act in different directions, must always destroy each other. Thus, the per-
pendicular pressure on the whole internal surface of a sphere filled with a
fluid, is three times as great as the weight of the fluid; but the force tending
to burst the sphere, in the circumference of any vertical circle, is only three
fourths of that weight.

If two fluids are of different specific gravities, that is, if equal bulks of
them have different weights, their opposite pressures will 'counterbalance each
other, when their heights above the common surface are inversely as their spe-
cific gravities; for it is obvious that the greater density of the one will pre-
cisely compensate for its deficiency in height. Thus, a column of mercury,
standing at the height of 30 inches, in a tube, will support the pressure of a
column of water, in another branch of the tube, exactly 34 feet high]: since
the weight of 30 cubic inches of mercury is equal to that of 408 cubic
inches of water. (Plate XIX. Fig. 246.)

"We have hitherto considered the properties of fluids in contact with solids
which are immoveable, and of invariable form; but it often happens that they
act on substances which are moveable; and they are sometimes contained in
vessels of which the form is susceptible of variation; in these cases, other con-
siderations are necessary for the determination of the equilibrium of fluids and
solids with each other; and in the first place the properties of floating bodies
require to be investigated,

VOL. I. M m -

255 LECTURE XXI.

When a solid body floats in a- fluid, it displaces a quantity of the fluid, equal
to itself in weight; and every solid, which is incapable of doing this, must sink.
For in order that the solid may remain at rest, the pressure of the fluid below
it, reduced to a vertical direction, must be precisely equal to its weight; but
before the body was immersed, the same pressure was exerted on the portion
of the fluid which is now displaced, and was exactly counterbalanced by its
weight; consequently that weight was equal to the weight of the floating
body.

Since the force, which supports the weight of a floating body, is the pres-
sure of the fluid immediately below it, if this pressure be removed or dimi-
nished, the body may remain at rest below the surface of the fluid, even when
it is specifically lighter. Thus a piece of very smooth wood will remain, for
some time, in contact with the flat bottom of a vessel of water, until the water
insinuates itself beneath it; and it will continue at the bottom of a vessel of
mercury, without any tendency to rise, since the mercury has no disposition
to penetrate, like water, into any minute interstices which may be capable of
admitting it. And, for a similar reason, if the pressure of the incumbent
fluid be removed from the upper surface of a solid substance, wholly immers-
ed in it, the solid may remain suspended, although heavier than an equal
bulk of the fluid. Thus, if a tube or vessel of any kind, open above and below
have a bottom of metal, ground so as to come into perfect contact with it,
without being fixed, the bottom will appear to adhere to the vessel, when it is
immersed to a sufficient depth in water, the vessel remaining empty.

In order that a floating body may remain in equilibrium, it is also neces-
sary that its centre of gravity be in the same vertical line with the centre of
gravity of the fluid displaced; otherwise the weight of the solid will not be
completely counteracted by the pressure of the fluid. The nature of the equi-
librium, with respect to stability, is determined by the position of the meta-
centre, or centre of pressure, which may be considered as a fixed point of
suspension, or support, for the solid body. It is obvious that when the lower
surface of the body is spherical or cylindrical, the metacentre must coincide
with the centre of the figure, since the height of this point, as well as the
form of the portion of the fluid displaced, must remain invariable inallcircum-
:4tances, and the nature of the equilibrium will depend on the distance of the

ON HYDROSTATICS. 267

centre of gravity above or below, the centre of the sphere or cylinder. And the
place of the metacentre may always be determined from the form and extent of
the surface of the displaced portion of the fluid, compared with its bulk, and
with the situation of its centre of gravity. For example, if a rectangular beam
be floating on its flat surface, the height of the metacentre above the centre of
gravity will be to the breadth of the beam, as the breadth to twelve times
the depth of tlie part immersed. Hence, if the beam be square, it will float
securely when either the part immersed or the part above the surface is less
than -rW of the whole; but when it is less unequally divided by the surface
of the fluid, it will overset. If, however, the breadth be so increased as to be
nearly one fourth greater than the depth, it will possess a certain degree of
stability whatever its density may be. (Plate XIX. Fig. 247.)

When the equilibrium of a floating body is stable, it may oscillate back-
wards and forwards in the neighbourhood of the quiescent position: and the
oscillations will be the more rapid in proportion as the stability is greater in
comparison with the bulk of the body. Such oscillations may also be com-
bined with others which take place in a transverse direction: a ship, for ex-
ample, may roll on an axis in the direction of her length, and may heel, at the
same time, upon a second axis in the direction of the beams. Besides these
rotatory vibrations, a floating body which is suffered to fall into a fluid, will
commonly rise and sink several times by its own weight; and in all these
cases, the vibrations of any one kind, when they are small, are performed
nearly in equal times: but various and intricate combinations may sometimes
arise/from the difference of the times, in which the vibrations of different kinds
are performed.

When a solid body is wholly immersed in a fluid, and is retained in its
situation by an external force, it loses as much of its weight as is equivalent
to an equal bulk of the fluid. For, conceiving the fluid, which is displaced
by the body, to have been converted into a solid by congelation, it is obvious
that it would retain its situation, and the difference of the pressures of the fluid
on its various parts would be exactly sufficient to support its weight. But
these pressures will be the same if a body of any other kind be substituted
for the congealed fluid ; their buoyant effect may, therefore, be always esti-
mated by the weight of a portion of the fluid equal in bulk to the solid.

268 LECTURE XXI.

Thus, when a little figure, containing a bubble of air, is immersed in a jar of
water, which is so covered by a bladder that it may be compressed by the
hand, the bulk of the figure with its bubble is diminished by the pressure, it
is, therefore, less supported by the water, and it begins to sink : and when
the hand is removed, it immediately rises again. (Plate XIX. Fig. 248.)

While a body is actually rising or sinking in a fluid, with an accelerated
motion, the force of gravity being partly employed in generating momentum,
either in the fluid or in the solid, the whole pressure on the bottom of the
vessel is necessarily somewhat lessened. Hence the apparent weight of a jar
of water will suffer a slight diminution, while a bullet is descending in it, or
while bubbles of air are rising in it, but the difference can seldom be great
enough to be rendered easily discoverable to the senses.

It sometimes happens that a solid body is partly supported by a fluid, and
partly by another solid; of this we have an example in one of Dr. Hooke's
ingenious inventions for keeping a vessel always full. A half cylinder, or a he-
misphere, being partly supported on an axis, which is in the plane of the sur-
face of the fluid, its weight is so adjusted, as to be equal to that of a portion
of the fluid of half its magnitude: when the vessel is full, it is half immersed,
and exerts no pressure on the axis : it descends as the fluid is exhausted, and
its tendency to turn round its axis can only be counteracted, by the pressure
of the fluid on its flat side, as long as the surface of the remaining portion
of the fluid retains its original level. (Plate XIX. Fig. 249.)

When a fluid is contained in a vessel of a flexible nature, the sides of the
vessel will always become curved, in consequence of the pressure, and the
more, in proportion as the pressure is greater; the form of the curved surface
will also be such that the common centre of gravity of the fluid^and the ves-
sel may descend to the lowest point that the circumstances of the case allow;
this form is generally of too intricate a nature to be determined by calcula-
tion : no mathematician has hitherto been able to investigate, for example,
the curvature which a square or rectangular bag of leather will assume when
filled with water or with corn. When, indeed, one dimension only of a ves-
sel is considered, for instance, when the bottom of a cistern is supposed to be
flexible, and to be fixed at two opposite sides, while the ends are simply ia

ON HYDROSTATICS. Q69

contact with upright walls, without allowing the water to run out, the na-
ture of the curve may be determined with tolerable facility,- whether the
weight of the bottom itself be considered or not. If the weight be exactly
equal to that of the water, the form of a semicircle will agree with the
conditions of equilibrium, as Bernoulli has demonstrated, supposing the
fixed points at the distance of its diameter; but if the weight of the bottom
be neglected, the curvature will be every where proportional to the distance
below the surface, the form being the same as that of an elastic rod, bent
by two forces in the direction of the surface. The same principles, with a
slight difference in the calculations, will serve to determine the forms adapt-
ed to the equilibrium of arches, intended for supporting the weight of superin-
cumbent fluids, or of such soft materials as approach nearly in their operation
to more perfect fluids. (Plate XIX. Fig. 250.)

\

sro

LECTURE XXII.

ON PNEUMATIC EQUILIBRIUM.

J. HE laws of the pressure and equilibrium of liquids, which are the peculiar
subjects of hydrostatics, are also appHcable in general to fluids of all kinds,
as far as they are compatible with the compressibility of those fluids, or with
their tendency to expand.

Elastic fluids are distinguished from liquids by the absence of all cohesive
force, or by their immediate tendency to expand when they are at liberty.
Such are atmospheric air, steam, and gases of various kinds; and the consi-
deration of these fluids, in the state of rest, constitutes the doctrine of pneu-
niatostatics, or of the equilibrium of elastic fluids.

That the air is a material substance, capable of resisting pressure, is easily
shown, by inverting an empty jar in water ; and by the operation of transfer-
ring airs and gases from vessel to vessel, in the pneumatic apparatus_xused by

' chemists. The tendency of the air to expand is shown by the experiment in
which a flaccid bladder becomes distended, and shrivelled fruit recovers its

^ full size, as soon as the external pressure is removed from it, by the operation
of the air pump: and the magnitude of this expansive force is more distinctly
seen, when a portion of air is inclosed in a glass vessel, together with some
mercury, in which the mouth of a tube is immersed, while the other end is
open, and without the vessel; so that when the whole apparatus is inclosed in
a very long jar, and the air of the jar is exhausted, the column of mercury
becomes the measure of the expansive force of the aif. (Plate XIX. Fig.
S51.)

If the diameter of the tube, in an apparatus of this kind, were very small in
comparison with tlie bulk of the air confined, the column of mercury would

ON PNEUMATIC ZQUHIBRIUM, S,7l

be raised, in the ordinary circumstances of the atmosphere, to tlie lieight of
nearly 30 inches. But supposing the magnitude of the tube such, that the
portion of air must expand to twice its natural bulk, before the mercury ac-
quired a height sufficient to counterpoise it, this height would be 15 inches
only. For it appears to be a general law of all elastic fluids, that their pres-
sure on any given surface is diminished exactly in the same proportion as
their bulk is increased. If, therefore, the column of mercury in the vacuum
of the air pump were 60 inches high, the air would be reduced to half its
natural bulk ; and for the same reason, the pressure of a column of 30 inches
of mercury in the open air will reduce any portion of air to half its bulk, since
the natural pressure of the atmosphere, which is equal to that of about 30
inches of mercury, is doubled by the addition of an equal pressure. In the
same manner the density of the air in a diving bell is doubled at the dej)th of
34 feet below the surface of the water, and tripled at the depth of 68 feet.
This law was discovered by Dr. Hooke; he found, however, that when a very
great pressure had been applied, so that the density became many times
greater than in the natural state, the elasticity appeared to be somewhat less
increased than the density ; but this exception to the general law has not
been confirmed by later and more accurate experiments.

Not only the common air of the atmosphere, and other permanently elastic
gases, but also steams and vapoMs of all kinds, appear to be equally subject
to thisuniversallaw: they must, however, be examined at temperatures suffici-
ent to preserve them in a state of elasticity ; for example, if we wished to deter-
mine the force of steam twice as dense as that which is usually produced, we
should be obliged to employ a heat 30 or 40 degrees above that of boiling water:"
we should then find that steam of such a density as to support, when confin-
ed in a dry vessel, the pressure of a column of 30 inches of mercury, would
be reduced to half its bulk by the pressure of a column of 60 inches. But if
we increased the pressure much beyond this, the steam would be converted
into water, and the experiment would be at an end.

That the air which surrounds us is subjected to the power of gra-
vitation, and possesses weight, may be shown by weighing a vessel which
has been exhausted by means of the air pump, and then allowing the air to
enter, and weighing it a second time. In this manner we may ascertain the

273 LECTURE xxir,

specific gravity of the air, even if the exhaustion is only partial, provided
that we know the pvoportion of the air left in the vessel to that which it
originally contained. The pressure derived from the weight of the air is also
the cause of the ascent of hydrogen gas, or of another portion of air which
is rarefied by heat, and carries with it the smoke of afire; and the effect is
made more conspicuous, when either the hydrogen gas, or the heated
air, is confined in a balloon. The diminution of the apparent weight of a
body, by means of the pressure of the surrounding air, is also shown by the
destruction of the equilibrium between two bodies of different densities, upon
their removal from the open air into the vacuum of an air pump. For this
purpose, a light hollow bulb of glass may be exactly counterpoised in the air
by a much smaller weight of brass, with an index, which shows, on a graduated
scale, the degree in which the large ball is made to preponderate in the re-
ceiver of the air pump, by the rarefaction of the air, lessening the buoyant
power which helps to support its weight. (Plate XIX. Fig. 252.)

From this combination of weight and elasticity in the atmosphere, it
follows, that its upper parts must be much more rare than those which are
nearer to the earth, since the density is every where proportional to the whole
of the superincumbent weight. The weight of a column of air one foot in
height is one twenty eight thousandth of the whole pressure; consequently
that pressure is increased one twenty eight thousandth by the addition of the
weight of one foot, and the next foot will be denser in the same proportion,
since the density is always proportionate to the pressure; the pressure thus in-
creased will therefore still be equal to twenty eight thousand times the weight
of the next foot. The same reasoning may be continued without limit, and it
may be shown, that while we suppose the height to vary by any uniform steps,
as by distances of a foot or a mile, the pressures and densities will increase in
continual proportion; thus, at the height of about 3000 fathoms, the density
will be about half as great as at the earth's surface; at the height of 6000, one
fourth ; at 9000, one eighth as great. Hence it is inferred that the height in
fathoms may be readily found from the logarithm of the number expressing the
density of the air: for the logarithm of the number 2, multiplied by 10000,
is 3010, the logarithm of 4, 6030, and that of 8, 9031; the logarithms of
numbers always increasing in continual proportion, when the numbers are
taken larger and larger by equal steps. (Plate XIX. Fig. 253.)

ON PNEUMATJC EQUILIBRIUM, 5173

Hence we obtain an easy method of determining the heights of mountains
with tolerable accuracy: for if a bottle of air were closely stopped on the
summit of a mountain, and, being brought in this state into the plain below,
its mouth were inserted into a vessel of water or of mercury, a certain portion
of the liquid would enter the bottle; this being weighed, rf it were found to
be one half of the quantity that the whole bottle would contain, it might be
concluded that the air on the mountain possessed only half of the natural
density, and that its height was 3000 fathoms. It appears also, from this
statement, that the height of a column of equal density with any part of the
atmosphere, equivalent to the pressure to which that part is subjected, is
every where equal to about 28000 feet.

Many corrections are, however, necessary for ascertaining the heights of
mountains with all the precision that the nature of this kind of measure-
ment admits; and they involve several determinations, which require a pre-
vious knowledge of the eifects of heat, and of the nature of the ascent of
vapours, which cannot be examined with propriety at present

We may easily ascertain, on the same principles, the height to which a
balloon will ascend, if we are acquainted with its bulk and with its weight:
thus, supposing its weight 500 pounds, and its bulk such as to enable it to raise
300 pounds more, its specific gravity must be five eighths as great as that of the
air, and it will continue to rise, until it reach the height, at which the air
is of the same density: but the logarithm of eight fifths, multiplied by 10000,
is 2040; and this is the number of fathoms contained in the height, which
will, therefore, be a little more than two miles and a quarter. It may be
found, by pursuing the calculation, that at the distance of the earth's semi-
diameter, or nearly 4000 miles, above its surface, the air, if it existed, would
become sff- rare, that a cubic inch would occupy a space equal to the sphere
of Satura's orbit: and on the other hand, if there were a mine about 42 miles
deep, the air would become as dense as quicksilver at the bottom of it.

It appears, therefore, that all bodies existing on or near the earth's surface
may be considered as subjected to the pressure of a column of air, 28000 feet
high, supposing its density every where equal to that which it possesses at the

VOL. I. N n

*274 lECTURE xxir.

earth's surface, and which is usually such, that 100 wine gallons weigh a pound
avoirdupois, creating a pressure equal to that of 30 inches of mercury, or 34 feet
.of water, and which amounts to 14|: pounds for each square inch. This pressure
acts in all directions on every substance which is exposed to it: but being
.counterbalanced by the natural elasticity of these substances, it produces in
common no apparent effects; when, however, by means of the air pump, or
otherwise, tlie pressure of the air is removed from one side of a body, while it
continues to act on the other, its operation becomes extremely evident. Thus,
when two hollow hemispheres, in contact with each other, are exhausted of air,
•they are made to cohere with great force; they are named Magdeburg hemis-
pheres, because Otto von Guerike,of Magdeburg, constructed two such hemis-
pheres, of sufficient magnitude to withstand the draught of the emperor's six
coach horses, pulling with all their force to separate them. By a similar pres-
sure,athin square bottle may be crushed when it is sufficiently exhausted, and
a bladder may be torn with a loud noise : and the hand being placed on the
mouth of a vessel which is connected with the air pump, it is fixed to it very
forcibly, when the exhaustion is performed, by the pressure of the air on the
back of the hand; the fluids also, which circulate in the bloodvessels of the
hand, are forced towards its lower surface, and the effect which is called suction
is produced in a very striking manner. It is on the same principle that cupping

. glasses are employed, a partial exhaustion being procured by means of the
flame of tow, which heats the air, and expels a great part of it: so that the
remainder, when it cools, is considerably rarefied.

It was Galileo that first explained the nature of suction from the effects
of the pressure of the atmosphere; and his pupil Torricelli confirmed his
doctrines by employing a column of mercury, of sufficient height to overcome
£he whole pressure of the atmosphere, and to produce a vacuum in the upper
part of the tube or vessel containing it. In the operation of sueking up a
fluid through a pipe, with the mouth or otherwise, the pressure of the air is
but partially removed from the upper surface of the fluid, and it becomes ca-
pable of ascending to a height which is determined by the difference of the
densities of the air within and without the cavity concerned: thus, an ex-
haustion of one fourth of the air of the cavity would enable us to raise water
to the height of 84- feet, and mercury to 7i inches, above the level of the re-

ON PNEUMATIC EQUILIBRIUM. 275

servoir from which it rises. \Ye can draw up a much higher column of mercury
by sucking with the muscles of the mouth only, than by inspiring with the
chest, and the difference is much more marked than the fiiiference in the
forces with which we can blow : for in sucking, the cavity of the mouth is
very much contracted by the pressure of the external air, and the same force,
exerted on a smaller surface, is capable of counteracting a much greater hy-
drostatic or pneumatic pressure.

When a tube of glass, about three feet long, closed at one end and open at
the other, is filled with mercury, and then immersed in a bason of the same
fluid, the pressure of the atmosphere is wholly removed from the upper sur-
face of the mercury in the tube, while it continues to act on the mercury in
the bason, and by its means on the lower surface of the column in tlie tube.
If such a tube be placed under the receiver of an air punip, the mercury will
subside in the tube, accordingly as the pressure of the atmosphere is diminished;
and if the exhaustion be rendered very perfect, it will descend very nearly to
the level of the open bason or reservoir. When the air is readmitted, the
mercury usually rises, on tl>e level of the sea, to the height of about 30 inches;
but the air being lighter at some times than at others, the height varies between
the limits of Ti and 3 1 inches. This well known instrument, from its use in mea-
suring the weight of the air, is called a barometer. In the same manner a co-
lumn of water from 30 to 35 feet in height may be sustained in the pipe of a
pump; but if the pipe Avere longer than this, a vacuum would be produced in
the upper part of it, aiul the pump would be incapable of acting.

In order to observe the height of the mercury in the barometer with greater
convenience and accuracy, the scale has sometimes been amplified by various
methods; either by bending the upper part of the tube into an oblique posi-
tion, as in the diagonal barometer, or by making the lower part horizontal,
and of much smaller diameter than the upper, or by making the whole tube
straight, and narrow, and slightly conical, or by placing a float on the sur-
face of the mercury in the reservoir, and causing an axis, which carries an
index, to revolve by its motion. But a good simple barometer, about one
third of an inch in diameter, furnished with a vernier, is perhaps fulty as
accurate as any of these more complicated instruments. In order to exclude
the air the more completely from the tube, the mercury must at least be

276 LECTURE XXII.

shaken in it for a considerable time, the tube being held in an inverted posi-
tion; and where great accuracy is required, the mercury must be boiled in
the tube. The reservoir most commonly employed is a flat wooden boxy
with a bottom of leather ; the cover, which is unscrewed at pleasure, being
cemented to the tube. Sometimes a screw is made to act on the leather,, by
means of which the surface of the mercury is always brought to a certain level,
indicated by a float, whatever portion of it may be contained in the tube;
but the necessity of this adjustuicnt may be easily avoided, by allowing the
mercury to play freely between two horizontal surfaces of wood, of moderate
extent,aii I at the distance of one seventh of an inch: the height may then be
always measured from the upper surface, without sensible error. But if the
surfaces were closer than this, the mercury would stand too high in the tube.
(Plate XIX. Fig. 254.)

The same method which is employed for determining the relation between
the heights and densities of elastic fluids, may be extended to all bodies
which are in any degree compressible, and of which the elasticity is subjected
to laws similar to those which are discoverable in the air and in other gases:
and it is not improbable that these laws are generally applicable to all bodies
in nature, as far as their texture will allow them to submit to the operation
of pressure, wi^'hout wholly losing their form. Water, for example, has
been observed by Canton to be compressed one twenty two thousandth of
its bulk by a force equal to that of the pressure of the atmosphere ; consequently
this force may be represented by that of a column of water 750 thousand feet
in height; the density of the water at the bottom of a lake, or of the sea, will
be increased by the pressure of the superincumbent fluid ; and sui)posing the
law of compression to resemble that of the air, it may be inferred that at the
depth of 100 miles, its detisity would be doubled; and that at 200 it would
be quadrupled. The same measures would also be applicable to the elasticity
of mercury. But there is reason to suppose that they are in both cases a
little too small.

err

LECTURE XXIII.

ON THE THEORY OF HYDRAULICS.

Having considered the principal cases of the equilibrium of fluids, both
liquid and aeriform, we proceed to examine the theory of their motions.
Notwithstanding the dithculties attending the mathematical theory of hy-
draulics, so much has already been done, by the assistance of practical inves-
tigations, that we may in general, by comparing the results of former experi-
ments with our calculations, predict the effect of any proposed arrangement,
without an error of more than one fifth, or perhaps one tenth of the whole:
and this is a degree of accuracy fully sufficient for practice, and which indeed
could scarcely have been expected from the state of the science at the begin-
ning of thfl last century. Many of these improvements have been derived from
an examination of the nature and magnitude of the friction of fluids, which,
although at first sight it might be supposed to be very inconsiderable, is
found to be of so much importance in the application of the theory of hy-
draulics to practical cases, and to affect the modes of calculation so materially,
that it will require to be discussed, hereafter, in a separate lecture.

There is a general principle of mechanical action, which was first distinctly
stated by Huygens, and which has been made by Daniel Bernoulli the basis of
his most elegant calculations in hydrodynamics. Supposing that no force is
lost In the communication of motion between different bodies, considered as
belonging to any system, they always acquire such velocities in descending
through any space, that the centre of gravity of the system is capable of as-
cending to a height equal to that from which it descended, notwithstanding
any mutual actions between the bodies. The truth of this principle may
easily be inferred from the laws of collision, compared with the properties of
accelerating and retarding forces. Thus, if an elastic ball, weighing 10
ounces, and descending froitt a height of 1 foot,be caused to act in any maanc*-

273 LECTURE XXIII.

on a similar ball of one ounce, so as to lose the whole of its motion, the smaller
ball will acquire a velocity capable of carrying it to the height of 10 feet. It is
true that some other suppositions must be made, in applying this law to the de-
termination of the motions of fluids, and that in many cases it becomes necessary
to suppose that a certain portion of ascending force or energy is lost, in conse-
quence of the internal motions of the particles of the fluid. But still, with pro-
per restrictions and corrections, the principle affords us a ready method of
obtaining solutions of problems, which, without some such assistance, it would
be almost impossible to investigate. The principal hypothesis which is assum-
ed by Bernoulli, without either demonstration, or even the appearance of
perfect accuracy, is this, that all the particles of a fluid in motion, contained in
anyone transverse section of the vessels or pipes through which it runs, must
always move with equal velocities ; thus, if water be descending through a
vessel of any form, either regular or irregular, he supposes the particles
at the same height to move with the same velocity ; so that the velocity of
every particle in every part of a cylindrical vessel 10 inches in diameter,,
through which a fluid is moving, must be one hundredth part as great as in.
passing through a circular orifice, an inch in diameter, made in its bottom.
It is evident that this cannot possibly be true of the portions of the fluid near-
est the bottom of the vessel, since the particles most distant from the orifice
must be nearly at rest, while those which are immediately over the orifice
ai-e in rapid motion; but still the calculations founded on the hj'pothesis
agree tolerably well with experiments. In this case the actual descent, in any
instant,may be estimated by the removal of the quantity discharged, from the
surface of the fluid to the orifice, since the intermediate space remains always
• occupied. The ascending force thus obtained is to be distributed throughout
the fluid, according to the respective velocities of its different portions; and it
may easily be shown, that when the orifice is small, the part which belongs to
the fluid in the vessel is wholly inconsiderable in comparison with the ascend-
ing force required for the escape af the small portion which is flowing through-
the orifice, and the whole ascending force may, therefore, be supposed t&
be employed in the motion of this portion; so that it will acquire the velocity
of a body falling from the whole height of the surface of the reservoir, or the
velocity due to that height. It appears also that very nearly the same velocity
is acquired by almost the first particles that escape from the orifice, so that
no sensible time elapses before the jet flows with its utmost velocity.

OK THE THEORY OF HYDRAULICS. 279

' - Tlus velocity may be found, as we have already seen, by multiplying the square
root of the height of the reservoir, expressed in feet, by 8, or more correctly, by
8^; thus, if the height be 4 feet, the velocity will be sixteen feet in a second ;
if the height be 9 feet, the velocity will be 24, the squares of 2 and 3 being
4 and 9; and if the height were 14 feet, the velocity would be 30 feet in a
second, and a circular orifice an inch in diameter would discharge exactlv an
ale gallon in a second. In the same manner, the pressure of the atmosphere
being equal to that which would be producetl by a column of air of uniform
density 28000 feet high, tlie air would rush into a vacuum with a velocity
of more than 1300 feet in a second.

The velocity is also equal, whatever may be the direction of the stream ;
for since the pressure of fluids acts equally in all directions, at equal depths,
the cause being the same, the effect must also be the same. And if the mo-
tion be occasioned by a pressure derived from a force of any other kind, the
effect may be found by calculating the height of a column of the fluid, which
would be capable of producing an equal pressure. When also the force
arises from the difference of two pressures, the velocity may be determined
in a similar manner. Thus, the pressure of a column of water, 1 foot in heio-ht,
would force the air through a small orifice, with a velocity of 230 feet in a
second, corresponding to the height of 830 feet ; a column of mercury 1 inch
high, would produce the same effect as a reservoir of water more than
thirteen times as high, and the force of the air confined in a closed bottle
under the receiver of the air pump, will cause a jet to rise to the same height
as a column of mercury which measures the difference of the elasticities of the
air in the bottle and in the receiver.

But these calculations are only confirmed by experiment in cases when
the ajutage through which the fluid runs is particularly constructed ; that
is, when it is formed by a short tube, of which the sides are so curved that
the particles of the fluid may glide along them for some distance, and escape in
a direction parallel to the axis of the stream, A short cylindrical pipe is found
to answer this purpose in some measure; but the end may be more completely
obtained by a tube nearly conical, but with its sides a little convex inwards,
so as to imitate the shape which a stream or vein of water spontaneously as-
sumes when it runs through an orifice in a thin plate : for in such cases the

)

280 LECTURE XXIII.

Stream contracts itself, after it has passed the orifice, for the distance of about
half its diameter, so that at this point its thickness is only four fifths as
great as at its passage j and the quantity discharged is only five eighths as
great as that which the whole orifice would furnish, according to the preced-
ing calculation: instead, therefore, of multiplying the square root of the height
by 8, we may employ the multiplier 5 for determining the actual discharge.
But the velocity, where the stream is most contracted, is only one thirtieth
less than that which is due to the whole height; and when the jet is dis-
charged in a direction nearly perpendicular, it rises almost as high as the sur-
face of the fluid in the reservoir.

This contraction of the stream, and the consequent diminution of the
discharge, is unquestionably owing to the interference of the particles of the
fluid coming from the parts on each side of the orifice, with those which are
moving directly towards it; and the eifect is more perceptible when the orifice
is made by a pipe projecting within the reservoir, so that some of the particles
approaching it must acquire in their path a motion contrary to that of the
stream. It ■would be possible to obtain an approximate calculation of the
magnitude of this contraction, from the equilibrium which must subsist be-
tween the centrifugal forces of the particles, as they pass out of the orifice,
describing various curves, according to their various situations, and the pres-
sure required for the contraction of the internal parts of the stream, which
obliges the particles to move more rapidly as they proceed, and which must
be proportional to the height required for producing this acceleration.
(Plate XX. Fig. 255.)

When a short cylindrical tube is added to the orifice, it is probable that the
motion of the fluid within the tube is still in some measure similar : but the
vessel must now be supposed to be prolonged, and to have a new orifice at the
end of the tube, at which the particles cannot arrive by any lateral motions,
and which will, therefore, not be liable to a second contraction: the discharge
may, therefore, be estimated nearly according to the true measure of this
orifice; the original pressure of the fluid continuing to act until the stream
escapes.

- The effect of a short pipe, in increasing the discharge, ceases when the

ON THE THEORY OF HYDRAULICS, 281

water separates from its sides, so that it is no longer filled by the stream:
since there is then nothing to distinguish its motion from that of a stream
passing through a simple orifice: but the increase is not owing merely to the
cohesion of the water to the sides of the pipe; for the effect, as I have found
by experiment, is nearly the same in tlie motion of air as in- that of water.
The contraction caused by the motion of the water at the entrance of the
short pipe, may be considered simply as a contraction in the pipe itself, and
the subsequent part of the pipe either as cylindrical or as nearly conical: for
in this case it follows, from the general law on which Bernoulli's calculations
are founded, that as long as the fluid remains in one mass, the discharge will
be nearly the same, as if the mouth of the pipe were the only orifice, suppos-
ing that no force is lost: and the exceptions which Bernoulli has made to the
general application of the principle in such cases, although partly supported by
experiments, have been extended somewhat further, both by himself and
by other authors, than those experiments have warranted. In the case of a
diverging conical pipe, or of a pipe with a conical termination, the discharge
is found to be considerably greater than that which a cylindrical pipe would
produce, but not quite so great as would be produced on the supposition that'
no force is lost. (Plate XX. Fig. 256.)

This analogy between the effects of a cylindrical and conical pipe is
strongly supported by the experiments of Venturi, compared with those of
Bernoulli. Bernoulli found that when a small tube was inserted into any
part of a conical pipe, in which the water was flowing towards the wider end,
not only none of the water escaped through the tube, but the water of a
vessel, placed at a considerable distance below, was drawn up by it; Venturi'
observed the same, when the tube was inserted into the side of a cylindrical
pipe, near to its origin; and in both cases air was absorbed, as well as water,,
so that cohesion could not be in any manner concerned. But the pressure of
the atmosphere is generally necessary for all eff'ects of this kind, and both'
Venturi and Dr. Matthew Young have observed, that a short pipe has no
effect, ill increasing the discharge through an orifice, in the vacuum of an air
pump: but even if the difference were sometimes found to exist in the ah--
sence of atmospherical pressure, it might be produced by an accidental co-
hesion, like that which sometimes causes a column of mercury to remain sus<--
pended in similar circumstances. (Plate XX. Fig. 25?.)
VOi. J. oo

i-r^

gSa l,KGTUBK XXIII.

Tlie effect of ajutages of different kinds, on the quantity of water dis-
charged through an orifice of a given magnitude may be most conveniently
exhibited by placing them side by side at the same height in a reservoir, and
suffering the water to begin to flow at the samt moment through any two of
them ; the quantities discharged in a given time will then obviously indicate
the respective velocities. If a very long pipe vreve employed, some time would
be required before the velocity became uniform ;but in such cases the retardation,
arising from friction is so considerable, as to cause a still greater deviatioa tiom
the quantity which would be discharged by a shorter pipe in the same time.

When the aperture, through which a tluid is discharged, instead of being
every way of inconsiderable magnitude, is continued throughout the height
of the vessel, and is every where of equal breadth, the velocity must be
materially different at different parts of its height; but we may fir^d the
quantity of the discharge, by supposing the whole velocity equal to two
thirds of the velocity at the lowest point. And we ma) find the quantity
discharged by an orifice not continued to the surface, but still of consider-
able height, by subtracting from the whole discharge of an orifice so con-
tinued, that which would have been produced by such a portion of it, as must
be shut up, in order to form the orifice actually existing. But in this case,
the result will seldom differ materially, from that which is found by consi-
dering the pressure, on the whole orifice, as derived from the height of the
fluid above its centre.

When a cylindrical vessel empties itself by a minute orifice, the velocity of
the surface, which is always in the same proportion to the velocity of the fluid
in the orifice, is, therefore, uniformly retarded, and follows, in its descent the
same la\v as a. heavy body, projected upwards, in its ascent; consequently
the space actually described, in the whole time of descent, is equal to half of
that which would have been described, if the initial motion had been uni-
formly continued; and in the time that such a vessel occupies, in emptying
itgelf, twice the quantity of the fluid would be discharged if it were kept
full by a new supply. This may be easily shown, by filling two cylindrical
vessels, having equal orifices in their bottoms, and while the one is left to
empty itself, pouring into the other the contents of two other equal vessels,
in succession, so as to keep it constantly full; for it: will be seen that both
operations will terminate at the same instant.

ON THE THEORY OF HYDRAULICS. tlS

A similar law may be applied to the filling of a lock, from a reservoir of
constant height; for in all such cases, twice as long a time is required for
the effect, as would be necessary if the initial velocity were continued. The im-
mersion of the orifice in a large reservoir has been found to make no differ,
ence in the magnitude of the discharge, so that the pressure may always be
estimated by the difference of the levels of the two surfaces. Thus, when
a number of reservoirs communicate with each other by orifices of any dimen-
sions, the velocity of the fluid flowing through each orifice being inversely
as the magnitude of the orifice, and being produced by the difference of the-
heights of the fluid in the contiguous reservoirs, this difference must be every
where as the square of the corresponding velocity. But if the reservoirs
were small, and the orifices opposite and near to each other, a much smaller
difference in the heights of the surfaces would be sufficient for producing the
required velocity. The same circumstances must be considered, in deter-
mining the velocity of a fluid, forced through a vessel divided by several par-
titions, with an orifice in each; if the orifices are small in proportion to their
distance from each other, and if they are turned in different directions, each
orifice will require an additional pressure, equivalent to the whole velocity
produced in it: but if the partitions occupy a small part only of the vessel,
and are placed near to each other, the retardation will be much less con-
siderable. Cases of this kind occur very frequently in the passage of water
through the pipes and valves of pumps, and it is, therefore, of consequence
to avoid all unnecessary expansions, as well as contractions, in pipes and in
canals, since there is always a useless expense of force in restoring the velocity
which is lost in the wider parts.

When a siphon, or bent tube, is filled with a fluid, and its extremities are
immersed in fluids of the same kind, contained in different vessels,if both their
surfaces are on the same level, the whole remains at rest; but if otherwise,
the longer column in the siphon preponderates, and the pressure of the at-
mosphere forces up the fluid from the higher vessel, until the equilibrium is
restored ; provided, however, that this pressure be sufficiently powerful : for
if the height of the tube were more than 34 feet for water, or than 30 inches
for mercury, the pressure of the atmosphere would be incapable of forcing
up the fluid to its highest part, and this part remaining empty, the fluid coiilck
no longer continue to run. (JPlate XX. Eig. 258.),

<2f84 LECTURE XXIII.

If the lower vessel be allowed to empty itself, the siphon will continue
running as long as it is supplied from the upper, with a velocity nearly cor-
responding to the height of that portion of the fluid in the longer leg, which
is not counterbalanced by the fluid in the shorter; that is, to the height of the
surface of the upper vessel above that of the lower one, or above the end of the si-
phon, when it is no longer immersed; for the height of the pipe is in all cases to
be considered as constituting a part of that height which produces the pressure.
Thus the discharge of a pipe, descending from the side or bottom of a vessel,
is nearly the same as from a similar horizontal pipe, inserted into a reservoir
of the whole height of the descending pipe and of the fluid above it; and
this is true even when the depth of the vessel is inconsiderable, in comparison
with the length of the pipe, if its capacity is sufficient to keep the pipe
running full. It appears at first sight extremely paradoxical, that the whole
water discharged, each particle of which is subjected to the action of gravi-
tation in a pipe 16 feet long, for half a second only, should acquire the velo-
city of 32 feet in a second, which woukl require, in common circumstance.%
the action of the same force of gravitation for a whole second, and this fact
may be considered as favourable to the opinion of those, who wish to esti-
mate the magnitude of a force, rather by the space through which it is con-
tinued, than by the time during which it acts; but if we attend to the nature
of hydrostatical pressure, we shall find that the effect of the column on the
atmosphere is such, as to produce, or to develope, a portion of accelerating force
M'hich is actually greater than the weight of the particles immediately con-
cerned. If a doubt could be entertained of the truth of this theory, it might
be easily removed by recurring to the general law of ascending force, since
it follows from that law, that each particle, which descends in any manner
through the space of 16 feet, niust acquire, either for itself or for some other
particles, a power of ascending to the same height; and on the other hand,
the event of the experiment confirms the general law. For if we fix a shallow
funnel on a vertical pipe, and pour water into it, so as to keep it constantly
full, while the pipe discharges itself into a reservoir, out of which the water runs
through a second pipe, placed horizontally, of exactly the same dimensions
with the first, the height, at which the water in the reservoir becomes sta-
tionary, will be very nearly equal to the height of the funnel above its sur-
face, so that the same height produces the same velocity in both cases.
^Plate XX. Fig. 259-)

ON THE THEOUY OF HVDUAULICS. 285

We may understand the action of the forces immediately concerned in this
experiment, by attending to the mutual effects of the water and of the at-
mosphere. The water entering the orifice must immediately acquire a velo-
city etjual to that of the whole water in the pipe, otherwise there would be
a vacuum in the upper part of the \npc, which the pressure of the atmo-
sphere will not permit ; and this pressure, considered as a hydrostatic force,
is equal to that which would be derived in any other way from a column of
the same height with the pipe, since the weight of the water in the pipe is
wholly employed in diminishing the counterprcssure of the atmosphere below,
not only in. the beginning, when it is at rest, but also while it is in motion ;
for that motion being uniform throughout its descent, the power of gravi-
tation is expended in producing pressure only; so that the pressure of the
atmosphere on the water in the funnel becomes completely analogous to the
pressure of a reservoir of water, of the same height with the pipe. The cir-
cumstance, which causes the appearance of paradox in this experiment, exists
also in the simplest case of the discharge of water; for it may be shown, that
the portion of accelerating force actually employed in generating the velocity
with which a stream is discharged through a small orifice, is twice as great
as the pressure of the fluid on a part of the vessel equal in extent to the ori-
fice; and in the same manner the quantity of force exerted by the atmosphere
on the water in the funnel, as well as that with which the descending fluid
impels the air below, is equal to twice the weight of the quantity existing
at any time in the pipe.

There is, however, a limit, which the mean velocity in such a pipe can
never exceed, and which is derived from the magnitude of the pressure of the
atmosphere. For the water cannot enter the pipe with a greater velocity
than that with which it would enter an exhausted pipe, and which is produced
by the whole pressure of the atmosphere ; and this pressure being equivalent to
that of a column of water 34 feet high, the velocity derived from it is about
47 feet in a second: so that if the vertical pipe were more than 34 feet long,
there would be a vacuum in a part of it near the funnel.

Wherever a pipe of considerable length descends from a funnel, if tlie sup-
ply of the fluid be scanty, and especially if it approach the orifice obliquely,
the pressure of the atmosphere, and the centrifugal force of the particles

S8(5 tzcTvnx xxiii.

which must necessarily revolve round tile orifice, will unite in producing a
vacuity in the centre; and when this happens, the discharge is considerably di-
minished.

In order that a siphon may run, it is obvious that it must first be filled;
and when it is once filled, it will continue to run till the reservoir is ex-
hausted, as far as the level of its upper orifice. And from this circumstance,
the phenomena of some intermitting springs have been explained, which
only begin to run, when the resei-voirs from which they originate have been
filled by continued rains, and then go on to exhaust them, even though the
weather may be dry. From a combination of several such siphons and re-
servoirs, a great number of alternations may sometimes be produced. (Plate
XX. Fig. 260.)

Since the velocity of a stream or jet issuing in any direction, out of a simple
orifice, or a converging one, is nearly equal to that of a heavy body falling
from the height of the reservoir, it will rise, if directed upwards, very nearly
to the same height, excepting a slight difference occasioned by the resistance of
the air, and by the force which is lost, in producing the velocity with which the
particles must escape laterally, before they begin to descend. The truth of
this conclusion is easily confinned by experiment. (Plate XX. Fig. 261.)

If a jet issue in an oblique or in a horizontal direction, its form will be
parabolic, since every particle tends, as a separate projectile, to describe the
same parabola in its range: and it may be demonstrated, that if it be emitted
horizontally from any part of the side of a vessel, standing on a horizontal
plane, and a circle be described, having the whole height of the fluid for its
diameter, the jet will reach the plane, at a distance from the vessel twice as
great as the distance of that point of the circle, through which it would have
passed, if it had continued to move horizontally. And if the jet rise in any
angle from the bottom of the vessel, the utmost height of its ascent will be
equal to that of the point in which it would meet the same semicircle, if it
continued to move in a right line, and the horizontal range will be equal to four
times the distance, intercepted between the same point and the side of the vessel.
This law is equally true with regard to pimple projectiles : but the experiment
is most conveniently exhibited in the motion of a jet. (Plate XX. Fig. 262.)

ON THE THEORY OF HYDRAULICS. 2^7

We have hitherto considered the motions of fluids as continued pvirtcipally
in the same direction ; but they are frequently subjected to alternations of
motion, which bear a considerable analogy to the vibrations of pendulums;
thus, if a long tube be immersed in a fluid, in a vertical direction, and the
surface of the fluid within the tube be elevated a very little, by some external'
cause, the whole contents of the fluid will be urged downwards by a force,
which decreases in proportion to the elevation of the surface above the
general level of the vessel, and when both surfaces have acquired the same
level, the motion will be continued by the inertia of the particles of the fluidi
until it be destroyed by the difl^erence of pressures, which now tends to retard'
it; and this alternation will continue, until the motion be destroyed by fi-ic-
tion and by otlier resistances. It is also obvious, that since any two vibra-
tions, in which the forces are proportional to the spaces to be described, arc
performed in equal times, these alternations will require exactly the sam^'
time for their completion, as the vibrations of a pendulum, of which the length-
is equal to that of the whole tube; for the relative force in the tube is to
the whole force of gravity as the elevation or depression is to the whole
length of the tube. Hence it follows, that if two such tubes were united'
below, so as to form a single bent tube, the vibrations might take place in
the whole' compound tube, in the same manner, and in the same time, as in
each of the separate tubes; nor would the effects be materially altered if
any part of the middle of the tube were in a horizontal or in an obHque di-
rection, provided that the whole length remained unaltered. In such a tube
also, all vibrations, even if of considerable extent, would be performed in the
same time, and would long remain nearly of the same magnitude; but in ai
single tube, open below, the vibrations would continually become less ex-"
tensive, and their duration would also be altered as well as their extent;
besides the unavoidable resistances, which would in both cases interfere with'
the regularity of the effects.

But it does not appear that the laws of the vibrations of fluids in pipes will
at all serve to elucidate the phenomena of waves. Sir Isaac Newton has sup-
posed that each wave may be compared with the fluid oscillating in a bent
pipe; but the analogy is by far too distant to allow us to found any demon-
stration on it. The motions of waves have been investigated in a new and
improved manner by Mr. Lagrange; and Ihave given a concise demonstra^

288 LECTURE XXIII.

tion of a theorem similar to his, but perhaps still more general and explicit. It
appears from these determinations, that sui)posing the fluids concerned to be
infinitely elastic, that is, absolutely incompressible, and free from friction
of all kinds, any small impulse, communicated to a fluid, would be transmitted
every way along its surface, with a velocity equal to that which a heavy body
would acquire in falling th.ough half the depth of the fluid; and I have
reason to believe, from observation and experiment, that where the elevation
or depression, of the surface is considerably extensive in proportion to the
depth, the velocity approaches nearly to that which is thus determined,
being frequently deficient one eighth or one tenth only of the whole; iu
other cases, where a number of small waves follow each other at intervals-
considerably less than the deptli, I have endeavoured to calculate the retar-
dation which must be occasioned by the imperfect elasticity or compressibility
of the fluid; but it seems probable that the motion of small waves is still,
much slower than this calculation appears to indicate.

Whatever corrections these detenninations of the velocity of waves may be
found to require, the laws of their propagation may still be safely inferred
from the investigation. Thus, it may be shown, supposing the waves to flow
in a narrow canal of equable depth, that, whatever the initial figure of the
waves may be, every part of the surface of the fluid will assume in succession the
same form, except that the original elevationsand depressions,extending their in-
fluence in both directions, will produce efi'ects only half as'great on each side,
and those effects will then be continued until they are destroyed by resist-
ances of various kinds. It may also be inferred, that the surface of a fluid
thus agitated by any series of impressions, will receive the effects of another
scries, in the same manner as a horizontal surface,and that the undulations, thus
crossing each other, will proceed without any interruption, the motion of each
particle being always the sum or diflterence of the motions belonging to the
separate series.

Supposing two equal and similar series of waves to meet each other in such
a canal, in opposite directions, the point in which their similar parts meet
must be free from all horizontal motion, so that any fixed obstacle in an up-
right position would have the same effect on the motions of the fluid on
either side as the opposition of a similar series; and this effect constitutes the

ON THE THEORY OP HYDRAULICS. . 289

reflection of a series of waves,which is easily observed, wlien they strike against a
steep wall or bank ; and when this reflection is sufficiently reg-ular,it is easy to
show, that the combination of the direct with the reflected motions must
constitute a vibration, of such a nature, that the whole surface is divided into
portions, which appear to vibrate alternately upwards and downwards, without
any progressive motion, while the points which separate the portions remain
always in their natural level. (Plate XX. Fig. §63.)

But those series of waves which are usually observable in any broad sur-
face, and which constitute a number of concentric circles, are usually re-
flected in such a manner as to appear to diverge after reflection from a centre
beyond the surface which reflects them, and to be subject to all those laws,
which are more commonly noticed in the phenomena of reflected light; but
as these laws are of more practical importance in their application to optics,
than to hydraulics, it is unnecessary at present to examine their consequences
in detail. It may, however, be easily understood, that a new series of waves,
proceeding from a centre at the same distance behind the reflecting surface,
as the centre of the original series is before it, would produce precisely the
same eflfect as a fixed obstacle; consequently the law of reflection at equal
angles is a very simple inference from this mode of reasoning. (Plate XX.
Fig. 264.)

When a series of waves proceeds in an equable canal, it is obvious that the
centre of gravity of the whole fluid neither rises nor falls; from this analogy, as
well as from the general application of thelawof ascending force, it is probable
that in all cases of the propagation of waves, the place of the centre of gravity
remains unaltered; so that when a circular wave spreads further and further
from its centre, its height is not diminished in the same ratio as its diameter
is increased, but the square of its height only varies in this proportion ; that
is, a wave which is a yard m diameter, and an inch high, will retain a height
of half an inch, when its diameter is increased to four yards. ♦

Many of the phenomena of waves may be very conveniently exhibited, by
means of a wide and shallow vessel, with a bottom of glass, surrounded by
sides inclined to the horizon, in order to avoid the confusion which would'
arise from the continual reflections produced by perpendicular surfaces, Tha-

VOL. I. J. p

&90 LECTURE XXIII.

waves may be excited by the vibrations of an elastic rod or wire, loaded
■with a weight, by means of which its motions may be made more or less rapid
at pleasure; and the form and progress of the waves may be easily observed,
by placing a light under the vessel, so that their shadows may fall on a white
surface, extended in an inchned position above. In this manner the minutest
inflections of the surface of the water may be made perfectly conspicuous.
(Plate XX. Fig. 265.)

• By means of this apparatus, we may examine the manner in which a wave
diverges, when a portion of it has been intercepted on either side or on both
sides. Thus, if a wave is admitted, by an aperture which is very narrow in pro-
portion to its own breadth, into the surface of a part of the water which is
at rest, it diverges from the aperture as from anew centre; but when the
aperture is considerably wider than the wave, the wave confipes its motion in
great measure to its original direction, with some small divergence, while it
is joined on each side by fainter circular portions, spreading from the angles
only. (Plate XX. Fig. 266.) ' .

When two equal series of circular waves, proceeding from centres near
each other, begin their motions at the same time, they must so cross, each
othei', in some parts of their progress, that the elevations of the one series tend
to fill up the depressions of the other; and this effect may be actually ob-
served, by throwing two stones of equal size into a pond at the same instant;
for we may easily distinguish, in favourable circumstances, the series of points
in which this effect takes place, forming continued curves, in which the water
remains smooth, while it is strongly agitated in the intermediate parts.
These curves are of the kind denominated hyperbolas, each point of the curve
being so situated with respect to its foci, as to be nearer to one than the
other by a-certain constant distance. (Plate XX. Fig. 267.)

The subject of waves is of less immediate importance for any practical ap-
plication than some other parts of hydraulics; but besides that it is intimately
connected with the phenomena of the tides, it affords an elegant employment for
speculative investigation, and furnishes us with a sensible and undeniable evi-
dence of the truth of some facts, which are capable of being applied to the ex-
planation of some of the most interesting phenomena of acustics and optics.

ON THI THEORY OP HYDRAULICS. 2pi

It may be shown, by steps nearly similar to those by which the velocity of
the motions of waves is investigated, that a fluid which is contained in an
clastic pipe, and which receives an impulse at any part of the pipe, will
transmit its effects, with the same velocity, as a Avave would have in a reser-
voir, of that depth which measures the elasticity of the pipe, that is, with
half the velocity which a body would acquire, in falling from the height at
which a portion of the fluid, connected with the contents of the pipe, would
stand in a vertical tube. It is in this manner that the blood is transmitted,
by means of the impulse given to it by the heart through the bloodvessels;
the pulse moves on with great rapidity, the elastic force of the vessels being
considerably assisted by the temporary actions of the muscular coats of the
arteries, which cause a contraction more rapid than the dilatation ; while the
whole mass of the arterial blood continues, at the same time, to advance
with a much smaller velocity ; like the slow stream of a river, on the surface
of which undulations are continually propelled, with motions independent of
it5 own.

!■;>■

293

LECTURE XXIV

ON THE FRICTION OF FLUIDS.

\V^E have hitherto considered the motions of fluids independently of the
resistance which they undergo from the vessels containing them, and from
the surfaces in contact with them, as well as from the interference of the
neighbouring particles Avith each other; there is, however, a variety of cases
of very common occurrence, in which these frictions most materially affect
the results of our calculations; so that before this subject was laboriously
and judiciously investigated by the Chevalier de Buat, it was almost impossi-
ble to apply any part of our theoretical knowledge of hydraulics to practical
purposes.

The effect of friction is particularly exemplified by the motions of rivers,
in which almost the whole force of gravity is employed in overcoming it.
When the inclination and the dimensions of a river continue uniform, the
velocity is also every where equal ; for otherwise the depth would become
unequal: here, therefore, the force of gravitation must be an exact counter-
poise to the resistance which is to be overcome, in order that the water may
flow with its actual velocity; this velocity having been originally derived
from the effect of a greater inclination near the origin of the river. When
the river is thus proceeding, with an equable motion, it is said to be in train;
and it is obvious that no increase of its length will produce any alteration
in its velocity. There is, therefore, a very material difference between the course
of a river, and the descent of a body, with an accelerated motion, along an in-
clined surface. For when a solid body is placed on an inclined plane, the
force of friction is either great enough to overpower its relative weight, and
to retain it at rest, or else the friction is constantly less than the gravita-
tion, and the motion is always accelerated. But the resistance to the mo-
tions of fluids arises princij^lly from different causes; not from the tenacity of

ON THE FRICTION OF FLU"lDS. 293

the fluids, which, where it exists, is a force nearly uniform, like that of
friction, but principally from the irregular motions and mutual collisions of
their particles ; and in this case, according to the laws of mechanics, it must
vary nearly in proportion to the square of the velocity. For when a body
is moving in a line of a certain curvature, the centrifugal force is always as
the square of the velocity; and the particles of water in contact with the sides
and bottom of a river or pipe, must be deflected, in consequence of the
minute irregularities of the surfaces on which they slide, into nearly the same,
curvilinear paths, whatever their velocity may be, so that the resistance, which
is in great measure occasioned by this centrifugal force, must also vary as the
square of the velocity. Thus also the curvature assumed by the outline of a
stream of water issuing from a simple orifice, which constitutes the contrac-
tion already described, is very nearly the same, whatever the velocity may
be: nor does the friction increase with the pressure, as is demonstrated by
an experiment of Professor Robison on the oscillations of a fluid through a
bent tube, terminated by two bulbs, which were performed in the same time,
whether the tube w^as in a horizontal or in a vertical position. Mr. Coulomb
has also proved the same fact by experiments on the vibrations of bodies
.immersed in fluids, and suspended by twisted wires; he finds that precisely
at the surface, the friction is somewhat greater than at any depth below it:
he also considers a certain part of the friction as simply proportional to the
velocity, and a very small portion only, in common fluids, as perfectly inde-
pendent of it.

It is obvious that wherever the friction varies as the square of the velocity,
or even when it increases in any degree with the velocity, there must always
be a limit, which the velocity can never exceed, by means of any constant
force, and this limit must be the velocity at which the resistance would be-
come equal to the force. It is for this reason that a light body, descending-
through the air, soon acquires a velocity nearly uniform ; and if it be caused,
by any external force, to move for a time more rapidly, it will again be speed-
ily retarded, until its velocity be restored very nearly to its original state.
In the same manner the weight of the water in a river, which has once ac-
quired a stationary velocity, is wholly employed in overcoming the friction
produced by the bottom and the banks. - .

394 lECTURE XXIV.

From considering the effect of the magnitude of the surface exposed to the
friction of the water, in comparison with the whole quantity contained in
the river, together with the degree in which the river is inclined to the ho-
rizon, we may determine, by following the methods adopted by Mr. Buat,
the velocity of any river of which we know the dimensions and the inclinar
tion. Supposing the whole quantity of water to be spread on a horizontal
surface, equal in extent to the bottom and sides of the river, the height, at
which it would stand, is called the hydraulic mean depth ; and it may be
shown that the square of the velocity must be jointly proportional to the
hydraulic mean depth, and to the fall in a given length. If we measure
the inclination by the fall in 2800 yards, the square of the velocity in a se-
cond will be nearly equal to the product of this fall multiplied by the hydraulic
mean depth. For example, in the Ganges, and in some other great rivers,
the mean depth being about 30 feet, and the fall 4 inches in a mile, the
fall in £800 yards will be about 6~ inches, which, multiplied by 360 inches,
gives 2340 inches for the square of the mean velocity, and 48^ inches, or
about four feet, for the mean velocity in a second, that is, not quite
three miles an hour, which is the usual velocity of rivers moderately rapid.
If, however, great precision were required in the determination, some fur-
ther corrections would be necessary, on account of the deviation of the resist-
ance from the exact proportion of the squares of the velocities; since the
friction, as we have already seen, does not increase quite so fast as this.

It is obvious that the friction of a fluid, moving on the surface of a solid
alone, would not produce any material retardation of its motion, if the par-
ticles of the fluid themselves were capable of moving on each other, without
the least resistance ; for in this case a small portion of the fluid, in immediate
contact with the solid, might remain at rest, and the remaining mass of the
fluid might slide over this portion without any retardation. It appears, how-
ever, that the water in contact with the bottom of a river moves with a very
considerable velocity, and the v/ater next above this only a little faster, so
that the velocity increases almost uniformly as we ascend towards the surface-
It follows, therefore, that the resistance must be much greater where the
particles of water slide on each other, than where they glide along the sur-
face of a solid. This internal friction operates gradually throughout the

ON THE I'-RICTIOV OF FLUIDS. 295

water; the surface being retarded by the particles immediately below it,
those particles i)y the next inferior stratum, and each stratum being actuated,
besides its OM'n relative weight, by the friction of the water above, tending
to draw it forwards, and by that of the water below, tending still more to
retard it; the retardation being communicated, from below upwards, isi
such a manner as to be every where equivalent to the relative weight of
the water above the part considered. It appears from observation, that when
we have determined the mean velocity in English inches, we may find the
superficial velocity, very nearly, by adding to it its square root, and the ve-
locity at the bottom, by subtracting from it the same number: thus the square
root of 48^- being nearly T, the superficial velocity of the Ganges will be about
55 inches, or 4 feet 7 inches in a second, and the velocity at the bottom 41-}.
There are, however, frequent irregularities in the proportions of the velocities
at different depths, and it has sometimes been observed, perhaps on account
of the resistance of the air, that the velocity is a little less, immediately at
the surface, than a few inches below it.

For similar reasons, the velocity of a river is also generally greater in the
middle than at the sides; and the motion of the particles in the middle must
be retarded, not only by those which are below them, but also by those on each
side, while these, on the contrary, are dragged on by the water in the middle:
the middle parts tend, therefore, to draw the sides towards tliem, which they
cannot do, without lowering the surface of the fluid next to the banks, in
such a degree as to make the difference of level an equivalent to this tendency
to approach the middle. This appears to be the reason, that the surface of a
large river may generally be observed to be slightly convex, or a little ele-
vated in the middle.

The course of a river is sometimes interrupted by a were or a fall, natural
or artificial; in such cases the velocity may be calculated in the same manner
as when a fluid is discharged from a reservoir through an aperture of consi-
derable height; supposing the whole section of the were to be such an aper-
ture, in a vessel so much higher, that the velocity of a fluid issuing from it
at the upper part of the aperture would be precisely equal to the actual velo-
city of the river. The extent of the swell caused by a were, or by any par-
tial elevation thrown acj-oss the bed of a river, may also be found by first

fi^5 LECTURE XXIV.

determining the height at which the surface must stand immediately above
the were, and then calculating the inclination of the surface which will be
required for producing the actual velocity, in the river thus made deeper;
which of course will determine the situation of the surface where the water
approaches the were ; and this surface, which is more nearly horizontal than
the general surface of the river, will be so joined to it as to have a curvature
nearly uniform throughout.

It appears from calculations of the effects of various changes in the dimen-
sions of rivers, as well as from immediate observation, that a considerable
diminution of the breadth of a river at a particular place, will often produce
but a small elevation of its surface. The velocity, however, may sometime*
be considerably increased by such a change, and where the bottom is of a
loose nature, its particles may be carried away by means of the increased ve-
locity, and the bed of the river may be deepened.

Where a river bends in a considerable degree, it is generally remarked that
the velocity of the water is greater near the concave than the convex side of
the flexure, that is, at the greatest distance from the centre of its curva-
ture. This effect is probably occasioned by the centrifugal force, which ac-
cumulates the water on that side; so that the banks are undermined, and the
channel is deepened by its friction. Some authors have been led to expect
that the velocity would be greater nearest to the convex bank, because the
inclination of the surface must be a little greater there; but the efJect of the
accelerating force, in any short distance, is inconsiderable, and it is more than
compensated by the want of depth. It may easily be understood^ that all
angles and flexures must diminish the general velocity pf the river's motion,
and the more as they are more abrupt.

It has sometimes been imagined, that because the pressure of fluids is pro-
pagated equally in all directions, their motions ought also to diverge in a si-
milar manner; but this opinion is by no means well founded, even with
respect to those particles which receive their motions in an unlimited reser-
voir from the impulse of a stream which enters it. An experiment, which sets
this fact in a clear point of view, was made long ago by Hauksbee. He
produced a very rapid current of air, by means[of a vessel, into which three or

ON THE FRICTION OF FLUIDS. 297

four times as much air as it naturally contained had been condensed by means
of a syringe, and causing the current to pass through a small box, in which
the bason of a barometer was placed, the mercury was depressed more than
two inches, in consequence of the rarefaction which the current produced iu
the air of the box. ( Plate XXI. Fig 268.)

Professor Venturi has also made several experiments of a similarnature on the
motion of water : he observes that not only the water in contact with a stream
is drawn along by it, but that the air in the neighbourhood of a jet is also made
to partake of its motion. When the mouth of a pipe, through which a stream of
water is discharged, is introduced into a vessel a little below the surface of the
water which it contains, and is allowed to escape by ascending an inclined sur-
face placed opposite to the pipe, and leading over the side of the vessel, the stream
not only ascends this surface without leaVing any portion of itself behind, but
carries also with it the whole of the water of the vessel, until its surface be-
comes level with the lowest part of the stream. (Plate XXI. Fig. 269.)

The effect of a jet of water, in drawing towards it a current of air, is in some
measure illustrated by an experiment which is often exhibited among the
amusements of hydraulics. A ball of cork, or even an egg, being placed in
the middle of a jet, which throws up a pretty large stream to a moderate
height, the ball, instead of falling,or being thrown off, as it might naturally
have been expected to do, remains either nearly stationary, or playing up and
down, as long as the experiment is continued. Besides the current of air which
Venturi has noticed, and which tends to support the ball in a stable equilibrimn,
theadhesionof the water, combined with its centrifugal force in turning round
the ball, assists in drawing it back, when it has declined a little on either side,
so that the stream has been principally in contact with the other side. A
similar effect may be observed in the motions of the air only, as I have
shown by some experiments of which an account is published in the Philo-
sophical Transactions. Thus, if we bend a long plate of metal into the form
of the letter S, and suspend it in the middle by a thread, so that it may move
freely on its centre, and if we then blow on its convex surface with a tube
directed obliquely towards the extremity, instead of retreating before the
blast, it will on the contrary appear to be attracted ; the pressure of the at-
mosphere being diminished by the centrifugal force of the current, which

VOL. I. Q q

glides along the convex surface, because it finds a readier .passage in the neigh-
bourhood of the solid, towards which it is urged by the: impulse. of the parti-
cles of the air approaching it on one side, and by the defect of pressure on the
other side, occasioned by the removal of a certain portion of the air which it
carries with it. (Plate XXI. Fig. 2/0, ^71.)

From considerations similar to those by whichithe.V'clocity of a river tis de-
termined, we may calculate the quantity of*. water discharged from a pipe of
any given dimensions, and in any position. The same expressions will serve
for estimating the magnitude of the friction in both cases; the pipe being
considered as a small river, of which the mean depth is one fourth of its dia-
meter: but a part only of the force of gravity is now expended in overcoming
the friction, the rest being employed in producing the momentum of the
water. We may obtain a sufficiently accurate determination of the velocity,
by supposing the height of the, reservoir above the orifice of the pipe to be
diminished in the same proportion as the diameter of the pipe would be in-
creased by adding to it one fiftieth part of the length, and finding the whole
velocity corresponding to four fifths of this height. Thus, if the diameter
of the pipe were one inch, and its length 100 inches, we must suppose the
effective height to be reduced to one third by the friction,and the discharge must
be calculated from a height four fifths as great as this,which may be considered
as a reduction derived from the interference of the particles, entering the pipe,
with each other's motions. If the diameter of the pipe had been two inches,
the height must only have been supposed to be reduced to one half by the
friction ; such a pipe would, therefore, discharge about five times as much
water as the former, although of only twice the diameter; and this circum-
stance requires the attention of all those who are concerned in regulating the
distribution of water by pipes for domestic use, or for any other purpose.

In such cases it becomes also frequently necessary to attend to the angle
in which a small pipe is inserted into a larger; whenever a pipe is bent, there
is a loss of force according to the degree of flexure, and to the velocity of the
Avater, which may be calculated, if it be required; hut if a pipe be fixed into
another through which the water is moving very rapidly, in a direction con-
trary to that of the stream, its discharge will not only be much smaller than
if the directions more nearly coincided, but sometimes such a pipe will dis-

ON THE FRICTION OF FLUIDS. 299

charge nothing at all ; on the contrary, like the air in Hauksbee's experiment,
the water which it contains may be dragged after the stream in the larger
pipe.

The bad effect of unnecessary dilatations, as well as contractions, in aque-
ducts and in pipes, may be understood from what has been already said of the
loss of force attendant on every change of velocity; a circumstance of a si-
milar nature sometimes happens in the animal economy. When an artery is
dilated so as to fsjrm an aneurism, it has been observed that the artery is
visually distended above the cavity; and this effect is easily understood from
the actual increase of resistance which the aneurism produces, united perhaps
with the previous debility of the artery... ,'U

Mr. Gerstner, has found by some very accurate observations on the motion
of water in v6ry small pipes, that the resistance is considerably affected by
the temperature at which the experiment is performed; but in the cases of
rivers, and of such pipes as are commonly used in practice, no variations of
temperature, to which they can be liable, will produce any sensible effects.
His experiments indicate a resistance, where the tubes are very small, which
follows a law so different from that which is observed in more common cases,
that it appears to be owing to some other cause : this cause is perhaps the ca-
pillary attraction of the open end of the tube, and it is the more probable
that the resistance depends on some such circumstance, as there is reason to
think that the irregularity may be in great measure removed by placing the
tube wholly under water.

/ -• 1 . t (J

300
LECTURE XXV..

■ ON HYDRAULIC PRESST^rW.

The mutual eflfects of fluids and moveable solids on each other depend
principally on the laws of hydraulic pressure, and of the resistance of fluids,
which have been considered by Bernoulli as constituting a separate depart-
ment of hydrodynamics, under the name of hydraulicostatics, and which are
of the utmost practical importance, since the application of the powers of
wind or water to the working of mills, and to the navigation of ships, are wholly
dependent on them. The impulse of a fluid differs very materially from that
of a solid, for in the motions of solids, the least possible finite momentum
must overpower the strongest possible pressure; but since the particles of
fluids are supposed to be infinitely small, the momentum of a fluid stream
may always be balanced by a certain determinate pressure, without producing
motion in the solid opposed to it; so that this division of the subject of hy-
draulics has nothing analogous to it in simple mechanics. It is true that
when a certain quantity of a fluid is made to concentrate its action almost
instantaneously, its effect is nearly similar to that of a solid; for here the
essential distinction, derived from the successive action of the particles, no
longer exists. Thus, when a stream of fluid filling a pipe acts suddenly on an
obstacle at the end of it, it requires to be resisted by a force far greater than
that which originally caused its motion, unless the action of the force be con-
tinued through a considerable space: and for this reason the strength of the
pipe ought to be so calculated as to be able to resist this action ; its inten-
sity may, however, be easily diminished by means of an air vessel com-
municating with the pipe, which will allow the motion to be changed in a
less abrupt manner. But in the principal cases Avhich we are about to consider,
the action of the fluid on the solid is supposed to be confined to such of its
particles as are nearly in contact with the surface.

ON HYDRAULIC PRESSURE. 301

When a part of the weight of any fluid is expended in producing a motion
in any direction, an equal force is deducted from its pressure on the vessel
in that direction: for the gravitation, employed in generating velocity, cannot
at tlie same time be causing pressure; and when the motion produced is in
any other direction than a vertical one, its obliquity must be immediately de-
rived from the reaction of the vessel, or of some fixed obstacle; for it is ob-
vious that a vertical force, like that of gravity, cannot of itself produce an
oblique or a horizontal motion.

If a small stream descends from the bottom of a vessel, the weight expend-
ed in producing its motion is equal to that of a column of the fluid standing
on a base equal to the contracted orifice, and of twice the height of the
vessel. Thus, if the vessel be 16 feet high, the velocity of the stream will
be 32 feet in a second, and a column 32 feet in length will pass through the
orifice in each second, with the whole velocity derivable from its weight
acting for the same time; so much, therefore, of the pressure of the fluid in
the reservoir must be expended in producing this motion, and must of course
be deducted from the whole force with which the fluid acts on the bottom of
the reservoir; in the same manner as when two unequal weights are connected
by means of a thread passing over a pulley, and one of them begins to des-
cend, the pressure on the pulley is diminished, by a quantity, which is^as much
less than the sum of the weights, as the velocity of their common centre of
gravity is less than the velocity of a body falling freely. If the stream issue
from the vessel in any other direction, the effect of the diminution of the
pressure in that direction will be nearly the same as if the vessel were sub-
jected to an equal pressure of any other kind in a contrary direction; andif
the vessel be moveable, it will receive a progressive or rotatory motion in
that direction. Thus, when a vessel or pipe is fixed on a centre, and a stream
of water is discharged from it by a lateral orifice, the vessel turns round at
first with an accelerated motion, but on* account of the force consumed in
producing the rotatory motion, in successive portions of the water, the velocity
soon becomes nearly stationary. (Plate XXI. Fig. 272.)

From similar reasoning it appears, that the effect of a detached jet on a
plane surface perpendicular to it must be equivalent to the weight of a portion
of the same stream equal in length to twice the height which is capable of pror

302 LECTURE XXV.

ducing the v'elocity. And this result is confirmed by experiments: but it is
necessary, that the diameter of the plane be at least four times as great as
that of the jet, in order that the full effect may be produced. When also a
stream acts on an obstacle in a channel sufficiently closed, on all sides, to pre-
vent the escape of any considerable portion of water, its effect is nearly the
same as that of a jet playing on a large surface. But if the plane, opposed to
the jet, be only equal to it in diameter, or if it be placed in an unlimited
stream, the whole velocity of the fluid column will not be destroyed, it will
only be divided and diverted from its course, its parts continuing to move
on, in oblique directions; in such cases the pressure is usually found to be
simply equivalent to the weight of a column equal in height to the reservoir, the ^
surface being subjected to a pressure nearly similar to that which acts on a
part of the bottom of a vessel, while a stream is descending through a large
aperture in another part of it. (Plate XXI. Fig. 273.)

It is obvious that, in all these cases, the pressure varies as the square of the
velocity, since the height required to produce any velocity is proportional to
its square. This inference was first made in a more simple manner, from com-
paring the impulse of a fluid on a solid with that of a number of separate
particles, striking the surface of the body, each of which would produce an
tifect proportional to its velocity, while the whole number of particles, acting
in a given time, would also vary in the same ratio. If the solid were in mo-
tion, and the fluid either in motion or at rest, it is obvious that the relative
velocity of the solid and the fluid, with regard to each other, would be the only
cause of their mutual effects, and that the hydraulic pressure or resistance
must be dependent on this velocity alone, except so far as the limited dimen-
sions of the reservoir, containing the fluid, might produce a difference in the
internal motions of its particles in different cases. Thus, where the fluid is so
confined, that the whole of the stream acts on a succession of planes, each
portion into which it is divided may be considered as an inelastic solid, strik-
ing on the surface exposed to it with a certain velocity: and in this case the
force must be considered as simply proportional to the relative velocity, and
not to its square. For want of this consideration, the effects of water wheels
have frequently been very erroneously stated.

When a jet .strikes a plane surface obliquely, its force, in impelling

ON HYDRAULIC PRESSURE. 303

the body forwards, in its own direction, is found to be very nearly pro-
portional to the height to which the jet would rise, if it were similarly in-
clined to the horizon. But when a plane is situated thus obliquely with
respect to a wide stream, the force impelling it in the direction of the stream
is somewhat less diminished by the obliquity, at least if we make allowance
for its intercepting a smaller portion of the stream: thus, if the anterior part
of a solid be terminated by a wedge more or less acute, the resistance, ac-
cording to the simplest theory of the resolution offerees, might be found bv
describing a circle on half the base of the wedge as a diameter, which would
cut off a part from the oblique side of the wedge that would be the mea-
sure of the resistance, tlie whole side representing the resistance to the sanie
solid without the wedge: but the resistance is always somewhat more than
this, and the portion to be added may be found, very nearly, by adding to
the fraction thus found one ten millionth of the cube of the number of de-
grees contained in the external angle of the wedge. (Plate XXI. Fig. 274.)

The pressure of a fluid, striking perpendicularly on a plane surface, has been
found to be very different at different parts of the surface; being greatest at
the centre, and least towards the edges; so that if an aperture be made in
the centre of a circular plane, covering the mouth of a bent lube, the fluid
within it will rise half as high again as if the whole mouth were open. It h
also observable, that two bodies, equal and similar in the form of the part
meeting the fluid, undergo very <lifferent degrees of resistance according to
the forms of their posterior terminations, and that a thin circular plate is
much more retarded than a long cyHnder of the same diameter. These cir-
cumstances are utterly inexplicable upon the vague approximation of sup-
posing the resistance produced by the immediate impidse of separate particles
of the fluid on the solid ; but they are no longer surprising, when we consider
the true mode of action of continuous fluids, since all the motion which is j)ro-
duced by the fluid in the solid or by the solid in the fluid is communicated
much more by means of pressure than by innnediate impulse. The minute
operations of this pressure are too intricate to be accurately developed, but we
may observe in general, that when a body moves along the surface of a resisting
medium at rest, or when an obstacle at rest is opposed to a fluid in equable mo-
tion, the pressure is increased before the moving substance, and diminished be-
hind it; so that the surface is elevated at the one part, and depressed at the other,

304 LECTURE xxr.

and the more as the velocity is greater. Now it is obvious that the pressure
must be greatest where the elevation is greatest, and hence a perforation at the
centre of the surface indicates a greater pressure than at the circumference.
Behind the body, this pressure becomes negative, and has sometimes been
called nonpressure; hence it happens that a tube, opening in the centre of the
posterior surface, exhibits the fluid witliin it depressed below the level of the
general surface of the water. Thus, if we suppose the velocity of a body,
terminated by perpendicular surfaces, to be 8 feet in a second, it will require
the pressure of about a foot, to produce such a velocity, and we may, there-
fore, expect an elevation of about a foot before the body, and an equal de-
pression behind it: consequently an equivalent difference must be found in
the pressure of the water at any equal depths on the anterior and posterior
surfaces of the body. The water elevated before tlie body escapes continually
towards each side, and the deficiency behind is also filled up in some measure
by the particles rushing in and following the body: but there is in both cases,
a certain quantity of water which moves forwards, and constitutes what is
called the dead water: before, where it is usually most observable, it forms
an irregular triangle, of which the sides are convex inwards. If the
posterior part of the body .be formed like a wedge, the water on each side will
be advancing to fill up the vacuity, even while it remains in contact with the
sides, and the negative pressure will be considerably diminished. For this
reason, the bottoms of ships are made to terminate behind in a shape some-
what resembling a wedge ; and the same economy may be observed in the
forms of fishes, calculated by nature for following their prey with t.he great-
est possible rapidity. In general, fishes, as well as ships, are of a more obtuse
form before than behind, but it is not certain that there would be any ma-
terial difference in the resistance in a contrary direction, although some experi-
ments seem to favour such an opinion. Perhaps if the natural form of the dead
water, moving before an obtuse body, were ascertained, it might serve to indi-
cate a solid calculated to move through the water with the least resistance;
for the water must naturally assume such a form for its own motions, and
the friction of fluids on solids being less than that of fluids moving within
themselves, the resistance would be diminished by substituting a solid of the
same form for a fluid. (Plate XXI. Fig. 275.)

Supposing a body to move through a fluid at a considerable depth below

ON HYDRAULIC PRESSURil. S05

its surface, there will still be an elevation before and a depression behind it,
the less in height, and the greater in extent, as the depth at which the body
is situated is greater. Such an elevation appears to be in some measure
analogous to the effect of a low were thrown across a river, which raises its
surface, and produces a swell.

If two or more bodies, differently formed, the resistances to the motions of
which had been ascertained, were caused to move through a fluid in contact
with each other, it is obvious that the paths described by the particles of the
fluid, in gliding by them, must be very materially altered by their junction;
and it seems natural to expect that the joint disturbance produced in the
motions of the fluid, when the surfaces are so united as to form a convex
outline, would be somewhat less than if each surface were considered sepa-
rately. Accordingly it is found that no calculation, deduced from experiments
on the resistance opposed to oblique plane surfaces, will determine with ac-
curacy the resistance to a curved surface. It appears from experiment that
the resistance to the motion of a sphere is usually about two fifths of the re-
sistance to a flat circular substance ©f an equal diameter. The resistance to
the motion of a concave surface is greater than to a plane, and it is easily
understood, that since the direction, in vi^hich the particles of the fluid recede
from the solid, must be materially influenced by the form of the solid exposed
to their action, their motion in this case must be partly retrograde, when-
they glide along towards the edges of the concave surface, and a greater
portion of force must have been employed, than when they escape with a small-
er deviation from their original direction. (Plate XXI. Fig. 276.)

For some reason which is not well understood, the hydraulic pressure of
the air appears to be somewhat greater, in proportion to its density, than that
of water. It has been found that the perpendicular impulse of the air,
on a plane surface, is more than equivalent to the weight of a column of air
of a height corresponding to the velocity, and the excess is said by some to
amount to one third, by others to two thirds of that weight. The resist-
ance appears also to be a little greater for a large surface, than for a number of
smaller ones, which are together of equal extent.

The resistance or impulse of the air, on. each square foot of a surface directly

VOL. T. B r

30& LECTURE XXV.

opposed to it, may in general be found, with tolerable accuracy, in pounds, by
dividing the square of the velocity in a second, expressed in feet, by 500.
Thus, if the velocity were 100 feet in a second, the pressure on each square
foot would be 20 pounds ; if 1000 feet, 2000 pounds. For a sphere of a foot
in diameter, we may divide the square of the velocity by 1600. We may
also find, in a similar manner, the utmost velocity that a given body can
acquire or retain in falling through the air; for the velocity at which the re-
sistance is equal to the weight must be its limit. Thus, if a sphere one foot
in diameter weighed 100 pounds, the square of its utmost velocity would be
160000, and the velocity itself 400 feet in a second; if a stone of such di-
mensions entered the atmosphere with a greater velocity, its motion would
'very soon be reduced to this limit; and a lighter or a smaller body would move
still more slowly. The weight of Mr. Garnerin's parachute, with its whole
load, was about a quarter of a pound for each square foot, the square of its
greatest velocity must, therefore, have been about 1 25, and the velocity 1 1 feet in a
second, which is no greater than that with which a person would descend, in leap-
ing from a height of two feet, without stooping. Mr. Garnerin found the velo-
city even less than this, and it is not improbable that^the concave form of the
parachute might considerably increase the resistance. Thus, Mr. Edgeworth
found that a plate 9 inches long, when bent into an arc of which the chord
was 7-^, had the resistance increased more than one seventh. The diminution
of the resistance of the air by the obliquity of the surface is still less than
that of the resistance of water: thus, the resistance on the oblique surfaces
of a wedge is not quite so much less than the resistance on its base, as its
breadth is less than the length of those surfaces.

When the velocity of a body moving through an elastic fluid is very great,
the resistance is increased in a much greater proportion than the square of
the velocity: thus, the retardation of a cannon ball moving with a velocity of
1000 feet in a second, or a little more, becomes suddenly much greater than
the calculation indicates. The reason of this change appears to be, that the
condensation of the air before the ball is necessarily confined to a smaller por-
tion, which is very intensely compressed, because the effect of the impulse can
only spread through the air with a certain velocity, which is not much greater
than that of the ball; and this smaller portion of air must necessarily be much
more condensed than a larger portion would have been. Thus, when a cannon

ON HYDRAULIC PRESSURE, 307

ball moves slowly, its effect at any instant is in some degree divided through-
out all that part of the atmosphere, which the sound of the report has reached;
and if the ball follows the sound very speedily, it is obvious that the portion
of the air before the ball, which partakes of the effect, must be very small.
The sound is observed to be propagated with a velocity of about 11 30 feet in
a second, and a cannon ball may be discharged with a velocity of aOOO; but
one half of this is very speedily lost, so as to be wholly useless with regard to
the effect of the ball. If, therefore, we wish to increase the range of a
cannon ball, we must increase its weight ; for the resistance increases only
in proportion to the surface of the ball, while the weight is determined by its
solid content.

It is not easy to explain, in a manner perfectly satisfactory, the reflection of
a cannon ball, or of a stone, which strikes the surface of the sea, or of a piece
of water, in an oblique direction. We may, however, assign some causes
which appear to be materially concerned in this effect. In the first place the
surface of the water, acting at first for some time on the lower part of the ball,
produces, by its friction, a degree of rotatory motion, by means of which the ball,
as it proceeds, acts upon the mass of water which is heaped up before it, and
is obliged by a similar friction to roll upwards, so that it mounts again to a
much greater height than it could possibly have attained by the mere hy-
drostatic pressure of the water at a depth so inconsiderable. But a more
powerful cause than this appears to be the continual succession of new sur-
faces which are to be depressed, and which may be supposed to react on the
ball, so as to produce the same effect, as a more intense pressure would have
done, if it had continued stationary; and the mutual action of the water and
the ball may be compared to the impulse of an obliqvie stream, moving with
the velocity of the ball, which would impel it much more powerfully than the
simple hydrostatic pressure at a much greater depth. It happens in this case,
as in many others, that the effects which appear to be the most familiar to us,
do not by any means admit the clearest and simplest explanation.

308

LECTURE XXVI.

ON HYDROSTATIC INSTRUMENTS, AND HYDRAULIC

ARCHITECTURE.

At E have now examined the fundamental laws of the principal departments
of hydrodynamics, which may be considered as constituting the theory of the
science: we are next to proceed to the application of this theory to a variety
of practical purposes. Following the same general order as we have observed
in mechanics, our first division will be analogous to the subject of statics,
and will relate to hydrostatic instruments ; the second to architecture, con-
taining some particulars respecting canals and embankments; the third to
machinery, comprehending the modification and application of the force of
fluids considered as inelastic; the fourth and the fifth to the methods of rais-
ing and removing weights, in which the principal hydraulic and pneumatic
machines will be respectively explained, and,as a part of this subject, the appli-
cation of pneumatic force will also be examined.

The principles of hydrostatics are very frequently applied to the determi-
nation of the specific gravities of the various productions of nature or of art.
The diminution of the apparent weight of a solid body, upon immersion into
a fluid, affbrds an easy method of comparing its density with that of the fluid.
For the weight of the solid being previously determined, if we examine how
much that weight iS diminished by plunging the body in pure water, we shall
have the weight of an equal bulk of water; and thence we may immediately
obtain the proportion of the specific gravity of the body to that of water,
which is the usual standard of comparison. And if we weigh a solid of
given magnitude, for instance, a ball of glass, first in water, and then in any
other fluid, the quantities of weight lost in each case will be in the same pro-
portion as the specific gravities of the two fluids. A balance adapted for such
-examinations is called a hydrostatic balance; on one sidfi it has a scale as

ON HTDROSTATIC INSTRUMENTS, AND HYDRAULIC ARCHITECTURE. 309

usual, and on the other a loop of fine wire, or of horse hair, for holding the
solid to be weighed, which may be changed occasionally for a ball of glass,
suspended in a similar manner: sometimes also a dish is added for holding any
loose substances which will sink in water, proper counterpoises being used as
equivalents for the weight of the dish either in air or in water; and when a
body lighter than water is examined, a weight of known magnitude and
density is employed for sinking it. (Plate XXI. Fig. 277.)

The specific gravities of any substances, and in particular of such as are
lighter than water, may also be very conveniently determined by means of a
common balance, employing a phial with a conical ground stopple, filling it
first with water, and then either with a given fluid, or with a portion of the
solid of which the weight has been ascertained, together with as much water
as is sufficient to exclude all the air.

For the speedy examination of a variety of fluids, differing but little in
specific gravity from some known standard, a hydrometer may be very con-
veniently employed. This instrument is said to have been invented by Ar-
chimedes: it consists of a hollow ball, with a weight below it, and a slender
stem above, so graduated as to express the specific gravity of the fluid by the
decree to which it sinks. Sometimes the instrument is sunk to a certain
mark, by means of weights placed in a dish at the end of the stem; or different
weights are fixed to it below, while the graduations of the scale are still ob-
served ; and it may even be applied to finding the specific gravities of solids,
the solid being first placed in the dish at the end of the stem, and then in a
second dish which is suspended from the bulb below the water. (Plate XXJ,
Fig. 278.)

Another mode of ascertaining the specific gravities of fluids differing bu<.
little from each other in density, is to have a series of globules of glass, so
loaded as to correspond to the specific gravities indicated by as many numbers,
which are marked on them ; and, throwing several of them together into the
fluid, to observe which of them remains nearly stationary, without either
vising to the surface or sinking. This method, though not expeditious, ap-
pears to be very secure from error: the globules are sold by patent, adapted
for the measurement of the strength of spirituous liquors.

kV

310 LECTURE xxvr.

In whatevei' manner we compare the specific gravities of bodies with that
of water, it is necessary, for very accurate experiments, either that the water
be employed at the temperature of the air when moderately warm, or that a
proper correction should be made for its change of bulk at different tempera-
tures. Platina, the densest known substance, is S3 times as heavy as dis-
tilled water, gold 194-, mercury 134-, lead 1]^, silver 11, copper 9, iron and
steel 7-|., stony substances usually about 24-, rectified spirits 1^, naphtha, the
lightest liquid-i^, cork about^-, conjmon air .g4^, steam -^sW, and pure hydrogen
gas , ,,000. From this comparison, the weight of a cubic foot of any of these
substances may be easily determined; since a cubic foot of water weighs
nearly 1000 ounces avoirdupois, or more nearly 998; thus a cubic foot of
gold would weigh about 195 000 ounces, and be worth above 60 000 pounds
sterling; a cubic foot of iron weighs 7750 ounces, and a cubic foot of com-
mon stone about 2500.

The method of measuring the bulk of solid bodies by immersing them in a
fluid was applied, by its inventor Archimedes, to the detection of a fraud in
the composition of a mixed metal: and at present the principal use of hydro-
meters is for ascertaining, by the specific gravity of a compound of alcohol and
water, the proportional quantities of its ingredients. But in all experiments of
this kind, it is necessary to be aware, that a considerable change of the joint
bulk of two substances is often produced by their mixture: and that in ge-
neral their dimensions are considerably contracted. Thus, 1 8 gallons of
water, and 18 of alcohol, instead of 36 gallons, make only 35, consequently
the specific gravity of the compound is one 35th greater than the mean of the
specific gravities of the ingredients. And in some cases the whole dimensions
of a single substance may even be contracted by the addition of another sub-
stance: thus iron, by the addition of one eighth of its bulk of platina, becomes
contracted one fortieth of that bulk.

The use of the spirit level depends on the tendency of all fluids to preserve
a horizontal surface, and the freedom, with which the particles qf fluids move
on each other, renders it an instrument capable of the greatest delicacy. A
tube, which is very slightly curved, being nearly filled with alcohol or ether,
and then perfectly closed, the bubble will always rise to the highest part of
the tube, and will never be stationary at the point which is marked as its

•ON HYDROSTATIC INSTRUMENTS, AND HYDRAULIC ARCHITECTURE. 311

proper place, unless the instrument be very accurately horizontal, or in tlie
same position in which the mark was adjusted. The surface of the bubble,
especially when it is small, cannot, in a strict sense, be called perfectly hori-
zontal, since its form approaches nearly to that of a sphere; but in order that
the centre of gravity of the water may attain the lowest possible situation, the
bubble must necessarily occupy the highest point of the tube. (Plate XXI.
Fig. 279.) , '

The principles of hydrostatics have been employed in various ways for sup-
plying lamps with oil. It is found that a lamp will burn, without consuming
any considerable portion of its wick, as long as it is amply supplied with oil ;
hence it becomes desirable that it should always Ijife level with the surface of the re-
servoir, and this may be effected sufficiently well by placing the wick at the ■
edge of a very large vessel,or atthe end of a tube projecting from such avessel,or
from a vessel closed above, and opening only by an orifice below, which lets in
the air as the oil escapes through it. But all these methods are often attended
with inconveniences of various kinds, especially where the lamp is to be em-
ployed like a candle, and placed on a table. A French artist has applied a
little pump, which is worked by means of a spring, for raising the oil from *
vessel under the lamp; but this refinement is too complicated to be practi-
cally useful. Mr. Keir's lamp contains a divided cavity, one part of which is
filled with oil, and the other with a saline or saccharine fluid of greater density,
so that when the oil contained in the upper part of the tube is exhausted, its
place is partly supplied by a fresh portion, which is forced up in consequence
of the descent of the denser fluid in a much larger vessel. Still, however, the
surface must be lowered by degrees; but by combining the invention with
Dr. Hooke's semicylindrical counterpoise, a little modified, the height of this
fluid may be so regulated, that the surface of the oil may remain almost in-
variable, until the reservoir is quite exhausted. For this purpose, the centre
of gravity of the counterpoise must be a little higher than the line which bi-
sects it; and its specific gravity must be about three fourths as great as that of
the fluid ; and in this manner it may be made to raise the surface of the hea-
vier fluid, in proportion as a greater quantity of it escapes, to supply the place of
the oil; and to keep it always at a sufficient height above the surface which
separates it from the oil, so that the wick may be amply and almost uniformly
supplied. (Plate XXI. Fig.-280.)

312 LECTURE XXVI.

The art of embankment is a branch of architecture entirely dependent on
hydrostatical and hydraulic principles. In Holland, and in some parts of
Germany, this art is indispensable to the existence of large tracts of country;
and even in this island,ithas been of extensive utility,in gaining and securing
ground on the sea coast. The construction of canals, and the management of
rivers and harbours, are also dependent on the same principles ; and these im-
portant subjects have been discussed by various writers, in many copious
treatises, expressly devoted to hydraulic architecture.

When a bank or dike is to be constructed, it must be composed of ma-
terials capable of resisting, by their weight, the effort of the fluid to overturn
them; by their laterval adhesion, the force tending to thrust them aside hori-
zontally; and by their density and tenacity, the penetration of the water into
their substance. If the water be in motion, they must also be able to resist
its friction, without being carried away by it, and they must be arranged in
such a form, as to be least liable to be undermined. For many of these
reasons, the surface of the bank exposed to the water must be inclined to the
horizon: the line expressing the general direction of the pressure of the water
ought to be confined entirely within its substance, so that no force thus
applied may be able to overturn it as a whole; and this condition
will always be fulfilled, when the sides of the bank make an angle with
each other not l^ss than a right angle. The pressure acting on a bank thus
inclined will also tend to condense the materials, and to increase their la-
teral adhesion, and the particles will become less liable to crumble away by
their weight, than if the surface were more nearly vertical. For embankments
opposed to the sea, a bank much inclined has also the additional advantage
of breaking the force of the waves very effectually. An embankment of this
kind is usually furnished with drains, formed by wooden pipes or by brick-
work,, closed by falling doors, or valves, which allow the water to flow out at
low water, but do not permit the tide to enter. To prevent the penetration
of the water, clay is often used, either mixed with gravel, or sunk in a deep
trench cut on each side of the canal or reservoir. (Plate XXI. Fig. 281.)

The greater or less velocity of a river must determine what substances are
capable of withstanding its tendency to disturb them; some are carried away by
a velocity of a few inches in a second, others remain at rest when the velocity

ON HYDROSTATIC INSTRUMENTS, AND HYDRAULIC ARCHITECTURE; 313-

amounts to several feet. But in general, the velocity of a river is sufficient to
produce a gradual transfer of the particles of its bed, which are shifted slowly
downwards, towards the sea, being occasionally deposited iu those parts
where the water has least motion, and serving at last to form the new land,
which is always advancing into the sea, on each side of the mouth of a large
river. It has been recommended, as a good form for a navigable river or
canal, to make the breadth of the horizontal bottom one fifth of that of the
surface, and the depth three tenths. (Plate XXI. Fig. aas.)

If a canal or a reservoir were confined by a perpendicular surface of boards*
and it were required to support it by a single prop, the prop should be placed,
as we have already seen, at the distance of one third of the whole height
from the bottom ; but it would be always more convenient in practice to fix
the side of the reservoir at the bottom, than to allow the whole pressure to be
supported by the prop, and it might also be strengthened by means of ribs,
thicker below than above, so as to produce an equal strength throughout,
wherever the prop might be placed: but if the side were formed of a single
plank, of unifonn thickness, the strain would be most equally divided by
placing the prop very near the middle of its height.

The strength of the materials employed for flood gates and sluices requires-
to be determined according to the principles, which have been laid down, in
treating of the passive strength of substances used for purposes simply me-
chanical ; but the calculations become in this case much more Intricate. Thus,
if we have a circular plate or plank, of a uniform elastic substance, constituting
the bottom of a pipe or cistern, and simply supported at the circumference,
a very complicated calculation is required for determining the proportion of
its strength to that of a square plate of the same breadth, supported only at
two opposite ends, since at each point of the circular piece, there are two cur-
vatures which require to be considered. The square plate will support a
column of fluid twice as heavy as the weight which would break it, if placed at
its centre; and if I have been correct in the calculation, a circular plate will
support a height of water nearly sixteen sevenths as great as a square plate. But
for ordinary purposes, it will be sufficient to consider the strength as derived
only from the resistance opposed to the flexure in one direction, since the addi-
tional strength, obtained from the lateral supports, may very properly be neg-

VOL. I. s s

314 LECTURE XXVI.

Iccted, as only assisting in affording that additional security which is always
necessary, to compensate for any accidental defects of the materials. It has
been asserted that the strength of a square plate is doubled when it is sup-
ported on both sides ; l)iit this appears to be a mistake.

We may, therefore, be contented with determining the strain on the ma-
terials in that direction in which they afford the greatest resistance, either
from the shorter distance between the supports, or by the disposition of the
fibres; and it will be always most eligible to combine these circumstances,
so that the fibres of the wood may be arranged in the direction of the short-
est dimensions of the sluice. If a sluice be supported above and below only,
the greatest strain will be at the distance of about three sevenths of its height
from the bottom ; and it is at this point that the greatest strength is required.
But if the boards forming the sluice be fixed across it, in horizontal direc-
tions, their strength must be greatest at the bottom. (Plate XXI. Fig.
283.)

In the construction of flood gates, the principles of carpentry must be ap-
plied in a manner nearly similar to that which serves for the determination of
the best forms of roofs. The flood gates, if they are double, without a solid
obstacle between them, must meet at an angle : and when this angle is very
open, the thrust against the walls or hinges must necessarily be very great.
If, however, the angle were too acute, the flood gates would require to be
lengthened, and in this case their strength would be far more diminished than
that of a roof similarly elevated, since the hydrostatic pressure acts always
with full force in a perpendicular direction. The thickness required for
each flood gate may be determined in the same manner as the thickness of a
sluice.

Where a sluice board of considerable dimensions is to be occasionally
raised, it may be necessary to ascertain the force which will be required for
overcoming its friction; this friction is nearly proportional to the whole pres-
sure of the water, and may be found, with suthcient accuracy, in pounds, by
multiplying the square of the depth of the sluice, in feet, by 10. Thus, if
the depth be 3 feet, the friction or adhesion will be about SO pounds for each
foot of the breadth.

ox HTDROSTATIC INSTRUMENTS, AND HYDRAULIC ARCHITECTURE. 31J

If the side of a canal gives way, it is sometimes of consequence to prevent,
as much as possible, theescape of the water. For this purpose it is usual to
have doors or valves in various parts of the canal, which, when the water is
at rest, lie nearly flat at the bottom ; but when it begins to run over them,
with a considerable velocity, they are raised by its force, and put a stop to
its motion.

The utility of the introduction of canals into a commercial country may
be estimated in some measure by the effect of the same labour, employed in.
removing weights by land carriage and by water. Thus, a single horse can
scarcely dra\r more than a ton weight on the best road, but on a canal, the
same horse can draw a boat of 30 tons at the same rate. ,

The construction of piers and quays, and the management of harbours, are
also important departments of hydraulic architecture ; it often happens that
besides the application of the general principles of mechanics and hydrostatics
to tliese purposes, the peculiar circumstances of the case may indicate to an
ingenious artist a mode of performing the required work in an effectual and
economical manner. We may find a good example of such an arrangement, in
the account given, by Mr. Smeaton, of the method which he adopted for the
improvement of the port of Ramsgate, and which indeed resembles some that
had been before employed in similar cases : by forming a larg-e excavation,
which is furnished with flood gates, and is constantly filled at high water,
he has procured a number of artificial torrents, which escape through the
sluices, and become powerful agents for carrying away the matter deposited by
the sea, and tending to impede the navigation of the harbour.

• 316

LECTURE XXVn.
I

ON THE REGULATION OF HYDRAULIC FORCES.

.L HOSIi motlificatioHs of the motions of fluids which are employed either for
conducting them from place to place, or for applying their powers to the pro-
duction of mechanical eft"ects,may be considered as constituting a separate di-
vision of practical hydrauHcs, which is analogous to the subject of general
machinery in practical mechanics.

A supply of water may be obtained from a reservoir, situated above the level
at which it is w^anted, whatever its distance may be, either by means of open
canals, or aqueducts, or of closed pipes. Where an uninterrupted declivity
cannot be obtained, it is necessary to employ pipes, which may be bent up-
wards or downwards at pleasure, provided that no part of them be more than
thirty feet above the reservoir, and when the pipe is once filled, the water will
continue to flow from the lower orifice ; but it is best in all such cases to
avoid unnecessary angles ; for when the pipe rises and falls again, a portion of
the air, which is always contained in water, is frequently collected in the
angle, and very materially impedes the progress of the water through the pipe.
When the bent part is wholly below the orifices of the pipe, this air may be
discharged by various methods. The ancients used small upright pipes, called
columnaria, rising from the convexity of the principal pipe, to the level of the
reservoir, and suffering tlie air to escape without wasting any of the water.
It may however frequently be inconvenient or impossible to apply a pipe of
this kind ; and the same purpose may be answered, by fixing on the pipe a
box containing a small valve, which opens downwards, and is supported by
a float, so as to remain shut while the box is full of water, and to fall open
when any air is collected in it. (Plate XXI. Fig. 288.)

Ifthejiipe were formed into a syjhon, having its flexure above both orifices,

ON THE REGULATION OF HlTDRAULIC Ft>IlC"E!S. 31/

it would be necessary to bend it upwards at the extremities, in order to kee{»
it always full : but in this case the accumulation of the air would be extremely
inconvenient, since it would collect so much the more copiously, as the water
in the upper part of the pipe would be more free from pressure, and neither of
the methods which have been mentioned would be of any use in extricatin(»
it. It has been usual in such cases to force a quantity of water vioientlv
through the pipe, in order to carry the air with it; but perhaps the same effect
might be produced much more easily, by making a small airtight valve -in the
upper part of the pipe, opening outwards, and a stopcock immediately before
it: the stopcock being suddenly turned as often as might Ire necessary, the
momentum of the water in the pipe would ptobably carry it forwards with
sufficient force to throw out the air ; or, if it were necessary external pressure
might be added, and the air might even in this manner be discharged by the
valve much more readily than without it. But it might be still simpler to
have a pretty large vessel of water screwed on to the pipe, which would not
be filled with air for a considerable time ; and which, when full, might be taken
off and replenished with water. (Plate XXI. Fig. 285.)

The diameter of a pipe, required for conveying a given quantity of water to
a given distance, may be calculated from the experiments of Mr. Buat, which
have been already mentioned. Pipes are usually made of wood, of lead, or of
cast iron ; but most commonly of lead; and of late tinned copper has beea,
employed with considerable advantage. A pipe of lead will bear the pressure
of a column of water 100 feet high, if its thickness be one hundredth of its
diameter, or even less than this; but when any alternation of motion is pro-
duced, a much stronger pipe is required, and it is usual to make leaden pipes"
of all kinds far thicker than in this proportion.

The form and construction of stopcocks and valves are very various, ac-
cording to their various situations and uses. Stopcocks usually consist of a
cylindrical or conical part, perforated in a particular direction, and capable of
being turned in a socket formed in the pipe, so as to open or shut the passage
©f the fluid, and sometimes to form a communication with either of two or
more vessels at pleasure. A valve is employed where the fluid is to be allowed
to pass in one direction only, and not to return. For Avatcr, those valves
arc the best which interrupt the passage least; and none appears to fulfil

318. LECTURE xxvrr.

this condition better than the common clack valve of leather, which is generally
either single, or divided into two parts; but it is sometimes composed of four
parts, united so as to forma pyramid, nearly resembling the double and triple
valves which are formed by nature in the hearts of animals. A board, or a
round flat piece of metal, divided unequally by an axis on which it moves,
makes also a very good simple valve. Where a valve is intended to intercept
the passage of steam, it must be of metal ; such a valve is generally a flat
plate, with its edge ground a little conically, and guided in its motion by a
wire or pin. For air, valves are commonly made of oiled silk, supported by a
perforated plate or grating. (Plate XXI. Fig. 286, 287.)

Before we consider the application of the force of fluids in motion to prac-
tical purposes, we must attend to the methods of measuring the velocity of
their motions. This may be done either by a comparison with linear mea-
sures, or by instruments founded on the laws of hydraulic pressure. One of
the best of such instruments is the tube invented by Pitot, and improved by
Buat. A funnel is presented to the stream, and the water in a vertical tube
connected with it is elevated above the level of the river, nearly to the height
corresponding to the velocity : but it is said that the result will be less liable
to error, if the funnel be covered by a plate with a small orifice in its centre,
the elevation being in this case always half as great again as the height due to
the velocity. Other instruments, intended for the same purpose, require some
previous experiments for determining the degree in which they are' affected by
different velocities ; in this manner the hydrometrical fly is adjusted ; the
impulse of the water on two inclined planes turning an axis to which they
are fixed, and by its means a series of wheels, with an index, which expresses
the space described during the time of observation. Instamients similar to
these have also sometimes been employed, for measuring the relative velocity,
with which a ship under way passes through the water ; and an apparatus, re-
sembling Pitot's,has been adapted to this purpose by Captain Hamilton, with the
addition of a tube inserted into it on a level with the surface of the water,
which continually discharges a small stream into a reservoir with a velocity
regulated by the pressure, and consequently equal or proportional to that of
the ship itself In this manner he obtains an accurate register of the M'hole
distance described, including the effect of all the variations of the velocity.
If the orifice be small, it will be necessary to attend to the temperature of the

ox THE ItlGUtATION OF HYDKAULIC rORCES. 319

water, since the discharge is considerably retarded by any considerable degree of
cold. But when the aperture, which determines the magnitude of the discharge,
^s .wholly under water, as Captain Hamilton has placed it, this source of error
is probably much diminished. (Plate XXII. Fig. 1288, 289.)

The motions of the air may also be measured by instruments similar to
those which are employed for determining the velocity of streams of water.
The direction of the wind is sometimes indicated by a wind dial, consisting
simply of an index, connected by wheels with a common vane or weather-
cock. Its velocity may be found by means of wind gages of different kinds :
these arc sometimes constructed by opposing a flat surface to the wind, the
pressure being measured by the flexure of a spring, or by the winding up of
a weight on a spiral barrel ; and sometimes by receiving the stream in the
mouth of a funnel, so as to raise a column of water, in a vertical tube, to a
height equivalent to the pressure, or to condense a quantity of air inclosed in
a cavity, to a degree which is indicated by the place of a small portion of
mercury, moving in a horizontal tube, which leads to the cavity. A little
windmill, like the hydrometrical fly, may also be employed for measuring the
velocity of the wind, with the assistance of a watch.

The principal methods of applying the force of fluids to useful purposes are
to employ their weight, their impulse, or their pressure. The weight of
"w^ater may be applied, by collecting it in a reservoir, which alternately ascends
and descends, by causing it to act within a pipe on a moveable piston, or by
conducting it into the buckets of a revolving M-hecl ; its impulse may be di-
rected either perpendicularly or obliquely against a moveable surface ; and its
pressure may be obtained, without any immediate impulse, by causing a
stream to flow horizontally out of a moveable pipe which revolves round an
axis. The force of the air can only be applied by means of its impulse, and
this may be employed either perpendicularly or obliquely.

When water is collected in a single reservoir, which serves to work a pump
or to raise a weight, the mode of its operation may be determined from me-
chanical considerations only ; and it is obvious that if we are desirous of pre-
serving the whole force of the water, we must employ a second reservoir to
be filled during the descent of the first, which may either descend in its turn,

320 LECTURE XXVII.

or empty itself into the first when it has ascended again to its original situa-
tion. The action of a column of water, inclosed in a pipe, is of a nature-
nearly similai- to that of such a reservoir, excepting that the apparatus is
more liable to friction; the arrangement of its parts is nearly similar, although
in an inverted position, to that which is more commonly employed for rais-
ing welter by means of pumps. But both these methods of employing the
weight of water, are in great measure confined to those eases in which it is
to be procured in a small quantity, and may be allowed to descend through a
considerable height, and when the circumstanceis do not allow us to employ
machines which require a greater space.

We have seen that in order to determine the effect of any force employed
in' machinery, we must consider not only its magnitude, but also the velo-
city with which it can be brought into action, and we rnujs^t estimate the ul-
timate value of the power, by the joint ratio, or the product, of the force and
the velocity. Thus, if we had a corn mill, for example, in which we wished
the millstone to revolve with a certain velocity, and to overcome a given
resistance, and supposing that this eifect could be obtained by means of
a certain train of wheels from a given source of motion; if the velocity
of the motion at its source be reduced to one- half, we must double the
diameter of one of the wheels by which the force is communicated, in
order to give the millstone the desired velocity, and thus we must introduce
a mechanical disadvantage, which can only be compensated by a double in-
tensity in the force at its origin.

If we apply this estimation of effect to the motion of an overshot wheel,
we shall find that the velocity of the wheel, and consequently its breadth, and
the magnitude of its buckets, is perfectly indifferent with respect to the
value of its operation : for supposing the stream to enter the buckets with the
uniform velocity of the wheel, the quantity of water in the wheel at any one
time, and .consequently the pressure, must be inversely as the velocity, so.
that the product of the force into the velocity will be the same, however
they may. separately A'ary. If, however, the velocity were to become very
considerable, it would be necessary to sacrifice a material part of the fall, in
order that the water might acquire this velocity before its arrival at the wheel;
but a fall of one foot, or even less, is sufficient for producing any velocity

ON THE REGULATION OF HYDRAVLIC FORCES. ~ 3ii 1

that would be practically convenient : and it is obvious, on the other hand,
that a certain velocity may be procured from a wheel moving rapidly, with
less machinery than from another which moves more slowly. In general the
velocity of the surface of the wheel is between two and six feet in a second :
and whether it be greater or smaller, the force actually applied will always
be equal in effect to the weight of a portion of the stream employed, equal in
length to the height of the wheel. In order to avoid the resistance which
might be occasioned by the stagnant water below the wheel, it is a good
practice to turn the stream backwards upon its nearer half, so that the water,
when discharged, may run off in the general direction of its motion. (Plate
XXII. Fig. 290.)

If we suffer the stream of water to acquire the utmost velocity that the
whole fall can produce, and to strike horizontally against the floatboards of
an undershot wheel, or if we wish to employ the force of a river running in a
direction nearly horizontal, the wheel must move, in order to produce the
greatest effect, with half the velocity of the stream. For the whole quantity
of water impelling the floatboards is nearly the same, whatever may be the ve-
locity, especially if the wheel is properly inclosed in a narrow channel, and
hence it is easy to calculate that the greatest possible effect will be produced
when the relative velocity of the stream, striking the floatboards, is equal to
the velocity of the wheel itself. The pressure on the floatboards is equal to
that of a stream containing the same quantity of water, and striking a fixed
obstacle with half the velocity, that is, such a stream as escapes from the
wheel, which must be twice as deep or twice as wide as the original stream,
since its motion is only one half as rapid; and a column of such a stream, of
twice the height due to its velocity, that is, of half the height of the fall,
being, as we have already seeri, the measure of the hydraulic pressure, this
force Avill be precisely half as great as that of a similar column, acting on an
overshot wheel, which moves with the same velocity. But the stream thu.s
retarded will not retain the other half of its mechanical power; since its
greatest effect will be in the same proportion to that of an equal stream acting
on an overshot wheel with one fourth of the fall of the former : and the re-
maining fourth of the power is lost in producing the change of form of the
water and in overcoming its friction. In whatever way we apply the
4brce of water, we shall find that the mechanical power which.it possesses

VOL. I. T t

522 LECTURE XXVII.

must be measured by the product of the quantity multiplied by the height
from which it descends: for example, a hogsiiead of water capable of descend-
ing from a height of 10 feet, possesses the same power as 10 hogsheads des-
cending from a height of one foot; and a cistern filled to the height of 10
feet above its orifice possesses 100 times as much power as the same cistern
filled to the height of one foot only. ^

When, therefore, the fall is sufficiently great, an overshot wheel is far pre-
ferable to an undershot wheel, and where the fall is too small for an overshot
wheel, it is most advisable to employ a breast wheel, which partakes of its
properties ; its floatboards consisting of two portions meeting at an angle, so
as to approach to the nature of buckets, and the water being also in some measure
confined within them by the assistance of a sweep or arched channel which fol-
lows the curve of the wheel, without coming too nearly into contact with it,
so as to produce unnecessary friction. When the circumstances do not
admit even of a breast wheel, we must be contented with an undershot
wheel : it is recommended, for such a wheel, that the floatboards be so placed
as to be perpendicular to the surface of the water at the time that they rise
out of it: that only one half of each should ever be below the surface, and
that from three to five should be immersed at once, according to the mag-
nitude of the wheel. Sometimes, however, it has been thought eligible to
employ a much smaller number : thus the water wheel which propels Mr.
Symington's steam boat has only six floatboards in its whole circumference.
(Plate XXII. Fig. 291, 292.)

V

Since the water escaping from an undershot wheel still retains a part of
its velocity, it is obvious that this may be employed for turning a second
wheel, if it be desirable to preserve as much as possible of the force. In this
case, by causing the first wheel to move with two thirds of the velocity of the
stream, the whole effect of both will l:>e one third greater than that of a single
wheel placed in the same stream ; but it must be considered that the expense
of the machinery will also be materially increased.

Considerable errors have frequently been made by mathematicians and
practical mechanics in the estimation of the force of the wind or the water
on oblioue surfaces : they h^^ve generally arisen from inattention to the distinc-

ON THE REGULATION OF HYDRAULIC FORCES. 323

tiou between pressure and mechanical power. It may be demonstrated that
the greatest possible pressure of the wind or water, on a given oblique sur-
face at rest, tending to turn it in a direction perpendicular to that of the wind,
is obtained when the surface forms an angle of about 55° with the wind ; but
that the mechanical power of such a pressure, which is to be estimated from
a combination of its intensity with the velocity of the surface, may be in-
creased without limit by increasing the angle of inclination, atid consequently
the velocity. The utmost effect that could be thus obtained would be equal
to that of the same wind or stream acting on the floatboards of an undershot
wheel : but since in all practical cases the velocity is limited, the effect will
be somewhat smaller than this : for example, if the mean velocity of the sails
or floatboards be supposed equal to that of the wind, the mechanical power
will be more than four fifths as great as that of an undershot wheel, that is, in
the case of a windmill, more than four fifths of the utmost effect that can be
obtained from the wind. In such a case Maclaurin has shown that the sails
ought to make an angle of 74° with the direction of the wind: but in practice
it is found most advantageous to make the angle somewhat greater than this,
the velocity of the extremities of the sails being usually, according to Mr.
Smeaton, more than twice as great as that of the wind. It appears, there-
fore, that the oblique sails of the common windmill are in their nature almost
as well calculated to make the best use of any hydraulic force as an undershot
wheel ; and since they act without intermission throughout their whole revo-
lution, they have a decided advantage over such machines as require the sails
or fans to be exposed to a more limited stream of the wind, during one half only
of their motion; which is necessary in the horizontal windmill, where a screen is
employed for covering them while they are moving in a direction contrary to
that of the wind : and such machines, according to Smeaton, are found to per-
form little more than one tenth of the work of those which are more usually
employed. The sails of a common windmill are frequently made to change their
situation according to the direction of the wind, by means of a small wheel, with
sails of the same kind, which turns round whenever the wind strikes, on
either side of it, and drives a pinion turning the whole machinery; ithe sails
are sometimes made to furl or unfurl themselves, according to the velocity of
the wind, by means of a revolving pendulum, which rises to a greater or less
height,in order to prevent the injury which the flour would suffer frorn too great
a rapidity in the motion, or any other accidents which might happen in a mill

324 LECTURE XXVII.

of a different nature. The inclination of the axis of a windmill to the horizon is
principally intended to allow room for the action of the wind at the lower
part, where it would be weakened if the sails came too nearly in contact with
the building, as they must do if they were perfectly upright. When it is
necessary to stop the motion of a windmill, a break is applied to the surface
of a large wheel, so that its friction operates with a considerable mechanical
advantage. Water wheels with oblique floatboards are sometimes used with
good cifect in China and in the south of France : for tide wheels, such float-
boards have the advantage that they may be easily made to turn on a hinge
with the stream, so as to impel the wheel in the same direction whether the
tide be flowing or ebbing. (Plate XXII, Fig. '2.93.)

A smoke jack is a windmill in miniature ; a kite affords a very familiar ex-
ample of the effect of the oblique impulse of the air, of which the action first
causes a pressure perpendicular to the surface of the kite, and this force,
combined with the resistance of the string, produces a vertical result capable
of counteracting the weight of the kite. (Plate XXII. Fig. 294.)

The counterpressure of the water, occasioned by the escape of a stream from
a moveable reservoir, was applied by Parent to the purpose of turning a mill-
stone, and various other authors have described machines of a similar nature :
they may be constructed with little or no wheel work, and it does not appear
to be necessary that much of the force of the water should be lost in their
operation; but they have never been practically employed with success, nor
have they perhaps ever had a fair trial.

The art of seamanship depends almost entirely on the management of the
forces and resistances of air and water, and if the laws of hydraulic pressure,
with respect to oblique and curved surfaces, were more completely ascertain-
ed, we might calculate not only what the motions of a ship would be under
any imaginable circumstances, but we might also determine precisely what
would be the best possible form of a ship, and what the best arrangement of
her rigging.

When a ship is sailing immediately before the wind, little or no art is required
m setting her sails, and her velocity is only limited by that of the wind, and

ON THE REGULATION OF HYDRAULIC FORCES. 3SS

by the resistance of the water: but for sailing with a side wind, it becomes
necessary that the immediate force of the wind should be considerably mo-
dified.

If we had a circular vessel or tub, with a single mast, and a sail perfectly
flat, and if the sail were placed in a direction deviating but little from that of
the wind, the tub would begin to move in a direction nearly at right angles
to that of the wind, since the impulse of the wind acts almost entirely in a
direction perpendicular to that of the sail : but the slightest inequality of the
dimensions of the sail, or of the force of the wind, would immediately disturb
the position of the vessel ; and in order to avoid this inconvenience, it would
be necessary to have a moveable body projecting into the water, so as to create
a resistance by means of which the vessel might be steered, and the sail con-
fined to its proper place : and this might be done more effectually by chang-
ing the form of the vessel from round to oval ; it would then also have the
advantage of moving much more easily through the water in the direction of
its length than a circular vessel of equal size, and of creating still more re-
sistance in a transverse direction, so that when urged by an oblique force, it
would move in some measure obliquely, but always much more nearly in the
direction of its length than of its breadth. The angular deviation from the
track of the ship is called its lee way, and if we know the direction of the
sails, and the actual proportions of the resistances opposed to the ship's
motion in different directions, we may calculate from these resistances the
magnitude of the angular deviation or lee way : but hitherto such calcula-
tions have generally indicated a lee way three or four times as great as that
which has been observed. The use of the keel is not only to assist in confin-
ing the motion of the ship to its proper direction, but also to diminish the
disposition to vibrate from side to side, which would interfere with the
effect of the sails, and produce many other inconveniences. When the prin-
cipal force of the wind is applied to the anterior part of the ship, her head
would be naturally turned from the wind if the rudder were not made to pro-
ject from the stern in a contrary direction, and to present the surface of an
inclined plane to the water which glides along the keel, so as to preserve the
ship, by means of the pressure which it receives, in any direction that may be
required for her manoeuvres. Commonly,however, although the sails may be so
arranged that the principal force of the wind appears to be on the fore part of

326 LECTURE XXVIT.

the ship, the curvature of the sails, or some other cause, throws the pressure
further backwards, and the action of the rudder is necessary to prevent the
ship's head turning towards the wind. (Plate XXII. Pig 2,95.)

When a ship is steering in this manner on a side wind, the effect of the
wind has a natural tendency to overset her, and if she is too crank, that is,
deficient in stability, she cannot sail well, otherwise than directly before the
wind. The place of the centre of gravity, compared with that of the meta-
centre, or imaginary centre of pressure, determines the degree of stability,
and the most general way of increasing it is to lessen the weight of the
upper part, and of the rigging of the vessel, to diminish her height, or to in-
crease her breadth, and to stow the ballast as low as possible in the hold.
Too little attention has frequently been paid to this subject, as well as to
many other departments of naval architecture ; and although mere theore-
tical investigations have hitherto been but of little service to the actual
practice of seamanship, yet it cannot be doubted that an attention to what
has already been discovered of the laws of hydrodynamics, as well as to the
principles of mechanics in general, must be of great advantage to the navigator,
iii enabling him to derive from his own experience all the benefits, which a
correct mode of reasoning is capable of procuring him.

32;

LECTURE XXVIII.

ON HYDRAULIC MACHINES.

VV E shall apply the denomination of hydraulic machines to such only, as
are intended for counteracting the gravity of water, that is, for raising it
from a lower situation to a higher. The simplest of these are buckets, bucket
wheels, and friction ropes; moveable pipes are the next in order ; and pumps of
various kinds constitute the most extensive and the most important part of
the subject. Besides these and some other similar machines, hydraulic air
vessels and artificial fountains will also require to be examined.

A series of earthen pitchers, connected by ropes, and turned by trundles
or pinions, over which they pass, has long been used in Spain, under the
name of noria : in this country, buckets of wood are sometimes employed in
a similar manner. A bucket wheel is the reverse of an overshot waterwheel,
and the water may be raised by buckets nearly similar to those which are
calculated for receiving it in its descent: sometimes the buckets are hung on
pins, so as to remain full during the M'^hole ascent; but these wheels are liable
to be frequently out of repair. Sometimes the reverse of an undershot wheel
or rather of a breast wheel, is employed as a throwing wheel, either in a verti-
cal or in an inclined position. Such M'heels are frequently used for draining
fens, and are turned by windmills ; the floatboards are not placed in the di-
rection which would be best for an undershot wheel, but on the same princi-
ple, so as to be perpendicular to the surface when they rise out of it, in order
that the water may the more easily flow off them. (Plate XXII. Fig.
296 . . 298.)

Instead of a series of buckets connected by ropes or chains, a similar effect
is sometimes produced by a simple rope, or a bundle of ropes, passing over a
wheel above, and a pulley below, moving with a velocity of about 8 or 10

J28 LECTURE XXVIII.

feet in a second, and drawing a certain quantity of water up by its friction.
It is probable that the water commonly ascends with about half the velocity
of the rope, and on this supposition we might calculate its depth on the rope
by comparing its relative motion with that of a little river : but the rules,
which serve for calculating the velocity of rivers, do not perfectly agree in
this case with the results of direct experiments ; for the friction required for
elevating the quantity raised by such a machine, appears from calculation to
. correspond to a velocity about twice as great as the actual relative velocity.
While the water is principally supported by the friction of the rope,
its own cohesion is amply sufficient to prevent its wholly falling, or being
scattered, by any accidental inequality of the motion. (Plate XXII. Fig.
299.)

The lateral friction of water has been applied in a very simple manner by
Venturi to the draining of land, by means of a stream which runs through it,
allowing the stream to acquire sufficient velocity to carry it over an inclined
surface, and to drag with it a certain portion of water from the lowest part
of this surface : but the quantity of water raised in this manner must be very
inconsiderable, and the loss of force by friction very great.

A system of spiral pipes may be placed in the plane of a wheel, receiving
the water at its circumference, and raising it by degrees, as the wheel turns,
towards the axis, where it is discharged ; the motion of the wheel being
usually derived from the same stream which supplies the pipes : but the
height to which the water is raised by this machine is very small in propor-
tion to its bulk, A single pipe wound spirally round a cylinder which re-
volves on an axis in an oblique situation, has been denominated the
screw of Archimedes, and is called in Germany the water snail. Its opera-
tion, like that of the flat spiral, may be easily conceived by imagining a
flexible pipe to be laid on an inclined plane, and its lower part to be gra-
dually elevated, so that the fluid in the angje or bend of the pipe may be
forced to rise ; or by supposing a tube, formed into a hoop, to be rolled up
the same plane, the fluid being forced by the elevation of the tube behind it
to run as it were up hill. This instrument is sometimes made by fixing a
spiral partition round a cylinder, and covering it with an external coating,
either of wood or of metal; it should be so placed with respect to the surface

ON HYDRAULIC MACHINES. 329

of the water as to fill in each turn one half of a convolution; for when the
orifice remains always immersed, its effect is much diminished. It is gene-
rally inclined to the horizon in an angle of hetwcen 45 and 60 degrees; hence
it is obvious that its utility is limited to those cases in which the water is
only to be raised to a moderate height. The spiral is seldom single, but
usually consists of three or four separate coils, forming a screw which rises,
slowly round the cylinder. (Plate XXII. Fig. 300, 301.)

An instrument of a similar nature is called by the Germans a water screw;
it consists of a cylinder with its spiral projections detached from the external
cylinder or coating, within which it revolves. This machine might not im-
properly be considered as a pump, but its operation is precisely similar to that
of the screw of Archimedes. It is evident that some loss must here be oc-
casioned by the want of perfect contact between the screw and its cover;
in general, at least one third of the water runs back, and the machine cannot
be placed at a greater elevation than 30° ; it is also very easily clogged by
accidental impurities of the water: yet it has been found to raise more water than
the screw of Archimedes, when the lower ends of both are immersed to a con-
siderable depth ; so that if the height of the surface of the water to be raised
were liable to any great variations, the water screw might be preferable to the
screw of Archimedes. (Plate XXII. Fig. 302.)

When a spiral pipe, consisting of many convolutions, arranged either in a
single plane, or in a cylindrical or conical surface, and revolving round a
horizontal axis, is connected at one end by a watertight joint with an as-
cending pipe, while the other end receives during each revolution nearly
equal quantities of air and water, the machine is called a spiral pump. It was
invented about 1746, by Andrew Wirtz, a pewterer at Zurich, and it is said to
have been used with great success at Florence and in Russia : it has also been
employed in this country by Lord Stanhope, and I have made trial of it for
raising water to a height of forty feet. The end of the pipe is furnished with
a spoon, containing as much water as will fill half a coil, which enters the
pipe a little before the spoon has arrived at its highest situation, the other
half remaining full of air, which conmiunicates the pressure of the column of
water to the preceding portion, and in this manner the effect of nearly all
the water in the wheel is united, and becomes equivalent to that of the co-

VOL I. ~ , u u

imp LECTURE XXVIII.

lumn of water, or of water mixed with air, in the ascending pipe. The air
nearest the joint is compressed into a space much smaller than that which it
occupied at its entrance, so that where the height is consider; ble, it be-
comes advisable to admit a larger portion of air than would naturally fill
half the coil, and this lessens the quantity of water raised, but it lessens also
the force required to turn the machine. The joint ought to be conical, in
order that it may be tightened when it becomes loose, and the pressure ought
to be removed from it as much as possible. 1 he loss of power, suppobmg
the machine well constructed, arises only from the friction of the water on '
the pipe, and the friction of the wheel on its axis ; and where a large quantity
of water is to be raised to a moderate height, both of these resistances may
be rendered inconsiderable. But when the height is very great, tl*e
length of the spiral must be much increased, so that the weight of the pipe
becomes extremely cumbersome, and causes a great friction on the
axis, as well as a strain on the machinery : thus, for a height of 40 feet, I
found tliat the wheel required above 100 feet of a pipe which was three
quarters of an inch in diameter ; and more than one half of ihe pipe being
always fiiU of water, we have to overcome the friction of about 80 feet of
such a pipe, which will require 24 times as much excess of pressure to pro-
duce a given velocity, as if there were no friction. The centrifugal force of
the water in the wheel would also materially impede its ascent if the velocity
were considerable, since it would be always possible to turn it so rapidly as
to throw the whole water back into the spoon. The machine which I had
erected being out of repair, I thought it more eligible to substitute for it a
common forcing pump, than to attempt to make any further improvement in
it, under circumstances so unfavourable. But if the wheel with its pipes were
entirely made of wood, it might in many cases succeed better : or the pipes
^might be made of tinned copper, or even of earthenware, which might be
cheaper and lighter than lead. (Plate XXII. Fig. 303.)

The centrifugal force, which is an impediment to the operation ofWirtz's
machines, has sometimes been employed, together wirh the pressure of the at-
mosphere, as an immediate agent in raising water, by means of the rotatory
pump. This machine consists of a vertical pipe, caused to revolve round its
axis, and connected above with a horizontal pipe, which is open at one or at
both enxis, the whole being furnished with proper valves to prevent the

ON HYDRAULIC MACHINES. 331

escape of the water when the machine is at rest. As soon as the rotation
becomes sufficiently rapid, the centrifugal force of the water in the horizon-
tal pipe causes it to be discharged at the end, its place being supplied by
means of the pressure of the atmosphere on the reservoir below, which forces
the water to ascend through the vertical pipe. It has also been proposed to
turn a machine of this kind by the counterpressure of ^another portion of
water, in the manner of Parent's mill, where there is fall enough to carry it
off. This machine may be so arranged that, according to theory, little of the
force applied may be lost ; but it has failed of producing in practice a very
advantageous effect. (Plate XXIII. Fig. 304.) *

A pump is a machine so well known, and so generally used, that the deno-
mination has not uncommonly been extended to hydraulic machines of all
kinds ; but the term, in its strictest sense, is to be understood of those ma-
chines, in which the water is raised by the motion of one solid within another,
and this motion is usually alternate, but sometimes continued so as to consti-
tute a rotation. In all the pumps most commonly used, a cavity is enlarged
and contracted by turns, the water being admitted into it through one valve,
and discharged through another.

One of the simplest pumps, for raising a large quantity of water to a small
height, is made by fitting two upright beams or plungers, of equal thickness
throughout, into cavities nearly of the same size, allowing them only room
to move without friction, and connecting the plungers by a horizontal beam
moving on a pivot. The water being admitted, during the ascent of each
plunger, by a large valve in the bottom of the cavity, it is forced, wheti the
plunger descends, to escape through a second valve in the side of the cavity,
and to ascend by a wide pipe to the level of the beam. The plungers ought
not to be in any degree tapered, because of the great force which would be un-
necessarily consumed, in continually throwing out the water, with great velocity,
as they descend, from the interstice formed by their elevation. This pump may
be worked by a labourer, walking backwards and forwards, either on the beam or
on a board suspended below it. By means of an apparatus of this kind, describ-
ed by Professor Robison,an active man, loaded with a weight of thirty pounds,
has been able to raise 580 pounds of water every minute, to a height of 1 In-
fect, for ten hours a day, without fatigue ; this is the greatest effect produced
by a labourer that has ever been correctly stated by any author ; it is equi-

532 LECTURE xxviir.

valent to somewhat more than 11 pounds raised through lOfcet in a second,
instead of 10 pounds, which is a fair estimate of the usual force of a man,
without any deduction for friction. (Plate XXIII. Fig. 305.)

It is obvious that if tlie plungers were so well fitted to the cavity as to
prevent the escape of any water between them, the ascending pipe might
convey the water to any required height ; the machine would then become a
forcing pump, and the plungers might be shortened at pleasure, so as to
assume the form of a piston sliding within a barrel. The piston might also
be situated above the level of the reservoir, and in this case the water would
be forced up after it by the pressure of the atmosphere to the height of about
30 feet, but not much further: and even this height would be somewhat too
great for practice, because the water might sometimes follow the piston in its
ascent too slowly. Such a pump, partaking of the nature of a forcing and a
sucking pump, is sometimes called a mixed pump. In Delahire's pump, the
same piston is made to serve a double purpose, the rod working in a collar
of leathers, and the water being admitted and expelled in a similar manner,
above and below the piston, by means of a double apparatus of valves and
pipes. (Plate XXIII. Fig. 306.)

For forcing pumps of all kinds, the common piston, with a collar of loose
and elastic leather, is preferable to those of a more complicated structure :
the pressure of the water on the inside of the leather makes it sufficiently
tight, and the friction is inconsiderable. In some pumps the leather is
omitted, for the sake of simplicity, the loss of water being compensated by
the greater durability of the pump; and this loss will be the smaller in propor-
tion as the motion of the piston is more rapid. (Plate XXIII. Fig. 307.)

Mr. Bramah has very ingeniously applied a forcing puYnp, by means of the
well known properties of hydrostatic pressure, to the construction ot a con-
venient and powerful press. The water is forced, by a small pump, into, a
barrel in which it acts on a much larger piston ; consequently this piston is
urged by a force as much greater than that which acts on the first pump rod,
as its surface is greater than that of the small one. (Plate XXIII. Fig.
308.)

In the common sucking pump, the valve through which the water escapes

ON HYDRAULIC SrACHINES. 333

is placed within the piston itself, so that the same barrel serves for the ascent
of the water, which rises in one continued line, while the piston is raised,
and rests on the fixed valve while it is depressed. The velocity of the stroke
ought never to be less than 4 inches in a second, nor greater than two or
three feet; the stroke should also be as long as possible, in order to avoid
unnecessary loss of water during the descent of the valves. The diameter of
the pipe, through which the water rises to the barrel, ought not to be less than
two thirds of the diameter of the barrel itself. (Plate XXIII. Fig. 309.)

A bag of leather has also been employed for connecting the piston of a
pump witli the barrel, and in this manner nearly avoiding all friction: but it
is probable that the want of durability would be a great objection to such a
machine. (Plate XXIII. Fig. 310.)

Where the height, throvigh which the water is to be raised, is considerable,
some inconvenience might arise from the length of the barrel through which
the piston lod of a sucking pump would have to descend, in order that the
piston might remain within the hmits of atmospheric pressure. This may be
avoided by placing the moveable valve below the fixed valve,and introducing
the piston at the bottom of the barrel. Such a machine is called a lifting pump :
in common with other forcing pumj)s, it has the disadvantage of thrusting the
piston before the rod, and thus tending to bend the rod, and produce an
unequal friction on the piston, while, in the sucking pump, the principal force
always tends to straighten the rod. (Plate XXIII. Fig. 311.)

The rod of a sucking pump may also be made to work in a collar of leather,
and the water may be forced througli a valve into an ascending pipe. By
applying an air vessel to this, or to any other forcing pump, its motion may
be equalised, and its performance improved ; for if the orifice of the air
vessel be sufficiently large, the water may be forced into it, during the stroke
of the pump, with any velocity that may be required, and with little resistance
from friction, while the loss of force, from the frequent accelerations and
retardations of the whole body of water, in a long pipe, must always be conr
siderable. The condensed air, reacting on the water, expels it more gra-
dually, and in a continual stream, so that the air vessel has un effect analo^
gous to that of a fly wheel in mechanics. (Plate XXIII. Fig. 312.)

334 LECTURE XJtVIII.

If, instead of forcing the water to a certain height through a pipe, we
cause it to form a detached jet, we convert the forcing pump into a fire engine ;
and in general two barrels, acting alternately, are connected, for this purpose,
with the same air vessel; so that the discharge is thus rendered very nearly
uniform. The form of the ajutage, or orifice of the pipe, is by no means in-
different to the eff^ect of the machine, since the height of the jet may be
much increased by making it moderately contracted, and a little conical
rather than cylindrical. When the air vessel is half filled with water, the
height of such a jet will be about 30 feet, when two thirds filled, about 60,
the height being always nearly proportional to the degree of condensation of
the air, or to the excess of its density above that of the surrounding atmo-
sphere. Sometimes a double forcing pump, or fire engine, is formed b}^ the
alternate rotatory motion of a flat piston within a cylindrical barrel: the
axis of its motion coinciding with that of the barrel, and the barrel Being
divided by a partition into two cavities, which are filled and emptied in the
same way as the separate barrels of the common fire engine. The mechani-
cal advantage of this machine is nearly the same as that of the n)ore usual
constructions, but it appears to be somewhat more simple than a common
engine of equal force. The partition may be extended throughout the
diameter of the cylinder, the opposite pairs of cavities being made to com-
municate with each other, and thus both sides of the piston may be employed
at once. (Plate XXIII. Fig. 313.)

A piston placed in a similar manner has sometimes been made to revolve
continually, and to force the water through a pipe by means of a slider or a
spring, which intercepts its passage in any other direction. Machines of this
kind have been invented and reinvented, by Ramelli, Cavalleri, Amontons,
Prince Rupert, Dr. Hooke, Mr. Braniah, and Mr. Gwynn. Mr. Gwynn's
engine, which has been employed in many cases with considerable success,
consists of a piston or roller nearly elliptical, well fitted to the cylinder
within which it revolves, with a valve pressed lightly against it by a spring,
which causes a considerable part of the water contained in the cylinder to
be forced in each revolution into the pipe : the whole machine is made of
brass; the spring requires very little force, for the pressure of the water on
the valve keeps it always close to the roller, and the friction arising from
this cause is even an objection to the machine. The stream, although never

ON HYDRAUtlC MACHINES. 356

wholly intermitted, is, however, by no means uniform in its velocity.
(Plate XXIII. Fig. 314. . 317)

The pipes, through which water is raised, by pumps of any kind, ought to
be as short and as straight as possible ; thus, if we had to raise water to a
height of 20 feet, and to carry it to a horizontal distance of 100 by means
of a forcing pump, it would be more advantageous to raise it first vertically into a
cistern 20 feet above the reservoir, and then to let it run along horizontally, or
find its level in a bent pipe, than to connect the pump immediately with a
single pipe carried to the place of its destination. And for the same reason
a sucking pump should be placed as nearly over the well as possible, iu
order to avoid a loss of force in working it. If very small pipes are used,
they will much increase the resistance, by the friction which they occasion.

Water has been sometimes raised by stuffed cushions, or by oval blocks of
wood, connected with an endless rope, and caused by means of two wheels
or drums, to rise in succession in the same barrel, carrying the water in a
continual stream before them ; but the magnitude of the friction of the
cushions appears to be an objection to this method. From the resemblance
of the apparatus to a string of beads, it has been called a bead pump, or a
paternoster work. When flat boards are united by chains, and employed
instead of these cushions, the machine may be denominated a cellular pump;
and in this case the barrel is usually square, and placed in an inclined posi-
tion, but there is a considerable loss from the facility with which the water
runs back. The chain pump generally used in the navy is a pump of this
kind, with an upright banel, through which leathers, strung on a chain, are
drawn in constant succession ; these pumps are only employed, when a
large quantity of water is to be raised, and they must be worked with con-
siderable velocity in order to produce any effect at all. Mr. Cole has im-
proved the construction of the chain pump, so as materially to increase the
quantity of water raised by it. (Plate XXIII. Fig. 318.)

It is frequently necessary to procure alternate motion in pumps by means
of wheelwork, and for this purpose the application of a crank is the most
usual and perhaps the best method. Provided that the bar by which it acts
be sufiiciently long, very little will be lost by the obliquity of its situatioji, and

■ - ■ (

'336 LECTURE XXVI r I.

it is easy, by means of rollers, or of a compound frame, to confine the head of
the pump rod to a rectilinear motion. When any other mode is employed, it
must be remembered that the motion of the pump rod ought always to be
slower at the beginning of each alternation, since a considerable part of the
force is consumed in setting the water in motion, especially where the pipe
is long, and the velocity considerable. But it may happen that, from the nature
of hydraulic pressure under other circumstances, the resistance may be nearly
equal throughout the stroke : for example, when the motion of the piston is
slow in comparison of th.at of the water in the pipe, or when the force em-
ployed in producing velocity is inconsiderable, in comparison with that which
is required for counteracting the pressure. In such cases it may sometimes
be eligible to employ inclined surfaces, of such forms as are best adapted
to communicate the most advantageous velocity to the pump rod by their
pressure on a roller, which may be confined to its proper direction by the
same means as when a crank is used. (Plate XIV. Fig. 184 . . 187.)

The Chinese work their cellular pumps, or bead pumps, by "walking on
bars which project from the axis of the wheel or drum that drives them, and
whatever objection may be made to the choice of the machine, the mode of
communicating motion to it must be allowed to be advantageous.

Pumps have sometimes been worked by means of the w^eight- of water
acting within a barrel, which resembles a second pump placed in an inverted
position. The only objection to the machine appears to be the magnitude of
the friction, and even this inconvenience may perhaps be inconsiderable.
The invention is by no means modern, but it is best known in Germany
under the name of HoU's machine, and it has been introduced into this
country by Mr. Westgarth and Mr. Trevithick. A cliain pump, or a series
of buckets, may also be applied, in a manner nearly similar, to the working.of
machinery of any kind. (Plate XXIII. Fig. 319-)

The mediation of a portion of air is employed for raising water, not only in
the spiral pump, but also in the air vessels of Schemnitz. A column of water,
descending through a pipe into a closed reservoir,, full of air, obliges the air
to act, by means of a pipe, leading from the upper part of the reservoir or
air vessel, on the water in a second reservoir, at any distance either below or

ON HTDRAULIC MACHINES. 33T

above it, and forces this water to ascend through a third pipe to any height
less than that of the first column. The air vessel is then emptied, and the
second reservoir filled, and the whole operation is repeated. The air must,
however, acquire a density equivalent to the pressure, before it can begin to
act ; so that if the height of the columns were 34 feet, it must be reduced to
half its dimensions before any water would be raised; and thus half of the
force would be lost; in the same manner, if the height were 68 feet, two
thirds of the force would be lost. But where the height is small, the
force lost in this manner is not greater than that which is usually spent in
overcoming friction and other imperfections of the machinery employed; for
the quantity of water, actually raised by any machine, is not often greater
than half the power which is consumed. The force of the tide, or of a
river rising and falling with the tide, might easily be applied by a machine of
this kind, to the purposes of irrigation. (Plate XXIII. Fig. 320,
321.)

The fountain of Hero precisely resembles in its operation the hydraulic
vessels of Schemnitz, which were probably suggested to their inventor
by the construction of this fountain. The first reservoir of the fountain is
lower than the orifice of the jet; a pipe descends from it to the air vessel,
which is at some distance below, and the pressure of the air is communi-
cated, by an ascending tube, to a third cavity, containing the water which
supplies the jet. Many other hydraulic and pneumatic instruments, intend-
ed for amusement only, and some of them of much more complicated
structure, are also described in the works of Hero. (Plate XXIII.
Fig. 322.) ,

The spontaneous vicissitudes of the pressure of the air, occasioned by
changes in the weight and temperature of the atmosphere, have been applied,
by means of a series of reservoirs, furnished with proper valves, to tiie purpose
of raising water by degrees to a moderate height. But it seldom happens that
such changes are capable of producing an elevation in the water of each re-
servoir of more than a few inches, or at mpst a foot or two, in a day: and
the whole quantity raised must, therefore, be very inconsiderable.

The momentum of a stream of water, flowing through a long pipe, has also
been employed for raising a small quantity of water to a considerable height.

VOL. I. > XX

*338

LECTURE XXVIII.

The passage of the pipe being stopped by a valve, which is raised by the
stream, as soon as its motion becomes sufficiently rapid, the whole column of
fluid must necessarily concentrate its action almost instantaneously on the
valve ; and in this manner it loses, as we have before observed, the character-
istic property of hydraulic pressure, and acts as if it were a single solid ; so
that, supposing the pipe to be perfectly elastic, and inextensible, the impulse
must overcome any pressure, however great, that might be opposed to it,
and if the valve open into a pipe leading to an air vessel, a certain quantity
of the water will be forced in, so as to condense the air, more or less rapidly,
to the degree that may be required, for raising a portion of the water
contained in it, to any given height. Mr. Whitehurst appears to have
been the first that employed this method: it was afterwards improved by
Mr. Boulton ; and the same machine has lately attracted much attention in
France under the denomination of the hydraulic ram of Mr. Montgolfier.
(Plate XXIII. Fig. 323.)

339

LECTURE XXIX.

ON PNEUMATIC MACHINES.

Pneumatic machines are such as are principally dependent, in theij
operation, upon the properties of elastic fluids ; they may be calculated either
for diminishing or increasing their density and pressure, as air pumps and
condensers; or for directing and applying their force, as bellows, ventilators,
steam engines, and guns.

The density and pressure of the air may be diminished, or the air may
be perfectly or very nearly withdrawn from a given space, either by means
of a column of mercury, or by the air pump. The ancients sometimes
exhausted a vessel imperfectly by the repeated action of the mouth, and
preserved the rarefaction by the assistance of a stopcock. The Torri-
cellian vacuum, obtained by inverting a receiver filled with mercury, and
furnished with a descending tube at least 30 inches long, is the most perfect
that can be procured ; but there is generally a portion of air adhering to the
vessels, and mixed with the mercury, which may often be considerably di-
minished by agitation, but can only be completely expelled by boiling the
mercury for some time in the vessel and its tube, previously to their inver-
sion. (Plate XXIV. Fig. 324.)

The construction of an air pump greatly resembles that of a common
sucking pump for raising water ; but the difference in the operation to be
performed requires a difference in several particular arrangements. The
objects are, to rarefy or exhaust the air as completely, as expeditiously, and
as easily, as possible. In order that the exhaustion may be complete, it is
necessary that no air remain in the barrel when the valve is opened, and that
the process be very long continued. For, supposing all the parts of an air
pump to be perfectly well fitted, and the exhaustion to be carried on for any

340 LECTURE XXIX.

length of time, the limit of its perfection will be a rarefaclion expressed
by the proportion of the air remaining in the barrel, when the piston is down,
to the whole air that the barrel is capable of containing ; for such will be the
rarity of the air in the barrel when the piston is raised. It becomes, there-
fore, of consequence to lessen the quantity of this residual air as much as
possible; and at the same time to take care that the valve may be capable of
being accurately closed and easily opened, or that a stojicock may be occa-
sionally substituted for it, which may be opened and shut by external force,
when the elasticity of the air remaining is too small to lift the valve. In
pumping water from a well, we raise an equal quantity at each stroke, but in
the air pump, we withdraw at most only equal bulks of the air diiferently rare-
fied, so that the quantity extracted is continually diminished as the operation
proceeds. Thus, if one tenth of the air were exhausted by the first stroke, only
nine tenths as much, that is, one tenth of the remainder, would be drawn out
by the second ; hence, in order that the process may be expeditious, it is
of importance to have the barrel as large as possible in proportion to the
receiver. In cases where the presence of aqueous vapour would be of no
consequence, the exhaustion might be made very rapidly by filling the whole
apparatus with water, which was the method first employed by Otto von
Guericke, the inventor of the modern air pump.

In order to lessen the labour of the operation, two barrels may be em-
ployed, and so connected as to work alternately ; in this manner the pressure
of the atmosphere, acting on both pistons at once, opposes no resistance to
their motion in either direction. In Smeaton's pump a single barrel has
nearly the same advantage, the rod of the piston working in a collar of
leathers with oil, and the air being excluded from the upper part of the
barrel by a valve, through which the air passes when the piston is raised
near to the top ; so that in the descent of the piston there is a vacuum
above it, and the air below opens the valve much earlier, and passes more
completely through it, than in the common air pump; and the piston is only
exposed to the whole pressure of the atmosphere during the discharge of the
air through the upper valve. (Plate XXIV. Fig. 3'^25.)

That the air is really removed by the operation of the air pump, may be
demonstrated by various experiments, which show the absenceof its resist-

2

ox PNEUMATIC MACHINES, 341

ance, of its buoyant effect, and of its pressure; such are the descent of a
guinea and a feather at the same time, the equal duration of the motion of
two fly. wheels, with their plates placed in different directions, the preponder-
ance of the largx-r of two bodies which balance each other in the open air,
the descent of mercury or of water in a barometrical tube, the playing of a
fountain urged by the expansion of a portion of confined air, and the ebul-
lition of etlier, or of water moderately warm. (Plate XXIV. Fig. 32.6,
327.)

The degree of perfection of the vacuum formed by the air pump, or the
rarity of the air remaining in the receiver, is measured by gages of different
kinds. The simplest gage is a short tube filled with mercury, and inverted
in a bason of the same fluid: in this the mercury begins to descend when
the elasticity of the air becomes diminished in the proportion of the height
of the gage to that of the barometer; but on account of the capillary at-
traction of the particles of mercury for each other, there is a depression
within the tube, differing in quantity according to its magnitude, which
renders it difficult to observe the exact situation of the surface when the,
height of the column is very small, although, if that height were correctly
ascertained, the allowance to be made for the depression might easily be
calculated. It is, however, more usual to employ the long barometer gage,
in which the pressure is removed from the upper surface of the column of
mercury in proportion as the exhaustion proceeds, and the height to which
it is raised by the pressure of the external atmosphere, is compared with that
of a common barometer, the difference always indicating the density of the
air left in the receiver. Sometimes also a bent tube is employed instead .of
the short gage, the difference of the height in its two branches indicating,
the pressure ; and this instrument has the advantage of requiring no cor-
rection on account of capillary attraction, since the depressions of the two co-
lumns exactly counterbalance each other. But in all these cases the mercury
must be well boiled in the tubes; and in the bent tube, or siphon gage, the
operation is somewhat difficult.

The pressure indicated by a gage of any kind depends on the elasticity
of the whole of the fluid remaining in the receiver; but this fluid is not
always atmospheric air alone. In all common temperatures, water.

342 LECTURE XXIX.

and many other liquids, have the property of emitting a vapour which pos-
sesses a very sensible degree of elasticity; so that if either water, or any
moist substance, be present under the receiver, it will be impossible to pro-
cure a total absence of pressure, the short mercurial gage commonly stand-
ing at the height of at least half an inch, in the best pumps. Hence, the
vacuum may be made more perfect when the receiver is ground to the plate
of the pump, with the interposition of an unctuous substance, than when
it is placed on wet leather, as it has sometimes been usual to do. The
quantity of atmospherical or incondensable air actually existing in the re-
ceiver, whether mixed with vapour or alone, is measured by means of
Smeaton's pear gage, which is left open under the receiver during the ex-
haustion, and. having its orifice then plunged, by means of a wire passing
through a collar of leather, into a bason of mercury, receives, upon the
readmission of the air, as much of the mercury as is sufficient to fill it, leaving
only in a tube rising from the neck of the gage, the small quantity of air
which had before filled the whole cavity, so that from the space occupied
by this air, compared, by means of previous measurements, with the capacity
of the gage, the degree of exhaustion of the pump with respect to a'lr may be
estimated. It is said that in an air pump of Cuthbertson's construction, such a
rarefaction has been procured that the air sustained but one hundredth part
of an inch of mercury, that is, it was expanded to nearly 3000 times its ori-
ginal bulk. The pear gage often indicates a much more complete exhaus-
tion, but this measurement relates only to the quantity of dry air presenti
(Plate XXIV. Fig. 328.)

♦

A condenser is the reverse of an air pump; and sometimes the same

machine is made to serve for both purposes ; but the condenser requires more
strength than the air pump, and less delicacy. The gage for measuring the
degree of condensation is a small portion of air contained in a graduated
cylindrical tube, the space that it occupies being indicated by a drop of
mercury which confines it. (Plate XXIV. Fig. 329-)

Diving bells were formerly supplied with air by means of barrels let down
continually from the surface of the water, and taken into the bell by the
divers ; but it is now more usual to force down a constant stream by means
of a pump resembling a condenser in its construction and operation : the

ON PNEUMATIC MACHINES. 3i3

heated air is suffered to escape by a stopcock at the upper part of the bell.
When proper care is taken to lower the machine gradually, the diver can
support the pressure of an atmosphere of twice or thrice the natural density.
It would be advisable that every diver should be provided with a float of
cork, or with a hollow ball of metal, which might be sufficient to raise him
slowly to the surface, in case of any accident happening to the bell; for want
of a precaution of this kind, several lives have been lost from confusion in
the signals. (Plate XXIV. Fig. 330.)

Bellows are commonly made of boards connected by leather, so as to
allow of alternately increasing and diminishing the magnitude of their cavities,
the air being supplied from without by a valve. The blast must be inter-
mitted while the cavity is replenished ; and in order to avoid this inconveni-
ence, a second cavity is sometimes added, and loaded with a weight, which
preserves the continuity of the stream. If great uniformity be required in the
blast, it will be necessary to take care that the cavity be so formed as to be
equally diminished while the weight descends through equal spaces ; but not-
withstanding this precaution, there must always be an additional velocity
while the new supply of air is entering from the first cavity. Sometimes the
construction of the bellows resembles that of a forcing pump ; and then, if
the barrel is single, a second barrel, loaded with a weight, must be provided,
in order to equalise the blast : or a vessel inverted in water, and either loaded
or fixed, may supply the place of the second barrel. The first cavity may
also be formed of a similar inverted vessel, suspended to a beam, so as to be
moved up and down in the water, and such a machine is much used, in large
founderies, under the name of hydraulic bellows. The quantity of water em-
ployed may be much diminished, and the operation expedited, by introduc-
ing, in the centre of the inverted vessel, a fixed solid, or an internal inverted
vessel, capable of nearly filling up the cavity of the moveable vessel when
it is in its lowest position, so that the water only occupies a part of the
interstice between the vessels. (Plate XXIV. Fig. 331.)

The gasometer differs little from the hydraulic bellows, except that it is
provided with stopcocks instead of valves, and the moveable cylinder is sup-
ported by a counterpoise, which, in the best kind, acts on a spiral fusee,

VT^TP

LECTURE XXIX.

calculated to correct the difference of pressure arising from the greater or less
immersion of the cylinder. (Plate XXIV. Fig. 332.)

A shower of water, or even an irregular stream, being conveyed through
a descending pipe, plunged into the water of a reservoir, a large quantity
of air is carried down with the water, and rises to the upper part of an in-
verted vessel which surrounds the pipe, whence it may be conveyed through
another pipe, in a rapid stream, for any required purpose; and the water es-
capes at the bottom of the air vessel into the general reservou-, from the
surface of which it runs off. The quantity of air supplied by these shower
bellows is, however, small. (Plate XXIV. Fig. 333.)

The velocity of the blast produced by any pressure, forcing the air through
a pipe of moderate dimensions, may readily be determined from the height of
a column of air equivalent to the pressure. Thus, if the hydraulic bellows
were worked with a constant pressure of 4 feet of water, the velocity would
correspond to a height of about 3300 feet, and the air would move through a
space of about 460 feet in a second. But in this calculation no allowance is
made for any of the causes which diminish in all cases the discharge of fluids,
and the velocity actually observed is only five eighths as great as that which cor-
responds to the height; that is, in the example here given, £85 feet in a
second, when the air escapes through a small orifice; but when it moves in
a pipe, about three fourths, or 345 feet. If the pipe were of considerable
length, there would also be a diminution of velocity on account of friction.
In some bellows actually employed, a pressure equivalent to 9 feet of water is
applied, and in this case the velocity must be about 500 feet in a second.

Bellows may be used for the ventilation of a mine, either by forcing air
into it, or by drawing it out through a pipe connected with the valve.
The wind may also be received by the mouth of a tube a little conical, and
may be made to cause a current where it is conveyed; such an instrument is
sometimes called a windsail, or a horse head. It has been proposed to draw
the air up through a pipe by the lateral, friction of a current of air received
by such a funnel, but the effect would probably be too small to be of much
practical utility.

ON PNEUMATIC MACHINES. iJI'i

A corn fan is turned by the hand, or by machinery ; its simplest operation
is to cause a portion of air to revolve with it, and to create a wind in the di-
rection of its circumference. But when a small fan is made to revolve with
great rapidity, as in Papin's Hessian bellows, the centrifugal force causes
the air admitted at the centre to rush towards the circumference, and to pass
with great velocity through a pipe inserted there. The common ventilator
placed in windows, which revolves in the same manner as a smoke jack, in
consequence of the impulse of a current of air, serves only to retard a little
the entrance of that current, to disperse it in some measure in different di-
rections, and to prevent any sudden increase of the intensity of the draught;
but it has little or no power of acting on the air, so as to prevent the decrease
of the velocity of the current. (Plate XXIV. Fig. 334.)

The operation of heat affords us also a very effectual mode of ventilation.
Its action upon air at common tempeiatures occasions an expansion of
about -j^TT for every degree that Fahrenheit's thermometer is raised; the air
becomes in the same proportion lighter, and the fluid below it is consequently
relieved from a part of its weight : the pressure of the surrounding atmosphere,
therefore, preponderates, and the lighter column is forced upwards. When the
shaft of amine communicates with the external air at two different heights,
there is generally a sufficient ventilation from the difference of the tempera-
tures of the air in the shaft, and of the surrounding atmosphere: for the
temperature of the earth is nearly invariable, it therefore causes the air in
the shaft to be warmer in winter than the external air, and colder in sum-
mer; so that there is a current upwards in winter, and downwards in sum-
mer; and in the more temperate seasons, the alternations take place
in the course of the day and night. For a similar reason, there is
often a current down a common chimney in summer ; but when the fire
is burning, the whole air of the chimney is heated, and ascends the more
rapidly as the height is greater. It would be easy, from the principles
of hydraulics, if the length of the chimney, and the mean temperature
of the air in it were given, to calculate the velocity of the draught: thus,
if the height of the chimney were 50 feet, and the air contained in it
10 degrees hotter than the external air, the expansion would be one fif-
tieth, and the pressure of the whole column being diminished one fif-
tieth, the difference would be equivalent to a column of one foot in height,

VOL, I. " y y

\

346 LECTURE XXIX.

and such a column would represent the pressure causing the draught, which
might, therefore, be expected to have a velocity of 6 feet in a second. If
the room were perfectly closed, the air contained in it would by degrees
become so much lighter than the «xternal air, as would be equivalent to one
foot of the height of the column causing the pressure, and the current
would then stop; if fresh air were gradually admitted by a small ori-
fice, the current would again go on, but the air in the room would always
remain somewhat rarer than the external atmosphere, unless a fresh supply
were admitted through ample openings.

The object of a chimney is not so much to ventilate the room, as to pro-
vide a sufficiently rapid supply of air for maintaining the process of com-
bustion, and to carry off" the products of that process : hence, it is desirable
to allow as little air as possible to enter the chimney without passing through
the fire ; and this is the best general mode of avoiding smoky chimnies.
For wind furnaces, the flue should be as equable as possible, throughout its
height, or widened rather than contracted in its ascent, and free from any
considerable angles.

'»'

The ascent of a balloon is an effect of the same kind as that of air in a
chimney, and arises sometimes from the same cause, when the air within it
is expanded by heat ; but more commonly from the greater rarity of hydro-
gen gas, with which the balloon is filled, and which, when pure, is only one
thirteenth as heavy as atmospherical air, but as it is commonly used, about
one fifth or one sixth.

The steam engine is perhaps the most magnificent effort of mechanical
power; it has undergone successive changes, and it appears to have been
brought very near to perfection by the improvements of Mr. Watt. The
pressure of steam Avas first applied by the Marquis of Worcester, and after-
wards by Savery, to act immediately on the surface of water contained in a
close vessel, and this water was forced, by the elasticity of the steam, to ascend
through a pipe. But a great degree of heat was required for raising water to
any considerable height by this machine : for, in order that steam may be
tnade capable of supporting, in addition to the atmospherical pressure, a
column of 34 feet of water, its temperature must be raised to 248" of Fahieu'-

4

ON PNEUMATIC MACHINES. ' 347

*

heit, and for a column of 68 feet, to i271°; such a pressure, also, acting
on the internal surface of the vessels, made it necessary that they should be
extremely strong; and the height to which water could be drawn up from
below, when the steam was condensed, was limited to 33 or 34 feet. A still
greater objection was, however, the great quantity of steam necessarily
wasted, on account of its coming into contact with the cold water and the
receiver, the surfaces of which required to be heated to its own temperature, '
before the water could be expelled ; hence a tenth or a twentieth part only
of the steam produced could be effective ; and there would probably have
been a still greater loss, but for the difficulty with which heat is conducted
downwards in fluids. These inconveniences were in great measure avoided
in Newcomen's engine, where the steam was gradually introduced into a
cylinder, and suddenly condensed by a jet of water, so that the piston was
forced down with great violence by the pressure of the atmosphere, which pro-
duced the effective stroke: this effect was, iiowever, partly employed in rais-
ing a counterpoise, which descended upon the readmission of the steam, and
worked a forcing pump in its return, when water was to be raised. The
condensation, although rapid, was, however, neither instantaneous, nor
complete, for the water injected into the cylinder had its temperature
considerably raised by the heat emitted by the steam during its condensation ;
it could only reduce the remaining steam to its own temperature, and at
this temperature it might still retain a certain degree of elasticity; thus, at
the temperature of 180° steam is found to be capable of sustaining about
half the pressure of the atmosphere, so that the depression of the piston
must have been considerably retarded by the remaining elasticity of the steam,
when the water was much heated. The water of the jet was let off when the
piston was lowest, and was afterwards pumped up to serve the boiler, as it had
the advantage of being already hot. This engine, with Beighton's apparatus for
turning the cocks, was until lately in general use, and it is still very frequently
employed. In this, as well as in other steam engines, the boiler is furnished
with a safety valve, which is raised when the force of the steam becomes a little
greater than that of the atmospheric pressure; and it is supplied with water by
means of another valve, which is opened, when the surface of the water within
it falls too low, by the depression of a block of stone, which is partly supported
by the water. (Plate XXIV. Fig. 335, 336.)

348 LECTURE XXIX.

The cylinder of Beighton's machine is ne_cessarily much cooled by the ad-
mission of the jet, and by exposure to the air. Mr. Watt has avoided this in-
convenience by performing the condensation in a separate vessel, into which
a small jet is flowing without intermission ; and by introducing the steam
alternately above and below the piston, the external air is wholly excluded ;
the piston rod working in a collar of leathers, so that the machine has a
double action, somewhat resembling that of Lahire's double pump; and the
stroke being equally effectual in each direction, the same cylinder, by means
of an increased quantity of steam, performs twice as much work as in the
common engine. We might also employ, if we thought proper, a lower
temperature than that at which water usually boils, and work in this man-
ner with a smaller quantity of steam; but there would be some difficulty in
completely preventing the insinuation of the common air. On the other
hand, we may raise the fire so as to furnish steam at 220° or more, and thus
obtain a power somewhat greater than that of the atmospheric pressure; and
this is found to be the most advantageous mode of working the engine; but
the excess of the force above the atmospheric pressure cannot be greater than
that which is equivalent to the column of water descending to supply the
boiler, since the water could not be regularly admitted in opposition to such
a pressure. The steam might also be allowed to expand itself within the cy-
linder for some time after its admission, and in this manner it appears from
calculation that much more force might be obtained from it than if it were
condensed in the usual manner as soon as its admission ceases; but the
force of steam thus expanding is much diminished by the cold which always
accompanies such an expansion, and this method would be liable to several
other practical inconveniences.

The peculiarities of Mr. Watt's construction require also some other ad-
ditional arrangements; thus, it is necessary to have a pump, to raise not only
the water out of the condenser, but also the air, which is always extricated
from the water during the process of boiling. If the water employed has
been obtained from deep wells or mines, it contains more air than usual, and
ought to be exposed for some time in an open reservoir before it is used ; for it ap-
vpears that the quantity of air, which can be contained in water, is nearly in propor-
■*^ion to the pressure to which it is subjected. The admission of the steam into

ON PNEUMATIC MACHINES. 349

the cylinder is regulated by the action of a double revolving pendulum.
The piston is preserved in a situation very nearly vertical by means of a
moveable parallelogram, fixed on the beam, which corrects its curvilinear
motion by a contrary curvature. In the old engines, a chain working on an
arch was sufficient, because there Avas'no thrust upwards. When a rotatory
motion is required, it may be obtained either by means of a crank, or of a sun
and planet wheel,with.the assistance of a flywheel; this machinery is generally
applied to the opposite end of the beam; but it is sometimes immediately con-
nected with the piston, and the beam is not employed. The cylinder is usually
inclosed within a case, and the interval is filled with steam, which serves to
confine the heat very effectually. (Plate XXIV. Fig. 337.)

The steam engines of Messrs. Boulton and Watt are said to save three fourths
of the fuel formerly used ; and it appears that only one fourth of the whole
force of the steam is wasted. Such a machine, with a thirty inch cylinder,
performs the work of 120 horses, working 8 hours each in the day.

When the water producing the condensation is to be raised from a great
depth, a considerable force is sometimes lost in pumping it up. Hence,
Mr. Trevithick has attempted, as Mr. Watt had indeed long before pro-
posed, to avoid entirely the necessity of condensation, by employing steam
at a very high temperature, and allowing it to escape, when its elasticity is
so reduced by expansion, as only to equal that of the atmosphere: the air
pump is also unnecessary i;i this construction, and for a small machine, it may
perhaps succeed tolerably well. But there must always be a very consi-
derable loss of steam, and although the expense of fuel may not be increased
quite in the same proportion as the elasticity of the steam, yet the differ,
ence is probably inconsiderable. A great number of less essential alterations
have also been made in Mr. Watt's arrangements by various engineers, but
they have generally been calculated either for obtaining some subordinate
purpose of convenience, or for imposing on the public by a fallacious appear-
ance of novelty. (Plate XXIV. Fig. 338.)

The force of steam, or of heated vapour, is probably also the immediate
agent in the astonishing effects produced by the explosion of gunpowder.
The initial elasticity of the fluid by which a cannon ball is impelled, ap-

350 LECTURE XXIX.

pears, from Bernoulli's calculation, to be at least equal to ten thousand times
the pressure of the atmosphere, and upon the most moderate computation,
from Count Rumford's experiments, to be more than three times as great as
this. The quantity of moisture, or of water of crystallization, contained in
the powder, is certainly too small to furnish steam enough for so great an
effect. We have no reason to suppose that the elasticity of a given quantity
> of any aeriform fluid or vapour is increased more than about one fivehundreth
for each degree of Fahrenheit that its temperature is elevated ; and if wt
suppose the heat to be raised to more than 5000 degrees, the force of each
grain of water converted into steam will only be increased tenfold ; so that
if the elasticity were 40 thousand times as great, the density must be 4
thousand times as great as that of ordinary steam, and the whole space must
be filled with an aqueous vapour almost twice as dense as water itself. It is,
therefore, probable that some other parts of the materials assume, together
with the water, the state of vapour, and possess in this form a much greater
elasticity than that of the steam: for the quantity of fluids permanently-
elastic, which are extricated, must be allowed to be wholly inadequate to the
effect.

The force of fired gunpowder is found to be very nearly proportional to
the quantity employed ; consequently, if we neglect the consideration of the
resistance of the atmosphere, the square of the velocity of the ball, the
height to which it will rise, and its greatest horizontal range, must be di-
rectly as the quantity of powder, and inversely as the weight of the ball.
Count Rumford, however, found that the same quantity of powder exerted
somewhat more force on z large ball than on a smaller one.

The essential properties of a gun are to confine the elastic fluid as com-
pletely as possible, and to direct the motion of the bullet in a rectilinear path ;
and hence arises the necessity of an accurate bore. The advantage of a rifle
barrel is principally derived from the more perfect contact of the bullet with
its cavity; it is also supposed to produce a rotation round an axis in the di-
rection of its motion, which renders it less liable to deviations from its path on
account of irregularities in the resistance of the air. The usual charge of
powder is one fifth or one sixth of the weight of the ball, and for battering

ON PNEUMATIC MACHINES. 351

one third. When a 24 pounder is fired with two thirds of its weight of powder, it
may be thrown almost four miles, the resistance of the air reducing the
distance to about one fifth of that which it would describe in a vacuum.

r
Bullets of all kinds are usually cast in separate moulds: shot are granu-
lated by allowing the lead, melted wilh a little arsenic, to pass through
perforations in the bottom of a vessel, and to drop in a shower into water.
The patent shot fall in this process through a height of 120 feet: the round-
est are separated by rolling them down an inclined plane slightly grooved,
those which are of an irregular form falling off at the sides.

Condensed air may also be employed for propelling a bullet by means of
an air gun, an instrument of considerable antiquity, but of little utihty. It
is obvious that no human force can so far increase the density of air as to
make its elasticity at all comparable to that of the fluid evolved by
fired gunpowder, and even if it were reduced to such a state, its effects
would still be far inferior to those of gunpowder; for the utmost velocity,
with which it could expand itself, would not exceed 1300 feet in a second,
and it would, therefore, be incapable of imparting to a ball a velocity even
as great as this, while the vapour of gunpowder impels a heavy ball with a
velocity of more than 2000 feet in a second. When, however, it is consi-
dered that by far the greatest part of such a velocity as this is uselessly em-
ployed, and that the mechanical power which is practically obtained from
gunpowder is much more expensive than an equivalent exertion of any of the
ordinary sources of motion, it must be allowed that the force of condensed
air may possibly be applied in some cases, with advantage, as a substitute for
that of gunpowder. (Plate XXIV. Fig. 339.)

352

LECTURE XXX.

ON THE HISTORY OF HYDRAULICS AND PNEUMATICS.

Notwithstanding a few observations and experiments made by
Aristotle and his predecessors, the properties of fluids had scarcely been the
subjects of much .accurate investigation before the time of Archimedes. The
progress, which the science of hydrostatics in particular made under this
eminent mathematician, does the highest honour to his genius and penetra-
tion. His treatise on floating bodies, although the theorems which it con-
tains are not so general as they have been rendered since the late improse-
ments in the methods of calculation, still affords us instances of very in-
genious determinations of the equilibrium of floating bodies of different
forms, grounded on the true principles of the opposition of the general direc-
tions of the weight of the body and of the pressure of the fluid ; and in this man-
ner he has shown in what cases the equilibrium of conical and conoidal solids
will be stable, and in what cases unstable. Archimedes was the inventor of
the mode of measuring the bulk of a solid by immersing it in a fluid: to us,
indeed, there appears to have been little difficulty in the discovery, but the
ancients thought otherwise. Vitruvius observes that this invention indicates
a degree of ingenuity almost incredible. The philosopher himself is said to
have valued it is so highly, that when it first occurred to him, in a public
bath, he hastened home in an ecstasy, without recollecting to clothe him-
self, in order to apply it to the determination of the specific gravity of
Hiero's crown, and to the detection of the fraud of the maker, who had re-
turned the crown equal in weight to the gold that was given him, but had
adulterated it with silver, and imagined, that on account of the complicated
form of the work, Avhich rendered it almost impossible to determine its bulk
by calculation, he must infallibly escape conviction. The hydrometer,
which has sometimes been attributed to Hypatia, a learned Greek lady of

ON THE HISTORY OF HYDEAULICS AND PNEUMATICS. 353

Constantinople, is mentioned by Fannius, an early writer on weights and
measures, and is ascribed by him to Archimedes.

The forcing pump, or rather the fire engine, was the invention of Ctesibiusof
Alexandria, the greatest mechanic of antiquity after Archimedes. He is
also said to have invented the clepsydra, for the hydraulic measurement of
time, and Philo informs us that he constructed an air gun, for propelling
a stone, or rather a ball, by means of air, previously condensed by a syringe.
The ball was not immediately exposed to the action of the air, but was im-
pelled by the longer end of a lever, while the air acted on the shorter.
Ctesibius is said to have been the son of a barber, and to have had his at-
tention turned to mechanics and pneumatics, by being employed to fit a
shutter, with a counterpoise sliding in a wooden pipe, for his father's shop
Avindow.

Hero was a cotemporary, and a scholar of Ctesibius; he describes, in his
treatise on pneumatics, a number of very ingenious inventions, a few of
which are calculated for utility, but the greater part for amusement only;
they are principally siphons variously concealed and combined, fountains,
and water organs, besides the syringe and the fire engine. The description
of this engine agrees precisely with the construction which is at this day
the most usual ; it consists of two barrels, discharging the water alternately
into an air vessel; and it appears from Vitruvius, that this was the
original form in which Ctesibius invented the pump. Hero supposes the
possibility of a vacuum in the intervals of the particles of bodies, ob-
serving that without it no body could be compressible; but he imagines that
a vacuum cannot exist throughout a perceptible space, and thence derives the
principle of suction. The air contained in a given cavity may be rarefied,
he says, by sucking out a part of it, and he describes a cupping instrument,
Avhich approaches very nearly to the nature of an imperfect air pump.
(Plate XXIV. Fig. 324.)

After the time of Ctesibius and Hero, the science of hydraulics made
little further progress, until the revival of lette;rs. The Romans had water
mills in the time of Juhus Caesar, which are described by Vitruvius; and
it appears that their ac[ueducts were well built, and their waterpipes well

VOL. I. z z

354 LECTURE XXX.

arranged. Pipes of lead were, however, less frequent than at present, from
an apprehension of the poisonous quality of the metal, which was not wholly
without foundation. Some say that the ancients had no chimnies, but
whatever may be the authorities, the opinion is extremely improbable.

It was in the middle ages that navigable canals began to be considerably
multiplied, first in China, and afterwards in other parts of the world. The
canal from the Trent to the Witham, which is the oldest in England, is said
to have been dug in 1134. The date of the earliest windmills has been re-
ferred to the year 1299. The invention of gunpowder possesses perhaps an
equal claim with theartof printing, to the honour of being considered as consti-
tuting the most marked feature, that distinguishes the character of ancient from
that of modern times; its introduction must necessarily have tended to
produce material alterations, and perhaps improvements, in the habits of
nations and of individuals. It is said to have been known long since to the
Chinese, and our countryman Roger Bacon was evidently acquainted with
its properties; but it was not actually employed in Europe or in its neighbour,
hood till about the year 1 330 ; and the earliest artillery appears to have been
that which was used by the Moors, at the siege of Algesiras, in 1334. King
Edward had four pieces of cannon at the memorable battle of Cressy, in
1346.

About the year 1600, Galileo made the important discovery of the eflPects of
the weight and pressure of the atmosphere, in the operation of suction, and in
various other phenomena. Before his time, it was generally supposed that
water was raised by a sucking pump, on account of the impossibility of the
existence of a vacuum : if, however, a vacuum had been impossible in'na-
ture,the water would have followed the piston to all heights.however great, but
Galileo found that the height of its ascent was limited to about 34 feet, and con-
cluded that the weight of a column of this height was the measure of the magni-
tude of the atmospherical pressure. His pupil Torricelli afterwards confirmed
the explanation, by showing that a column of mercury was only supported
when its weight was equal to that of a column of -water standing on the
same base; hence the vacuum obtained by means of mercury is often called
the Torricellian vacuum. Torricelli corrected also, in 1644, the mistake of
Castelli respecting the quantities of water discharged by equal orifices, at

OK THE HISTORY Of HYDRAULICS AND PNEUMATICS. 535

difterent distances below the surface of the water in the reservoir. Castelli's
experiments, made about \6iO, were the first of the kind, and some of
them really tended to the improvement of the science of hydraulics,
but others appeared to show, that a double height of the head of water
produced a double discharge. Torricelli's more accurate observations
proved that a quadruple height was required in order to produce a double
velocity; and his assertions were afterwards fully confirmed by Mariotteand
by Gughelmini.

A little before the year l65i, Otto von Guericke, of Magdeburg, first
constructed a machine similar to the air pump, by inserting the barrel of a fire
engine into a cask of water, so that when the M'ater was drawn out by the
operation of the piston, the cavity of the cask remained nearly void of all
material substance. But finding that the air rushed in between or through
the staves of the cask, he inclosed a smaller cask in a larger one, and made
the vacuum in the internal one more complete, while the intervening space
remained filled with water; yet still he found that the water was forced into
the inner cask through the pores of the wood. He then procured a sphere of
copper, about two feet in diameter, and was exhausting it in the same way,
when the pressure of the air crushed it, with a loud noise. This machine
was more properly a water pump, than an air pump, but the inventor soon
after improved his apparatus, and made all the experiments which are to this
day the most usually exhibited with the air pump, such as the apparent
cohesion of two exhausted hemispheres, the playing of a jet by means of the
expansion of a quantity of air inclosed in a jar, the determination of the
air's weight, and others of a similar nature. He also observed, that for
very accurate experiments; the valve of the pump might be raised at each
stroke by external force; and he particularly noticed the perpetual production
of air, from the water that he generally employed, which caused an imper-
fection in the vacuum. An account of his experiments was first published
in different works, by Caspar Schott, and afterwards by himself, in his
book intitled Experimenta nova Magdeburgica, printed in 1672 at Am-
sterdam.

In the year 1658, Hooke finished an air pump for Boyle, in whose la-

356 lECTURK XXX.

boratory he was an assistant: it was more convenient than Guericke's, but
the vacuum was not so perfect; yet Boyle's numerous and judicious experi-
ments gave, to the exhausted receiver of the air pump, the name of the Boy-
lean vacuum, by which it was long known in the greatest part of Europe.
Hooke's air pump had two barrels, and with some improvements by Hauks-
bee, it remained in common use, until the introductiian of Smeaton's pump,
which, however, has not wholly superseded it. The theory of pneumatics
was also considerably indebted to Hooke's important experiments on the
elasticity of the air, which were afterwards confirmed and extended by
Mariotte and Amontons,in France, by Hales in this country, and by Richmann
at Petersburg.

About the same time the first steam engine was constructed, by the cele-
brated Marquis of Worcester. Hints of the possibility of such a machine had
been given a hundred years before, by Matthesius, in a collection of sermons
intitled Sarepta, and at a subsequent period by Brunau ; but the Marquis of
Worcester professes to have carried the project into full effect, as we are inform*-
ed by his account of what he called a fire water work, which is one of his
Century of Inventions, first published in 1663, and which is thus described:
" I have taken a piece of a whole cannon, whereof the end was burst,and filled it
three quarters full of water, stopping and screwing up the broken end, as
also the touch hole; and making a constant fire under it, within 24 hours
it burst, and made a great crack: so that having a way to make my vessels,
so that they are strengthened by the force within them, and the one to fill
after the other, I have seen the water nin like a constant fountain stream
forty foot high. One vessel of water, rarefied by fire, driveth up forty of
cold water ; and a man that tends the work is but to turn two cocks, that
one vessel of water being consumed, another begins to force and refill with
cold water, and so successively, the fire being tended and kept constant,
which the self same person may likewise abundantly perform in the interim
between the necessity of turning the said cocks." The machine was, how-
ever, not at that time practically introduced, and it was soon forgotten ;
Savery's engines were constructed in a manner precisely similar, some time
before 1700; and it is uncertain whether he adopted the Marquis of
Worcester's ideas, or reinvented a similar machine. About 1/10, the piston
4

ox THE HISTORT OF HYDRAULICS A^'D PNEUMATICJ. ~ S57

and cylinder were invented by Newcomen, and with Beighton's apparatus for
turning the cocks by its own motion, the engine remained nearly stationary
for many years.

As early as the year 1667, the pressure of fluids in motion, and the resist-
ance opposed by fluids at rest to the motion of solid bodies, were experi-
mentally examined by Huygens, and some other members of the Parisian
Academy. Pardies, whose works were published in 1673, attempted to
determine, although upon some inaccurate suppositions, the effects of the
wind on a ship's sails, under different circumstances. His principles were
adopted by Renaud, who published a work on the subject in 1689; their im-
perfections were, however, soon after pointed out by Huygens, and by
James Bernoulli; and in 1714', John Bernoulli published an extensive
treatise on the manoeuvres of ships, which at last compelled Renaud to sub-
mit to so many united authorities.

It must be confessed, that the labours of Newton added fewer improve-
ments to the doctrines of hydraulics and pneumatics, than to many other
departments of science; yet some praise is undeniably due both to his com-
putations and to his experiments relating to these subjects. No person
before Newton had theoretically investigated the velocity with which fluids
are discharged, and although his first attempt was unsuccessful, and the
method Avhich he substituted for it in his second edition is by no means free
from objections, yet either of the determinations may be considered in some
cases as a convenient approximation ; and the observation of the contrac-
tion of a stream passing through a simple orifice, which was then ngw,
serves to reconcile them in some measure with each other. His modes
of considering the resistance of fluids are far from being perfectly just,
yet they have led to results which, with proper corrections, ai-e tolerably
accurate; and his determination of the oscillations of fluids, in bent tubes,
was a good beginning of the investigation of their alternate motions in
general. . ,

o

The accurate experiments of Poleni were published in 1718: he has the
merit of having first distinctly observed that the quantity of water, discharg-
"ed by a short pipe, is greater tliau by a simple orifice of the same diameter;

/

358 LECTunE XXX.

although there is some reason to suppose that Newtow was before acquainted
with the circumstance.

In 1727, Mr. Bouguer received a prize from the academy of Paris for his
essay on the masts of ships, which is said to be ingenious, but by no means
practically useful. He was probably tempted by this encouragement to con-
tinue his application to similar studies, and about twenty years afterwards
he published his valuable essay on the construction and manoeuvres of ships,
which appears to have superseded all that had been done before respecting the
subjects of his investigation.

The first researches of Daniel Bernoulli, concerning the properties and mo-
tions of fluids, bear also the date of 1727. This justly celebrated man was as
happy in his application of mathematies to natural philosophy, as he was
ready and skilful in his calculations. The greatest part of his hydraulic
theorems are founded on the principle first assumed by Huygens, and called
by Leibnitz the law of living or ascending force, which is confessedly only
true where there is no loss of velocity, from the imperfection of the elasti.
city of the bodies concerned ; for it is only with this limitation, that the mo-
tions of any system of bodies are always necessarily such, as to be capable of
carrying the common centre of gravity to the height, from which it has des-
cended, while the bodies have been acquiring their motions. This law of
ascending force is of considerable utility in facilitating the solution of a great
variety of problems ; it is certain that mechanical power is always to be es-
timated by the product of the mass of a body into the height to which it is
capable of ascending; and whatever objections may have been made to the
employment of this product as the measure of the force of a body in motion,
which is indeed an expression inconsistent with a correct definition of the term
force, yet it must be confessed, on the other hand, that some of the best
English mathematicians have fallen into material errors for want of paying
sufficient attention to the general principle. Bernoulli estimates very justly
in this manner the mechanical power of a variety of natural and artificial
agents, and among the rest, he examines that of gunpowder ; but from an
accidental combination of errors, he states the force of a pound of gunpow-
der, as equivalent to the daily labour of 100 men, vvhile in fact the effect
which is actually obtained from two tons of powder is no greater than that

ON THE HISTORY OF HYDRAULICS AND PNEUMATICS. 359

which is here attributed to a pound. His calculations of the motions of
fluids, in some very intricate cases, are very ingenious and satisfactory, and
they are in general sufficiently confirmed by well imagined experiments. He
examines the force of the Avind acting on the sails of a windmill, but by
another mistake in calculation, which Maclaurin has detected, of two angles
which answer the conditions of the determination, he has taken the wrong
one, and assigned that position of the sail as the most effectual, which pro-
duces absolutely no effect at all.

It may be objected to Bernoulli's calculations, that some of the circum-
stances which are necessarily neglected in them, produce a very material effect
in the results of all experiments; but it must be allowed that the corrections
required, on account of this unavoidable omission, may easily be deduced
from simple experiments, and then applied to the most complicated cases.
It is, however, a more material objection, that the fundamental law of the
preservation of ascending force can only be adopted with certain limitations;
thus, when a small stream passes through a large reservoir, Bernoulli is
obliged to suppose the whole of its force consumed by the resistance which it
meets. The immediate mode, in which the accelerating forces must be sup-
posed to act, remains also wholly undetermined; and it was principally for
this reason, that John Bernoulli attempted to substitute, for his son's calcula-
tions, a method of deducing the motions of fluids more immediately from the
gravitation of their different parts. The peculiarity of- John Bernoulli's
mode of investigation consists in his imagining the weight of each indi-
vidual particle to be transferred to the surface of the fluid, causing there a
pressure in the direction of gravity; and he examines the manner in which
this force must operate, in order to produce every acceleration which is re-
quired for the motion of fluids, in vessels of all imaginable forms.

Maclaurin, in his treatise of fluxions, investigated several of the proper-
ties of fluids in his usual concise and elegant manner. His remarks on the
positions of the sails of windmills and of ships are peculiarly interesting: he
added much to what had been done respecting the effects of the wind, and
showed the possibility of arranging the sails of a ship in such a manner as to
make her advance with a greater velocity than that of the wind itself. At
that time, however, the science of hydraulics had been too little assisted by

$60 LECTDRE XXX.

experiments to be capable of affording determinations of all questions which
are of very frequent occurrence in practice. AnappHcation was made to Mac-
laurin, and at the same time to Desaguhers, a man of considerable eminence
in the mechanical sciences, respecting the quantity of water that might be
brought, by a train of pipes of certain dimensions, to the city of Edinburgh.
The project was executed with a confidence founded on their opinions, but
the quantity actually obtained was only about one sixth of Desaguliers's cal-
culation, and one eleventh of Maclaurin's. At a still later period, the
French Academicians were consulted respecting a great undertaking of a
similar nature; and their report was such as to dissuade the projectors from
making the attempt, which was consequently at the point of being abandoned,
till a celebrated practical architect insisted, from a rough estimation, deduced
from his general experience, that more than double the quantity assigned
by the Academicians might be obtained; and the event justified his
assertion.

The experiments and calculations of Robins, respecting the resistance of
the air, and the operation of gunpowder, deserve to be mentioned with com-
mendation on account of their practical utility ; but he appears to have been
less successful in his theoretical mvestigations than Daniel Bernoulli had
been a few years before.

Dalembert attempted, in his treatise on the motions of fluids, which was
published in 1744, to substitute, for the suppositions of John Bernoulli, a
more general law, relating to all changes produced in the motions of a system
of bodies, by their mutual actions on each other ; but his calculations are
more intricate, and less easily understood, than some others, which are
capable of an application equally extensive. 'The late Professor Kaestner of
Gottingen has defended Bernoulli against Dalembert's objections with some
success, and has in many instances facilitated and extended Bernoulli's
theory ; but there is often a singular mixture of acuteness and prolixity in
this author's works. By the side of an intricate and difficult fluxional calcu-
lation, he inserts along string of logarithms for performing a simple multi-
plication; and in a work which comprehends the whole range of the mathe-
matical sciences, he does not venture to determine the square root of 10 with-
out quoting an authority.

ON THE HISTORV OF HrDRAULrCS AND PNEUMATICS. 361

About the same time, the profound Leonard Euler applied himself, with
some success, to the examination of the motions of fluids, particularly as
they are connected with the subjects of seamanship and naval architecture;
but the investigations of Euler are in general more remarkable for raathe-
inatical address, than for philosophical accuracy and practical application;
although his calculation of the resistance of the air to the motions of pro-
jectiles may be employed with considerable advantage by the gunner.

The beginning of the modern experimental improvements in hydraulics
may perhaps be dated from the investigations of Smeaton respecting the
effects of wind and water, which were published in the Philosophical Trans-
actions for 1759. His observations are of material importance, as far as they
are capable of immediate application to practice, but he has done little to il-
lustrate their connexion with the general principles of mechanics. It was
JVIr, Borda that first derived from a just theory, about 10 years after, the
same results, respecting the effects of undershot water wheels, as Smeatoil
had obtained from his experiments. Before this time, the best essay on the
subject of water wheels was that of Elvius, published in 1742; his calcula-
tions are accurate and extensive; but they are founded, in great measure,
on the imperfect suppositions respecting the impulse of a stream of water,
which were then generally adopted.

Our countryman Mr. "Watt obtained, in 17^9, a patent for his improre-
ments of the steam engine, which includes almost every essential change
that has been made since the time of Beighton. On a subject so important,
it cannot be superfluous to insert the words of the inventor, whose admiraWc
application of the sciences, to practical purposes, most justly entitles him to
a rank among philosophical mechanics, not inferior to that of Ctesibius a!i»d
Dr. Hooke.

** My method of lessening the consumption of steam, and consequently
fuel, in fire engines," says Mr. Watt, in his specification of his patent, " con-
sists of the following principles. First, that vessel in which the powers of
steam are to be employed, to work the engine, which is called the cylinder
in common fire engines, and which I call the steam vessel, must, during
the whole time the engine is at work, be kept as hot as the steam that

VOL I. 3 a

362 LECTURE XXX.

enters it; first, by inclosing it in a case of wood, or any other materials that
transmit heat slowly; secondly, by surrounding it with steam, of other heated
bodies; and thirdly, by suffering neither water, nor any other substance
colder than the steam, to enter or touch it during that time. Secondly, in
engines that are to be worked wholly or partially by condensation of steam,
the steam is to be condensed in vessels distinct from the steam vessels, or cy-
linders, although occasionally communicating with them ; these vessels I
call condensers; and, whilst the engines are working, these condensers
ought at least to be kept as cold as the air in the neighbourhood of the en-
gines, by application of water, or other cold bodies. Thirdly, whatever air or
other elastic vapour is not condensed by the cold of the condenser, and may
impede the working of the engine, is to be drawn out of the steam vessels, or
condensers, by means of pumps, wrought by the engines themselves, or
otherwise. Fourthly, .1 intend, in many cases, to employ the expansive
force of steam to press on the pistons, or whatever may be used instead of
them, in the same manner as the pressure of the atmosphere is now employed
in common fire engines: in cases where cold water cannot be had in plenty,
the engines may be wrought by this force of steam only, by discharging the
steam into the open air after it has done its office. Fifthly, where motions
round an axis are required, I make the steam vessels in form of hollow
rings, or circular channels, with proper inlets and outlets for the steam,
mounted on horizontal axles, like the wheels of a water mill; within them
are placed a number of valves, that suffer any body to go round the channel
in one direction only ; in these steam vessels are placed weights, so fitted to
them as entirely to fill up a part or portion of their channels, yet capable
of moving freely in them by the means herein after mentioned or specified.
When the steam is admitted in these engines, between the weights and the
valves, it acts equally on both, so as to raise the weight to one side of the
wheel, and, by the reaction of the valves, successively, to give a circular
motion to the wheel, the valves opening in the direction in Avhich the
weights are pressed, but not in the contrary; as the steam vessel moves
round, it is supplied with steam from the boiler, and that which has per-
formed its office may either be discharged by means of condensers, or into
the open air. Sixthly, I intend, in some cases, to apply a degree of cold,
not capable of reducing the steam to water, but of contracting it considera-
bly, so that the engines may be worked by the alternate expansion and con-

ON THE HISTORY OF HYDRAULICS AKD PNEUMATICS. 363

traction of the steam. Lastly, instead of using water to render the piston or
other parts of the engines air and steam tiglit, I employ oils, wax, resinous
bodies, fat of animals, quicksilver, and other metals, in their fluid state."

It is probable that the rotatory engines described by Mr. Watt, although
they appear to produce some advantage in theory, will never be generally
introduced, on account of the diflficulty of constructing steam vessels so
large, and of so complicated a form, as would be necessary, in order to give
full effect to the machine. The term of this patent was prolonged by act of
parliament until the year 1799 ; but although the legal privilege of the ori-
ginal manufacturers is expired, yet the superiority of their workmanship still
gives thfeir engines a decided preference.

Much of the labour of the later writers on hydraulics has been employed
en the determination of the resistance of fluids to bodies of different forms,
which move through them; a subject which derives great importance from
its immediate application to the manoeuvres of ships. The most ex-
tensive experiments on these subjects were made by Bossut, and
some other members of the Academy of Sciences. About the same time Don
George Juan, a gentleman who had enjoyed the best possible opportunity
for actual observation and practical study in serving with Ulloa, published
at Madrid his Examen Maritime, which appears to be the most ingenious
and useful treatise on the theory and practice of seamanship that has yet
appeared. But unfortunately his deductions, however refined and diversi-
fied, are principally founded on a mistaken theory respecting the effects of
hydraulic pressure; since he tacitly assumes, in his fundamental proposition
on the subject, that a double force, acting in a given small space, will pro-
duce a double velocity; while it is well known that in such clrcuinstances
a quadruple force would be required. Hence he derives some conclusions
which indicate that the resistance must vary very materially at different
depths below the surface of the water, and alleges In support of the assertion
a few imperfect experiments of Mariotte and of his own, in which some acci-
dental circumstances not noticed may easily have caused great irregularities.
Mr. Prony, in his Architecture Hydraulique, appears to have followed Juan ;
and Professor Robison very justly observes, in speaking of this work, that
if the pressure of the water alters the magnitude of tlve resistance at different

3^4 LECTURE XXX.

^pths> that of the atmosphere ought by no means to be omitted in the cal-
culation. But if a more correct mathematician and mechanic would take the
pains to model Juan's book anew, to correct his errors, and to adapt his
modes of calculation to the laws of resistance previously deduced from ac-
curate experiments rather than from theory, there is no doubt but that the
work thus modified might essentially improve the science of seamanship.
He alleges indeed that the results of his calculations are in almost every in-
stance rigidly conformable to observation and experience, but it is probable
that where such a coincidence really exists, it must i)e owing to some com-
bination of errors compensating each other; and it is indeed very possible
that his calculations, with all their errors, may approach nearer to the truth
than the imperfect approximations which had been before employed. Juan
has generally made use of the English weights and measures, on account of
their convenience in computations respecting the descent of falling bodies
^nd the impulse of water.

The works of Chapman and of Romme, upon various departments of sea-
manship, possess also considerable merit. These authors appear to have
avoided the errors of Juan, but without entering so minutely into the detail
of nautical operations as he lias done.

The accurate experiments of Dr. Hutton and of ('ount Rumford on the
force of fired gunpowder, and the resistance of the air, deserve to be men-
tioned as affording valuable materials to the speculative investigator, and
useful information to the practical gunner. Robins had very erroneously
supposed that the whole of the effects of gunpowder might be derived from the
expansive force of fluids permanently elastic; but Vandelli soon after main-
tained a contrary opinion in the commentaries of Bologna, and Count Rum-
ford has very satisfactorily shown the insufficiency of the agents considered
by Robins, although he has been unsuccessful in attempting ta deduce th»
■whole force from the elasticity of aqueous vapour alone.

The theory of practical hydraulics, as affected by friction, may be consir
dered as having been began and completed by the highly meritorious labours
of the Chevalier du Buat. He had some assistance in expressing the results
of hh experiments by meana of general rules or formulae^, aad. these, air

ON THE HISTORY OF HTDRAUIICS AND PNEUMATICS. 365

though they agree sufficiently well with the experiments, have not always
been reduced to the simplest and most convenient forms ; nor have they been
much improved either by Langsdorf or Eytelwein in Germany, or by Robi-
son in this country, who have gone over nearly the same ground with each
other, and have shown the way in which the results of Buat's investigations
may be applied to a variety of cases, which occur in hydraulic architec-
ture.

One of the latest inventions, which require to be mentioned in speaking of
the history of pneumatics, is that of the aerostatic globe or air balloon.
The suggestions of Lohmeier, of Albertus, and of Wilkins, respecting the
various modes of passing through the air, had long remained disregarded as
idle speculations; and Rosnier, who, in the l/th century, descended ob-
liquely over some houses, by means of wings, was wholly unable to employ
them in ascending. Dr. Black had exhibited in his lectures a bladder fdled
with hydrogen gas, and floating in the air by means of its smaller specific
gravity, many years before Montgolfier conceived the idea of applying a si-
milar machine to the elevation of human beings into the aerial regions. It
was in 1783 that this project was first executed, and persons of a warm ima-
gination were disposed to believe that the discovery would be of great import-
ance to the convenience of mankind. But if we coolly consider the magni-
tude of the force with which the wind unavoidably impels a surface so large
as that of a balloon, we shall be convinced of the absolute impossibility of
counteracting it, in such a manner, as to direct the balloon in any course,
materially different from that of the wind which happens to blow. With
this limitation, the invention may still in some cases be capable of utility,
wherever we are only desirous of ascending to a great height, without re-
garding the place in which we are to descend : or where we wish to attain
only a height so moderate that the machine may be kept by ropes in the
situation which is desired. In France the balloon has lately been employed
with considerable success as a meteorological observatory ; Mr. Blot and Mr.
Gay Lussac having ascended to a height of above four miles, for the laudable
purpose of ascertaining some facts relating to the constitution of tlie atmosphere,
and to the magnetic properties of the earth.

366

LECTURE XXX.

CHRONOLOGY OF AUTHORS ON HYDRODYNAMICS.

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367

LECTURE XXXI.

ON THE PROPAGATION OF SOUND.

-L HE theory of sound, which constitutes the science of acustics, is on many
accounts deserving of particular attention, for it not only involves many in-
teresting properties of the motions of elastic substances, but it also affords
us considerable assistance in our physiological inquiries respecting the nature
and operation of the senses. The subject has usually been considered as ex-
ceedingly abstruse and intricate, but the difficulty has in some measure ori-
ginated from the errors which were committed in the first inquiries respect-
ing it; and many of the phenomena belonging tO it are so remarkable, and
so amusing, as amply to repay the labour of examining them by the enter-
tainment that they afford. We shall consider first the nature and propaga-
tion of sound in general, secondly, the origin of particular sounds, and the
effects of single sounds; thirdly, the consequences of the combinations of
sounds variously related, constituting the doctrine of harmonics, and
fourthly, the construction of musical instruments, and the history of the
science of acustics.

Sound is a motion capable of affecting the ear with the sensation peculiar
to the organ. It is not simply a vibration or undulation of the air, as it is
sometimes called ; for there are many sounds in which the air is not concern-
ed, as when a tuning fork or any other sounding body is held by the teeth:
nor is sound always a vibration or alternation of any kind; for every noise is
a sound, and a noise, as distinguished from a continued sound, consists of a single
impulse in one direction only, sometimes without any alternation ; while a
continued sound is a succession of such impulses, which, in the organ of
hearing at least, cannot but be alternate. If these successive impulses form
a connected series, following each other too rapidly to be separately distin-
guished, they constitute a continued sound, like that of the voice in speak-

368 LECTURE XXXI.

ing; and if they are equal among themselves in duration, they produce a
musical or equable sound, as that of a vibrating chord or string, or of the
voice in singing. Thus, a quill striking against a piece of wood causes a
noise, but, striking against the teeth of a wheel or of a comb, a continued
sound ; and if the teeth of the wlieel are at equal distances, and the ve-
locity of the motion is constant, a musical note.

Sounds of all kinds are most usually conveyed through the medium of the
air; and the necessity of the presence of this or of some other material
substance for its transmission is easily shown by means of the air pump; for
the sound of a bell struck in an exhausted receiver is scarcely perceptible.
The experiment is most conveniently performed in a moveable receiver or
transferrer, which may be shaken at pleasure, the frame which suspends the bell
being supported by some very soft substance, such as cork or wool. As the air
is gradually admitted, the sound becomes stronger and stronger, although it
is still much weakened by the interposition of the glass : not that glass is in
itself a bad conductor of sound, but the change of the medium of communi-
cation from air to glass, and again from glass to air, occasions a great di-
minution of its intensity. It is perhaps on account of the apparent facility
with which sound is transmitted by air, that the doctrine of acustics has
been usually considered as immediately dependent on pneumatics, although
it belongs as much to the theory of the mechanics of solid bodies as to that
of hydrodynamics.

A certain time is always required for the transmission of an impulse through
a material substance, even through such substances as appear to be the hardest
and the least compressible. It is demonstrable that all minute impulses are con-
veyed through any homogeneous elastic medium, whether solid or fluid, with a
uniform velocity, which is always equal to that which a heavy body would
acquire by falling througli half the height of the modulus of elasticity, that
is, in the case of the air, half the height of the atmosphere, supposed to be
of equal density; so that the velocity of sound passing through an atmo-
sphere of a uniform elastic fluid must be the same with that of a wave moving
on its surface. In order to form a distinct idea of the manner in which
sound is propagated through an elastic substance, we must first consider the
motion. of a single particle, which, in the case of a noise, is pushed for-

ON THE PROPAGATION OF SOUND. 3t)9

wards, and then either remains stationary, or returns back to its original
situation ; but in the case of a musical sound, is continually moved back-
wards and forwards, with a velocity always varying, and varying by differ,
ent degrees, according to the nature or quality of the tone ; for instance,
differently in the notes of a bell and of a trumpet. We may lirst suppose for
the sake of simplicity, a single scries of particles to be placed only in the same
line with the direction of the motion. It is obvious that if these particles were
absolutely incompressible, or infinitely elastic, and were also retained in
contact with each other by an infinite force of cohesion or of compression,
the whole series must move precisely at the same time, as well as in the same
manner. But in a substance which is both compressible and extensible or
expansible, the motion must occupy a certain time in being propagated to
the successive particles on either side, by means of the impulse of the first
particle on those which are before it, and by means of the diminution of
its pressure on those which are behind ; so that when the sound consists of a
series of alternations, the motion of some of the particles will be always in a
less advanced state than that of others nearer to its source; while at a greater
distance forwards, the particles will be in the opposite stage of the unduktion,
and still further on, they will again be moving in the same manner with the
first particle, in consequence of the effect of a former vibration.

The situation of a particle at anytime maybe representedby supposing it to
mark its path, on a surface sliding uniformly along in a transverse direction.
Thus,if wefix asmall pencil in a vibrating rod, and draw a sheet of paper along,
against the point of the pencil, an undulated line will be marked on the paper,
and will correctly represent the progress of the vibration. Whatever the na-
ture of the sound transmitted through any medium may be, it may be shown that
the path thus described will also indicate the situation of the different particles
at any one time. The simplest case of the motion of the particles is that in which
they observe the same law with the vibration of a pendulum, which is always
found opposite to a point supposed to move uniformly in a circle: in this case
the path described will be the figure denominated a harmonic curve ; and it may
be demonstrated that the force, impelling any particle backwards or forwards,
will always be represented by the distance of the particle before or behind its
natural place; the greatest condensation and the greatest direct velocity, as

VOL. I. 3 b

370 ^ LECTURE XXXI.

well as the g]:eatest rarefaction and retrograde velocity, happening at the
instant when it passes through its natural place.

We are ready to imagine that very hard bodies transmit motion instan-
taneously, because we have no easy means of measuring the interval of time
that elapses between the action of pushing the end of a rod, and the pro-
trusion of an obstacle at the other end, or between the instant of pulling a
bell rope, and that of the ringing of the bell. But it is demonstrable that
in order to transmit an impulse in a time infinitely small, the hardness of
, the substance must be infinitely great, and it must be absolutely incom-

pressible and inextensible by any force, which is a property not discoverable
in any natural bodies: the hardest steel and the most brittle glass being very
susceptible both of extension and compression.

The least elastic, substance that'has been examined, is perhaps carbonic acid gas,
^ or fixed air, which is considerably denser than atmospheric air exposed to an

equal degree of pressure. The height of the atmosphere, supposed to be ho- '
■?■ njogencous, is in ordinary circumstances, and, at the sea side, about 28 000

feet, and in falling through half this height a heavy body would acquire a
velocity of 946 feet in a second. But from a comparison of the accurate ex-
periments of Derham, made in the day time, with those of the French Aca-
demicians, made chiefly at night, it appears that the true velocity of sound
is about 1 130 feet in a second, which agrees very nearly with some observa-
tions made with great care by Professor Pictet. This difference between
calculation and experiment has long occupied the attention of natural phi-
losophers, but the difficulty appears to have been in great measure removed
by the happy suggestion of Laplace, who has attributed the cff'ect to the
elevation of temperature, which is always found to accompany the action of
condensation, and to the depression produced by rarefaction. It is true that
a greater change of temperature would be required than Mr. Dalton's experi-
ments on the compression of air appear to indicate; but those experiments
do not perfectly agree among themselves; and the observation which has-
been made in France, that a heat, sufficient to set tow on fire, may be pror
duced by the operation of a condensing syringe, seems to show that Mr.
Dalton's results are somewhat below the truth. In this manner the theory

5

ticj/l*-*^ K U

ON THE PROPAGATION OF SOUND. 371

may be completely reconciled with experiments; we may estimate the mo-
dulus of the air's effective elasticity,which is the measure of its immediate force,
from the velocity which is thus observed, and its height will appear to be
ZQ 800 feet, instead of 27 800, which is the supposed height of the atmo-
sphere. This velocity remains unchanged by any alternation of pressure in-,
dicated by the barometer, but it may be aftected by a change of temperature, - ; ^
For when an elastic fluid is compressed, its elasticity is increased in the same
ratio as its density; and the height of a homogeneous atmosphere equiva-
lent to the pressure, remains the same, consequently the velocity calculated
from that height remains unaltered; but the identity of the acceleration,
from the effect of heat which has been mentioned, can only be inferred
from observation : this identity may, however, be satisfactorily shown, by
means of experiments on the sounds of organ pipes, whicli are intimately
connected with the velocitv of the transmission of sound through the air,
and which are found to remain precisely the same, however the air may be
rarefied or condensed. . The Academicians del Cimento inclosed an organ
pipe, with bellows worked by a spring, in the receiver of an air pump and
of a condenser, and they found-" that, as long as the sound was audible,
its pitch remained unchanged. Papin screwed a whistle on the orifice
winch admits the air into the receiver of the air pump, and 1 have fixed an
organ pipe in the same manner; and the result agreed with the experiment,
of the academicians. But if the density of the air is changed, while its elas-
ticity remains unaltered, which happens when it is expanded by heat, or con-
densed by cold, the height of the column, and consequently the velocity,
will also be altered; so that for each degree of l-'ahrenheit's thermometer the
velocity will vary about one part in a thousand. Bianconi has actually ob-
served this difference of velocity according to the different heights of the
thermometer, and it may be shown less directly by means of the sounds of
pipes; but it has not been accurately determined. whether or no the correc-
tion on account of the effect of compression in causing heat, remains unal-
tered, although Bianconi's experiments agree very well with the supposition
tliat no material change takes place in this respect. The velocity of sound
must also be in some measure influenced by the quantity of moisture con-
tained in the atmosphere : it must be a little diminished by cold fogs, which
add to the density, without augmenting the elasticity, and increased by
warm vapours, which tend to make the air lighter; and these two opposite

372 LECTURE xxxr.

states are probably often produced in succession in wind instruments blown
by the mouth, the air within them being at first cold and damp, and after-
wards warm and moist.

In pure hydrogen gas, the velocity of sound ought, from calculation, to be
"" more than threje times as great as in common air, but the difference does not

appear to have been so great in any experiment hitherto made on, the sounds
of pipes in gases of different kinds. For such experiments, the comparative
specific gravity of the gas may be most conveniently ascertained by Mr.
Leslie's method of observing the time employed in emptying a vessel through
a small orifice, by means of the pressure of an equal column of water; ac-
cording to the simple theory, the velocities of the gas thus discharged ought
to be in the same proportion as the respective velocities with which sounds
would be transmitted by them: and if any variation from this proportion
were discovered, it must be attributed to the different degrees of heat pro^
duced by condensation in the different fluids. Steam, at the temperature
of boiling water, is only one third as heavy as common air; consequently
the velocity of sound in steam must be nearly three fourths greater thaa
in air.

It does not appear tlmt any direct experiments have been made on the
velocity with wliich an impulse is transmitted through a liquid, although
it is well known that liqaids are capable of conveying sound without dififi-
culty ; Professor Robison informs us, for example, that he heard the sound
of a bell transmitted by water at the distance of ]20{)feet. It is, however,
^ pasy to calculate the velocity with which sound must be propagated in any

^.•^,yft** liquid of which the compressibility has been measured. Mr. Canton has
„^ _. J ascertained that the elasticity of water is about 22 000 times as great as that

of air; it is, therefore, measured by the height of a column which is in the
same proportion to 34 feet, that is 750- thousand feet, and tlie velocity cor-
responding to half this height is 4900 feet in a second. In mercury, also,
it appears from Mr. Canton's experiments, that the velocity must be nearly
the same as in water, in spirit of wine a little smaller. These ex])eriments
were made by filling the bulb of a thermometer with water, and observing
the effects of placing it in an exhausted receiver, and in condensed air;
taking care to avoid changes of tcn>perature, and other sources of error:

OK THE PROPAGATION OF SOUND. 373

the fluid rose in the tube when the pressure was removed, and subsided
when it was increased. A shght correction is, however, required on ac-
count of the expansion and contraction of the glass, which must have tended
to make the elasticity of the fluids appear somewhat greater than it really
was.

It is also well known that solid bodies in general are good conductors of
sound: thus, any agitation communicated to one end of a beam is readily
conveyed to the ear applied to the other end of it. The motion of a troop
of cavalry is said to be perceived at a greater distance by listening with the
head in contact with the ground, than by attending to the sound conveyed
through the air; and we may frequently observe that some parts of the furniture
of a house are a little agitated by the approach of a wagon, before we hear the
noise which it immediately occasions. The velocity, with which impulses
are transmitted by solids, is in general considerably greater than that with
which they are conveyed by the air: Mr. Wunsch has ascertained this by
direct observations on a series of deal rods closely united together, which ap-
peared to transmit a sound instantaneously, while a sensible interval was re-
quired for its passing through the air: I have also found that the blow of a-
hammer on a wall, at the upper part of a high house, is heard as if double by a
person standing near it on the ground, the first sound descending through tlie
wall, the second through the air. It appears from experiments on the flexure
of solid bodies of all kinds, that their elasticity, compared with their density,
is much greater than that of the air: thus, the height of the modulus of elasti-
city of fir M'ood, is found, by means of such experiments, to be about
9 500 000 feet, whence the velocity of an impulse co-nveyed through it must be
17 4-00 feet, or more than three miles, in a secoml. It is obvious, therefore,
that in all common experiments such a transmission must appear perfectly
instantaneous. There are various methods of ascertaining tliis velocity from
the sounds produced under different circumstances by the substances to be
examined, and Professor C-hladni has in this manner compared the proper-
ties of a variety of natural and artificial productions.

We have hitherto considered the propagation of sound in a single right
line, or in parallel lines only; but it usually happens, at least when a sound
is transmitted through a fluid, that th? impulse spreads ia every direction, so-

97* LECTURE XXXI.

as to occupy at any one time nearly the whole of a spherical surface. But it
is impossible that the whole of this surface should be affected in a similar man-
ner by any sound, originating from a vibration confined to a certain direc-
tion, since the particles behind the sounding body must be moving towards
the centre, whenever the particles before it are retreating from the centre; so
that in one half of the surface, the motions may be called retrograde or nega-
tive, while in the other they are direct or positive; consequently at the sides,
where these portions join, the motions can be neither positive nor negative,
and the particles must remain at rest; the motions must also become gra-
dually less and less sensible as they approach to the limit between the two
hemispheres. And this statement may be confirmed by an experiment on
the vibration of a body of which the motion is limited to a certain direction,
the sound being scarcely audible when the ear is in a direction precisely per^
pendicular to that of the vibration.

The sound thus diverging must always be spread through a part of a
spherical surface, because its velocity must be equal in every direction, so
that the impulse will always move forwards in a straight line passing through
the centre of the sphere, or the vibrating body. But when a hemispherical
pulse arrives at the surface of a plane solid obstacle, it is reflected, precisely
in the same manner as we have already seen that a wave of water is reflected,
and assumes the form of a pulse proceeding from a centre at an equal dis-
tance on the opposite side of the surface. This reflection, when it returns
back perpendicularly, constitutes what is commonly called an echo : but in
order that the echo may be heard distinctly, it is necessary that the reflect-
ing object be at a distance moderately great, otherwise the returnii^- sound
will be confused with the original one; and it must either have a smooth
surface, or consist of a number. of surfaces arranged in a suitable form ; thus
there is an echo not only from a distant wall or rock, but frequently from
, the trees in a wood, and sometimes, as it is said, even from a cloud.

B (xmam^ h4^^' If ^ sound or a wave be reflected from a curved surface, the new direction

' which it will assume may be determined, either from the condition that the

velocity with which the impulse is transmitted must remain unaltered, or

from the law of reflection, which requires that the direction of the reflected

pulse or wave be such as to form an angle with the surface, equal to tliat

ON THE PROPAGATION OF SOUND. , 37o

which the incident pulse before formed with it. Thus, if a sound or wave
proceed from one focus of an ellipsis, and be reflected at its circumference,
it will be directed from every part of the circumference towards the other
focus; since the distance which every portion of the pulse has to pass over in
the same time, in following this path, is the same, the sum of the lines
drawn from the foci to any part of the curve being the same; and it may
also be demonstrated that these lines form always ecjual angles with the curve on
each side. The truth of this proposition may be easily shown by means of the ap-
paratus already described for exhibiting the motions of the waves of water ;
we may also confirm it by a simple experiment on a dish of tea: the curva-
ture of a circle differs so little from that of an ellipsis of small eccentricity,
that if we let a drop fall into the cup near its centre, the little wave which is
excited will be made to converge to a point at an equal distance on the other
side of the centre. (Plate XXV. Fig. 340, 341.)

If an ellipsis be prolonged without limit, it will become a parabola: hence
a parabola is the proper form of the section of a tube, calculated for collect-
ing a soond which proceeds from a great distance, into a single point, or
for carrying a sound nearly in parallel directions to a very distant place.
It appears, therefore, that a parabolic conoid is the best form for a hearing-
trumpet, and for a speaking' trumpet; but for both purposes the parabola
ought to be much elongated, and to consist of a portion of the conoid re-
mote from the vertex ; for it is requisite, in order to avoid confusion, that
the sound should enter the car in directions confined within certain limits:
the voice proceeds also from the mouth without any very considerable diverg-
ence, so that the parts of the curve behind the focus would in both cases be
wholly useless. A trumpet of such a shape does not very materially differ from
apart of a cone; and conical instruments are found to answer sufficiently
well for practice; it appears, however, unnecessary to suppose, as Mr.
Lambert has done, that they differ essentially in principle from parabolic
trumpets. It is not yet perfectly decided whether or no a speaking trumpet
has any immediate effect in strengthening the voice, independently of the
reflection of sound. (Plate XXV. Fig. 342.)

An umbrella, held in a proper position over the head, may serve to collect

t/ferrt^

S76 LECTURE XXXI.

the force of a distant sound by reflection, in the manner of a hearing
trumpet; but its substance is too slight to reflect any sound very perfectly,
unless the sound fall on it in a very oblique direction. The whisperino- o-al-
lery at St. Paul's produces an effect nearly similar, by a continued repetition
of reflections. Mr. Charles's paradoxical exhibition of the Invisible Girl has
also been said to depend on the reflection of sound; but the deception is
really perfonned by conveying the sound through pipes, artfully concealed,
and opening opposite to the mouth of the trumpet, from which it seems to
proceed.

When a portion of a pulse of sound is separated by any means from the
rest of the spherical or hemispherical surface to which it belongs, and proceeds
through a wide space, without being supported on either side, there is a cer-
tain degree of divergence, by means of which it sometimes becomes audible
in every part of the medium transmitting it: but the sound thus diverging
is comparatively very faint; and more so indeed than the effect of a wave
of water, admitted under similar circumstances, into a wide reservoir, which
we have already examined. Hence, in order that a speaking trumpet may
produce its full effect, it must be directed in a right line towards the hearer:
and the sound collected into -the focus of a concave mirror is far more
powerful than at a little distance from it, which could not happen if, as
.some have erroneously supposed, sound in all cases tended to spread equally
in all directions. The sounds that enter a room, in which there is an open
window, are generally heard by a mixture of this faint divergence with the
reflection from various parts of the window and of the room, and with the
effect of the impulse transmitted through the walls. This diverging portion,
however faint, probably assists in preserving the rectilinear motion of the
principal sound, and gradually gains a little additional strength at the ex-
pense of this portion.

The decay of sound is the natural consequence of its distribution through-
out a larger and larger quantity of matter, as it proceeds to diverge every
way from its centre. The actual velocity of the particles of the medium
transmitting it appears to diminish simply in the same proportion as the
distance from the <?entre increases; consequently their energy, which is to

ON THE PROPAGATION OF SOUND. 377

be considered as the measure of the strength of sound, must vary as the
square of the distance ; so that, at the distance of ten feet from the sounding
body, the velocity of the particles of the medium becomes one tenth as
great as at the distance of one foot, and their energy, or the strength of the
sound, only one hundredth as great.

V.OL. I, 3 c

378

LECTURE XXXII.

ON THE SOURCES AND EFFECTS OF SOUND.

J. HE examination of the origin of sound might naturally be deemed anterior
to the inquiry respecting its propagation ; but it will appear, that the pro-
perties of many of the most usual sources of sound depend immediately on
the velocity, with which an impulse of any kind is transmitted through an
elastic medium ; it was therefore necessary to consider this velocity, before
the production of sound in general could be discussed.

The origin of a simple sound, without any alternation, requires very little
investigation : it appears that the only condition necessary for its production
is a sufficient degree of velocity in the motion or impulse which occasions it.
A very moderate velocity must be sufficient for producing an impression on
the ear; there is reason to believe, that, when the sound is continued, it may
remain audible with a velocity of no more than one hundredth of an inch in
a second, and perhaps even with a velocity much smaller than this : but, at its
origin, it is probable that the velocity of the motion, constituting a sound,
must always be considerably greater.

A continued sound may be produced by a repetition of separate impulses
independent of each other, as when a wheel strikes in rapid succession the
teeth of a pinion, so as to force out a portion of air from between them;
when a pipe, through which air is passing, is alternately opened and shut,
either wholly or partially, by the revolution of a stopcock or valve; or when a
number of parallel surfaces is placed at equal distances in a line nearly per-
pendicular to them, and a noise of any kind is reflected from each of them
in succession; a circumstance which may often be observed when we are
walking near an iron railing, an acute sound being heard, which is com-
posed of such reflections from the surfaces of the palisades.

ON THE SOURCES AND EFFECTS OF SOUND. 379

Musical sounds are, however, most frequently produced by the alternate ^^.at-^*^-h^^
motions of substances naturally capable of isochronous vibrations, and these
substances may be either fluids or solids, or instruments composed of a com-
bination of fluids with solids. The resonance of a room or passage is one of UMin^^^^'^ /
the simplest sources of a musical sound; the walls being parallel, the impulse
is reflected backwards and forwards continually, at equal intervals of time,
so as to agree with the definition, and to produce the eflfect, of a musical
sound. When we blow obliquely and uniformly into a cylindrical pipe
closed at one end, it is probable that the impulse or condensation must lyJtf^ t^^-Ci-'-i
travel to the bottom and back, before the resistance is increased ; the cur-
rent of our breath will then be diverted from the mouth of the pipe, for
an equal time, which will be required for the diminution of the resistance
by the discharge of the condensed air, so that the whole time of a vibration
will be equal to the time occupied by an impulse of any kind in passing
through four times the length of the pipe. An open pipe may be considered
nearly as if it consisted of two such pipes, united at their closed ends,
the portions of air contained by them being agitated by contrary motions,
so as always to aft^brd each other a resistance similar to that which
the bottom of the stopped pipe would have furnished. It is probable
that when an open pipe is once filled with air a little condensed, the oblique
current is diverted, until the effect of the discharge, beginning at the remoter
end, has returned to the inflated orifice, and allowed the current to reenter the
pipe. Where the diameter of the pipe is different at different parts of its
length, the investigation of the sound becomes much more intricate; but it
has been pursued by Daniel Bernoulli with considerable success, although
upon suppositions not strictly consistent with the actual state of the motions
concerned.

In the same manner as an open pipe is divided by an imaginary basis,
so as to produce the same sound with a stopped pipe of half the length, a
pipe of any kind is capable of being subdivided into any number of such
pipes, supposed to meet each other's corresponding ends only; and in
general the more violently the pipe is inflated, the greater is the number of
parts into which it subdivides itself, the frequency of the vibrations being
always proportional to that number. Thus, an open pipe may be divided not
only into two, but also into four, six, eight, or more portions, producing
the same sounds as a pipe of one half, one third, one fourth, or any other

380 LECTURE XXXII.

aliquot part of the length; but a stopped pipe cannot be divided into any
even number of similar parts; its secondary sounds being only those of a
pipe of which the proportion is determined by the odd numbers, its length
being, for example, one third, one fifth, or one seventh of the original
length. These secondary notes are sometimes called harmonics; they are
not only produced in succession from the same pipe, but they are also often
faintly heard together, while the fundamental note of the pipe continues to
sound. When the pipe has a large cavity connected with it, or consists
principally of such a cavity, with a small opening, its vibrations are usually
much less frequent, and it is generally incapable of producing a regular
series of harmonics.

J . _ It is obvious from this statement of the analogy between the velocity of

/ U^.^lt^'^-^ sound and the vibrations of the air in pipes, that they must be affected in

a similar manner by all alterations of temperature. Thus, the frequency of
the vibrations of a pipe must be increased nearly in the ratio of 33 to 34 by
an elevation of 30 degrees of Fahrenheit's thermometer ; and if this change
be accompanied by a transition from dampness to simple moisture, the sound
will be still more altered.

/ / Dr. Chladni has discovered that solids of all kinds, when of a proper form,.

*"*** are capable of longitudinal vibrations, exactly resembling in their nature those

f^^^-f

of the air in an organ pipe, having also their secondary or harmonic notes
related to them in, a similar manner. These vibrations are always far more
frequent than those of a column of air of equal length, the velocity, with
which an impulse is transmitted by a solid of any kind, being usually from 5
to \6 times as great as the velocity of sound in air; so that the longitudinal
sounds are always extremely acute, when they are produced by substances^
of moderate length. These sounds afford perhaps the most accurate mode
of determining the velocity of the transmission of an impulse through any
elastic substance, and of obtaining from that velocity the exact measure of
its elasticity : they may be easily exhibited by holding a long bar or wire of
iron or brass in the middle, and striking it at one end witli a. small hammer^
in the direction of its length. ,

The vibrations by which solid bodies most usually produee sound are»
however, not longitudinal, but lateral, and they are governed either by a

ON THE SOURCES AND EFFECTS OF SOUND. 381

tension, derived from the operation of a weight, or of some other external
force, or by tlie natural elasticity of the substance. The vibrations of ex-
tended substances resemble most in their properties those of elastic fluids,
and they occur the most frequently in practice, although the vibrations
produced by the elasticity of the substance may be considered as the mo&t
natural.

Vibrations derived from tension are either those of chords or musical
strings, or those of membranes; but the vibrations of membranes afford
little variety, and have not hitherto been very accurately investigated, the
drum being almost the only instrument in which they are concerned ; they
do not however appear to diifer materially in their properties from the vibra-
tions of strings. A musical string or chord is supposed to be perfectly
flexible, and of uniform thickness, to be stretched between two fixed point^
by a force incomparably greater than its own weight, and to vibrate in a
single plane through a minute space on each side of its natural position.
Its motions may then be traced through all their stages, by comparing the
chord to a portion of an elastic medium of the same length, contained be-
tween two bodies capable of reflecting any impulse at each end; for example,
to a portion of air situated between two walls, or inclosed in a pipe stopped
at both ends; for the vibration of such a medium will be performed in the
time occupied by any impulse in travelling through twice its length;
and the vibration of the chord will be performed in the same time, suppos-
ing the height or depth of the medium equal to the length of a portion of
the chord, of which the weight is equivalent to the force applied to stretch
it, and which may be called with propriety the modulus of the tension. If
the chord be at first bent into a figure of any kind, and then set at liberty,
the place of any part of it at every subsequent time will be such, that it will
always be in a right line between two points moving along the figure each
way with the appropriate velocity; but in order to pursue this determination,^
we must repeat the figure of the chord on each side of the fixed points in an
inverted position, changing the ends as well as the sides. Hence it appears
that, at the end of a single vibration, the whole chord will assume a similar
figure on the opposite side of its natural place, but iu an inverted position,
and after a complete or double vibration, it will return precisely to the form
which it had in the beginning. The truth of this result is easily shown by

^SiJ I.ECTUIIE XXXIl.

inflecting any long chord near one of its ends, having first drawn a line
under its natural position, and it will then be evident that the chord returns
in each vibration nearly to the point of inflection, and passes at that end
but to a much shorter distance on the opposite side of the line, while at the
other end its excursions are greatest on the opposite side Of the line. The
result of the calculation of the frequency of vibration agrees also perfectly
with experiment, nor is the coincidence materially affected by the inflexi-
bility or elasticity of the string, by the resistance of the air, nor by the
slight increase of the tension occasioned by the elongation of the string
when it is inflected: thus, if the weight or force causing the tension of a
string were equal or equivalent to the weight of 200 feet of the same string,
that is, if the modulus of tension were 200 feet long, the velocity corres-
ponding to half this height would be 80 feet in a second; and every impulse
would be conveyed with th's velocity from one end of the string to the
other, so that if the string were 1 foot long, it would vibrate 40 times in a
second, if 6 inches, 80 times, and if it were 40 feet long, only once in a
second. Hence, it is obvious that the time of vibration of any chord is
simply proportional to the length ; and this may be shown either by means
of such vibrations as are slow enough to be reckoned, or by a comparison with
the sounds of pipes, or with other musical sounds. But if the tension of a
chord of given length were changed, it would require to be quadrupled in
order to double the frequency of vibration; and if the tension and length
remained unaltered, and the weight of the chord were caused to vary, it
would also be necessary to make the weight four times as great in order to
reduce the frequency of vibration to one half.

It appears from the mode of tracing the progress of a vibration, which
lias already been laid down, that every chord vibrates in the same manner
us if it were a part of a longer chord, composed of any number of such
chords, continually repeated in positions alternately inverted; consequently
if a long chord be initially divided into any number of such equal portions,
its parts will continue to vibrate in the same manner as if they Avere sepa-
rate chords; the points of division only remaining always at rest. Such
subordinate sounds are called harmonics: they are often produced in violins
by lightly touching one of the points of division with the finger, when the
bow is applied, and in all such cases it may be shown, by putting small

ON THE SOURCES AXD EFFECTS OF SOUND. 383

feathers or pieces of paper on the string, that the remaining points of divi-
sion are also quiescent, while the intervening portions are in motion. (Plate
X^V. Fig. 343.)

These harmonic sounds are also generally heard together with the funda-
mental sound of the chord, and it is, therefore, necessary, in such cases, tQ^
consider the subordinate vibrations as combined with a general one. It is
not, however, universally true that the fundamental sound must always be
accompanied by all the harmonics of which the chord is susceptible; for I
have found that by inflecting the chord exactly at any point in which the
cliord might be divided into a number of equal parts, and then suffering
it to vibrate, we lose the effect of the corresponding harmonic. There is
some difficulty in explaining the reasonof the distinct production of these
sounds, in cases where the theory appears to indicate a single and simple
vibration only ; but it appears to be most probable that they usually become
audible in consequence of some imperceptible irregularity in the form or
weight of the chord, which is just sufficient to derange the perfect coinci-
dence of the actual motions with those which the theory indicates, without
producing a discordance capable of offending the ear. That a chord ir-
regularly loaded may have the relations of its harmonics disturbed, may
easily be understood by considering the effect of a small weight placed at
one of the points of division, which will obviously retard the principal
vibration, without materially afi'ecting that of the portions terminated by it.
An abrupt and irregular agitation appears also in many cases to make the
secondary notes more audible, while a gradual and delicate impulse, like
that of the wind on the strings of an Aeolian harp, produces a sound almost'
entirely free from subordinate harmonics.

It usually happens that the vibration of a chord deviates from the plane
of its first direction, and becomes a rotation or revolution, which may be
considered as composed of various vibrations in different planes, and which
is often exceedingly complicated. These vibrations may be combined in the
first instance in a manner similar to that which has been already ex-
plained respecting the vibrations of pendulums; and if the motion
of the chord be supposed to follow the same law as that of a pendulum, the
result of two entire vibrations thus united, may be either a vibration in an

384

LECTURE XXXII.

intermediate direction, or a revolution, in a circle or in an ellipsis. But
besides these compound vibrations of the whole chord, it is also frequently-
agitated by subordinate vibrations, which constitute harmonic notes of
different kinds, so that the whole effect becomes very intricate; as we
may observe by a microscopic inspection of any luminous point on the sur-
face of the chord, for instance the reflection of a candle in the coil of a fine
wire wound round it. The velocity of the motion is such that the path of
the luminous point is marked by a line of light, in the same manner as when
a burning coal is whirled round; and the figures, thus described, are not
only different at different parts of the same chordjbutthey often pass through
an amusing variety of forms during the progress of the vibration; they
also vary considerably according to the mode in which that vibration is
excited. (Plate XXV. Fig. 344, 345.)

The vibrations immediately dependent on elasticity are those of rods,
plates, rings,and vessels. These admit of much greater variety, and are of more
difficult investigation than the vibrations of chords. A rod may be either
wholly loose, or fixed at one end only, or at both ; and it may either be
loosely fixed, in situation only, or firmly fixed, in direction as well as in
situation; and these conditions may be variously combined with each other;
the rod may also have a variety of secondary vibrations besides the principal
or fundamental sound. All these cases have been examined by various
mathematicians: the subject was begun by Daniel Bernoulli, and much ex-
tended by Euler, some of whose conclusions have been corrected by Riccati;
and Chladni has compared them all with experiment. The sounds produced
by the same rod, either under different circumstances, or as harmonics which
may be heard at the same time, are scarcely ever related to each other in any
simple proportion, except that when a rod is loosely fixed at both ends, the frequen-
cy of the vibrations of the subordinate notes is expressed by the series of the
squares of the natural numbers,as l,4,9,and l6. But the times occupied by any
similar vibrations of rods, similarly circumstanced, are always directly as
the squares of their lengths, and inversely as their depths. When the rod
is wholly at liberty, two at least of its points must be at rest, and these
are at the distance of about one fifth of its length from either end: in the
next sound of the same rod, the middle point is at rest, with two others near
the ends. There is by no means the same regularity in the progress of the

ON THE SOURCES AND EFFECTS OF SOUND. 385

vibrations of rods of different kinds as in those of chords ; it can only hap-
pen in particular cases that the rod will return after a complete vibration
to its original state, and these cases are probably such as seldom occur in
nature.

The vibrations of plates diifer from those of rods in the same manner as
the vibrations of membranes differ from those of chords, the vibrations which
cause the plate to bend in different directions being combined with each other,
and sometimes occasioning singular modifications. These vibrations may be
traced through wonderful varieties by Professor Chladni's method of strewing
dry sand on the plates, which, when they are caused to vibrate by the operation
of a bow, is collected into such lines as indicate those parts, which remain
either perfectly or very nearly at rest during the vibrations. Dr. Hooke had
employed a similar method, for showing the nature of the vibrations of a bell,
and it has sometimes been usual, in military mining, to strew sand on a drum,
and to judge, by the form in which it arranges itself, of the quarter from
which the tremors produced by countermining proceed. (Plate XXV. Fig.
346 . . 348.)

The vibrations of rings and of vessels are nearly connected with those of
plates, but they are modified in a manner which has not yet been sufficiently
investigated. A glass, or a bell, divides in general into four portions
vibrating separately, and sometimes into six or eight; they may readily be
distinguished by means of the agitations excited by them in a fluid contained in
the glass. It is almost unnecessary to observe, that the fluid thus applied,
by adding to the mass of matter to be moved, makes the vibration slower,
and the sound more grave.

In some cases the vibrations of fluids and solids are jointly concerned in
the production of sound: thus, in most of the pipes of an organ denominated
reed pipes, the length of a tongue of metal is so adjusted, as to be capable of
vibrating in tiie same time with the air contained in the pipe. Sometimes,
however, the air only serves to excite the motion of the solid, as jn some
other organ pipes, which are usually much shorter than Avould be required
for producing the proper note alone, and. pvobably in the glottis, or organ
of the voice, of animals. On the other hand, the alternate opening and shut-

VOL. 1. So

386 LECTURE XXXII.

ting of the lips, in blowing the trumpet or French horn, can scarcely be
called a vibration, and the pitch of the sound is here determined by the
properties of the air in the pipe only. The vibrations of a solid may be excited
by an undulation propagated through a fluid; thus, when a loud sound strikes
against a chord, capable of vibrating, either accurately, or very nearly, with
the same frequency, it causes a sympathetic tone, resembling that from
which it originated ; and the chord may produce such a sound either by
vibrating as a whole, or by dividing itself into any number of equal parts.
Thus, if the daniper be raised from any of the strings of a harpsichord, it
may be made to vibrate, by striking or singing any note, of which the sound
corresponds either to that of the whole string, or to that of any of its aliquot
parts. Sometimes also two chords that are very nearly alike, appear, when
sounding together,to produce precisely the same note, which differs a little from
each of those which the chords would produce separately; and a similar
circumstance has been observed with respect to two organ pipes placed near
each other. In these cases the vibrating substances must affect each other
lliTOugh the medium of the air ; nearly in the same manner as two clocks,
which rest on the same support, have been found to modify each other's
motion?, so as to exhibit a perfect coincidence in all of them.

It is uncertain whether any fibres in the ear are thus sympathetically agi-
tated in the process of hearing, but if there are any such vibrating fibres, their
motions must necessarily be of short duration, otherwise there would be a
perpetual ringing in our ears, and we should never be able to judge accu-
rately of the termination of a sound. Besides, a sympathetic vibration may
be excited not only by a sound producing vibrations of equal frequency,
but also by a sound, of which every alternate, or every third or fourth vibration,
coincides with its motions: it would, therefore, be difficult to distinguish
such sounds from each other, if hearing depended simply on the excitation
of sympathetic vibrations. It is true that we generally distinguish, in listen-
ing to a loud and deep sound, precisely such notes as would be thus produced ;
but it is only when the sounding body is capable of affording them from the
nature of its vibrations; for we may listen for them in vain in the sound of a
bell or of a humming top. There is, however, no doubt that the muscles^
with which the different parts of the ear are furnished,are concerned in accom-
modating the tension of some of them to the better-transmission of sound;

ON THE SOURCES AND EFFECTS OF SOUND. 3S7

and it is equally certain that their operation is not absolutely necessary in
the process.

The external ear serves in some measure for collecting the undulations of
soiinds transmitted through the air, and reflecting them into the auditory
passage, at the bottom of which they strike against the membrane of the
tympanum or drum, which, being larger and more moveable than some of
the subsequent parts, is capable of transmitting a stronger impulse than
they would immediately receive. In the same manner we may often feel
the tremors produced in a sheet of thick paper, held in the hand, by the
agitation of the air, derived from a loud sound, which would not otherwise
have affected the organ of touch. The impulse received by tlie membrane
of the tympanum is conveyed by the hammer and anvil, two small bones,
which together constitute a kind of bent lever, through a third minute flat-
tened bone, to a fourth called the stirrup, which serves merely as a handle
to its basis, a plate covering the orifice of a cavity called the vestibule, and
communicating the impulse to the mucous fluid which fills this cavity. The
fluid of the vestibule, thus agitated, acts immediately on the terminations '
of the nerves, which form a loose membranous tissue, almost floating in it,
Avhile another portion of them is distributed on the surface of three semi-
circular tubes or canals, opening at both ends into the cavity, and a third
portion supplies the cochlea, a detached channel, which appears to be ar-
ranged with singular art as a micrometer of sound. It resembles the spiral
convolutions of a snail shell, and if uncoiled, would constitute two long
conical tubes connected at their summits, the base of one opening into
the vestibule, that of the other being covered by a membrane only, which
separates the fluid from the air contained in the general cavity of the ear,
or the tympanum. It is evident from the properties of fluids moving in
conical pipes, that the velocity of any impulse atfecting the fluid at the
base of the cone must be extremely increased at its vertex, while the flexi-
bility of the membrane at the base of the second channel allows this motion
to be effected without difficulty. It has also been supposed that a scries
of fibres are arranged along the cochlea, which are susceptible of sympathetic
vibrations of different frequency according to the nature of the sound which
acts on them; and, with some limitations, the opinion does not appear to be
wholly improbable. We must, however, reason with great caution respect-

.')88 " LECTURE XXXII.

ing the functions of every part of the ear, since its structure varies so much
in different animals, that we cannot pronounce with certainty respecting the
indispensable necessity of any one arrangement for the perfection of the sense.
And even in the case of the human ear, many of these parts may be spared
withoyt great inconvenience ; thus, we hear very perfectly, by means of im-
pressions communicated to the teeth, and through them to the large bones,
of the head; and even when the membrane of the tympanum, and all the
small bones of the ear have been destroyed by disease, the undulations
of the air still continue to affect the organ in the usual manner.. (Plate
XXV. Fig. 349. . 351.)

Such is t^e delicacy of the organs of hearing in their perfect state, that
we readily distinguish not only the frequency of the vibrations of a sound,
whether constant or variable, and its loudness or softness, but also the
quality of tone, depending on the law which governs each separate vi-
bration, and which constitutes the difference between instruments of differ-
ent kinds, or different instruments of the same kind, or even the same instrument
differently employed. Thus, we can distinguish very accurately the voices of
our friends, even Avhen they whisper, and those modifications of the same voice
which constitute the various vowels and semivowels, and which, with the
initial and final noises denominated consonants, compose the words of a
language. We judge also, without an error of many degrees, of the exact
direction in which the sound approaches us; but respecting the manner in
Vhich the ear is enabled to make this discrimination, we cannot reason upon
any satisfactory grounds.

389

LECTURE XXXIir.

ON HARMONICS.

The philosopliical theory of harmonics, or of the combinations of sounds,
was considered by the ancients as affording one of the most refined em-
ployments of mathematical speculation ; nor has it been neglected in modern
times, but it has been in general either treated in a very abstruse and confused
manner, or connected entirely with the practice of music, and habitually
associated with ideas of mere amusement. We shall, however, find the
difficulties by no means insuperable, and the subject will appear to be
worthy of attention, not only on its own account, but also for the sake of
its analogy with many other departments of science.

It appears both from theory and from experience, that the transmission
of one sound does not at all impede the passage of another through the same
medium. The ear too is capable of distinguishing, without difficulty, not
only two sounds at once, but also a much greater number. The motions
produced by one series of undulations being wholly indiffisrent with respect ^
to the effect of another series, and each particle of the medium being neces-
sarily agitated by both sounds, its ultimate motion must always be the
result of the motions which would have been produced in it by the
separate sounds, combined according to the general laws of the composi-
tion of motion, which are the foundation of the principal doctrines of
mechanics. When the two sounds, thus propagated together, coincide
very nearly in direction, the motions belonging to each sound may
be resolved into two parts, the one in the common or intermediate direction,
and the other transverse to it; the latter portions will obviously be very small ;
they will sometimes destroy each other, and may always be neglected in determin-
ing the effect of the combination, since the ear is incapable of distinguishing
a difference in the directions of sounds which amounts to a very few degrees

390 LECTURE XXXIII.

only. Thus, when two equal undulations, of equal frequency, coincide in
this manner, and when the particular motions are directed the same way
at the same time, the velocities in each direction are added together, and
the joint effect is doubled, or perhaps quadrupled, since it appears that the
strength of sound ought to be estimated from the squares of the veloci-
ties of the particles: but when the particular motions of the two sounds
counteract each other, both their effects are wholly destroyed. These com-
binations resemble the effects of the waves of water in similar circumstances,
which we have already examined, and they may be illustrated by drawing
two curved lines representing the motions which constitute the sounds, in
the same manner as we have already supposed them to be described, by a
vibrating particle, on a surface moving uniformly in a transverse direction ;
these figures being placed side by side, the joint effect may be represented
by a third curve drawn in such a direction as to be always in the middle
between the corresponding points of the first two. A similar result, but
still more strongly marked, may be obtained mechanically, by cutting two
boards or plates of any kind into the form of the curves, and then dividing
one of them into a number of thin pieces or sliders, by lines perpendicular
to the general direction of the curve, or to the termination of the plate
which is parallel to it: the bottom of these sliders being then placed on the
other curve, their general outline will represent the effect of the combination.
OWe may assume for this purpose the form of the harmonic curve , which
represents the motions of a body vibrating like a pendulum, and which
probably agrees very nearly with the purest and simplest sounds. (Plate
XXV. Fig. 359,.)

If the two undulations differ a little from each other in frequency, they
alternately tend to destroy each other, and to acquire a double or perhaps a quadru-
ple force, and the sound gradually increases and diminishes in continued suc-
cession at equal intervals. This intension and remission is called a beat, and
furnishes us with a very accurate mode of determining the proportional
frequency of the vibrations, when the absolute frequency of one of them is
known, or the absolute frequency of both, when their proportion is known;
since the beats are usually slow enough to be reckoned, although the vibra-
tions themselves can never be distinguished. Thus, if one sound consisted
of 100 vibrations in a second, and produced with another acuter sound a single

ON HARMONICS. 391

beat in ei'ery second, it is obvious that the second sound must consist of
101 vibrations in a second. Again, if we have two portions of a similar
chord equally stretched, or two simple pipes, of whicli the lengths are in
the proportion of 15 to 16, they will produce a beat in 15 vibrations of the
longer; and if we count the numbei' of beats in 15 seconds, we shall find
the number of vibrations in a single setond. The easiest way of procuring
two such strings or pipes, in practice, is to tune them by a third, so that
they may be respectively 4- and -J of its length; the vibrations of the third
pipe in a second will also be equal to the number of beats of the first two in
12 seconds. (Plate XXV. Fig. 353.)

When the beats of two sounds are too frequent to be heard as distinct
augmentations of their force, they have the same effect as any other impulses
which recur in regular succession, and produce a musical note, which has
been denominated a grave harmonic. Thus, two sounds in the proportion of
4 to 5, produce, when they are both very low or grave, an audible succes-
sion of beats; but when they are higher or more acute, a grave harmonic,
which may be separately distinguished as a third sound by an attentive ear.
Those combinations of sounds, which produce beats distinctly audible, have
in general a harsh and coarse effect, and are called discords; but those of
which the vibrations are so related, as to have a common period after a few
alternations, and which may be observed to produce a third sound, constitute
concords, which are in themselves the more perfect as the common periods
are shorter. (Plate XXV. Fig. 353.)

The natural association of the secondary sounds, which generally ac-
company almost all musical notes, serves in some measure as a foundation
for the science of harmonics, the same sounds, as are tlms frequently con-
nected in nature, being found to be agreeable when united by art. But it
appears to depend still more immediately on a love of order, and a predilec
tion for a regular recurrence of sensations, primitively implanted in the
human mind. Hence, when two sounds are heard together, those propor-
tions are the most satisfactory to the ear, which exhibit a recurrence of a
more or less perfect coincidence at the shortest intervals, expressed by the
smallest numbers of the separate vibrations: for though Ave cannot im-
mediately estimate the magnitude of the vibrations, yet the general effect of

39S . LECTURE xxxtir.

a regular or irregular succession necessarily produces the impression of sweet-,
ness or harshness. The same sounds, as form the best accompaniment for each
other, are also in general the most agreeable for melodies, consisting of
a succession of single notes; their intervals are, however, too large to be
sufficient for the purposes of music, and they require to be mixed with
other sounds which arc related to them in a manner nearly similar.

The same constitution of the human mind, which fits it for the perception
of harmony, appears also to be the cause of the love of rhythm, or of a re-
gular succession of any impressions whatever, at equal intervals of time. Even
the attachment to the persons and places to which we are accustomed, and
to habits of every kiud, bears a considerable resemblance to the same prin-
ciple. The most barbarous nations have a pleasure in dancing ; and in this case, a
great part of the amusement, as far as sentiment and grace are not concerned,is
derived from the recurrence of sensations and actions at regular periods of
time. Hence not only the elementary parts of music, or the single notes,
are more pleasing than any irregular noise, but the whole of a composition
is governed by a rhythm, or a recurrence of periods of greater or less extent,
generally distinguished by bars, which are also the constituent parts of larger
periods, and are themselves subdivided into smaller. An interruption of tlie
rhythm is indeed occasionally introduced, but merely for the sake of con-
trast; nearly in the same manner as, in all modern pieces of music, discords
are occasionally mixed with concords, in order to obtain an agreeable variety
of expression.

In a simple composition, all the intervals are referred to a single funda-
mental or key note. Thus, any air which can be played on a trumpet or on a
bugle horn, must consist of the harmonics of a single sound only : andwhen an
accompaniment is performed by a French horn, the length of the instrument is
fust adjusted to the principal note, and all the sounds which it is to produce
are selected from this natural series. But the notes constituting the most
natural scale are not, without exception, comprehended among the har-
monics; they are, however, all immediately dependent on a similar relation.
A sound of which the vibrations are of equal frequency with those of another,
is called a unison; if two vibrations occur for every one of the fundamental
note, the sound is called its superior octave, being the eighth of those

ON HARMONICS. SgS

which are commonly considered as filling up the scale ; and on account of
its great resemblance to the fundamemtal note, it is described by the same
letter of the alphabet, or by the same syllable; so that all audible sounds are
considered as repetitions of a scries contained within the interval of an
octave. One third part of the string or pipe gives the fifth above the octave;
one fourth the double octave, and one fifth of the string its third. Thus
we obtain the common accord or chord, or the harmonic triad, consisting of
the fundamental note, with its third and fifth, which produces the most
perfect harmony, and which also contains the constituent parts of the most
simple and natural melodies. But we are still in want of intermediate steps
for the scale ; these are supplied by completing first, the triad of the fifth,
which gives us the second, and the seventh, of which Sand 15 vibrations
correspond respectively to 8 of the fundamental, and which may also be
found in the ascending series of natural harmonics; and in the" second place,
by adding the fourth and sixth in such proportions as to make up another
perfect triad with the octave; the respective notes consisting of 4 and 5
vibrations, while the fundamental note makes 3, and being no where found
among the natural harmonics. The complete scale is, therefore, formed by
these harmonic triads contiguous to and connected with each other; the
middle one being the triad of the key note, the superior one that of its
fifth, which is sometimes called the dominant or governing note, and the
inferior one that of the fourth, or subdominant. This scale is derived from
principles so simple, that it may properly be considered as a natuial arrange-
ment, and it appears to be found with little variation in barbarous as well as
in civilised countries. (Plate XXV. Fig. 354.)

A long piece would, however, be too monotonous, unless the fundamental
note were sometimes changed; we may, therefore,^ take at pleasure one of
the auxiliary triads for the principal harmony, and we may continue the
modulation or progression, until every note of the scale becomes in succession a
key note. But, in order to fill up the intervals of these several scales in just
proportion, it becomes necessary to add several new notes to the first series ,
for instance, if we take the seventh for a key note, we shall want five new
sounds within the octave, making twelve in the whole, which is the num-
ber usually employed in music The interval between any two adjoin-
ing sounds of tlie twelve is called a semitone or half note, two semitones

VOL. I. 3 E

3g4 ii;cTt;Ri: xxxnr.

making a tone or note; these terms are, however, sometimes employed with
various subordinate distinctions and limitations. The five additional sounds
have no separate names, but they are denominated from the neigh-
bouring notes on either side, Avith the addition of the term sharp or flat,
accordingly as they are a semitone higher or lower than the notes of
which they bear the names.

For still further variety, we sometimes cbange the place of the middle
note of each triad, placing the minor third, or the interval expressed by the
ratio of 5 to 6, below the major, which is in the ratio of 4 to 5; and the
scale thus formed is called the scale of the minor mode, in contradistinction
to the major, the three principal thirds being depressed a semitone. Some-
times, however, the alteration is made in the third of the key note only,
especially in ascending, in order to retain the seventh of the major scale
which leads so naturally into the octave, as to be sometimes called the
characteristic semitone of the key; and it is for this reason, that the triad,
in which it is found, is called the accord of the dominant, which, in all regu-
lar compositions, immediately precedes the termination in the key note.

The major and minor triads, with the discord of the flat seventh, may be
considered as constituting the foundation of all essential harmonies. The
flat seventh is principally used with the major triad, in transitions from the
fundamental key into its fourth, to which that seventh naturally belongs as
a concord; so that it serves to introduce the new key, by strongly marking
the particular note in which it differs from the old one ; and in such cases the
flat seventh always descends into, or is followed by, the third of the new key,
and the third of the first triad ascends into the new key note. Other dis-
cords are also sometimes introduced, but they are in general either partial
continuations of a preceding, or anticipations of a following accord. Two
difi'erent parts of a harmony are never allowed, in regular and serious com-
positions, to accompany each other in successive octaves or fifths, since
such a succession is found to produce a disagreeable monotony of effect,
except when a series of octaves is continue for some time, so as to be con-
sidered as a repetition of the same part.

These are almost the only principles, upon which the art of accompaniment,

/

/

ON HARMONICS. 595

as well as the general theoryof practical music, is founded. Many prolrx treatises
Jiave been written on the subject, but they only contain particular illustra-
tions of the application of these principles, together with a few refinements
upon -them. The art of composition, however, depends much more on a
good taste, formed by habitual attention to the best models, and aided,
perhaps, by some little natural predisposition, than upon all the precepts of
science, which teach us only how to avoid what is faulty, without in-
structing us in the mode of attaining what is beautiful or sublime.

It is impossible to assign any such proportions foi the twelve sounds thus
employed, that they may be perfectly appropriate to all the capacities in
which they are used; their number is, therefore, sometimes considerably
increased; and in some instruments they may be varied without limit, at the
performer's pleasure, as in the voice, in instruments with finger boards, and
in some wind instruments; but in many cases this is impracticable, nor
could any imaginable alteration make all the intervals perfect, unless
every note were varied, whenever we returned to it by steps different
from those by which we had left it. The simplest mode of arranging the
twelve sounds, is to divide the octave into twelve equal intervals,
all the notes being in the same proportion to those which immedi-
ately follow them: this is called the equal temperament, because the imper-
fection is equal in all keys. In this system of temperament, the fifths, which
consist of seven semitones, are a littfe too flat, that is, the interval is a little too
small; the minor thirds, consisting of three semitones, are also too flat,and the
,major thirds too sharp. But it has generally been esteemed best to preserve
some keys rnore free from error; partly for variety, and partly because some
are more frequently used than others : this cannot, however, be done with-
out making some of the scales more imperfect than in the equal temperament. •
A good practical mode of performing it, is to make six perfect fifths, in de-
scending from the key note of the natural scale, and six ascending fifths
equally imperfect among themselves. We thus retain a slight imperfection
in the scales most commonly used, and make the keys which are most
remote from them considerably less perfect. Anoth*er method, which is
perhaps somewhat more easily executed, is to make the fifth and third of
the natural scale perfectly correct, to interpose between their octaves, the
second and sixth, so as to make three fifths equally tempered, and to de-

Sg6 , LECTUEE.XXXIir.

scend from the key note by seven perfect fifths, which will complete the
scale. Any of these modes of temperament may be actually executed, either
by the estimation of a good ear, or, still more accurately, by counting the fre-
quency of the beats which the notes make with each other.

For denoting precisely the absolute as well as the relative frequency of the
sounds of the different octaves, we employ the first seven letters of the
alphabet; A being the key note of the minor mode, in the scale of natural
notes, and C of the major. The peculiar characters used in music are gene-
rally disposed on five or more lines, with their intervening spaces, each im-
plying a separate step in the scale, setting out from any line at pleasure*
which is marked with an ill formed G, a C, or an F; a sharp or a flat im-
plying that all the notes written on the line, or in the space, to which it
belongs, are to be raised or depressed a semitone, and a natural restoring the
note to its original value. The actual frequency of the vibration of any note,
according to the pitch most usually employed, may be found, if we recollect
to call a noise, recurring every second, the first C, then the C denoted by the
mark of the tenor cliff will be the ninth, consisting of 256 vibrations in a
second. The fifth, consisting of sixteen vibrations, Avill be nearly the low-
est audible note, and the fourteenth the highest note used in music, but
the sixteenth, consisting of above 30 000 vibrations in a second, may perhaps
be an audible sound. The frequency of the vibrations of the other notes
may easily be calculated from the known relations which they bear to the
note thus determined. (Plate XXV. Fig. 355.)

397

LECTURE XXXIV.

ON MUSICAL INSTRUMENTS.

The application of the theory of harmonics to practice depends on the
construction of musical instruments of different kinds: of these we shall
only be able to take a cursory view, and we shall afterwards attend to the
historical order of the most remarkable steps, by which both the theory and
practice of music have been advanced to a high degree of refinement.

Musical instruments may be most conveniently arranged, accordingly
as they are principally calculated for exciting sound by the vibrations
of chords, of membranes, of elastic plates, or of the air; or by the
joint effects of the air and a solid body vibrating together. The es-
sential varieties of stringed instruments are found in the harp, the
harpsichord, the pianoforte, the clavichord, the guitar, the violin, the
vielle or monochord, and the aeolian harp. In all these, the immediate force
of the sound of the strings is increased by means of a sounding board, which
appears to be agitated by their motion, and to act more powerfully on the
air than the strings could do alone.

In the harp, the sound is produced by inflecting the string with the
finger, and suffering it to return to its place. The lyre of the ancients
differed from the harp only in its form and compass, except that the per-
former sometimes used a plectrum, which was a small instrument, made of
ivory, or some other substance, for striking the strings. Each note in the
harp has a separate string; and in the Welch harp there are two strings to
each note of the principal scale, with an intermediate row for the ficm'tones;
but in the pedal harp, the half notes are formed by pressing pins against the
strings, so as to shorten their effective length. Instead of this method, an
attempt has lately been made to pxoduce the semitones by changing the

398 LECTURE XXXIV.

tension of the strings, which is said to have succeeded tolerably well
although it appears at first sight somewhat unpromising.

In the harpsichord, and in the spinet, which is a small harpsichord, the
quill acts like the finger in the harp, or the plectrum in the lyre, and it is fixed
to the jack by a joint with a spring, allowing it without difficulty to repass
the string, which is here of metal. Sometimes leather is used instead of
quills; and tliis serves to make the tone more mellow, but less powerful.
Besides two strings in unison, for each note, the harpsichord has generally a
third which is an octave above them. Different modifications of the tone
are sometimes produced by striking the wire indifferent parts, by bringing
soft leather loosely into contact with its fixed extremity, and by some other
means. When the finger is removed from the key, a damper of cloth falls
on the string, and destroys its motion. In all instruments of this kind, the
perfection of the tone depends much on the construction and situation of
,the sounding board: it is usually made of thin deal wood, strengthened at
different parts by thicker pieces fixed below it.

In the pianoforte, the sound is produced by a blow of a hammer, • raised
by a lever, which is as much detached from it as possible. The dulcimer, or
hackbrett of the Germans, is also made to sound by the percussion of ham-
mers, but they are simply held in the hand of the performer.

The clavichord, the clavier of the Germans, differs from other keyed
instruments in the manner in which the length of the string is determined;
it is attached at one end to a l:)ridge, and at the other to a pin or screw as
usual; but the effective length is terminated on one side by the bridge,and on
the other by a flat wire projecting from the end of the ke}', which strikes
the string, and at the same time serves as a temporary bridge as long as the
sound continues: the remaining portion of the string is prevented from
sounding by being in contact with a strip of cloth, which also stops the
whole vibration as soon as the hammer falls. The instrument is capable of
great delicacy and neatness of expression, but it is deficient in force. The
guitar is generally played Avith the fingers, like a harp; but each string is
made to serve for several notes, by means of frets, or cross wires, fixed to the
finger board, on which it is pressed down by the other hand. But in the

ON MUSICAL INSTRUMENTS. 359

pianoforte guitar, hammers are interposed between the fingers and the strings,
acting like those of tlie pianoforte. The mandoline and lute are species of
the guitar: and the arch lute was a very powerful instrument of the same kind,
formerly much ulsed in full pieces.

In' the violin, and in other instruments resembling it, all the strings arc
capable of having their length altered at pleasure, by being pressed down on
the finger board. The sound is produced by the friction of the bow, rubbed
with resin: the string is carried forwards by its adhesion to the bow, and
when its resistance has overcome this adhesion, it begins to return in oppo-
sition to the friction ; for the friction of bodies in motion is generally less
than their adhesion when they are at rest with respect to each otlier, besides
that the contact of the string with the bow is usually in great measure in-
terrupted by subordinate vibrations, which may be distinguished, by the
assistance of a microscope, in the manner already described; but when the
string changes once more the direction of its motion, it adheres again to the
bow, and is accelerated by it as before. The original instrument appears to
have been the viola or tenor, its diminutive the violino, its intensitive, ex-
pressing a greater bulk, the violone or double bass, and the diminutive of
this,, the violoncello, or common bass. The viola di gamba had one or more
long strings separate from the finger board, serving as an occasional accom-
paniment.

The vielle, or raonochorcl, commonly called the hurdy gurdy, has frets
which are raised by the action of the fingers on a row of keys; and instead
of a bow, the string is made to vibrate by the motion of a wooden wheel :
there is a second string serving as a drone, producing always the same sound ;
this is furnished with a bridge loosely fixed, which strikes continually against
the sounding board, and produces a peculiar nasal effect. The trumpet
marine, or trumpet Marigni, was a string of the same kind, which was
lightly touched at proper points, so as to produce harmonic notes only ; it was
impelled by a bow. The aeolian harp, when agitated by the wind, affords
a very smooth and delicate tone, frecpiently changing from one to another
of the harmonics of the string, accordingly as the force of the wind varies,
and as it acts more or less unequally on different parts of the string. (Plate
XXV. Fig. 356.) '

400

*"" L?:CTURE XXXIV.

The human voice depends principally on the vibrations of the membranes
of the glottis, excited by a current of air, which they alternately intercept
and suffer to pass; the sounds being also modified in their subsequent
progress through the mouth. Perhaps the interception of the air by these
membranes is only partial ; or it may be more or less completely intercepted in
sounds of different kinds: the operation of the organs concerned is not
indeed perfectly understood, but from a knowledge of their structure, we
may judge in some measure of the manner in which they are employed.

The trachea, or windpipe, conveys the air from the chest, which serves for
bellows: hence, it enters the larynx, which is principally composed of five
elastic cartilages. The lowest of these is the cricoid cartilage, a strong ring,
which forms the basis of the rest: to this are fixed, before, the thyreoid car-
tilage, and behind, the two arytaenoid cartilages, composing together the
cavity of the glottis, over which the epiglottis inclines backwards, as it
ascends from its origin at the upper part of the thyreoid cartilage. Within
the glottis arc extended its ligaments, contiguous to each other before,
where they are inserted into the thyreoid cartilage, but capable of diverging
considerably behind whenever the arytaenoid cartilages separate. These
ligaments, as they vary their tension, in consequence of the motions of the
arytaenoid cartilages, are susceptible of vibrations of various frequency, and
as they vibrate, produce a continuous sound. Properly speaking, there are
two ligaments on each side; but it is not fully understood how they operate;
probably one pair only performs the vibrations, and the other assists, by
means of the little cavity interposed, in enabling the air to act readily on
them, and in communicating the vibrations again to the air. (Plate XXVI.
Fig. 357, 358.)

The vowels and semivowels are continuous sounds, chiefly formed by this
apparatus in the glottis, and modified either in their origin or in their pro-
cress by the various arrangements of the different parts of the mouth. Of
simple vowels sixteen or eighteen may be enumerated in different languages:
in the French nasal vowels the sound is in part transmitted through the
nostrils, by means of the depression of the soft palate: the perfect semivowels
differ from" the vowels only in the greater resistance which the air undergoes
in its passage through the mouth; there are also nasal and semiuasal semi-

ON MUSICAL INSTRUMENTS. 401

vowels. The perfect consonants may be either explosive, susurrant, or
mute; the explosive consonants begin or end with a sound formed in the
larynx, the others are either whispers, or mere noises, without any vocal sound.
By attending to the various positions of the organ, and by making experi-
ments on the effects of pipes of different forms, it is possible to construct
a machine which shall imitate very accurately many of the sounds of the
human voice; and this has indeed been actually performed by Kratzenstein and
by Kempelen. (Plate XXVI. Fig. 359.)

Although the vibrating ligaments of the glottis may be anatomically
denominated membranes, yet their tension is probably confined to the
direction of their length, and their action is, therefore, the same with
that of a simple string or chord. But in the case of a tambourine and
a drum, the membrane is stretched in every direction, and the force of
tension consequently acts in a different manner. The principal character
of such instruments is their loudness, derived from the magnitude of the sur-
face which strikes the air, and the short duration of the sound, on account of
the great resistance necessarily produced by the air's reaction.

Musical instruments which produce sotinds, by means of vibrations depend-
ing on the elasticity of solid bodies, are less frequently employed than
others; they have a peculiar character of tone, which is by no means
unpleasant, but which renders them less fit to be mixed with other instru-
ments, since their secondary harmonics are in different proportions. Such is
the stacada, a series of cylinders of glass, or of metal, struck either imme-
diately with hammers, or by means of keys ; the tuning fork, the gong, the
cymbal, and the bell. Bells and other similar instruments are usually made
of a mixture of copper, and tin, with a little brass or zinc, which is more highly
elastic than either of the component parts taken separately. The harmonica
consists of a series of vessels of glass, either placed side by side, or fixed on
a common axis, and made to sound by the friction of the fingers, and some-
times by that of rubbers of cork. The vibrations of an elastic plate, agi-
tated by a current of air, which it continually admits and excludes, con-
stitute the sound of the vox humana and regal organ pipes, resembling the
human voice as much in their effects as in the mechanism on which they de-
pend. (Plate XXVI. Fig 360 . . 36i.) ' .

VOL I. 3 I'

402 LECTURE XXXIV.

Of Simple Avlnd instruments, in which the quality of the sound is deter-
mined by the vibrations of the air, the principal are the syrinx, the flute,
the flageolet, the diapason organ pipe, whether open, stopped, or with a
chimney, the humming top, and the cavity of the mouth in whistling, or in
playing on the Jew's harp. The pipes of the syrinx are adjusted to their
respective notes by cutting them, or filling them up, until they are reduced to
a proper length; and the efl^ective length of the flute and flageolet is altered
. at pleasure by opening or shutting the holes made at proper distances in them ;
the opening a hole at any part having the same effect as if the pipe were cut
off a little beyond it, and the elevation of the tonebeing somewhat greater as
the hole is larger. The instruments differ little except in the mechanism, by
which the breath is directed, in such a manner as to excite a sound; and
the flageolet, when furnished with bellows, becomes a bagpipe. The tongue
of the Jew's harp is an elastic plate, but the sound, which it immediately
produces, serves only as a drone; its vibration, however, appears to act like
the motion of the bow of a violin in exciting another sound : this sound,
although faint, is still sufficiently musical, and appears to be determined by
the magnitude of the cavity of the mouth, nearly in the same manner as that
of the humming top, or as the sound of the same cavity produced in whist-
ling, by a current of air which is forced through it. (Plate XXVI. Fig.
563 . . 367.)

In mixed wind instruments, the vibrations or alternations of solid bodies
are made to cooperate with the vibrations of a given portion of air. Thus,
in the trumpet, and in bonis of various kinds, the force of inflation, and
perhaps the degree of tension of the lips, determines the number of parts
into which the tube is divided, and the harmonic which is produced. In the
serpent, the lips cooperate with a tube, of which the effective length may
be varied by opening or shutting holes, and the instrument which has been
called an organized trumpet appears to act in a similar manner; the trom-
bone has a tube which slides in and out at pleasure, and changes the actual
length of the whole instrument. Tlie hautboy, and clarinet have mouth
pieces of different forms, made of reeds or canes, and the reed pipes of an
organ, of various constructions, are furnished with an elastic plate of metal,
which vibrates in unison with the column of air that they contain. An
organ generally consists of a number of different series of such pipes, so

2

ON MUSICAL INSTRUMENTS. . 403

arranged, that by means of registers, the air proceeding from the bellows
may be admitted to supply each series, or excluded from it, at pleasure, and
a valve is opened, when the proper key is touched^ which causes all the pipes
belonging to the note, in those series of which the registers are open, to
sound at once. These pipes are not only such as are in unison, but fre-
quently also one or more octaves above and below the principal note, and
sometimes also twelfths and seventeenths, imitating the series of natural
harmonics. But these subordinate sounds ought to be comparatively faint,
otherwise their irregular interference would often occasion an intolerable dis-
cord, instead of the grand and sublime effect which this instrument is capa-
ble of producing, when it is judiciously constructed and skilfully employed.
(Plate XXVI. Fig. 368.)

The practice of music appears to be of earlier origin than either its theory,
or any attention to the nature and general phenomena of sound. The first
lyre, with three strings, is said to have been invented in Egypt by Hermes,
under Osiris, between the years 1800 and 1500 before Christ; but a tradi-
tion so remote, concerning a personage so enveloped in fable, can scarcely be
considered as constituting historical evidence: we cannot, therefore, expect
to ascertain with any certainty the proportions of these strings to each other;
some suppose that they were successive notes of the natural scale, others that
they contained the most perfect concords; perhaps in reality each performer
adjusted them in the manner which best suited his own fancy. The trumpet
is said to have been employed about the same time; its natural harmonics
might easily have furnished notes for the extension of the scale of the lyre, but
it does not appear that the ancients ever adopted this method of regulating the
scale. The lyre with seven strings is attributed to Terpander, about 700
years before our era, and two centuries afterwards, either P) thagoras, or Si-
monides, completed the octave, which consisted of intervals differing verv
little from the modern scale, the key note being nearly in the middle of the
series. In subsequent times the number of the stiings was much increased ; the
modulations, and the relations of the intervals, became very intricate, and were
greatly diversified in a variety of modes or scales, which must have afforded an
inexhaustible supply of original and striking melodies, but which could scarcely
admit so man} pleasini;' combinations, as our more modern systems. Although
it is certain that the ancients had frequent accompaniments in perfect harmony

404 LECTURE XXXIV.

with the principal part, yet they had no regular art of counterpoint, or of
performing different melodies together ; nor does it appear that they ever
employed discords. The tibia of the ancients resembled a hautboy or clari-
net, for it had a reed mouth piece, about three inches long; the same per-
former generally played on two of these instruments at once. There were,
however, several varieties of the tibia; and it is not improbable that some of
them may have had the simple mouth piece of the flageolet.

The first philosophical observer of the phenomena of sound, after Pytha-
goras, appears to have been Aristotle; he notices a great variety of curious
, facts in harmonics among his mechanical problems; and he entertained a
very correct idea of the true nature of the motions of the air constituting
sound. He knew that a pipe or a chord of a double length produced a
sound of which the vibrations occupied a double time; and that the properties
of concords depended on the proportions of the times occupied by the vibra-
tions of the separate sounds. It is not indeed improbable that at least as much as
this was known to Pythagoras, since he established correctly the numerical
ratios between various sounds; but so little justice has been done to his dis-
coveries by the imperfect accounts of them which have been preserved, that
we cannot expect to be able to ascertain his opinions on any subject with
accuracy.

The invention of the organ, by Ctesibius of Alexandria, about 2000 years
ago, forms a remarkable epoch in harmonics. The larger instruments of this
kind Avere furnished with hydraulic bellows, the smaller with bellows of
leather only ; and they had keys which were depressed, like those of the
modern organs, by the fingers of the performer, and which opened valves
communicating with the pipes.

The modern system of music is one of the few sciences, if such it can be
Galled, which owe their improvement to the middle ages. The old ecclesi-
astical music was probably founded in great measure on that of the Greeks; its
peculiar character consisted in the adoption of any note of the scale at pleasure
for a key note, without altering materially the other intervals; and in this man-
ner they obtained a variety much resembhng that of the modes or kinds of music
in use among the ancients. Pope Gregory, about the year 600, distinguished

ON MUSICAL INSTRUMENTS. 405

the notes by literal characters; the rules of counterpoint were formed by
degrees from the experience of the ecclesiastical musicians; and early in the
eleventh century, Guido of Arezzo, otherwise called Aretin the monk,
introduced, together with some improvements in the theory and practice of
music, a new method of naming the notes by syllables.

Some curious experiments on sound may be found in the works of Bacon,
but they added very little to the true theory of aeustics, and some of them are
not perfectly accurate, Galileo rediscovered what was well known to Aris-
totle, respecting the nature of sound; for the words of Aristotle had been
so much misunderstood and misinterpreted, that he could have profited but
little by them. His cotemporaries Mersenne and Kircher made a variety of
very ingenious experiments and observations, on sound and on soundin<i-
bodies, many of them unknown to authors of later date. The theory of
the ancient music was very accurately investigated, in the middle of the
17th century, by Meibomius : our countryman Wallis, also, besides employ-
ing much learning and penetration in the illustration of the ancient
music, observed some insulated facts in harmonics which were new and
interesting.

Sir Isaac Newton's propositions respecting the velocity of the propagation
of sound were the beginning of all the more accurate investigations relating
to aeustics. It must not be denied that these propositions contain some very
inconclusive reasoning respecting the nature of the motions constituting
sound, by which the determination of a particular case is erroneously extended
into a general solution of the problem. The velocity is, however, truly cal-
culated, because it is in fact independent of the particular nature of the vibra-
tion, and all that is wanting to generalise the proposition is the remark, that
if the velocity of sound is the same in all cases, it must be such as the calculation
. indicates. An error nearly similar was committed by Brook Taylor, who in the
year 1714 investigated the time occupied by the vibration of a string or
chord upon a particular supposition, which he co:>sidered as a necessary
condition, but which in fact confined the inquiry to a limited case. It
happensjhowever, that the same determination of the frequency of vibration is
equally true in all possible cases. Sauveur obtained, about the same time

4.06 tECTURE XXXIV.

a similar conclusion from reasoning still less accurate: his merits with respect
to the theory of acustics in general are, however, by no means contemptible.
Lagrange and Euier have corrected and much extended the investigations
of Newton, and of Taylor; and Bernoulli and Daleinbert have also materi-
ally contributed to the coijiplete examination and discussion of the
subject.

About the year 1750, Daniel Bernoulli succeeded in obtaining a solution
of a problem still more diificult than those which relate to the motions of
chords: he determined the frequency of the vibrations of an elastic rod
fixed at one end, as well as the relations of its subordinate sounds. Thesolution
is not indeed absolutely general, but it may perhaps be adapted to all possible
cases, by considering the effect of a combination of various sounds produced
at the same time. Euler has also great merit in extending and facilitating the
mathematical part of this investigation, although he has committed several
mistakes respecting the meclianical application of it, some of which he
has himself corrected, and others have been noticed by Riccatiand Chladni,

The grave harmonics produced by the combination of two acute sounds
were noticed about the same time by Romieu and by Tartini, but first by
Romieu: their existence is not only remarkable in itself, but particularly as
it leads to some interesting consequences respecting the nature of sound and
hearing in general.

Bernoulli has also investigated, in a very ingenious manner, the sounds
produced by the air in pipes of various forms, although confessedly on
suppositions deviating in some measure from the truth: the results of his
computations have, however, been amply confirmed by the experiments of
Lambert on the sounds of flutes.

Dr. Chladni's method of examining the sounds of plates has affbrded a
Very interesting addition to our knowledge of the nature of vibrations; his
discovery of the longitudinal sounds of solids is of considerable importance,
and he is said to be engaged in an extensive work on tlie subject of acustics
in general. Some remarks which I have made in the Philosophical Trans-

ON MUSICAL INSTRUMENTS.

407

actions may perhaps also be considered as tending to illustrate the vi-
brations of chords. The latest improvement which deserves to be mention-
ed, with respect to the theory of sound, is Laplace's explanation of the increase
of its velocity on account of the effect of heat, which appears to afford a
satisfactory explanation of a difficulty so much the more important, as it
tended to lessen our confidence in every part of a theory, which differed so
widely from the most accurate and best established observations.

CHRONOLOGY OF ACUSTICS.

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40S

LECTURE XXXV.

ON THE THEORY OV OPTICS.

J. HE science of optics is one of the most elegant, and the most important
branches of natural and mechanical philosophy. It presents us with experi-
ments attractive by their beauty and variety, with investigations affording
an ample scope for mathematical refinementSj and with instruments of exten-
sive utility both in the pursuit of other sciences, and in the common em-
ployments of life; nor is there any department of the study of nature in
which an unprejudiced observer is more convincingly impressed with the
characteristic marks of the perfect works of a supremely intelligent Artist.

We shall first consider the essential properties which we discover in light,
and which are the basis of our calculations, together with the conclusions
immediately deducible from those properties; and next, the application of
these laws to practical purposes, in the construction of optical instruments.
We shall afterwards proceed to examine the more complicated phenomena,
which are derived from the same laws, and which are observed as well in
natural as in artificial circumstances, constituting the subdivision of physical
optics. The description of the eye, and the explanation of the sense of
vision, by means of which all these effects are connected with the human
mind, is properly a continuation of the subject of physical optics: the intimate
nature of light will be the next subject of investigation, and a historical sketch
of the progress of the science pf optics will conclude the second part of this
course of lectures.

In order to avoid all hypothesis in the beginning, it will be necessary to de-
fine light from its sensible qualities. The sensation of light is sometimes pro-
duced by external pressure on the eye; we mu>>t exclude this sensation from the
definitionof light, and must therefore call light an influence capable of entering

5

ON THE THEORV OF OPTICS. 409

eye, and of affecting it with a sense of vision. A body, from which this
influence appears to originate, is called a luminous body. We <lo not
include i n this definition of the term light the invisible influences which
occasion heat only, or blacken the salts of silver, although they both appear
to differ from light in no other respects than as one kind of light differs
from another; and they might probably have served the purpose of light, if
our organs had been differently constituted.

A ray of light is considered as an infinitely narrow portion of a stream of
light, and a pencil as a small detached stream, composed of a collection of such
rays accompanying each other. As a mathematical line is sometimes conceiv-
ed to be described by the motion of a mathematical point, so a ray of light may
be imagined to be described by the motion of a point of light. We cannot exhi-
bit to the senses a single mathematical line, except as the bountlary of two
surfaces; in the same manner, Ave cannot exhibit a single ray of light, except
as the confine between light and darkness, or as the lateral limit of a pencil
of light.

When light passes through a space free from all material substances, it
moves, with great velocity, in a direction perfectly rectilinear; when also
it passes through a material substance perfectly uniform in its structure, it
probably always moves in a similar manner. But in many cases its motions
are much interrupted. Those substances through which light passes the
most freely, and in straight lines, are called homogeneous transparent
mediums. Perhaps no medium is, strictly speaking, absolutely transparent;
for even in the air, a considerable portion of light is intercepted. Ithas
been estimated that of the horizontal sunbeams, passing through about 200
miles of air, one two thousandth part only reaches us; and that no sensible
light can penetrate more than 700 feet deep into the sea ; a length of seven
feet of water having been found to intercept one half of the light which
enters it. .

It is possible that mediums, not in other respects identical, may be homo-
geneous with respect to the transmission of light ; for example, a glass may
be filled,with a fluid of such a density, that the light may pass uninterruptedly
through their common surface; but it generally happens, that whenever the

VOL. I. ^ 3 G

410 ^ LECTURE XXXV.

nature of the medium is changed, the path of Ijght dcA'iates from a straight
line: thus, the apparent places of the sun and stars are changed by the effect of
the atmosphere, because the light, by which we judge of their situations, is
deflected, in its passage out of the empty space beyond the atmosphere,
first into the rarer and then into the denser air. In the same manner, when
we view a distant object over a fire or a chimney, it appears to dance and
quiver, because the rays of light, by which it is seen, are perpetually thrown
into new situations, by the different changes of the density of the air in con-
sequence of the action of heat.

"When rays of light arrive at a surface, which is the boundary of two me-
diums not homogeneous, they continue their progress without deviating
from those planes, in which their former paths lay, and which are perpen-
dicular to the surface of the mediums; but they no longer retain the same
direction, a part of them, and sometimes nearly the whole, is reflected back
from the" surface, while the remaining part is transmitted and refracted, or
bent. The name refraction is derived from the distortion which it occasions
in the appearance of an object viewed in part only by refracted light: thus
an oar, partially immersed in water, appears to be bent, on account of the re-
fraction of the light by which its lower part is seen, in its passage out of the
water into the air.

There is no instance of an abrupt change of the density of a medium,
without a partial reflection of the light, passing either into the denser or into
the rarer medium; and the more obliquely the light falls on the
surface, the greater, in general, is the reflected portion. No body
is so black as to reflect no light at all, and to be perfectly invisible
in a strong light; although at the surface separating two very rare bodies,
as two kinds of gas, the reflection is too faint to be perceptible; but in this
case the separation is seldom perfectly abrupt.

The angles of incidence and reflection are the angles made by a ray of
light, before and after its reflection, with a line perpendicular to the reflecting
surface; and these angles are always equal to each other; consequently
the inclination of the rays to the surface remains also the same. The
quantity of light reflected, when other circumstances are equal, appears to

ON THE THEORY OF OPTICS. 411

be always greatest when the difFereace of the optica) or refractive density of
the two substances is greatest. Thus the reflection from the common sur-
face of glass and water' is much weaker, than from a surface of glass ex-
posed to the air. Metals in general reflect a great proportion of the light
falling on them, and even the reflection from the common surface of glass
and mercury appears to be but little weaker than the reflection from the
surface of mercury immediately exposed to the air, so that the optical den-
sity of the metals must be exceedingly great.

It appears also that a portion of the light falling on a reflecting surfiice
is always transmitted, at least to a certain depth, notwithstanding the appa-
rent opacity of any large masses of the substance. Thus, if we cover a small
hole of a window shutter with the thinnest leaf gold, we shall find that it
transmits a greenish light, which must have passed the reflecting surface,
but which, if the gold had been but one ten thousandth of an inch in thick-
ness, would have been wholly intercepted, and probably almost in the same
manner as by passing through 700 feet of water. In transparent substances,
however, the greater part of the light penetrates to ail distances with little
interruption, and all rays of the same kind, thus transmitted by the same
surface, form with the perpendicular an angle of refraction which is ultimately
in a certain constant proportion to the angle of incidence ; that is, for instance,
one half, three fourths, or two thirds, according to the nature of the sur-r
ffice. Thus, if the refractive properties of the substance were such, tliat an-
incident ray, making an angle of one degree with the perpendicular, would
be so refracted as to make an angle of only half a degree with the same line,
another ray, incident at an angle of two degrees, would be "re-
fracted, without sensible error, into an angle of one degree. IJut Avhen the
angles are larger, they vary from this ratio, their sines only preserving the
proportion with accuracy: for example, if the angle of incidence at the sup-
posed surface were increased to 90°, the angle of refraction would be 30"
only, instead of 45". Rays of the same kind are in general distinguished
by the same colour, although some rays, Avhich differ from each other in
refrangibility, have scarcely a discernible difference of colour; and it is
possible, on the other hand, to find a surface at which the ratio of the angles
is the same for rays of all kinds. (Plate XXVI. Fig. 369, 370.)

41<i LKCTURTE XXXV.

In order to obtain the eifects of regular reflection and transmission, wc
must have perfectly smooth and polished substances; for all rough bodies, and
sometimes even such as to the touch seem tolerably smooth, have their surfaces
divided into innumerable eminences and depressions, constituting, in realit}', as
many separate surfaces, disposed in all imaginable directions, so that from
the e(|uality of the angles of incidence and reflection, with respect to each of
these surfaces, the light must be scattered every way, and no regularity can
be observed in its direction. It is true that by continuing the mechanical
operation of polishing, we only render these surfaces more minute and more
numerous; but when they are so much reduced in magnitude as not to be
elevated or depressed more than about the millionth part of an inch, they
appear to become, for some physical reason, incapable of acting separately,
and only to conspire in the general effect.

In all cases of refraction, as well as of reflection, if the ray of light re-
turned directly backwards in the same line to the surface, it would proceed,
after a second refraction or reflection, in the direction precisely opposite
~to that in which it first was incident, so that the same lines would mark its
path in both cases. Thus, if we stand before a looking glass, with one eye
shut, and cover its place on the glass with a finger, the same finger will hide
the other eye as soon as it is shut, and the first is opened in its place; and a
similar effect might be observed, if the glass were under water, or behind any
other refracting substance. (Plate XXVI. Fig. 371.)

The medium, in wliich the rays of light are caused to approach nearest to
the line perpendicular to its surface, is said to have the greatest refractive
density. In general there is a considerable analogy between this re&active
density and the specific gravity of the substance: thus water is more refrac-
tive than air, and glass than water. But inflammable bodies are usually
more refractive than bodies of the same specific gravity, which are not in-
flammable; and it is well known that from the high refractive power of the
diamond, in proportion to its actual density,Sir Isaac Newton most ingeniously
conjectured that it was combustible, as more modern experiments have actually
shown it to be. It is still more singular that he also imagined, from the
same analogy, that water consists of a combination of oily or inflammable
particles, with others earthy or not inflammable. In the order of refractive

ON THE THEORY OF OPTICS. ' 413

density, beginning from the lowest, or a vacuum, we liave airs and gases
of different rarities, water, which is the least refractive of allliquids, and
•which is still less refractive when frozen into ice: alcohol, oils, glass, and
lastly the diamond; but probably some metallic substances are much more
refractive than even the diamond.

The refractive powers of different substances, are usually estimated by a
comparison of the. refractions produced at their surfaces in contact with the
air, which, in all common experiments, has the same sensible effect as a
vacuum or an empty space; the ratio of the angles of refraction and inci-
dence, when small, and that of their sines, in all cases, being expressed by
the ratio of 1 to a certain number, which is called the index of the refrac-
tive density of the medium. Thus, when a ray of light [passes out of air
into water, the sines of the angles are in the ratio of 3 to 4, or of 1 to-t,
which is, therefore, the index of the refractive density of water. In the
same manner, for crown glass, the ratio is that of 2 to 3, and the index 1^;
but for flint glass it is somewhat greater, the ratio being nearly that of 5 to 8.

It may easily be shown that a refractive substance, limited by parallel sur-
faces, must transmit a ray of light, after a second refraction at its posterior
surface, in a direction parallel to that in which it first passed through the
air. It is also found by experiment that such a substance, interposed between
any two mediums of difi'erent kinds, produces no alteration in the whole an-
gular deviation of a ray passing from one of them into the other. Hence
it may be inferred, that the index of refraction at the common surface of any
two mediums is the quotient of their respective indices. For instance,, a
plate of c rown glass being interposed between water on one side and air on
the other, it produces no change in the direction of a ray of light entering
the water; and the index of refraction at the common surface of glass and
water is |. (Plate XXVI. Fig. 372, 373.)

There is one remarkable consequence of the general law, by which the angles
of incidence and refraction are related, that whenthe angle of incidence exceeds
a certain magnitude, the refraction may become impossible; and in this case the
ray of light is wholly reflected, in an angle equal to the angle of incidence.

414 LECTURE XXXV.

Thus, if the law of refraction required the sine of the angle of refraction to
be twice as great as that of incidence, this condition could not take place if
the angle of incidence were greater than 30", so that when a ray passing
within a dense medium falls very obliquely on its surface, it must be wholly
reflected ; and the greater the density of the medium, the more frequently
will the light be totally reflected. This reflection is more perfect than any
other; the diamond owes much of its brilliancy to it: the great refractive
density of this substance not only giving a lustre to its anterior surface,
but also facilitating the total reflection of such rays as fall obliquely on its
posterior surface. If we hold a prism, near a window, in a proper position,
we may observe that its lower surface appears to be divided into two parts,
the one much brighter than the other; the common partial reflection taking
place in one, and the total reflection in the other. The tw^o surfaces are
separated by a coloured arch : it is coloured, because the total reflection
commences at different angles for the rays of different colours ; and it is
curved, because the points, at which the light passing to the eye
forms a given angle with the surface, do not lie in a straight line ;
and if we throw a light on a wall by a reflection of this kind, we may easily
observe, as we turn the prism, the point at which the brightness of the
'mage is very conspicuously increased. (Plate XXVI. Fig. 374:)

Such are the principal properties which we discover in light. Before we
consider their immediate application to optical instruments, we must exa"
.niine the general theory of refraction and reflection, at surfaces of different
kinds, or the doctrines of dioptrics and catoptrics.

The rays, which constitute a pencil of light, are sometimes parallel to each
other, sometimes divergent from a point, and sometimes convergent to a
point. The intersection of the directions of any two or more rays of light
is called their focus; and the focus is either actual or virtual, accordingly as
Ihey either meet in it, or only tend to or from it. Thus, a small luminous
object may represent an actual focus of diverging rays, since the light
spreads from it in all directions; and the small surface, into which the image
of such an object, or of the sun, is collected by a lens or mirror, may re-
present the actual focus of converging rays. It was to such an image of the

ON THE THEORY OF OPTICS.

415

8un that the term focus, meaning a fireplace, was first applied. But if the
rays tending to this focus be intercepted, and made to diverge, the point will
then be their virtual focus, since they will never actually arrive at it, being
made to diverge as if they proceeded from a new point, which will also be a
virtual focus. When the divergence or convergence of rays of light is altered
by refraction or reflection at any surface, the foci of the incident and re-
fracted or reflected rays are called conjugate to each other: the new focus
is also called the image of the former focus. Thus, in the case already
mentioned, where the convergence of the rays to one focus is converted
into divergence from another, the two virtual foci are conjugate to each
other; and the original focus of the lens or mirror is conjugate to the place
of the sun, or of the luminous object. If the object had been put in the
place of its image, the image would then have occupied that of the object; a pror
perty which follows from the direct return of every ray of light through the
path by which it has arrived, and which may easily be illustrated by experi-
mental confirmation. (Plate XXVII. Fig. 375.)

Whenever light is reflected by a plane surface, the conjugate foci are at
equal distances from it, and in the same perpendicular. Thus, every point
of an image in a looking glass is perpendicularly opposite to the correspond-
ing point of the object, and is at the same distance behind the looking glass,
as the point of the object is before it. (Plate XXVII. Fig. 376.)

The focus into which parallel rays are collected, or from which the}' are
made to divei-ge, is called the principal focus of a surface or substance. The
sun is so distant, that the rays, proceeding from any point of his surface,
aifect our senses as if they were perfectly parallel, and the principal focal
distance of a surface or substance may often be practically determined by
measuring the distance of the image of the sun, or of any other remote
object, which is formed by it.

In order that the rays of light, proceeding from or towards any one point,
may be made to converge by reflection towards another, the form of the surface
must be elliptical, parabolic, or hyperbolic; there are also curves of still more
intricate forms, which possess the same property with respect to refrac-

416 LECTURE XXXV.

tion. A small portion, however, of any of these curves, differs very
little from a circle; and a spherical surface is ahuost universally substituted
in practice for all of them, except that the mirrors of large reflecting tele-
scopes are sometimes made parabolical.

The principal focus of a spherical reflecting surface, whether convex or
concave, is half way between the surface and its centre. If a luminous point
be placed in the centre of a concave mirror, the rays will all return to the same
point; if the point be beyond the centre, the image will be between the centre
and the principal focus, its distance from that focus being always inversely as
that of the radiant point. Such a focus is never absolutely perfect, for the
rays are never collected from the whole surface of the mirror into the same
point, except when both the point and its image are in the centre: but,
provided that the surface be only a small portion of that of the whole sphere,
the aberration will be too small to be easily observed : and the same is true
of the foci produced by refracting surfaces. (Plate XXVII. Fig. 377,
378.)

When a ray of light passes through two surfaces forming an angle with
each other, including a denser medium, as in the case of a prism of glass,
it is always deflected from the angle in which the two surfaces meet. A
greater number of surfaces, placed in different directions, constitute what is
sometimes called a multiplying glass, each of them bending the rays of light
into a diff'erent direction. (Plate XX VII. Fig. 379, 380.) '

A lens is a detached portion of a transparent substance, of which the op-
posite sides are regular polished surfaces, of such forms as may be described
by lines revolving round a common axis. These lines may be portions of
circles, of ellipses, hyperbolas, or of any other curves, or they may be right
lines. But in general, one of the sides is a portion of a spherical surface, and
the other either a portion of a spherical surface or a plane; whence we have
double convex, double concave, planoconvex, planoconcave, and meniscus
lenses. The figures of all these are sufficiently described by their names,
except that the term meniscus, which properly implies a little m oon or
crescent, is applied in general to all lenses which are convex on the one side,

ON THE THEORY OF OPTICS. 4J7

and concave on the other, although they may be thicker at the edges than
in the middle. Sometimes, however, a lens of this kind is distinguished by
the term concavoconvex. A lens is generally supposed, in simple cal-
culations, to be infinitely thin, and to be denser than the surrounding medium.
(Plate XXVII. Fig. 381.)

The general effect of a lens may be understood, from conceiving its surface
to coincide at any given point with that of a prism; for if the angle of the
prism be external, as it must be when the lens is convex, the rays will be
inflected towards the axis; but if the base of the prism be external, and the
lens concave, the rays will be deflected from the axis: so that a convex lens
either causes all rays to converge, or lessens their divergence, and a concave
lens cither causes them to diverge, or lessens their convergence. (Plate
XXVII. Fig. 382.)

The principal focus of a double convex or double concave lens, of crown
glass, is at the distance of the common radius of its surfaces ; and the focal
length of a planoconvex lens is equal to the diameter of the convex surface.
If the radii of the surfaces are unequal, their effect will be the same as if
they were each equal to the harmonic mean between them, which is found by
dividing the product by half the sum ; or, in the meniscus, by half the dif-
ference. Thus, if one of the radii were; two inches, and the other six, the
effect would be the same as that of a lens of three inches radius; and if it
were a meniscus, the same as that of a lens of six inches. (Plate XXVII.
Fig. 383, 384.)

The focal length of a lens of flint glass, of water, or of any other substance,
may be found, by dividing that of an equal lens of crown glass by twice
the excess of the index of refraction above unity. Thus, the index for
water being 1-i, we must divide the radius by ^, or increase it one half, for
the principal focal distance of a double convex or double concave lens of
water.

When a radiant point is at twice the distance of the principal fOcus from
a convex lens, the image is at an equal distance on the other side; when the

VOL. I. 3 H

4.18 LECTURE XXXV.

radiant point is nearer than this, the image is more remote, tlie distance of
the image from the principal focus nearest to it being always inversely as the
distance of the 'object from the principal focus on the opposite side. (Plate
XXVII. Fig. 385.)

The joint focus of two lenses, in contact with each other, is also found by
multiplying together their separate focal lengths, and dividing the product
by their sum or difference, accordingly as they agree or differ with respect
to convexity and concavity.

We have hitherto considered the place of the focus only in relation to a
single point, placed in the axis of the lens or mirror; but it is equally neces-
sary to attend to other points, out of the principal axis; for, in order to
form a picture, the rays from a great number of such points must be col-
lected into as many distinct points of the image. Some of the rays proceed-
ing from every radiant point must be considerably bent, in order to be col-
lected into a, common focus; others remain nearly straight; and if Ave can
discover which of the rays are ultimately either in the same line with their
original direction, or in a direction parallel to.it, we may determine the line
in which the image of the point in question is to be found. For this purpose,
we employ the property of the optical centre, which is a point so situated,
that all rays which pass through it, or tend towards it, while they are within
the lens, must ultimately acquire a direction parallel to their original direction.
In some cases, the optical centre may be without the lens, but no practical
inconvenience results from supposing it to be always situated within the
lens, especially when its thickness is inconsiderable; so that all rays which
pass through the middle point of the lens must proceed, without sensible
error, in the same straight line, and the irnage of any radiant point must
consequently be found somewhere in this line: but in the case of a mirror,
the centre of its figure is also the optical centre. Now when any radiant point
is removed a little from the axis of a lens or mirror, the distance of its image
is in general a little diminished, but the difference is too small to be ob-
servable in common cases. We may, therefore, suppose it to be at
the same distance as if the point remained in the axis, or even to be in
a plane crossing the axis perpendicularly at that distance, so as to form

ON THE THEORY OF OPTICS. 419

part of a flat image, of which the magnitude is determined by straight lines
drawn from the. extremities of the object through the centre of the
lens. This is, however, an approximation which is only admitted for
the greater convenience of computation and representation, the image
being almost always in reality considerably curved. (Plate XXVII. Fig.
386.)

420

LECTURE XXXVI.

ON OPTICAL INSTRUMENTS.

Among the great variety of instruments depending on optical principles,
it is more consistent with our plan to attend first to those which may be
denominated optical measures, which are calculated either for the determina-
tion of the quantity or intensity of light itself, or for the examination of the
properties of various material substances with respect to light. Reflecting
quadrants and circles, which are often used in astronomical and nautical
observations, although they derive their utility in some measure from optical
laws, may most pr.operly be considered as belonging to the subject of practical
astronomy.

It is a problem of frequent occurrence in economical investigations, to
compare the intensity of the light afforded by any two luminous objects.
For this purpose, it is necessary to assume as a principle, tliat the same
quantity of light, diverging in all directions from a luminous body, remains
undiminished at all distances from the centre of divergence. Thus, we must
suppose that the quantity of light falling on every body is the same as would
have fallen on the place occupied by its shadow: and if there were any
doubt of the truth of the supposition, it might be confirmed by some simple
experiments. It follows that since the shadow of a square inch of any sur-
face, occupies, at twice the distance of the surface from the luminous point,
the space of four square inches, the intensity of the light diminishes as the
square of the distance increases. We can judge with tolerable accuracy of
the equality of two lights by the estimation of the eye, but we cannot form
any idea of the proportions of lights of different intensities: if, however,
we remove two sources of light to such distances from an object, that they
may illuminate it in equal degrees, we may conclude that their original

OK OPTICAL INSTRUMENTS. 421

intensities are inversely as the squares of their distances. Count Rumford's
photometer performs this very conveniently, by casting two shadows of a
given object near each other, on the same surface, the lights being removed
to such distances that the shadows appear equally dark. (Plate XXVII
Fig. 387, 388.)

For determining the refractive density of solids, it has been usual to form
them into a prism, and to measure the angular deviations which they
produce ; and for fluids, to inclose them either in a hollow prism, or between
two meniscus lenses, and to measure the angular deviations produced by the
prisms, and the focal distances of the lenses. But in most cases. Dr. Wol-
laston's apparatus is far preferable to both these methods: it is arranged for
ascertaining the angle at which light, moving within a certain dense trans-
parent substance, begins to be totally reflected from the common surface of
that substance and the solid or fluid which is to be examined. Thus, if we
first measure the angle, at which light begins to be totally reflected from the
posterior surface of a prism of glass, in contact with air, we may readily
determine its refractive power; and then, having caused a drop of a fluid
to adhere to that surface, or iixed a solid to it by a small portion of some
fluid denser than itself, we may observe, as we turn the prism round its
axis, at what angle the drop or spot begins to disappear, and may thence
calculate the refractive density of the substance; and even without actual
measurement of the angle, we may readily compare the disappearance of the
drop or spot with that of others placed near it, of which the properties are
known. Dr. Wollaston has, however, rendered the process still easier and
"more simple, by employing a rectangular prism of glass, with sights fixed to
a jointed frame, of such a construction as to enable him to read oft^ by a
vernier, without any calculation, the index of the refractive power of
any substance less dense than glass. (Plate XXVII. Fig. 3S9.)

All instruments strictly optical are employed for forming an image of an
external object: the simplest are mirrors and lenses, which form a single
image only, either actual or virtual, and sometimes depict it on a surface
calculated for receiving and exhibiting it. Other instruments repeat the
image once or more under several forms, in general enlarging it continu-

422 LECTURE XXXVI.

ally; and these are cither microscopes or telescopes, which present us with
great diversity in their arrangements, and in the appurtenances subservient to
their uses.

It is a general rule, that when an image of an actual object is formed by
any lens or speculum, if the rays converge to an actual focus, the image
is inverted; but erect, if they diverge from a virtual focus, and the object and
image subtend equal angles at the centre of the lens or speculum. Hence,
a convex lens and a concave mirror form an inverted image, smaller than the
object, whenever the object is at a greater distance than twice the principal
focal length; but larger, when the object is within this distance; and when
it is within the principal focal distance, the magnified image is virtual and
erect, and may be seen by looking into the concave mirror, or by looking
through the lens towards the object. But a concave lens and a convex
mirror always form a virtual image of a real object, which is erect, and
smaller than the object. (Plate XXVII. Fig. 390 . . 394.)

When the object is precisely in the principal focus of a convex lens or a
concave mirror, the virtual image becomes infinitely distant; so that from
whatever point in the neighbourhood of the lens it may be viewed, it must
•subtend the same angle, which is always equal to that which the object sub-
tends at the centre of the lens: and since this angle ma/y easily be much
greater than that under which the object can be conveniently viewed by the
naked eye, such a lens or mirror is often used as a simple microscope; and
its magnifying power may be ascertained from a comparison of the angles
which the object and image subtend. Thus, if a person cannot see a minute
object with the naked eye at a distance less than eight inches, a lens of half
an inch focal length will represent it to him in an angle 16 times as great:
but if he can see it without the lens at the distance of four inches, the lens
will magnify it to his eye but eight times. Supposing, however, the eye to
be applied close to the lens, the object may be viewed a little within
the focal distance, and its apparent angular magnitude may be increas-
ed 17 times instead of l6, and 9 times instead of 8. (Plate XXVII.
rig. 395, 596.)

Since the magnifying power of a lens is the greater, the smaller its focus,

ON OPTICAL INSTRUMENTS. 423

it is usual ot employ the minutest lenses that can be ground, and sometimes
a small globule is formed by fusion in a lamp. Even a drop of water, placed
in the perforation of a plate, makes a tolerable magnifier; and it has been pro-
posed to substitute for water a transparent varnish, which is less liable t^
evaporate. •

Supposing the whole light that proceeds from a distant object, and falls on g,
lens or speculum, to be collected in the image, its intensity must be increased
in the ratio of the surfaceof the lens or speculum to that of tile image. The image
is greater in proportion as the object is greater; consecpiently the deoree of
condensation produced by any lens is the greater as the object is smaller, thus
if the diameter of a lens were an inch, and the image of the sun formed by it
were also an inch in diameter, the density of the light would be unaltered;
but the image of a star would be infinitely brighter than the direct light of
the star falling on the lens. The illumination of any image formed by a
lens or mirror, supposing no light to be lost, is always the same as would
be produced by the direct light of the surface of the lens or mirror, if it were
equally luminous with the surface of the object which emits the li<>-ht. It
may also be shown, that 'when two lenses are of similar forms, their focal
lengths being proportional to their diameters, they must produce the same
degree of illumination in the image: but as far as the heat excited may be
supposed to be a measure of the quantity of light, this conclusion is not
confirmed by experiment: it is probable, however, that the greater heat,
produced by a larger lens, is only derived from the greater extent of surface
exposed at once to the solar rays.

Lenses are most commonly made of glass, but sometimes of rock crystal,
or of other transparent substances. It is difficult to find'glass, especially
flint glass, for large lenses, sufficiently free from veins: it has been proposed
to suffer the melted glass to cool without agitation, and to cut the lens out
of any of its strata taken in a horizontal direction; but this method appears
to be liable to several practical objections. Mirrors are made either of glass,
coated with an amalgam of mercury anil' tin, or of metal, as of platina, of
silver, or of an alloy of copper and tin, to which a little arsenic and silver
are sometimes added. Mirrors of metal are more perfect than those of glass,
because they are free from the inconvenience of a double reflection ; but thev

424 LECTURE XXXVI.

are more .expensive, and are liable to tarnish. Where a large mirror is re-
quired, with a weak reflection only, we may employ a single surface of
glass, the back of the piece being covered with a black coating of some
substance diftering little from glass in its refractive density, by means of
which the second reflection is avoided.

When the image formed by a lens or mirror is received on a smooth but
unpolished surface, which is capable of irregular reflection, it is visible in
every direction. Such an image is exhibited in the camera obscura, the
solar microscope, and the magic lantern, or lucernal microscope.

The general effect of the camera obscura is the same as may often be
observed in a dark room, where there is a small hole in the window shutter-
the great masses of light and shade, before the windows, being represented
an an inverted position, in the parts of the room diametrically opposite to
them, which are illuminated in dift^erent degrees, according to the quantity
of light which can reach them in straight lines from the external objects.
A lens, of a focal length somewhat smaller than the distance of the surface
on which the picture is projected, renders the images much more distinct;
but some of them are unavoidably imperfect and ill defined, unless the
objects happen to be situated at the same distance from the aperture ; for
the focus of the lens can never be adjusted at once to nearer and more re-
mote objects; nor would the picture be rendered more natural by such an
adjustment, for it would present to the eye at one view, with equal distinct-
ness, objects which never can be seen at once without some degree of con-
fusion. Sometimes the picture is intercepted, by a speculum placed obliquely,
and is thrown upwards on the surface of a plate of ground glass, upon which
its outline may be traced with a black lead pencil, and an impression may
be taken from it on moist paper, which will represent the natural situation
of the objects without inversion. Another arrangement is, to place the
lens horizontally, with the speculum above it, which throws the image
through the lens, upon a flat surfiice placed below, on which the objects
may be delineated in their natural position, but not without some impedi-
ment from the interception of the light by the hand and the instrument
employed. Such a surface, however, ought not to be perfectly flat, in
order to aiford the most distinct image, although by means of a meniscus

ox OPTICAL insthumexts. 425

lens, with a cover admitting the light only through a small aperture near its
centre, on the principle of Dr. Wollaston's periscopic spectacles, an image
nearly flat might be obtained ; but in this case too much of the light would
be excluded. It has been usual to consider the image of a very distant
object, formed by a convex lens, as a portion of a spherical surface, of which
every part is equally distant from the centre of the lens ; but this estimate is ex-
tremely erroneous, for the eflectof the obrujuity of the different pencils of rayg
materially increases the curvature of the image. In fact no pencil of rays,
falling obliquely on a spherical surface, can be collected any where to a perfect
focus: the image of a circle would become most distinct at one distance,
and that of its diameter at another; but for both these images, the surface
ought to be much more curved than that which has been usually considered,
and the mean of the curvatures required for them, which must be the best
form for the ground or bottom of a camera obscura, is equal to that of a
sphere of which the radius is three eighths of the focal distance, when a
double convex lens of crown glass is employed. (Plate XXV^II. Fig,
397 . . 399. )

In the solar microscope, an image is formed on a wall or screen, by mean*
of a lens of small focal length, near to which the object is placed, so that
the image is very much magnified. For this purpose the room must be
darkened, and the object strongly illuminated by the sun"s light, which is
condensed by means of a large lens, and sometimes by two or more lenses
placed at a distance from each other; but care must be taken to avoid burn
ing the object by bringing it exactly into the focus; and, on the other hand,
if it be much beyond the focus, the light will be thrown upon a small [part
of the image only; the best arrangement appears to be, to bring the focus
of the condensing lenses very near to the small lens; and in order to adjust
the instrument in the most convenient manner, the distances of all the
lenses ought to be moveable at pleasure: the want of this precaution is a
material defect in the usual construction of the instrument. The speculum
which first receives the light must be capable of motion in all angular direc-
tions, in order to allow us to accommodate its position to the changeable
place of the sun; and the adjustment has sometimes been performed by
means of a heliostate, an instrument calculated for turning the speculuaj

VOL I. 3 I

426 LECTURE XXXVI.

by clockwork, into such a position as always to reflect the sun's light in the
required direction. An easier method would be to employ two speculums,
the one moveable round an axis parallel to that of the earth, and reflecting
the sun's light into the direction of its axis, the other fixed, and changing
this direction into any other that might be required. When an opaque object
is to be examined, the light may be thrown on it either by a plane mirror
placed obliquely, or by a perforated concave mirror; and if the object is
small, the concave mirror appears to be the more eligible. (Plate XXVIII.
Fig. 400.)

By night, a lamp, with a large lens before it, may supply the place of the
sun's light, and the instrument will become a lucernal microscope, which,
when painted glass sliders are employed as objects for the amusement of
children, is called a magic lantern: and this, exhibited on a larger scale, and
projecting an image on a semitransparent screen of taifetas, instead of a wall, has
of late been the source of much entertainment under the name of the phan-
tasmagoria, a term which implies the raising of spectres. In order to
favour the deception, the sliders are made perfectly opaque, except where
the figures are introduced, the glass being covered, in the light parts, with
a more or less transparent tint, according to the effect required. Several
pieces of glass may also be occasionally placed behind each other, and may
be made capable of such motions as will nearly imitate the natural motions
of the objects which they represent. The figures may also be drawn with
water colours on thin paper, and afterwards varnished. By removing
the lantern to difl'erent distances, and altering at the same time more or less
the position of the lens, the image may be made to increase or di-
minish, and to become more or less distinct at pleasure, so that to a person
unaccustomed to the effects of optical instruments, the figures may appear
actually to advance and retire. In reality, however, these figures become
much brighter as they are rendered smaller, while in nature the imperfect
transparency of the air causes thein to appear fainter when they are remote
than when they are near: this imperfection might be easily remedied by the
interposition of some seraiopaque substance, which might gradually be
caused to admit more light as the figure became larger, or by uncovering a
larger 6r a smaller portion of the lamp, or of its lens. Sometimes, by throw-

ON OPTICAL INSTRUMENTS. 427

mg a strong light upon an actual opaque object, or on a living person, its
image is formed on the curtain, retaining its natural motions : but in this
case the object must be considerably distant, otherwise the images of its
nearer and remoter parts will never be sufticiently distinct at once, there-
fraction being either too great for the remoter, or too small for the nearer
parts: and there must also be a second lens, placed at a sufficient distance
from the' first to allow an inverted image to be formed between them, and
to throw a second picture of tliis image on the screen, in its natural erect
position, unless the object be of such a nature that it can be inverted with-
out inconvenience. This effect was very well exhibited at Paris by Robert-
son; he also combined with his pictures the shadows of living objects,
which imitate tolerably well tlie appearance of such objects in a dark night, or
by moonshine: and while the room was in complete darkness, concealed
screens were probably let down in various parts of it, on which some of the
images were projected; for they were sometimes actually situated over the
heads of the audience. (Plate XXVIII. Fig. 401.)

In almost all telescopes and compound microscopes, the image formed by
one lens or mirror stands in the place of a new object for another. The
operation of such instruments may be illustrated by placing a screen of fine
gauze at the place of the image, which receives enough light to make the
image visible in all directions, and yet transmits enough to form the sub-
sequent image. The simplest of such instruments is the astronomical tele-
scope. Here the object glass first forms an actual inverted image, nearly in
the principal focus of the eye glass, through which this image is viewed as
by a simple microscope, and therefore still remains apparently inverted.
In order to find the angular magnifying power, we must divide the focal
length of the object glass by that of the eye glass: this (juotient is conse-
quently the greater as the focal length of the object glass is greater, and as
that of the eye glass is smaller; but the power of the instrument cannot be
increased at pleasure by lessening the focal length of the eye glass, because
the object glass would not furnish light enough to render the view distinct,
if the magnifying power were too great. (Plate XXVIII. Fig. 402.)

The double or compound microscope resembles in its construction the as-

428 LECTURE XXXVI.

tronomical telescope, except that the distance of the lenses much exceeds their
joint focal length; and the angular magnitude is greater than when the
same object is viewed through the eye glass alone, in proportion as the first
image is further from the object glass than the object itself. (Plate XXVIII.
Fig. 403.)

In the Galilean telescope, or opera glass, a concave eye glass is' placed so
near the object glass, that the first image would be formed beyond it, and
near its principal focus; and the second image, formed by the eye glass,
Avhich is the virtual image viewed by the eye, being on the opposite side of the
centre, is inverted with respect to the first image, and erect with respect to
the object. In this case also the magnifying power is indicated by the
quotient of the numbers expressing the focal lengths of the glasses. (Plate
XXVIII. Fig. 404.)

The inverted image of the astronomical telescope may be made erect by
means of an additional eye glass. In the common day telescope of Rheita,
two such eye glasses are employed, of nearly equal focus, which have the ad-
vantage of procuring a greater extent in the field of view; they are usually
so placed as to have little or no effect on the magnifying power. (Plate
XXVIII. Fig. 405.)

Dr. Herschel's reflecting telescopes resemble, in their effects, the simple
astronomical telescope; a concave speculum, or mirror, being substituted
for the object glass, and the eye glass being so placed as to magnify the
image formed by the speculum. But smce the speculum, if it received the
principal rays perpendicularly, would send them back in the same direction,
it is necessary, in this construction, to have them reflected somewhat ob-
licjuely, the speculum being a little inclined to the axis of the telescope, in
order that the light may have free access to it. An arrangement of this kind
Avas proposed long ago by Maire, but it has been very little employed before
Dr. Herschel's time. This excellent philosopher and mechanic has carried
the perfection of his telescopes to a degree far exceeding all that could have
been expected from the labours of former opticians. His instruments allow
liim to extend the linear dimensions of his objects several thousand times :

5

OK OPTICAL INSTRUMENTS. 429

but he commonly finds it more eligible to employ only powers of 5 or 600,
which afford a much stronger illumination. (Plate XXVIII. Fig. 406.)

The Newtonian reflector has a plane speculum placed in its axis, at the
inclination of half a right angle, which intercepts the rays about to form the
image, and throws them into the focus of an eye glass fixed in the side of the
tube. The plane speculum which he employed was the posterior surface of
a rectangular prism of glass, which produces a total reflection: but Dr.
Herschel has found that the sources of error are diminisJied by wholly omit
ting this speculum. (Plate XXVIII. Fig. 407.)

In the Gregorian telescope, the object speculum is perforated, and the
image formed by it is received into the focus of a smaller concave speculum,
which returns it to be viewed through the aperture by the eye glasses. It has
been objected to this form of the reflecting telescope, which is the first that
Avas invented, that the best part of the speculum is sacrificed by the perfora-
tion. But Dr. Herschel has found that the image formed by the external
part of a speculum is in general more perfect than that which is formed by
the central part. (Plate XXVIII. Fig. 408.)

For the smaller concave speculum of Gregory, Mr. Cassegrain substituted
a convex one, placing it within the focal distance of the large speculum, so as
to form the first actual image nearly in the same place as the second image
of the Gregorian telescope; but this image is inverted. The instrument has
some advantage in theory, with respect to the perfection of the focus; but
it is little used. (Plate XXVIII. Fig. 409.)

Dr, Smith's reflecting microscope resembles Cassegrain's telescope, but the
rays of light are first admitted through a perforation in the small speculum,
that part of them which tends to fall immediately on the eye being inter-
cepted by a screen. The convexity of the one mirror is nearly equal to the
concavity of the other; and the instrument, although seldom employed, is
said to succeed extremely well. (Plate XXVIII. Fig. 410.)

The image of a very distant object, formed by a speculum of any kind, is

4^0 LECTURE XXXVI.

considerably less curved than that which is depicted by a lens of equal focal
length. There is a similar imperfection in the nature of the focus of oblique
pencils, but it is confined within narrower limits, the remotest part of the
image in which any radiating lines would be most distinctly represented,
being a flat surface, and the nearest, in which circles would become most
distinct, being a part of a sphere touching the speculum : so that the radius
of the mean curvature is equal to the focal distance. (Plate XXVIII. Fig.
411.)

The magnifying power of a refracting telescope may often be measured, by
comparing the diameter of the object glass with that of the narrowest space,
into which the beam of light is contracted beyond the eye glass, provided
that none of the light has been intercepted in its passage through the tele-
scope: for the object will be viewed through the telescope in an angle as
much greater tlian that which it naturally subtends, as the diameter of the
object glass is greater than that of this contracted pencil, which may be con-
sidered as an image of the object glass. But in the Galilean telescope, this
method cannot be employed, since no such image is formed. Th? field of
view, in a simple telescope, or the angular magnitude of that part of an
object which can be seen through it at once, is nearly equal to the magnitude
of the eye glass as seen from the object glass.

If a lens be added to any refracting telescope at the place of the first
image, it will have no effect either on the place or on the magnitude of any
subsequent image, but it will enlarge the field of view, by throwing more
pencils of light on the original eye glass. If, however, the image fell
exactly on such a lens, it would be liable to be impaired by any accidental
impurities of its substance or on its surface, every opaque particle inter-
cepting the whole of the light belonging to one of its points, which would not
happen if the image were at a small distance from the lens. A field gLs«
is, therefore, usually placed, both in telescopes, and in the common com-
pound microscope, a little nearer to the object glass than the place of the
first image. The best places for the various lenses, in an eye piece, are partly
determined from similar considerations, but they require also in general to be ad-
justed by experiment, for several circumstances are concerned in the perform-

ON OPTICAL INSTRUMENTS. 431

ance of a telescope, which are ahnost too intricate for practical calculation,
although some assistance may certainly be obtained fi'om theory with regard
to the most important of them. The curvature of the image produced by
any lens has already been mentioned: it may be in some measure remedied by
Mr. Ramsden's method of placing a planoconvex lens a little beyond the
image, with its, flat side turned towards it. !Mr. Ramsden also employs
an eye piece constructed on this principle instead of a simple microscope,
under the name of a double magnifier. The aberration of the different
parts of any single pencil of rays, from the corresponding point of the
image, requires also to be considered in the construction of telescopes: its
magnitude is such, in the case of a double convex lens of crown glass,
that those parts of a pencil of parallel rays which fall on it near the cir-
cumference meet each other in a point, which is within the true focus, by a
distance a little more than half as great again as the thickness of the lens.
In an image formed by a concave speculum, of equal focal length, this
aberration would be only i-V ^s great; it may, however, be slmost entirely
corrected, in refracting telescopes, by employing proper proportions in the
dimensions of the various lenses. (Plate XXVIII. Fig. 412, 413.)

A still more important aberration, from which reflecting telescopes are
also wholly free, is that which arises from the different refrangibilities of
the rays of light of different colours, which form an infinite number of
images, neither agreeing perfectly in situation nor in magnitude, so that
the objects are rendered indistinct by an appearance of colours at their edges:
this imperfection, however, Mr. DoUond has in great measure obviated,
by his achromatic object glasses: the construction of which depends on
the important discovery, that some kinds of glass separate the rays of differ-
ent colours from each other much more than others, while the whole deviation
produced in the pencil of light is the same. Mr. Dollond combined, therefore,
a concave lens of flint glass with a convex lens of crown glass, and sometimes
with two such lenses; the concave lens of flint glass being sufficiently power-
ful to correct the whole dispersion of coloured light produced by the crown
glass, but not enough to destroy the effect of its refraction, which was still
sufficient to collect the rays of light into a distant focus. For this purpose,
it is necessary that the focal lengths of the two lenses should be in the same

433 LECTURJR XXXVI.

proportion as the dispersive powers of the respective substances, when the
mean deviations of the pencils are equal; that is, in the case of the kinds
of glass commonly used, nearly in the ratio of 7 to 10. Sometimes also
the chromatic aberration, that is, the error arising from the different re-
frangibilities of the different rays, is partially corrected in an eye piece, by
placing a field glass in such a manner, as considerably to contract the di-
mensions of the image formed by the least refrangible rays, which is nearest
to the eye glass, and to cause it to subtend an equal angle with the image
formed by the most refrangible rays, this image being little afliected by the
glass. (Plate XXVIII. Fig. 414, 415.)

The apparent magnitude of an object, viewed through a telescope, may
be measured, with great accuracy, by a scale or by wires, introduced at the
place of the last image, reducing afterwards the angle thus ascertained
according to the magnifying power. Care must, however, be taken to
avoid as much as possible tbe distortion which usually accompanies any
curvature of the image; and the wires, one of which is sometimes made
moveable by means of a micrometer screw, must be sufficiently illuminated
to be distinctly visible. Sometimes a scale is introduced, which, from the
apparent magnitude of a known object, such as that of a man of ordinary
height, or of a portion of a wall built with bricks of the usual size, enables
ns at once to read ofi^' its actual distance, which is expressed on the scale in
hundreds of yards. The angular magnitude of an object, seen through a
telescope, may also be found, by viewing at the same time, with the other eye,
cither a scale, or any other object of known dimensions, placed at a given dis-
tance: the lucid disc micrometer of Dr. Herschel is employed in this man-
ner for judging of the magnitude of the celestial bodies. The divided
object glass micrometer affords another mode of measurement: the object
glass being divided into two semicircular portions, one of which slides on
the other; each portion acts as a separate lens, and two images of every
part of the object being formed, the angular distance of any two points
is determined by bringing their images together, and measuring the dis-
placement of the moveable portion of the object glass, which is required
for procuring the coincidence. Sometimes also a similar purpose is answered
by inserting a divided glass in the eye piece, which acts nearly on the same

ON OPTICAL INSTRUMENTS. ♦ 435

principle, and which seems to be somewhat less liable to error. In a reflect-
ing telescope of Cassegrain's construction, Mr. Ramsden has also pro-
duced the same effect by dividing the convex speculum, and causing a
part of it to turn round an axis. All these arrangements particularly
deserve the attention of those who are employed "n practical astro-
norriy and in geography, since the advancement of these sciences much
depends on the accuracy of the telescopic and microscopic measures, which
are performed by means of optical instruments, (Plate XXVIII. Fig.
416, 417.)

VOL. 1. ^K

434

LECTURE XXXVIL

ON PHYSICAL OPTICS.

Having examined the general theory of optics, and the construction
of optical instruments, we are now to consider those properties and affectiots
of Hght, which rather belong to its natural history, than to its mechanical
effects; to trace its relations to the particular phenomena of nature; to in-
vestigate the manner in which it is connected with our sensations, and to
inquire on what intimate mode of action the various effects of light depend.
All these subjects may be properly comprehended under the denomination
of physical optics, but we shall find it convenient to reserve each of the
two last for a separate examination. The sources of light, the velocity of
its motion, its interception and extinction, its dispersion into different
colours ; the manner in which it is affected by the variable density of the at-
mosphere, the meteorological appearances in which it is concerned, and the
singular properties of particular substances with regard to it, will be the first
subjects of our investigation.

The sources, from which light is commonly derived, are either the sun or
stars, or such terrestrial bodies as are undergoing those changes which consti-
tute combustion. The process of combustion implies a change in which a
considerable emission of light and heat is produced; but it is not capable of
a very correct definition: in general it requires an absorption, or at least a
transfer, of a portion of oxygen; but there appear to be some exceptions
to the universality of this distinction; and it has been observed that both
heat and light are often produced where no transfer of oxygen takes place,
and sometimes by the effect of a mixture which cannot be called combus-
tion.

Light is also afforded, without any sensible heat, by a number of vegetable

ON PHYSICAL OPTICS. ' 4,35

and animal substances, which appear to be undergoing a slow decomposition,,
not wholly unlike combustion. Thus decayed wood, and animal substance*
slightly salted, often afford spontaneously a faint light, without any elevation
ef temperature ; and it is not improbable that the light of the ignis fatuus
may proceed from a vapour of a similar nature.

The effects, which are commonly attributed to the motions of the electrical
fluid, are often attended by the production of light; and violent or rapid
friction frequently seems to be the immediate cause of its appearance. But
it is diificult to ascertain whether friction may not be partly concerned in
the luminous phenomena attributedto electricity, or electricity in the apparent
eflf'ects of friction. Light is sometimes produced by friction with a much lower
degree of heat than is required for combustion, and even when it is accom-
panied by combustion, the heat produced by the union of these causes may be
very moderate : thus it is usual in^some coalmines, to obtain a train of light by
the continual collision of flint and steel, eflfected by the machine called a
fire wheel, in order to avoid setting fire to the inflammable gas emitted by the
coal, which would be made to explode if it came near the flanie of a candle.

There is a remarkable property, which some substances possess in arv
eminent degree, and of which few, except metals and water, are entirely
destitute. These substances are denominated solar phosphori; besides the
light which they reflect and refract, they appear to retain a certain portion,
and to emit it again by degrees till it is exhausted, or till its emission is in-
terrupted by cold. The Bolagnan phosphorus was one of the first of these
substances that attracted notice ; it is a sulfate of bary tes, found in the st.ate
of a stone; it is prepared by exposuri to heat, and is afterwards made up into
cakes: these, when first placed in abeam of the sun's light, and viewed after-
wards in a dark room, have nearly the appearance of a burning coal,or a red hot
iron. Burnt oyster shells,and muriate of lime have also the same property, and
some specimens of the diamond possess it in a considerable degree. From the
different results of experiments apparently accurate, made by difterent
persons, there is reason to conclude that some of these phosphori emit only
the same kind of light as they have received, while others exliibit the same ap-
pearances, to whatever kind of light they may have been exposed. Sometimes
.it has even been found that light of a particular colour has been most effita-

%

435 '^tECTURE XXXVII.

cious in exciting in a diamond the appearance of another kind of light, which
it was naturally most disposed to exhibit. The application of heat to
solar phosphori in general expedites the extrication of the light which they
have borrowed, and hastens its exhaustion; it also produces, in many sub-
stances, which are not remarkable for their power of imbibing light, a tem-
porary scintillation, or flashing, at a heat much below ignition: the most re-
markable of these are fluor spar in _po\\^der, and some other crystallized
substances. It appears that luminous bodies in general emit light equally in
every direction, not from each point of any of their surfaces, as some have
supposed, but from the whole surface taken together, so that the surface,
when viewed obliquely, appears neither more nor less bright than when viewed
directly.

However light of any kind may have at first originated, there is reason
to believe that the velocity with which it passes through a given medium
is always the same. It has been ascertained by the astronomical ob-
servations of Roemer and of Bradley, that each ray of light, emitted by the
sun, arrives at the earth in eight minutes and one eighth, when the
earth is at its mean distance of about 95 millions of miles. Roemer deduced
this velocity from observations on the eclipses of the satellites of Jupiter,
and Bradley confirmed it by his discovery of the cause of the apparent aber-
ration of the fixed stars.

This aberration is produced by the eflfect of the revolution of the earth in its
orbit, combined with that of the progressive motion of light. Since light
proceeds always in right lines, when its motion is perfectly undisturbed, if
a fine tube were placed so as to receive a ray of light, passing exactly
through its axis when at rest, and then, remaining in the same direction,
were moved transversely with great velocity, it is evident that the side
of the tube would strike against the ray of light in its passage, and that in
order to retain it in the axis, the tube must be inclined, in the same manned"
as if the light, instead of coming in its actual direction, had also a transverse
motion in a contrary direction to that of the tube. The axis of a telescope,
or even of the eye, may be considered as reseuibling such a tube, the passage
of the light through tlie refracting substances not altering the necessary in-
clination of the axis. In various parts of the earth's orbit, the aberration

ON PHYSICAL OPTICS. 437

of any one star must be different in quantity and in direction; it never exceeds
20 seconds each way, and must, therefore, in common observations, be
wholly insensible. (Plate XXIX. Fig. 418.)

The quantity of light, which is reflected by a substance of any kind,
depends not only on the nature of the substance, but also on the ob-
liquity of its incidence: and it sometimes happens, that a surface, which
reflects a smaller portion of direct light than another, reflects a greater
portion when the light falls very obliquely on its surface. Bouguer found
that the surface of water reflected only one fifty fifth part of the light fall-
ing perpendicularly on it, that of glass one fortieth, and that of quicksilver
more than two thirds: but when the obliquity was as great as possible, the
water reflected nearly three fourths of the incident light, and the glass about
two thirds only.

Of the light which passes by a dense substance of any kind, the greatest
part pursues its course undisturbed, but there is always a certain divergence^
which has been called by Grimaldi diffraction, and by Newton inflection.
This effect is usually attended by the production of colours, and will
therefore require to be more particularly considered hereafter.

The separation of colours by refraction is one of the most striking of all
optical phenomena. It was discovered by Newton that white light is a com-
pound of rays of different kinds, mixed in a certain proportion, that these
rays differ in colour and in refrangibility, that they constitute a series, which
proc'eeds by gradual changes from red to violet, and that those substances
whifch appear coloured when placed in white light, derive their colours only
from the property of reflecting some kind of rays most abundantly, and of
transmitting or extinguishing the rest. Dr. Herschel has added to this series
rays of heat less refrangible than the red, and Hitter and Dr. Wollaston have
discovered, beyond the violet, other still more refrangible rays, which blacken
the salts of silver.

It has generally been supposed, since the time of Newton, that when the
rays of light are separated as completely as possible by means of
refraction, they exhibit seven varieties of colour, related ■ to each

T.

43S LECTURE XXXVIl.

Other with respect to the extent that they occupy, in ratios nearly analo-
ffous to those of the ascendino; scale of the minor mode in music. The
ohservations were, however, imperfect, and the analogy was wholly imagin-
ary. Dr. Wollaston has determined the division of the coloured image or
spectrum, in a much more accurate manner than had been done hefore: by
looking through a prism, at a narrow line of light, he produces a more effec-
tual separation of the colours, than can be obtained by the common method
of throwing the sun's image on a wall. The spectrum formed in this manner
tonsists of four colours only, red, green, blue, and violet, which occupy
spaces in the proportion of \6, 23, 36, and 25, respectively, making together
100 for the whole length; the red being nearly one sixth, the green and the
violet each about one fourth, and the blue more than one third of the length.
The colours differ scarcely at all in quality within their respective limits.
but they vary in brightness ; the greatest intensity of light being in that
part of the green, which is nearest to the red. A narrow line of yellow is
generally visible at the limit of the red and green, but its breadth scarcely
pxceeds that of the aperture by which the light is admitted, and Dr. Wollaston
attributes it to the mixture of the red with the green light. There are also
several dark lines crossing the spectrum within the blue portion and in its
neighbourhood, in which the continuity of the light seems to be ii\terrupted.
This distribution of the spectrum Dr. Wollaston has found to be the same,
whatever refracting substance may have been employed for its formation ;
and he attributes the difference, which has sometimes been observed in the
proportions, to accidental variations of the obliquity of the rays. The angu-
lar extent of the spectrum formed by a prism of crown glass is one 27th of
the deviation of the red rays; by a prism of flint glass, one 19th. (Plate
XXIX. Fig. 419.)

In light produced by the combustion of terrestrial substances, the spectrum
is sometimes still more interrupted ; thus, the bluish light of the lower part
of the flame of a candle is separated by refraction into five parcels of various
colours; the light of burning spirits, which appears perfectly blue, is chiefly
composed of green and violet rays; and the light of a candle into which salt
is thrown abounds with a pure yellow, inclining to green, but not separable
by refraction. The electrical spai k furnishes also a light which is differently
divided in different circumstances. (Plate. XXIX. Fig. 420.)

ON PHYSICAL OPTICS. 439

If the breadth of the aperture viewed through a prism is somewhat in-
creased, the space occupied by each variety of hght in tiie spectrum is aug-
mented in the same proportion, and each portion encroaches on the neigh-,
bouring colours, and is mixed with them: so that the red is succeeded by
orange, yellow, and yellowish green, and the blue is mixed on the one
side with the green, and on the other with the violet; and it is in this state
that the prismatic spectrum is commonly exhibited. (Plate XXIX. Fig.
421.)

When the beam of light is so much enlarged as to exceed the angular mag
nitude of the spectrum, it retains its whiteness in the centre, and is term i-"
nated by two different series of colours at the different ends. These series are:
still divided by well marked lines: on the one hand the red remains unmixed;
the space belonging to the green and blue becomes a greenish yellow, nearly
uniform throughout, and here the appearance of colour ends, the place pf
the violet being scarcely distinguishable from the neighbouring white light:-
on the other hand, the space belonging to the red, green, and blue, of thft
simple spectrum appears of a bluish green, becoming more and more blue till
it meets the violet, which retains its place without alteration. This second
series is also the same that accompanies the limit of total reflection at the pos-
terior surface of a prism. (Plate XXIX. Fig. 422.)

Sir Isaac Newton observed that the effect of white light on the senso
of sight might be imitated by a mixture of colours taken from different parts
of the spectrum, notwithstanding the omission of some of the rays naturallyl
belonging to white light. Thus, if we intercept one half of each of the four
principal portions into which the spectrum is divided, the remaining halves
will still preserve, when mixed together, the appearance of whiteness; so
that it is probable, that the different parts of those portions of the spectrum,
which appear of one colour, have precisely the same effect on the eye. It is
certain that the perfect sensations of yellow and of blue are produced respec-
tively, by mixtures of red and green, and of green and violet light, and there
is reason to suspect that those sensations are always compounded of the separate
aensations combined: at least this supposition simplifies the theory of colours;
it may, therefore, be adopted with advantage, until it be found inconsistent
-with any of the phenomena; and w^ may consider. white light gis composed of

440 LECTURE xxxvri,

a mixture of red, green, and violet, only, in the proportion of about two
parts red, four green, and one violet, with respect to the quantity or intens-
ity of the sensations produced.

If \vc mix together, in proper proportions, any substances exhibiting these
colours in their greatest purity, and place the mixture in a light sufficiently
strong, we obtain the appearance of perfect whiteness ; but in a fainter light
the mixture is grey, or of that hue which arises from a combination of white
and black ; black bodies being such as reflect white light but in a very
scanty proportion. For the same reason, green and red substances mixed to-
gether usually make rather a brown than a yellow colour, and many yel-
low colours, when laid on very thickly, or mixed with black, become brown. The
sensations of various kinds of light may also be combined in a still more satisfac-
tory manner by painting the surface of a circle with different colours,in any way
that may be de,sired, and causing it to revolve with such rapidity, that the whole
may assume the appearance of a single tint, or of a combination of tints,
resulting from the mixture of the colours. (Plate XXIX. Fig. 423 . . 426.)

From three simple sensations, with their combinations, we obtain seven
primitive distinctions of colours ; but the different proportions, in which they
may be combined, afford a variety of tints beyond all calculation. The three
simple sensations being red, green, and violet, the three binary combina-
tions are yellow, consisting of red and green; crimson, of red and violet;
and blue, of green and violet; and the seventh in order is white light, composecl
by all the three united. But the blue thus produced, by combining the whole of
the green and violet rays, is not the blue of the spectrum , for four parts of green
and one of violet make a blue differing very little from green; while the blue
of the spectrum appears to contain as much violet as green : and it is for this
reason that red and blue usually make a purple, deriving its hue from the pre-
dominance of the violet.

It would be possible to exhibit at once to the eye the combinations of any
three colours in all imaginable varieties. Two of them might be laid down
on a revolving surface, in the form of triangles placed in opposite directions,
and the third on projections perpendicular to the surface, which,
while the eye remained at rest in any one point, obliquely situated, would

ON PHYSICAL OPTICS." .441

exhibit more or less of their painted sides, as they passed through their dif-
ferent angular positions: and the only further alteration, that could be pro-
duced in any of the tints, would be derived from the different degrees of light ,_^
only. The same effect may also be exhibited by mixing the colours in differ- -
ent proportions, by means of the pencil, beginning from three equidistant
points as the centres of the respective colonrs, (Plate XXIX. Fig. 427.) ..j*.

The ordinary atmospherical refraction cannot be determined in the usual
manner from the knowledge of its density, and of the angular direction of. the
incident or refracted light, since the constitution of the atmosphere is such,
that its density varies every where Avith its height, and the curvature of the
earth's surface causes the inclination of the strata through which the ray
passes to be perpetually changed; the difference of temperature at different
elevations increases also the difficulty of an exact calculation, and it is only
very lately that Mr. Laplace, by a comparison of astronomical with meteorologi-
cal observationSjhas given a satisfactory solution of the problem in all its extent.
But for practical uses, the refraction may be determined with sufficient
accuracy by an approximation which is easily remembered; the deviation
being at a^^l altitudes one sixth part as great as the refracted ray would
undergo, at the horizontal surface of a medium six times as dense as the air.
When a celestial object appears exactly in the horizon, it is actually more
than half a degree below it, since tlie refraction amounts to 33 minutes,
when the barometer stands at 29-^ inches, and Fahrenheit's thermometer
at 50'. ' * ■

The accidental variations of the temperature of the air, at different paits.
produce, however, great irregularities in its refraction, especially near thfe
horizon. The most remarkable of these is occasioned by the rarefac-
tion of the air in the neighbourhood of the surface of wrater,' of a building*
or of the earth itself, in consequence of which a distant object appears to be -
depressed instead of being elevated, and is sometimes seen at once both de-
pressed and elevated, so as to appear double, one of the images being gene-
rally in an inverted position, as if the surface possessed a reflective powei ; ~
and there seems indeed to be a considerable analogy between this kind of refrac-
tion and the total reflection which happens within a denser medium. These
effects arc known by the appellations looming, mirage, and Fata Morgana:

VOL. I. , 3 L

442 LECTURE XXXVII.

they may be very completely imitated, as Dr. Wollaston has shown, by
looking at a distant object along a red hot poker, or through a saline or
saccharine solution with water and spirit of wine floating on it. The effect
of refraction on the apparent places of terrestrial objects must be frequently
disturbed by circumstances of this kind; but its magnitude is usually about
one tenth of the angular distance of the object, considered as a part of the
earth's circumference. (Plate XXIX. Fig. 428, 429.)

The atmospherical phenomena of rainbows and halos present us with ex-
amples of the spontaneous separation of colours by refraction. The rainbow-
is universally attributed to the refraction and reflection of the sun's rays in
the minute drops of falling rain or dew, and the halos, usually appearing in
frosty atmospheres, are in all probability produced by the refraction of small
triangular or hexagonal crystals of snow. It is only necessary, for the for-
mation of a rainbow, that the sun should shine on a dense cloud, or a shower of
rain, in a proper situation, or even on a number of minute drops of water, scat-
tered by a brush or by a syringe, so that the light may reach the eye after
having undergone a certain angular deviation, by means of various refraction^
and reflections; and the drops so situated must necessarily be found some-
Avhere in a conical surface, of which the eye is the vertex, and must present
the appearance of an arch. The light, which is reflected by the external sur-
face of a sphere, is scattered almost equally in all directions, setting aside the dif-
ference arising from the greater efficacy of oblique reflection ; but when it first
enters the drop, and is there reflected by its posterior surface, its deviation never
exceeds a certain angle, which depends on the degree of refrangibility, and is,
therefore, different for light of different colours: and the density of the light
being the greatest at the angle of greatest deviation, the appearance of a lumi-
nous arch is produced by the rays of each colour at its appropriate distance.
The rays which never enter the drops produce soother effect, than to cause a
bright ness, or haziness round the sun, where the reflection is the most oblique:
those which are once reflected within the drop exhibit the common internal
or primary rainbow, at the distance of about 41 degrees from the point op-
posite to the sun: those which are twice reflected, the external or secondary
rainbow, of 52" : and if the effect of the light, three times reflected, were
sufficiently powerful, it Mould appear at the distance of ab<mt 42 degrees
trom the sun. The colours of both rainbows encroach considerably on each

/ ON PHYSICAL OPTICS. ' 445

Other ; for each point of the sun may be considered as affording a distinct
arch of each colour, and the whole disc as producing an arch about half a
degree in breadth for each kind of light; so that the arrangement nearly re-
sembles that of the common mixed spectrum. There is, however, another '
cause of a further mixture of the colours: the arch of any single colour, which
belongs to any point of the sun, is accurately'defined on one side only, while
on the other it becomes gradually fainter, the breadth of the first minute con-
taining about five times as much light as a minute at the distance of a quarter
of a degree: the abrupt termination is on thesideof the red, that is, without
the inner bow, and within the outer, so that, for this reason, the order of colours
partakes, in some degree, of the nature of the red termination of a broad beam
of light seen through a prism ; but it is more or less affected by this cause, on
account of some circumstances, which will be explained when we examine
the supernumerary rainbows, which sometimes accompany the bows more com-
monly observed. A lunar rainbow is much more rarely seen than a solar one,
but its colours differ little, except in intensity, from those of the common
rainbow. (Plate XXIX. Fig. 430.)

In the highest northern latitudes, where the air is commonly loaded with
frozen particles, the sun and moon usually appear surrounded by halos or
coloured circles, at the distances of about 22 and 46 degrees from their
centres; this appearance is also frequently observed in other climates, espe^
cially in the colder months, and in the light clouds which float in the highest
regions of the air. The halos are usually attended by a horizontal white
circle, with brighter spots, or parhelia, near their intersections with this circle,
and with portions of inverted arches of various curvatures: the horizontal
circle has also sometimes anthelia, or bright spots nearly opposite to the sun.
These phenomena have usually been attributed to the effect of spherical
particles of hail, each having a central opaque portion of a certain magnitude,
mixed with oblong particles, of a determinate form, and floating with a
certain constant obliquity to the horizon. But all these arbitrary supposi-
tions, which were imagined by Huyg^ris, are in themselves extremely com-
plicated and improbable, and are wholly unauthorised by observation. A
much simpler, and more natural, as well as more accurate explanation, which
was suggested at an earlier period by Mariotte, had long been wholly for-
gotten, until the same idea occurred to me, without any previous knowledge
of what Mariotte had done. The natural tendency of water to crystallize, in

444 ' LECTURE xxxvir.

fi-eezing, at an angle of 60 degrees, is sufficiently established, to allow us
to assume this as the constant angle of the elementary crystals of snow,
which are probably either triangular or hexagonal prisms:, the deviation
produced by such a prism differs very little from the observed angle at which
the first circle is usually seen; and all the principal phenomena, which attend
this circle, may be explained, by supposing the axis of the crystals to assume
a vertical or a horizontal position, in consequence of the operation of gravity:
thus the parhelia, which are sometimes a little more distant from the sun
than the halo, are attributed by Mariotte to the refraction of the prisms
which are situated vertically, and produce a greater deviation, on account of
the obliquity of the rays of light with respect to their axes. The horizontal
circle may be deduced from the reflection, or even the repeated refractions
of the vertical facets ; the anthelia from two refractions with an intermediate
reflection, and the inverted arch from the increase of the deviation, in the
light passing obliquely, through prisms lying in a horizontal position. The
external circle may be attributed either to two successive refractions through
different prisms, or with greater probability, as Mr. Cavendish has suggested
to me, to the effect of the rectangular terminations of the single crystals.
The appearance of colours, in halos, is nearly the same as in rainbows, but
less distinct; the red being nearest to the luminary, and the whole halo being
externally very ill defined. (Plate XXIX. Fig. 431, 432.)

From the observed magnitude of these halos, I had concluded that the
refractive power of ice must be materially less than that of water, although
some authors had asserted that it was greater: and Dr. Wollaston afterwards
fully confirmed this conclusion by means of the very accurate instrument
which has already been described: his measurement agreeing precisely with
the mean of the best observations on these halos; so that ice must be con^
sidered as the least refractiv'e of any known substances not aeriform.

Sometimes the figures of halos and parhelia are so extremely complicated,
as to defy all attempts to account for the formation of their different parts:
but if we examine the representations which have been given,by various authors,
of the multiplicity of capricious forms frequently assumed by the flakes of
snow, we shall see no reason to think them inadequate to the production of
all these appearances. (Plate XXIX. Fig. 433, 434.)

ON PHYSICAL OPTICS. 445

- The most singular of all the phenomena of refraction is perhaps tlie property
of some natural substances, which have a double eftect on the light transmitted
tlirough them, as if two mediums of different densities freely pervaded each
other, the one only acting on some of the rays of light, the other on the remain-
ing portion. These substances are usually crystallized stones, and their refrac-
tions have sometimes no further peculiarity; but the rhomboidal crystals of
calcarious spar, commonly called Iceland crystals, possess the remarkable
property of separating such pencils of light, as fall perpendicularly on them,
into two parts, one of them only being transmitted in the usual manner,
the other being deflected towards the greater angle of the crystal. It appears
from the experiments of Huygens, confirmed and extended by Dr. Wollas-
ton, that the medium, which causes the unusual refraction, has a different
refraqtive power, according to tlae direction in which the light passes through
it, and that if an oblate or flattened spheroid be described within a crystal,
its axis being in the middle of one of the obtuse solid angles, and its princi-
pal diameters in the proportion of 9 to 10, the refractive power, with respect
to light passing in any direction, will always be inversely as the diameter
of the spheroid which is parallel to it; and where it is greatest, will be equal
to that of the medium wliich produces the usual refraction, of which the
index is ^. A ray of light, falling perpendicularly on any surface of the spar,
its point of incidence being considered as the centre of the spheroid, will
meet the surface of the spheroid at the point where it is parallel to that of
the spar; and a ray incident on the same surface in any other direction, will
preserve a relation to the perpendicular ray, which is nearly the same as in
ordinary refraction. (Plate XXIX. Fig. 435.)

It is also remarkable, that tbe two portions of light, thus separated, will not
be further subdivided by a transmission through a second piece, provided
that this piece be in a position parallel to that of the first; but if it be placed
in a transverse direction, each of the two pencils will be divided into
two others; a circumstance Avhieh appears to be the most unintelligible
of any that has been discovered respecting the phenomena of double re-
fraction.

The appearances of colours, which are protluced by transparent plates of

446 LECTURE xxxvir.

different thicknesses, and of those which are seen in light variously diffracted or
inflected, will be more conveniently examined, when we investigate the inti-
mate nature of light, since the general explanation of these colours, which
will then be given, will enable us to follow them through all their varieties,
with much more ease than could be done at present, without the help of some
theory respecting their origin.

447

LECTURE XXXVIIL

ON VISION.

The medium of communication, by which we become acquainted with all
the objects that we have been lately considering, is the eye; an organ that
exhibits, to an attentive observer, an arrangement of various substances, so
correctly and delicately adapted to the purposes of the sense of vision, that
we cannot help admiring, at every step, the wisdom by which each part is
adjusted to the rest, and made to conspire in effects, so remote from what
the mere external appearance promises, tlut we have only been able to un-
derstand, by means of a laborious investigation, the nature and operations
of this wonderful structure, while its whole mechanism still remains far be-
yond all rivalship of human art..

The eye is an irregular spheroid, not very widely differing from a sphere ;
it is principally composed of transparent substances, of various refractive,
densities, calculated to collect the rays of light, which diverge from each
point of an object, to. a focus on its. posterior surface, which is capable of
transmitting to the mind the impression of the colour and intensity of the;
light, together with a distinction of the situation of the focal point, as de.-
termined by the angular place of the object. (Plate XXX. Fig. 436.),

The first refraction happens at the surface of the cornea, or that transparent
eoat which projects forwards from the ball of the eye; but the cornea,
being very nearly of equable thickness, has little effect by its own refractive
power, and serves only to give a proper form to. the aqueous humour, which
fills its concavity, and distends it. This humour is partially divided by the
uvea or iris, which is of different colours in different persons, having a perfora-
tion in its centre, called the pupil. Immediately behind the uvea, and closely
connected, to its base, are the ciliary processes, the summits of which hang,.

448 • LKCTURE XXXVIII.

like a short fringe, before the crystalline lens, a substance much more re-
fractive than the aqueous humour, and increasing in density towards its
centre. The remaining cavity is fdled by an aqueous fluid, lodged in a eel"
lular texture of extremely fine membrane, and called the vitreous humour.
The retina lines the whole posterior part of this cavity; it is semitransparent,
and is supported by the choroid or chorioid coat, a very opaque black or
brown membrane, continued from the uvea and ciliary processes: but imme-
diately where the retina is connected with the optic nerve, thechoroid is
necessarily perforated; and at this part a small portion of the retina is nearly
insensible. The whole is surrounded by an opaque continuation of the cor-
nea, called the sclerotica.

The rays of light, which have entered the cornea, and passed through the
pupil, being rendered still more convergent by the crystalline lens, are col-
lected into foci on the retina, and form there an image, which, according to
the common laws of refraction, is inverted, since the central rays of each
pencil cross each other a little behind the pupil; and the image may easily"
be seen in a dead eye, by laying bare the posterior surface of the retina.
(Plate XXX. Fig. 437.)

By means of this arrangement of the various refracting substances, many
peculiar advantages are procured. The surface of the cornea only, if it had
been more convex, could not have collected the lateral rays of a direct pen-
cil to a perfect focus, without a different curvature near its edges; and then
the oblique pencils would have been subjected to greater aberration, nor
could they have been made to converge to any focus on the retina. A second
refraction performs both these offices much more completely, and has also
the advantage of admitting a greater quantity of light. If also the surfaces
of the crystalline lens, thus interposed, had been abrupt, there would have been
a reflection at each, and an apparent haziness would have interfered with
the distinct view of every luminous object; but this inconvenience is avoided by
the gradual increase of density in approaching the centre, which also
makes the crystalline equivalent to a much more refractive substance of
equal magnitude; while, at the same time, the smaller density of the lateral
parts prevents the usual aberration of spherical surfaces, occasioned by the
too great refraction of the lateral rays of direct pencils, and causes also the

ON VISION. 449

focus of each oblique pencil to fall either accurately or very nearly on the
concave surface of the retina, throughout its extent.

Opticians have often puzzled themselves, without the least necessity, in
order to account for our seeing objects in their natural erect position, while
the image on the retina is in reality inverted: but surely the situation of a
focal point at the upper part of the eye could be no reason for supposing the
object corresponding to it to be actually elevated. We call that the lower
end of an object which is next the ground ; and the image of the trunk of a
tree being in contact with the image of the ground on the retina, we may
naturally suppose the trunk itself to be in contact with the actual ground:
the image of the branches being more remote from that of the ground, we
necessarily infer that the branches are higher and the trunk lower: and
it is much simpler that we should compare the image of the floor with the
image of our feet, with which it is in contact, than with the actual situation
of our forehead, to which the image of the floor on the retina is only acci-
dentally near, and with which indeed it would perhaps be impossible to com- ,
pare it, as far as we judge by the immediate sensations only.

We might indeed call in experience to our assistance, ahdhabitually correct
the errors of one sense by a comparison with the perceptions of another.
But it appears that some philosophers have been too hasty in supposing, that
the use of all our senses is derived from experience alone, and in disbelieving
the existence of instinct independent of it. Without any other authority
than that of their own imaginations, they have denied the observation re-
corded by Galen, on the instincts of a kid, which is sufficiently credible to
counterbalance much more than bare assertion. The instant after its birth,
accompanied by the loss of its mother, the little animal ran to some green
vegetables, and having first smelt them, chewed and swallowed them. The
kid could have been taught by no experience to be tempted by the sight,
to act with the proper muscles of locomotion, to go near and smell, and to
be induced by the smell to masticate, and by the taste to swallow and digest
its food, had it not been provided with some fundamental instinct, by the
same intelligence, which so calculated the adjustments of the eye, that the
lens should be able to produce a perfect image of every object, and that the

VOL. I. 3 M

ioO LECTURE XXXVIII.

retina should be of that precise form, which is exactly suited to the reception
of the image to be depicted on it.

The whole surface of the retina appears to be usually occupied by such an
image, but it is not all of equal sensibility; a certain portion only, near the
axis, is capable of conveying distinct impressions of minute objects. But
the perfection of this limited distinctness is a far greater advantage to us,
than a more extensive field of moderately accurate vision would have been;
for by means of the external muscles, we can easily so change the position
of the eye, that the image of any object before us may be maile to fall on
the most sensible part of the retina. We may readily observe the want of
sensation at the entrance of the optic nerve, by placing two candles so that
the distance of each from the eye may be about four times their distance
from each other: then if we direct our right eye to to the left hand candle,
the right hand candle will be lost in a confused mass of faint light, its image
on the retina falling on the point at which its sensibility is deficient.

When the attention is not directed to any particular object of sight, the
refractive powers of the eye are adapted to the formation of an image of
objects at a certain distance only, which is different in different individuals,
and also generally increases with increasing age. Tims, if we open our
eyelids suddenly, without particular preparation, we find that distant objects
onlv appear as distinct as we are able to make them ; but by an exertion of
the will, the eye may be accommodated to the distinct perception of nearer
objects, yet not of objects within certain limits. Between the ages of 40
and and 50, the refractive powers of the eye usually begin to diminish, but
it sometimes happens that where they are already too great, the defect con-
tinues unaltered to an advanced age. It appears also that after 50 or 60,
the power of changing the focus of the eye is always much impaired, and
sometimes wholly lost.

The mode, in which the accommodation of the eye to different distances is
effected, has long been a subject of investigation and dispute among opti-
cians and physiologists, but I apprehend that at present there is little further
loom for doubting, that the change is produced by an increase of the con^

ov VISION. 451

vexity of the crystalline ]e"s, arising from an internal cause. The argu-
ments in favour of this conclusion are of two kinds; some of them are nega-
tive, derived from the impossibility of imagining any other mode of perform-
ing the accommodation, without exceeding the limits of the actual dimen-
sions of the eye, and from the examination of the eye in its different states
by several tests, capable of detecting any other changes if they had existed:
for example, by the application of water to the cornea, which co!r.r)lctely re-
moves the effect of its convexity, without impairing the power of altering the
focuSj'wand by holding the whole eye, when turned inwards, in sucl^ a
manner as to render any material alteration of its length utterly impossible.
Other arguments arc deduced from positive evidence of the change of form
of the crystalline, furnislied by the particular effects of refraction and aber-
ration which are observable in the different states of the eye; effects which
furnish a direct proof that the figure of the lens must vary; its surfaces, which
are nearly spherical in the quiescent form of the lens, assuming a different
determinable curvature when it is called into exertion. The objections
which have been made to this conclusion are founded only on the appearance
of a slight alteration of focal length in an eye from which the crystalline
had been extracted; but the fact is neither sufficiently ascertained, nor was
the apparent change at all considerable : and even if it were pro^ved that an
eye without the lens is capable of a certain small alteration, it would by no
means follow that it could undergo a change five times or ten times as great.

The iris serves, by its variable magnitude, to exclude more or less of the
light falling on the cornea, when its intensity would otherwise be too great;
hence the pupil is usually smallest by day, and its increased magnitude at
night sometimes gives the eye a greater apparent lustre. The iris also in-
tercepts such rays as would fall on parts incapable of refracting them regu-
larly; and by its contraction when a nearer object is viewed, it lessens the
confusion which would arise, in such eves as cannot accommodate them-

7.4/

selves sufficiently, from the magnitude of the imperfect focal points on the
retina. Such a contraction almost always accompanies the diminution of
the focal length, even in a perfect eye, and it may easily be rendered visible
by walking gradually up to a looking glass, and observing the magnitude
of the pupil as we approach nearer and nearer to our image. It would be
difficult to assign a reason for this change of the state of the pupil within the

452 LECTURE xxxvrir.

limits of perfect vision, unless we allowed the irregularity of the form as-
sumed by the marginal parts of the crystalline lens. The iris is also pecu-
liarly useful in excluding such parts of lateral pencils of light as fall very
obliquely on the cornea, and are too much refracted, while a smaller pencil
only, which enters the eye more directly, is admitted into the pupil.

The refractive powers and properties of the eye may be very conveniently
ascertained by means of an instrument to which I have given the name
optometer, a term first employed in a sense nearly similar by Dr. Porterfield.
If two or more separate parcels of the rays of the same pencil be admitted
at distant parts of the pupil, they will only be reunited on the retina when
the focus is perfect, so that if we look through two small perforations, or slits,
at a minute object, to the distance of which the eye is not accommodated, it
will appear as if double; and when the object is aline directed nearly towards
the eye, each point of it will appear double, except that which is at the
distance of perfect vision, and an image of two lines will be seen,
crossing each other in this point; so that the measurement of the focal
length of the eye is immediately performed by inspection of the optometer
only. The scale may be extended by the addition of a lens, which enables
us to produce the effect of a longer line, while the instrument still remains
portable.

When the eye is possessed of too great a refractive power for the distinct
perception of distant objects, the pupil is generally large, so that the con-
fusion of the image is somewhat lessened by partially closing the eyelids;
and from this habit an eye so formed is called myopic. In such cases, by
the help of a concave lens, the divergence of the rays of light may be
increased, and a virtual image may be formed, at a distance so much smaller
than that of the object as to afford perfect vision. For a long sighted or
presbyopic eye, on the contrary, a convex lens is required, in order to
obtain a virtual image at a greater distance than the object; and it often
happens that the rays must be made not only to diverge less than before, but
even to converge towards a focus behind such an eye, in order to make
its vision distinct. Presbyopic persons have in general a small pupil, and,
therefore, seldom acquire the habit of covering any part of it with their
eyelids.

ON VISION. 453

When the imao-es of the same object fall on certain corresponding points
of the retina in each eye, they appear to the sense only as one; but if they
fall on parts not corresponding, the object appears double; and in general,
all objects at the same distance, in any one position of the eyes, appear alike
either double or single. The optical axes, or the directions of the rays falling on
the points of most perfect vision, naturally meet at a great distance ; that is,
they are nearly parallel to each other, and in looking at a nearer object we make
them converge towards it, wherever it may be situated, by means of the external
muscles of the eye; while in perfect eyes the refractive powers are altered, at
the same time, by an involuntary sympathy, so as to form a distinct image
of an object at the given distance. This correspondence of the situation of
the axes with the focal length is in most cases unalterable ; but some have
perhaps a power of deranging it in a slight degree, and in others the adjust-
ment is imperfect: but the eyes seem to be in most persons inseparably con-
nected together with respect to the changes that their refractive powers
undergo, although it sometimes happens that those powers are originally very
different in the opposite eyes.

These motions enable us to judge pretty accurately, within certain limits,
of the distance of an object ; and beyond these limits, the degree of distinct-
ness or confusion of the image still continues to assist the judgment. We
estimate distances much less accurately with one eye than with both, since
we are deprived of the assistance usually afforded by the relative situation of
the optical axes; thus we seldom succeed at once in attempting to pass a
finger or a hooked rod sideways through a ring, with one eye shut. Our
idea of distance is also usually regulated by a knowledge of the real magni-
tude of an object, while we observe its angular magnitude; and on the other
hand a knowledge of the real or imaginary distance of the object often directs
our judgment of its actual magnitude. The quantity of light intercepted by
the air interposed, and the intensity of the blue tint which it occasions, are
also elements of our involuntary calculation: hence, in a mist, the obscurity
increases the apparent distance, and consequently the supposed magnitude,
of an unknown object. We naturally observe, in estimating a distance,
the number and extent of the intervening objects ; so that a distant church
in a woody and hilly country appears more remote than if it were situated
in a plain; and for a similar reason, the apparent distance of an object seen

454 LECTURE XXXVIII.

at sea, is smaller than its true distance. Tiie city of Lo rid on is unquestion-
ably larger than Paris; but the ditTerence appears at first sight much greater
than it really is; and the smoke, produced by the coal fires of London, is proba-
bly the principal cause of the deception.

The sun, moon, and stars, are much less luminous when they are near
the horizon, than wdien they are more elevated, on account of the greater
quantity of their light that is intercepted, in its longer passage through the
atmosphere: we also observe a much greater variety of nearer objects almost
in the same direction: we cannot, therefore, help imagining them to be
more distant, when they rise or set, than at other times; and since they sub-
tend the same angle, they appear to be actually larger. For similar reasons
the apparent figure of the starry heavens, even when free from clouds, is
that of a flattened vault, its summit appearing to be much nearer to us than
its horizontal parts, and any of' the constellations seems to be considerably
larger when it is near the horizon than when in the zenith. (Plate XXX.
Fig. 438.)

The faculty of judging of the actual distance of objects is an impediment
to the deception, which it is partly the business of a painter to produce. Some
of the effects of objects at different distances may, however, be imitated in
painting on a plane surface. Thus, supposing the eye to be accommodated to
a given distance, objects at all other distances may be represented with a
certain indistinctness of outline, which would accompany the images of the
objects themselves on the retina: and this indistinctness is so generally
necessary, that its absence has the disao:reeable efltcct called hardness. The
apparent magnitude of the suSjects of our design, and the relative situations
of the intervening objects, may be so imitated by the rules of geometrical
perspective as to agree perfectly with nature, and we may still further im-
prove the representation of distance hy attending to the art of aerial perspec-
tive, which consists in a due observation of the loss of light, and the bluish
tinge, occasioned by the interposition of a greater or less depth of air between
us and the ditfcrent parts of the scenery.

We cannot indeed so arrange the picture, that either tlie focal length of
the eye,- or the position of the optical axes, may be such as would be required

ON visiox, 455

I-

by the actual objects: but we may place the picture at such a distance that
neither of these criterions can have much power in detecting the Tallacy ;
or, by the interposition of a large lens, we may produce nearly the same
effects in the rays of light, as if they proceeded from a picture at any requir-
ed distance. In the panorama, which has lately been exhibited in many
parts of Europe, the effects of natural scenery are very closely imitated : the
deception is favoured by the absence of all other visible objects, and by the
faintness of the light, which assists in concealing the detects of the repre-
sentation, and for which the eye is usually prepared, by being long detained
in the dark winding passages, which lead to the place of exhibition.

The impressions of light on the retina appear to be always in a certain
degree permanent, and the more so as the light is stronger; but it is uncer-
tain whether the retina possesses this property merely as a solar phosphorus,
or in consequence of its peculiar organization. The duration of the impres-
sion is generally from one hundredth of a second to half a second, or more;
hence a luminous object revolving in a circle makes a lucid rinff; and a
shooting star leaves a train of light behind it, which is not always real. If
the object is painfully bright, it generally produces a permanent spot, which
continues to pass through various changes of colour for some time, without
much regularity, and gradually vanishes: this may, however, be considered
as a morbid efl'ect.

When the eye has been fixed on a small object of a bright colour, and is
then turned away to a white surface, a faint spot, resembling in form and
magnitude the object first viewed, appears on the surface, of a colour oppo-
site to the first, that is, of such a colour as would be produced by with-
drawing it from white light; thus a red object produces a bluish green spot;
and a bluish green object a red spot. The reason of this appearance is pro-
bably that the portion of the retina, or of the sensorium, that is affected, has
lost a part of its sensibility to the light of that colour, with which it has been
impressed, and is more strongly affected by the other constituent parts of
the white light, A similar effect is also often produced, when a white,or grey
object is viewed on a coloured ground, even without altering the position
of the eye: the whole retina being affected by sympathy nearly in the same
manner as a part of it was affected in the former case. These appearances

456 ' LECTURE XXXVIII.

I

are most conveniently exhibited by means of the shadows of objects placed
in coloured ligh't: the shadow appearing of a colour opposite to that of the
stronger light, even when it is in reality illuminated by a fainter light of
the same colour. It seems that the eye cannot perfectly distinguish the
intensity of a colour, either when the light is extremely faint, as that of
many of the fixed stars, which Dr. Herschel has found to be strongly
coloured, or when the light is excessively vivid ; and that when a consider-
able part of the field of vision is occupied by coloured light, it appears to
the eye either white, or less coloured than it is in reality : so that when a
room is illuminated either by the yellow light of a candle, or by the red
light of a fire, a sheet of writing paper still appears to retain its whiteness;
and if from the light of the candle we take away some of the abundant
yellow light, and leave or substitute a portion actually white, the effect is
nearly the same as if we took away the yellow light from white, and sub-
stituted the indico which would be left: and we observe accordingly, that
in comparison with the light of a candle, the common daylight appears of
a purplish hue. (Plate XXX. Fig. 439 • • 441.)

457

LECTURE XXXIX.

ON THE NATURE OF LIGHT AND COLOURS.

X HE nature of light is a subject of no material importance to the concerns of
life or to the practice of the arts, but it is in many other respects extremely in-
teresting, especially as it tends to assist our views both of the nature of our sen-
sations, and of the constitution of the universe at large. The examination of
the production of colours, in a variety of circumstances, is intimately con-
nected with the theory of their essential properties, and their causes ; and we
shall find that many of tliese phenomena will afford us considerable assistance
in forming our opinion respecting the nature and origin of light in general.

It is allowed on all sides, that' light either consists in the emission
of very minute particles from luminous substances, which are actually pro-
jected, and continue to move, with the velocity commonly attribut-
ed to light, or in the excitation of an undulatory motion, analogous to
that which constitutes sound, in a highly light and elastic medium pervading
the universe; but the judgments of philosophers of all ages have been
much divided with respect to the preference of one or the other of these opi-
nions. There are also some circumstances which induce those, who entertain
the first hypothesis, either to believe, with Newton, that the emanation of
tlie particles of light is always attended by the undulations of an etherial
medium, accompanying it in its passage, or to suppose, with Boscovich,
that the minute particles of light themselves receive, at the time of their
emission, certain rotatory and vibratory motions, which they retain as long
as their projectile motion continues. These additional suppositions, how-
ever necessary they may have been thought for explaining some particular
phenomena, have never been very generally understood or admitted, although
no attempt has been made to accommodate the theory in any other manner to
tiiose phenomena.

VOL. I. 3 N

458 LECTURE XXXIX.

We shall proceed to examine in detail the manner in which the two principal
hypotheses respecting light may be applied to its various properties and
affections; and in the first place to the simple propagation of light in right
lines through a vacuum, or a very rare homogeneous medium. In this
circumstance there is nothing inconsistent with either hypothesis; but it
undergoes some modifications, which require to be noticed, when a portion
of light is admitted through an aperture, and spreads itself in a slight
degree in every direction. In this case it is maintained by Newton that the
margin of the aperture possesses an attractive force, which is capable of in-
flecting the rays: but there is some improbability in supposing that bodies
of different forms and of various refractive powers should possess an equal force
of inflection, as they appear to do in the production of these effects; and there
is reason to 'conclude from experiments, that such a force, if it existed, must
extend to a very considerable distance from the surfaces concerned, at least
a quarter of an inch, and perhaps much more, which is a condition not easily
reconciled with other phenomena. In the Iluygenian system of undulation,
this divergence or diffraction is illustrated by a comparison with the motions
of waves of water and of sound, both of which diverge when they are ad-
mitted into a wide space through an aperture, so much indeed that it has
usually been considered as an objection to this opinion, that the rays of light
do not diverge in the degree that would be expected if they were analogous
to the waves of water. But as it has been remarked by Newton, that the
pulses of sound diverge less than the waves of water, so it may fairly be in-
ferred, that in a still more highly elastic medium, the undulations, constituting
light, must diverge much less considerably than either. (Plate»XX. Fig. 266.)

With respect, however, to the transmission of light through perfectly
transparent mediums of considerable density, the system of emanation labours
under some difficulties. It is not to be supposed that the particles of ligh
can perforate with freedom the ultimate atoms of matter, which compose a
substance of any kind; they must, therefore, be admitted in all directions
through the pores or interstices of those atoms : for if we allow such suppo-
sitions as Boscovich"s, that matter itself is penetrable, that is, immaterial, it h
almost useless to argue the question further. It is certain that some substances
retain all their properties when they are reduced to the thickness of the ten
millionth of an inch at most, and we cannot therefore suppose the distances

ON THE NATURE OF LIGHT AND COLOURS. 459

of the atoms of matter in general to be so great as the hundred milllonjth of
an inch. Now if ten feet of the most transparent water transmits, without
interruption, one half of the light that enters it, each section or stratum of
the thickness of one of these pores of matter must intercept only about
one twenty thousand millionth, and so much must the space or area occupied
by the particles be smaller than the interstices between them, and the dia-
meter of each atom must be less than the hundred and forty thousandth part
of its distance from the neighbouring particles: so that the whole space oc-
cupied by the substance must be as little filled, as the whole of England
would be filled l^y a hundred men, placed at the distance of about thirty
miles from each other. This astonishing degree of porosity is not indeed
absolutely inadmissible, and there are many reasons for believing the state-
ment to agree in some measure with the actual constitution of material sub-
stances; but the Huygenian hypothesis does not require the disproportion to
be by any means so great, siuce the general direction and even the intensity
of an undulation would be very little affected by the interposition of the
atoms of matter, while these atoms may at the same time be supposed
to assist in the transmission of the impulse, by propagating it through their
own substance. Euler indeed imagined that the undulations of light might
be transmitted through the gross substance of material bodies alone, precisely
in the same manner as sound is propagated; but this supposition is for many
reasons inadmissible.

A very striking circumstance, respecting the propagation of light, is the
uniformity of its velocity in the same medium. According to the projectile
hypothesis, the force employed in the free emission of light must be about a
million million times as great as the force of gravity at the earth's surface;
and it must either act with equal intensity on all the particles of light, or
must impel some of them through a greater space than others, if its action
be less powerful, since the velocity is the same in all cases; for example, if
the projectile force is weaker with respect to red light than with
respect to violet light, it must continue its action on the red rays to a
greater distance than on the violet rays. There is no instance in
nature besides of a simple projectile moving with a velocity uniform in
all cases, whatever may be its cause, and it is extremely difficult to imagine
that so immense a force of repulsion can reside in all substances capable of

460 • LECTURE XXXIX.

becoming luminous, so that the light of decaying wood, or of two pebbles
rubbed together, may be projected precisely M'ith the same velocity, as the light
emitted by iron burning in oxygen gas, or by the reservoir of liquid fire on
the surface of the sun. Another cause would also naturally interfere with
the uniformity of the velocity of light, if it consisted merely in the motion
of projected corpuscles of matter; Mr. Laplace has calculated, that if any of
the stars were 250 times as great in diameter as the sun, its attraction
would be so strong as to destroy the whole momentum of the corpuscles of
light proceeding from it, and to render the star invisible at a great distance ;
and although there is no reason to imagine that any of thg stars are actually
of this magnitude, yet some of them are probably many times greater than
our sun, and therefore large enough to produce such a retardation in the
motion of their light as would materially alter its effects. It is almost unneces-
sary to observe that the uniformity of the velocity of light, in those spaces which
are free from all material substances, is a necessary consequence of the Huy-
genian hypothesis, since the undulations of every homogeneous elastic
medium are always propagated, like those of sound, with the same velocity,
as long as the medium remains unaltered.

On either supposition, there is no difficulty in explaining the equality of
the angles of incidence and reflection ; for these angles are equal as well in
the collision of common elastic bodies with others incomparably larger, as in
. the reflections of the waves of water and of the undulations of sound. And
it is equally easy to demonstrate, that the sines of the angles of incidence and
refraction must be always in the same proportion at the same surface,
whether it be supposed to possess an attractive force, capable of acting on
the particles of light, or to be the limit of a medium through which the
undulations are propagated with a diminished velocity. There are, however,
some cases of the production of colours, which lead us to suppose that the
velocity of light must be smaller in a denser than in a rarer medium; and
supposing this fact to be fully established, the existence of such an attractive
force could no longer be allowed, nor could the system of emanation be
maintained by any one.

The partial reflection from all refracting surfaces is supposed by Newton
to arise from certain periodical retardations of the particles of liglit, caused

ON THE NATURE OF LIGHT AND COLOURS. 46l

by undulations, propagated in all cases through an ethereal medium. Tlie
mechanism of thesf supposed undulations is so complicated, and attended by
so many difficulties, that the few who have examined them have been in
general entirely dissatisfied with them: and the internal vibrations of the
particles of light themselves, which Boscovich has imagined, appear scarcely
to require a serious discussion. It may, therefore, safely be asserted, that
in the projectile hypothesis this separation of tlie rays of light of the same
kind by a partial reflection at every refracting surface, remains wholly unex-
plained. In the undulatory system, on the contrary, this separation follows
as a necessary consecjuence. It is simplest to consider the ethereal medium
Avhich pervades any transparent substance, together with the material atoms
of the substance, as constitutmg together a compound medium denser than
the pure ether, but not more elastic; and by comparing the contiguous
particles of the rarer and the denser medium with conunon elastic bodies of
different dimensions, we may easily determine not only in what manner,
but almost in what degree, this reflection must take place in different circum-
stances. Thus, if one of two equal bodies strikes the other, it communi-
cates to it its whole motion without any reflection; but a smaller body
striking a larger one is reflected, Avitlr the more force as the difference of
their magnitude is greater; and a larger body, striking a smaller one, still
proceeds with a diminished velocity ; the remaining motion constituting, in
the case of an undulation falling on a rarer medium, a part of a new scries
of motions which necessarily returns backwards with the appropriate velocity:
and we may observe a circumstance nearly similar to this last in a portion
of mercury spread out on a horizontal table; if a wave be excited at any
part, it will be reflected from the termination of the mercury almost in tlie
same manner as from a solid obstacle.

The total reflection of light, falling, with a certain obliquity, on the
surface of a rarer medium, becomes, on both suppositions, a particular case
of refraction. In the undulatory system, it is convenient to suppose the
two mediums to be separated by a short space in which their densities ap-
proach by degrees to each other, in order that the undulation may be turned
gradually round, so as to be reflected in an equal angle: but this supposition
is not absolutely necessary, and tlie same effects may be expected at the
surface of two mediums separated by an abrupt termination.

462 tECTURE XXXIX.

The chemical process of combustion may easily be imagined either to dis-
engage the particles of light from their various combinations, or to agitate
the elastic medium by the intestine motions attending it: but the operation
of friction upon substances incapable of undergoing chemical changes, as
well as the motions of the electric fluid through imperfect conductors, afford
instances of the production of light in which there seems to be no easy way
of supposing a decomposition of any kind. The phenomena of solar phos-
phori appear to resemble greatly the s^'mpathctic sounds of musical instru-
ments, which are agitated by other sounds conveyed to them tbrough the
air: it is difficult to understand in wliat state the corpuscles of light could
be retained by these substances so as to be reemittcd after a short space or
time; and if it is true that diamonds are often found, which exhibit a red
light after having received a violet light only, it seems impossible to explain
this property, on the supposition of the retention and subsequent emission
of the same corpuscles.

The phenomena of the aberration of light agree perfectly well with the
system of emanation ; and if the ethereal medium, supposed to pervade the
earth and its atmosphere, were carried along befoie it, and partook materia^y
in its motions, these phenomena could not easily be reconciled with the
theory of undulation. But there is no kind of necessity for such a supposi-
tion: it will not be denied by the advocates of the Newtonian opinion that
all material bodies are sufficiently porous to leave a medium pervading them
almost absolutely at rest; and if this be granted, the effects of aberration
will appear to be precisely the same in either hypothesis.

The unusual refraction of the Iceland spar has been most accurately and
satisfactorily explained by Iluygens, on the simple supposition that this
crystal possesses the property of transmitting an impulse more rapidly in one
direction than in another; whence he infers that the undulations constilutintr
light must assume a spheroidical instead of a spherical form, and lays down such
laws for the direction of its motion, as are incomparably more consistent
with experiment than any attempts which have been made to accoiiimndate
the phenomena to other principles. It is true that nothing has yet been
done to assist us in understanding the effects of a subsco" nt refraction by
a second crystal, unless any person can be satisfied with the name of polarity

ON THE NATURE OF LIGHT AND COLOUKS. 463

assigned by Newton to a property which he attributes to the particles of
light, and which he supposes to direct them in the species of refraction
which they are to undergo: but on any hypothesis, until \vc discover the reason
why a part of the light is at first refracted in the usual manner, and another
part in the unusual manner, we have no right to expect that we should un-
derstand how thes^ dispositions are continued or modified, when the process is
repeated.

In order to explain, in the system of emanation, the dispersion of the rays
of different colours by means of refraction, it is necessary to suppose that all
refractive medmnis have an elective attraction, acting mOre powerfully pn the
violet rays, in proportion to their mass, than on the red. But an elective at-
traction of this kind is a property foreign to mechanical pliilosophy, and when
we use the term in chemistry, we only confess our incapacity to assign a mechani-
cal cause for the effect, and refer to an analogy with other facts, of which the
intimate nature is perfectly unknown to us. It is not indeed very easy to give a
demonstrative theory of the dispersion of coloured light upon the supposition of
undulatory motion ; but we may derive a very satisfactory illustration from the
well known effects of waves of different breadths. The simple calculation of the
velocity of waves, propagated in a liquid perfectly elastic, or incompressible,
and free from friction, assigns to them all precisely the same velocity, what-
ever their breadth may be: the compressibility of the fluids actually existing
introduces, however, a necessity for a correction according to the breadth
of the wave, and it is very easy to observe, in a river or a pond of consider-
able depth, that the wider waves proceed much more rapidly than the nar-
rower. We may, therefore, consider the pure ethereal medium as analogous
to an infinitely elastic fluid, in which undulations of all kinds move wi-th
equal velocity, and material transparent substances, on the contrary, as
resembling those fluids, in which we see the large waves advance beyond the
smaller; and by supposing the red light to consist of larger or wider undu-
lations and the violet of smaller, we may sufficiently elucidate the greater
refrangibility of the red than of the violet light.

It is not, however, merely on the ground of this analogy that we may be
induced to suppose the undulations constituting red light to be larger
than those of violet light: a very extensive class of phenomena leads us<still

454 LECTURE xxxrx.

more directly to the same conclusion ; they consist chiefly of the production
of colours by means of transparent plates, and by diflraction or inflection,
none of which have been explained, upon the supposition of emanation, in
a manner suiliciently minute or comprehensive to satisfy the most candid
even of the advocates for the projectile system; while on the other liand all of
them may be at once understood, from the effect of the interference of
double lights, in a manner nearly similar to that which constitutes in sound
the sensation of a beat, when two strings, forming an imperfect unison, arc
lieard to vibrate together.

Supposing the light of any given colour to consist of undulations, of »
given breadth, or of a given frequency, it follows that these undulations
must be liable to those effects which we have already examined in the case
of the waves of water, and tiie pulses of sound. It has been shown that
two equal series of waves, proceeding from centres near each other, may be
seen to destroy each other's effects at certain points, and other points at to re-
double them; and the beating of two sounds has been explained from a similar
interference. We are now to apply the same principles to the alternate union
and extinction of colours. (Plate XX. Fig. 267.)

In order that the effects of two portions of light may be thus combined,
it is necessary that they be derived from the same origin, and that they
arrive at the same point by different paths, in directions not much deviating
from each other. This deviation may be produced in one or both of the
portions by diffraction, by reflection, by refraction, or by any of these effects
combined ; but the simplest case appears to be, when a beam of homogeneous
light falls on a screen in which there are two very small holes or slits, which
may be considered as centres of divergence, from whence the light is diffract-
ed in every direction. In this case, when the two newly formed beams are
received on a surface placed so as to intercept them, their light is divult'd by
dark stripes into portions nearly equal, but becoming wider as the surface is
more remote ftom the a])ertures, so as to subten : very nearly c^ual angles
from the apertures at all distances, and wider also in the same proportion as
the apertures art closer to each other. Tlie middle of the two portions is
always light, and the bright stripes on each side arc at such distances, that the
light, coming to them from one of the ai^rtuies, must have passed through a

ON THE NATURE OF LIGHT AND COLOURS. A6S

longer space than that which conies from the other, by an interval which is
equal to the breadth of one, two, three, or more of the supposed undulations,
while the intervening dark spaces correspond to a difference of half a sup-
posed undulation, of one and a half, of two and a half, or more.

From a comparison of various experiments, it appears that the breadth of
the undulations constituting the extreme red light must be supposed to be,
in air, about one 36 thousandth of an inch, and those of the extreme violet
about one 60 thousandth; the mean of the whole spectrum, with respect to
the intensity of light, being about one 45 thousandth. From these dimen-
sions it follows, calculating upon the known velocity of light, that almost 500
millions of millions of the slowest of such undulations must enter the eye in
a single second. The combination of two portions of white or mixed light,
when viewed at a great distance, exhibits a few white and black stripes, cor-
responding to this interval ; although, upon closer inspection, the distinct
effects of an infinite number of stripes of different breadths appear to be com-
pounded together, so as to produce a beautiful diversity of tints, passing by
degrees into each other. The central whiteness is first changed to a yellow-
ish, and then to a tawny colour, succeeded by crimson, and by violet and
blue, which together appear, when seen at a distance, as a dark stripe; after
this a green light appears, and the dark space beyond it has a crimson hue;
the subsequent lights are all more or less green, the dark spaces purple and
reddish; and the red light appears so far to predominate in all these effects,
that the red or purple stripes occupy nearly the same place in the mixed
fringes as if their light were received separately.

The comparison of the results of this theory Avith experiments fully esta-
blishes their general coincidence ; it indicates, however, a slight correction
in some of the measures, on account of some unknown cause, perhaps con-
nected with the intimate nature of diffraction, which uniformly occasions the
portions of light, proceeding in a direction very nearly rectilinear, to be divided
into stripes or fringes a little wider than the external stripes, formed by the
light which is more bent (Plate XXX. Fig. 442, 443.)

When the parallel slits are enlarged, and leave only the intervening sub-
stance to cast its shadow, the divergence from its opposite margins still con-
VOL. I. 3 o

466 LECTURE XXXIX.

tinues to produce the same fringes as before, but they arc not easily visible,
except within the extent of its shadow, being overpowered in other parts by
a stronger light; but if the light thus diffracted be allowed to fall on the
eye, either within the shadow, or in its neighbourhood, the stripes will still
appear; and in this manner the colours of small fibres are probably formed.
Hence if a collection of equal fibres, for example a lock of wool, be held before
the eye when we look at a luminous object, the series of stripes belono-ino-
to each fibre combine their effects, in such a manner, as to be converted into
circular fringes or coronae. This is probably the origin of the coloured
circles or coronae sometimes seen round the sun and moon, two or three of
them appearing together, nearly at equal distances from each other and from
the luminary, the internal ones being, however, like the stripes, a little
dilated. It is only necessary that the air should be loaded with globules of
moisture, nearly of equal size among themselves, not much exceeding one
two thousandth of an inch in diameter, in order that a series of such coronae,
at the distance of two or three degrees from each other, maybe exhibited.
(Plate XXX. Fig. 444.)

4

If, on the other hand, we remove the portion of the screen which separates
the parallel slits from each other, their external margins will still continue to ex-
hibit the effects of di.ffracted light in the shadow on each' side; and the
experiment will assume the form of those which were made by Newton on
the light passing between the edges of two knives, brought very nearly into
contact; although some of these experiments appear to show the influence of
a portion of light reflected by a remoter part of the polished edge of the
knives, which indeed must unavoidably constitute a part of the light con-
cerned in the appearance of fringes, wherever their Avhole breadth exceeds
that of the aperture, or of the shadow of the fibre.

The edges of two knives, placed very near each other, may represent the
opposite margins of a minute furrow, cut in the surface of a polished sub-
stance of any kind, which, when viewed with different degrees of obli-
quity, present a series of colours nearly resembling those which are exhibited
within the shadows of the knives: in this case, however, the paths of the
two portions of light before their incidence are also to be considered, and
the whole difference of these paths will be found to determine the appearance of

2

\

ON THE NATURE OF LIGHT AND COLOURS. 467

colour in the usual manner; thus when the surface is so situated, that the
image of the luminous point would be seen in it by regular reflection, the
difference will vanish, and the light will remain perfectly white, but in other
cases various colours will appear, according to the degree of obliquity.
These colours may easily be seen, in an irregular form, by looking at any
metal, coarsely polished, in the sunshine; but they become more distinct
and conspicuous, when a number of fine lines of equal strength are drawn
parallel to each other, so as to conspire in their effects.

It sometimes happens that an object, of which a shadow is formed in abeam
of light, admitted through a small aperture, is not terminated by parallel sides;
thus the two portions of light, which are diffracted from two sides of an
object, at right angles with each other, frequently form a short series of curv-
ed fringes within the shadow, situated on each side of the diagonal, which
were first observed by Grimaldi, and which are completely explicable from
the general principle, of the interference of the two portions encroaching
perpendicularly on the shadow. (Plate XXX. Fig. 445.)

But the most obvious of all the appearances of this kind is that of the
fringes, which are usually seen beyond the termination of any shadow, formed
in a beam of light, admitted through a small aperture: in white light three
of these fringes are usually visible, and sometimes four; but in light of one
colour only, their number is greater ; and they are always much narrower as
they are remoter from the shadow. Their origin is easily deduced from the
interference of the direct light with a portion of light reflected from the
margin of the object which produces them, the obliquity of its incidence
causing a reflection so copious as to exhibit a visible effect, however nar-
row that margin may be; the fringes are, however, rendered more obvious
as the quantity of this reflected light is greater. Upon this theory it follows
that the distance of the first dark fringe from the shadow should be half as
great as that of the fourth, the difference of the lengths of the different paths
of the light being as the squares of those distances; and the experiment
precisely confirms this calculation, with the same slight correction only as
is required in all other cases; the distances of the first fringes being always a
little increased. It may also be observed, that the extent of the shadow itself
is always augmented, and nearly in an equal degre^ with that of the fringes : the

4fi8 LECTURE XXXIX.

reason of this circumstance appears to be the gradual loss of light at the
edges of every separate beam, which is so strongly analogous to the phenomena
visible in waves of water. The same cause may also perhaps have some effect
in producing the general modification or correction of the place of the first
fringes, although it appears to be scarcely sufficient for explaining the whole
of it. (Plate XXX. Fig. 446.)

A still more common and convenient method, of exhibiting the effects of
the mutual interference of light, is afforded us by the colours of the thin
plates of transparent substances. The lights are here derived from the suc-
cessive partial reflections produced by the upper and under surface of the plate,
or when the plate is viewed by transmitted light, from the direct beam
which is simply refracted, and that portion of it which is twice reflected
within the plate. The appearance in the latter case is much less striking
than in the former, because the light thus affected is only a small portion of
the whole beam, with which it is mixed; while in the former the two reflected
portions are nearly of equal intensity, and may be separated from all other
light tending to overpower them. In both cases, when the plate is gradually
reduced in thickness to an extremely thin edge, the order of colours may
be precisely the same as in the stripes and coronae already described; their
distance only varying when the surfaces of the plate, instead of being plane,
are concave, as it frequently happens in such experiments. The scale of an
oxid, which is often formed by the effect of heat on the surface of a metal,
in particular of iron, affords us an example of such a series formed in reflect-
ed light; this scale is at first inconceivably thin, and destroys none of the
light reflected, it soon, however, begins to be of a dull yellow, Avhich
changes to red, and then to crimson and blue, after which the effect is de-
stroyed by the opacity which the oxid acquires. Usually, however, the
series of colours produced in reflected light follows an order somewhat dif-
ferent: the scale of oxid is denser than the air, and the iron below than the
oxid; but where the mediums above and below the plate are either both
rarer or both denser than itself, the different natures of the reflections at its
different surfaces appear to produce a modification in the state of the undu-
lations, and the infinitely thin edge of the plate becomes black instead of
white, one of the portions of light at once destroying the other, instead of
cooperating with it. Thus when a film of soapy water is stretched over a

ON THE NATURE OF LIGHT AND COLOURS. 469

wineglass, and placed in a vertical position, its upper edge becomes ex-
tremely thin, and appears nearly black, while the parts below are divided by
horizontal lines into a series of coloured bands; and when two glasses, one
of which is slightly convex, are pressed together with some force, the plate
of air between them exhibits the appearance of coloured rings, beginning
from a black spot at the centre, and becoming narrower and narrower, as the
curved figure of the glass causes the thickness of the plate of air to increase
more and more rapidly. The black is succeeded by a violet, so faint as to
be scarcely perceptible; next to this is an orange yellow, and then crimson
and blue. When water, or any other fluid, is substituted for the air between
the glasses, the rings appear where the thickness is as much less than that
of the plate of air, as the refractive density of the fluid is greater; a circum-
stance which necessarily follows from the proportion of the velocities with
which light must, upon the lluygenian hypothesis, be supposed to move in
different mediums. It is also a consequence equally necessary in this theory,
and equally inconsistent with all others, that when the direction of the light
is oblique, the effect of a thicker plate must be the same as that of a thinner
plate, when the light falls perpendicularly upon it; the difference of the
paths described by the different portions of light precisely corresponding
with the observed phenomena. (Plate XXX, Fig. 447 . . 449.)

Sir Isaac Newton supposes the colours of natural bodies in general to be
similar to these colours of thin plates, and to be governed by the magnitude
of their particles. If this opinion were universally true, we might always
separate the colours of natural bodies by refraction into a number of different
portions, with dark spaces intervening; for every part of a thin plate, which
exhibits the appearance of colour, affords such a divided spectrum, when
viewed through a prism. There are accordingly many natural colours in
which such a separation may be observed; one of the most remark-
able of them is that of blue glass, probably coloured with cobalt, which
becomes divided into seven distinct portions. It seems, however, im-
possible to suppose the production of natural colours perfectly identical
with those of thin plates, on account of the known minuteness of the
particles of colouring bodies, unless the refractive density of these par-
ticles be at least 20 or 30 times as great as that of glass or water; which is
indeed not at all improbable with respect to the ultimate atoms of bodies^

470 LECTUUE XXXIX.

but difficult to believe with respect to any of their arrangements constituting
the diversities of material substances.

The colours of mixed plates constitute a distinct variety of the colours of
thin plates, which has not been commonly observed. They appear when the
interstice between two glasses, nearly in contact, is filled with a great num-
ber of minute portions of two different substances, as water and air, oil and
air, or oil and water: the light, which passes through one of the mediums,
moving with a . greater velocity, anticipates the light passing through the
other; and their effects on the eye being confounded and combined, their
interference produces an appearance of colours nearly similar to those of the
colours of simple thin plates, seen by transmission; but at much greater thick-
nesses, depending on the difference of the refractive densities of the sub-
stances employed. The effect is observed by holding the glasses between the
eye and the termination of a bright object, and it is most conspicuous in the
portion which is seen on the dark part beyond the object, being produced by the
light scattered irregularly from the surfaces of the fluid. Here, however, the
effects are inverted, the colours resembling those of the common thin plates,
seen by reflection ; and the same considerations on the nature of the reflec- ■
tions are applicable to both cases. (Plate XXX. Fig. 450.)

The production of the supernumerary rainbows, which are sometimes seen
within the primary and without the secondary bow, appears to be intimately
connected with that of the colours of thin plates. We have already seen
that the light producing the ordinary rainbow is double, its intensity being
only greatest at its termination, where the common bow appears, while the
whole light is extended much more widely. The two portions concerned in
its production must divide this light into fringes; but unless almost all the
drops of a shower happen to be of the same magnitude, the effects of these
fringes must be confounded and destroyed: in general, howeyer, they must
at least cooperate more or less in producing one dark fringe, which must
cut off the common rainbow much more abruptly than it would otherwise
have been terminated, and consequently assist the distinctness of its colours.
The magnitude of the drops of rain, required for producing such of these rain-
bows as are usually observed,- is between the 50th and the 100th of an inch:
they become gradually narrower as they are more remote from the common

ON THE NATUEE OF LIGHT AND COLOURS. 471

rainbows, nearly in the same proportions as the external fringes of a shadow,
or the rings seen in a concave plate. (Plate XXX. Fig. 451.)

The last species of the colours of double lights, which it will be necessary
to notice, constitutes those which have been denominated, from Newton's
experiments, the colours of thick plates, but which may be called, with
more propriety, the colours of concave mirrors. The anterior surface of a
mirror of glass, or any other transparent surface placed before a speculum of
metal, dissipates irregularly in every direction two portions of light, one
before, and the other after its reflection. When the light falls obliquely on
the mirror, being admitted through an aperture near the centre of its curvature, it
is easy to show, from the laws of reflection, that the two portions, thus dissipated*
will conspire in their effects, throughout the circumferenceof a circle, passing
through the aperture; this circle will consequently be white, and it will be
surrounded with circles of colours very nearly at equal distances, resembling
the stripes produced by diffraction. The analogy between these colours
and those of thin plates is by no means so close as Newton supposed it ;
since the effect of a plate of any considerable thickness must be absolutely
lost in white light, after ten or twelve alternations of colours at most, while
these effects would require the whole process to remain unaltered, or rather to
be renewed, after many thousands or millions of changes. (Plate XXX. Fig.
452.)

It is presumed, that the accuracy, with which the general law of the inter-
ference of light has been shown to be applicable to so great a variety of foots,
in circumstances the most dissimilar, will be allowed to establish its validity
in the most satisfactory manner. The full confirmation or decided rejection
of the theory, by which this law was first suggested, can be expected from
time and experience alone; if it be confuted, our prospects will again
be confined within their ancient limits, but if it be fully established, we may
expect an ample extension of our views of the operations of nature, by
means of our acquaintance with a medium, so powerful and so universal, as
that to which the propagation of light must be attributed.

472

LECTURE XL

ON THE HISTORY OF OPTICS.

A HE science of optics is not one of those which had been cultivated with
the greatest diligence and success by the philosophers of antiquity: almost
every refinement relating to it has originated in the course of about two
centuries; and some of its greatest improvements have been made within these
fifty years. The reflection of the rays of light is indeed an occurrence too
frequent and too obvious to have escaped the notice even of the earliest
observers: a river or a fountain was the first mirror; its effect was ea5ily
imitated by speculums of metal; and as soon as any philosophical attention
was paid to the phenomenon, it was easy to collect the equality of the angles
of incidence and reflection ; but although it was well known that^an oar, partial-
ly immersed in water, no longer appeared straight, it was long before any
attempts were made to ascertain the relation between the angles of incidence
and refraction. The Greeks were, however, acquainted with the properties
of the burning glass, which was sold as a curiosity in the toy shops; for it
is well known, that one of the personages, introduced by Aristophanes,
proposes to destroy the papers of his adversary by the assistance of this in-
strument. The magnifying powers of lenses were, however, but little
understood, although it is scarcely credible that they could have escaped the
notice of a person in possession of a burning glass; it appears from Seneca
that the Romans at least were informed of the effects of spherical refracting
substances, and it is not improbable that some use was occasionally made of
them in the arts.

Empedocles is perhaps the first person on record that wrote systematically
on light. He maintained that it consisted of particles projected from
luminous bodies, and that vision was performed both by the effect of these
particles on the eye, and by means of a visual influence, emitted by the eye

ON THE HISTORY OF OPTICS. 4:7'^

itself. Both of these doctrines were combated by Aristotle, who thought it ab-
surd to suppose that a visual influence §hould be emitted by the eye, and that
it should not enable us to see in the dark; and who considered it as more pro-
bable that light consisted in an impulse, propagated through a continuous
medium, than in an emanation of distinct particles. Light, he says, is the
action of a transparent substance; and if there were absolutely no medium
between the eye and any visible object, it would be absolutely impossible
that wc should see it.

It is said that Archimedes made a compound burning mirror, of sufficient
power to set on fire the Roman ships: in this form the story is scarcely pro-
bable, although the possibility of burning an object at a great distance by a
collection of plane mirrors has been sufficiently shown by the experiments
of Buffon. It is, however, not unlikely that Archimedes was acquainted
with the properties of reflecting surfaces, and that he confirmed his theories
by some experimental investigations. The work on catoptrics, attributed
to Euclid, contains the determination of the eflfects of reflecting surfaces of
different forms; but it is not supposed to be genuine. The existence and
the magnitude of the atmospheric refraction were well known to Ptolemy,
and a treatise of this astronomer on the subject is still extant in manu-
script.

The mathematical theory of optics, or the science of dioptrics and cat-
optrics, made some advances in the middle ages from the labours of Alhazen
and Vitellio. Alhazen was mistaken in some of his propositions respecting
refraction ; Vitellio, a native of Poland, gave a more correct theory of this
subject, and constructed a table of refractive densities, showing the supposed
proportions of the angles of incidence and refraction in the respective
mediums.

The invention of the magic lantern is attributed to Roger Bacon, and
the lens was soon afterwards commonly applied to the assistance of defective
sight. It has been much disputed whether or no Bacon was acquainted with
telescopes; the prevalent opinion is, that the passages, which have been alleged
to prove it, are insufficient for the purpose; but there is reason to suspect,
from the testimony of Recorde, who wrote in 1551, not only that Bacon had

VOL. I. 3 p

474 LECTURE XL.

actually invented a telescope, but that Recorde .himself knew something of
its construction. Digges also, in a work published in 1571, has a passage
of a similar nature, and from Bacon's own words it has been conjectured that
an instrument resembling a telescope was even of much higher antiquity.
But the first person, who is certainly known to have made a telescope, is
Janson, a Dutchman, whose son, by accident, placing a concave and a convex
spectacle glass at a little distance from each other, observed the increased
apparent magnitude of an object seen through them; the father upon
this fixed two such glasses in a tube a few inches long, and sold the
instrument in this form. He also made some telescopes of greater powers,
and one of his family discovered a satellite of Jupiter with them. Galileo
had heard of the instrument, but had not been informed of the particulars of
its construction, he reinvented it in I6O9, and the following year redis-
covered also the satellite which Janson had seen a little before.

It was, however, Kepler that first reduced the theory of the telescope to
its true principles; he laid down the common rules fur finding the focal
lengths of simple lenses of glass; he showed how to determine the magnify-
ing power of the telescope, and pointed out the construction of the simple
astronomical telescope, which is more convenient for accurate observations
than the Galilean telescope, since the micrometer may be more easily applied to
it; a third glass, for recovering the erect position of the object, was after-
wards added by Scheiner, and a fourth, for increasing the field of view, by
Rheita. Kepler made also some good experiments on the nature of coloured
bodies, and showed the inverted situation of the image formed on the retina
of the eye. Maurolycus of Messina had demonstrated, in 1575, that the
pencils of light are brought to focal points on the retina; Kepler's observa-
tions were thirty or forty years later.

The next great step in optics was made by De Dominis, who in 16II first
explained the cause of the interior or primary rainbow, and this was soon
followed by a still more important discovery respecting the nature of refrac-
tion, first made by Snellius, who ascertained, about I62I, that the sines of
the angles of incidence and refraction are always in the same proportion to
each other at the same surface; he died, however, in 16^6, without having
made his discovery public. Descartes, is generally supposed to have

ON THE HISTORY OF OPTICS. ' 475"

seen Snellius's papers, although he published the law of refraction without
acknowledging to whom he was indebted for it. Descartes also explained
the formation of the secondary rainbow, and truly determined the angular
magnitude of both the bows from mathematical principles; he did not, how-
ever, give a sufficient reason for the production of colours in either case.
Descartes imagined light to consist in motion, or rather pressure, transmit-
ted instantaneously through a medium infinitely elastic, and colours he at-
tribsted to a rotatory motion of the particles of this medium. He supposed
that light passed more rapidly through a denser medium than through a rarer;
other philosophers about the same time maintained a contrary opinion, with-
out deciding with respect to any general theory of light : thus Fermat and
Leibnitz deduced, on tliis supposition, the path of refracted light from the
natural tendency of every body to attain its end by the shortest possible way;
and Barrow derived the same law, in a more geometrical manner, from a simi-
lar hypothesis respecting the velocity of light, by considering a pencil of
light as a collection of collateral rays influencing each other's motions.
We are indebted to this learned mathematician for the first accurate inves-
tigation of the properties of refracting and reflecting surfaces, and for the
most general determination of the situations of focal points.

The industrious Mr. Boyle had noticed with attention the phosphorescence of
diamonds, the colours produced by the eflfect of scratches on the surfaces of
polished metals, and the diversified tints which a bubble or a film of soapy
water usually assumes. His'assistant, Dr. Hooke, investigated these and
other similar appearances with still greater accuracy, and proposed, in his
Micrographia, which was published in 1665, a theory of light considerably
resembling that of Descartes: he supposes that light is an impulse propagated
through a medium highly, but not infinitely, elastic; that refraction is pro-
duced by the readier transmission of light through the denser medium, and
that difference of colour consists in the different law of the particular im-
pulse constituting coloured light, so that red and blue differ from each other
in the same manner as the sound of a violin and of a flute. He explained
the colours of thin plates from the interference of two such pulses partially
reflected from the upper and under surface; but the hypothesis which he
assumed, respecting the nature of colours, renders this explanation wholly

476 LECTURE XL. '

inadequate, nor were the phenomena at that time sufficiently investigated
for a complete solution of the difficulties attending them.

It was still believed that every refraction actually produces colour, instead
of separating the colours already existing in white light; but in the year 1666,
Newton first made the important discovery of the actual existence of colours
of all kinds in white light, which he showed to be no other than a compound
of all possible colours, mixed in certain proportions with each other, and ca-
pable of being separated by refraction of any kind.

About the same time that Newton was making his earliest experiments on
refraction, Grimaldi's treatise on light appeared; it contained many inte-
resting experiments and ingenious remarks on the effects of diffraction,
which is the name that he gave to the spreading of light in every direction
upon its admission into a dark chamber, and on the colours which usually ac-
company these effects. He had even observed that in some instances the
light of one pencil tended to extinguish that of another, but he had not
inquired in what cases and according to what laws such an .interference
must be expected.

The discoveries of Newton were not received without some controversy
either at home or abroad; the essential points of his theory were, however^
soon established, but Dr. Hooke very warmly opposed the hypothesis which
Newton had suggested respecting the nature and propagation of light. On
this subject Newton professed himself by no means tenacious ; he was not,
however, convinced by Ds. Hooke, and disliked the dispute so much, that he
deferred the publication of his treatise on optics till after Hooke's death
in 1703. Very soon after his first communication to the Royal Society, in
1672, he had sent them a description of his reflecting telescope, which was
perhaps the first that had been constructed with success, although Gregory
had invented his instrument some years before, and a plan of a similar kind
had been suggested by Eskinard as early as l6l5. The principal parts of the
treatise on optics had been communicated at diflf'erent times to the Royal
Society; besides the experiments on refraction and the theory of the rain-
bow, they consist of an elegant analysis of the colours of thin transparent

Oisr THE HISTORY OF OPTICS. , 477

substances, in which the phenomena are reduced to their simplest forms,
and of a collection of miscellaneous experiments on the colours produced in
cases of inflection or diffraction.

With respect to the nature of light, the theory which Newton adopted
was materially different from the opinions of most of his predecessors. He
considered indeed the operation of an ethereal medium as absolutely neces-
sary to the production of the most remarkable effects of light, but he denied
that the motions of such a medium actually constituted light; he asserted, on
the contrary, that the essence of light consisted in the prv)jection of minute
particles of matter from the luminous body, and maintained that this pro-
jection was only accompanied by the vibration of a medium as an accidental
circumstance, which was also renewed at the surface of every refractive or
reflective substance.

In the mean time Bartholin had called the attention" of naturalists and
opticians to the singular properties of the Iceland crystal, and had hastily
examined the laws of its unusual refraction. On this subject Huygens had
been much more successful-: his analysis of the phenomena of the double re-
fraction is a happy combination of accurate experiment with elegant theory;
it was published in I690, making apart of his treatise on light, the funda-
mental doctrines of which he had communicated to the Academy of Paris in
1678. They scarcely differ in their essential parts from those of our country-
man Dr. Hookc, but the subject of colours Huygens has left wholly un-
touched. Roemer had then lately made the discovery of the immense velo-
city with which light passes through the celestial regions, by observing the
apparent irregularities of the eclipses of Jupiter's satellites; and Huygens
readily admitted this property into his system; althougli Hooke, by a
singular caprice, professed himself more ready to believe that the propagation
of light might be absolutely instantaneous, than that its motion could be
successive, and yet so inconceivably rapid. The merits of Huygens in the
mathematical theory of optics were no less considerable than in the investi-
gation of the nature of light; his determinations of the aberrations of lenses
were the first refinement on the construction of telescopes.

In the year 1720 Dr. Bradley had the good fortune to discover both the

478 LECrUKE XL.

existence and the cause of the aberration of the fixed stars. He had for
some time observed an irregularity in the places of the stars, which he was
wholly unable to explain, and the idea of attributing it to a combination of
the effect of the earth's motion in its orbit, with the progressive motion of
light, occurred to him first as he happened to observe the apparent direction
of the wind on board of a boat which was moving in a transverse direction.
He also determined with accuracy the magnitude of the atmospherical refrac-
tion, which had been theoretically investigated by Newton and by Taylor,
but never before practically ascertained with sufficient precision. The for-
mula, which Bradley appears to have deduced from observation only, agrees
precisely with an approximation which was obtained by Simpson from calcu-
lation; but it cannot be considered as rigidly accurate.

The optics of Bouguer were first published in 1729, and an improved
edition appeared thirty years afterwards; the merits of this author in the exmai-
nation of the properties of a variety of substances, with respect to the trans-
mission and reflection of light in different circumstances, and in the comparison
of lights of different kinds, require to be mentioned with the highest commen-
dation. Dr. Porterfield's investigations of the functions of the eye tended
greatly to illustrate the economy of this admirable organ, and some valuable
remarks of Dr. Jurin on the same subject were soon after published in Dr.
Smith's elaborate treatise on optics, which contains all that had been done
at that time with respect to the mathematical part of the science.

The invention of achromatic telescopes is with justice universally attri-
buted to our countryman Mr. DoUond, but there is reason to believe that he
was not absolutely the first author of the improvement. Mr. Hall, a gen-
tleman of Worcestershire, is said to have discovered, about the year 1729, Sir
Isaac Newton's mistake, in supposing that the rays of different colours must
of necessity be equally separated by all surfaces which produce an equal
mean refraction ; and by combining the different dispersive properties of
different kinds of glass, he constructed, in 1733, several compound object
glasses, which were calculated not only for avoiding all appearance of colour,
but also for correcting the imperfect refractions of the spherical surfaces of
the separate lenses. He did not, however, make known the particulars of
his investigations, and his invention was soon wholly forgotten. It was in

2

ON THE HISTORY OF OPTICS. 479

consequence of a discussion with Euler, Klingenstierna, and some other
mathematicians, that Mr. DoUond was led to make experiments on the re-
fraction of different kinds of glass; these gentlemen had not questioned the
general truth of Newton's opinion respecting the dispersion of the different
colours, but Euler had asserted that the eye itself produced a refraction free
from the appearance of colour, and Klingenstierna had shown the possibility
of producing a deviation by refraction, without a separation of colour, ac-
cording to the laws of refraction laid down by Newton himself. When
Dollond had once discovered the material difference which exists between
the dispersive properties of flint glass and of crown glass, it was easy to
produce the combination recjuired; but this ingenious artist was not satis-
fied with the advantage of freedom from colours only; he adjusted the
forms and apertures of his lenses in the most skilful manner to the correction
of aberrations of various kinds, and he was also particularly fortunate in being
able to obtain, about the time of his discovery, a glass of a quality superior
to any that has been since manufactured.

This opinion of Euler respecting the eye was, however, by no means well
founded, for the eye acts very differently on rays of different colours, as we may
easily observe by viewing a minute object in different parts of a beam of light,
transmitted through a prism. It must be allowed that this great mathema-
tician was less fortunate in his optical theories than in many other depart-
ments of science; his mathematical investigations of the effects of lenses are
much more intricate and prolix than the subject actually requires, and with
respect to the nature and propagation of light, he adopted several paradoxical
opinions. Assuming the theory of Huygens, with the additional hypothesis
respecting the nature of colours, which had been suggested by Newton, and
maintained by Pardies and Malebranche, that is, that the difference of co-
lours, like that of tones in music, depends on the different frequency of the
vibrations constituting light; he imagined that opaque bodies are not seen
by reflected light, but that their particles are agitated by the impulse of the
light which falls on them, and that the vibrations of these particles render
the bodies again visible in every direction; he also conceived that the undu-
lations of light are simply propagated through the solid substances of trans-
parent mediums, in the same manner as sound travels through the air. But
on these suppositions, all bodies would have the properties of solar phos-

480 LECTURE XL.

phori, and the refraction of the rarest of natural bodies would be incompa-
rably greater than that of the densest is actually found to be : and on the
whole, although the character of Euler has been so highly and so deservedly
respected as to attach a certain degree of authorit}' to all his opinions, so that
in this instance the name of Iluygens has been almost superseded by that of
Euler, yet in fact he has added no argumentative evidence whatever to the
theory, but, by inaccurate and injudicious reasoning, has done a real injury
to the cause which he endeavoured to support.

The researches of Lambert may be considered as a continuation of those of
Bouguer; they present us with many interesting observations on the natural
history of light, and the properties of various bodies with regard to it. Mr.
Lambert first ascertained that a luminous surface emits its light very nearly
with eqvial intensity in all directions, so that any part of it appears almost
equally brilliant to an eye placed in any direction, while the light thrown
by each square inch or square foot of the surface in any direction differs ac-
cording to the obliquity of that direction. The mathematical theory of
optics is considerably indebted to the labours of Clairaut, Dalembert, and
Boscovich ; Jeaurat, Beguelin, Redern, and Kliigel have also continued the
investigation; their calculations may be of considerable utility to the prac-
tical optician, but it requires the ingenuity of a Dollond or a Ilamsden to
apply the whole of the results to any useful purposes.

The experiments of Maz6as on the colours of thin plates are mere repeti-
tions of those of Newton under disadvantageous circumstances; Mr. Dutour
has, however, considerably diversified and extended these experiments, as
well as those on the colours which are produced in diffracted light, yet without
obtaining any general results of importance. Comparetti's experiments on
inflection have every appearance of accuracy, but they are much to^o in-
tricate to be easily compared with each other, or with those of former
observers.

The late Dr. Priestley rendered an essential service to'.the science of optics,
considered as a subject for the amusement of the general reader, by an
elegant and well written account of the principal experiments and theories,
which had been published before the year 1770. But this work is very defi-

ON THE HISTORY OF OPTICS. 481

cient in mathematical accuracy, and the author was not sufficientlj' master of
the science to distinguish the good from the indift'erent.

Mr. Delaval's experiments on colours appear to show very satisfactorily,
that all the colouring substances, in common use, owe their tints to rays,
which are separated from white light, during its passage through them, and
not, as Newton supposed, to the reflection of a particular colour from the first
surface. It has been observed that Kepler and Zucchius had long ago made
experiments nearly similar to those of Mr. Delaval. Dr. Robert Darwin's
investigation of the eti'ects of strong lights on the eye appears to comprehend
almost all possible varieties of these ocular spectra, but it does not lead to
any fundamental analogy, capable of explaining the most intricate of them.

The phenomena of the unusual atmospheric refraction, which frequently
produces double or triple images of objects seen near a heated surface, have
been successively illustrated by Mr. Huddart, Mr. Vince,and Dr. Wollaston,
so that at present there appears to be little doubt remaining with respect to
their origin. Dr. WoUaston's instrument, for the measurement of refractive
densities, very much facilitates the examination of the optical properties of sub-
stances of various kinds : he has applied it very successfully to the confirmation
of Huygens's theory of double refraction; he has corrected the common
opinion respecting the division of the prismatic spectrum; he discovered,
without being acquainted with the observations of Hitter, the dark rays which
blacken the salts of silver ; and he has remarked a singular property in some
natural as well as artificial crystals, which appear of one colour when viewed in
the direction of the axis, and of another when in a transverse direction.

To Dr. Herschel the sciences of optics and astronomy are equally indebted.
He has carried the construction of the reflecting telescope to a degree of per-
fection, far exceeding all that had been before attempted, and the well known
improvements, which astronomy has derived from his observations, are nume-
rous and important. In the course of his researches for the attainment of
his more immediate objects, he has also had the good fortune to discover the
separation of the rays of heat from those of light by means of refraction; a
fact which has been sufficiently established by the experiments of several
other persons.

VOL. I. Sq

482 LECTURE XX.

The investigations of ^Ir. Laplace, relating to atmospherical refraction, may

be considered as the latest application of refined mathematics to the purposes

of optics and of astronomy. I have myself attempted to attain a degree of

certainty, in attributing the changes of the refractive powers of the eye

to a variation in the form of the crystalline lens; I have discovered a general

law of the mutual action of two portions of light interfering with each other,

to, which no exception has yet been shown ; and by reviving a theory of

liglit similar to that of Ilooke and Hiiygens, with an improvement originally

suggested by Newton, respecting the nature of colours, I have endeavoured

to obtain a satisfactory explanation of many circumstances, which appear, upon

a minute examination, to be in every other hypothesis difficulties absolutely

insuperable. It cannot be expected that all objections to such a system will

at once be silenced, but if a full and candid discussion only of the facts, which

I have advanced, should be excited, I trust that the science of optics will be

essentially benefited, even if the theory should be ultimately confuted.

ON THE HISTORY OF OPTICS.

CHRONOLOGY OF OPTICAL AUTHORS.

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KLINGENSTIERNA

ON. .LAMBERT.

D U T 0 U R

COURSE OF LECTURES

ON

NATURAL PHILOSOPHY

AND THE

MECHANICAL ARTS.

PART III.

PHYSICS.

I ui

COURSE OF LECTURES

OI7

NATURAL PHILOSOPHY

AND THE

MECHANICAL APiTS.

LECTURE XLI.

ON THE FIXED STARS.

The departments of natural philosophy, which are to be the subjects of
the third and last division of these lectures, are included in the description
implied by the term physics, or the history of the particular phenomena of
nature; and the account, which will be given of these phenomena, will be
accompanied by as much of mechanical theory and analogical reasoning, as
can be applied to them with sufficient certainty, and without too great in-
tricacy of calculation.

The science of astronomy might, without any great impropriety, have been,
considered as a part of mechanics; but. there are circumstances intimately
connected with it, for the complete investigation of which, a knowledge of
the motions of fluids in general, and also of optics, is absolutely necessary.
It could not, therefore, hold any other place in a strict order of arrangement,
than that which is here allotted to it; and, since it will not be in our power

488 LECTURE XLI.

to enter completely into a mathematical examination of all the motions of
the heavenly bodies, although we shall be able to pursue the detail of the
most remarkable appearances which they exhibit, we may for this reason
more properly consider such a view of astronomy as belonging to descriptive
than to theoretical philosophy. This method of treating the subject is some-
times denominated plain astronomy, in contradistinction to the mechanical
theory of the science, which is called physical astronomy;, but it is obvious
that in the sense which we are at present annexing to the word physics, that
which is commonly called plain astronomy must be termed physical or de-
scriptive, and what is usually called physical, must be denominated mathe-
matical astronomy. We shall, therefore, confine ourselves in great measure
to descriptive, astronomy, and shall take only a general view of the laws of
gravjitation, as an illustration of the phenomena previously described. After
having considered the magnificent objects of astronomy, which are scattered
throughout the universe, we descend to geography, or the particular history
of the terraqueous globe, and to the tides, produced by the influence of the
celestial bodies on the ocean: and then, quitting the aft'ections of the larger
features of the matter, that constitutes the earth, we come naturally to the
properties and powers of its individual particles, and to the phenomena
of heat, electricity and magnetism, which are either qualities of matter, or
dependent on substances differing in some respects from -common matter;
and in the next place, to the combination of all these substances and actions
in meteorology, and in the phenomena of vegetable and animal life, a general
view of which will complete our discussions on the subject of physics. The
science of chemistry, or the doctrine of the qualities of particular kinds of
matter, might be said to belong to the investigation of the properties of
matteu in general; but this science is of too great extent and importance to
occupy a subordinate place in a system of natural philosophy, and must,
therefore, be considered as requiring a separate course of study.

In our astronomical inquiries, we shall first examine the phenomena of the
heavens and earth in their simplest form, not as they immediately appear to
our observation, but as they are shown by unexceptionable proofs to be na-
turally arranged. The stars and sun, the planets and their satellites, and
lastly the comets, will be severally described; the causes of the motions of

ON THE FIXED STAIIS. '" 485

these bodies will be superficially indicated; their sensible effects with respect
to the inhabitants of the earth will be shown, and the practical modes of
determining their situations and orbits will be explained.

When we begin to consider,on a large scale, the affections of matter and of
space, we are impressed, at the first sight, with the inconceivable disproportion
between the magnitude of space and of sensible matter : and we are naturally
led to inquire if the apparently void expanse of the universe is wholly with-
out all matter or all substance. The atmospheres of the planets cannot
indeed be said absolutely to terminate at any given point, but they must become
iare beyond all imagination at a very moderate distance. The substance which
produces the sensation of light must, -however, be every where found, at
least without any sensible interval: for if an eye were placed in any point of'
the regions of unbounded space, wherever human investigation or fancy
can penetrate them, some luminous object would at each instant be visible to
it, and, in general, objects without number might be seen in every direction.
Light, therefore, must be every where present, whether we suppose it to
consist of separate projected corpuscles, or to be an affection of a highly
clastic ether, pervading the universe in a state so rare, that although it
constitutes a continuous medium, it suffers all bodies to move through it
without sensible resistance, and is admitted even into their pores with per-
fect freedom; and if we follow Newton's opinion of the nature of light, wc
must suppose both such an ethereal medium, nearly at rest, and the particles
of light also, moving swiftly through it, to exist together in all places: to
say nothing of the possibility of the coexistence of a thousand other unseen
and unknown substances, essences, and influences, in the same individual
place, which may for ever set at defiance the pride of a presumptuous phi-
losophy, that would aspire to comprehend, within its own contracted sphere,
the whole extent of the mighty work of the creation.

The expanse of the universe is strewed, at immense distances, with detached
portions of a substance, which we suppose to be matter, constituting stars,
or suns, planets, and comets; bodies which certainly agree with each other
in the power of emitting or reflecting light, and which, in all probability, have
many other properties in common. Such of these, as emit their own light, are

VOL.. I, 3 R ,

4gO LECTURE XLI.

called fixed stars; and this appears to be the only criterion that we can apply-
to a star: for the word fixed is only to be understood in a comparative
sense.

The stars must necessarily shine by their own light; for if we grant that they
consist of gravitating matter, it must be allowed that no star could be near
enough to another to be seen by reflected light, without a very sensible
change of the places of both in consequence of their mutual gravitation, nor
would it be possible, on account of their immense distance from us, to distin-
guish two such bodies from each other. It follows also, on the same sup-
position of the universality of the force of gravity, that the form of the stars
must be nearly spherical.

The light of the stars appears to the naked eye to be generally white;
being too faint to excite the idea of a particular colour ; but when it is con-
centrated by Dr. Herschel's large speculums, it becomes in various stars of
various hues; and indeed to the naked eye some of the stars appear a little
redder and others a little bluer. The cause of the twinkling of the stars is
not fully ascertained, but it is referred, with some probability, to changes
which are perpetually taking place in the atmosphere, and which aflfect its
refractive density. It is said that in some climates, where the 'air is re-
markably serene, the stars have scarcely any appearance of twinkling.

Above two thousand stars are visible to the naked eye; and when a tele-
scope is employed, their number appears to increase without any other limit
than the imperfection of the instrument. Dr. Herschel has observed in the
milky way above ten thousand stars in the space of a square degree. Lucre-
tius and Dr. Halley have argued that their number must be absolutely infi-
nite, in order that all of them may remain at rest by the opposition of attrac-
tions acting in every possible direction ; but we are by no means certain that
they do remain in perfect equilibrium.

Of the actual magnitude of the stars we can give no exact account; but
they are divided into seven or more orders, according to the degrees of
their apparent brightness. There is, however, reason to suppose, from the
quantity of light emitted by the brightest stars, that some of them are much

ON THE FIXED STARS. 4£)l

larger than the sun. Those stars which are below the sixth magnitude arc
scarcely visible without the help of telescopes. The distances of all the stars
from us and from one another are so great, as not to be capable of being im-
mediately compared with their diameters; for no star subtends an angle large
enough to be ascertained by direct observation. The more perfect the instru-
ments that we employ, the smaller are the apparent diameters of the fixed
stars. Dr. Herschel found that one oi' the stars of the first magnitude, when
viewed in his best telescopes, appeared to be about one third of a second in
diameter. But there is always a limit to the perfection of the focus of the
telescope and of the eye, and, however accurate both may be, the image of
every radiant point will occupy on the retina a space of a certain magnitude,
not depending on that of the object: so that it will perhaps be for ever im-
possible to measure any angle, which is only a very small fraction of a second*
(Plate XXXI. Fig. 453, 454.)

There is, however, reason to suppose, that the angle subtended by the
nearest stars is in reality more than a hundred times less than the angle
measured by Dr. Herschel, for it may be conjectured that our distance from
the nearest stars is about a hundred million million miles ; taking about one
third of a second for the annual parallax of the earth, that is, for the change
of the apparent places of some of the fixed stars in consequence of the earth's
annual motion. This seems to be nearly the utmost amount of an annual
parallax that could wholly have escaped observation ; for Dr. Herschel
supposes that, by means of double stars, a parallax of one tenth of a second
only might become sensible, and even this has never yet been discovered;
on the other hand, if the parallax were really much smaller than this, it
would be necessary to suppose the actual magnitude or splendour of the bright-
est stars to be incomparably greater than that of the sun; for at the distance
of a hundred million million miles, our sun would appear, according to
Lambert's calculations, but about one fourth as bright as Saturn, or like
a star of the second or third magnitude only. Perhaps, indeed, the stars
may differ as much from each other in magnitude as the planetary bodies,
but it is somewhat more natural to imagine them more nearly equal, until we
have some reason for supposing any material inequality in their dimensions. At
any rate there is little doubt, that the diversity of their apparent magnitudes
is principally owing to their different distances ; perhaps none of them are

49l8 LECTURE XLI.

much nearer to each other than the nearest to us ; and there may still be a
very great variety in their actual dimensions. There can be only twelve
points on the surface of a sphere as far from each other as Irom the
centre; in a sphere of twice tlie radius, there may be about 50 points at
the same distance; in a sphere of three times the radius, more than 100: and
it has been observed that these numbers do not greatly differ from the actual
numbers of tlie stars of the first, second, and third magnitudes; although it
is true that they are not by any means placed at equal angular distances
from each other. But, from a comparison of the light of ditierent stars, we
may infer, that if their real magnitudes are nearly equal tlieir distances
must increase much faster than in this arithmetical progression; that is,
that the stars of the second magnitude are more than twice as remote as those
of the first, and those of the third more than three times as remote. Mr.
Michell found the light of Sirius between 400 and 1000 times as great as that
of a star of the sixth magnitude; consequently, supposing these stars actually
equal, their distances must differ in the ratio of 1 to 20 or 30; since light
always diminishes in proportion to the square of the distance of the luminous
object. The light of stars of different magnitudes, situated near each other,
may be compared by viewing them through two apertures of different sizes,
cut in cards, one held before each eye, the apertures being reduced to such
magnitudes, that the stars may appear equally bright; and the com-
parison may be extended to the light of the sun, by finding a star
and a planet of equal brightness, and calculating what proportion of the
sun's light must be reflected by the planet, upon the most probable sup-
position respecting the disposition of its surface to reflect more or less of the
light which falls on it.

The stars are in general dispersed without any regular order, but we may
observe in many parts of the heavens that a number of them are so much nearer
together than to the rest, as to form a cluster or nebula. The ancients had notic-
ed some of the most conspicuous nebulae, but Huygens first directed the atten-
tion of modern astronomers to the large one situated in the constellation Orion.
Herschel has now given us catalogues of 2500 nebulae: many of them can be
resolved by very high magnifying powers into separate stars; but others appear
to consist of a luminous matter, spread uniformly in the neighbourhood of the
•everal itars to which ihey seem to belong. (Plate XXI. I'ig. 45o . . 46"3.)

3

ON THE TIXED STAR8. 4S>5

It has been conjectured that all stars are disposed in nebulae, and that
those, which apj)ear to us to be more widely separated, are individual s ars of
that particular nebula in which we are placed, and of which the marginal
parts may be observed, in the form of a lucid zone, which is called the
milky way, being too distant to allow the single stars to be perceived by
thfe naked eye. This opinion was first suggested by Professor Kant, the
author of the system of metaphysics called the critical philosophy. The idea
was adopted by Lambert, who considers the largest stars as constituting a
distinct nebula placed among a multitude of others, which together produce
the appearance of a continued zone ; and Dr. Herschel has investigated very
particularly the figure of a single nebula, which would be capable of being
pnjected into the form of the milky way. We must not, however, suppose
that each of Dr. Herschel's 2500 nebulae can be at all comparable in mag-
nitude to this supposed nebula, since many of them are almost as much re-
solved by the telescope into single stars as the milky way itself; which
would be utterly impossible, if the stars which they contain were equally
numerous with those of the nebula to which the milky way belongs. Sup-
posing all the stars of this nebula to be as remote from each other as the
nearest of them are from the sun, it may be calculated that the most distant
are abuut 500 times as far from us as the nearest, aud that light, which is
probably 15 or 20 years in travelling to us from Sirius, would be nearly
twenty thousand in passing through the whole diameter of the milky way.
A nebula of the same size as this, appearing like a diffused light of a degree
in diameter, must be at such a distance, that its light would require a
million ifears to reach us. (Plate XXXI. Fig. 464.)

The stars are not, properly speaking, absolutely fixed with respect to each
other, for several of t:,em have particular motions, which have been dis-
covered by a comparison of accurate observations, made at very <listant times.
Arcturus, for instance, has a progressive motion, amounting to more than
two seconds annually. Dr. Maskelyne found, that out of S6 stars, of which
he ascertained the places with great precision, 35 had a proper motion. Mr.
Michell and Dr. llerschcl have conjectured, that some of the stars revolve round
others which are apparently situat<>d very near them; and perhaps even all
the stars may in reality change their places more or less, although their re-

494 LECTURE XLI.

relative situations, and the directions of their paths may often render their
motions imperceptible to us.

Respecting all these arrangements of stars into different systems, Dr.
Herschel has lately entered into a very extensive field of observation and
speculation, and has divided them into a number of classes, to each of which
he has assigned a distinct character. Some he supposes, like our sun, to be
insulated stars, beyond the reach of any sensible action of the gravitation of
others; and around these alone he conceives that planets and comets revolve.
Double stars, in general, he imagines to be much nearer to each other, so as
to be materially affected by their mutual gravitation, and only to preserve
their distance by means of the centrifugal force derived from a revolution
round their common centre of inertia; an opinion which, he thinks, is
strongly supported by his own observations of some changes in the positions
of double stars. Others again he supposes to be united in triple, quadruple,
and still more compound systems. A fourth class consists of nebulae like
the milky way, the clusters of stars being rounded, and appearing brightest
in the middle. Groups of stars Dr. Herschel distinguishes from these by a
want of apparent condensation about a centre of attraction; and clusters by
a still greater central compression. A seventh class includes such nebulae as
have not yet been resolved into stars, some of which Dr. Herschel supposes
to be so remote, that the light emitted by them must actually have been two
millions of years in travelling to our system. The nebulae of another de-
scription resemble stars surrounded by a bur, or a faint disc of light: a diffused
milky nebulosity, apparently produced by some cause distinct from the
mmediate light of any stars, is the next in order: and Dr. Herschel has
distinguished other more contracted nebulous appearances, in different states
of condensation, into the classes of nebulous stars, and planetary nebulae,
with and without bright central points. Many of these distinctions are
perhaps too refined to be verified by common observers ; but the discovery
of the existence of double and triple stars, revolving round a common centre,
will, if it be confirmed, add one more to the catalogue of Dr. Herschel's
important improvements.

It is however fully ascertained, that some of the stars liave periodical

ON THE FIXED STARS. 495

changes of brightness, which are suppnsed to arise either from the temporary
interpositioa of opaque bodies revolving round them, or, still more probably
from a rotatory motion of their own, which brings at certain periodical times
a less luminous part of the surface into our view. Thus, the star Algol,
which is usually of the second magnitude, becomes, at intervals of ^ days
and 21 hours each, of the fourth only, and occupies 7 hours in the gradual
diminution and recovery of its light. A less probable conjecture respecting
this change of brightness was advanced by Maupertuis, who imagined that
the disc of the star might be greatly flattened by a rapid rotation, and its
edge occasionally presented to us, in consequence of the disturbances produc-
ed by the attraction of planets revolving round the luminary. Other irregular
variations may possibly be occasioned by the appearance and disappearance of
spots, occurring, like the spots of the sun, without any determinate order
or assignable cause; and many stars have in the course of ages wholly disap-
peared, and sometimes have been again recovered ; others have made their ap-
pearance for a short time, where no star had before been seen. Such a temporary
star was observed by Hipparchus, 120 years before our era, and the circum-
stance suggested to him the propriety of making an accurate catalogue of all
the stars, with their respective situations, which is still extant, having been
preserved by Ptolemy, who added 4 stars to the 1022 that it contained. In
1572, Cornelius Gemma discovered a new star in Cassiopeia, which was so
bright as to be seen in the day time, and gradually disappeared in sixteen
months. Kepler, in 1604, observed a new star in Serpen tarius, more bril-
liant than any other star or planet, and changing per{>etually into all the
colours of the rainbow, except when it was near the horizon ; it remained
visible for about a year. Many other new stars have also been observed at
different times.

For describing the particular fixed stars according to their relative situa-
tions, it is necessary to consider them as they are visible to the inhabitants
of the earth. They have been divided, for the sake of convenience, into
parcels, making up imaginary forms, denominated constellations. This
division is of very remote antiquity, and though it may be useless, and
sometimes even inconvenient, for the purposes of minute observation, yet for
a general recollection of the great features of the heavens, these arbitrary
names and associations cannot but greatly assist the memory. It is also

496 LECTURK XLI.

usual to describe particular stars by their situation with respect to the imagi-
nary figure to which they belong, or, more commonly, at present, by the
letters of the Greek alphabet, which were first applied by Bayer in \60S, and
in addition to these, by the Roman letters, and by the numbers of particular
catalogues.

There are two principal modes of representing the stars; the one by
delineating them on a globe, where each star occupies the spot in which
it would appear to an eye placed in the centre of the globe, and where the
situations are consequently reversed, when we look on them from without, in the
same manner as a word appears reversed when seen from the back of the
paper: the other mode is by charts, which are generally so arranged as to
represent the stars in positions similar to their natural ones, or as they would
appear on the internal concave surface of the globe. Sometimes also the
stars have been delineated as they would be projected on imaginary surfaces,
without any reference to a globe ; for instance, on the surfaces of transparent
cones or cylinders. The art of constructing all such projections belongs to
the subject of perspective.

In describing the particular stars, it will be most convenient to begin with
such as never set in our climates, and we may then refer the situations of
others to their positions with respect to these.

The great bear is the most conspicuous of the constellations which never
set; it consists of seven stars, placed like the four wheels of a waggon, and
its three horses, except that the horses are fixed to one of the wheels. The
two hind wheels are the pointers, which direct us to the pole star, in the
extremity of the tail of the little bear: and further on, to the constellation
Cassiopeia, which is situated in the milky way, where it is. nearest to the pole,
and which consists of several stars, nearly in the form of the letter W. The two
northernmost wheels of the great bear, or wain, point at the bright star
Capella, the goat, in Auriga. Descending along the milky way from Cas-
siopoia, if we go towards Capella, we come to Algenib, in Perseus; and a
little further from the pole we find Algol, or Medusa's head: but if we take
the opposite direction, we arrive at Cygnus, the swan; and beyond it, a
iittle out of the milky way, is the bright star Lyra. The dragon consists of

OM THE FIXED STARS. 497

a chain of stars partly surrounding the little bear; and between Cassiopeia
and the swan is the constellation Cepheus.

Near Algenib, and pointing directly towards it, are two stars of Andro-
meda, and a third is a little beyond them. A line drawn through the
great bear and Capclla passes to the Pleiades, and then, turning at a right
angle towards the milky way, reaches Aldebaran, or the bull's eye, and the
shoulders of Orion, who is known by his belt, consisting of three stars,
placed in the middle of a quadrangle. Aldebaran, the Pleiades, and Algol,
make the upper, and Menkar, or the whale's jaw, with Aries, the lower
points of a W. In Aries we observe two principal stars, one of them with a
smaller attendant.

A line drawn from the pole, midway between the great bear and Capella,
passes to the twins and to Procyon; and then, in order to reach Sirius, it
must bend across the milky way. Algol and the twins point at Regulus, the
lion's heart, which is situated at one end of an arch, with Denebola at the
other end.

The pole star and the middle horse of the wain direct us to Spica Vir-
ginis, considerably distant: the pole and the fust horse nearly to Arcturus,
in the waggoner, or Bootes. Much further southwards, and near the milky
way, is Antares, in the scorpion, forming, Avith Arcturus and Spica, a
triangle, within which are the two stars of Libra. The Northern crown
is nearly in a line between Lyra and Arcturus, and the heads of Hercules
and Serpentarius are between Lyra and Scorpio.

In the milky way, below the part nearest to Lyra, and on a line drawti
from Arcturus through the head of Hercules, is Aquila, making with Lyra and
Cygnus a conspicuous triangle. The last of the three principal stars in An-
dromeda makes, with three of Pegasus, a square, of which one of the sides
points to Fomalhaut, situated at a considerable distance in the southern fish,
and in the neighbourhood of the whale, which has already been mentioned.

By means of these allineations, all the principal stars that are ever- visible
VOL. I. 3 s

498 LECTURK XU.

in Britain may be easily recognised. Of those which never rise above our
horizon, there are several of the first magnitude ; Canopus, in the ship Argo,
and Achernar, in the river Eridanus, are the most brilliant of them; the feet of
the centaur, and the crosier are the next; and according to Humboldt's
observations, perhaps some others may require to be admitted into the
same class. (Plate XXXVI, XXXVII.)

499

LECTURE XLll. sEmT^^

j(lUN

ON THE SOLAR SYSTEM.

JL HE most conspicuous of all the celestial bodies, which we have becH
examining, is the sun, that magnificent luminary which occupies the ceiitrc
of the system that comprehends our earth, together with a variety of other
primary and secondary planets, and a still greater number of comets.

The sun agrees with the fixed stars in the property of emitting light con-
tinually, and in retaining constantly its relative situation with very little
variation; it is probable also that these bodies have many other properties
in common. The sun is, therefore, considered as a fixed star comparatively
near us; and the stars as suns at immense distances from us: and we infer
from the same analogy, that the stars are possessed of gravitation, and of
the other general properties of matter; they are supposed to emit heat as
well as light; and it has with reason been conjectured that they serve to
cherish the inhabitants of a multitude of planetary bodies revolving round
them.

The sun, like many other stars, has probably a progressive motion, .which
is supposed, from a comparison of the apparent motions of a great number
of the stars, to be directed towards the constellation Hercules. It is beyond
all question that many of the stars have motions peculiar to themselves,
and it is not certain that any of them are without such motions: it is, there-'
fore, in itself highly probable that the sun may have such a motion. But
Dr. Herschel has confirmed this conjecture by arguments ahnost demon-
strative. He observes that the apparent proper motions of 44 stars out of
56 are very nearly in the direction which would be the result of such a real
motion of the solar system: and that the bright stars Arcturus and Sirius,
which are probably the nearest to us, have, as they ought to have, the

500 LECTURE XLII.

greatest apparent motions. Besides, the star Castor appears, Avhen viewed
with a telescope, to consist of two stars, of nearly equal magnitude; and
though they have both a considerable apparent motion, they have never been
found to change their distance a single second; a circumstance which is
easily understood if both their apparent motions are supposed to arise from a
real motion of the sun, but which is much less probable on the supposition
of two separate and independent motions.

Besides this progressive motion, the sun is subjected to some small change
of place, dependent on the situations of the planetary bodies, which was
lono- inferred from theory only, but which has been actually demonstrated by
modern observations. Supposing all the planets to be in conjunction, or
nearly in the same direction from the sun, the common centre of inertia of
the system is at the distance of about a diameter of the sun from his centre:
and since the centre of inertia of the whole system must ,be undisturbed by
any reciprocal actions or revolutions of the bodies composing it, the sun
must describe an irregular orbit round this centre, his greatest distance from
it being equal to his own diameter. Wc may form an idea of the magnitude
of this orbit by a comparison with the orbit of the moon: a body revolving
round the sun, in contact with his surface, must be nearly twice as remote
from his centre as the moon is from the earth, and the sun's revolution round
the common centre of gravity of the system must therefore be, where it is
most remote, at four times the distance of the moon from the earth.

The sun revolves on his axis in 25 days 10 hours, with respect to the
fixed stars: this axis is directed towards a point about half way between the
pole star and Lyra, the plane of the rotation being inclined a little more than
7° to that in which the earth revolves. The direction of this motion is from
west to east, terms which we can only define from our presupposed know-
ledge of the stars, by saying that the motion is such, that a point of the
sun's surface at first opposite Aries, moves towards Taurus. Nor have we any
better mode of describing north and south, or right and left : we can only say
comparatively, that if we are placed with our heads northwards, and looking to-
wards the centre, our right hands will be eastwards, and our left westwards.
All the rotations of the diflferent bodies which compose the solar system, as
far as they have been ascertained, are in the same direction, and all their
3

ON THE SOLAR SYSTEM. 501

revolutions, excepting those of some of the comets, of which the motions
are retrograde, and those of some of the satellites of the Georgian planet,
which revolve in planes so distant from those of the other planetary motions,
that the directions of their revolutions can scarcely be called either direct
or retrograde.

The time and direction of the stm's rotation is ascertained by the change
of the situation of the spots, which are usually visible on his disc, and which
some astronomers suppose to be elevations, but others, apparently on
better foundations, to be excavations or deficiencies in the luminous matter
covering the sun's surface. These spots are frequently observed to appear
and disappear, and they are in the mean time liable to great variations,
but they arc generally found about the same points of the sun's surface.
Lalande imagines that they are parts of the solid body of the sun, which,
by some agitations of the luminous ocean, with which he conceives the sun
to be surrounded, are left nearly or entirely bare. Ur. Wilson and Dr.
Herschel are disposed to consider this ocean as consisting rather of a flame
than of a liquid substance, and Dr. Herschel attributes the spots to the
Anission of an aeriform fluid, not yet in combustion, which displaces the
general luminous atmosphere, and which is afterwards to serve as fuel for
supporting the process; hence he supposes the appearance of copious
spots to be indicative of the approach of warm seasons on the surface of the
earth, and he has attempted to maintain this opinion by historical evidence.
The exterior luminous atmosphere has an appearance somewhat mottled,
some parts of it, appearing brighter than others, have generally been called
faculae; but Dr. Herschel distinguishes them by the names of ridges and
nodules. The spots are usually surrounded by margins less dark, than them-
selves, which Dr. Herschel calls shallows, and which he considers as parts
of an inferior stratum consisting of opaque clouds, capable of protecting tlie
immediate surface of the sun from the excessive heat produced by combus-
tion in the superior stratum, and perhaps of rendering it habitable to ani-
mated beings. (Plate XXXI. Fig. 465 . . 469.)

But if we inquire into the intensity of the heat which must necessarily
exist wherever this combustion is performed, we shall soon bd conviucecJ
that no clouds, however dense, could impede its rapid transmission to the

\.

502 LECTURE XLII.

parts below. Besides, the diameter of the sun is 1 1 1 times as great as that
of the earth; and at its surface, a heavy body would fall through no less
than 450 feet in a single second: so that if every other circumstance per-
mitted human beings to reside on it, their own weight would present an
insuperable difficulty, since it would become nearly thirty times as great as
upon the surface of the earth, and a man of moderate size would weigh
above two tons. Some of the most celebrated astronomers have imaained
from the comparative light of different parts of the sun's disc, or apparent
surface, that he is surrounded by a considerably dense and extensive at-
mosphere, imperfectly transparent; conceiving that,without such an atmosphere'
the marginal parts, which are seen most obliquely, must appear consider-
ably the brightest ; but this opinion is wholly erroneous, and the inferences
which have been drawn from it," respecting the sun's atmosphere, are con-
sequently without foundation.

We are, however, assured, by direct observation, of the existence of some
aerial substance in the neighbourhood of the sun, producing the appearance
called the zodiacal light, which is sometimes seen, nearly in the plane
of the sun's rotation on its axis, extending beyond the orbit of Mer-
cury. It is said to have been first distinctly described in Childrey's Bri-
tannia Baconica, a work published in l66l, and it was afterwards more par-
ticularly observed by Cassini, Mairan, and others. In the torrid zone it is
almost constantly visible; and in these climates, it may often be distin-
guished in the beginning of March, after the termination of twilight, ex-
hibiting the appearance of a narrow triangle, somewhat rounded off, of a
whiteness resembling the milky way, ascending from the sun as a base, likjC
the projection or section of a very flat spheroid, and extending to a distance
of more than 50° from the sun. The whole orbit of Venus never subtend*
80 great an angle from the earth as 96°, consequently this substance must
occasionally involve both Mercury and Venus; and if- it were not extremely
rare, it would produce some disturbance in their motions ; while in fact it
does not appear to impede the progress even of the tails of the comets, which
are probably themselves of very inconsiderable density. It cannot be a
continuous fluid atmosphere, revolving with the same velocity as the sun;
for the gravitation of such an atmosphere would cause it to assume a form
more nearly spherical; and the only probable manner in Avhich it' can be
4

ON TH£ SOLAR SYSTEM. 503

supposed to retain its figure, is by means of a revolution much more rapid
than the sun's rotation. Some persons have attributed the appearance to
the refraction of the earth's atmosphere only ; but if it arose from any such
cause as this, its direction could scarcely be oblique with respect to the
horizon, and it is highly improbable that it should always happen to coincide
with the plane of the sun's rotation. (Plate XXXI. Fig. 470.)

The sun is accompanied in his progressive motion "among the fixed stars
by ten planetary bodies, of different magnitudes, revolving round him, from
west to east, in orbits approaching to circles, and visible to us by means of
the light which they receive from him. These are Mercury, Venus, the Earth,
Mars, Juno, Pallas, Ceres, Jupiter, Saturn, and the Georgian planet. It
is unnecessary to adduce at present any arguments to prove the actual
existence or direction of any of these motions; their complete agreement with
the visible phenomena of the heavens, and with the laws of gravitation, will
hereafter appear to afi^brd sufficient evidence of the accuracy of the received
theory of the arrangement of the solar system. The motion of the earth is
the most unanswerably proved by the apparent aberration of the fixed stars,
derived from the different directions of this motion at different times, and
corresponding precisely with the known velocity of light, deduced from
observations of a very different kind. That the planets receive their hghc
from the sun, is undeniably shown by the appearance of the discs of
many of them, when viewed through a telescope, those parts of their surfaces
only being luminous, on which the sun shines at the time of observation.

These planets are neither all in one plane, nor does any one of them remain
precisely in the same plane at all times; but their deviations from their
respective planes are inconsiderable, and they are commonly represented by
supposing each planet to revolve in a plane passing through the sun, and
the situation of this plane to be liable to slight variations. There is, however,
a certain imaginary plane, determinable from the situations, the velocities,
and the masses of the planets, which, like the centre of inertia, never changes
its position on account of any mutual actions of the bodies of the system,
and this plane of inertia is called the fixed ecliptic. Its situation is nearly
half way between the orbits of Jupiter and of Saturn; and it is inclined in a
small angle only to the plane of the earth's orbit, which is called the earth's
ecliptic, or simply the ecliptic.

504 LECTURE XLII.

Tlie ecliptic passes through the constellations denomiuated the signs of
the zodiac, between Aries, the Pleiades, the twins, and Ilegulus, to the north,
and Aldebaran, Spica, and Antares, to the south. Its position has varied
slowly in the course of many ages, so that its northmost point is now more
than one third of a degree more remote from the pole »tar than it was in
the time of Eratosthenes, who observed its place 230 years before the birth of
Christ. It appears from Lagrange's calculations, that the limit of its great-
est possible variation is about 10 or 11 degrees. The ecliptic is supposed
to be divided into twelve angular parts, or signs, each containing thirty
degrees: they are named Aries, Taurus, Gemini, Cancer, Leo, Virgo,
Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. Those who
prefer the cadence of a Latin distich, in order to assist the memory, may
repeat them thus.

Sunt Aries, Taurus, Gemini, Cancer, Leo, Virgo,
Libraque, Scorpius, Arcitcnens, Caper, Amphora, Pisces.

The planes of the orbits of the other primary planets, excepting the three
minute planets lately discovered, intersect the ecliptic in small angles, and
the lines of intersection are called lines of the nodes. The nodes of all the
planets move very slowly, but not quite uniformly, from east to west, that
is, with respect to the fixed stars. At present the inclinations of all the
orbits appear to be somewhat diminishing: that of the orbit of Jupiter is less
by 6 minutes than it was in the time of Ptolemy. ,

The orbit of each planet is very nearly an ellipsis, one of the foci of which
coincides with the sun, or rather with the common centre of inertia of the
sun and planet. The extremities of the greater axis, where the orbit is
furthest from the sun and nearest to it, are called the upper and the lower
apsis, or the aphelion and perihelion; the mean distance being at either
end of the lesser axis ; and the distance of the centre of the ellipsis from the
sun is called the eccentricity. The slight deviations of the planets from
these elliptic paths are expressed by considering the apsides as moveable,
and this motion is direct, that is, from west towards east, in the case of
all the planets except Venus, of which the aphelion has a retrograde
motion, with respect to the fixed stars.

The elliptic motion of the planets was first discovered by Kepler; and

ON THE SOLAR SYSTEM. 505

he found that a right line, joining the sun and any planet, describes always
equal areas in ecjual ^imes. 1 he ohsi-rvations, on which Ktpler founded these
important laws, were made pnntipally on the phmet Mars. He determined
by calculation, upon the supposition which was then generally adopted, of a
motion in an eccentric circle, what must be nearly the situati;)n of the
planet, with respect to the sun, that is, its heliocentric place, and observing
its geocentric place, with respect to the earth, he was thus able to construct
a triangle representing the situation of the three bodies; repeating this
operation in various parts of the orbit, he discovered its form; and having
done this, the velocity of the motion in different parts of the orbit was easily
determined from the apparent change of place in a given time. (Plate
XXXII. Fig. 471.)

The same as'' ronomer also ascertained, that the squares of the times of re-
volution of the different planets are in proportion to the cubes of their mean
distances from the sun. For example, if oneplann were four times as distant
as aiother, it wjuld revolve in a period eight times as.long, since the cube of
4 is equal to the square of 8; thus Mars is nearly four times as remote from
the sun as Mercury, and the Georgian planet four times as remote as Jupifer,
and their periods are nearly eight times as long respectively.

It is probable that all the planets have a rotatory motion from west to east,
cither perfectly or very nearly equable. This motion has been observed in
Venus, the Earth, Mars, Jupirer, and Saturn; and from some phenomena
of the satellites of the Georgian planet, Mr. Laplace thinks that it may also
be assumed as nearly certain that this planet has also a rotatory motion.
The figure of the planets is spheroidical; they are more or less flattened
at the poles, as they revolve more or less rapidly on their axes. These
axes retain, with a very slight deviation, a situation always parallel, in
every part of the orbits.

But, in the course of time, the gradual change of the position of the axis
produces a sensible effect. In the case of the earth, this effect is denomi-
nated the precession of the equinoxes. The equinoctial points are the in-
tersections of the apparent ecliptic, or the path of the sun in the heavens,

VOL. I 3 T

506 LECTURE XLII.

with the plane of the equinoctial, which is perpendicular to the earth's axis
and which passes through the equator on the earth's surface; these points of
intersection have a retrograde motion, from east to west, on the ecliptic.
This motion was discovered by Hipparchus, in the year 128 before Christ,from
a comparison of his own observations with those of Timocharis, made 155
years before; and since the time of Hipparchus, the equinoctial points have
receded about 2(5^°. Hence it happens that the constellations, called the signs
of the zodiac, are now at a considerable distance from those divisions of the
ecliptic which bear the same names.

The earth's axis has also a small periodical change of inclination, or a
nutation, performed in about 19 years, and amounting in the whole to 18
seconds only. Its existence was determined by Newton from theory, al-
though he failed in the attempt to ascertain its quantity with accuracy ; it
was first actually observed by Dr. Bradley, about the year 1747. The abso-
lute direction of the axis in the heavens is also liable to some variation, in the
course of many ages, but this change has not always been sufficiently dis-
tinguished from the change of the position of the ecliptic. The inclination
ot* the equator to the ecliptic is now very nearly 23° 28'.

In order to retain in memory a general idea of the proportional distances
of the primary planets from the sun, we may call that of the earth 10 and
that of Saturn 100; the distance of Mercury will then be 4, to which we
must add 3 for Venus, making 7; twice 3 or 6 for the earth, making 10;
twice 6 or 12 for Mars, making 16; twice 12 or 24, making 28, for the
three small planets, Juno, Pallas, and Ceres; twice 24 or 48, making 52, for
Jupiter; twice 48 or 96 for Saturn, making 100 ; and twice 96 or 162,
making I96, for the Georgian planet; and these sums will represent
the distances, without any material exception, in the nearest integer num-
bers. \

The planet Mercury is little more than one third as large as the earth in
diameter. He performs his revolution in somewhat less than three months,
at about two fifths of the distance of the earth. His orbit is more eccentric,
and more inclined to the ecliptic, than those of any of the planets ex-

V

ON THE SOLAR SYSTEM. 507

cept the three small ones lately discovered; the eccentricity being one fifth
of the mean distance, and the inclination 7°. Of his density and his rota;
tion we know nothing but from conjecture.

Venus is very nearly as. large as the earth; Dr. Herschel thinks her even
ahtcle larger. Her revolution occupies about 7 months, her distance from the
sun being about seven tenths of that of the earth, and her orbit nearly cir-
cular, inclined in an angle of 3° 24' to the ecliptic . Mr. Schroeter attributes
to her mountains much higher than those of the earth, he has observed
strong indications of an atmosphere surrounding her, and he assigns for her
rotation on her axis the period of 23 hours 21 minutes. Her density has been
estimated from the perturbations, occasioned by her attraction, in ttie motions
of the other planets, and it has been supposed to be a little less thjin that of
the earth.

The distance of the earth from the sun is about 95 million English miles;
and this determination is generally supposed to be so far accurate, that
there is no probability of an error of more than a million or two, at most,
although some authors are still disposed to believe tliat the distance may be even
greater than a hundred millions. The period of its revolution, with respect to the
equinoctial points, which are the usual standard of comparison, since their
situation determines the annual return of the seasons, is 365 days, 5 hours,
48 minutes, and 48 seconds; and this is called its tropical revolution; that of
its absolute Or sidereal revolution is 36"5days,6 hours,9minutes,and 8 seconds;
the difference, which is 20 minutes and 20 seconds, being the time occupied
in passing over the space,through which the equinoctial points have retreated
in the course of the tropical year. By a day, we always understand the time
which elapses during the rotation of the earth with respect to the sun; a
sidereal day is about four minutes shorter.

At a distance from the sun exceeding that of the earth by one half, the
planet Mars revolves, in about a year and seven eighths. He is of half
the earth's linear dimensions: he has spots which change their form, and,
therefore, probably, an atmosphere. Dr. Herschel found his rotation per-
formed in 39 minutes more than a day; his equator inclined 28* 42' to the
plane of his orbit, and his figure so much flattened at the poles, that his axis

508 LECTURE xnr.

is ^lyth shorter than his equatorial diameter. From this form, compared with
the time of his rotation, it may be inferred that his density must be very
unequal in different parts: Laplace supposes it from calculation to be on the
whole about three fourths as great as that of the earth.

In the interval between Mars and Jupiter, and nearly at the distance
where, from a dependance on the regularity of the progression already men-
tioned, a number of astronomers had for some years been seeking for a pri-
mary planet, the observations of Mr. Piazzi, Dr. Olbers, and Mr. Harding
have placed three very small bodies, differing but little in their mean distance
and their periodical time. They have named them Ceres, Pallas, and Juno:
none of them subtends an angle large enough to be measured by our best
instruments; and all the circumstances of their motions are yet but imper-
fectly established. Juno, however, appears to be somewhat less remote tlian
the other tMo; all their orbits are considerably inclined to the ecliptic, espe-
cially that of Pallas, which is also extremely eccentric. Dr. Herschel does
not admit that they deserve the name of planets, and chooses to call them
asteroids.

Jupiter is the largest of all the planets, his diameter being 1 1 times as great
as that of the earth, and the force of gravitation at his surface being triple
the terrestrial gravitation. He revolves in about 12 years, at a little more
than five times the earth's distance from the sun. His rotation is performed
in less than ten hours, his equator being inclined about three degrees to his
ecliptic, which makes an angle of 1° ly' with ours. His belts are supposed
by many to be clouds in his atmosphere ; they seem to have a rotation some-
what slower than that of the planet.

The diameter of Saturn is ten times as great as that of the earth, but, on
account of the smaller density of his substance, the force of gravity at his
surface scarcely exceeds its force at the surface of the earth. He revolves
in 29 years and a half, in an orbit incHned 24-° to the ecliptic, at the distance
4)f 94: semidiameters of the earth's orbit: his rotation occupies only 10^ hours,
and his equator is inclined about 30° to our ecliptic. The most remarkable
circumstance attending him is the appearance of a double ring, which is
suspended over his equator, and revolves with a rapidity almost as greSt as

ON THE SOLAR SYSTEM. --^y

that of the planet, F^is figu"- appears also, according to Dr. Hcrschel's
observations, to be extremely singular; deviating very considerably from that
of an elliptical spheroid, which is the form assumed by all the other planets
that appear flattened, and approaching in some degree to a cylinder with its
angles rounded off. Such a form can only be derived from some very great
irregularities in the density of the internal parts of his substance.

The Georgian planet, discovered by Dr. Herschel in 1780, sometimes also'
called Herschel, and sometimes Uranus, revolves in 83:1 years, at a distance
from the sun equal to 19 times that of the earth. Its diameter is a little
more than 4 times that of the earth, and the weight of bodies at its surface a
little less than here. Notwithstanding its dimensions are by«no means compara-
tively small, it appears to us as a star of the sixth or seventh magnitude,
and is seldom seen by the naked eye. Its orbit approaches very near to the
ecliptic; its disc is said to be somewhat flattened, and it is supposed to re-
volve with considerable rapidity.

These ten planetary bodies are the only ones hitherto discovered which
have any title to be considered as primary planets, that is, as bodies revolving
round the sun, in orbits so nearly circular, as to remain always within the
reach of bur observation. It has been conjectured that the number of
planets may in reality be much greater, that not only many small and perhaps
invisible bodies may be revolving in the intervals of the planets with
which we are acquainted, but that larger bodies also may belong to our
system, which never approach within such a distance as to be seen by us.
Some have even bestowed names, borrowed from the ancient mythology, on
these imaginary planets; but the idea of such an appropriation of terms Is
rather to be regarded as belonging to the regions of poetical fiction than to
those of solid philosophy.

The largest and the most remote of the primary planets have their attend-
ant satellites, or secondary planets, accompanying them in their respective
revolutions round the sun, and moving, at the same time, in subordinate
orbits, round the primary planets. The earth is attended by the moon,
Jupiter by four moons or satellites, Saturn by seven, besides his ring, and
the Georgian planet by six moons. All these satellites move in the direct

5lU tECTURE XLII.

Older of the signs, and in planes not very remuu from the ecliptic, except,
ing those of the Georgian planet, which revolve in planes nearly perpendi-
cular to the ecliptic. Each of these planets thus becomes the central lumi-
nary of a little system of its oAV'n,in which the motions'and the periods observe
the same general laws as prevail in the solar system at large. Of the 28
primary and secondary planets, we are indebted to Dr. llerschel for the
knowledge of 9; the Georgian planet, with its six satellites, and the two
' innermost moons of Saturn.

The motions of some of these satellites, in particular of those of Jupiter>
and of the niQon, are of considerable importance for the assistance they aftbrd
us in determinations of time, and of the relative situations of places. They
are subjected to considerable irregularities, but the united labours of various
astronomers have enabled us to calculate all their motions with the greatest
accuracy.

The moon performs a complete sidereal revolution in 27 days 7^ hours,
and a synodical revolution, during which she returns to the same position
with respect to the earth and sun, in 29 days IQ^ hours; a period which
constitutes a lunation, or a lunar month. Her orbit is inclined to the
ecliptic in an angle of a little more than five degrees, but this inclination is
liable to great variations: the place of its nodes is also continually changing,
their motion being sometimes retrograde, and sometimes direct, but on the
whole the retrograde motion prevails. The form of the moon's orbit is
irregularly elliptic, and the velocity of its motion deviates considerably from
the Keplerian law of the description of equal areas in equal times; the ap-
sides, or the extremities of the greater axis of the ellipsis, which are called
the apogee and perigee, have on the whole aidirect motion. From a com- -
parison of modern observations with the most ancient, the mean motion of
the moon is found to be somewhat accelerated.

The moon revolves on her own axis with a very equable motion, and the
period of her rotation is precisely equal to the mean periodof her revolution
round tbe earth; so that she always presents to us the same portion of her
surface, excepting the apparent librations produced by her unequal velocities
in her orbit, and by the position of her axis, which is inclined I'' A'3' to the ^

ON THE SOLAR SYSTEM. 511

ecliptic, and sometimes as much as 7° to her own orbit. Her distance from
the earth is about 240 000 miles; her diameter -,?- of that of the earth, or
2160 miles; and the weight of bodies at her surface is supposed to be about
one fifth of their weiglit at the surface of the earth.

The surface of the moon presents to us, when viewed with a telescope, a
great diversity of light and shade, the principal features of which are visible
even to the naked eye. Many of these inequalities resemble very strongly
the effects of volcanos; several astronomers have imagined that they have
seen volcanos actually burning in the unenlightened part of the planet;
and Dr. Herschel's Instruments have enabled him to obtain satisfactory evi-
dence of the truth of the conjecture. The appearance of a perforation, which
UUoa supposed that he observed near the margin of the Moon's disc, in a solar
eclipse, has been attributed by some to a volcano actually burning. Dr.
Halley and Mr. Weidler have also observed flashes of light on the dark part
of the moon, considerably resembling the effect of lightning. The height
of the lunar mountains has been commonly supposed to exceed very consider-
ably that of the mountains of the earth; but Dr. Herschel is of opinion
that none of them are so much as two miles high. The names, which hare
been given by astronomers to various parts of the moon's surface, are of some
utility in the observation of the progress of an eclipse.

Of the satellites of Jupiter, some are a little larger, and others smaller than
the moon: they all revolve in planes inclined between Sf and 3^° to the
orbit of the planet, and they are therefore always seen nearly in the same
line. It is inferred, from some periodical changes of light which they under-
go, that, like our moon, they always present the same face to their primary
planet. >

The ring of Saturn is inclined 31 degrees to our ecliptic; of his seven
satellites, six are nearly in the same plane with the ring; but the plane of
the seventh or outermost satellite is but half as much inclined to the ecliptic.
The ring has been observed by Dr. Herschel to revolve in 104- hours, which
is considerably less than the time that would be occupied by the revolution
of a satellite at the same distance. The planes of the six satellites of the

5ig ' LECTURE XLir.

Georgian pknet are nearly perpendicular to the ecliptic; and some of tlieir
re/olutions are supposed to be rather retrograde than direct.

Besides the bodies which revolve completely round the sun, within the li-
mits of our observation, there are others, of which we only conclude from
analogy, that they perform such revolutions. These are the comets; they
generally appear attended by a nebulous light, either surrounding them as a
coma, or stretched out to a considerable length as a tail; and they sometimes
seem to consist of such light only. Their orbits are so eccentric, that in
their remoter situations the comets are no longer visible to us, although at
other times they approach much nearer to the sun than any of the planets:
for the comet of ]6'80, when in its perihelion, was at the distance of only
one sixth of the sun's diameter from his surface. Their tails are often of
great extent, appearing as a faint ligbt, directed always towards a point
nearly opposite to the sun: it is quite uncertain of what substance they con-
sist; and it is difficult to determine which of the conjectures respecting them
can be considered as the least improbable; it is possible that, on account of
the intense cold, to which the comets are subjected in the greatest part of
their revolutions, some substances, more light than any thing we can imagine
on the earth, may be retained by them in a liquid, or even in a solid form,
until they are disengaged by the effect of the sun's heat: but we are still
equally at a loss to explain the rapidity of their ascent : for the buoyancy of the
sun's atmosphere cannot possibly be supposed to be adequate to the effect; and
on the whole there is, perhaps, reason to believe that the appearances are derived
from some cause, bearing a considerable analogy to the fluid, supposed to be
concerned in the effects of electricity. It is probable that the density of the
nucleus, or the body of the comet itself, is comparatively small, and its at-
traction for the tail consequently weak, so that it has little tendency to re-
duce the tail, even if it consists of a material substance, to a spherical form:
for since some comets have no visible nucleus at all, there is no difficulty in
supposing the nucleus, when present, to be of very moderate density, and
perhaps to consist of the same kind of substance as constitutes the tail or
coma, in a state of somewhat greater condensation. If, therefore, it should
ever happen to a planet to fall exactly in the way of a comet, of which there
is but very little probability, it is to be supposed that the inconvenience
4

ON THE SOLAR SYSTEM. 513

suffered by the inhabitants of the planet might be merely temporary and lo-
cal: the chances are, however, much greater, that a comet might interfere in
such a manner with a planet, as to deflect it a little from its course, and retire
again without coming actually into contact with it.

Nearly 500 comets are recorded to have been seen at different times, and
the orbits of about a hundred have been correctly ascertained : but ue have
no opportunity of observing a sufficient portion of the orbit of any comet, to
determine with accuracy the whole of its form as an ellipsis, since the part
which is within the limits of our observation does not sensibly differ from the
parabola, which would be the result of an ellipsis prolonged without end.

Two comets at least, or perhaps three, have been recognised in their re-
turn. A comet appeared in 1770, which Prosperin suspected to move in an
orbit materially different from a parabola: Mr. Lexell determined its period
to be 5 years and 7 months, and its extreme distances to be between the
orbits of Jupiter and of Mercury; but it does not appear that any sub-
sequent observations have confirmed his theory. It has, however, been cal-
culated, that supposing the theory correct, it must afterwards have approach-
ed so near to Jupiter as to have the form of its orbit entirely changed.

Dr. Halley foretold the return of a comet about 1758, which had appeared
in 1531, in 1607. and in 1682, at intervals of about 75 years; and with
Clairaut's further correction for the perturbations of Jupiter and Saturn, the
time agreed within about a month. The mean distance of this comet from
the sun must be less than that of the Georgian planet; so that by improving
our telescopes still more highly, we may, perhaps, hereafter be able to con-
vert some of the comets into planets, so far as their remaining always visible
would entitle them to the appellation. Dr. Halley also supposed the comet
of 1680 to have been seen in 1 106, in 531, and in the year 44 before Christ,
having a period of 575 years; and it has been suspected that the comets of
1556 and 1264 were the same, the interval being 292 years ; a conjecture which
will either be confirmed or confuted in the year 1 848. Some persons have
even doubted of the perfect coincidence of the orbits of any comets, seen at
different times, with each other, and have been disposed to consider them as

VOL. I. 3 u

514 lECTURE XLII.

messengers forming a communication between the neighbouring systems of
the sidereal world, and visiting a variety of stars in succession, so as to have
their courses altered continually, by the attraction towards many different
centres; but considering the coincidenc« of the calculation of Hal ley and
Clairaut with the subsequent appearance of the comet of 1759, this
opinion can scarcely be admitted to be in any degree probable with respect
to the comets in general, however possible the supposition may be in some
particular cases. (Plate XXXII. Fig. 472 . . 475. Plate XXXIII. Fig.
476 . . 485.)

515

LECTURE XLIII.

ON THE LAWS OF GRAVITATION.

At was first systematically demonstrated by Sir Isaac Newton, that all the
motions of the heavenly bodies, which have been described, may be deduced
from the eflfects of the same force of gravitation which causes a heavy body
to fall to the earth ; he has shown that in consequence of this universal
property of matter, all bodies attract each other with forces decreasing as the
squares of the distances increase; and of later years the same theory has been
still more accurately applied to the most complicated phenomena. We are at
present to take a general view of the operation of this law, in the same order
in which the affections of the celestial bodies have been enumerated. It will
not be possible to investigate mathematically the effects of gravity in each
particular motion, but we may in some measure illustrate the subject, by
considering in what manner astronomers have proceeded in their explanations
and calculations, and we may enter sufficiently into the principles of the
theory, to understand the possibility of its applications.

The bodies which exist in nature are never single gravitating points; and
in order to determine the effects of their attraction, we must suppose the ac-
tions of an infinite number of such points to be combined. It was shown by
Newton, that all the matter of a spherical body, or of a spherical surface,
may be considered, in estimating its attractive force on other matter, as'
collected in the centre of the sphere. Tlie steps of the demonstration arc
these: a particle of matter, placed at the summi^t of a given cone or pyramid,
is attracted by a thin surface, composed also of attractive matter, occupying
the base of the cone, with equal force, whateve r may be the length of the
cone, provided that its angular position remain unaltered : hence it is easily
inferred that if a gravitating point be placed any where within a hollow
sphere, it will remain in equilibrium, in consequence ot the opposite and

516 LECTURE XLIir.

equal actions of the infinite number of minute surfaces, terminating the oppo-
site pyramids into which the sphere may be divided: it is also demonstrable,
by the assistance of a fluxional calculation, that a point, placed without the
surface, is attracted by it, precisely iii the same manner, as if the whole
matter which it contains were collected in the centre; consequently the
same is true of a solid sphere, which may be supposed to consist of an in-
finite number of such hollow spheres. If, however, the point were placed
-within a solid sphere, it would be urged towards the centre, by a force
which is simply proportional to its distance from that centre. This propo-
sition tends very much to facilitate all calculations of the attractions of the
celestial bodies, since all of them are so nearly spherical,, that their action on
any distant bodies is the same, as if the whole of the matter of which they
consist were condensed into their respective centres; but if the force of gra-
vity varied according to any other law than that which is found to prevail,
this simplification would no longer be admissible, even with respect to a
sphere.

It can scarcely be doubted that the power of gravitation extends from one
fixed star to another, although its effects may in this case be much too in-
considerable to be perceived by us. It may possibly influence the progres-
sive motions of some of the stars; and if, as Dr. Herschel supposes, there
ave double and triple stars revolving round a common centre, they must be
retained in their orbits by the force of gravity. Dr. Herschel also imagines
that the motion of our sun is in some measure derived from the same cause,
being directed nearly towards a point in which two strata of the milky way
meet; the attraction of the stars, other things being equal, must, however,
be proportional to their brightness, and that part of the heavens, to which
the sun is probably moving, appears to afford less light than almost any
other part, nor does the hemisphere, of which it is the centre, abound so
much in bright stars as the opposite hemisphere. If Sirius is a million times
as far from the sun as the earth, and if he should descend towards the sun
by means of their mutual gravitation only, he would move, on a rough esti-
mate, but about 40 feet in the first year, and in 1000 years only 8000 miles.
It has been conjectured that the mutual gravitation of the stars of a nebula
is sometimes the cause of the peculiar form of the aggregate, which some-
what resembles that of a drop of a liquid, held together by its cohesion: hut

ON THE LAWS OF GRAVITATION. 517

unless the form of the nebula was originally spherical, it could scarcely have
acquired that form from the operation of gravity, since the spherical form of
a drop is owing as much to the elasticity as to the attractive force of the par-
ticles of water, and it would be necessary, in order to preserve the analogy,
that the stars should also be floating in an incompressible fluid.

The sun's change of place, dependent on the relative situation of the pla-
nets, is so inconsiderable, that it escaped observation until its existence had
been deduced from theory. Not but that this change would be suihciently
conspicuous if we had any means of detecting it, since it may amount in the
whole to a distance equal to twice the sun's diameter, or seven times the dis-
tance of the moon from the earth ; and this change is readily deducible from
the general and unquestionable law of mechanics, tliat the place of the cen-
tre of inertia of a system cannot be changed by any reciprocal or mutual ac-
tion of the bodies composing it, the action of gravity being found to be per-
fectly reciprocal. But the earth accompanies the sun in great measure in this
aberration, and the other planets are also more or less aff'ected by similar
motions ; so that the relative situations are much less disturbed than if the
sun described this irregular orbit by the operation of a cause foreign to the
rest of the system.

The simple revolution of a body, in a given plane, indicates, at first sight,
the existence of an attractive force directed to some point within the orbit;
and the Keplerian law of the equality of the areas described in equal times,
by a line drawn from each planet to the sun, agrees precisely with what is
demonstrable of the effects of central forces, and points at once to the sun
as the centre of attraction of the system. And since the orbits of the planets
are elliptical, and the sun is placed in one of the foci of each, it may be ma-
thematically pfoved that the force directed to the sun must increase in pro-
portion as the square of the distance decreases.

The times of the revolutions of the planets are also in perfect conformity
with the laws of gravitation, that is, the squares of the times are proportional
to the cubes of the distances from the sun. It was easy to infer, from what
Huygens had already demonstrated of centrifugal forces, that this Keplerian
law must be true of bodies revolving in circles by the force of gravitation ;

518 LECTURE XLIII.

but Newton first demonstrated the same proportion with respect to elliptic
orWts, and showed that the time of revolution in an ellipsis is equal to the
time of revolution in a circle, of which the diameter is equal to the greater
axis of the ellipsis, or the semidiameter to the mean distance of the planet.

The universality of the laws of gravitation, as applied to the different
planets, shows also that the matter, of which they are composed, is equally
subjected to its power; for if any of the planets contained a portion of an
inert substance, requiring a force to put it in motion, and yet not liable to
the force of gravitation, the motion of the planet would be materially dif-
ferent from that of any other planet similarly situated.

The deviations of each planet from the plane of its orbit, and the motions
of its nodes, or the points in which the orbit intersects the plane of the
ecliptic, as well as the motions of the aphelion, or the point where the orbit
is remotest from the sun, have also been deduced from the attractions of the
other planetary bodies; but the calculations of the exact quantities of these
perturbations are extremely intricate. In general, each of the disturbing
forces causes the nodes to have a slight degree of retrograde motion ; but on
account of the peculiar situation of the orbits of Jupiter and Saturn, it hap-
pens that the retrograde motion of Jupiter's node, on the plane of the orbit
of Saturn, produces a direct motion on the ecliptic, so that the action of
Saturn tends to lessen the effect of the other planets in causing a retrograde
motion of Jupiter's nodes on the ecliptic.

The secular diminution of the obliquity of the ecliptic, or that slow vari-
ation of its position, which is only discovered by a comparison of very dis-
t^mt observations, is occasioned by the change of position of the earth's orbit,
in consequence of the attractions of the other planets, especially of Jupiter.
It has been calculated that this change may amount, in the course of many
ages, to 10" or 11*, with respect to the fixed stars; but the obliquity of the
ecliptic to the equator can never vary more than two or three degrees, since
the equator will follow, in some measure, the motion of the ecliptic.

The mutual attraction of the particles of matter, composing the bulk of
each planet, would naturally dispose them, if they were either wholly or

ON THE LAWS OF GRAVITATION. 519

partially fluid, to assume a spherical form: but their rotatory motion would
require, for the preservation of this form, an excess of attraction in the
equatorial parts, in order to balance the greater centrifugal force arising
from the greater velocity of their motion : but since the attractive force of
the sphere on the particles at an equal distance from its centre is every Adhere
equal, the equatorial parts would necessarily recede from the axis, until the
greater number pf particles, acting in the same column, compensated for the
greater effect of the centrifugal force. The form would thus be changed
from a sphere to an oblate or'flattened spheroid; and the surface of a fluid,
cither wholly or partially covering a solid body, must assume the same
figure, in order that it may remain at rest. The surface of the sea is there-
fore spheroidical, and that of the earth deviates so far only from a spheroi-
dical figure, as it is above or below the general level of the sea. (Plate
XXXI V. Fig. 436.)

The actions of the sun and moon, on the prominent parts about tlie earth's,
equator, produce a slight change of the situation of its axis, in the same
manner as the attractions of the other planets occasion a deviation from the
plane of its orbit. Hence arises the precession of the equinoxes, or the re-
trograde motion of the equinoctial points^ amounting annually to about 50
seconds. The nutation of the earth's orbit is a small periodical change of
the same kind, depending on the position of the moon's notles; in conse-
quence of which, according to Dr. Bradley's original observations, the pole
of the equator describes in the heavens a little ellipsis, of which the diameters
are 16 and 20 seconds. The same cause is also concerned in modifying the
secular variation of the obliquity of the ecliptic; and on the other hand, this
variation has a considerable effect on the apparent precession of the equi-
noxes. On account of the different quantity of the precession at different
times, the actual length of the tropical year is subjected to a slight varia-
tion; it is now 4 or 5 seconds shorter than it was in the time of Hipparchus.
The utmost change, that can happen from this cause, amounts to 43 seconds.

The exact computation of the moon's motion is one of the most difficult, as
Hrell as the most important problems in astronomy; but it is easy to under-
stand, in general, how the dilierence in the quantity and direction of the
sun's actions ofi the moon and earth, may cause such a derangement of the

SQO LECTURE XLIII.

moon's gravitation towards the earth, that the inclination of the orbit must
be variable, that the nodes must have a retrograde, and the apsides a direct
motion; and that the velocity of the moon must often be different from that
which she would have, according to the Keplerian law, in a simple elliptic
orbit.

For, the sun's attraction as far as it acts equally on the earth and the moon,
can have no effect in disturbing their relative position, being always employed
in modifying their common annual revolution ; but the difference of the forces,
occasioned by the difference of distances, always tends to diminish the effect
of their mutual attraction; since the sun acts more powerfully on the nearer
than on the remoter of the two bodies. The difference of the directions, in
which the sun acts on the earth and the moon, produces also a force, which
tends, in some degree, to bring them nearer together; but this force is, on the

, whole, much smaller than the former; and the result of both these disturbing
forces is alwaj's directed to some point in the line which joins the earth and the
sun, on the same side of the earth with the moon. It is obvious that when

■ the nodes are also in this line, the disturbing force can have no effect, either
on their position, or on the inclination of the orbit, since it acts wholly in
the plane of that orbit; but when they are in any other situation, the dis-
turbing force must cause a deviation from the plane, towards the side on
which the sun is situated, so that the inclination of the orbit increases and
decreases continually and equally; but whatever may be the position of the
nodes, it will a])pear that they must recede during the greater part of the
moon's revolution, and advance during the smaller. (Plate XXXIV.
Fig. 487.) • .

When the disturbing force tends to separate the earth and moon, it de-
ducts from the gravitation of the moon towards the earth a portion which
increases with the distance, and therefore causes the remaining force to de-
crease more rapidly than the square of the distance increases; and the re-
verse happens when the disturbing force tends to bring the earth and moon
nearer together ; but the former effect is considerably greater than the latter.
Now in the simple ellipsis, when the body descends from the mean distance,
the velocity continually prevails over the attractive force, so as to turn away
the direction of the orbit more and more from the revolving rJdius, until, at

Oy THE LAWS OF GRAVITATIOX. 521

a certain point, which is called the lovver apsis, it becomes per])endicular to
it: but if the central force increase in a greater proportion than is necessary
for the description of the ellipsis, the point where the velocity prevails over
it will be more remote than in the ellipsis; and this is expressed by saying
that the apsis moves forwards. When, on the contrary, tlie force varies
more slowly, the apsis has a retrograde motion. Since, therefore, the force
attracting the moon towards the earth, increases, on the whole, a little more
rapidly than the square of the distance decreases, the apsides must have, on
the whole, a direct motion. And a similar theory is applicable to the mutual
perturbations of the primary planets. (Plate XXXlV. Fig. 488.)

The secular acceleration of the moon's mean motion, which had long pre-
sented a difficulty amounting almost to an exception, against the sufficiency
of the theory of gravitation, has at last been satisfactorily deduced by Mr.
Laplace from the effect of the gradual change of the eccentricity of the earth's
orbit, which is subject to a very slow periodical variation, and which causes
a difference in the magnitude of the sun's action on the lunar revolution.

The perfect coincidence of the period of the moon's rotation, with that of
a mean revolution, has been supposed to be in some degree an effect of the
attraction exerted by the earth on a prominent part of her surface; there are
however, many reasons to doubt of the sufficiency of the explanation. If
the periods had originally been very nearly equal, we might imagine that
the motion of the earth would have produced a librAtion or oscillation in the
position of the moon, retaining it always within certain limits with respect
to the earth: no libration is, however, observed, that can be derived from
any inequality. in the moon^s rotation; and it has very properly been sug-
gested that the same attraction towards the earth ought to have made the
moon's axis precisely perpendicular to the plane of her orbit, instead of
being a little inclined to it. At the same time the appearance of a similar
coincidence, in the periods of the rotation and revolution of many other
satellites, makes it probable that some general cause must have existed, which
has produced the same effect in so many different cases.

The orbits of the comets afford no very remarkable singularity in the applica-
tion of the laws of gravity, excepting the modifications whicli depend on
VOL. I. 5 X

522 LECTUHK XLIll.

their near approach to the parabolic form, and the great disturbance which
their motions occasionally suffer, when they happen to pass through the
neighbourhood of any of the larger planets. The velocity of a comet in its
perihelion is such, that its square is twice as great as the square of the velocity
of a body revolving in a circle at the same distance. It was determined by
Halley and Clairaut, that the attractions of Jupiter and Saturn would delay
the return of rhe comet of 1759 about 618 days; and the prediction was ac-
complished within the probable limits that they had assigned for the error of
the calculation. The labours of Clairaut have indeed in many respects im-
proved the science of mathematical astronomy ; he was the first that ob-
tained a complete determination of the effects of the mutual actions of three
gravitating bodies, disturbing each other's motions; and his investigations,
which were founded on those of Newton, led the way to still further improve-
ments and refinements, which have been since made in succession by Euler,
Lagrange, and Laplace.

523

LECTURE XLIV.

ON THE APPEARANCES OF THE CELESTIAL BODIES.

tVe are next to proceed to examine the sensible effects produced by those
motions which we have first considered in their simplest state, and after-
wards with regard to their causes and their laws. Many authors have
chosen rather to pursue a contrary method, and have attempted to imitate the
original and gradual developement of the primitive motions from their apparent
effects. But no conception is sufficiently clear, and no memory sufficiently
strong, to comprehend and retain all these diversified appearances with accuracy
and facility, unless assisted by some previous idea of the real changes which
produce them, or by some temporary hypothesis respecting them, which may
have been of use in its day for the better connexion of the phenomena,
although it does not at present deserve to be employed for a similar purpose,
in preference to simpler and better theories, which happen to be historically
of a later date.

The proper motions of the fixed stars, as they are subjected to our obser-
vation, undergo two modifications; the one from the relative direction of
the motion, by which it may be more or less concealed from our view; the
other from the proper motion of the sun, and the planets attending him.
This motion has indeed only been inferred from the apparent motions of a
great number of stars, which are either partly or ro Uy referable to it, and
which could scarcely i'ave agreed so correctly as they do, if they had arisen
from the real and separate motion of each star. _

Among the motions of the primary planets, that of the earth itself requires
a principal share of our attention. The apparent places of the fixed stars are
not sensibly affected by the earth's annual revolution: if any of them had been
considerably less remote tlian they are, it is probable that this motion would

SQi IKCTURE XLty.

have occasioned a sensible annual parallax, or a change of their relative
situation, according to the earth's place in its orbit round the sun; for if this
orbit, viewed from any of the stars, subtended an angle even of a single
second, the place of that star might be observed to vary a second at diiferent
times of the year. Dr. Hooke supposed at one time that he had discovered
such a parallax, but later observations have not confirmed those of Dr.
Hooke. The stars have, however, a small aberration, in consetjuence of the
progressive motion of the earth in its orbit, combined with the limited
velocity of light; and the standard of comparison being the earth's axis, its
nutation must also in some degree affect the apparent places of the stars. It
Avas in endeavouring to ascertain the annual parallax, that Dr. Bradley

discovered both the aberration of light and the nutation of the earth's

axis.

The revolution of the earth, in its orbit round the sun, produces the ap-
parent motion of the sun among the stars, by which he describes his annual
path in the ecliptic, with an apparent angular velocity equal to the angular
velocity of the earth, which varies considerably at various times. It required
some investigation of the magnitudes and distances of the heavenly bodies,
to be convinced that the sun and stars had not in reality the motion which
a superficial inspection of the heavens would naturally lead a spectator to
attribute to them; but it is at present perfectly unnecessary to enter into
arguments to prove that the true cause of these apparent motions is the real
motion of the earth. The effect of the earth's annual revolution is the
change of place of the sun among the fixed stars: it is obvious that -the
sun will always appear, when viewed from the earth, in a place diametrically
opposite to that in which the earth would appear, if seen from the sun: con-
sequently, since the earth and sun remain in the same plane, the apparent
path of the sun will mark the same circle among the stars as the earth would
appear to describe, if viewed from the sun, that is, the ecliptic. If the light
of the stars were much stronger, or that of the sun much weaker, we might
see him pass by the stars in each part of the ecliptic, as we do the moon ; but
we are now obliged to observe what stars are in turn diametrically opposite
to the sun, or at certain distances from him, and thus we obtain a correct
knowledge of his path.

ON THE APPEARANCES OF THE CELESTIAL BODIES. 525

The sun's apparent diameter is larger by one thirtieth in January than in
June; of course the earth is so much nearer to the surt in winter than in
summer; and since the revolving radius of the earth's orbit describes equal
areas in equal times, the angular motion must increase as the square of the
distance diminishes, or about twice as fast as the distance itself diminishes ;~
so that the whole variation of the apparent diurnal motion of the sun is one
fifteenth of his mean motion : hence, the srui passes through the vviaiter half
of the ecliptic in a time 7 or 8 days shorter than the summer half. Accord-
ing to the different situations of the earth, with respect to the plane of the
sun's equator, his rotation on his axis causes the paths of his spots to assume
different forms; when the earth is in that plane, the paths appear straigiit,
but in all other situations, elliptical.

The rotation of the earth on its axis produces the still more obvious vicis-
situdes of day and night; and, in combination with its annual motion, oc-
casions the change of seasons. Since the axis remains always parallel to
itself, and is inclined to the plane of the ecliptic in an angle of about 66^°,
the plane of the equator, which is perpendicular to the axis> must pass twice
in the year through the sun. VVhen this happens, the limit of illumination,
or the circle which separates the dark portion of the earth from the enlightened
part, will then pass through the poles; and as the earth turns on its axis,
each point of its surface must remain for an equal length of time in light and
in darkness. Hence the points of the ecliptic, in which the sun is situated at
such times, are called the equinoctial points. At all other times, one pole of
the earth is in the light, and the other in the shadow; and all the points of
the earth nearest to the illuminated pole have their day longer than their
night, while the parts on the opposite side of the ecjuator, which are conse-
quently nearer to the unenlightened pole, have their day sliorter. Tlie parts
nearest to the poles have also one of their days and one of their nights pro-
tracted to a period of several common days, or even months, whenever they
revolve entirely within the limit of illumination. (Plate XXXIV. Fig. 489.)

The sun appears to describe. every day a circle in the heavens, more or less
distant from the plane of the equator, according to the actual situation of the
earth's axis ; this distance being always the same as that of the poles from the
limit of illumination, and never exceeding £34°; so that by determining the

5^6 LECTUUK XLIV.

sun's path at the time of the equinoxes, or the apparent place of the equinoctial
in the heavens, for any given point on the earth's surface, we may represent the
sun's path at any other time by a smaller circle parallel to it. Speaking
however, more correctly, the sun's apparent path is a spiral, formed by the
continuation of these supposed circles into each other.

The effect of the centrifugal force, derived from the earth's rotation, is
perceptible, at the equator, in the retardation of the vibrations of pendu-
lums. The whole centrifugal force at the equator is found, by computation,
to be -i^T of the force of gravity ; tut the diminution of the force of gravi-
tation appears, by experiments on pendulums, to be T-'-g-; this diminution
being the sum of the centrifugal force, and of the decrease of gravity on
account of the oblate figure of the earth, the equatorial parts being further
removed from its centre, and the force of gravity being less powerful there.
The changes of inclination in the earth's axis are observable in the places of
the equinoctial points, and in the situation of the plane of the earth's equator
with respect to the fixed stars; and the secular diminution of the obliquity
of the ecliptic is discoverable by a comparison of distant observations
on the sun's apparent motion, and on the places of the fixed stars with
respect to the ecliptic.

For the phenomena of twilight, we are principally indebted to the light
reflected by the atmosphere: when the sun is at a certain distance only below
the horizon, he shines on some part of the air immediately visible to us,
which affords us a portion of reflected light. The distance, at which this
may happen, has been variously estimated, and it is perhaps actually dif-
ferent in different climates, being a little greater in countries near the poles
than in those which are nearer the equator: there is also sometimes a second-
ary twilight, when the parts of the atmosphere, which reflect a faint light on
the earth, are themselves indebted for this light to an earlier reflection.
Some have assigned 18° as the limit of twilight,and on this supposition, allow-
ing for refraction, the atmosphere must be capable of reflecting sensible
light at the height of about 40 miles. Mr. Lambert, on the contrary, makes
the limit only about 6^°. The duration of twilight is greater or less as the
sun moves more or less obliquely with respect to the horizon ; it is, therefore,
shortest near the time of the equinoxes, since the equinoctial intersects the

ON THE APPEARANCES OF THE CELESTIAL BODIES. 527

horizon less obliquely than any lesser circle parallel to it. (Plate XXXIV.
Fig. 490, 491.)

The revolutions of the primary planets, combined with that of the earth,
necessarily produce the various relations, in which they are either in opposi-
tion or conjunction, with respect to each other or to the sun, and in which the
apparent motion is direct or retrograde, or the planet is stationary, accord-
ing to the directions and the comparative velocities of the real motions. If
the earth were at rest, the inferior planets would appear to be station;uy when
they are at the greatest elongation or angular distance from the sun; but,
on account of the effect of the earth's motion, Venus is stationary at an
elonga*^ion of about 29°, while her greatest elongation is between 45° and
48°. The greatest elongation of Mercury, in each revolution, is from 28-j°
to 17t°> according to the position of his orbit, which is very eccentric. All
these appearances are precisely the same as if the sun actually revolved round
the earth, and the planets accompanied him in his orbit, performing at the
same time their several revolutions round him; and the path which would
thus be described in the heavens, and which is of a cycloidal nature, re-
presents correctly the true positions of the planets with respect to tiie earth.
The apparent angular deviation from the ecliptic, or the latitude of the planet,
is also greater or less, accordingly as the earth is nearer or remoter to the planet,
as well as according to the inclination of its orbit and its distance from the
node. (Plate XXXIV. Fig. 492 . . 494.)

The various appearances of the illuminated discs, especially of the inferior
planets, and the transits of these planets over the sun, depend on their
positions in their orbits, and on the places of the nodes, with respect to tlie
earth. Jupiter, Saturn, and the Georgian planet, are so remote in com-
parison of the earth's distance from the sun, that they appear always fully
illuminated. Venus is brightest at an elongation of about 40° fron) the sun,
in that part of her orbit which is nearest to the earth; she then appears like
tlie moon when 5 days old, one fourth of her disc being illuminated; slie
casts a shadow, and may even be seen in the day time in our climates, if she
happens to be far enough north: a circumstance which occurs once in about
8 years. In order that there may be a transit of Venus over the sun, she
must be within the distance of 15^° of Jier node at the time of conjunction,

528 LF.CTUHE XLIV.

Otherwise she wijl pass either to the north or to the south of the sun, instead
of being immediately interposed between him and the earth.

The phases and eclipses of the moon are very obviously owing to the
same causes; that part of the nroon only, on which the sun shines, being
strongly illuminated, although the remaining part is faintly visible, by-
means of the light reflected on it from the earth; it is, therefore, most easily
seen near the time of the new moon, when the greatest part of the earth's
surface turned towards the m )on is illuminated. The parts of the moon
which are immeaditely op|)osed to the earth, appear to undergo a libration,
or chang-e of situation, of two kinds, each amounting to about 7 degrees: the
one arising from the inequality of the moon's velocity in her orbit at different
times, the other from the inclination of the axis of her rotation to her orbit;
besides these changes, the diurnal rotation of the earth may produce, to a
spectator situated on some parts of it, a third kind of libration, or a change of
almost two degrees in the appearance of the moon at her rising and setting.
(Plate XXX IV. Fig. 495.)

When the moon passes the conjunction, or becomes new, near to the node,
she eclipses the sun, and when she is full, or in opposition, in similar circum-
stances, she herself enters the earth's shadow. 1 he earth's shadow consists
of two parts, the true shadow, within which none of the sun's surface is
visible, and the penumbra, which is deprived of a part only of the sun's light;
the true shadow forms a cone terminating in a point at a little more than 34
limes the mean distance of tiie moon; the penumbra, on the contrary, consti-
tutes, together with the shadow, a portion of a cone diverging from the earth
without limit; but the only effect of this imperfect shadow^ is, that it causes
the beginning of a lunar eclipse to be incapable of very precise determina-
tion; for the limit of the darkened part of the moon, as it appears in the
progress of the eclipse, is that of the true shadow, very little enlarged by the
penumbra. The true shadow, where the moon crosses it, is about 80 minutes
in diameter, as seen from the earth, while the moon herself is only 30. This
shadow is not, however, wholly deprived of the sun's light; for the atmo-
spheric refraction inflects the light passing nearest to the earth, in an angle
of 66 minutes, and causes a great part of the shadow to be filled with light
of a ruddy hue, by means of which the moon remains still visible to us, the

ON THE APPEARANCES OF THE CELESTIAL BODIES. 53,9

cone of total darkness extending to somewhat less than two thirds of the
m/)on's distance. But it has sometimes happened, probably from the effect
of clouds occupying the greatest part of our atmosphere, that the moon has
totally disappeared. (Plate XXXIV. Fig. 496.)

When the sun is eclipsed, it depends on the situations of the earth and moon
in their orbits, whether the sun or moon subtends the greatest angle as seen
from the earth ; since at their mean distances their apparent diameters arc
each about half a degree. If the sun's apparent diameter is the greater, the
eclipse, when the centres coincide, must be annular, the margin of the
sun's disc being still visible in the form of a ring: when the moon's appar-
ent diarmeter is greater than the sun's, the eclipse, if central, becomes total;
but still a ring of pale light is seen round the disc, which has been attri-
buted to the effect of the sun's atmosphere, since that of the moon is pro-
bably too inconsiderable to produce the appearance: a red streak is also
sometimes observed at the margin, before the actual emersion of the sun.
The degree of darkness depends on the situation of the place of observation
within the shadow, on account of the greater or less illumination of the
atmosphere within view : sometimes a considerable number of stars may be
seen during a total eclipse of the sun.

It is obvious that, since the earth is much larger than the moon, the whole
shadow of the moon will only pass over a part of the earth's surface: and
that no solar eclipse can be visible in the whole of the hemisphere turned
to the sun: while lunar eclipses, on the contrary, present the same appearance
wherever the moon is visible. In the same manner, to a spectator on the moon,
an eclipse of the earth, or a transit of the moon's shadow over the earth'*
disc, would have nearly the same appearance wherever he might be stationed;
but an eclipse of the sun by the earth would be total to that part of the
moon's surface only, which to us appears dark at the same time. (Plate
XXXIV. Fig. 497 . . 499.)

The moon's nodes arrive very nearly at the same situation with respect to
the eartb after 2^3 lunations, or revolutions of the moon, which are per-
formed in 18 years of 365 days each, 15 days,7 hours, and 43|: minutes ; so that
after a period of about 18 years, the series of eclipses reeommences nearly in
the, same order. This circumstance was observed by the ancients, and i&

VOL. I. 3y

530 Lt;CTUUE XLIV.

mentioned by Ptolemy and by Pliny. When the full moon happens within
74.° of the node, there must be a lunar eclipse and there may be an eclipse
at the distance of 13" from the node. An eclipse, of the sun may happen
when the moon changes, or comes into conj unction with the sun, at any dis-
tance within 1 r-j° of the node. The mean number of eclipses which occur
in a year is about 4; and there are sometimes as many as 7: there must
necessarily be two solar eclipses, but it is possible that there may not be
even one lunar. In speaking of the magnitude of the part of the sun or
moon eclipsed, it is usual to consider the whole diameter as divided into
12 parts, called digits, each of which contains 30 minutes: thus if o n
fifth part of the diameter were dark, the extent of the eclipse would be
called 2 digits 12 minutes.

The moon travels through the heavens with a motion contrary to their
apparent diurnal revolution. Hence she rises and sets, on an average, about
three quarters of an hour later every day. The least possible difference
between the time sof the moon's rising on two successive days, is, in London,
17 minutes; and this circumstance occurs once in about 19 years, which is
nearly the period of the moon's nodes with respect to the heavens : t\^e great-
est possible difference is 1 hour 17miivute3. But it happens every month that
the difference becomes greater and less by turns, and when the least differ-
ence is at the time of the fuU moon, it is usually called the harvest moon.
In parts nearer to the poles, the moon often rises at the same hour on two
succeeding days.

The eclipses of the satellites of Jupiter exhibit appearances extremely in-
teresting for their utility in identifying the same instant of time in different
places. On account of the small inclination of their orbits to the plane of
Jupiter's orbit, the fii-st three never pass the shadow without being plunged
into it, and the fourth but seldom; while those of Saturn are much less fre-
quently liable to be eclipsed, on account of their greater deviation from the
plane of his ecliptic. These satellites are also frequently hidden behind the
body of the planet, and this circumstance constitutes an occultation: hence
it happens that we can never see both the immersion of the first satellite into
the shadoM' of Jupiter, and its emersion from it; but both the immersion and
emersion of the three outer satellites are sometimes observable. The ring of

ON THE APPEARANCES OF THE CELESTIAL BODIES. 531

Saturn exhibits a variety of forms according to its angular position: it dis-
appears to common observation when either its edge or its dark side is pre-
sented to us : but to Dr. Herschel's telescopes it never becomes invisible ; the
light reflected from the planet being probably sufficient for illuminating in
some measure the side not exposed to the sun's direct rays.

The comets are seen for a short time, and are again lost to our view ; their
tails are in general situated in the planes of their orbits, following them in
their descent towards the sun, and preceding them in their ascent, with a
slight degree of curvature in their forms; they must also appear to us more
or less arched, and of different extent, according to their distances, and to
the angular position of the orbits with respect to the ecliptic.

The proportion of the light afforded by the different heavenly bodies has
been variously estimated by various authors; but there is little reason to call
in question the accuracy of the experiments and calculations of Mr. Bou-
guer. He states the intensity of the moon's light as only one three hundred
thousandth of that of the sun. These calculations have been extended by Euler
and by Lambert; Euler considers the direct light of the sun as equal to that
of 6560 candles of a moderate size, supposed to be placed at the distance of 1
foot from the object : that of the moon to the effect of 1 candle, at the distance
of 7-i feet; the light of Venus to a candle at 421 feet, and of Jupiter to a
candle at 1620 feet; so that the sun would appear as bright only as Jupiter
if he were removed to a distance 131 thousand times as great as his present
distance. (Plate XXXIV. Fig. 500.)

"When we reflect on the magnificence of the great picture of the universe,
the outlines of which we have been considering, we are lost in the conterri-
plation of the immensity of the prospect, and returning to the comparatively
diminutive proportions of our individual persons, and of all the objects with
which we are most immediately connected, we cannot help feeling our own
insignificance in the material world. The mind, notwithstanding, endea-
vours to raise itself above the restraints which nature has imposed on the
body, and to penetrate the abyss of space in search of congenial existences.
But in speculations of this kind, reason and argument must give way to coa-

^32 LECTUHE XLIV.

jecture and imagination ; and thus, from natural philosophy, our imaginations
wander into the regions of poetry ; and it must be confessed that the union of
poetical embellishment with natural philosophy is seldom very happy. A
poet has few facts to communicate, and these he wishes to expand and diver-
sify ; he dwells on a favourite idea, and repeats it in a thousand emblemati-
cal forms ; his object is, to say a little, very elegantly, in very circuitous, and
somewhat obscure terms. But the information, which the natural philoso-
pher has to impart, is too copious to allow of prolixity in its detail ; his sub-
jects are too intricate to be compatible with digressions after amusement,
which, besides interrupting, are too likely to enervate the mind ; and if he is
ever fortunate enough to entertain, it must be by gratifying the love of truth,
and satisfying the thirst after knowledge. We have, however, a favourable
specimen of highly ornamented philosophy in Fontenelle's Plurality of
Worlds; a work which must be allowed to convey much information in
a very interesting form, although somewhat tinctured with a certain frivolity
which is not always agreeable. We need not attempt to accompany all the
flights of Fontenelle's imagination ; it will be sufficient for our purpose to
pursue his ideas in a simple enumeration of the most remarkable phenomena,
that would occur to a spectator placed on each of the planets.

Of Mercury we know little except the length of his year, which is shorter
than three of our months. Supposing all our heat to come from the sun, it
is probable that the mean heat on Mercury is above that of boiling quick-
silver; and it is scarcely possible that there should be any point about his
poles where water would not boil. The sun's diameter would appear, if
viewed from Mercury, more than twice as great as to us on the earth.

Venus must have a climate far more temperate than Mercury, yet much
too torrid for the existence of animals or vegetables, except in some circum-
polar parts; her magnitude and diurnal rotation differ but little from those
of the earth, and her year is only one third shorter ; so that her seasons, and
her day and night, must greatly resemble oui-s. The earth, when in oppo-
sition to the sun, must be about four times as bright as Venus ever appears to
us, and must, therefore, always cast a shadow; it must be frequently, and
perhaps generally, visible in tlie day ; and together with the moon, must eK»

ON THE APrEARA'NCES OF THE CELKSTIAL BODIES. 533

hibit a very interesting object. The atmosphere of Venus is supposed to be
nearly like our own, or somewhat more rare.

The inhabitants of the moon, if the moon is inhabited, must be capable of
living with very little air, and less water: there is reason to think their at-
mosphere less than a mile high, and it is never clouded: so that the sun must
shine without intermission for a whole fortnight on the same spot, without
having his heat moderated by the interposition of air, or by the evaporation
of moisture. The want of water in the moon is not, as some have supposed,
the necessary consequence of the want of an atmosphere; but it is inferred
partly from the total absence of clouds, and partly from the irregular ap-
pearance of the margin of the moon, as seen in a solar eclipse; no part of it
being terminated by a line sufficiently regular to allow us to suppose it the
surface of a fluid. The earth must always appear to occupy nearly the same
part of the sky, or rather to describe a small oval orbit round a particular
point, exposing a surface 13 times as great as that of the moon appears to us.
This large surface, suspended, with phases continually changing, like those
of the moon, must aiford, especially when viewed with a telescope, an ex-
cellent timepiece; the continents and seas coming gradually and regularly
into view, and affording a variety equally pleasing and useful. To us such
a timepiece would be of inestimable value, as it would afJbrd us an easy me-
thod of discovering the longitude of a place, by comparing its motion with
the solar time : but in the moon, the relative position of the earth and sun,
or of the earth and stars only, would be sufficient for determining the situation
of any place in sight of the earth ; if, however, there are no seas and no na-
vigation, astronomical observations of this kind would be of very little
utility. The assistance of the earth's phases in the measurement of time
might, however, still be very useful, for many purposes, to the inhabitants
of the nearer half of the moon ; and probably the remoter part is much de-
serted, for in their long night of half a month, they must be extremely in
want of the light reflected from the earth, unless the inhabitants have the
faculty of sleeping through the whole of their dark fortnight. The surface
of the moon appears to be very rocky and barren, and liable to frequent dis-
turbances from volcanos. These have been supposed to project some of their
contents within the 'reach of the earth's attraction, which they might easily
do, if they could throw them out with a velocity of about eight thousand feet

534 LICTURE XLir.

in a second, which is only four times as great as that of a cannon ball : and
these stones, falling through the atmosphere, might very possibly generate so
much heat, by compressing the air, as to cause the appearance of fiery me-
teors, and to fall in a state of ignition. The appearance of the moon, as
viewed through a good telescope, is extremely well imitated by Mr. Russels
lunar globe, which is also capable of exhibiting, with great accuracy, the
changes produced by its librations.

The climate of Mars is as much colder than ours, as that of Venus Is
warmer; in other respects there is no very striking difference: the inclina-
tion of his axis to his echptic being nearly the same as that of the earth's
axis, the changes of seasons must be nearly like our own. Dr. Herschel has
observed a constant appearance of two bright spots or circles near the poles
of Mars, which he attributes to the ice and snow perpetually surrounding
them. It is not, however, probable that water could remain fluid in any
part of Mars, and even quicksilver and alcohol would, perhaps, be frozen
in his temperate climates. It is pretty certain that Mars has an atmosphere,
and his dark spots seem to be occasioned by clouds: this atmosphere may,
perhaps, also be tne cause of the ruddy hue of his light.

It appears to be doubtful, whether either of the three little planets newly
discovered can be sufficiently solid, to give a firm footing to any material
beings: we should probably weigh only a few pounds each if transported
there. According to Dr. Herschel's opinion, neither Ceres nor Pallas is much
larger than a good Scotch estate, although they must, sometimes, appear tp
each other as planets of a most respectable size. The light reflected from
Ceres is of a more ruddy hue than that of Pallas; both of these planets are
attended by more or less of a nebulosity, proceeding, perhaps, fiom copious
atmospheres; and in this respect, as Avell as in the great inclination of their
orbits, they appear to have some affinity to comets. It is tolerably certain
that neither of them is 200 miles in diameter; and Juno is also probably
about the same size.

It is obvious that the most striking features of the heavens, when contem-
plated from Jupiter, would be the diversified positions and combinations of
his satellites; their light must be faint, but yet of service; and to a traveller

ON THE APTEARANCES OF THE CELESTIAL BODIES. 555

on the surface of this vast globe they must aflord useful information, as well
with respect to time as to place. Our little earth must probably be always
invisible to a spectator situated on Jupiter, on account of its apparent proxi-
mity to the sun, in the same manner as a planet at half the distance of Mer-
cury would be invisible to us. The year of Jupiter must contain nearly ten
thousand of his days, and that of Saturn almost thirty thousand Saturnian
days. Besides the vicissitudes of the seven satellites revolving round Saturn,
his ring must aftbrd, in different parts of his surface, very diversified appear-
ances of magnificent luminous arches, stretched across the heavens, especi-
ally in that hemisphere which is on the same side of the ring with the sun.

From the Georgian planet the sun must be seen but as a little star, not
one hundred and fiftieth part as bright as he appears to us. The axis of this
planet being probably near to the plane of its ecliptic, it must be directed
twice in the year towards the sun, and the limit of illumination must ap-
proach to the equator, so that almost every place on his surface must some-
times remain,for a great number of diurnal revolutions, in light and in dark-
ness; the most moderate climates having one night, in their long year, equal
in duration at least to several of our years: and it must be confessed that
this planet would afford but a comfortless habitation to those accustomed to
our summer sunshine, even if it were possible to colonise it. (Plate XXXIV.
rig. 501.)

On the whole,'we are tempted, from an almost irresistible analogy, to con-
clude that the planets are all in some manner or other inhabited ; but at the
same time we can scarcely suppose that a single ecipses of terrestrial animals or
even vegetables could exist in any of them; their minerals may, perhaps, re-
semble ours, and if the stones which Mr. Howard has analysed are realiy lu-
nar productions, we ha/e proofs that the moon at least contains some sub-
stances resembling those which compose the eartli; but the seas and rivers of
the other planets must consist of some fluid unknown to us, since almost all
our liquids would either be frozen, or converted into vapour, in any of them.

536

LECTURE XLV.

/

ON PRACTICAL ASTRONOMY

It is generally most convenient in practical astronomy to neglect the real,
and to consider only the apparent motions of the sun the stars, and planets,
for the visible effects must be precisely the same, whether the sun or the
earth perform a revolution in the plane of the ecliptic, and whether the earth
actually move on its axis, or the whole of the celestial bodies move round it
in a day. We may, therefore, suppose the sun to move, as he appears to do,
from west to east in the ecliptic, so as to advance almost a degree in S-i
hours, and from east to west, together with all the stars and planets, so as'
to perform a whole revolution in a day. Speaking more correctly, the sun
appears to describe, in every sidereal day, a spiral, which differs a little from a
circle, and is also about a degree shorter, so that about four minutes more are
required for the return of the sun to the same part of the heavens, and the
completion of a solar day.

In order to determine the place of any point in the heavens, it is usual to
compare its situation either with the plane of the earth's e(juator, or with the
ecliptic ; its angular distance from the equator being called its declination,
and from the ecliptic, its latitude; these distances must be measured in
planes perpendicular to those of the equator or ecliptic, and the distances of
these planes from their intersection, or from the equinoctial point in Aries,
are called respectively the right ascension and the longitude of the point to
be described. For the stars, the declination and right ascension are most
usually laid down; but with respect to the sun and the planets, performing
their revolutions in or near the ecliptic, it is most convenient to calculate
their latitude and longitude.

The plane passing through the earth's axis and the place of a spectator is

ON PRACTICAL ASTBONOMY. 537

the plane of the meridian of that place; and a plane touching the earth in any
point is its horizon. With respect to the appearances of the fixed stars,
this plane may be considered as passing through the earth's centre in the
same direction: and the difference is scarcely sensible with respect to the sun
and the primary planets; but in observations of the moon's place, these
planes must be carefully distinguished. (Plate XXXV. Fig. 502. )•

The instruments requisite for astronomical observations are principally
referable to geometrical or to optical apparatus, or to the measurement of
time. Particular constructions and combinations are, however, necessary
for the accommodation of quadrants, graduated circles, telescopes, and
transit instruments, to the uses of observatories; and astronomical observa-
tions are as necessary to the correct determination of time, as artificial time-
keepers afe useful for other astronomical purposes.

The most accurate standard of time is the diurnal rotation of the earth on
its axis, as ascertained by its situation with respect to the fixed stars. The
time elapsing between two successive passages of any star over the same
meridian, which constitutes a sidereal day, may be measured with great
precision; and the star may for this purpose be observed, witli almost equal
accuracy, in any other situation, and sometimes with greater convenience.
The length of the sidereal day may be considered as perfectly constant, the
inequalities arising from the aberration of light, and from the nutation of
the earth's axis, being too small to be easily discovered; but the correction
for the aberration may be applied when it is necessary. For observations of
this kind, it is usual to have a clock adjusted to sidereal time, which not only
admits of a more ready comparison with the transits or passages of any one
star over the meridian, but, by the difference of the times of any two transits,
shows at once the difference of right ascension of the stars or planets, ex-
pressed in time instead of degrees.

The solar days are not only about four minutes longer than the sidereal
days, but they are also unequal among tliemselves ; and this inequality
arises from two causes; the one, that even if the sun's motion in the ecliptic
were uniform, his diurnal changes of right ascension would be different at
different times, and the difl^'erence between his path in every sidereal day, and

VOL. I. 3 z

5S8 lECTURE XLV.

a whole circle, depending- on this change, would also vary; the other 'that the
sun's motion in the ecliptic is actually variable, consequently the diurnal
chano-e of right ascension is liable to adouble inequahty. Hence it happens
that the solar time agrees at four instants in the year only with the mean
time, derived from supposing the whole 365 days to be divided into as many equal
parts; the difference is called the equation of time, and amounts sometimes to as
much as 16 minutes. The term equation is commonly applied in astronomy
to any small quantity, which is to be added to, or subtracted from, another,
quantity; thus it is usual, in calculating the place of a planet, to find from the
tables of its motion, the mean place, in which it would be found if its orbit
were circular, and thence to derive the true place, by means of various cor-
rections called equations. In France the solar time is considered as the
true time, and is used for all civil purposes, so that the clocks are sometimes
embarrassed with a complicated apparatus, calculated forimitating the inequali-
ties of the actual apparent motion of the sun. (Plate XXXV. Fig. 503.)

The art of dialling consists principally in projecting, on a given surface,
such lines as will coincide with the shadow of an index or gnomon parallel
to the earth's axis, at intervals corresponding to the different hours of the
day: so that nothing more is necessary for the construction of a dial, than
to determine the intersections of the surface on which the dial is to becon-
structed, with planes passing through the edge of the gnomon, and situated
at equal angular distances from each other: thus, supposing the plane of the
dial perpendicular to the gnomon, and parallel to the equinoctial, the hour
lines of the dial will be at equal distances from each other; but in other cases
their distances will be unequal, and must be determined either by calcula-
tion or by construction. A point may also be used as a gnomon, as well as
aline; but in this case the hour lines must cover a larger portion of the
surface, in order that the shadow of the point may always fall among them.
(Plate XXXV. Fig. 60i . . 506.)

The changes of the seasons depend on the return of the sun to the same
position Avith respect to the equator, or on the length of the tropical year, so
called from the tropics, which are circles supposed to be parallel to the
equator, and between which the sun travels continually backwards and
forwards, appearing to remain for some time, when he is near them, with

ON PRACTICAL ASTRONOMT. 539

very little change of declination ; whence the time when tlie sun touches
either tropic is called the solstice. The vicissitudes of light and darkness
depending also on the solar day, it is necessary, for the regulation of the
civil calendar, to establish the proportion between the periods of the solar
dav and the tropical year; and since the tropical year exceeds the time of
365 days, by 5 hours, 48 nnnu*-es and 48 seconds, it is usual to add to the
common year an intercalary day once in about four years. The ancient
Egyptians reckoned only 365 days in a year, and their nominal new year
arrived continually earlier and earlier, so that after 1507 of their years, it
would have happened successively on each of the 365 days, and returned to
the original place: the same mode of computation was also adopted by
the Greek astronomers. The Romans inserted intercalary days, at first with-
out much regularity, according to the direction of their augurs, until the
time of Julius Caesar; who, observing that the year was almost 6 hours
longer than 365 days, added a day every fourth year to the calendar, by
reckoning twice the day in February called sexto calendas Martias, whence
this year of 366 days was denominated a bissextile year. The new moon
immediately following the winter solstice, in the 707th year of Rome, was-
made the first of January of the first year of Caesar; the 25th of December
in his 45th year is considered as the date of the Nativity of Christ, and
Caesar's 46th year is reckoned the first of our era. The preceding year is-
commonly called by astronomers the year 0, but by chronologists the year
before Christ. The correction introduced by Caesar was, however, t
great, the error being exactly 7 days in 900 years; so that in 1582 it amount- ■
ed to about 12 days. This error was not wholly removed by Pope Gregory,
who reformed the calendar; he omitted 10 days only of the usual reckoning',
in order to bring back the course of the moveable feasts to the same state, in
which they had been established by the Nicene council, in the fourth cen-
tury. He determined at the same time that the last year of every century
should be passed without an intercalary day, excepting that of every fourth
century, which was still to be bissextile. Thus every year divisible by four,
without a remainder, is in general a bissextile or leap year, but the last
year of every century must be a common year, unless the number of the
century be divisible by 4; the year 1800 being a common year, and 2000 a
bissextile. In this manner 27 Julian bissextiles are omitted in 3600 years,,
while the true length of the year would require tlie omission of 28; but so»

540 LECTURE XLIV.

small a difference can be of no material consequence. The Persians had in-
troduced into their calendar, in the 1 1th century, an intercalation still more
accurate; they make 8 bissextiles only every 33 years, reckoning four common
years together instead of three, at the end of this period, so that in 13'i years
they have 32 leap years instead of 33 ; and the error is only a day in about five
thousand years. If any change in the Gregorian calendar were thought
necessary, it would be easy to make the last year of every fourth and fifth
century alternately a bissextile, and this correction would be quite as accu-
rate as it is possible for our calculations to render it. The adoption bf the
Gregorian calendar in this country was for some time delayed by religious
prejudices; one of the best founded objections to it was, that 2 days of the
real error was still uncorrected ; but better arguments at last overcame these
difficulties, and the new stile was introduced on the 14 September 1754,
"which would have been called, according to the old stile, the third.

Any tolerable approximation of this kind, when once generally established,
appears to be more eligible than the mode which was lately adopted in France,
where the republican year began at the instant of the midnight preceding
the sun's arrival at the autumnal equinox. Mr. Lalande very judiciously
observes, that there are several years, in which the sun will pass the equinox
so near to midnight, that it is not at present in the.power of calculation to
determine on what day the republican year ought to begin; and perhaps
these arguments have cooperated with others in facilitating the restoration of
the ancient calendar.

The revolutions of the sun and moon are not very obviously commen-
surable, the solar year containing 12 lunations and almost 11 days; but
Meto discovered, more than 2000 years ago, that 19 solar j'ears contain
exactly 235 lunations; and this determination is so accurate, that it makes
the lunar month only about half a minute too long. Hence it happens, that
in every period of 19 years, the moon's age is the same on the same day of
the year. The number of the year, in the Metonic cycle, is called the golden
number, the calendar of Meto having been ordered, at the celebration of
the Olympic games, to be engraved in letters of gold on a pillar of marble.
At present, if we add 1 to the number of the year, and divide it by 19, the
remainder will be the golden number; thus, for 1806, the golden number is 2.

ON IPRAcrlCAh ASTRONOJir. 541

If we subtract 1 from the golden number, then multiply by 11, and
divide by 30, the remainder Avill be the epact, which is the moon's age on
the first of January, without any material error; thus, for 1806, the epact
is 11, and the moon is actually 11 days old on the first of January.

From a combination of chronological periods of various kinds, Scaliger
imagined the Julian period, as an epoch to which all past events might with
convenience be referred, beginning 4713 years before the birth of Christ.
Laplace proposes, as a universal epoch, the time when the earth's apogee was
at right angles with its nodes, in the year 1250, calling the vernal equinox
of that year the first day of the first year. But the fewer changes of this
kind that we make, the less confusion we introduce into our chronology.
The astronomical year begins at no'on on the 31st of December, and the date of
an observation expresses the days and hours actually elapsed from that time.
Thus, the first of January 1806, at 10 in the morning, would be called, in as-
tronomical language, 1805 December 31 days 22 hours, or more properly
1806 January 0 day 22 hours.

For ascertaining, by immediate measurement, the position of any of the
heavenly bodies, it is usual to determine its meridian altitude by quadrants,
and the time of its passing the meridian by transit instruments. The large qua-
drants, generally used for this purpose in observatories, are fixed to vertical walls,
in order to give them greater stability, and are thence called mural quadrants;
sometimes a smaller portion of an arc only is adapted for observations near
the zenith, under the name of a zenith sector. A transit instrument is a
telescope so fixed on an axis as to remain always in the plane of the meridian;
the axis being perpendicular to this plane, and consequently in a horizontal
position, and directed east and west. Those who are in the constant habit of
observing with attention, can estimate, in this manner, the precise time of the
passage of a celestial object over the meridian ; without an error of the tenth
of a second, so that its angular right ascension may be thus determined
Avithin about a second of the truth. A very convenient mode of adjusting a
transit instrument is to direct it to the north polar star, at the same time that
the last of the three horses in the wain is perpendicularly above or below it:
this process, in 1751, gave precisely the true meridian; but since that time.

542 LECTURE XLV.

the precession of the equinoxes, which produces a slight change in the places
of the stars, has made it necessary to wait 1 minute 134- seconds for every
ten years that have elapsed. Thus, in 1806, if we wait 6~ minutes, the
pole star will then be precisely in the meridian, and will serve for the
correct adjustment of the instrument. (Plate XXXV. Fig. 507 • • 510.)

The quadrant in most common use, especially for nautical observations,'
was first proposed by Newton, but improved, or perhaps reinvented, by
Hadley. Its operation depends on the effect of two mirrors which bring
both the objects, of which the angular distance is to be measured, at once
into the field of view; and the inclination of the speculums by which this is per-
formed serves to determine the angle. The ray proceeding from one of the
objects is made to coincide, after two reflections, with the ray coming immedi-
ately from the other, and since the inclination of the reflecting surfaces is then
half the angular distance of the objects, this inclinatoin is read off on a scale
in which every actual degree represents two degrees of angular distance, and
is marked accordingly. There is also a kcond fixed speculum, placed a
right angles to the moveable one, when in its remotest situation, which then
produces a deviation of two right angles in the appareut place of one of the
objects, and which enables us, by moving the index, to measure any angle
between 180" and 90°. This operation is called the back observation; it is
however seldom employed, on account of the difficulty of adjusting the spe-
culum for it with accuracy. The reflecting instrument originally invented by
Hooke was arranged in a manner somewhat different. (Plate XXXV. Fig. 511.)

From the meridian altitude of any point, it is easy, when the elevation of
the pole is known, to deduce its declination: and its right ascension may be
found from the time of its passage over the meridian after that of the equi-
noctial point, allowing 15 degrees for each sidereal hour. (Plate XXXV.
Fig. 512.)

In all astronomical observations it is necessary to make proper corrections,
according to the rules of optics, for the effects of atmospherical refrac-
tion; and also, in observations on the moon more especially, for those of
parallax, or the difference of the apparent place of the luminary with

ON PRACTICAL ASTRONOMr, 545,

respect to the earth's' centre, and to the place of the spectator, which is
equal to the angle subtended at the centre of the luminary by the seniidia-
meter of the earth passing through the place of observation; since all cal-
culations of the geocentric places of the heavenly bodies are referred to the
earth's centre. This angle, which is to be added to the apparent altitude,
amounts sometimes, in the case; of the moon, when near the horizon, to more
than a degree; the refraction, which is in a contrary direction, and is to be
subtracted from the altitude, being at the horizon about 33 minutes. (Plate
XXXV. Fig. 513.)

The most important applications of practical astronomy are in the de-
termination of the latitudes and longitudes of places on the earth's surface.
The latitude, which is the angular distance of the place from the equator, or
the angle formed by the plane of its horizon with the earth's axis, is easily
ascertained by finding the meridian altitude of a body, of which the decli-
nation is known; since, by deducting or adding the declination, we have at
once the elevation of the equinoctial, or of the plane of the equator, above the
horizon, and subtracting this from a right angle, we find the elevation of the
pole, or the latitude. (Plate XXXV. Fig. 512.)

It is also common to determine the latitude of a place by means of two
altitudes observed at different times in the same day, noticing accurately the
interval of time that elapses between the observations. This method has
a great advantage in cloudy weather, when it is, not possible to insure an
observation of a meridian altitude.

The longitude of a place, or the relative position of its meridian, is by -no
means so readily determined. For this purpose it becomes necessary to as-
certain the time that elapses between the passages of a given point in the
heavens over its meridian and some other meridian wliich serves as a standard
of comparison. Thus, if the sun arrives three hours later at the meridian of
any place than at the meridian of London, that place must necessarily be
45 degrees west of London, or in 45* west longitude: and if we know, when
it is noon at the given place, that it is three o'clock in the afternoon at
Greenwich, we maybe certain that we are in some part of a meridian 45° west
i)i' that of Greenwich. Had we perfect timekeepers, we might easily adjust them

544 LECTURE XLV.

to the time of our first meridian, and then, by comparison with the usual
determinations of time in any other place, to which they might be carried,
the longitude of this place might be found with perfect accuracy. Such
timekeepers as we have are indeed sufficiently correct, to be of considerable
utility, but it is necessary to compare them frequently with astronomical
observations of phenomena, which occur at times capable of a correct calcu-
lation. Sometimes the transits of Mercury and Venus, or the eclipses of
the moon, are employed for this purpose, but more usually the eclipses of the
satellites of Jupiter; these, however, cannot be well observed without a
more powerful telescope than can be employed at sea; and the theory of the
moon's motion, has of late years been so much improved, that her distance
from the sun or from a fixed star can be calculated, with sufficient accuracy,
for determining the time in London or at Paris without an error of one third
of a minute; so that supposing the observation could be rendered perfectly
correct, the longitude might be thus ascertained within aboutone twelfth of
a degree, or at most five nautical miles.

The observed parallax of the sun and moon may be employed for the
determination of their distances from the earth ; but in the ease of the sun. the
simple comparison of his calculated with his apparent altitude is insufficient for
ascertaining the magnitude of the parallax with accuracy. Sometimes the
parallax of Mars, which is considerably greater than the sun's, has been
directly measured; but the most correct mode of ascertaining the actual
dimensions of the solar system is, to observe a transit of Venus over the sun's
disc, at two places situated in opposite parts of the earth's surface. For,
since the diurnal motion of some parts of the earth is directed the same way
Avith the motion of Venus iu her orbit, and that of others the contrary way,
the different effects of these motions must furnish a mode of comparing the
rotatory velocity of the earth, with the progressive velocity of Venus, and
consequently of inferring, from the known velocity with which the earth's
surface revolves, the actual velocity of Venus, and her distance from the
sun; whence the distances of all the other planets may be readily deduced.
(Plate XXXV. Fig. 514.)

Our countryman Horrox was the first that particularly attended to the phe-
nomena of a transit of Venus over the sun's disc: Dr. Halley, when be

ON" PnACTICAL ASTRONOMY. 566

observed a transit of Mercury at St. Helena, thought that he could ascertain
the times of immersion and emersion Avithout an error of a single second;
and hence he concluded, that by means of a transit of Venus, the sun's dis-
tance might be determined within a five hundredth part. The most advan-
tageous places for the experiment being such as diifer most in longitude,
and are most remote from each other. Captain Cook was se^nt by the British
government to the South Seas, in tne years I76I and 1/69, in order to ob-
serve the transits of Venus in the island of Otaheite. These observations
were compared with those which were made at Wardhuys,iu Danish Lapland;
the difference of the times occupied by the transit at these places was found
to be 23 minutes 10 seconds, and from this comparison, corrected by a num-
"ber of collateral observations, the sun's mean parallax was found to be 8 se-
conds and two thirds, or perhaps 85; for it does not appear that we are
sure of having avoided even an error of one fortieth part of the whole; al-
though Mr. Laplace's determination of the sun's distance, from the lunar mo-
tions, agrees very well with that which is usually considered as the result of
the observations of the transit of Venus.

The comparative densities of the sun, and of such planets as have satellites,
may be calculated from the periods and distances of the bodies revolving
round them; the densities of the other planets have sometimes been assigned
from conjecture only, but of late years the mathematical theory of the planet-
ary perturbations has been rendered so perfect, that some dependence may
perhaps be placed on the density assigned to them from calculations of this
kind. It was formerly supposed that the densities of the planets were re-
gularly greater as they were nearer to the sun; but it is now certain that the
Georgian planet is more dense than Saturn, and it is probable that Venus is
somewhat less dense than the earth. The mass of the moon is deduced from
a comparison of the effects of her attraction on the earth and sea with those
of the sun's attraction.

The artificial globe serves as a useful instrument for determining, in a rough
manner, without calculation, the affections of the heavenly bodies at par-
ticular times; their places being first ascertained from tables, or, in the caSe
of the sun, m.erely from a scale on the globe's horizon, or on its surface. We
have only to adjust the elevation of the pole of the globe in such a manner,

VOL. I. 4 a

^66 LECTURE XLV.

yr

that its axis may form the same angle with its horizon as the axis of the eartU
does with the real horizon of the place; then finding a point on its surface
corresponding to the place of the sun or planet, we may represent its apparent
motion by the motion of this point, and the time occupied by that motion
will be shown by the index of the globe; thus we may find the length of the
day and night, and the time and place of rising and setting; and by means of
a graduated circle, perpendicular to tlfS horizon, we may measure the al-
titude of the sun or planet at any other time, and also itsazimuthi or th«
distance of this circle from the north or south point of the horizon. If we
have a ring of any kind parallel to the horizon, and 33 minutes below it, we
may consider this ring as the apparent horizon, allowing for the effects of re-
fraction; if it be still 15 or 16 minutes lower, it will represent the rising or
setting of the extreme margin of the sun or moon: we might also have a circle
/about a degree above either of these, which might represent the sensible or
apparent horizon with regard to the moon, including the correction for her
parallax ; and a similar ring, placed still lower, would show the duration of
twilight, on any supposition that might be formed respecting the depression
of the sun required for producing total darkness. By means of the celestial
globe, the apparent motions of the fixed stars may be represented in a man-
ner nearly similar, proper attention being paid to the situation of the sun ia
the ecliptic, as determining the time corresponding.

Many of these operations may also be performed with equal convenience
with a planisphere, which is a stereographical projection of the globe on a
plane surface. Professor Bodc's planisphere comprehends in one view all tlie
stars that are ever visible at Berlin : he has added to it a moveable circle, re-
presenting the horizon of that place, carrying with it the circles of altitude
and azimuth, delineated on a transparent paper, which is adjusted, by gradu-
ations at the margin of the chart, to the day and hour for which we wish to
ascertain the apparent places of the heavenly bodies. Any other chart of
the stars, having the pole in its centre, may be applied to a similar use, by
cutting out a circle, or a part of a circle, to represent the horizon of a place
of which the latitude is given ; and if the stars are projected, as is usual, on
two equal charts, they must have two equal arcs to represent the respective
parts of the horizon belonging to them. A simple construction may also
often be made to serve for solving many problems of a similar nature. (Plate

OJf PRACTICAL ASTRONOMY. SSj

XXXV. Fig. 515, 516. Plate XXXVI. Fig. 517. Plate XXXVII»
Fig. 518.)

For representing the real as well as the apparent motions of the different
parts of the solar system, planetariums or orreries have sometimes been era-
ployed, in which the comparative periods of the revolutions have been cx^
pressed by various combinations of wheelwork. Of these instruments Ar-
chimedes was the original inventor, and Iluygens revived them, with many
improvements, in modern times. The construction of the large planetarium,
which has been made in the house of the Royal Institution, was principally
directed by Mr. Pearson. I suggested to him, that the instrument might be
placed in a vertical position, and that the eccentricities of the planetary
orbits might be shown by the revolution of short arms, retained in their
situation by weights, and their deviation from the plane of the ecliptic by
inclining the axes of these arms, in a proper angle, to the plane of the instru-
ment. The other parts of the arrangement, which have any claim to novelty,
were entirely of Mr. Pearson's invention, and he appears to have rendered the
instrument in many respects more accurate than any other planetarium that
has ever been constructed.

sns

LECTURE XLVI.

ON GEOGRAPHV.

From the consideration of the stars, the sun, and the planets in general,
we are now to descend to that of the earth, the particular planet which we
inhabit, and which we can examine more minutely than the other parts of
the solar system. Its external form, its divisions, whether astronomical or
natural, its most remarkable features, and its internal structure, will require
to be separately investigated.

The general curvature of the earth's surface is easily observable in the dis-
appearance of distant objects, and in particular, when the view is limited by
the sea, the surface of which, from the common property of a fluid, becomes
naturally smooth and horizontal: for it is well known that the sails and.rig-
ging of a ship come into view long before her hull, and that each part is the
sooner seen as the eye is more elevated. On shore, the frequent inequalities
of the soird parts of the earth usually cause the prospect to be bounded by
some irregular prominence, as a hill, a tree, or a building' so that the
general curvature is the less observable.

to

The surface of a lake or sea must be always perpendicular to the direction
of a plumb line, which may be considered as the direction of the force of
gravity; and by means either of a plumb line or of a spirit level, we may as-
certain the angular situation of any part of the earth's Surface with respect to
a fixed star passing the meridian; by going a little further north or south,
and repeating the observation on the star, we may find the difference of the
inclination of the surfaces at both points; of course, supposing the earth a
sphere, this difference in latitude will be the angle subtended at its centre by
the given portion of the surface, whence the whole circumference may be
determined; and on these principles the earliest measurements of the earth

ON GEOGRAPHT. S69

were conducted. The first of these, which can be considered as accurate, was
executed by Picart in France, towards the end of the seventeenth century.

But the spherical form is only an approximation to the truths it was cal-
culated by Newton, and ascertained experimentally by the French Acade-
micians, sent to the equator and to the polar circle, that, in order to represent
the earth, the sphere must be flattened at the poles, and prominent at the
equator. We may therefore consider the earth as an oblate elliptic spheroid;
the curvature being greater, and consequently every degree shorter, at the
ecjuator, than nearer the poles. If the density of the earth were uniform
throughout, its ellipticity, or the difterence of the length of its diameters,
would be ^li of the whole; on the other hand, if it consisted of matter of
inconsiderable density, attracted by an infinite force in the centre, the el-
lipticity would be only ^^5 ^^^^ whatever may be the internal structure of
the earth, its form must be between these limits, since its internal parts
must necessarily be denser than those parts which are nearer the surface. If
indeed the earth consisted of water or ice, equally compressible with common
water or ice, and following the same laws of compression with elastic fluids,
its density would be several thousand times greater at the centre than at the
surface; and even steel would be compressed into one fourth of its bulk, and
stone into one eighth, if it were continued to the earth's centre; so that there
can be no doubt but that the central parts of the earth must be much more
dense than the superficial. Whatever this difterence may be, it has been de-
monstrated by Clairaut, that the fractious expressing the ellipticity and the
ap|)arent diniinntion of gravity at the equator must always make together -j-fg-,
and it has been found, by the most accurate observatioiis on the lengths of
])endulums in difterent latitudes, that the force of gravity is less powerful by
vf^ at the equator than at the pole, whence the ellipticity is found to be -j-^-g-
of the equatorial diameter, the form being the same as would be produced, if
about three eighths of the whole force of gravity were directed towards a
central particle,' the density of the rest of the earth being uniform.

This method of determining the general form of the earth is much lesa
liable to error and irregularity, than the measurement of the lengths of de-
grees in various parts, since the accidental variations of curvature produced
by local diftcrences of density, and even by superficial elevations, may oftea

o70 LECTURE XLVl.

produce considerable errors in the inferences which might be deduced from
these measurements. For example, a degree measured at the Cape of Good
Hope, in latitude 33" south, was found to be longer than a degree in France,
in latitude 46^ north, and the measurements in Austria, in Nortli America,
and in Eugland, have all exhibited signs of similar irregularities. There ap-
pears also to be some difference in the length of degrees under the same la-
titude, and in different longitudes. We maj-, however, imagine a regular
elliptic spheroid to coincide very neariy with any small portion of the earth's
surface, although its form must be somevvhat different for different parts :
thus, for tiie greater part of Europe, that is, for England, France, Italy,
and Austria, if the measurements have been correct, this osculating spheroid
must have an ellipticity of txs--

The earth is astronomically divided into zones, and into climates. The
torrid zone is limited by the tropics, at the distance of 23° 28' on each side
of the equator, containing all such places as have the sun sometimes vertical,
or immediately over them; the frigid zones are within the polar circles, at
the same distance from the poles, including all places which remain annually
within the limit of light and darkness, for a whole diurnal rotation of the
earth, or longer; the temperate zones, between these, have an uninterrupted
alternation of day and night, but are never subjected to the sun's vertical
rays. At the equator, therefore, the sun is vertical at the equinoxes, his
least meridian altitude is at the solstices, when it is 66° 32', that is, more
than with us at midsummer, and this happens once on the north and once
on the south side of the hemisphere. Between the equator and the tropics,
he is vertical twice in the year, when his declination is equal to the latitude
qf the place, and his least meridian altitudes, which are unequal between
themselves, are at the solstices. At the tropics, the meridian sun is vertical
once only in the year, and at the opposite solstice, or the time of midwinter,
his meridian altitude is 43° 4', as with us in April, and the beginning of Sep-
tember. At the polar circles, the sun describes on midsummer day a com-
plete circle, touching the north or south point of the horizon ; and in mid-
winter he shows only half his disc above it for a few minutes in the opposite
point; that is, neglecting the elevation produced by refraction, which, in
these climates especially, is by no means inconsiderable. At either pole,
the corresponding pole of the heaven being vertical, the sun must annually

ON GEOSBAPHT. 571

describe a spiral, of which each coil is nearly horizontal, half of the spiral
being abo\'e the horizon, and half below ; the coils being much opener in the
middle than near either end.

The climates, in the astronomical sense of the word, are determined by
the duration of the longest day in different parts of the earth's surface; but
this division is of no practical utility, nor does it furnish any criterion for
judging of the climate in a meteorological sense.

The natural division of the surface of the globe is into sea and land: about
three fourths of the whole being occupied by water, although probably no
Avhere to a depth comparatively very considerable, at most of a few miles on
an average. The remaining fourth consists of land, elevated more or less
above the level of the sea, interspersed, in some parts, with smaller collec-
tions of water, at various heights, and, in a few instances, somewhat lower
than the general surface of the main ocean. Thus the Caspian sea is said to
be about 300 feet lower than the ocean, and in the interior part of Africa
there is probably a lake equally depressed.

We cannot observe any general symmetry in this distribution of the earth's
surface, excepting that the two large continents, of Africa and South
America,-bave some slight resemblance in their forms, and that each of them
is terminated to the eastward by a collection of numerous islands. The large
cap^s projecting to the southward have also a similarity with respect to their
form, and the islands near them: to the west the continents are excavated
into large bays, and the islands are to the east: thus Cape Horn has the
Falkland Islands, the Cape of Good Hope IMadagascar, and Cape Comorin
Ceylon, to the east. (Plate XLII, XLIII.)

The great continent, composed of Europe, Asia, and Africa, constitutes
about a seventh of the whole surface of the earth, America about a sixteenth,
and Australasia or New South Wales about a fiftieth; or, in hundredth
parts of the whole, Europe contains 2, Asia 7, Africa 6, America 6, and
Australasia 2, the remaining 77 being sea; although some authors assign 72
parts only out of 100 to the sea, and 2S to the land. These proportions nid.y
be ascertained with tolerable accuracy by weighing the paper made for cover-

57^2,

LECTURE XLVl.

ino- a globe, first entire, and then cnt out according to the terminations of
the ditterent countries: or, if still greater precision were required, the greater
part of the continents might be divided into known portions of the whole
spherical surface, and the remaining irregular portions only weighed.

The general inclinations and levels of the continents are discovered by the
course of their rivers. Of these the principal are, the River of Amazons, the
Senegal, the Nile, the River St. Laurence, the Iloangho, the River La-
plata, the Jenisei, the Mississippi, the Volga, the Oby, the Amur, tlie Oro-
nooko, the Ganges, the Euphrates, the Danube, the Don, the Indus, the
Dnieper, and the D\yina; and this is said to be nearly the order of their
magnitudes. But if we class them according to the length of country through
which they run, the order will, according to Major Rennel's calculation, be
somewhat different: taking the length of the Thames for unity, he estimates
that of the River of Amazons at 15^, the Kian Kew, in China, 1.54:, the
Iloangho 134, the Nile 12-^, the Lena II4., the Amur 11, the Oby 104, the
Jenisei 10, the Ganges, its companion the Burrampooter, the rive^ of Ava,
and the Volga, each 94-, the Euphrates 84, the Mississippi 8, the Danube 7,
the Indus 54, and the Rhine 5^.

We may form a tolerably accurate idea of the levels-of the ancient continent,
by tracing a line across it in such a direction as to pass no river, which will '
obviously indicate a tract of country higher than most of the neighbouring
parts. ' Beginning at Cape Finisterre, we soon arrive at the Pyrenees, keep--
ing to the south' of the Garonne and the Loire. After taking a long turn
northwards, to avoid the Rhine, we come to Swisserland, and we may ap-
proach very near to the Mediterranean in. the state of Genoa, taking care
not to cross the branches of the Po. We make a circuit in Swisserland, and
pass between the sources of the Danube and of the branches of the Rhine in
Swabia. Crossing Franconia, we leave Bohemia to the north, in order to
avoid the Elbe, and coming near to the borders of Austria, follow those of
Hungary, to the south of the Vistla. The Dnieper then obliges us to go north-
wards through Lithuania, leaving the Don wholly to the right ; and the Volga,
/to pass still further north, between Petersburg and Moscow, a little above Bjele-
sero. We may then go eastwards to the boundary of Asia, and thence northwards
to Nova Zembla. Hence we descend to the west of the Oby, and then to the

OJf GEOGRAPHY. 573

fast of the branches of the "Volga, and the other inland rivers flowing into
the lake Aral and the Caspian sea. Here we are situated on the widely ex-
tended elevation of India, in the neighbourhood of the sources of the Indus:
and, lastly, in our way from hence towards Kanischatka, we leave the Jenisei
and Lena on the left, and the Ganges, the Kiang Kew, the Hoangho, and
the Amur to the right.

The direction of the most conspicuous mountains is, however, a little dif-
ferent from this, the principal chain first constitutes the Pyrenees, and divides
Spain from France, then passes through Vivarais and Auvergne, to join the
Alps, and through the south of Germany to Dalmatia, Albania, and Mace-
donia; it is found again beyond the Euxine, under tlie names of Taurus,
Caucasus, and Imaus, and goes on to Tartary and to Kamschatka. The
peninsula of India is divided from north to south by the mountains of Gate,
extending from the extremity of Caucasus to Cape Comorin. In Africa,
Mount Atlas stretches from Fez to Egypt, and the mountains of the moon
run nearly in the same direction : there is also a considerable elevation be-
tween the Nile and tlie Red Sea. In the new world, the neighbourhood of
the western coast is in general the most elevated ; in North America the
Blue mountains, or Stony mountains, are the most considerable ; and the
mountains of Mexico join the Andes or Cordeliers, which are continued along
the whole of the west coast of South America,

There are several points in both hemispheres from which we may observe
rivers separating to run to difterent seas ; such are Swisserland, Bjelosero
Tartary, Little Tibet, Nigritia or Guinea, and Quito. The highest moun-
tains are Chimborapao and some others of the Cordeliers in Peru, or perhaps
Descabesado in Chili, Mont Blanc, and the Peak of Tenerifte. Chimborafao
is about 7000 yards, or nearly 4 miles, above the level of the sea ; Mont
Blanc 5000, or nearly 3 miles; the Peak of Teneriffe about 4000, or 2 miles
and a quarter : Ophir, in Sumatra, is said to be 5 or 6 hundred feet higher.
It has, however, been, asserted that some of the snowy mountains, to the
north of Bengal, are higher than any of those of South America. The
plains of Quito, in Peru, are so much elevated, that the barometer stands at
the height of 15 inches only, and the air is reduced to half its usual density.
But none of these heights is equal to a thousandtli part of the earth's semi-

VOL. I. 4 b

57* tECTORE XLVI.

diameter, and the greatest of them might be represented on a six inch globe
by a single additional thickness of the paper with which it is covered.
Mount Sinai in Japan, Mount Caucasus, Etna, the Southern Pyrenees, St.
George among the Azores, Mount Adam in Ceylon, Atlas, Olympus, and
Taurus are also high mountains: and there are some very considerable eleva-
tions in the island Owhyhee. Ben Nevis, in Scotland, is the loftiest of the
British hills, but its height is consideraljly less than a mils. (Plate
XXXVIII. Fig. 5iy.)

The most elevated mountains, excepting the summits of volcanos, con-
sist of rocks, more or less mixed, without regular order, and commonly of
granite or porphyry. These are called primary mountains ; they run ge-
nerally from east to west in the old world, and from north to south in the
new; and many of them are observed to be of easier ascent on the east than
on the west side. The secondary mountains accompany them in the same
direction, they consist of strata, mostly calcarious and argillaceous, that is,
of the nature of limestone and clay, with a few animal and vegetable re-
mains, in an obscure form, together with salt, coals, and sulphur. The ter-
tiary, mountains are still smaller; and in these, animal and vegetable remains-
are very abundant ; they consist chiefly of limestone, marble, alabaster,
building stone, mill stone, and chalk, with beds of flint. Where the se-
condary and tertiary mountains are intersected by vallies, the opposite strata,
often correspond at equal heights, as if the vallies had been cut or washed
from between them, but sometimes the mountains have their strata disposed
as if they had been elevated by an internal force, and their summits had
afterwards crumbled away, the strata which are lowest in the plains being
highest in, the mountains. The strata of these mountains are often inter-
mixed with veins of metal, running in all possible directions, and occupying,
vacuities which appear to be of somewhat later date than the original forma-
tion of the mountains. The volcanic mountains interrupt those of every
other description without any regularity, as if their origin were totally in-
dependent of that of all the rest.

The internal constitution of the earth is little known from actual observa-
tion, for the deptlis to which we "have penetrated are comparatively very in-
considerable, the deepest mine scarcely descending half a mile perpendicularUv

/ OV GEOGRAPHY. 575

It appears that the strata are more commonly in a direction nearly horizontal
than in any other; and their thickness is usually almost equable for some
little distance; but they are not disposed in the order of their specific gravity,
and the opinion of their following each other in a similar series, throughout
the greater part of the globe, appears to rest on very slight foundations.

From observations on the attraction of the mountain Shehallion, Dr.
Maskelyne inferred the actual mean density of the earth to be to that of
water as 44- to 1, judging from the probable density of the internal substance
of the mountain, which he supposed to be a solid rock. Mr. Cavendish haS'
concluded more directly, from experiments on a mass of lead, that the mean
density of the earth is to that of water as 54- to 1. Mr. Cavendish's experi-
ments, which were performed with the apparatus invented and procured by
the late Mr. Michell, appear to hare been conducted wi^th all f)ossible ac-
curacy, and must undoubtedly be preferred to conclusions drawn from the
attraction of a mountain, of which the internal parts are perfectly unknown
to us, except by conjectures founded on its external appearance. Supposing
both series of experiments and calculations free from error, it will only follow
that the internal parts of Shehallion are denser, and perhaps more metallic,
than was before imagined. The density assigned by Mr. Cavendish is not
at all greater than might be conjectured from observations on the vibrations of
pendulums; Newton had long ago advanced it as a probable supposition that
the mean density of the earth might be about 5 or 6 times as great as that of
water', and the perfect agreement of the result of many modern experiments
with this conjecture affords us a new proof, in addition to many others, of
the accuracy and penetration of that illustrious philosopher.

570

LECTURE XLVir.

ON THE TIDES.

The form and structure of the solid parts of the globe have afforded but
few remarkable features capable of arresting our attention, except the general
distribution of land and water, and the permanent differences of elevation of
different parts of the earth. But the sea exhibits a series of phenomena far
more interesting to the mathematical philosopher, because they admit of a
methodical investigation, and of a deduction from general causes, the action
of which may be traced in detail. For the height of the surface of the sea
at any given place is observed to be liable to periodical variations, which are
found to depend on the relative position of the moon, combined in some
measure with that of the sun. These variations are called tides ; they were
too obvious to escape the observation even of the ancients, who inhabited
countries where they are least conspicuous : for Aristotle mentions the tides
of , the northern seas, and remarks that they vary with the moon, and are less
conspicuous in small seas than in the ocean : Caesar, Strabo, Pliny, Seneca,
and Macrobius give also tolerably accurate accounts of them,

Tliere are in the tides three orders of phenomena which are separately
distinguishable: the first kind occurs twice a day, the second twice a month,
and the third twice a year. Every day, about the time of the moon's
passing over the meridian, or a certain number of hours later, the sea become*
elevated above its mean height, and at this time it is said to be high water.
The elevation subsides by degrees, and in about six hours it is low water,
the sea having attained its greatest depression ; after this it rises again when
the moon passes the meridian below the horizon, so that the ebb and flood
occur twice a day, but} become daily later and later by about 50^ minutes,
which is the excess of a lunar day above a solar one, since 284- lunar days
are nearly equal to S9i solar ones.
4

ON THE TtDES, ^ 577

The second phenomenon is, that the tides are sensibly increased at the time
of the new and full moon; this increase and diminution constitute the spring
and neap tides; the augmentation becomes also still more observable when
the moon is in its perigee, or nearest the earth. The lowest as well as the
highest water is at the time of the spring tides; the neap tides neither rise so
high nor fall so low.

The third phenomenon of the tides is the augmentation which occurs at the
time of the equinoxes: so that the greatest tides are when a new or full moou
happens near the equinox, while the moon is in its perigee. The effects of
these tides are often still more increased by the equinoctial winds, which
are sometimes so powerful as to produce a greater tide before or after the
equinox, than that which happens in the usual course, at the time of the
equinox itself.

These simple facts are amply sufficient to establish the dependence of the
tides on the moon; they were first correctly explained by Newton as the
necessary consequences of the laws of gravitation, but the theory has been
still further improved by the labours of later mathematicians. The whole of
the investigations has been considered as the most difficult of all astronomical
problems ; some of the circumstances depend on causes which must probably
remain for ever unknown to us; and unless we could every where measure
the depth of the sea, it would be impossible to apply a theory, even if abso-
lutely perfect, to the solution of every difficulty that might occur. A very in-
judicious attempt has been made to refer the phenomena of the tides to causes
totally different from these, and depending on the annual melting of the
polar ice: the respectability of its author is the only claim Avhich it possesses
even to be mentioned; and a serious confutation of so groundless an opinion
would be perfectly superfluous.

A detached portion of a fluid would naturally assume, by its mutual gra-
vitation, a spherical form, but if it gravitate towards another body at a
distance, it will become an oblong spheroid of which the axis will point to
the attracting body: for the difference of the attraction of this body on its
different parts will tend to separate them from each other in the greatest part
of the sphere, that is, at all places within the angular distance of 794-° froii^

578 LECTURE XLYII.

the line passing througli the attracting body, either in the nearer, or in the re-
moter hemisphere; but to urge them towards the centre, although with a smaller
force, in the remaining part. Hence, in order that there may be an equi-
librium, the depth of the fluid must be greatest where its gravitation, thu»
composed, is least ; that is, in' the line directed towards the attracting body,
and it may be shown that it must assume the form of an oblong elliptic spheroid.

If the earth were wholly fluid, and the same part of its surface were
always turned towards the moon, the pole of the spheroid being immediately
under the moon, the lunar tide would remain stationary, the greatest eleva-
tion being at the points nearest to the moon and furthest from her, and the
greatest depression in the circle equally distant from these points; the eleva-
tion being, however, on account of the smaller surface to which it is confined
twice as great as the depression. The actual height of this elevation would
probably be about 40 inches, and the depression 20, making together a tide
of 5 feet. If also the waters were capable of assuming instantly such a form
as the equilibrium would require, the summit of a spheroid equally elevated
would still be directed towards the moon, notwithstanding the earth's rota-
tion. This may be called the primitive tide of the ocean: but on account of
the perpetual change of place which is required for the accommodation of the
surface to a similar position with respect to the moon, as the earth revolves,
the form must be materially different from that of such a spheroid of equili-
brium. The force employed in producing this accommodation may be esti-
mated by considering the actual surface of the sea as that of a wave moving
on the spheroid of equilibrium, and producing in the water a sufficient
velocity to preserve the actual form. We may deduce, from this mode of consi-
dering the subject, a theory of the tides which appears to be more simple and
satisfactory than any which has yet been published: and by comparing the
tides oi' narrower seas and lakes with the motions of pendulums suspended on
vibrating centres, we may extend the theory to all possible cases.

If the centre of a pendulum be made to vibrate, the vibrations of the pen-
dulum itself, when they have arrived at a state of permanence, will be perform-
ed in the same time with those of the centre; but the motion of the pendulum
will be either in the same direction with that of the centre, or in a contrary
direction, accordingly as the time of this forced vibration is longer or sliortcf!-

ox THE TIDES, 57!)

than that of the natural vibration of the pendulum; and in the same manner
it may be shown that the tides either of an open ocean or of a confined lake
may be either direct or inverted with respect to the primitive tide, Avhich
woukl be produced if the waters always assumed the form of the spheroid of
equilibrium, according to tlie depth of the ocean, and to the breadth as well
as tlie depth of the lai<e. In the case of a direct tide, the time of the passage
of the luminary over the meridian must coincide with that of high w ater, and
in the case of an inverted tide with that of low water. '

In order that the lunar tides of an open ocean may be direct, or synchro-
nous, its depth must be greater than 13 miles, and for the solar tides than
14. The less the depth exceeded these limits, the greater the tides would be,
and in all cases they would be greater than the primitive tides. But in fact the
height of the tides in the open ocean is always far short of that which would
be produced in this maii|ier; it is therefore improbable that the tides are ever
direct in the open ocean, and that the depth of the sea is so great as 13
miles.

In order that the height of the inverted or remote lunar tides may be five
feet, or equal to that of the primitive tides, tlie depth of the open sea must
be 64- miles ; and if the height is only two feet, which is perhaps not far from
the truth, the depth must be 3 miles and five sevenths.

The tides of a lake or narrow sea differ materially from those of the open
ocean, since the height of the water scarcely undergoes any variation in the
middle of the lake; it must always be high water at the eastern extremity
when it is low water at the western: and this must happen at the time when
the places of high and low water, with respect to the primitive tides>
are equally distant from the middle of the lake. (Plate XXXVIII. Fig.
520.)

The tides may be direct in a lake 100 fathoms deep and less than 8 degrees
wide; but if it be much wider, they must be inverted. Supposing the depth
a mile, they will be direct when the breadth is less than 25'^; but if a sea,
like the Atlantic^ were 50 or 60 degrees wide, it must be at least four miles

580 LKCTURE XLVII.

deep, in Older that the time of high water might coincide with that of the
moon's southing.

Hitherto we have considered the motion of the water as free from all resist-
ance ; but M'here the tides are direct, they must be retarded by the effect of
a resistance of any kind ; and where they are inverted, they must be accele-
rated ; a small resistance producing, in both cases, a considerable difference in
the time of high water.

Where a considerable tide is observed in the middle of a limited portion of
the sea, it must be derived from the effect of the elevation or depression of
the ocean in its neighbourhood ; and such derivative tides are probably combined
in almost all cases with the oscillations belonging to each particular branch of
the sea. Mr. Laplace supposes that the tides, which are observed in the most
exposed European harbours,are produced almost entirely by the transmission of
the cfl^'ect of the main ocean, in about a day and a half; but this opinion does
not appear to be justified by observation; for the interval between the times of
the high water belonging to the same tide, in any two places between Brest and
the Cape of Good Hope, has not been observed to exceed about twelve hours
at most; nor can we trace a greater difference by comparing the state of the
tides at the more exposed situations of St. Helena, the Cape Verd Islands,
the Canaries, the ISladeiras, and the Azores, which constitute such a suc-
cession as might be expected to have indicated the progress of the principal
tide, if it had been such as My. Laplace supposes. The only part of the
ocean, which we can consider as completely open, lies to the south of the two
great continents, chiefly between the latitudes 30® and 70° south, and the ori-
ginal tide, which happens in this widely extended ocean, where its depth is suffi-
ciently uniform, must take place, according to the theory which has been ad-
vanced, at some time before the sixth lunar hour. It sends a wave into the At-
lantic, which is perhaps 12 or 13 hours in its passage to the coast of France, but
certainly not more. This tide, which would happen at the sixth lunar hour
after the moon's transit, if there were no resistance, is probably so checked by
the resistance, that tjie water begins to subside about the fourth, and in some
seas even somewhat earlier, although in others it may follow more nearly
its natural course. There is scarcely a single instance which favours the

Oy THE TIDES. 581

supposition of the time of high water in the open sea being within an hour
of the moon's southing, as it must be if the depth were very great: so that
neither the height of the tides nor the time of high water will allow us to
suppose the sea any where quite so deep as 4 miles.

The tide entering the Atlantic appears to advance northwards at the rate of
about 500 miles an hour, corresponding to a depth of about 3 miles, so as to
reach Sierra Leone at the 8th hour after the moon's southing; rliis part of
Africa being not very remote from thc'meridian of the middle of the south
Atlantic ocean, and having little share in the primitive tides of that ocean.
The southern tide seems then to pass by Cape Blanco and Cape Bojador, to
arrive at Gibraltar at the 13th hour, and to unite its eifects with those of other
tides at various parts of the coast of Europe.

Wc may therefore consider the Atlantic as a detached sea about 3500 miles
broad and 3 miles deep; and a sea of these dimensions is susceptible of tides
considerably larger than those of the ocean, but how much larger we
cannot determine without more accurate measures. These tides would happen
on the European coasts, if there were no resistance, a little less than 5 hours
after the moon's southing, and on the coast of America, a little more than
seven hours after; but the resistance opposed to the motion of the sea may
easily accelerate the time of high water in both cases about two hours, so
that it may be a little before the third hour on the western coasts of Europe
and of Africa, arid before the fifth on the most exposed parts of"the eastern
coast of America; and in the whole of the Atlantic, this tide may be com-
bined more or less both with the general southern tide, and with the par-
tial effects of local elevations or depressions of the bottom of the sea, which
may cause irregularities of various kinds. The southern tide is, however,
probably less considerable than has sometimes been supposed, for, in tlie
latitudes in which it must originate, the extent of the elevation , can only
be half as great as at the equator; and the Islands of Kergulen's Land
and South Georgia, in the latitudes of about 50" and 55°, have their
tides delayed till the 10th and 11th hours, apparently because they receive
them principally from distant parts of the ocean, which are nearer to the
equator.

4 c #

58f LECTURE XLVri.

On the western coasts of Europe, from Ireland to Cadiz, on those of Africa,
from Cape Coast to the Cape of Good Hope, and on the Coast of America, from
California to the streights of Magellan, as well as in the neighbouring islands,
it is usually high water at some time between two and four hours after the
moon's southing; on the eastern coast of South America between four and six,
on that of North America between seven and eleven; and on the eastern coasts
of Asia and New Holland between four and eight The Society islands arc
perhaps too near the middle of the Pacific ocean to partake of the effects of
its primitive tide, and their tide, being secondary, is probably for this
reason a few hours later. At the Almirantes,near the eastern coast of Africa,
the tide is at the sixth hour; but there seem to be some irregularities in the
tides of the neighbouring islands.

The progress of a tide may be very distinctly traced from its source in
the ocean into the narrow and shallow branches of the sea which constitute
our channels. Thus the tide is an hour or two later at the Scilly Islands
than in the Atlantic, at Plymouth three, at Cork, Bristol, and Weymouth
four, at Caen and Havre six, at Dublin and Brighthelmstone seven, at
Boulogne and Liverpool eight, at Dover near nine, at the Nore eleven, and
at London bridge twelve and a half. Another portion appears to proceed
round Ireland and Scotland into the North Sea; it arrives from the Atlantic
at' Londonderry in about three hours, at the Orkneys in six, at Aberdeen in
eleven, at Leith in fourteen, at LeostofFe in twenty, and at the Nore in
about twenty four, so as to meet there the subsequent tide coming from the
south. From the time occupied by the tide in travelling from the mouth of
the English channel to Boulogne, at the rate of about 50 miles an hour, we
may calculate that the mean depth of the channel is about 2S fathoms, in-
dependently of the magnitude of the resistances of various kinds to be over-
come, which require us to suppose the depth from 30 to 40 fathoms. In
the great river of Amazons, the eifects of the tides are still sensible at the
streights of Pauxis, 500 miles from the sea, after an interval of several days
spent in their passage up: for the slower progressive motion of the water no
more impedes the progress of a wave against the stream, than the velocity
of the wind prevents the transmission of sound in a contrary direction^
(Plate XXXVIIL Fig. 521.)

OK THE TIDES. 583

Such are the general outlines of the lunar tides; they are, however, liable
to a great variety of modifications, besides their combination with the tides
produced by the sun. When the moon is exactly over the equator, the
highest part of the remoter, or inferior, as well as of the nearer or superior
tides, passes also over the equator, and the effect of the tide in various lati-
tudes decreases gradually from the equator to the pole, where it vanishes ;
but when the moon has north or south declination, the two opposite summits
of the spheroid describe parallels of latitude, remaining always diametrically
opposite to each other. Hence the two successive tides must be unequal at
every place except the equator, the greater tide happening when the nearer
elevation passes its meridian : and the mean between both is somewhat smaller
than the equal tides which happen when the moon passes the equator. This
inequality is, however, much less considerable than it would be if the sea
assumed at once the form of the spheroid of equilibrium; and the most
probable reasons for this circumstance, are, first, that our tides are partly de-
rived from the equatorial seas; secondly, that the effects of a preceding tide
are in some measure continued so as to influence the height of a succeeding
one ; and, thirdly, that the tides of a narrow sea are less affected by its lati-
tude than those of a wide ocean. The height of the sea at low water is the
same whatever the moon's declination may be. There is also a slight differ-
ence in the tides, according to the place of the moon's nodes, which allows
her declination to be greater or less, and this difference is most observable in
high latitudes, for instance, in Iceland ; since, in the neighbourhood of the
poles, the tides depend almost entirely on the declination.

In all these cases, the law of the elevation and depression of each tide may
be derived, like that of the vibrations of a pendulum and of a balance, from
the uniform motion of a point in a circle. Thus, if we conceive^ a circle to be
placed in a vertical plane, having its diameter equal to the whole magnitude
of the tide, and touching the surface of the sea at low water, the point, in
which the surface meets the circumference of the circle, will advance with a
uniform motion, so that if the circle be divided into I'i parts, the point will
pass over each of these parts in a lunar hour. It sometimes happens, how-
ever, in confined situations, that the rise and fall of the water deviates con-
siderably from this law, and the tide rises somewhat more rapidly than it
falls; and in rivers, for example in the Severn, the tide frequently advances

584 - LECTURE XLVII.

suddenly with a head of several feet in height. These deviations probably
depend on the magnitude of the actual displacement of the water, which in
such cases bears a considerable proportion to the velocity of the tide, while
in the open ocean a very minute progressive motion is sufficient to produce
the whole elevation. The actual progress of the tides may be most con-
veniently observed, by means of a pipe descending to some distance below the
surface, so as to be beyond the reach of supe'rficial agitations, and having
Avithin it afloat, carrying a wire, and indicating the height of the Avater on a
scale properly divided.

We have hitherto considered the tides so far only as they are occasioned)
by the moon; but in fact the tides, as thej' actually exist, depend also ort
the action of the sun, which produces a serves of effects precisely similar ta
those of the moon, although much less conspicuous, on account of the
greater distance of the sun, the solar tide being only about two fifths of the
lunar. These tides take place independently of each other, nearly in the
same degree as if both were single; and the combination resulting from
them is alternately increased and diminished, accordingly as they agree, or
disagree, with respect to the time of high water at a given place; in the
same manner as if two series of waves, equal among themselves, of whiclt
the breadths are as 29 to 30, be supposed to pass in the same direction over
the surface of a fluid, or if two sounds similarly related be heard at the same
time, a periodical increase and diminution of the joint effect will in either
case be produced. Hence are derived the. spring and neap tides, the effects
of the sun and moon being united at the times of conjunction and ojjposition,
or of the new and full moon, and opposed at the quadratures, or first and
last quarters. The high tides at the times of the equinoxes are produced by
the joint operation of the sun and moon, when both of them are so situated
as to act more powerfully than elsewhere.

The lunar tide being much larger than the solar tide, it must always de-
termine the time of high and law water, which, in the spring and neap tides,
remains unaltered by the efTcct of the sun; so that in the neap tides, the
actual time of low water is that of the solar high water; but at the inter-
inctliate times, the lunar high water is more or less accelerated or retarded.
The progress of this alteration may easily be traced by means of a simple

ON THE TIDES. 585

construction. • If we make a triangle of which two of the sides are two feet
and five feet in length, the external angle which they form being equal to
twice the distance of the luminaries, the third side will show precisely the
magnitude of the compound tide, and the halves of the two angles opposite
to the first two sides the acceleration, or retardation, of the times of high
water belonging to the separate tides respectively. Hence it aj)pears that
the greatest deviation of the joint tide from the lunar tide amounts to 11*
48' in longitude, and the time corresponding, to 47 minutes, supposing the
proportion of the forces to remain always the same; but in fact the forces
increase in proportion as the cubes of the distances of their respective lu-
minaries diminish, as well as from other causes; and in order to determine
their joint effects, the lengths of the sides of the triangle must be varied ac-
cordingly. In some ports, from a combination of circumstances in the chan-
nel, by which the tides reach them, or in the seas, in which they originate,
the influence of the sun and moon may acquire a propartion somewhat dif-
ferent from that which naturally belongs to them: thus at Brest, the in-
fluence of the moon appears to be three times as great as that of the sun;
when it is usually only twice and a half as great. (Plate XXXVIIL
Fig. 5^22.)

The greatest and least tides do not happen immediately at the tinres of the
new and full moon, but at least two, and commonly three tides after, evert
at those places which are most immediately exposed to the effects of the
general tide of the ocean. The theory which has been advanced will afford
us a very satisfactory reason for this circumstance; the resistance of fluids
in general is as the square of the velocity, consequently it must be mucli
greater for the lunar than for the solar tide, in proportion to the magnitude'
of the force, and the acceleration of the lunar tide produced by this cause
must be greater than that of the solar; hence it may happen that when the
lunar tide occurs two or three hours after the transit of the moon, the solar
title may be tju-ee or four hours after that of the sun, so as to be about an
hour later, at the times of conjunction and opposition, and the tides^ wilt
be highest when the moon passes the meridian about an hour after the sun;
while at the precise time of the new and full moon, the lunar tide will be-
retarded about a quarter of an hour by the effect of the solar tide.

586 ^ LECTURK XLVII.

The particular forms of the channels, through which the tides arrive at dif-
ferent places, produce in them a great variety of local modifications; of
which the most usual is, that from the convergence of the shores of the chan-
nels, the tides rise to a much greater height than in the open sea. Thus at
Brest the height of the tides is about 20 feet, at Bristol 30, at Chepstow 40,
at St. Maloes ^0; and at Annapolis Royal, in the Bay of Fundy, as much
sometimes as 100 feet ; although perhaps in some of these cases a partial
oscillation of a limited portion of the sea may be an immediate effect of the
attraction of the luminary. In the Mediterranean the tides are generally
inconsiderable, but they are still perceptible; at Naples they sometimes
amount to a foot, at Venice to more than two feet, and in the Euripus, for
a certain number of days in each lunation, they are very distinctly observ-
able, from the currents which they occasion. In the West Indies, also, and in the
gulf of Mexico, the tides are less marked than in the neighbouring seas, perhaps
on account of some combinations derived from the variations of the depth
of the ocean, and from the different channels by which they are propagated.

In order to understand the more readily the effects of such combinations,

we may imagine a canal, as large as the river of Amazons, to communicate

at both its extremities with the ocean, so as to receive at each an equal series

of tides, passing towards the opposite extremity. If we suppose the tides to

enter at the same instant at both ends, they will meet in the middle, and

continue their progress without interruption : precisely in the middle the

times of high and low water belonging to each series will always coincide,

and the effects will be doubled; and the same will liappen at the points,

where a tide arrives from one extremity at the same instant that an earlier

or a later tide comes from the other ; but at the intermediate points the

effects will be diminished, and at some of them completely destroyed, where

the high water of one ti^e coincides with the low water of another. The

tides at the port of Batslia in Tonkin have been explained by Newton from

considerations of this nature. In this port there is only one tide in a day ;

it is high water at the sixth lunar hour,or at the moon's setting, when the moon

has north declination, and at her rising, when she has south declination;

and when the moon has no declination there is no tide. In order to explain

this circumstance, we may represent the two xmequal tides which happen in

succession every day, by combining with two equal tides another tide, in-

ox THE TIDE3. 557

dependent of them, and happening only once a day; then, if a point be so
situated in the canal which we have been considering, that the effects of the
two equal semidiurnal tides may be destroyed, those of the daily tides only
will remain to be combined with each other ; and their joint result will
be a tide as much greati^r than either, as the diagonal of a square is
greater than its side; the times of high and low water being intermediate
between those which belong to the diurnal tides considered separately.
Thus, in the port of Batsha, the greater tide probably arrives at the third
lunar hour directly from the Pacific ocean, and at the ninth from the gulf of
Siam, having passed between Sumatra and Borneo; so shat the actual time
of high water is at the sixth lunar hour. The magnitude of this compound
tide is by no means inconsiderable; it sometimes amounts to as much as
13 feet. (Plate XXXVIII. Fig. 523, o24.)

Besides the variations in the height of the sea, which constitute the tides,
the attractions of the sun and moon are also supposed to occasion a retardation
in its rotatory motion, in consequence of which it is left a little behind the
solid parts of the earth ; and a current is produced, of which the general
direction is from east to west. This current comes from the Pacific and
Indian oceans, round the Cape of Good Hope, along the coast of Africa^
then crosses to America, and is there divided and reflected southwards to-
wards the Brazils, and northwards into the Gulf stream, which ti'avels round
the gulf of Mexico, and proceeds north eastwards into the neighbourhood
of Newfoundland, and then probably eastwards and south eastwards once
more across the Atlantic. It is perhaps on account of these currents that
the Pted Sea is found to be about 25 feet higher than tlte Mediterranean:
their direction may possibly have been somewhat changed in the course of
many ages, and with it the level of the Mediterranean also; since the floor
of the cathedral at Ravenna is now several feet lower with respect to the sea
than it is supposed to have been formerly, and some steps have been found
in the rock of Malta, apparently intended for ascending it, which are at
present under water.

The atmosphere is also liable to elevations and depressions analogous to
those of the sea, and perhaps these changes may have some little effect on
the winds and on tlie weather; but their influence must be very incousider-

588 LECTURE XLVir.

able, since the addition of two or three feet to the height of the atmosphere
at any part can scarcely be expected to be perceptible. The height of an
aerial tide must be very nearly the same with the observed height of the
principal tides of the sea; and the variation of atmospherical pressure, which
is measured by the difference between the actual form and the spheroid of
equilibrium, must be equivalent to the weight of a column of about 10 feet
of air, or only -ri-^ •jf an inch of mercury. A periodical variation five times
as great as this has indeed been observed near the equator, where the state of
the atmosphere is the least liable to accidental disturbances ; but this change
cannot in any degree be referred to the effect of the moon's action, since it
happens always about the same hour of the day or night. The atmosphere is
also affected by a general current from east to west, like that of the sea, and
there is reason, from astronomical observations, to suppose that a similar
circumstance happens in the atmosphere of Jupiter, on account of the actions
of his satellites, which must be considerably more powerful thau that of the
mooa.

589

LECTURE XLVIII.

ON THE HISTORY OF ASTRONOMY.

V\' E have now taken a general view of the most striking phenomena of the
universe at large, of the great features of the solar system, and of the pecu-
liarities of the planet which we inhabit, with respect both to its solid and to
its fluid parts. All these are departments of astronomy, and we shall con-
clude our examination of the subject with a summary of the history of the
science, principally extracted and abridged from Laplace's Exposition du
syst^me du monde.

In all probability the astronomy of the earliest ages was confined to ob--
servations of the obvious motions and eclipses of the sun and moon, the
rising, setting, and occultations of the principal stars, and the apparent mo-
tions of the planets. The progress of the sun was followed, by remarking
the stars as they were lost in the twilight, and perhaps also by the variation
of the length of the shadow- of a detached object, observed at the time of the
day when it was shortest. In order to recognise the fixed stars, and their
diflferent motions, the heavens were divided into constellations; and twelve
of these occupied the zone denominated the zodiac, within the limits of
which the sun and planets were always found;

The entrance of the sun into the constellation aries, or the ram, denoted,
in the time of Hipparchus, the beginning of the spring; and as the season
advanced, the sun continued his progress through the bull, the twins, and
the other signs in order; some of which appear to have been denominated from
their relation to the agriculture and to the climates of the countries in which
they were imagined. and others from the celestial phenomena attending the sun's
passage through them; the crab, for example, denoting his retrograde motion
after the time of the solstice, and the balance the equality of day and

VOL. r. 4 p

jgO LECTURE XLVIIT.

night at the autumnal equinox. But the motion of the equinoctial points
having changed in some degree the course of the seasons with regard to the
stars, the signs of the ecliptic, by which the places of the sun and planets
are described, no longer coincide precisely with the constellations of the
zodiac from which they derive their names.

The most ancient observations of which we are in possession, that are suffi-
ciently accurate to be employed in astronomical calculations, are those made
at Babylon in the years 719 and 720 before the Christian era, of three
eclipses of the moon. Ptolemy, who has transmitted them to us, employed
them for determining the period of the moon's mean motion, and, therefore,
had probably none more ancient on which he could depend. The Chaldeans,
however, must have made a long series of observations before they could
discover their Saros or lunar period of 65854- <J^ys, or about 18 years, in
which, as they had learnt at a very early time, the place of the moon, her node,
and apogee, return nearly to the same situation with respect to the earth and
sun, and of course a series of nearly similar eclipses recurs. The observations
attributed to Hermes indicate a date seven hundred years earlier than those of
the Babylonians, but their authenticity appears to be extremely doubtful.

The Egyptians were very early acquainted with the length of the year, as
consisting nearly of 365 days and a quarter, and they derived from it their
Sothic period of 1460 years, containing 36.5 days each. The accurate corres-
pondence of the faces of their pyramids with the points of the compass is con-
sidered as a proof of the precision of their observations: but their greatest
merit was the discovery that Mercury and A'^enus revolve round the sun, and not
round the earth, as it had probably been before believed : they did not, however,
suppose the same of the superior planets. (Plate XXXVIII. Fig. 5^5, 62,6.}

In Persia and in India, the origin of astronomy is lost in the darkness
which envelopes the early history of those countries. We find the annals of
no country so ancient and so well authenticated as those of China, which are
C)nfjrmed by an incontestable series of historical monuments. The regula-
tion of the calendar, and the prediction of eclipses, were regarded in this
country as important objects, for which a mathematical tribunal was esta*
blished at a very early period. But the scrupulous attachment of the Chinese

OV THE HISTORT OF ASTRONOMV^ 5,91

to their ancient customs, extending itself even to their astronomy, has im-
peded its progress, and retained it in a state of infancy. The Indian tables
indicate a much higher degree of perfection in tlie early state of the science,
than it had attained in China; but we have every reason to believe that they
are not of very remote antiquity. " Here", says Mr. Laplace, who must be
allowed to be free from prejudices in favour of established opinions, " I am
sorry to be obliged to differ from an illustrious philosopher, Mr. Bailly, who,
after having distinguished his career by a variety of labours useful to the
sciences, and to mankind at large, fell a victim to the most sanguinary ty-
ranny that ever disgraced a civilised nation. The Indian tables are referred
to two principal epochs, which are placed the one 3102 years before Christ,
the other 1491. These are connected by the mean motions, and not the
true motions, of the sun, the moon, and the planets ; so that one of the
epochs must necessarily be fabulous. The celebrated author, who has been
mentioned, has sought to establish, in his treatise on Indian astronomy, that
the former of these epochs is founded on observation. But if we calculate
from our own improved tables, we shall find that the general conjunction of
the sun, moon, and planets, which the Indian tables suppose, in reality never
happened, although it may be deduced, according to those tables, by ascend-
ing from the later series. The equation of the sun's centre, depending on
the eccentricity of the earth's orbit, appears indeed to indicate a still higher
antiquity; but its magnitude, as deduced from eclipses, must have been
affected by a contrary error with respect to the moon's place: and the de-
termination of the mean motion of the moon seems to make it probable that
these tables are even of a later date than Ptolemy."

In astronomy, as well as in other sciences, the Greeks were the disciples of
the Egyptians; they appear to have divided the stars into constellations 13 or
1400 years before Christ. Newton attributes this arrangement to Chiron, and
he supposes that he made the middle of the constellations correspond to the
beginning of the respective signs. But until the time of the foundation of
the school of Alexandria, the Greeks treated astronomy as a science purely
speculative, and indulged themselves in the most frivolous conjectures respect-
ing it. It is singular that amidst the confusion of systems heaped up on each
other, without aftbrding the least information to the mind, it should never have

592 ' LECTUnE XLVIII.

occurred to men of so great talents, that the only way to become accurately ac-
quainted with nature, is to institute experimental inquiries throughout her works.

Thales of Miletus, who was born in the year 640 before Christ, having
travelled and studied in Egypt, founded, on his return, the Ionian school of
philosophy, in which he taught the sphericity of the earth, and the obliquity
of the ecliptic with respect to the equator. He also explained the true causes
of eclipses, which he was even able to foretel, unquestionably by means of
the information that he had obtained from the Egyptian priests.

Pythagoras of Samos was born 590 years before Christ; he probably profited
by the information which Thales had acquired, and travelled also into Egypt
for his further improvement. It is conjectured that he was acquainted with
the diurnal and annual motions of the earth, but he did not publicly profess
the true system of the world. It was taught after his death, by his disciple
Philolaus, about the year 450, as well as by Nicetas, and by others of the
school. They considered all the planets as revolving round the sun, and as
inhabited globes; and they understood that the comets were only eccentric
planets. Some time after this, the lunar period of Meto was publicly made
known at the Olympic games, and was universally adopted as the basis of
the calendar. (Plate XXXVIII. Fig. 527.)

The next occurrence which deserves to be noticed, with respect to astronomy
is the foundation of the school of Alexandria, which was the first source of
accurate and continued observations. Upon the death of Alexander, and the
subsequent division of his empire, the province of Egypt fell to the lot of
Ptolemy Soter; a prince whose love of science, and whose munificence towards
its professors, attracted to his capital a great number of learned men from
various parts of Greece. His son, Ptolemy Philadelphus, continued and in-
creased the benefits conferred on them by his father, and built the magnificent
edifice which contained, together with the celebrated library, collected by
Demetrius] Phalereus, an observatory, furnished with the necessary books
and instruments. The first astronomers, who were appointed to occupy this
building, Avere Aristyllus and Timocharis; they flourished about 300 years
before Christ, and observed with accuracy the places of the principal stars of

ON THE HISTORY OF ASTRONOMY. $93

the zodiac. Aristarchus of Samos was the next; he imagined a method of
finding the sun's distance, by observing the portion of the moon's disc that, is
enlightened, when she is precisely in the quadrature, or 90° distant from the
sun; and although he failed in his attempt to determine the sun's distance
with accuracy, yet he showed that it was much greater than could at that
time have been otherwise imagined; and he asserted that the earth was but
as a point in comparison with the magnitude of the universe. His estimation
of the distance of the sun is made by Archimedes the basis of a calculation
of the number of grains of sand that would be contained in the whole
heavenly sphere, intended as an illustration of the powers of numerical
reckoning, and of the utility of a decimal system of notation, which was the
foundation of the modern arithmetic.

Eratosthenes, the successor of Aristarchus, is known by his observation
of the obliquity of the ecliptic, and his measurement of a certain portion
of the earth's circumference ; the whole of which he determined to
be 250 000 stadia; but the length of his stadium is uncertain. Pto-
lemy, calculating perhaps from the same measures, or from some others
still more ancient, calls it 180 000; which, if the stadium is determined from
the Nilometer at Cairo, and from the base of the pyramid, is within one
thousandth part of the truth, the length of the base of the pyramid being equal
to 400 Egyptian cubits, or to 729 feet 10 inches English.

Hipparchsu of Bithynia flourished at Alexandria about the year 140 before
Christ. Employing the observations of Timocharis, and comparing them
with his own, he discovered the precession of the equinoxes. He also
observed that the summer was 9 days longer than the winter, and that the
solstices divided each of these seasons a little unequally. In order to explain
this, Hipparchus supposed the sun to move uniformly in an eccentric circle,
the distance of its centre from that of the earth being -^ "of the radius, and
placed the apogee in the sixth degree of gemini. Probably the annual equa-
tion of the moon, which has some influence on the time of eclipses, was the
cause of his making the eccentricity too great; had he assumed it but one
fifth part less, the supposition would have represented the sun's place with
tolerable accuracy. Hipparchus appears to have been the first that employed

594 LECTURE XLVIII.

astronomical observations for determining the latitudes and longitudes of
places.

The interval of three centuries, which elapsed between Hipparchus and
Ptolemy, offers us little that is remarkable in the progress of astronomy,
except the reformation of the calendar, by Julius Caesar, who was assisted in
making the arrangement by Sosigenes, an astronomer of the same school that
gave birth to all the preceding discoveries, as well as to the improvements of
Ptolemy. This great astronomer was born at Ptolemais in Egypt, and
flourished about the year 140 of our era. He continued the vast project,
begun by Hipparchus, of reforming the whole science which he studied. He
discovered the evection of the moon, or the change of her velocity, occasion-
ed by the position of the apogee with respect to the sun; he determined the
quantity of this equation with great precision; and in order to represent it,
he supposed the moon to perform a subordinate revolution in an epicycle, or a
smaller circle, of which the centre was carried round in the line of the general
orbit, which he considered as an eccentric circle. This mode of approxima-
tion is exceedingly ingenious; it is said to have been the invention of Apol-
lonius of Perga, the mathematician, and although it sometimes becomes com-
plicated, yet it is very convenient for calculation ; and it may be employed
with advantage in the representation of the planetary motions by machinery.
Ptolemy adopted the most ancient opinion with respect to the solar system,
supposing all the heavenly bodies to revolve round the earth; the moon
being nearest, then Mercury, Venus, the Sun, Mars, Jupiter, and Saturn.
This opinion had long been the most general, although some astronomers had
placed Mercury and Venus at greater distances than the sun, and some at-
tributed to the earth a diurnal motion only; but the doctrine of the Pytha-
goreans appears to have been wholly exploded or forgotten. Ptolemy deter-
mined the quantity of the precession of the equinoxes from a comparison of
his own observations with those of Hipparchus; but he made it sHialler than
the truth; and he probably formed his table of the places of the stars by
applying this erroneous correction to the tables of Hipparchus, in order to
accommodate them to his own time. Both these errors may, however, be
otherwise explained, by supposing him to have followed Hipparchus in the
length of the tropical year, which being somewhat too great, caused an error

ON THE HISTORY OF ASTRONOMT. 59S

in the calculation of the sun's place, to which that of the stars was referred ;
but upon this supposition, he must also have been mistaken in three obser-
vations of the place of tiie equinoctial points. Ptolemy's principal work is
his mathematical system of astronomy, M-hich was afterwards called the great
syntax or body of astronomy, and is at present frequently quoted by the
Arabic name Almagest. He also wrote a treatise on optics, in which the
phenomena of atmospherical refraction are described, and which is extant
in manuscript in the National library at Paris. (Plate XXXVIII. Fig.
528.;

Ptolemy was the last as well as the greatest of the Alexandrian astronomers*
and the science made no further progress till the time of the xArabians. The
first of these was Almamoun, was the son of the celebrated Aaron Reschid;
he reigned at Bagdad in 814, and having conquered the Greek emperor,
Michael the Third, he made it a condition of peace, that a copy of the works
of each of the best Greek authors should be delivered to him ; and among
them were the works of Ptolemy, of which he procured an Arabic transla-
tion. Almamoun also observed the obliquity of the ecliptic, and measured
the length of a degree in the plains of Mesopotamia.

Among the astronomers protected by this prince and his successors, Al-
bategni was the most eminent. He ascertained with great accuracy, in 880,
the eccentricity of the solar motion, and discovered, the change of the place of
the sun's apogee, or of the earth's aphelion.

Ibn Junis-made his observations at Cairo, about the year 1000; he was a
very assiduous astronomer, and determined the length of the year within
2 seconds of the truth. At this time the Arabians were in the liabit of em-
ploying, in their observations, the vibrations of a pendulum.

The Persians soon after applied themselves to astronomy; and in the
eleventh century they invented the approximation of reckoning 8 bissextiles-
in 33 years, which was afterwards proposed by Dominic Cassini as an im-
provement of the Gregorian calendar. The most illustrious of this nation-
was Ulugh IJeigh, who observed in his capital Samarcand, about the year
1437| with very elaborate iostrumeuts. In the mean time Cocheouking. had

S96 LECTURE XLVIII.

made in China, some very accurate observations, which are valuable for the
precision Avith which they ascertain the obliquity of the ecliptic: their date is
about 1278.

It was not long after the time of Ulugh Beigh, that Copernicus laid the
foundation of the more accurate theories which modern improvements have
introduced into astronomy. Dissatisfied with the complicated hypotheses of
the Ptolemaean system, he examined the works of the ancients, inquest of
more probable opinions. He found from Cicero that Nicetas and other
Pythagoreans had maintained, that the sun is placed in the centre of the
system, and that the earth moves round him in common with the other
planets. He applied this idea to the numerous observations which the dili-
gence of astronomers had accumulated, and he had the satisfaction to find
them all in perfect conformity with this theory. He quickly discarded the
Ptolemaean epicycles, imagined in order to explain the alternations of the
direct and retrograde motions of the planets; in these remarkable phenomena,
Copernicus saw nothing but the consequences necessarily produced by the
combination of the motions of the earth and planets round the sun; and from
a minute examination of these circumstances he calculated the relative dis-
tances of the planets from the sun, which till then had remained unknown.
In this system, every thing had the marks of that beautiful simplicity which
pervades all the works of nature, and which, when once understood, carries with
itself sufficient evidence of its truth. Copernicus was born at Thorn, in Polish
Prussia, in the year 1475; he studied in Italy; he taught mathematics at
Rome, and afterwards settled on a canonicate at Frauenberg, where, in
56 years of retirement and meditation, he completed his work on.the celes-
tial revolutions, which was scarcely published when he died.

About this time, William the Fourth, Landgrave of Hesse Cassel, not only
enriched astronomy by his own observations, but also exerted his influence
with Frederic, King of Denmark, to obtain his patronage for the celebrated
Tycho Brahe. Frederic agreed to give him the little island Huen, at the
entrance of the Baltic, where Tycho built his observatory of Uraniburg,
and, in a period of 21 years, made a prodigious collection of accurate obser-
vations. After the death of his patron, his progress was impeded, and he
sought an establishment at Prague, under the emperor Rudolph. Here he

ON THE HISTORY OF ASTRONOMY. 5^7

died soon after, at the age of 55. Struck with the objections made to the
system of Copernicus, principally such as were deduced from a misinterpre-
tation of the scriptures, he imagined a new theory, which, although mechani-
cally absurd, is still astronomically correct; for he supposed the earth to
remain at rest in the centre, the stars to revolve round it, together with the
sun and all the planets, in a sidereal day, and the sun to have, besides, an
annual motion, carrying with him the planets in their orbits. Here the
apparent or relative motions are precisely the same as in the Copernican
sj'stem; the argument that Tycho Brahe drew from the scriptures in favour
of his theory was, therefore, every way injudicious; for it is not to be
imagined that any thing but relative motion or rest could be intended in the
scriptures, when the sun is said to move, or to standstill. But in the Copernican
system, there was an evident regularity in the periods of all the planets, that
of the earth being longer than that of Venus, and shorter than that of Mars,
which were the neighbouring planets on each side; and when Tycho imagined
the sun to move round tlie earth, this analogy was entirely lost. Tycho
Brahe was the discoverer of the variation and of the annual equation of the
moon, the one being an irregularity in its velocity, dependent on its position
with respect to the sun, the other a change in the magnitude of all the per-
turbations produced by the sun, dependent on his distance from the earth.
(Plate XXXVIII. Fig. 529.)

Kepler was the pupil and assistant of Tycho, whose observations were the
basis of his important discoveries: he succeeded him in his appointments at
Prague, and enjoyed the title of Imperial Mathematician. Adopting the
Copernican system, which was then becoming popular, he proceeded to
examine the distances of the celestial bodies from each other at various time?};
and after many fruitless attempts to reconcile the places of the planets with
the supposition of revolutions in eccentric circles, at last discovered that
their orbits are ellipses, and demonstrated, chiefly from his observations on
the planet Mars, that the revolving radius, or the line drawn from the sun to
the planet, always describes equal areas in equal times. By comparing the
periods and the mean distances of the different planets with each other, he
found, after 17 years calculation, tliat the squares of the times of revolution
are always proportional to the cubes of the mean distances from the sun.

VOL. I. 4 E

59$ tSXTUftE XLVIII.

Kepler died in 1630: before his death he had the satisfaction of applying^
his theory to the motions of the satellites of Jupiter, which, as well as the
phases of Venus, and the spots of the sun, had lately been discovered in Italy
by the telescopic observations of Galileo. This great man, celebrated as
well for his theory of projectiles, as for his zealous defence of the Coperaican
system, was born at Pisa in J 564, and lived to the age of 7«, fuli of that
enthusiasm which made him despise the threats of the Inquisition, and submit
patiently to its persecutions. He died in 1642, the year in which Newton
was born.

The invention of logarithms, by Baron Napier, requires to be noticed for
its importance to practical astronomy, and the laborious observatiions of
Hevelius deserve also to be mentioned with commendation. The discoveries
of the form of the ring of Saturn, and of one of his satellites, by Huygens,
and of four more, together with the belts and rotation of Jupiter, by Dominic
Cassini, were among the early improvements derived from the introduction
of the telescope. But, without dwelling on any of these subjects, we hasten
to the establishment of the system of gravitation, which has immortalised
the name of Newton, and done unrivalled honour to the country that gave
him birth.

The mutual attraction of all matter seems to have been suspected by the
Epicureans, but Lucretius never speaks of it in such terms as are sufficient
to convey by any means a distinct idea of a reciprocal force. Gregory, ia
tlie preface of his Astronomy, has endeavoured to prove that Pythagoras must
have been acquainted even with the law of the decrease of gravitation; and
Lalande appears to assent to his arguments; but they rest only on the bare
possibility that Pythagoras might have deduced an analogy from the tension of
chords, which we have no reason to suppose that he even completely understood :
and this merely because he fancifully imagined, that there was a correspon-
dence between the planets and the strings of a lyre. But the nature of gra-
vitation had long been in some measure suspected ; Plutarch had asserted that
the moon is retained by it in her orbit, like a stone in a sling; and Bacon,
Copernicus, Kepler, Fermat, and Roberval were aware of its efficacy.
Bacon, in his Novum organum, calls the tkscent of heavy bodies the motion

©N THE BTSTORT OF ASTRONOMY. 599

of '' general congregation", and attributes the tiJcs to the attraction of the
moon. Kepler mentions also the perfect reciprocality of the action of gravita-
tion, and considers the lunar irregularities as produced by the attraction of the
sun. But our most ingenious countryman, Dr. Hooke, was still more decided
in attributing the revolutions of the planets to the combination of a pro-
jectile motion with a centripetal force ; he expresses his sentiments on thd
subject very clearly in his Attempt to prove the motion of the earth, pub-
lished in J 674, and had his skill in mathematics been equal to his practical
sagacity, he would probably have completed, or at least have published,
the discovery before his great cotemporary.

It must be confessed that Newton's good fortune was equal to his talents
and his application ; for had he lived earlier, he might probably have Cott-
fined his genius to speculations purely mathematical; had he beeii later,
his discoveries in natural philosophy might have been anticipated by others;
and yet Newton would perhaps have improved still more on their labours than
they have done on his. It was in I676, when he was 34 years old, that he first
demonstrated the necessary connexion of the planetary revolutions in elliptic
orbits, with an attractive force varying inversely as the square of the distance.
But he had collected the law of the force, from the discoveries of Kepler respect-
ing the periods of the different planets, some time before 1(571, as he asserts to
Dr. Halley, and, to the best of his recollection, about 1668, although in his
Principiahe allows, with the most laudable candour, to Wren, Hooke, and Halley,
the merit of having made the same discovery, without any connexion with each
other's investigations, or with his own. The manner, in which Newton was
led to attend particularly to the subject, is thus related by Pemberton, in the
preface to' his View of Sir Isaac Newton's philosophy.

" The first thoughts," says Pemberton, " which gave rise to his Principia,
he had, when he retired from Cambridge in 1666, on account of the plague.
As he sat alone in a garden, he fell into a speculation on the power of gra-
vity: that as this power is not found sensibly diminished at the remotest
distance from the centre of the earth, to which we can rise, neither at the
tops of the loftiest buildings, nor even on the summits of the highest
mountains; it appeared to him reasonable to conclude, that this power must
extend much further than was usually thought; why not as high as the moon ?

600 LECTURE XLVIII.

said he to himself; and if so, her motion must be influenced by it; perhaps
she is retained in her orbit thereby. However, though the power of gravity
is not sensibly weakened in the little change of distance, at which Ave can
place ourselves from the centre of the earth; yet it is very possible that so
high as the moon this power may differ much in strength from what it is
here. To make an estimate, what might be the degree of this diminution,
he considered with himself, that if the moon be retained in her orbit by the
force of gravity, no doubt the primary planets are carried round the sun by
the like power. And by comparing the periods of the several planets with
their distances from the sun, he found, that if any power like gravity held
them in their courses, its strength must decrease in the duplicate proportion

- of the increase of distance. Tliis he concluded by supposing them to move
in perfect circles concentrical to the sun, from which the orbits of the great-

• est part of them do not much differ. Supposing, therefore, the power of
gravity, when extended to the moon, to decrease in the same manner, he
computed whether that force would be sufficient to keep the moon in her
orbit. In this computation, being absent from books, he took the common
estimate in use among geographers and our seamen, before Norwood had
measured the earth, that 60 English miles were contained in one degree of
latitude on the surface of the earth. But as this is a very faulty supposition,
each degree containing about 69^ of our miles, his computation did not
answer expectation; whence he concluded tliat some other cause must at least
join with the action of the power of gravity on the moon. On this account
he laid aside for that time any further thoughts upon this matter. But some
years after, a letter, which he received from Dr. Hooke, put him on inquiring
what was the real figure, in which a body let fall from any high place
descends, taking the motion of the earth I'ound its axis into consideration.
Such a body, having the same motion, which by the revolution of the earth
the place has from whence it falls, is to be considered as projected forwards,
and at the same time drawn down to the centre of the earth. This gave
occasion to his resuming his former thoughts concerning the moon; and
Picart, iu France, having lately measured the earth, by using his measures, the
moon appeared to be kept in her orbit purely by the power of gravity ; and
consequently, that this power decreases as you recede from the centre of the
tarth, in the manner our author had formerly conjectured. Upon this prin-
ciple he found the line described by a falling body to be an ellipsis, the centre

ON THE HISTORY OF ASTRONOMY. " 601

of the earth being one focus. And tlie primary planets moving in such
orbits round the sun, he had the satisfaction to see, that this inquiry, which
he had undertaken merely out of curiosity, could be applied to the greatest
purposes. Hereupon he composed near a dozen propositions relating to the
motion of the primary planets about the sun. Several years after this, some
discourse he had with Dr. Halley, who at Cambridge made him a visit,
engaged Sir Isaac Newton to resume again the consideration of this subject;
and gave occasion to his writing the treatise which he published under the
title of Mathematical principles of natural philosophy. This treatise, full of
such variety of profound inventions, was composed by him, from scarce any
other materials than the few propositions before mentioned, in the space of
one year and a half."

The astronomers of Great Britain have not been less diligent in the practi-
cal, than successful in the theoretical part of the science. The foundation of
the observatory at Greenwich was laid in 1675, some years before the com-
pletion and publication of the discoveries of Newton. It is with the erection
of this edifice that the modern refinements in practical astronomy may be
said to have commenced; its immediate object was to assist in the perfection
of the science of navigation, and the series of observations, which have been
made in it/»has afforded an invaluable fund of materials to astronomers of
every country. A reward had been proposed, more than half a century
before, by Philip the Third, of Spain, for the discovery of a mode of determin-
ing the longitude of a ship at sea; and the states of Holland had followed
his example: a large reward was also offered by the French government in
the minority of Louis the Fifteenth. In 1674,. Mr. St. Pierre, a Frenchman,
had undertaken to determine the longitude of a place from observations of
the moon's altitude, and King Charles the Second had been induced to
appoint a commission to examine his proposq.ls. Mr. Flamsteed was con-
sulted by the commissioners, and was added to their number: he showed the
disadvantages of the method proposed by I\Ir. St. Pierre, and the inaccuracy
of the existing tables of the lunar motions, as well as of the catalogues of the
places of the stars, but expressed his opinion, that, if the tables were improved,
it would be possible to determine the longitudes of places with suiScient ac-
curacy by lunar observations. The king, being informed of Flamsteed 's repre«

6&S ttcfttRt «inii.

scntations, is said to have replkd with earnestness, that he " ftiust have the
places of the stars anew observed, examined, and corrected, for the use of his sea-
men"; upon this Flamsteed was appointed Astronomer Royal, with a salary of
^100 a year, and it was proposed to have an observatory built either in Hyde
Park, or at Chelsea college; but, upon Sir Christopher Wren's recommendation^
the situation of Greenwich Park was preferred.

In the year 1714', the British Parliament offered .£20 01)0 for a determina-
tion of the longitude of a ship at sea, without an error of 30 miles, and a
smaller sum for a less accurate method, appointing at the same time a Board
of Longitmle for the examination of the methods which might be proposed.
Under this act several rewards were assigned, and in ] 77^^, it was superseded
by another, which offers .£5000 for the invention of any timekeeper, or other
method, capable of determining the longitude of a place within 1 degree,
and cflOOOO if within 30 miles ; and a reward of .=£'5000 to the author of any
lunar tables, which should be found within 15 seeonds of the truth; allowing
the Board also the power of granting smaller sums at their discretion. Time-
keepers are at present very commonly employed in the British navy, atid some
of them have been capable of determining the longitude within half a degree,
after having been two or three months at sea. The lUnar tables, which have
been employed for the Nautical Almanacs, are those of Professor Mayer,
who adopted the methods of calculation invented by Leonard Euler ; but
the tables of Mr. Burg, of Vienna, are still mo-re accurate, and are said to
be always within about ten seconds of the truth.

The progress of astronomy, since the death of Newton, in 1727, has been^
fully adequate to what its most sanguine votaries could have hoped. The
great discoveries of the aberration of the fixed stars, and of the nutation of
the earth's axis, were made by our countryman Bradley, with the assistance of
the instruments for which he was indebted to the delicate workmanship of
our artists. Among these the names of Bird, Short, Sisson, Graham, Dol-
lond, Harrison, and Ramsden have long been celebrated throughout Europe,
The geographical operations, which have been performed in every part of the
globe, have been chiefly conducted by the liberality of the French and English
governments, although other countries have not been deficient in taking

ON THX HMTORT OF ASTnONOMT. €03

their share of the labour. The observations of the transit of Venus were
twice made in the south seas by British navigators, whom the munificence of
our present sovereign enabled to undertake so arduous a voyage for this
express purpose; and we are indebted to the fund which was granted on the
occasion, as well as to the zeal of the Astronomer Royal, for the experiments
on the attraction of mounfeiins, which -wete instituted jifter their return. In
this country also. Dr. Herschel, besides many other important additions to
our astronomical knowledge, has discovered a primary planet, and eight
secondary ones, unknown before. The astronomers of Sicily and Germany
h&ve, however, the honaur of the first discovery of tlie three humbler mem-
bers of the solar system which have been last introduced to our acquaintance,
Ceres by Piazzi, Pallas by Gibers, and Juno by Harding: and the mathe-
maticians of France have excelled all their predecessors in the elaborate and
refined application of the theory of gravitation, to the investigation of the
Djost minute and intricate details of the celestial motions.

604

ON THE HISTORY OF ASTRONOMT.

CHRONOLOGY OF ASTRONOMERS.

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605

LECTURE XLIX.

ON THE ESSENTIAL PROPERTIES OF MATTER.

JL.UE objects, which have lately occcupied 6ur inquiries, are the most
sublime and magnificent tliat nature any where exhibits to us, and the con-
templation of them naturally excites, even in an uncultivated mind, an
admiration of their dignity and grandeur. But all magnitude is relativCj
and if we examine Avith more calm attention, 'we shall find still greater
scope for our investigation and curiosity, in the microscopic, than in the
telescopic world. Pliny has very justly observed, that nature no where
displays all her powers with greater activity, than in the minutest objects
perceptible to our senses ; and we may judge how wide a field of research the
corpuscular affections of matter aftbrd, from the comparatively small progress
that has hitherto been made in cultivating it. For while the motions of the
vast bodies, which roll through the heavens, have been completely subjected
to the most rigorous calculations, we know nothing, but from experience only,
of the analogies by which the minute actions of the particles of matter are
regulated. It is probable, however, that they all depend ultimately on the same
mechanical principles. We have seen, for example, that the widely extended
elevations and depressions of the ocean, which are raised by the attractive
powers of the two great luminaries, and cover at once a half of the globe," are
governed and combined according to the same laws, which determine the
motions of the smaller waves excited by different causes in a canal, the rapid
tremors of a medium transmitting sound, or the inconceivably diminutive
undulations which are capable of accounting for the phenomena of light, and
which must be exerted in spaces as much smaller than those of soundi as a
grain of sand is smaller than a mountain. Thus the annihilation of the effects
of the semidiurnal changes of the tide, and the preservation of the diurnal
change, in the harbour of Batsha, may be explained precisely in the same
manner as the reflection of red light from a transparent substance, of such a

VOL. I. 4 J"

606 ^ LECTURE XI.IX.

thickness, as to be capable of destroying a portion of violet light under the
same circumstances.

We are at present to descend from the affections of the large masses of matter,
which fonn the great features of the universe, to the particular properties of
the matter which constitutes them, as far as they are common to all matter
in general; but those properties which are peculiar to certain kinds of matter
only, being the subjects of chemical science, are not to be included In the
discussion. If we are asked for a definition of matter, it will be somewhat
difficult to avoid all circuitous expressions. We may make gravitation a test of
matter, but then we must say, that whatever is attracted by other matter, is
also to be denominated matter, and this supposes the subject of our definition
already known; besides that tiie property of attraction may also possibly
belong to substances not simply material ; for the electrical fluid, if such a
fluid exists, is probably attracted by matter, and yet it seems to be different
in most respects from any modification of common matter. A similar diffi-
culty would occur if we attempted to define matter by its impenetrability or
mutual repulsion, or if we considered every thing as material that is capable
of aftecting the senses. We must, therefore, take it for granted that matter
is known without a definition, and we may describe it as a substance occupy-
ing space, or as a gravitating or ponderable substance.

It cannot be positively determined whether matter is originally of one
kind, owing its different appearances only to the form and arrangement of
its parts; or whether there are various kinds of simple matter, essentially
distinct from each other ; but the probability appears to be in favour of the
former supposition. However this may be, the properties of matter are by
no means so simple in their nature, nor so easily reducible to general laws, as
the more mathematical doctrines of space and motion ; and since our know-
ledge of them depends more on experience than on abstract principles, they
may properly be considered as belonging to particular physics. We have found
no inconvenience from the omission of the doctrine of matter as apart of
the subject of mechanics ; although, in treating of the streugth of materials,
as subservient to practical mechanics, it was necessary to consider the effit^cts
of some of these properties as deduced from experiment; but it will appear
that it was impossible to examine their origin and mutual connexion, without

'2

ON THE ESSENTIAL PROPERTIES OF MATTER. 60/

supposing a previous knowledge of many other departments of natural phi-
losophy.

We may distinguish the general properties of matter into two principal
classes, those which appear to be inseparable from its constitution, and those
which are. only accidental, or which are not always attached to matter of
all kinds. The essential properties are chiefly extension and divisibility,
density, repulsion, or impenetrability, inertia, and gravitation ; the acci-
dental properties are in great measure dependent on cohesion, as liquidity,
solidity, symmetry of arrangement, cohesive elasticity, stiffness, toughness,
strength, and resilience.

The extension of matter can scarcely be considered as a property separate
from its impenetrability, unless we conceive that it can occupy space, without
excluding other bodies from it. This opinion has indeed been maintained
by some philosophers, who hav^e imagined that the minute particles which
they suppose to constitute light, may penetrate the ultimate atoms of other
matter without annihilating or displacing them; and if this hypothesis were
admitted, it would be necessary to consider each particle of matter as a sphere
of repulsion, extended without being impenetrable.

The divisibility 6f matter is great beyond the power of imagination, bat
wc have no reason for asserting that it is infinite; for the demonstrations,
which have sometimes been adduced in favour of this opinion, are obviously
applicable to space only. The infinite divisibility of space seems to be essen-
tial to the conception that we have of its natur^; and it may be strictly de-
monstrated, that it is mathematically possible, to draw an infinite number of
circles between any given circle and its tangent, none of which shall touch
either of them, except at the general point of contact; and that a ship, following
always the same oblique course with respect to the meridian, for example, sailing
north eastwards, would continue perpetually to approach the pole without
ever completely reaching it. But when Ave inquire into the truth of the
old maxim of the schools, that all matter is infinitely divisible, we are by no
means able to decide so positively. Newton observes, that it is doubtful
whether any human means may be sufficient to separate the particles of mat-
ter beyond a certain limit; and it is not impossible that there may be some.

608 LECTURE XLIX.

constitution of atoms, or single corpuscles, on which tbeir properties, as
matter, depend, and which would be destroyed if the units were further
divided; but it appears to be niOre probable that there are no such atoms;
and even if there are, it is ahnost certain that matter is never thus annilii-
lated in the common course of nature.

It remains to be examined how far we have any experience of the actual extent
of the divisibility of matter; and we shall find no appearance of any thing like
a limit to this property. The smallest spherical object, visible to a good eye, is
about vo'oo- of an inch in diameter; by the assistance of a microscope, we may
perhaps distinguish a body one hundredth part as large, or^-^^'-o-^-o of aninch
in diameter. The thickness of gold leaf is less than this, and the gilding of
lace is still thinner, probably in some cases not above one ten millionth of an
inch ; so that -^-^^ of a grain would cover a square inch, and a portion, barely
large enough to be visible by a microscope, might weigh only the 80 million
millionth part of a grain. A grain of musk is said to be divisible into 320
quadrillions of parts, each of which is capable of affecting the olfactory
nerves. There are even living beings, visible to the microscope, of which a
million million would not make up the bulk of a common grain of sand.
But it is still more remarkable, that, as far as we can discover, many of
these animalcules are as complicated in their structure as an elephant or a
whale. It is true that the physiology of the various Classes of animals is
somewhat more sinlplc as they deviate more from the form of quadrupeds,
and from that of the human sjjecies ; the solid particles of the blood do not
by any means vary in their magnitude in the same ratio with the bulk of the
animal; and some of the lower classes appear to approximate very much to
the nature of the vegetable world. But there are single instances that seem
wholly to destroy this gradation : Lyonnet has discovered a far greater variety
of parts in the caterpillar of the willow butterfly, than we can observe in many
animals of the largest dimensions ; and amofig the microscopic insects in par-
ticular, we see a prodigality of machinery, subservient to the various purposes
of the contracted life of the little animal, in the structure of which nature ap-
pears to be ostentatious of her power of giving perfection to her minutest works.

If Newton's opinion, respecting the origin of the colours of natural bodies
III general, were suificieutly established, it would afford us a limit to the dl-

ON Tin ESSENTIAL PROPERTIES OT MATTER. 609

visibility of matter with respect to coloured substances; for the colours of
thin transparent substances, which he considers as resembling those of most
other substances, are no longer observable, in any known medium, when the
thickness is less than about -ro-s-'o^-s- of an inch. But we have positive evi-
dence that coloured substances may be reduced to dimensions far below this
limit; besides the instance of the gilt wire, which has already been mentioned,
a particle of carmine may still retain its colour, when its thickness is no more
than one thirty milliontli of an inch, or one sixtieth part of the limit deduced
from the supposition of Newton ; and it is tlierefore scarcely possible that the
colours of such substances can precisely resemble those of thin plates, although
they may perhaps still be in some measure analogous to them.

Impenetrability is usually attributed to matter, from the common observa-
tion that two bodies cannot occupy the same place at once. And it is thus
that we distinguish matter from space; for example, when we dip an in-
verted jar into mercury, the air contained in the jar depresses the surface of
the mercury, and prevents its occupying the space within the jar: but if the
jar had been void of matter, like the space above the mercury of a barometer,
nothing would have prevented its being filled by the mercury, as soon as
either its weight, or the pressure of the atmosphere, urged it to enter
the jar.

But it does not appear that our senses are fully competent to extend this
proposition to all substances, whether material or not. We cannot prove
experimentally that the influence of gravitation; is incapable of pervading even
the ultimate particles of solid ,matter, for this power appears to suffer no di-
minution nor modification, when a third body is interposed between the two
gravitating masses. In the same manner, a magnet operates as rapidly on a
needle, through a plate of glass or of gold, whatever its thickness may be, as
if a vacuum only intervened. It may, however, be inquired if the gold or
the glass has riot certain passages or pores, through which the influence may
be transmitted : and it may be shown, in many instances, that substances, ap-
parently solid, have abundant orifices into which other substances may enter ;
thus mercury may easily be made to pass through leather, or through wood,
by the pressure of the atmosphere, or by any other equal foxce : and, how-
ever great we may suppose the proportion of the pores to the solid matter, it

I
did tECtURE XLfX. * - .

may be observed, that it requires only a more or less minute division of the
matter, to reduce the magnitude of the interstices between the neighbouring
particles within any given dimensions. Thus platina contains, in a cubic
inch, above 200 thousand times as many gravitating atoms as pure hydrogen
gas, yet both of these mediums are free from sensible interstices, and appear
to be equally continuous; and there may possibly be other substances in na-
ture that contain in a given space 'iOO thousand times as many atoms as pla-
tina; although this supposition is not positively probable in all its extent;
for the earth is the densest of any of the celestial bodies with which we arc
fully acquainted, and the earth is only one fourth as dense as if it were com-
posed entirely of platina ; so that we have no reason to believe that there
exists in the solar system any considerable quantity of a substance even so
dense as platina.

Besides this porosity, there is still room for the supposition, that even the
ultimate particles of matter may be permeable to the causes of attractions of
various kinds, especially if those causes are immaterial: nor is there any
thing in the unprejudiced study of physical philosophy that can induce us to
doubt the existence of immaterial substances; on the contrary we see ana-
logies that lead us almost directly to such an opinion. The electrical fluid
is supposed to be essentially different from common matter; the general me-
dium of light and heat, according to some, or the principle of caloric, ac-
cording to others, is equally distinct from it. We see forms of matter dif-
fering in subtility and mobility, under the names of solids, liquids, and
gases; above these are the semimal:erial existences which produce the pheno-
mena of electricity and magnetism, and either caloric or a universal ether;
higher still perhaps are the causes af gravitation, and the immediate agents
in attractions of all kinds, which exhibit some phenomena apparently still
more remote from all that is compatible with material bodies ; and of these
diiferent orders of beings, the more refined and immaterial appear to pervade
freely the grosser. It seems therefore natiKal to believe that the analogy
may be continued still further, until it rises into existences absolutely im-
material and spiritual. We know not but that thousands of spiritual worlds
may exist unseen for ever by human eyes; nor have we any reason to sup-
pose that even the presence of matter, in a given spot,* necessarily excludes
these existences from it. Those who maintain tlmt nature always teems with

ON THE ESSENTIAL PROPERTIES OF MATTER. 6ll

life, wherever living beings can be placed, may therefore speculate with free-
dom on the possibility of independent worlds ; some existing in different parts
of space, others pervading each other., unseen and unknown, in the same
space, and others again to which space may not be a necessary mode of
existence.

Whatever opinion we may entertain with respect to the ultimate impene-
trability of matter inthis sense, it is probable that the. particles of matter are
absolutely impenetrable to each other. This impenetrability is not however
commonly called into effect in cases of apparent contact. If the particles of
matter constituting water, and steam, or any other gas, are of the same na-
ture, those of the gas cannot be in perfect contact; and when water is con-
tracted by the effect of cold, or when two flukls have their joint bulk di-
minished by mixture, as in the case of alcohol, or sulfuric aciti, and water,
the particles cannot have been in absolute contact before, although they
would have resisted with great force any attempt to compress them. JNIetals
too, of all kinds, which have been melted, become permanently more dense
when they are hammered and laminated. A still more striking and elegant
illustration of the nature of repulsive force is exhibited in the contact of two
pieces of polished glass* Th^ colours of thin plates afford us, by comparison
with the observations of Newton, the most delicate micrometer that can be
desired, for measuring any distances less than the ten thousandth of an inch:
it was remarked by Newton himself, that when two plates of glass are within
about this distance of each other, or somewhat nearer, they support each
other's weight in the same manner as if they were in actual contact, and
that some additional force is required, in order to make them approach still
nearer ; nor does it appear probable that th^; contact is ever perfect, other-
wise they might be expected to cohere in such a manner as to become one
mass. Professor Robison has ascertained by experiment the force necessary
to produce the greatest possible degree of contact, and finds it equivalent to
a pressure of about a thousand pounds for every square inch of glass. It is
therefore obvioua that in all common cases of the contact of two distinct
bodies, it n)ust be this repulsive force that retains them in their situation.
I have found that glass,placed on a surface of metal, exhibits this force nearly
in the same degree as if placed on another piece of glass ; it is also inde-
pendent of the presence of air; but under water, it disappears..

612 tECTUBE XLIX.

The existence of a repulsive force, extending beyond the actual surface
of a material substance, being proved, it has been conjectured by some that
such a force, unconnected with any central atom, may be sufficient for pro-
ducing all the phenomena of matter. This representation may be admitted
without much difficulty, provided that it be allowed that the force becomes
infinite at or near the centre; but it has been sometimes supposed that it is
every where less than infinite, and conse(iuently that matter is not abso-
lutely impenetrable; such a supposition appears however to lead to the ne-
cessity of believing that the particles of matter must sometimes be annihilated,
which is not a very probable opinion.

The magnitude of the repulsive force, by which the particles of any single
body are enabled to resist d^mpression, increases nearly in proportion to the
degree of compression, or to the decrease of the distances between the part-
icles. This is almost a necessary consequence of any primary law that
can be imagined, for the immediate actions of the particles: for instance, if
the repulsion increased either as the square or as the cube of the distance di-
minished, the effect of a double change of dimensions would ahvaj's be
nearly a double chaage of the repulsive force; that is, if an elastic substance
were compressed one thousandth part of its bulk, it would in either case re-
sist twice as much as if it were only compressed one two thousandth.

It is obvious that if the particles of matter are possessed of a repulsive
force decreasing in any regular proportion Avith the increase of distance,
they can never remain at rest without the operation of some external pres-
sure, but will always retain a tendency to expand. This is the case of all
elastic fluids, the density of which is found to vary exactly as the compress-
ing force, whence it may be demonstrated, that the primary repulsive force
of the particles must increase in the same proportion as the distance de-
- creases. It follows also that this force can only be exerted between such
particles as are cither actually or very nearly in contact with each other;
since it requires no greater pressure, acting on a given surface, to retain a
gallon of air in the space of half a gallon, than to retain a pint in the space
of half a pint; which could not be, if the particles exercised a mutual re-
pulsion at all possible distances.

ON THE ESSENTIAL PROPERTIES OF MATTER. 6l$

Mr. Dalton has proposed a singular theory respecting the constitution artd
mutual repulsion of elastic fluids; he imagines that when any two gases of
different kinds are mixed, the particles of each gas repel only the similar
particles of the same gas, without exerting any action on those of the other
gas, except when the ultimate solid atoms chance to interfere. The idea is
ingenious and original, and may perhaps be of use in connecting some facts
together, or in leading to some other less improbable suppositions; but it
may easily be shown, that Mr. Dalton's hypothesis cannot possibly be true
in all its extent, since it would follow from it, that two portions of gases, of
different kinds, could not exist, for a sensible time, in the same vessel, without
being uniformly diffused throughout it, while the fact is clearly otherwise ;
for hydrogen gas remains, when left completely at rest, a very considerable
time above, and carbonic acid gas below, a ffortion of common air with
which it is in contact; nor is there any circumstance, attending the mixture
of gases, which may not be explained without adopting so paradoxical an
opinion. Mr. Dalton thinks that, from the laws of hydrostatics, no two gases,
not chemically united, could remain mixed, if their particles acted mutually on
each other: but the laws of hydrostatics do not apply to the mixture of
single particles of fluids of different kinds; since they are only derived from
the supposition of a collection of particles of the same kind.

In liquids and m solids, this repulsive force appears at first sight to be want-
ing; but when we consider that the particles both of liquids and of solids are
actuated by the attractive force of cohesion, we shall see the necessity of the
presence of a repulsive force, in order to balance it ; it is, therefore, probable
that the particles of aeriform fluids still retain their original repulsive powers,
when they are reduced to a state of liquidity or of solidity, by being subjected
to the action of a second force, which causes them to cohere.

The mutual repulsion of the particles of matter is a reciprocal force, actino-
equally, in opposite directions, on each of the bodies concerned. It scarcely
requires either experiment or argument to show, that if two bodies repel each
other, neither of them will remain at rest, but both of them will move, with
equal quantities of motion. Thusj if a portion of condensed air be made to
act upon the bullet of an air gun, it will force the gun backwards with as
much momentum as it impels the bullet forwards.

VOL. I. 4g

6*14 LECTURE XLIX.

xinertia is that property of matter, by which it retains its state of rest" or
of uniform motion, with regard to a quiescent space, as long as no foreign
cause occurs to change that state. This property depends on the intimate
constitution of matter; it is generally exhibited by means of the force of
repulsion, which enables a body in motion to displace another, in order to
continue its motion, or by means of some attractive force, which causes two
bodies to approach their common centre of inertia with equal momenta.

Another universal property of matter is reciprocal gravitation, of which
the force is directly in the joint proportion of the quantities of matter attract-
ing each other, and inversely as the square of their distance. In order to
prove that the gravitation towards a given substance, for instance, the
weight of a body, or its gravitation towards the earth, is precisely in pro-
portion to the mass or inertia of the moveable matter of which it consists,
Sir Isaac Newton made two equal pendulums, with hollow balls of equal size :
in order that the resistance of the air might be the same with respect to both,
he placed successively within the balls a variety of different substances, and
found that the time of vibration remained always the same; whence he inferred
that the attraction was proportional in all cases to the quantity of matter
possessing inertia. For if any of these substances had contained particles,
capable of receiving and communicating motion, yet without being liable to
gravitation, they would have retarded the vibrations of the pendulum, by
adding to the quantity of matter to be moved, without increasing the moving
force. The law of gravitation, which indicates the rario of its increase with
the diminution of the distance, is principally deduced from astronomical
observations and computations: it is the simplest that can be conceived for
any influence, that either spreads from a centre, or converges towards a centre;
for it supposes the force acting on the same substance to be always propor-
tional to the angular space that it occupies.

Newton appears to have considered these laws of gravitation,, which he
first discovered, rather as derivative than as original properties of matter;
and although it has often been asserted that we gain nothing by referring
them to pressure or to impulse, yet it is undoubtedly advancing a step in the
explanation of natural phenomena, to lessen the number of general principles;
and if it were possible to refer either all attraction to a modification of re-

OK THE ESSENTIAL PROPERTIES OF MATTER. 6l5

pulsion, or all repulsion to a modification of attraction, we should make an
improvement of the same kind, as Newton made, when he reduced all the
diversified motions of the heavenly bodies to the universal laws of gravitat ion.
only. We have, however, at present, little prospect of such a simplifij
tion.

It has been of late very customary to consider all the phenomena of nature lp^^,, ''
as derived from the motions of the co rpuscles of matter, agitated by forces
varying according to certain intricate laws, which are supposed to be pri-
mary qualities, and for which it is a kind of sacrilege to attempt to assign
any ulterior cause. This theory was chiefly introduced by Boscovich, and it has
prevailed very widely among algebraical philcsoj.hers, who have been in the
habit of deducing all their quantities from each other by mathematical rela-
tions, making, for example, the force a certain function or power of the dis.
tance, and then imagining that its origin is sufficiently explained; and when
a geometrician has translated this language into his own, and converted th^
formula into a curve, with as many flexures and reflections as the labyrinth
of Daedalus, he imagines that he has depicted to the senses the whole pro-
cedure of nature. Such methods may often be of temporary advantage, as long
as we are contented to consider them as approximations, or as classifica-
tions of phenomena only; but the grand scheme of the universe must surely*
amidst all the stupendous diversity of parts, preserve a more dignified sim-
plicity of plan and of principles, than is compatible with these complicated
Suppositious.

" To show", says Newton, in the preface to the second edition of
his Optics, " that 1 do not take gravity for an essential property" of
bodies, I have added one question concerning its cause, choosing to
propose it by way of a question, because I am not yet satisfied about
it, for want of experiments." In the query here mentioned, he pro-
ceeds from the supposition of an elastic medium, pervading all space ;
a supposition, which he advances with considerable confidence, and which
he supports by very strong arguments, deduced as well from the phe-
nomena of light and heat, as from the analogy of the electrical and mag-
netic influences. This medium he supposes to be much rarer within the
dense bodies of the sun, the stars, the planets, and the comets, than in.

6\6 ~ LECTUIiE XLIX.

the empty celestial spaces between them, and to grow more and more dense
at greater distances from them, so that all these bodies are naturally forced
towards each other by the excess of pressure.

The effects of gravitation might be produced by a medium thus constituted,
if its particles were repelled by all material substances with a force decreasing,
like other repulsive forces, simply as the distances increase; its density would
then be every where such as to produce tlie appearance of an attraction vary-
ing like that of gravitation. Such an ethereal medium would therefore have
the advantage of simplicity, in the original law of its action, since the re-
pulsive force which is known to belong to all matter, would be sufficient,
when thus modified, to account for the principal phenomena of attraction.

It may be questioned whether a medium, capable of producing the effects of
gravitation in this manner, would also be equally susceptible of those modifi-
cations which we have supposed to be necessary for the transmission of light.
In either case it must be supposed to pass through the apparent substance
of all material bodies with the most perfect freedom, and there would, there-
fore, be no occasion to apprehend any difficulty from a retardation of the
celestial motions ; the ultimate impenetrable particles of matter being perhaps
scattered a? thinly through its external form, as the stars are scattered in a
nebula, which has still the distant appearance of a uniform light and of a con-
tinuous surface : and there seems no reason to doubt the possibility of the
propagation of an undulation through the Newtonian medium with the actual
velocity of light. It must be remembered that the difference of its pressure
is not to be estimated from the actual bulk of the earth or any other planet
alone, but from the effect of the sphere of repulsion of Avhich that planet is
the centre; and we may then deduce the force of gravitation from a medium
of no very enormous elasticity.

We shall hereafter find that a similar (pombination of a simple pressure with
a variable repulsion is also observable in the force of cohesion ; and suppos-
ing two particles of matter, floating in such an elastic medium, capable of pro-
ducing gravitation, to approach each other, their mutual attraction would at
once be changed from gravitation to cohesion, upon the exclusion of the
portion of the medium intervening between them. This supposition is.

Ojr THE ESSENTIAL PROPERTIES OF MATTER. 61/

however, directly opposite to that which assigns to the elastic medium the
power of passing freely through all the interstices of the ultimate atoms of
matter, since it could never pass between two atoms cohering in this manner;
we cannot therefore, at present, attempt to assert the identity of the forces of
gravitation and cohesion so strongly, as this theory would allow us to do, if
it could be established. In short, the whole of our inquiries, respecting the
intimate nature of forces of any kind, must be considered merely as specula-
tive amusements, which are of no further utility than as they make ovir views-
more general, and assist our experimental investigations.

618

LECTURE L.

ON COHESION.

Those properties of matter, which we have lately examined, if they are not
absolutely inseparable from its constitution, are, at least, always found attached
to such matter as we are able to submit to our experiments. There are, however,
many other general affections, to which all matter appears to be liable,
although none is perpetually subjected to them, and these are principally, if
not entirely, dependent on the force of cohesion.

In order that any two particles of matter may cohere, it is necessary that
they be within a very small distance of each other, and the density of any
substance, composed of cohesive particles, must probably always be more than
half as great as that of water. There are indeed some solids apparently a
little hghter than this, but they appear to be extremely porous; and perhaps
the solid substances of some of the celestial bodies may also be a Httle more
rare. It frequently happens, that the compression of an elastic fluid alone is
suflicient to cause the force of cohesion to take place between its particles;
thus, if common steam be exposed, in a close vessel, to a pressure greater
than that of the atmosphere, it will be wholly condensed into water, pro-
vided that no elevation of temperature be allowed ; and the same has been
experimentally shown of many other aeriform fluids, which may be reduced
to liquids by pressure; but others of these fluids retain their elasticity, not-
withstanding any force which human art can apply to them.

It is probable that as soon as the particles of any elastic fluid are brought
within the reach of the force of cohesion, it commences at once in its full
extent, so as to cause them to rush together, until it is balanced by that of
repulsion, which continually increases as the particles approach nearer to each
other; they must then remain, perhaps after some vibrations, in a state of

OV COHESION. ' 619

equilibrium; and if any cause should tend to separate them, or to bring them
nearer together, they would resist it, in either case, with a force proportional
to the degree of extension or compression. The distance, at which the force
of cohesion commences, is not the same for all kinds of matter, nor even for
the same substance at different temperatures; it is smaller for vapours of all
kinds, in proportion as their temperature is higher, the cohesion itself being
also smaller. If the experiments on the density of steam have been correct,
it follows that the force of repulsion must increase more rapidly than the
distances diminish, for the elasticity of water is nearly ten times as great as
that which would be inferred from the compression of steam into a substance
of equal density : this supposition agrees also with the eicperiments on the
mean density of the earth,- which is probably not so great as it would be if
the force of repulsion increased in the simple ratio of the density. The law
of repulsion appears also to l)e in some degree modified by the effect of heat,
which increases its force at greater distances more considerably than at smaller.
It appears indeed, from the diminution of the elasticity of a spring by heat-
ing it, that the repulsive force of the particles of bodies at very small dis-
tances is even diminished by heat, unless the force be again supposed to
decrease much more rapidly than the distance diminishes: thus the diminu-
tion of the elasticity of iron by heat is about thirty times as great as the increase
of the distance of its particles; so that the original repulsive force must
probably be somewhat diminished, although less tlian the cohesive force.
At greater distances, however, the force of repulsion is certainly increased ; for
the elasticity of vapours and gases of all kinds is evidently greater as the tem-
perature is higher. (Plate XXXIX. Fig. 530.)

The cohesion of two or more particles of matter to each other does not
interfere with their power of repelling other particles situated in a different
direction: thus, two pieces of glass require to be brought together with con-
siderable force, and generally with some friction, before they can begin to
cohere; and a small drop of water, falling lightly on the surface of a pond, may
remain for some instants without coming into perfect contact with it; the same
circumstance is also still more observable in spirit of wine a little warmed.

The first and simplest effect of cohesion is to produce liquidity. That
all liquids possess some cohesion, is very obvious, from their tendency to
assume a spherical form when they are sufhciently detached from other subr-

620 recTURE l.

stances, and from' the suspension of a drop from any solid, to which its upper
surface adheres with sufficient force. Without cohesion, indeed, a liquid
would be only a very fine powder, except that the particles of powders have
not the power of moving with perfect freedom on each other, which consti-
tutes fluidity. The apparent weakness of the cohesion of liquids is entirely
owing to tliis mobility, since their form may be clianged in any degree with-
out considerably increasing the distances of their particles, and it is only
under particular circumstances that the effects of their cohesion can become
sensible.

When a liquid is considered as unlimited in its extent, the repulsion of its
particles, situated in all possible directions with regard to each other, may
be supposed in all cases precisely to balance the cohesion, which is derived
from the actions of particles similarly situated; and this must also be the
state of the internal parts of every detached portion of a liquid, where they
are so remote from the surface as to be beyond the minute distance which is
the limit of the action of these forces. But the external parts of the drop
will not remain in the same kind of equilibrium: they may be considered as
a thin coating of a liquid surrounding a substance which resists only in a
direction perpendicular to its surface, and does not interfere with the mutual
actions of the particles of the liquid. Now since the repulsive force increases
as the distance diminishes, it must be exerted more powerfully by the nearest
particles, while the cohesion is directed equally towards all the particles within a
certain distance, and wherever the surface is curved, the joint cohesive force
Avill be directed to a remoter part of the curve than the repulsive force
opposed to it, so that each particle will be urged, by the combination of these
forces, towards the concave side of the curve, and the more as the curvature
is greater; hence the coating of the liquid, thus constituted,must exert a force
on the parts in contact with it, precisely similar to that of a flexible surface,
which is every where stretched by an equal force ; and from this simple prin-
ciple we may derive all the effects produced by a cohesion of this kind, which,
from its being most commonly observed in the ascent of water in capillary
tubes, has been denominated capillary attraction. (Plate XXXIX. Fig.
-531.)

It is, therefore, a general law, that the surface of every detached portion
of a fluid must every where have such a curvature, as to be able to withstand

ON COHESION. ^21

the hydrostatical pressure which acts against It; and hence we may calculate
in many cases the properties of the curve which it must form ; but in other cases
the exact calculation becomes extremely intricate, and perhaps impracticable.
A drop descending in a vacuum would be perfectly spherical; and if its mag-
nitude were inconsiderable, it would be of the same form when descending
through the air; a small bubble rising in a hquid must also be spherical; but
where the drop or the bubble is larger, its curvature will be greatest where
the internal pressure is greatest, or where the external pressure is least, and
in different cases this pressure may be differently distributed. Where a drop
is suspended from a solid, its length may be such that the pressure at its
upper part may become negative, and its surface will then be concave instead
of convex: and when a bubble rises to the surface of a liquid, it often carries
with it a film of the liquid, of which the weight is probably smaller than the con-
tractile force with which the surface resists the escape of the air, so that, from
the magnitude of the contractile force, we may determine the greatest possible
weight of a bubble of given dimensions. A slight imperfection of fluidity
probably favours the formation of detached bubbles, by retarding the ascent
of the air, but it has a still greater effect in prolonging their duration when
formed. (Plate XXXIX. Fig. 532.)

In order to determine the forms of the surfaces of liquids in the cases which most
commonly occur, it is necessary to examine how they are aflfected by the action of
other liquids, and of solids of different descriptions. Supposing the horizontal sur-
face of a liquid to be in contact with a vertical plane surface of a solid of half the
attractive power, it will remain at rest in consequence of the equilibrium of at-
tractions; for the particles situated exactly at the junction of the surfaces may be
considered as actuated by three forces ; one deduced from the effect of the liquid,
the other two from that of the two equal portions of the solid above and below the
surface of the fluid; and itmaybe shown that the combination of thesethree forces
will produce a joint result in the direction of gravity; consequently the direction
of the surface must remain the same as when it is subjected to the force of gravity
alone, since the surface of every fluid at rest must be perpendicular to the joint
direction of all the forces acting on it. But if the attractive power of the solid
be more than half as great as that of the liquid, the result of the forces will be
inclined towards the solid, and the surface of the liquid, in order to be per-
pendicular to it, must be more elevated at the side of the vessel than else-

VOL. I. 4 H

62f lECTURE L.

where, and therefore concave; consequently the fluid,, mu,st ascend until, a[^
arrives at a position capabb v4 aftording an equilibrium i,u this manner: if^
on the contrary, the attractu-e power of the solid be wealter, the- liquid will
descend, and its surface will be convex. (Plate;XX^IX. Fig. S32.)

■ if . -■'■.
It may also be shown, that if the attractive power of, the solid be equal to
that of the liquid, or still greater, it will be wetted by the liquid, which will
rise until its surface acquires the same direction with that of the solid; and
in other cases the angle of contact will be greater in proportion as the solid
is less attractive. These conclusions are obtained by comparing the jconunon
surface of the liquid and solid with the surface of a single liquid, of which
the attractive power is equal only to the difference of th^, respective powers of
the substances concerned; and the comparison is equally applicable to the
contact of two liquids of different densities.

The magnitude of the superficial cohesion or contractility of a liquid may
be expressed, for a certain extent, by a certain weight; thus every inch of
the surface of water is stretched each way by a force equal to the weight
of the hundredth part of a cubic inch of water, or to two grains and a
half: and for each inch of the surface of mercury, the force is equi-
valent to 17 grains, which is the weight of -^-^ of a cubic, inch of. mer-
cury. Thus if a solid of any form, of which the surfaces are vertical,
and which is capable of being wetted by either of these fluids, be immersed
■into a reservoir containing it, the fluid will be elevated around it to such a
height, that 24: or 17 grains, for each inch of the circumference of the solid,,
will retnain above the general level of the reservoir, the surface assuming
nearly the same form as a very long and slender elastic rod, fixed horizontally
at one end, and bearing a large weight at the other. (Plate XXXIX. Fig.
534.)

The elevation of^ the summit of an extended surface of water, in contact
with the flat and upright surface of a solid which is wetted by it, is one ^
seventh of an inch: but when two such surfaces, for instance, two plates of
glass, are brought near to each other, the elevation of the water between them
must be greater than this, in order that each inch of the line of contact may
support its proper weight : thus, if the distance were one fiftieth of an inch,

O.N <:OHESI0N-. 6io

the elevatioi^ woukl he a whole inch; and if the distance were smaller than
this, ,tl>e. eleMatioQ would he greater in the same proportion ; so that when two
plates are placed in such a manner as to touch each other at one of their
upright edges, the outline of the water raised between them assumes the form
of a hyperbola. (Plate XXXIX. Fig. 535.)

The weight S'upportcd by the cohesion of the water in a tube may be de-
termin-e<l.,in a similar manner, from the extent of the circumference ; the height
being an inch in a, tul>e, one twenty fifth of an inch in diameter, or as much
greater as the diameter of the tube is smaller: and iii a tube wetted with
mercmy the height would be half as ;great. It is obvious that if the Ipwer
part of the tube be either contracted or dilated, the height of the fluid will
remain unaltered, while its weight may be varied without limit; for the
hydrostatical pressure on the surface isthe same, in both these cases, as if .the
diameter of the tube were equal throughout its length. (Plate XXXIX.
Fig. 536.)

The attractive force of glass, to misjcury is less than half as great as the
mutual attraction of the particles of mercury, and the surface of mercury in
a dense glass vessel becomes, therefore, convex and depressed ; the angle of
contact being about 140°, and the depression one 17th of an inch. Between
two .plates of glass, the depression of mercury is an inch when their distance
is ..j4t» and in a tube, when its diameter is-g^ of an inch. (Plate XXXIX.
Fig. 537, 538.)

A liquid may also adhere to a horizontal surface which is gradually raised
from it, until the hydrostatical pressure becomes sufficient to overpower the
cohesion of its superficial parts; the internal part of the fluid being usually
raised, not immediately by the force of cohesion, but by the pressure of the
atmosphere. The solid bears the whole weight of the liquid which is elevated
above the surface; and when the surface is perfectly wetted, this weight is
equal, at the moment of separation, to the hydrostatical pressure, or rather
suction, corresponding to the height ; but in other cases the weight may be
somewhat greater than the hydrostatical pressure on the surface of the
solid, on account of the elevation which surrounds the body, and which
is not compensated by the excavation immediately under it. A surface thus

624 LECTURE X.

'^^ raised from water will elevate it to the height of one fifth of an inch, and
will require a force of 504- grains for each square inch, in order to overcome
the apparent attraction of the water; and for mercury the utmost height is
about one seventh of an inch. (Plate XXXIX. Fig. 5S9, 540.)

A detached portion of a liquid may stand on any surface, which it is not
capable of wetting, at a height which is different according to its magnitude,
and to the attraction of the surface. If the drop is very small, its form may
be nearly spherical; but when its extent becomes considerable, its height
must always be less than that at which the liquid would separate from a hori-
zontal surface; and it will approach the nearer to this limit, as its attraction
to the surface on which it stands is weaker. Thus a wide portion of mercury
stands on glass at the height of ^^ of an inch, and on paper nearly at -f;
and a portion of water will stand on a cabbage leaf, or on a table strewed
with the seeds of lycopodium, nearly at the height of one fifth of an inch.
(Plate XXXIX. Fig. 541.)

For the operation of a powder like lycopodium, it appears to be only necessary,
that it should possess a weaker power of attraction than water, and should,
therefore, be incapable of being readily wetted by it: each particle of the
powder, being then but partially in contact with the water, will project
beyond its surface, and prevent its coming into contact with any of the
surrounding bodies, while the surface assumes such a curvature as is suffi-
cient to withstand the pressure of the internal parts. (Plate XXXIX. Fig.
542.)

When a dry and light substance of any kind is placed on the surface of
water, its weight is not sufficient to bring it within the distance at which
cohesion commences, and it floats, surrounded by a slight depression. Any
substance of this kind, or any other substance surrounded by a depression^
as a ball of glass or iron floating on mercury, appears to be attracted by another
similar substance in its neighbourhood; for the depression between the Iwo
substances is increased,and the pressure of the fluid on that side is consequently
lessened, so that they are urged together, by a force which varies inversely
as the square of the distance. And in the same manner, when two bodies,
surrounded by an elevation, approach each other, they exhibit an attractive

ON COHESION. ' 625

force of a similar nature, the pressure of the atmosphere being diminished
by the weight of the water, which is raised between them to a greater height
than on the opposite sides. But when a body, surrounded by a depression,
approaches another, which is surrounded by an elevation, they seem to repel
each other, the pressure of the water urging the one, and that of the atmo-
sphere the other, in opposite directions. (Plate XXXIX. Fig. 543.)

If two smooth plates of any kind are perfectly wetted by a fluid, and
brought into contact, they exhibit an appearance of cohesion, which is so
much the greater as the quantity of fluid is smaller: if we attempt to separate
them, the fluid is drawn inwards, so as to have its surface made concave,
and it resists the separation of the plates with a certain force, which acts with
a hydrostatic advantage so much the greater, as their distance is smaller, and
hence produces the appearance of a cohesion varying in proportion to the
distance. (Plate XXXIX. Fig. 544.)

Supposing the two plates to be separated at one end, and the fluid between
them to assume the form of a drop, one of the marginal surfaces of the drop,
being narrower than the other, will act with a greater advantage, like a tube
of smaller diameter, and will tend to draw the drop towards it; and the ap-
parent attraction towards the line of contact of the glasses will increase in
proportion as the square of the distance decreases. This result was experi-
mentally observed almost a century ago, but it has been usually explained
on mistaken grounds. CPlate XXXIX. Fig. 545.)

The attractive power of water being greater than that of oils> a small
portion of oil thrown on water is caused to spread on it with great rapidity
by means of the force of cohesion; for it does not appear that airy want of
chemical affinity, between the substances concerned, diminishes their cohe-
sive power; water readily adheres to tallow when solid, and probably essen-
tial oils would adhere still more readily to ice. There is, however, some
difficulty in understanding how these oils can so suddenly come within the
limit of the cohesive force of water, while the drops of water themselves some-
times remain for a few seconds beyond it.

A sponge affords us a familiar instance of the application of capillary at-

#25 ]l:cctu!RE t,.

traction to usefiU puifroses: it is well known, that in order to its speetlj.
operatian, it Tequires to be previously moistened, by the .assistauce of a little
pressure, otherwirse it exhibits the same appearance of repulsion that is ob-
servable in many other cases where the contact is imperfect. The absorp-
tion of moisture hy sugar depends on the same principle, and .here the tuibes
are so minute, that the height of ascent appears to be almost unlimited.

The magiritude of the cohesion between flnids and solids, as well as of
the particles of fluids with each other, is more directly shown by an ex-
periment on the continuance of a column of mercury, in the tube of a
l)arometer, at a height considerably greater than that at which it usually
stands, on account of the pressure of the atmosphere. If the mercury has
been well boiled in the tube, it may be made to remain in contact with the
closed end, at the height of 70 inches or more; and by agitation only it may be
made to cohere so strongly, as to occupy the whole length of the tube of a
common barometer, which is several inches more than the height at which
the pressure of the atmosphere sustains it. A small siphon may also convey
mercury from one vessel into another in the vacuum of an air pump: and in
both these cases it is obvious that no other force than cohesion can retain
the upper surface of the mercury in contact with the glass, or its internal
parts in contact with each other.

The force of cohesion may also be exerted by solid substances on other
solids, either of the same kind, or of diiferent kinds. Thus two masses of
lead, when once united by pressure, assisted by a little friction, require a
very considerable force to separate them, and it may be shown either by
measuring this force, or by suspending the lead in the vacuum of the air-
pump, that the pressure of the atmosphere is not materially concerned in
producing this appearance of cohesion, since its magnitude much exceeds
that of the atmospherical pressure. A cohesion of this kind is sometimes of
practical utility in the arts ; little ornaments of laminated silver remaining
attached to iron or steel, with which they have been made to cohei'e by the
powerful pressure of a blow, so as to form one mass with it.

The contact of two pieces of lead, although intimate enough to produce a
considerable cohesion, is by no means so complete as to unite the parts into

ON COHESION. 627

que mass ; the unlou, however, appears to be nearly of the same kind as the
camniou cohesion of aggregation ; and if the lead were softened into an
amalgam by the addition of aiercury, the cohesion of the two masses would
liecome precisely the same as the internal cohesion of each mass. Harder
substances, such as marble or glass, cohere but weakly, . perhaps because,
their surfaces are never so perfectly adjusted to eacli pthex as to touch
throughout. The interposition of a fluid usually increases the apparent at-
traction of such substances, but this circumstance has already been explained
from the eifect of the capillary contraction of its surface; and when the
substances are wholly immersed in a fluid, the cohesion is little if at all in-
creased.

The immediate cause of solidity, as distinguished from liquidity, is the
lateral adhesion of the particles to each other, to which the degree of hard-
ness or solidity is always proportional. This adhesion prevents any change
of the relative situation of the particles, so that they cannot be withdrawn
from their places, without experiencing a considerable resistance from the
force of cohesion, while those of liquids may remain equally in contact
with the neighbouring particles, notwithstanding their change of form. When
a perfect solid is extended or compressed, the particles, being retained in
their situations by the force of lateral adhesion, can only ajjproach directly,
to each other, or be withdrawn further from each other, and the resist-
ance is nearly the same,as if the same substancc,in a fluid state, were inclosed
in an unalterable vessel, and forcibly compressed or dilated,- Thus the resist-
ance of ice to extension or compression is found by experiment to diifer
very, little from that of water contained in a vessel ; and the same effect may
be produced e\'en when the solidity is not the most perfect which the sub-
stance admits; for the immediate resistance of iron or steel to flexure is the
same whether it may be harder or softer. It often happens, however, that
the iiingnitude of the lateral adhesion is so much limited as to allow a greater
facility of extension or compression, and it may yet retain a pow er of restor-
ing the bodies to their original form by its reaction. This force may even be
the pitncipal or perhaps the only source of the body's elasticity: thus when
a piece of elastic gum is extended, the mean distance of its particles is not
materially increased, for it is said to become rather more than less dense
during its extension ; consequently the change of form is rather to be attributed
to a displacement of the particles, than to their separation to a greate*"

628 LECTURE L.

distance from each other, and the resistance must be derived from the lateral
adhesion only: some other substances also, approaching more nearly to the
nature of liquids, may be extended to many times their original length, with a
resistance continually increasing ; and in such cases there can scarcely be any
material change of the specific gravity of these substances. Professor Robison
has mentioned the juice of bryony as affording a remarkable instance of such
a viscidity.

It is probable that the immediate cause of the lateral adhesion of solids is
a symmetrical arrangement of their constituent parts: i^'is certain that
almost all bodies are disposed, in becoming solid, to^sume the form of
crystals, which evidently indicates the existence of pitch an arrangement ;
and all the hardest bodies in nature are of a crys^fline form. It appeaffe,
therefore, consistent both with reason and with Experience to supposS-ttfkf k
crystallization more or less perfect is the universal cause of soli{fftj|^,j„
may imagine that when the particles of matter ai^disposed without am
order, they can afford no strong resistance to a motion in any direction,!?
but when they are regularly placed in certain situations with respect to each
other, any change of form must, displace them in such a manner, as to increase
the distance of a whole rankat once; and hence they may be enabled to coope-
rate in resisting such a change. Any inequality of tension in a particular part
of a solid is also probably so far the cause of hardness, as it tends to increase
the strength of union of any part of a series of particles which must be dis-
placed by a cliange of form.

The immediate resistance of a solid to extension or compression is most
properly called its elasticity ; although this term has sometimes been used to
denote a facility of extension or compression, arising from the weakness of
this resistance. A practical mode of estimating the force of elasticity has
already been explained, and according to the simplest statement of the nature
of cohesion and repulsion, the weight of the modulus of elasticity is the
^ measure of the actual magnitude of each of these forces; and it follow? that
an additional pressure, equal to that of the modulus, would double the force of
cohesion, and require the particles to be reduced to half their distance in order
that the repulsion might balance it; and in the same manner an extending
force equal to the weight of half the modulus would leduce the force of cohe-
sion to one halfjand extend the substance to twice its dimensions. But, if, as

OV COHESlO'V. ' ^2^

there i*,softie reason to suppose, the mutual repulsion of the particles of
solids varies a little more vapidly than their distance, the modulus of elas-
ticity will be a little greater than the true measure of the whole cohesive and
repulsive force: this difference will not, however, affect the truth of our
calculations respecting the properties of elastic bodies, founded on the mag-
nitude of the modulus as already determined.

The stiffness of a solid is measured by its immediate resistance to any force
tending to change its form ; in this sense, if the force be applied so as to
extend or to compress it, or to overcome its lateral adhesion by the effect
which we have fonnerly called detrusion, the primitive elasticity and rigid-
ity of the substance, together with its magnitude, will determine its stiffness :
but if the force be otherwise applied, so as to produce flexure or torsion,
the form of the body must also be taken into the calculation, in the manner
which has already been explained in the lecture on passive strength. The
stiffness of a body with respect to any longitudinal force is directly as its
transverse section, and in\ersely as its length; for the same force will com-
press or extend a rod 100 yards long so as to change its length an inch,
that will produce a change of only half an inch in a rod 50 yards long. We
have seen that the space through which a body may be extended or com-
pressed, without any permanent alteration of form, constitutes its toughness:
that its strength, or the ultimate resistance which it affords, depends on the
joint magnitude of its toughness and elasticity or stiffness, and that ^its
resilience, or the power of overcoming the energy or impetus of a body in
motion, is proportional to the strength and toughness conjointly.

Softness, or want of solidity, is in general accompanied by a proportional
susceptibility of permanent alteration of form without fracture; sometimes,
however, from a want of cohesion, a soft body is at the same time brittle.
Soft substances which are capable of direct extension to a considerable degree
are called viscous or tenacious; of these, birdlime, sealing wax, and glass
sufficiently heated, are some of the most remarkable. Harder substances
which have the same property are called ductile, and when the alteration is
made by percussion and compression, they are termed malleable. Of all
substances gold is perhaps the most ductile; the thinness of leaf gol<[ and
of the gilding of silver wire has already been mentioned; and it is said that

VOL. I. 4 J

630 LECTURE L.

a single grain of gold has been drawn into a wire 500 yai'ds in length, and
consequently little more than-j-^Wof an inch in diameter. The ductility
or tenacity of a spider's web is of a different kind, it is particularly shown
by its capability of being twisted, almost without limit, and of accommodat-
ing itself to its new position without any effort to untwist.

With respect to the ultimate agent by which the effects of cohesion arc
produced, if it is allowable to seek for any other agent than a fundamental
property of matter, it has already been observed, that appearances extremely
similar might be derived from the pressure of a universal medium of great
elasticity; and we see some effects, so nearly resembling them, Avhich are
unquestionably produced by the pressure of the atmosphere, that one can
scarcely avoid suspecting that there must be some analogy in the causes.
Two plates of metal, which cohere enough to support each other in the
open air, will often separate in a vacuum.:; when a boy draws along a stone by a
piece of wet leather, the pressure of the atmosphere, appears to be materially
concerned. The well known experiment, of the two exhausted hemispheres
of Magdeburg, affords a still more striking instance of apparent cohesion
derived from atmospherical pressure; and if wq place betweea them ift. thick
ring of elastic gum, we may represent the natural equilibrium between the
forces of cohesion and of repulsion ; for the ring would resist any small
additional pressure with the same force as, would be required for separating
the hemis|»heres so far, as to allow it to, expand in an .equal degree: and at
a certain point the ring would expand no more; the air, would be admitted,
and the cohesion destroyed, in the same manner as when a solid of any
kind is torn asunder. But all suppositions founded on these analogies must
be considered as merely conjectural ; and our knowledge of every thing
which relates to the intimate constitution of matter, partly from the in-
tricacy of the subject, and partly for want of sufficient experiments, is at
present in a state of great uncertainty and imperfection. One of the most
powerful agents, in changing and modifying the forms of matter, is the
operation of heat, by which the states of solidity, liquidity, and elastic
fluidity are often produced in succession; and the investigation of the nature
and effects of heat will constitute the subject of the two next lectures.

631

LECTURE LL

ON THE SOURCES AND EFFECTS OF HEAT.

It may appear doubtful to some whether the subject of heat belongs most
properly to mechanical or to chemical philosophy. Its influence in chemistry
is unquestionable and indispensable; but its mechanical effects are no less
remarkable: it could not therefore with propriety be omitted either in a
course; of chemical or of physical lectures, especially by those who are per-
suaded that what we call heat is, in its intimate nature, rather a mecha-
nical affection of matter than a peculiar substance. We shall first inquire
into the nature of the principal sources of heat, and next into the mode of
its communication, and its most common effects, whether temporary or per-
manent: the measures of heat, and the most probable opinions respecting its
nature, will afterwards be separately considered.

Heat is an influence capable of affecting our nerves in general with the
pecvdiar sensation which bears its name, and of which the diminution produces
the sensation denominated cold. Any considerable increase of heat gives us
the idea of positive warmth or hotness, and its diminution excites the idea of
posiilve cold. Both these ideas are simple, and each of them might be de-
rived either from an increase or from a diminution of a positive quality: bdt
there are many reasons for supposing heat to be the positive quality, and cold
the diminution or absence of that quality; although we have no more expe-
rience of the total absence of heat, than of its greatest possible accumulation,
which might be called the total absence of cold. Our organs furnish us, in
some cases, with very delicate tests of any increase or diminution of heat;
but it is more usually recognised by the enlargement of bulk, generally pro-
duced in those bodies to which heat is attached in an increased quantity, and
the contraction of those from which it is subtracted.

632 LECTURE LI.

The simplest modes of exciting heat appear to be. the compression of elas-
tic fluids, and the collision or friction of solid bodies; although a more usual
and a more powerful source of heat is found in various chemical combinations
and decompositions, which are produced by the peculiar elective attractions
of different substances for each other, or from the influence of the solar rays,
which are probably emitted in consequence of the chemical processes that
continually take place at the surface of the sun. '«- :!.If J'

The effects of the condensation and rarefaction of elastic fluids are shown
by the cendenser and the air pump; Avhcn an exhaustion is made with rapid-
ity, the thermometer, placed in the receiver of the air pump, usually sinks a
degree or two; and when the air is readmitted abruptly into a partial va-
cuum, the sudden condensation of the rarefied air raises the mercury: and a
similar elevation of temperature is produced by the operation of the con-
denser. Much of this heat is soon dissipated, but by observing the velocity with
which the thermometer rises, Mr. Dalton has estimated that air, compressed
to half its dimensions, has its temperature elevated about 50 degrees of Fah-
renheit; and some of his experiments indicate, when accurately examined, a
still greater change. For the present we may define the sense of the term
degree, in Fahrenheit's scale, as corresponding to an expansion of a portion of
mercury amounting to one ten thousandth part of its bulk; and a degree of
Reaumur originally corresponded to an expansion of a weak spirit of wine,
amounting to one thousandth part of its bulk. It may be inferred from the
velocity of sound, supposing that the excess of its velocity, above the common
calculation, is wholly derived from the heat and cold produced by condensa-
tion and expansion, that a condensation amounting to ^rs- ^f fhe bulk of
any portion of air will raise its temperature one degree of Fahrenheit.
When air is very rapidly compressed in the condenser of an air gun, it is
sometimes so much heated as actually to set on fire a small portion of tow,
placed near the end of the barrel.

The production of heat by friction is too well known to require an experi-
mental proof; but Count Rumford has taken particular pains to ascertain
every circumstance which can be supposed to be concerned in the operation
of this cause; and the results of his experiments are so striking, that they de-

t ON THE SOURCES AND EFFECTS OF HEAT. 633

serve to be briefly related. He took a cannon, not yet bored, having a pro-
jection of two feet beyond its muzzle, a part M-^hich is usMally cast with the
piece, in order to insure the solidity of the metal throughout, by the pressure
which its weight occasions. This piece was reduced to the form of a cylin-
der, joined to the cannon by a smaller neck, and a large hole was bored in it:
the whole cannon was then made to revolve on its axis by means of the force
of horses, while a blunt steel borer was pressed against the bottom of the hol-
low cylinder, by a force equal to about 10 000 pounds avoirdupois; the sur-
face of contact of the borer with the bottom of the cylinder being about 2
square inches. This apparatus was wrapped up in flannel, when its temperature
was about 60°. In half an hour, when the cylinder had made i)()0 turns, the
horses being stopped, a mercurial thermometer was introduced into a perfora-
tion in the bottom of the cylinder, extending from the side to the axis, and
it stood at 130°, which Count Rumford considers as expressing very nearly
the mean temperature of the cylinder. The dust or scales, abraded by the
borer, weighed only 837 grains, or about -§4^ of the whole weight of ihe cy-
linder. In another experiment, the cylinder was surrounded by a tight deal box,
fitted with collars of leather, so as to allow it to revolve freely, and the in-
terval between the cylinder and the box was filled with 19 pounds of cold
water, which was excluded from the bore of the cylinder by oiled leathers
fixed on the borer; and after two hours and a half, the water was made to
boil. Hence Count Rumford calculates that the heat produced in this man-
ner, by the operation of friction, was equal to that of 9 wax candles, each
three quarters of an inch in diameter, continuing to burn for the same
time.

A still more rapid increase of temperature may be obtained, where the rela^
tive velocity of the bodies is more cotisiderable, or where they strike each
other with violence. Thus a soft nail may be so heated, by three or four
blows of a hammer, that we may light a match with it ; and by continuing
the operation, it may be made red hot: two pieces of wood may also be set
on fire by means of a lathe. When a waggon takes fire, for want of having
its wheels properly greased, the friction is probably increased by the tenacity
of the hardened tar, which perhaps becomes the more combustible as it
dries.

634 LECTURE LI.

One of the most remarkable circumstances, attending the production of
heat by friction, is the discovery of Professor Pictet, that it is often much
more powerfully excited by soft substances than by harder ones. . In making
some experiments in a vacuum, in order to examine how far the presence pf
air might be concerned in the effects of friction, he accidentally interposed
some cotton between the bulb of his thermometer and the cup^, which was sub-
jected to the friction of various substances as it revolved ; and he found that
the soft filaments of the cotton excited much mpre heat, than any other of tlie
substances employed.

The chemical productioii of heat is of greater practical importance^fhan its
mechanical excitation ; but by what means chemical changes operate in excit-
ing heat, we cannot attempt to determine. There is certainly no general law
of composition or decomposition that can be applied to all such cases: most
commonly heat is produced when oxygen exchanges an aeriform for a solid
state, or enters into a new combination, and still. remains elastic; but in the
case of gunpowder, heat is disengaged while an -elastic .fluid, is produced from
a solid; and in some other cases the oxygenous principle is wholly uncon-
cerned. It appears on the whole, that however heat may be excited, the corpus-
cular poAvers of cohesion and repulsion are always disturbed and called into
action, their equilibrium being destroyed and again restored, whether by me-
chanical or by chemical means. A wax candle, ^ of an inch in diameter, loses
a grain of its weight in 37 seconds, and consumes about three grains, or 9
cubic inches, of oxygen gas, producing heat enough to raise the temperature
of about 15 000 grains of water a single degree. .According to the experi-
ments of Mr. Lavoisier and Mr. Laplace, the combustion of ten grains of
phosphorus requires the consumption of 15 grains of oxygen, the combustion
of ten grains of charcoal 2C, and of hydrogen gas 56; and by the heat pro-
duced during the combustion of a pound of phosphorus, 100 pounds of ice
may be melted, during that of a pound of charcoal 96i, of hydrogen gas
^95^ of wax 133, and of olive oil 149; and during the deflagration of a
pound of nitre with about one sixth part of its weight of charcoal, twelve
pounds of ice may be melted.

The manner in which heat, when excited or extricated by any of these
means, passes from one body to another, requires to be very particularly exa-

OS THE SOURCES AND EFEECTS OF HEAT. 635

mined. We shall find that this communication happens in one of both of two
Avays, by contact, or by radiation; and that it may also differ both with re-
spect to the quantity of heat concerned, and to the time occupied by the pro-
cess. Whatever heat may be, we may safely conclude that in substances of
the same kind, at the sailie temperature or apparent degree of warmth or
coldness, its quantity must be proportional to tlae mass or weight; for instance,
that a quart of the water of a given cistern contains twice as much heat as a
pint; and where this is true of the different parts of any substance, they must
remain in equilibrium with respect to heat. But if two equal portions of the
same substance, containing different quantities of heat, be in contact, they will
affect each other in such a manner as to have their temperatures equalised,
and the more rapidly as the contact is more perfect. Thus, if two portions
of a fluid at different temperatures be mixed together, they will acquire imme-
diately an intermediate temperature; and when two solids are in contact, the
quantity of heat, communicated by the hotter to the colder in a given time, is
nearly proportional to the difference of the temperatures. Hence it would
follow, that they could never become precisely of the same temperature in
any finite time; but in fact the difference of temperature is rendered, in a mo-
derate time, too small to be perceptible. The nature of the substances con-
cerned has also a material effect on the velocity with which heat is commu-
nicated through their internal parts; metallic bodies in general conduct it
the most readily, earthy and vitreous bodies, the least; but the various metals
possess this power in different degrees; silver and copper conduct heat more
rapidly than iron, and platina transmits it but very slowly. Professor
Pictet supposes that heat ascends within solid bodies more readily than it de-
scends; but the effect of the air remaining in the imperfect vacuum of the
air pump may be sufficient to explain his experiments; the difference of terrt-
perature producing an ascending current in the neighbourhood of the heated
body, by means of which the cold air continually approaches its lower parts,
and carries the heat upwards: and it has been found that the rarefaction of air
does not by any means diminish its power of conducting heat, in proportion
to the diminution of its density.

Count Rumford's experiments have shown that all fluids are very imperfect
conductors of heat by immediate contact, although it is scarcely credible that
they can be absolutely nonconductors; but heat is usually communicated

636 ' LECTUBE LI.

between cliiFerent portions of the same fluid, almost entirely by the mixture
of their particles: hence a fluid heated on its surface transmits the lieat very
slowly downwards, since the parts which are first lieated, being rendered spe-
cifically lighter, retain their situation above the colder and heavier parts;
while, on the contrary, any cause of heat, applied at the bottom of a vessel,
very soon reduces all its contents to a uniform temperature. It appears also,
from some late experiments, that the immediate transmission of heat within
the internal parts of solids is much slower than has commonly been supposed;
and it has been found almost impossible to keep a thermometer, at the centre
of a large and solid globe of metal, at the same temperature with that of its
superficial parts.

Besides the communication of heat by contact, it is usually, if not always,
emitted from the surfaces of bodies in the form of radiant heat, which is
thrown off in all directions, wherever it meets no obstacle from a substance
impervious to it, and is propagated nearly in the same manner as light, and
probably with the same velocity, without producing any permanent effect on
the temperature of the medium transmitting it. Thus, a thermometer, sus-
pended by a fine thread under the receiver of an air pump, or in the Torricel-
lian vacuum, will continue to vary its temperature with that of the surround-
ing bodies: and in this case the whole of the heat must be communicated by
radiation. Mr. Leslie has discovered that the quantity of heat thus emitted
depends not only on the temperature, but also on the nature of the surface
concerned, a polished surface of tin emitting only -r^, or less than one
eighth part as much, as the same surface blackened. A surface of tin scraped
with a file in one direction has its powers of radiation more than doubled;
but by crossing the scratches, they are reduced nearly to their original state;
and a coating of isinglass, resin, or writing papers, or a glossy surface of any
kind, produces an eft'ect nearly approaching to that of black paint. This radia-
tion from a heated surface, like that of light, takes place in almost equal degrees
■in every direction; and its magnitude is nearly independent of the nature of
the fluid in contact with the surface, provided however that it be an elastic
fluid ; for water does not seem to transmit every kind of radiant heat with
freedom. It appears that the radiant heat emitted by a surface of glass, or of
black paint, is about one third greater than that which is at the same time
carried off by the atmospheric air; but that the radiation from a metallic sur-

ON THE S0URCE3 AND EFFECTS OF HEAT. 637

face is only one sixth of that which the air receives. Mr. Leshe has also
found that the same surfaces which emit heat the most freely, are also the
readiest to receive it from the radiation of other bodies.

The solar heat radiates freely through air, glass, water, ice, and many
other transparent mediums, without producing any sensible effect on their
temperatures, and even when it is concentrated by the effect of a burning
mirror, it scarcely affects the air through which it passes, and other transpa-
rent mediums but little. But the heat of a fire warms a piece of common
glass very rapidly, and its further progress is almost entirely interrupted by
the glass, although probably a certain portion still continues to accompany
the light in all cases. Hence a sci-een of glass is sometimes practically con-
venient for allowing us the sight of a fire, and protecting us at the same
time from its too great heat. Mr. Lambert showed that culinary heat was
much more strongly reflected by mirrors of metal than of glass, although lit-
tle diff'erence was observable in the quantity of light, and he very justly at-
tributed this difference to the interception of a part of the heat by the glass,
which operated with respect to it like an opaque substance, although it trans-
mitted the light with freedom. Opacjue substances in general appear to be
wholly impervious to radiating heat of all kinds; but Dr. Herschel has found
that dark red glass, which transmits a very small portion of light only, suffers
some kinds of radiant heat to pass through it with very little interruption.

In other respects, radiating heat is subject, in all cases, to the optical laws
which govern the reflection and refraction of light. Dr. Hoffmann appears
to have been the first that collected the invisible heat of a stove into a focus
by the reflection of one or more concave mirrors. Buff'on, Saussure, Pictet,
and Mr. King, made afterwards similar experiments on the heat of a plate of
iron and of a vessel of boiling water. Mr. Pictet, as well as Hoff^mann, em-
ployed two mirrors facing each other; and by means of this arrangement the
experiment may be performed when the thermometer is placed at a considera-
ble distance from the heated body.

The temperature of the air, not being affected by the radiation of heat, is
probably in all respects indifferent to its emission iir this manner; and as the
raj's of light cross each other freely in all possible directions, so it appears

VOL. I. 4 k

638 LECTURE LT.

that heat may flow in different directions through the same medium without
being interrupted; nor does there seem to be any more reason that a hot
body should cease to emit heat while it is receiving heat from anotlier body,
than that a luminous body should cease to afford light when another body
shines on it. This continual interchange of heat, constituting in common
cases a kind of equilibrium of motion, appears t ohave been first suggested by
Mr Provost, as an explanation of an experiment on the reflection of cold, re-
vived by Mr. Pictet, but originally made some centuries before, by Plempius,
and by the Academicians del Cimento. A thermometer, for example, must be
supposed to retain its temperature by means of the continual accession of ra-
diant heat from the surrounding bodies, supplying the place of that which is
continually thrown off in all directions towards those bodies. Supposing the
thermometer to be placed near the focus of a metallic speculum, not much less
than a hemisphere, about one half of the heat, which the thermometer would
otherwise have received from the surrounding bodies, must be intercepted by
the mirror, which, being metallic, emits itself but little radiant heat, but
reflects, notwithstanding, an equal quantity of heat from the objects on the
opposite side, so that the temperature of the thermometer remains unaltered.
But all the heat, which falls on the thermometer from the mirror, must have
passed through the conjugate or corresponding focus; and if a body at the
same temperature be placed in that focus, the radiation will still be the same:
but if a substance absolutely cold were placed there, the whole of the heat be-
fore reflected by the mirror would be intercepted, that is, almost half of that
which was received by the thermometer from the surrounding bodies; and if
a piece of ice be put in the conjugate focus, a delicate thermometer will in-
stantly show its effect in depressing the temperature ; as if the cold were ab-
solutely reflected in the same manner as heat or light.

Dr. Herschel's experiments have shown that radiant heat consists of various
parts, which are differently refrangible, and that in general, invisible heat is
less refrangible than light. This discovery must be allowed to be one of the
greatest that has been made since the days of Newton, although the theories
of some speculative philosophers might have led to it a few years earlier. Dr.
Herschel was occupied in determining the properties of various kinds of co-
loured glass, which rendered them more or less fit for enabling the eye to view
the sun through a telescope ; and for this purpose it was necessary to inquire

ON THE SOURCES AND EFFECTS OF HEAT. ' 639

which of the rays would furnish the greatest quantity of light, without sub-
jecting the eye to the inconvenience of unnecessary heat. He first observed
that the heat became more and more considerable as the thermometer ap-
proached the extreme red rays in the prismatic spectrum; and pursuing the
experiment, he found not only that the heat continued beyond the visible
spectrum, but that it was even more intense when the thermometer was at a
little distance without the limits of the spectrum, than in any point within
it. (Plate XXXIX. Fig. 546,547.)

Sir Henry Englefield has repeated these experiments with many additional
precautions, and Mr. Davy was a witness of their perfect accuracy: the excess
of heat beyond the spectrum was even considerable enough to be ascertained
by the sense of warmth occasioned by throwing it on the hand. The skin
appears, when compared' with a thermometer, to have its sensibility more
adapted to the perception of radiant heat than to that of heat imparted by
contact, perhaps because a much smaller quantity of heat is sufficient to raise
the temperature of the thin cuticle very considerably, than would be required
in order to affect any thermometer in the same degree.

It was first observed in Germany by Ritter, and soon afterwards in
England by Dr. Wollaston, that the muriate of silver is blackened by invisible
rays, which extend beyond the prismatic spectrum, on the violet side. It is
therefore probable that these black or invisible rays, the violet, blue, green,
perhaps the yellow, and the red rays of light, and the rays of invisible heat,
constitute seven different degrees of the same scale, distinguished from each
other into this limited number, not by natural divisions, but by their effects
on our senses: and we may also conclude that there is some similar relation
between heated and luminous bodies of different kinds.

The effects of heat, thus originating, and thus communicated, may be
divided into those which are temporary only, and those which are permanent.
The permanent effects are principally confined to solids, but the temporary
eitects are different with respect to substances in different states of aggrega-
tion, and they also frequently comprehend a change from one of these states
to another. The effect of heat on an elastic fluid is the simplest of all these,
being merely an expansion of about one five hundredth of its bulk for each
degree of Fahrenheit that the temperature is raised ; or an equivalent aug-

(5^40 tECTURE hi.

iTientation of the elastirfty when the fluid is confined to a certain space. This
expansion is very nearly the same for all gases and vapours, amounting to
^l^ for each degree, at the common temperature of 50° of Fahrenheit, but
at higher temperatures it is less than -j-^-o- of the bulk of the gas, and at lower
temperatures somewhat more, being nearly the same in quantity for the same
portion of the fluid at all temperatures.

When an elastic fluid is contracted by cold within certain limits, determined
by the degree of pressure to M'hich it is exposed, as well as by the nature of the
fluid, its particles become subjected to the force of cohesion ; they rush still
nearer together, and form a liquid. Thus, when steam, under the common
atmospheric pressure, is cooled below the heat of boiling water, it is instantly
condensed, and becomes water: but with a pressure of two atmospheres, it would
be condensed at a temperature 36° higher, and with the pressure of half our
atmosphere only, it might be cooled without condensation 33° lower than the
common temperature of boiling water. And similar effects take place in
vapours of other kinds at higher or lower temperatures, a double pressure pro-
ducing, in all cases an equal disposition to condensation, with a depression of
temperature of between 20 and 40 degrees, and most commonly of about 35°,
of Fahrenheit. Thus, the vapour of spirit of wine is usually condensed at
175° of Fahrenheit; but with a double pressure it is condensed at a temperature
39° higher; and with the pressure of half an atmosphere, at a temperature 35°
lower|; and the vapour of ether, which is commonly condensed at 10£°,
requires a temperature 38° higher, with a double pressure, or as much lower,
■with half the usual pressure. If the temperature be below the freezing point
of the liquid, the pressure being sufticiently lessened, the vapour may still
retain its elasticity, but a further reduction of temperature or increase of
pressure will convert it immediately into a solid.

The expansion of liquids by the eflfect of heat is much less uniform and
regular than that of elastic fluids, since it varies considerably, not only in
different liquids, but also in the same liquid at different temperatures, being
in general greater as the temperature is more elevated, and sometimes almost
in proportion to the excess of the temperature above a certain point, at which
it begins. This variation appears to be the least considerable in mercury,
although even this fluid expands a little more rapidly as it becomes more
heated ; but the expansion is always very nearly one ten thousandth for each

ON THE SOUnCJES AND EFPJECTS OF HEAT. 641

degree: that of water is equal to this at the temperature 6i°, and is greater
or less nearly in proportion to the distance from 39°, where it hegins, hut
in high temperatures it varies less, since it is not quite four times as great at
the heat of boiling water. The expansion of spirit of wine at 70° is six times
as great as that of mercury: its utmost variation is much less than that of
water, although it is at least twice as great in some parts of the scale as in
others.

It has already been observed that an elevation of temperature consider-
ably diminishes the powers of cohesion and of repulsion in solid bodies: the
same is also true of liquids; for the height to which a liquid rises in a capil-
lary tube is diminished somewhat less than -^o- for each degree of Fahren-
heit that the temperature is raised, the force of superficial cohesion being
diminished both by the diminution of the immediate actions of the particles,
and by that of the distances to which they extend.

When the temperature of a liquid is so much elevated as to become equal
to that of its vapour in a state capable of sustaining the atmospherical pres-
sure, or any other pressure which may be substituted for it, a certain por-
tion of the liquid is converted into vapour, and the heat being generally
applied at the bottom of the vessel, the vapour rises up in bubbles, and the
effect is called boiling. The whole liquid is not converted at once into
vapour, because a certain quantity of heat appears to be consumed by the
change, and a constant supply of heat is necessary, in order that the opera-
tion may be continued.

It is not, however, only at the boiling point that a fluid begins to be con-
verted into vapour: the pressure of the atmosphere is not sufficient wholly to
prevent the detachment of a certain quantity of vapour from its surface, at
a temperature which is incapable of supporting it separately in the form of
Steam in the open air, and it may be thus suspended, when mixed either with
common air, or with any other elastic fluid, at the ordinary temperature of the
atmosphere. And it appears that thet^uantity, which is thus suspended, bears
very nearly some constant proportion to the density of which the steam is
capable at the given temperature in a separate state, the interposition of the
air either not affecting the distance at which the cohesion would take place,

642 LECTURE Lr.

or altering it equally in all cases. It seems to be most probable that the
density of vapour, suspended in this manner in the atmosphere, is always
about twice as great, or at least half as great again, as that of steam existing
independently at the same temperature. There is .perhaps no liquid absolutely
free from a disposition to evaporate : even mercury rises in the vacuum of the
barometer, and lines the cavity with small globules; and it is said that the
effect of light is favourable to this slow evaporation. At whatever tempera-
ture evaporation takes place it is always accompanied by the production of
cold ; hence it is usual in warm climates, to em])loy various methods of pro-
moting evaporation, in order to lower the temperature of the air, to cool
liquids for drinking, or even to procure ice for domestic uses.

It appears that all aqueous fluids are contracted by cold, until we arrive at
a certain point, which is generally about 7 or 8 degrees higher than their
freezing point: they then expand agam almost in an equal degree as they
are still more cooled ; and provided that they be free from agitation, they may
remain liquid at a temperature considerably below the point, at which they
usually freeze, and at which their ice always melts. Water may be cooled
in this manner to about 10' of Fahrenheit, and if it be then agitated, or
especially if a small particle of ice or snow be thrown into it, a certain part
of it will instantly congeal, and its temperature will be raised at once
to 32°, in consequence of the heat which is always produced or extri-
cated in the act of freezing. In most cases, although not in all, the solid
occupies more space than the fluid; thus, it is probable that ice, when per-
fectly free from air bubbles, is at least one l6th lighter than water at the same
temperature. A saturated solution of Glauber's salts, or sulfate of soda,in hot
water, may be cooled slowly to the temperature of the atmosphere, when the
pressure of the air is excluded, and may be made to crystallize by admitting
it suddenly, the liquor becoming at the same tiir^e warm in consequence of
the heat which is extricated ; and there is no doubt but that the congelation
of water, and perhaps of all other substances, is a crystallization of the same
kind. '

The expansions of solid bodies appear to be more regular than those of
liquids or even of elastic fluids; they vary little at any temperature, although
it is said that they do not always take place in their full extent at the instant

2

ON THE SOURCES AND EFFECTS OF HEAT. 643

that "the substance has become heated, and that a blow, or the agitation
produced vvhen they are made to sound by the friction of the bow of a vioHn,
may sometimes be observed to cause them to assume the state of equilibrium
with greater rapidity. Brass expands about one hundred thousandth of its
length for each degree of Fahrenheit, copper and gold a little less ; silver
somewhat more; glass and platina less than half as much; iron and steel about
two thirds as much; tin one third more, and lead and zinc about half as
much more. Wood and earthenware are the least expansible of all known
solids. The diminution of the elasticity of iron and steel by the elevation of
their temperature amounts to about -j-bW of the whole for each degree: but
probably various substances are variously aiFected in this respect.

/
The liquefaction of solids, and their conversion into fluids by the operation
of heat, is liable to fewer irregularities than any other of its effects; the
change depending only on the temperature, and not being accelerated or retard-
ed by any accidental circumstances. When the temperature is too low, or
the pressure too small, for the existence of the substance in a liquid form, it
may still be ccnverted into vapour, either mixed with air, or in a separate
state: thus ice loses weiglit when it is exposed to a dry frosty wind; and
camphor, benzoin, and ammonia are sublimed by heat without being melted,
although it is probable, that a pressure sufficiently strong might enable them
to e>ist as liquids in elevated temperatures. In all changes from solidity to
liquidity or to elastic fluidity, a certain quantity of heat disappears, except
some cases in which a chemical decomposition has accompanied the change;
thus, in the detonation of gunpowder, a large quantity of gas acquires
the state of elasticity, but at the same time a great degree of heat is pro-
duced.

The effects of the expansion of bodies by heat, and of their contraction by
cold, are observed in the frequent accidents which happen to glass and to
porcelain from a sudden change of temperature. Glass conducts heat so
slowly, that one side of a vessel may become much heated, and consequently
expanded, while the other remains much colder, and if the vessel canno>t
readily accommodate its form to this change of proportions, it will most com-
monly crack, the colder parts dividing, in consequence of their being too
much stretched by the adjoining hotter parts. Hence the thinner the ^lass is,

fl44 LECTURE LI.

the less liable it is to crack from any sudden expansion; and if it be very
thick, however simple its form may be, it will still crack ; for no flexure,
which it can assume, can be sufficient for the equilibrium of the externul
parts without being too great for that of the parts near the middle.

When glass in fusion is very suddenly cooled, its external parts become
solid first, 'and determine the magnitude of the whole piece ; while it still
remains fluid within. The internal part, as it cools, is disposed to contract
still further, but its contraction is prevented by the resistance of the external
parts, which form an arch or vault round it, so that the whole is left in a state
of constraint; and as soon as the equilibrium is disturbed in any one part, the
whole aggregate is destroyed. Hence it becomes necessary to anneal all
glass, by placing it in an oven, where it is left to cool slowly ; for, without this
precaution, a very slight cause would destroy it. The Bologna jars, some-
times called proofs, are small thick vessels,made for the purpose of exhibiting
this effect; they are usually destroyed by the impulse of a small and sharp
body, for instance a single grain of sand, dropped into them; and a small
body appears to be often more effectual than a larger one; perhaps because
the larger one is more liable to strike the glass with an obtuse part of its
surface. In the same manner the glass drops, sometimes called Prince
Rupert's drops, which are formed by suffering a portion of green glass iu
fusion to fall into water, remain in equilibrium while they are entire ; but
when the small projecting part is broken off, the whole rushes together with
great force, and rebounding by its elasticity, exhibits the effect of an explosion.
The ends of these drops may, sometimes, but not always, be gradually
ground off without destroying them, so that the concussion produced by
breaking the drop seems to be concerned in the destruction of the equili»
brium.

The tempering of metals appears to bear a considerable analogy to the'
annealing of glass; when they are made red hot, and suddenly cooled, they
acquire a great degree of hardness, which renders them proper for some
purposes, while the brittleness wliich accompanies it would be inconvenient
for others. By heatmg them again to a more moderate temperature, and
suffering them to cool more gradually, they are rendered softer and more flexible,
and the more as the heat which is thus applied is the more considerable.

3

/

ON THE SOURCES A^D EFFECTS OF HEAT. 645

which forms itself on the surface of polished iron or steel, serves as a test of
the degree of heat which is applied to it, the yellowish colour which it assume^
indicating the first stage of tampering,- the violet the second, and the blue
the last; and if the heat be raised till the surface becomes grey, the steel
will be rendered perfectly soft. Th e density of metals is also a little increased
by tempering them, probably for the same reason as .water is more dense than
ice. In what manner the unequal distribution of the mutual actions of
the particles of bodies contributes to increase their hardness, cannot be very-
positively ascertained, although some conjectures might be formed which
would, perhaps, be in some measure explanatory of the fact^;'i)iit it is safer,
in the present state of our knowledge, to be contented \vitli tracing the
analogy between these effects in substances of different kinclg, and under
different circumstances, without attempting to understand completely the
immediate operation of the forces which are concerned.

VOL. I. 4 L

646

LECTURE LII.

ON THE MEASURES AND THE NATURE OF HEAT.

XhE principal particulars concerning the origin, the progress, and the effects
of heat, having been noticed in the last lecture, we now proceed to examine
the most usual modes of measuring its degrees and its quantity,and to inquire
into the most probable opinions respecting its intimate nature and its imme-
diate operation.

The expansion of solids is measured by a pyrometer, which is calculated
for rendering the smallest change of dimensions perceptible either by me-
chanical or by optical means. The first of these methods was adopted by
those who first investigated these ejects; a bar of metal being placed in a
vessel of water, or of oil, which was heated by lamps, while the extremities
of the bar were in contact with a fixed point on one side, and on the other
with a series of levers, which multiplied the expansions, so as to render them
easily observable by means of the end of the last lever, serving as an index.
But it is obvious that the expansion of the fixed part of the instrument, and
the irregular changes of temperature of the levers themselves, must very
much interfere with the accuracy of such an instrument. A much more cor-
rect mode of determination is to employ two microscopes, fixed to an appara-
tus, which is always kept, by means of ice, at a constant temperature, and to
observe with a micrometer the change of place of either end of the heated
bar. - •

For such purposes, the degrees of heat may be ascertained by the natural
measures of the freezing and boiling points of certain liquids, and of water in
particular; but for subdividing the intervals betM'een these points,, other
means must be employed. The most natural mode o^determining the inter-
mediate degrees of heat, which must be considered as the standard for the

ON THE MEASURES AND THE NATURE OF HEAT. 647

-comparison of all others, is too laborious and complicated for common use.
If we mix together equal quantities of the same liquid at two different tem-
peratures, they will obviously acquire an intermediate temperature, which is
the natural mean between the separate temperatures, provided that no heat
be lost or gained during the process ; and provided that no irregularity be
produced from the approach of the liquid to a state of congelation, the exist-
ence of which might be detected by a comparison of experiments on various
liquids at the same temperatures. 13y repeating the operation, we may subdi-
vide the interval* as often as we please, or we may mix the liquids in any
other proportion, so as to obtain at once any otheripoint of the scale, which
may afterwards be identified by a thermometer of any description.

There is also another method of comparing thcdivisions of a thermometer
with those of the natural scale, but it is not wholly free from objections; the
instrument being placed in a cone of the sun's rays, made to converge by
means of a lens or mirror, the quantity of lieat falling on it must be nearly
in the inverse proportion of the square of its distance from the focus j and
the elevation of a common thermometer appears to be nearly proportional to
the lieat which is throwft_ott It ia .this manner.

The expansion of solids probably approaches the nearest to the steps of the
natural scale, although even in this there seems to be some inequality; but
that of mercury is scarcely Jess regular, and a portion of mercury inclosed
in a bulb of glass, having a fine' tube connected with it, forms a thermometer
the most convenient, and most probably the mostaccuratc,of any, for common
use; the degrees corresponding very nearly with those of the natural scale,
although, according to the most accurate experiments, they appear to indi-
cate, towards the middle of the common scale of Fahrenheit, a temperature
2 or 3 degrees too low. There is an inequality of the same kind, but still
greater, in the degrees of the spirit thermometer; and this instrument has
also the disadvantage of being liable to burst in a heat below that of boiling
water; although it is well calculated for the measurement of very low tem-
peratures, since pure alcohol has never yet been frozen, while mercury has
been reduced to a solid by the cold of Siberia and of Hudson's Bay: but both
mercury and linseed oil support a heat of between .5 and 600° without ebul-
lition. For higher temperatures than this, a thermometer has been made of

1

648 LECTURE Lir.

semitransparent porcelain, containing a fusible metal, which may he com-
pared with the upper part of the mercurial scale, and then continued further;
and the expansion of such of the metals, as are difficult of fusion, affords an-
other mode of determining the highest degrees of heat. Mr. Wedgwood's
thermometer derives its properties from the contraction of a small brick of
prepared clay, which contracts the more, as the heat to which it is exposed is
higher : it may be extremely useful for identifying the degree of heat which
is required for a particular purpose : but for the comparison of temperatures
by an extension of the numerical scale, we have not sufficient evidence of its
accuracy ,to allow us to depend on. its indications ; and it is scarcely credible
that the operation of farnaces, of any kind, can produce a heat of so many
thousand degrees of a natural scale, as Mr, Wedgwood's experiments have led
liim to suppose; nor is the i^upposition consisteiat with the. observations of
other philosophers. ' )/i ■'[.': ■-.[,■•• [- .,;,

Mercurial thermometers are in general hermetically sealed, the tube being
perfectly closed attheend, inordertoexcludedust, andtopreventthedissipation
of the mercury. When a standard therm ometer is to be adjusted, its freezing
point is readily fixed by immersing it wholly in melting snow or pounded ice; but
for the boiling point, some further precautions are required; the easiest method
appears to be, to immerse its bulb in an open vessel of boiling water, to cover it
with several folds of cloth, and to pour hot water continually over it ; for if it
were immersed to a considerable depth, the pressure would raise the temperature
of the boiling point, and if it were not covered, the mercury in the tube would
be too cold. Attention must also be paid to the state of the barometer; it must
either stand at 30 inches, or the place of the boiling point must be raised, when
the barometer is lower. than 30, and lowered when it is higher; the difference
of nine tenths of an inch either way requiring an alteration amounting to -,4^
of the interval between freezing and boiling. This interval is subdivided, in
Fahrenheit's thermometer, into 180 degrees; in Reaumur's, into 80, and in
the centigrade thermometer of Celsius and of the French, into 100; and in
making the subdivision, care must be taken to examine the equality of the
bore throughout, by observing the length occupied by a detached portion cxf
mercury, and to allow for any irregularities which may have been thus de-
tected. The scales of Reaumur and of Celsius begin at the freezing point
of water; but in that of Fahrenheit the freezing point stands at 32"", the

ON THE MEASURES AND THK NATURE OF HEAT. 649

scale beginning from the cold produced by a freezing mixture, which was
supposed by Fahrenheit to be the greatest that would ever occur in nature.

The expansion, which is observed in a mercurial thermometer, is in reality
only the difference of the expansions of mercury and of glass; but this cir-
cumstance produces no difference in the accuracy of the results. The
separate effects of the expansion of glass are, however, sometimes perceptible;
tlms, when a thermometer is plunged suddenly into hot water, the glass,
being first heated, expands more rapidly than the mercury, and, for a
moment, the thermometer falls. This circumstance would perhaps be still
more observable in a thermometer of spirit or of water; for an equal bulk of
these liquids would be much longer in acquiring tlie temperature of the sur-
rounding: medium than a mercurial thermometer.

'o

The expansion of elastic fluids affords in some cases a test of heat, which is-
very convenient from its great delicacy, and because a very small quantity of
heat is sufficient to raise their temperature very considerably. The thermo-
meter first invented by Drebel was an air thermometer; but instruments of
this kind, when they are subject to the variations of the pressure of the
atmosphere as well as to those of its temperature, are properly called
manometers, and require, for enabling us to employ them as thermo-
meters, a comparison with the barometer; while on the other hand, they may
be used as barometers, if the temperature be otherwise ascertained. They
are however, very useful even without this comparison, in delicate experi-
ments of short duration, since the changes of th« barometer are seldom very
rapid; and they may also.be wholly freed from the effects of the pressure of
the atmosphere, in various ways. Bernoulli's method consists in- closing
the bulb of a common barometer, so as to leave the column of mercury in equili-
brium with the air contained in the bulb at its actual temperature, and capable
of indicating, by the changes of its height and of its pressure, any subse-
quent changes in the temperature of the air, which must afl'ect both its bulk
and its elasticity. Mr. Leslie's photometer, or differential thermometer, has
some advantagesover this instrument, but it can only be employed where the
changes of temperature can be confined to a part only of the instrument. The
elasticity of the air contained in the bulb is here counteracted, not by the pres-
sure of a column of mercury, but by the elasticity of another portion of ak

(SiSO iECTURE LH.

in a second bulb, which is not to be exposed to the heat or cold that is to
be examined: and the difference between the temperatures of the two bulbs
is indicated by the place of a drop of a liquid, moving freely, in the tube
M-hich joins them. (Plate XXXIX. Fig. 548 . . 550.)

The degree of heat, as ascertained by a thermometer, is only to be considered
as a relation to the surrounding bodies, iu virtue of which a body supports
the equilibrium of temperature when it is in the neighbourhood of bodies
equally heated; thus, if a thermometer stands at 60°, both in a vessel of
water, and in another of mercury, wc may infer that the water and the
mercury may be mixed without an}' change of their temperature: but the
absolute quantity of heat, contained in equal weights, or in equal bulks, of any
two bodies at the same- temperature, is by no means the same. Thus, in order
to raise tlie temperature of a pound of water from 50° to 60°, we need only to
add to it another pound of water at 70°, which, while it loses 10° of its own heat,
will communicate 10° to the first pound; but the temperature of a pound of
mercury at 50° may be raised 10°, by means of the heat imparted to it, by
mixing with it one thirtieth part of a pound of water, at the same tem-
perature of 70°. Hence we derive the idea of the capacities of different bodies
for heat, which was first suggested by Dr. Irvine, the capacity of mercury
being only about one thirtieth part as great as that of water. And by similar
experiments it has been ascertained, that the capacity of iron is one eighth of
that of water, the capacity of silver one twelfth, and that of lead one twenty
fourth. But for equal bulks of these different substances, the disproportion
is not quite so great; thus, copper contains nearly the same quantity of heat
in a given bulk as water; iron, brass, and gold, a little less, silver ■!■ as
much, but lead and glass each about one half only.

It is obvious that if the capacity of a body for heat, in this sense of the word,
were suddenly changed, it would immediately becomehotterorcoldtr, according
to the nature of the change, adiminution of the capacity producing beat, and an
augmentation cold. Such a change of capacity is often a convenient mode of re-
presentation for some of the sources of heat and cold : thus, when heat is produc-
ed by the condensation ofa vapour, or by the congelation of a liquid, we may ima-
gine that the capacity of the substance isdimiuished; and that it overflows, as a
vessel would doif its dimensions were contracted. It appears also from directex-

ON THE MEASUREir AWD THE NATURE OF HEAT. 651

perimcnts,in some such cases, that the capacity of the same substance is actually
greater in a liquid than in a solid state, and in a state of vapour, than in cither;
and both Dr. Irvine and Dr. Crawford have attempted to deduce, from a
comparison of the proportional capacities of water and ice, with the quantity
of heat extricated during congelation, a measure of the whole heat which is
contained in these substances, and an estimation of the place which the
absolute privation of heat, or the natural zero, ought to occupy in the scale
of the thermometer. Thus, when a pound of ice, at 32°, is mixed with a
pound of water at 172° of Fahrenheit, the whole excess of 140° is absorbed
in the conversion of the ice into water, and the mixture is reduced to the
temi)€rature of 32°; and, on the other hand, when a pound of ice freezes, a
certain quantity of heat is evolved which is probably capable of raising the tem-
perature of a pound of water 140°, or that of 140 pounds a single degree.
Pr. Crawford found, by means of other experiments, that a quantity of heat
capable of raising the temperature of water 9° would raise that of ice as much
as 10°; hence he inferred that the capacity of ice wasT?,- as great as that of
water, and that if this capacity, instead of being reduced to -^, had been
Avholly destroyed, the quantity of heat extricated would have been 10 times,
as great, or about 1400°, which has, therefore, been considered as tl>e whole
quantity of heat contained in a pound of water at 32°, and the beginning of
the, natural scale has been placed about 13^8° below the zero of Fahren-
lielt. ; Dr. Irvine makes tl>e capacity of ice still less considerable, and places-
the natural zero about 900- degrees below tliat of Fahrenheit.

If direct experiments on the quantities of heat, required for producing
certain elevations of temperature, in different states of the same substance,
compared in this, maimer with the emission or absorption of heat which takfes
place while those changes are performed, agreed with similai- experiment*
made on different substances, there could be no objection to the mode of
representation. But if it should appear that such compaiTsous frequently
present us with contradictory results, we could no longer consider the theory
of capacities for heat as sufficient to explain the phenomena. With respect to the
simple changes constituting congelation and liquefaction, comlensationandeva-
poration, and compression and rarefaction, there appears to be at present noevi-
dcnce of the insufficiency of this theory ; it has not perhaps yet been shown that the
heat absorbed in any one cliange is always precisely equalto that which is emitted

55-2 LECTURE LII.

ill the return of the substance to its former state, but nothing has yet been
advanced which renders this opinion improbable; and tlie estimation of the
natural zero, which is deduced from this doctrine, may at least be considered
as a tolerable approximation.

if, how-ever, we attempt to deduce the heat produced by friction and by
combustion from changes of the capacities of bodies, thus estimated, we shall
find that the comparison of a very few facts is sufficient to demonstrate the
imperfection of such a theory. Count Rumford found no sensible difference
between the capacities of solid iron and of its chips; but if we even suppose,
for the sake of the argument, that the pressure and friction of the borer had
lessened the capacity of tlie iron one twelfth, so as to make it no greater than
that of copper; we shall then find that one twelfth of the absolute heat of
the chips, thus abraded, must have amounted to above 60 000 degrees of
Fahrenheit, and consequently that the natural zero ought to be placed above
700 000 degrees below the freezing point, instead of 14 or 1500 only. It is,
therefore, impossible to suppose that any alteration of capacities can account
for the production of heat by friction : nor is it at all easier to apply this
theory correctly to the phenomena of combustion. A pound of nitre contains
about half its weight of dry acid, and the capacity of the acid, when diluted, is
little more than half as great as that of water ; the acid of a pound of nitre
must therefore contain less heat than a quarter of a pound of water: but
Lavoisier and Laplace have found, that the deflagration of a pound of nitre
produces a quantity of heat sufficient to melt twelve pounds of ice, conse-
quently the heat extricated by the decomposition of a pound of dry nitrous
acid must be sufficient to melt 24 pounds of ice ; and even supposing the
gases, extricated during the deflagration, to absorb no more heat than the char-
coal contained, which is for several reasons higlijy improbable, it follows
that a pound of water ought to contain at least as much heat, as would be
sufficient to melt 48 pounds of ice, that is, about 6720 degrees of Fahren-
heit.

In short, the further we pursue such calculations, the more we shall be
convinced of the impossibility of applying them to the phenomena. In such
a case as that of the nitrous acid, Dr. Black's term of latent heat might
he thought applicable, the heat being supposed to be contained in the

OV THE MEASURKS AKD THE NATURE OF HEAT. 653

SuTfstance, withovit being comprehended in the quantity required for main-
taining its actual temperaturCi But even this hypothesis is wholly inap-
plicable to the extrication of heat by friction, where all the qualities of the
substances concerned remain precisely the same after the operation, as before
It. If any further argument were required in confutation of the opinion, that
the heat excited by friction is derived from a change of capacity, it might
be obtained from Mr. Davy's experiment on the mutual friction of two
pieces of ice, which converted them into water, in a room at the tempera-
ture of the freezing point: for in this case it is undeniable that the capacity
of the water must have been increased during the operation ; and the heat
produced could not, therefore, have been occasioned by the diminution of
the capacity of the ice.

This discussion naturally leads us to an examination of the various theories
which have been formed respecting the intimate nature of heat; a subject
upon which the popular opinion seems to have been lately led away by very
superficial considerations. The facility with which the mind conceives the
existence of an independent substance, liable to no material variations, except
those of its quantity and distribution, especially when an appropriate name,
and a place in the order of the simplest elements has been bestowed on it,
appears to have caused the most eminent chemical philosophers to overlook
some insuperable difficulties attending the hypothesis of caloric. Caloric has
been considered as a peculiar elastic or ethereal fluid, pervading the substance
or the pores of all bodies, in different quantities, according to their different
capacities for heat, and according to their actual temperatures; and being*
transferred from one body to another upon any change of capacity, or upon
any other disturbance of the equilibrium of temperature: it has also beert
commonly supposed to be the general principle or cause of repulsion ; and in
its passage from one body to another, by radiation, it has been imagined by
some to flow in a continued stream, and by others in the form of separate
particles, moving, with inconceivable velocity, at great distances from each
other.

The circumstances which have been already «tated, respecting the produc-
tion of heat by friction, a^ipear to afford an unanswerable confutation of the
VOL. I. 4 m

^'54 tECTURE Lll,

whole of this doctnne. If the heat is neither received from the suirouiuHng
bodies, which it cannot be without a depression of their temperature, nor
derived from the quantity aheady accumulated in the bodies themselves,
which it could not be, even if their capacities were diminished in any imagin-
able degree, there is no alternative but to allow that heat must be actually
generated by friction; and if it is generated out of nothing, it cannot b^
matter, nor even an immaterial or semimaterial substance. The collateral
parts of the theory have also their separate difficulties: thus, if heat were
the general principle of repulsion, its augmentation could not diminish
the elasticity of solids and of fluids; if it constituted a continued fluid, it
. could not radiate freely through the same space in different directions; and
if its repulsive particles followed each other at a distance, they would still
approach near enough to each other, in the focus of a burning glass, to have
their motions deflected from a rectilinear direction.

If heat is not a substance, it must be a quality ; and this quality can only
be motion. It was Newton's opinion, that heat consists in a minute vibra-
tory motion of the particles of bodies, and that this motion is communicated
through an apparent vacuum, by the undulations of an elastic medium, which
is also concerned in the phenomena of light. If the arguments which have
been lately advanced, in favour of the undulatory nature of light, be deemed
valid, there will be still stronger reasons for admitting this doctrine respect-
' ing heat, and it will only be necessary to suppose the vibrations and undula-
tions, principally constituting it, to be larger and stronger than those of light,
while at the same time the smaller vibrations of light, and even the blackening
raySjderived from still more minute vibrations, may, perhaps, when sufficiently
condensed, concur in producing the effects of heat. These effects, beginning
from the blackening rays, which are invisible, are a little more perceptible
in the violet, which still possess but a faint power of illumination; the
yellow green afibrd the most light; the red give less light, but much more
heat, while the still larger and less frequent vibrations, which have no effect
on the sense of sight, may be supposed to give rise to the least refrangible
rays, and to constitute invisible heat.

, It is easy to imagine that such vibrations may be excited in the component

ON THE MEASUllEi: AND THE IfATURE OF HEAT. 65S

parts of bodies, by percussion, by friction, or by the destruction of the
equilibrium of cohesion and repulsion, and by a change of the conditions ori
which it may be restored, in consequeiice of combustion, or of any other
chemical change. It is remarkable that the particles of fluids, which are
incapable of any material change of temperature from mutual friction, have
also very little power of communicatii>g heat to each other by their imme-
diate action, so that there may be some analogy, in this respect, between
the communication of heat and its mechanical excitation.

The effects of heat on the cohesive and repulsive powers of bodies, have
sometimes been referred to the centrifugal forces and mutual collisions of the
revolving and vibrating particles ; and the increase of the elasticity of aeri-
form fluids has been very minutely compared with the force which would be
derived from -an acceleration of these internal motions. In solids and in
liquids, however, this. increase of elasticity is not observable, and the imme-
diate effect of heat diminishes not only the force of cohesion, but also in
some degree, that of repulsion, so that these vibrations, if they exist, must
derive their effect on the corpuscular forces from the alterations which they
produce on the situation of the particles, with respect to the causes of these
forces.

The different chemical effects of heat and light are far from furnishing any
objection to this system ; it is extremely easy to imagine the attraction
between two or three bodies to be modified by the agitations, into which their
particles are thrown. If certain undulations be capable of affecting one of the
three bodies only, its cohesion with both the others may be weakened, and
hence their mutual attraction may be comparatively increased ; and from
various combinations of such differences, in the operation of different kinds
of heat and light, a great diversity of effects of a similar kind may be
derived.

If heat, when attached to any substance, be supposed to consist in minute
vibrations, and when propagated from one body to another, to depend on
■: the undulations of a medium highly elastic, its effects must strongly resem-
ble tloose of sound, since every sounding body is in a state of vibration^ and

656 LECTURE txr.

the air, or any other medium, which transmits sound, conveys its undulation
to distant parts by means of its elasticity. And we shall find that the prin-
cipal phenomena of heat may actually be illustrated by a comparison with
those of sound. The excitation of heat and sound are not only similar, but
often identical ; as in the operations of friction and percussion : they are
both communicated sometimes by contact and sometimes by radiation; for
besides the common radiation of sound through the air, its effects are com-
municated by contact, when the end of a tuning fork is placed on a table, or
on the sounding board of an instrument, which receives from the fork an
impression that is afterwards propagated as a distinct sound. And the
effect of radiant heat, in raising the temperature of a body upon which it-
falls, resembles the sympathetic agitation of a string, when the sound of
another string, which is in unison with it, is transmitted to it through the air.
The water, which is dashed about by the vibrating extremities of a tuning fork
dipped into it, may represent the manner in which the particles at the surface
of a liquid are thrown out of the reach of the force of cohesion, and convert-
ed into vapour; and the extrication of heat, in consequence of condensation,
may be compared with the increase of sound produced by lightly touching
a long chord which is slowly vibrating, or revolving in such a manner as to
emit little or no audible sound; while the diminution of heat by expansion,
and the increase of the capacity of a substance for heat, may be attributed to
the greater space afforded to each particle, allowing it to be equally agitated
with a less perceptible effect on the neighbouring particles. In some cases,
indeed, heat and sound not only resemble each other in their operations, but
produce precisely the same effects; thus, an artificial magnet, the force of
which is quickly destroyed by heat, is affected more slowly in a similar
manner, when made to ring for a considerable time; and an electrical jar
may be discharged, either by heating it, or by causing it to sound by the
friction of the finger.

All these analogies are certainly favourable to the opinion of the vibratory
nature of heat, which has been sufficiently sanctioned by the authority of
the greatest philosophers of past times, and of the most sober reasoners of
the present. Those, however, who look up with unqualified reverence ta
the dogmas of the modern schools of chemistry, will probably long retain %

ON THE MEASUnES AND THE NATURE OP HEAT. 657

partiality for the convenient, but superficial and inaccurate, modes of reason^
jng, which have been founded on the favourite hypothesis of the existence
of caloric as a separate substance ; but it may be presumed that in the end a
careful and repeated examination of the facts, which have been adduced in
confutation of that system, will make a sufficient impression on the minds
of the cultivators of chemistry, to induce them to listen to a less objection-
able theory.

658

LECTURE LIII.

ON ELECTRICITY IN EQUILIBRIUM.

JL HE phenomena of electricity are as amusing and popular in their external form
as they are intricate and abstruse in their intimate nature. In.examiiiing these
phenomena, a philosophical observer will not be content with such exhibitions as
dazzle the eye for a moment, without leaving any impression that can be instruct-
ive to the mind, but he will be anxious to trace the connexion of the facts with
their general causes, and to compare them with the theories which have been
proposed concerning them : and although the doctrine of electricity is in
many respects yet in its infancy, we shall find that some hypotheses may be
assumed, which are capable of explaining the principal circumstances in a
simple and satisfactory manner, and which are extremely useful in connect-
ing a multitude of detached facts into an intelligible system. These hypo-
theses, founded on the discoveries of Franklin, have been gradually formed
into a theory, by the investigations of Aepinus and Mr. Cavendish, combined
with the experiments and inferences of Lord Stanhope, Coulomb, and
Robison.

We shall first consider the fundamental hypotheses on, which this
system depends, and secondly the conditions of equilibrium of the
substances concerned in it; determining the mode of distribution
of the electric fluid, and the forces or pressures derived from its action
when at rest; all which will be found to be deduced from the theory
precisely as they are experimentally observable. The motions of the
electric fluid will next be noticed, as far as we. can form any general con-
clusions respecting them; and the manner in which the equilibrium of elec-
tricity is disturbed, or the excitation of electricity, will also be considered ;
and, in the last place, it will be necessary to take a view of the mechanism or the

3

Oy ELECTRICITY IN EQUILIBRIUM. 659

practical part of electricity, and to examine the natural and artificial appara-
tus concerned in electrical phenomena, as well as in those effects, which
have been denominated galvanic.

It is supposed that a peculiar ethereal fluid pervades the pores, if not the
actual substance, of the earth and of all other material bodies, passing through
thfm with more or less facilit}', according to their different powders of conduct-
ing it: that the particles o: this fluid repel each other, and are attracted by
the particles of common matter: that the particles of common matter also
repel each other: and that these attractions and repulsions are equal among
themselves, and vary inversely as the squares of the distances of the particles.

The effects of this fluid are distinguished from those of all other substances
by an,attractive or repulsive quality, which it appears to communicate ta
different bodies, and which differs in general from other attractions and
repu sions, by its immediate diminution or cessation, when the bodies,acting on
each other, come into contact, or when they are touched by other bodies.
The pame electricity is derived from electrum, amber; for it was long ago
observed that amber, when rubbed, continues for some time to attract small
bodies ; but at present electricity is usually excited by other means. In
general a body is said to be electrified, when it contains, either as a whole, or
in any of its parts, more or less of the electric fluid than is natural to it; and it is
supposed that what is called positive electricity depends on a redundancy,
and negative electricity on a deficiency of the fluid.

These repulsions and attractions are supposed to act, not only between two
particles which are either perfectly or very nearly in contact with each other,
but also between all other particles at all distances, whatever obstacles may
be interposed between them. Thus, if two electrified balls repel each other,
the effect is not impeded by the interposition of a plate of glass: and if any
other substance interposed appears to interfere with their mutual action, it
is in consequence of its own electrical aflections. In these respects, as well
as in the law of their variation, the electrical forces differ from the common
repulsion which operates between the particles of elastic fluids, and resemble
more nearly that of gravitation. Their intensity, when separately consider-
ed, is much greater than that of gravitation, and they might be supposed

^60 LECTURE LIII.

to be materially concerned in the great phenomena of the universe; but in
the common neutral state of all bodies, the electrical fluid, which is every
where present, is so distributed, that the various forces hold each other
exactly in equilibrium, and the separate results are destroyed ; unless we choose
to consider gravitation itself as arising from a comparatively slight inequality
between the electrical attractions and repulsions.

The attraction of the electric fluid to common matter is shown by its com-
munication, from one body to, another, which is less copiously supplied
with it, as well as by many other phenomena; and this attraction of the
fluid of the first body, to the matter of the second, is precisely equal to its
repulsion for the quantity of the fluid, which naturally belongs to the secon<l,
so as to saturate the matter. For the excess or deficiency of the fluid in the
first body does not immediately produce either attraction or repulsion,
so long as the natural distribution of the fluid in the second body remain*
unaltered.

Since also two neutral bodies, the matter which they contain being saturated
by the electric fluid, exhibit no attraction for each other, the matter in
the first must be repelled by the matter in the second; for its attraction for
the fluid of the second would otherwise remain uncompensated. We are,
however, scarcely justified in classing this mutual repulsion among the
fundamental properties of matter; for useful as these laws are rn explaining
electrical appearances, they seem to deviate too far from the magnificent
simplicity of nature's works, to be admitted as primary consequences of the
constitution of matter: they may, however, be considered as modifica-
tions of some other more general laws, which are yet wholly unknown
to us.

When the equilibrium of these forces is destroyed, the electric fluid is put
in motion; those bodies, which allow the fluid a free passage, are called
perfect conductors; but those which impede its motion, more or less, are
nonconductors, or imperfect conductors. For example, while the electric
fluid is received into the metallic cylinder of an electrical machine, its ac-
cumulation may be prevented by the application of the hand to the cylinder
which receives it, and it will pass off through the person of the operator to

ON ELECTRICITY IN EQUILIBRIUM. 66'l

the ground; hence the human body is called a conductor. But when the
metallic cylinder, or conductor, of the machine is surrounded only by dry
air, and supported by glass, the electric fluid is retained, and its density
increased, until it becomes capable of procuring itself a passage, some inches
in length, through the air, which is a very imperfect conductor. If a person,
connected with the conductor, be placed on a stool with glass legs, the
electricity will no longer pass through him to the earth, but may be so ac-
cumulated, as to make its way to any neighbouring substance, which is capable
of receiving it, exhibiting a luminous appearance, called a spark; and a
person or a substance, so placed as to be in contact with nonconductors only,
is said to be insulated. When electricity is subtracted from the substance
thus insulated, it is said to be negatively electrified, but the sensible effects
are nearly the same, except that in some cases the form of the spark is a little
different.

Perfect conductors, when electrified, are in general either overcharged or
undercharged with electricity in their most distant parts at the same time; but
nonconductors, although they have an equal attraction for the electric fluid,
are often differently affected in difterent parts of their substance, even when,
those parts are similarly situated in every respect, except that some of them have
had their electricity increased or diminished by a foreign cause. This property
of nonconductors may be illustrated by means of a cake of resin, or a plate
of glass, to which a local electricity may be communicated in any part of
its surface, by the contact of an electrified body; and the parts thus electri-
fied may afterwards be distinguished from the rest, by the attraction which
they exert on any small particles of dust or powder projected near them; the
manner, in which the particles arrange themselves on the surface, indicating
also in some cases the species of electricity, whether positive or negative,
that has been employed ; positive electricity producing an appearance some-
what resembling feathers; and negative electricity an arrangement more like
spots. The inequality in the distribution of the electric fluid in a noncon-
ductor may remain for some hours, or even some days, continually di-
minishing till it becomes imperceptible.

These are the fundamental properties of the electric fluid, and of the dif-^
ferent kinds of matter as connected with that fluid. We are next to examia<i:

VOL. I. 4iX

^6j[ LECTURE LIII.

its distribution, and the attractive and repulsive effects exhibited by it, under
different forms. Supposing a quantity of redundant fluid to exist in a-
spherical conducting body, it will be almost wholly collected into a minute
space contiguous to the surface, while the internal parts remain but little
overcharged. For we may neglect the actions of the portion of fluid which
is only occupied in saturating the matter, and also the etlJect of the matter
thus neutralised, since the redundant fluid is repelled as much by the one
as it is attracted by the other; and we need only to consider the mutual
actions of the particles of this superfluous fluid on each other. It may then
be shown, in the same manner as it is demonstrated of the force of gravita-
tion, that all the spherical strata which are remoter from the centre than any
given particle, will have the whole of their action on it annihilated by the
balance of their forces, and that the effective repulsion of the interior strata
will be the same, as if they were all collected in the centre. This repulsion
will, therefore, impel the particles of the fluid towards the surface, as long
as it exists, and nothing will impede the condensation of the redundant fluid
there, until it is exhausted from the neighbourhood of the centre. In the same
manner it may be shown, that if there be a deficiency of fluid, it will be only
in the external parts, the central parts remaining always in a state of neu-
trality: and since the quantity of electric fluid taken away from a body, in
any common experiment, bears but a very small proportion to the whole
.that it contains, thedeflciency will also be found in a very small portion of the
sphere, next to its surface. And if, instead of being spherical, the body be
of any other form, the effects of electricity will still be principally confined
to its surface. This proposition was very satisfactorily investigated by Mr.
Cavendish; and it was afrerwards more fully shown, by Dr. Gray's experi-
ments, that the capacities of different bodies, for receiving electricity, depend
much more on the quantity of their surfaces, than on their solid contents:
thus, the conductor of an electrical machine will contain very nearly or quite
as much electricity if hollow as if solid.

■ If two spheres be united by a. cylindrical conducting substance of small di-
mensions, there will be an equilibuum, when the actions of the redundant
fluid in the spheres,on the whole fluid in the cyliuderjare equal; that is, uhtn
both the spheres have their surfaces electrified in an equal degree: but if the
length of 'the cylinder is consid&iable, the fluid within it.caa only remain at

ON ELECTRICITY IN EQUILIBRIUM, 665

rest when the quantities of redundant fluid are nearly equal ii^ both spheres,
and consequently when the density is greater in the smaller. And for a simi-
lar reason, in bodies of irregular forms, the fluid is always most accumulated
in the smallest parts; and when a conducting substance is pointed, the fluid
becomes so dense at its extremity, as easily to overcome the forces which
tend to retain it in its situation. (Plate XXXIX. Tig. 551.)

In this distribution we find a very characteristic difference between the
pressure of the electric fluid and the common hydrostatic pressure of liquids
or of simple elastic fluids; for these exert on every surface similarly situated a
pressure proportionate to its magnitude; but the electric fluid exerts a pres-
sure on small and angular surfaces greater, in proportion to their magnitudes,
than the pressure on larger parts: so that if the electric fluid were in general
confined to its situation by the pressure of the atmosphere, that pressure
might easily -be too weak to oppose its escape from any prominent points. It
does not appear, however, that this pressure is the only cause which prevents
the escape of the electric fluid ; nor is it certain that this fluid can pass
through a perfect vacuum, although it has not yet been proved, that a body
placed in a vacuum is perfectly insulated. Whatever the resistance may be,
which prevents the dissipation of electricity, it is always the more easily over-
come, as the electrified substance is more pointed, and as the point is more
prominent; and even the presence of dust is often unfavourable to the suc-
cess of electrical experiments, on account of the great number of pointed ter-
. minations which it affords.

The general effect of electrified bodies on each other, if their bujk is sniall
in comparison with their distance, is, that they are mutually repelled when in
similar states of electricity, and attracted when in dissimilar states. This is a
consequence immediately deducible from the mutual attraction of redundant
matter and redundant fluid, and from the repulsion supposed to exist between
any two portions either of nratter or of fluid, and it may also easily be con-
firmed by experimental proof. A neutral body, if it were a perfect noncon-
ductor, would not be affected either way by the neighbourhood of.an electri-
fied body : for while the whole matter contained in it remains barely saturated
with the electric fluid, the attractions and repulsions balance each other, Eut
in general, a neutral body appears to be attracted by an electrified body, on

664 lECTURE LIII.

account of a change of the disposition of the fluid which it contains, upon
the approach of a body either positively or negatively electrified. The elec-
trical affection produced in this manner, without any actual transfer of the
fluid, is called induced electricity.

When a body positively electrified approaches to a neutral body, the re-
dundancy of the fluid expels a portion of the natural quantity from the near-
est parts of the neutral body, so that it is accumulated at the opposite extre-
mity; while the matter, which is left deficient, attracts the redundant fluid
of the first body, in such a manner as to cause it to be more condensed in the
neighbourhood of the second than elsewhere; and hence the fluid of this body
is driven still further ofi", and all the cff'ects are redoubled. The attraction of
the redundant fluid of the electrified body, for the redundant matter of the neu-
tral body, is stronger than its repulsion for the fluid which has been expelled
from it, in proportion as the square of the mean distance of the matter is
smaller than that of the mean distance of the fluid : so that in all such cases
of induced electricity, an attraction is produced between the bodies concerned.
And a similar attraction will happen, under contrary circumstances, when a
neutral body and a body negatively electrified, approach each other.

The state of induced electricity may be illustrated by placing a long con-
ductor at a little distance from an electrified substance, and directed towards it ;
and by suspending pith balls or other light bodies from it, in pairs, at different
parts of its length : these will repel each other, from being similarly electrified, at
the two ends, which are in contrary states of electricity, while at acertain point
towards the middle, they will remain at rest, the conductor being here perfectly
neutral. It was from the situation of this point that Lord Stanhope first inferred
the true law of the electric attractions and repulsions, although Mr. Cavendish
had before suggested the same law as the most probable supposition.

The attraction, thus exerted by an electrified body upon neutral substances,
is strong enough, if they are suflSciently light, to overcome their gravitation,
and to draw them up from a table at some little distance: upon touching
the electrified body, if it is a conductor, they receive a quantity of electricity
from it, and are again repelled, until they are deprived of their electricity by
Contact with some other substance, which^ if sufficiently near to the first, is
4

©N ELECTRICITY IN EQUILIBRIUM. 665

usually in a contrary state, and therefore renders them still more capable of
returning, when they have touched it, to the first substance, in conseciuence
of an increased attraction, assisted also by a new repulsion. This alternation-
has been applied to the construction of severalelectrical toys ; a little hammeiv
for example, has been made to play between two bells; and this instrument has
been employed for giving notice of any change of the electrical state of the
atmosphere. The repulsion, which takes'place between two bodies, in a similar
state of electricity, is> the cause of the currents of air which always accompany
the discharge of electricity, whether negative or positive, from pointed sub-
stances; each particle of air, as soon as it has received its electricity from the
point, being immediately repelled by it ; and this current has also been supposed
to facilitate the escape of the electricity, by bringing a continual succession of
particles not already overcharged.

If two bodies approach each other, electrified either positively or negatively
in different degrees, they will either repel or attract each other, according to-
their distance: when they are very remote, they exhibit a repulsive force,,
but when they are within a certain distance, the effects of induced electricity
overcome the repulsion, which would necessarily take place, if the distribution!
of the fluid remained unaltered by their mutual influence.

When a quantity of the electric fluid is accumulated on one side of a non-
conducting substance, it tends to drive off the fluid from the other side; and
if this fluid is suffered to escape, the remaining matter exerts its attrac-
tion on the fluid which has been imparted to the first side, and allows it to be
accumulated in a much greater quantity than could have existed in an equal
surface of a conducting substance. In this state, the body is said "to
be charged; and for producing it the more readily, each surface is usually
coated with a conducting substance, which serves to convey the fluid to and
from its different parts with convenience. The thinner any substance is, the
greater quantity of the fluid is required for charging it in this manner, so as
to produce a given tension, or tendency to escape: but if it be made too thiti,
it will be liable to break, the attractive force of the fluid, for the matter on the
opposite side overcoming the cohesion of the substance, and perhaps forcing;
its way through the temporary vacuum which is formed.

666 LECTURE LIII.

When a comnninication is made in any manner by a conducting substance
between the two coatings of a charged plate or vessel, the equilibrium is re-
stored, and the effect is called a shock. If the coatings be removed, the
plate will still remain charged, and it may be gradually discharged by mak-
ing a communication between its several parts in succession, but it cannot be
discharged at once, for want of a common connexion; so that the presence
of the coating is not absolutely essential to the charge and discharge of the
opposite surfaces. Such a coated substance is most usually employed in the
form of ajar. Jars were formerly filled with water, or with iron filings; the
instrument having been principally made known from the experiments of
Musschenbroek and others at Leyden, it was called the Leyden phial; but
at present a coating of tin foil is commonly applied on both sides of the jar,
leaving a sufficient space at its upper part, to avoid the spontaneous discharge,
which would often take place between the coatings, if they approached too
near to each other ; and a ball is fixed to the cover, which has a communication
with the internal coating, and by means of which the jar is charged, while
the external coaling is allowed to communicate with the ground. A collect-
ion of such jars is called a battery, and an apparatus of this kind may be made
so powerful, by increasing the number of jars, as to exhibit many striking
effiects by the motion of the electric fluid, in its passage from one to the
other of the surfaces.

The conducting powers of diff"erent substances are concerned, oiot only in
the facility with which the motions of the electric fluid are directed into a
particular channel, but also in many cases of its equilibrium, and particularly
in the properties of charged substances, which depend on the resistance op-
posed by nonconductors to the ready transmission of the fluid. These pow-
ers may be compared, by ascertaining the greatest length of each of the sub-
stances to be examined, through which a spark or a shock will take it course,
in preference to a given length of air, or of any other standard of comparison.
The substances, which conduct electricity the most readily, are metals, well
burnt charcoal, animal bodies, acids, saline liquors, water, and very rare air.
The principal nonconductors are glass, ice, gems, dry salts, sulfur, amber,
resins, silk, dry wood, oils, dry air of the usual density, and the barometrical
vacuum. Heat commonly increases the conducting powers of bodies; ajar of

ON ELECTRICITY IN EQUILIBRIUM. 667

glass may be discharged by a moderate heat, and liquid resins are capable of
transmitting shocks, although they are by no means good conductors: it is
remarkable also that ajar may be discharged by miuute agitation, when it is
caused to ring by the friction of the finger, Ic has oeen observed that, in a
great variety of cases, those substances, which are the best conductors of heat,
attbrd also the readiest passage to electricity; thus, copper conducts heat
more rapidly, and electricity more readily, than iron, aijd platina less than
almost any other metal; glass also presents a considerable resistance to the
transmission of both these influences. The analogy is, however, in many re-
spects imperfect, and it affords us but little light, with regard either to the
natore of heat, or to that of the electric fluid.

668

LECTURE LIV.

ON ELECTRICITY IN MOTION.

XHE manner in which the electric fluid is transferred from one body to an-
other, the immediate effects of such a transfer, the causes which originally
disturb the equilibrium of electricity, and the practical methods, by which all
these circumstances are regulated and measured, require to be considered as
belonging to the subject of electricity in motion. Among the modes of ex-
citation by which the equilibrium is originally disturbed, one of the most inter-
esting is the galvanic apparatus, which has been of late years a very favourite
subject of popular curiosity, and of which the theory and operation will be
briefly examined, although the subject appears rather to belong to the che-
mical than to the mechanical doctrine of electricity.

The progressive motion of the electric fluid through conducting substances
is so rapid, as to be performed in all cases without a sensible interval of time.
It has indeed been said, that when very weakly excited, and obliged to pas«
to a very great distance, a perceptible portion of time is actually occupied ia
its passage; but this fact is somewhat doubtful, and attempts have been made
in vain, to estimate the interval, employed in the transmission of a shock
through several miles of wire. We are not to imagine that the same particles
of the fluid, which enter at one part, pass through the whole conducting sub-
stance, any more than that the same portion of blood, which is thrown out of
the heart, in each pulsation, arrives at the wrist, at the instant that the pulse is
felt there. The velocity of the transmission of a spark or shock far exceeds
the actual velocity of each particle, in the same manner as the velocity of a
wave exceeds that of the particles of water concerned in its propagation; and
this velocity must depend both on the elasticity of the electric fluid, and on the
force with which it is confined to the conducting substance. If this force
were merely derived from the pressure of the atmosphere, we might infer the

ON ELECTRICITY IN MOTION. 669

density of the fluid from the velocity of a spark or shock, compared with that
of sound; or we might deduce its velocity from a determination of its density.
It has heen supposed, although perhaps somewhat hastily, that the actual ve-
locity is nearly equal to that of light.

When a conducting substance approaches another, which is electrified
the distribution of the electric fluid within it is necessarily altered by
induction, before it receives a spark, so that its remoter extremity is
brought into a state similar to that of the first body: hence it happens that
when the spark passes, it produces less effect at the remoter end of the sub_
stance, while the part presented to the electrified body is most affected, on account
of its sudden change to an opposite state. But if both ends approach
bodies in opposite states of electricity, they will both be strongly affected
■when the shock takes place, while the middle of the circuit undergoes but
little change.

The manner in which the electric fluid makes its way, through a more or less
perfect nonconductor, is not completely understood: it is doubtful whether
the substance is forced away on each side, so as to leave a vacuum for the
passage of the fluid, or whether the newly formed surface helps to guide
it in its way; and in some cases it has been supposed that the gradual com-
munication of electricity has rendered the substance more capable of conduct-
ing it, either immediately, or, in the case of the air, by first rarefying it.
However this may be, the perforation of a jar of glass by an overcharge, and
that of a plate of air ,by a spark, appear to be effects of the same kind,
although the charge of the jar is principally contained in the glass, while
the plate of air is perhaps little concerned in the distribution of the elec-
tricity.

The actual direction of the electric current has not in any instance been
fully ascertained, although there are some appearances which seem to justify
the common denominations of positive and negative. Thus, the fracture
of a charged jar of glass, by spontaneous explosion, is well defined on the
positive, and splintered on the negative side, as might be expected from the
passage of a foreign substance from the former side to the latter; and a candle,
held between a positive and a negative ball, although it apparently vibrates

VOL. I. 4 o

G/O LECTURE LIV.

between them, is found to heat the negative ball much more than the posi-
tive. We cannot, however, place much dependence on any circumstance
of this kind, for it is doubtful whether any current of the fluid, which we
can produce, possesses sufficient momentum to carry with it a body of sensible
magnitude. It is in fact of little consequence to the theory, whether the terms
positive and negative be correctly applied, provided that their sense remain
determined; and that, like positive and negative quantities in mathematics,
they be always understood of states which neutralise each other. The
original opinion of Dufay, of the existence of two distinct fluids, a vitreous
and a resinous electricity, has at present few advocates, although some have
thought such a supposition favoured by the phenomena of the galvanic de-
composition of water.

When electricity is simply accumulated without motion, it does not appear
to have any effect, either mechanical, chemical, or physiological, by which
its presence can be discovered ; the acceleration of the pulse, and the ad-
vancement of the growth of plants, which have been sometimes attributed
to it, have not been confirmed by the most accurate experiments. An un-
interrupted current of electricity, through a'perfect conductor, would perhaps
be also in every respect imperceptible, since the best conductors appear to
be the least affected by it. Thus, if we place our hand on the conductor of
an electrical machine, the electricity will pass oft' continually through the
body, without exciting any sensation. A constant stream of galvanic elec-
tricity, passing through an iron wire is, however, .capable of exciting a
considerable degree of heat, and if it be transmitted through the hands of
the operator, it will produce a slight numbness, although in general some in-
terruption of the current is necessary in order to furnish an accumulation
sufficient to produce sensible effects; and such an interruption may even
increase the effect of a single spark or shock; thus, gunpowder is more readily
fired by the discharge of a battery passing through an interrupted circuit,
than through a series of perfect conductors.

The most common effect of the motion of the electric fluid is the production
of light. Light is probably never occasioned by the passage of the fluid
through a perfect conductor; for when the discharge of a large battery renders
a small wire luminous, the fluid is not wholly confined to the wire, but

a

ON ELECTRICITY IN" MOTION. 67I

overflows a little into the neiglibouring space. There is always an appearance
of light whenever the path of the fluid is interrupted by an imperfect con-
ductor; nor is the apparent contact of conducting substances sufficient to
prevent it, unless they are held together by a considerable force; tluis, a
chain, conveying a spark or shock, appears luminous at each link, and the
rapidity of the motion is so great, that we can never observe any difference
in the thnes of the appearance of the light in its different parts; so that
a series of luminous points, formed by the passage of the electric fluid,
between a string of conducting bodies, represents at once a brilliant delinea-
tion of the whole figure in which they are arranged. A lump of sugar, a
piece of wood, or an egg, may easily be made luminous in this manner ; and
many substances, by means of their properties as solar phosphor), retain for
some seconds the luminous appearance thus acquired Even water is so im-
perfect a conductor, that a strong shock may be seen in its passage through
it; and when the air is sufficiently moistened or rarefied to become a con-
ductor, the track of the fluid through it is indicated by streams of light,
which are perhaps derived from a series of minute sparks passing between
the particles of water or of rarefied air. When the air is extremely rare, the
light is greenish; as it becomes more dense, the light becomes blue, and
then violet, until it no longer conducts. The appearance of the electrical
light of a point enables us to distinguish the nature of the electricity with which
it is charged; a pencil of light, streaming from the point, indicating that
its electricity is positive, while a luminous star, with few diverging rays,
shows that it is negative. The sparks, exhibited by small balls, differently
electrified, have also similar varieties in their forms, according to the nature
of their charges. (Plate XL. Fig. 552.)

The production of heat by electricity frequently accotnpanies that of light,
and appears to depend in some measure on the same circumstances. A fine
wire may be fused and dissipated by the discharge of a battery; and without
being perfectly melted,it may sometimes be shortened or lengthened, accordingly
as it is loose or stretched during the experiment. The more readily a metal con-
ducts, the shorter is the portion of it which the same shock can destroy; and it
has sometimes been found that a double charge of a battery has been capable
of melting a quadruple length of wire oFthe same kind.

The mechanical effects of electricity are probably in many cases the consc-

572 LECTURE LIV. , '

quences of the rarefaction produced by the heat which is excited; thus, the
explosion, attending the transmission of a shock or sparii through the air,
may easily be supposed to be derived from the expansion caused by heat; and
the destruction of a glass tube, which contains a fluid in a capillary bore,
Avhen a spark is caused to pass through it, is the natural consequence of the
conversion of some particles of the fluid into vapour. But when a glass jac
is perforated, this rarefaction cannot be supposed to be adequate to the effect.
It is remarkable that such a perforation may be made by a very moderate
dischar<i-e, when the glass is in contact with oil or with sealing wax; and no
sufHcicnt explanation of this circumstance has yet been given.

A stron"" current of electricity, or a succession of shocks or sparks, trans-
mitted through a substance, by means of fine wires, is capable of producing
many chemical combinations and decompositions, some of which may be
attributed merely to the heat which it occasions, but others are wholly diiFer-
ent. Of these the most remarkable is the production of oxygen and hy-
drogen gas from common water, which are usually extricated at once, in
such quantities, as, when again combined, will reproduce the water which
has disappeared ; but in some eases the oxygen appears to be disengaged
most copiously at the positive wire, and the hydrogen at the negative.

When the spark is received by the tongue, it has generally a- subacid taste;
anil an explosion of any kind is usually accompanied by a smell somewhat like
that of sulfur, or rather of fired gunpowder. The peculiar sensation, which
the electric fluid occasions in the human frame, appears in general to be
derived from the spasmodic contractions 6f the muscles through wh.ich it
passes; although in some cases it produces pain cf a different kind;
thus, the spark of a conductor occasions a disagreeable sensation in the skin,
and when an excoriated surface is placed in the galvanic current, a sense of
smarting, mixed with burning, is experienced. Sometimes the effect of
a shock is felt most powerfully at the joints, on account of the diiliculty
which the fluid finds in passing the articulating surfaces which form the cavity
of the joints. The sudden death of an animal, in consequence of a violent shock,
is probably owing to the immediate exhaustion of the whole energy of the
nervous system. It is remarkable th!i,t a very minute tremor, communicated to
the most elastic partsof the body,in particular to the chest, produces an agita-
tion of the nerves, whicli is not wholly unlike the effect of a weak eltjctricity.

ON ELECTRICITY IN MOTIOW^ 673*

The principal modes, in which the electric equiUbrium is primarily de-
stroyed, are simple contact, friction, a change of the fofm of aggregation,,
and chemical combinations and decompositions. The electricity produced
by the simple contact of any two substances is extremely weak, and can only
be detected by very delicate experiments : in general it appears tlvit the substance,,
which conducts the more readily, acquires a slight degree of negative elec-
tricity, while the other substance is positively electrified in an equal degree.
The same disposition of the fluid is also usually produced by friction, the
one sutxstance always losing as much as the other gains ^ and commonly
although not always, the worst conductor becomes positive. At thq instant
in which the friction is applied, the capacities or attractions of the bodies for
electricity appear to be altered, and a greater or less quantity is required for
saturating them; and upon the cessation of the temporary cliange, this re-
dundancy or deficiency is rendered sensible. When two substances of the
same kind are rubbed together, the smaller or the rougher becomes nega-
tively electrified; perhaps because the smaller surface is more heated, in con-
se(|uence of its undergoing more friction than an equal portion of the larger^
and bence becomes a better conductor; and because the rougher is in itself
a better conductor than the smoother, ana may possibly have its conducting
powers increased by the greater agitation of its parts which the friction pro-
duces. The back of a live cat becomes positiveh' electrified, with whatever
substance it is rubbed; glass is positive in most cases, but not when rubbed
with mercurj' in a vacuum, although sealing wax, which is generally nega-
tive, is rendered positive by immersion in a trough of mercury. When a
white and a black silk stocking are rubbed together, the white stocking
acquires positive electricity, and the black negative, perhaps because the blacL
dye renders tlie silk both rougher and a better conductor..

Those substances, which have very little conducting power, are some-
times called electrics, since they are capable of exhibiting readily the
electricity which friction excites on their surf^ices, where it remains
accumulated, so that it may be collected into a conductor; while the
surfaces of such substances, as have greater conducting powers, do not
so readily imbibe the fluid from others with which they are rubbed, since
they may be supplied from the internal parts of the substances themselves^
when their altered capacity requires it; thus, glass, when heated to 110° of"
Fahrenheit, can with difficulty be excited, becoming an iniperfect conductor :;

574 - lECTORE X.IV.

but a thin plate of a conducting substance, when insulated, may be excited
almost as easily as an electric, commonly so called.

Vapours are generally in a negative state, but if they rise from metallic
substances, or even from some kinds of heated glass, the effect is uncertain,
probably on account of some chemical actions which interfere with it. Sul-
fur becomes electrical in cooling, and wax candles are said to be sometimes found
in a state so electrical, when they are taken out of their moulds, as to attract
the particles of dust which are floating near them. The tourmalin, and
several other crystallized stones, become electrical when heated or cooled, and
it is found that the disposition, assumed by the fluid, bears a certain relation
to the direction in which the stone transmits the light most readily; some
parts of the crystal being rendered always positively and others negatively
electrical, by an increase of temperature.

The most remarkable of the phenomena, attending the excitation of elec-
tricity by chemical changes, are those which have lately received the appella-
tion of galvanic. Some of the effects which have been considered as belong-
ing to galvanism are probably derived from the electrical powers of the animal
body, and the rest have been referred by Mr. Volta, and many other philo-
sophers on the continent, to the mere mechanical actions of bodies possessed
of diflferent properties with regard to electricity. Thus, they have supposed
that when a circulation of the electric fluid is produced through a long series
of substances in a certain direction, the differences of their attractions and of
their conducting powers, which must remain the same throughout the process,
keep up this perpetual motion, in defiance of the general laws of mechanical
forces. In this country it has been generally maintained, that no explanation
founded on such principles could be admissible, even if it were in all other
respects sufficient and satisfactory, which the mechanical theory of galvanism
certainly is not.

The phenomena of galvanism appear to be principally derived from an in-
equality in the distribution of the electric fluid, originating from chemical
changes, and maintained by means of the resistance opposed to its motion, by
a continued alternation of substances of different kinds, which furnishes a
much stronger obstacle to its transmission than any of those substances alone
would have done. The substances employed must neither consist wholly of

aN ELECTRICITY IN MOTION. 675

solids nor of fluids, and they must be of three different kinds, possessed of
different powers of conducting electricity; but whether the difference of
their conducting powers is of any other consequence than as it accompanies
different chemical properties, is hitherto undetermined. Of these three
substances, two must possess a power of acting mutually on each other, while
the other appears to serve principally for making a separate connexion between
them: and this action may be of two kinds, or perhaps of more ; the one is
oxidation, or the combination of a metal or an inflammable substance with a
portion of oxygen derived from water or from an acid, the other sulfuration,
or a combination with the sulfur contained in a solution of an alkaline sulfuret.

We may represent the effects of all galvanic combinations, by considering the
oxidation as producing positive electricity in the acting liquid, and the sulfuration
as producing negative electricity, and by imagining that this electricity is always
communicated to the best conductor of the other substances concerned, so as
to produce a circulation in the direction thus determined. For example, when
two wires of zinc and silver, touching each other, are separately immersed in an
acid, the acid, becoming positively electrical, imparts its electricity to the silver,
and hence it flows back into the zinc: when the ends of a piece of charcoal
are dipped into water and into an acid, connected together by a small tube,
the acid, becoming positive, sends its superfluous fluid through the charcoal
into the water; and if a wire of copper be dipped into water and a solution
of alkaline sulfuret, connected with each other, the sulfuret, becoming nega-
tive, will draw the fluid from the copper on which it acts; and in all these
cases the direction of the current is truly determined, as it may be shown
hy composing a battery of a number of alternations of this kind, and either
examining the state of its different parts by electrical tests, or connecting
wires with its extremities, which, when immersed into a portion of water,
will exhibit the production of oxygen gas where they emit the electric fluid,
and of hydrogen where they receive it. These processes of oxidation and
of sulfuration may be opposed to each other, or they may be combined in
various ways, the sum or difference of the separate actions being obtained by
their union; thus it usually happens that both the metals employed are oxid-
able in some degree, and the oxidation, which takes place at the surface of the
better conductor, tends to impede the Avhole effect, perhaps by impeding
the passage of the fluid through the surface. The most oxidable of the

676 LECTURE LIV.

metals, and probably the worst conductor, is zinc ; the next is iron ; then
come tin, lead, copper, silver, gold, and platina. (Plate XL. Fig. 553 . . 555.)

In the same manner as a wire charged with positive electricity causes an
extrication of oxygen gas, so thesiipply of electricity through the more con-
ducting metal promotes the oxidation of the zinc of a galvanic battery ; and
the eftect of this circulation may be readily exhibited, by fixing a wire of zinc,
and another of silver or platina, in an acid, while one end of each isloos^, and
may be brought together or separated at pleasure: for at the moment that the
contact takes place, a stream of bubbles rising from the platina, and a white
cloud of oxid falling from the zinc, indicate both the circulation of the fluid
and the increase of the chemical action. But when, on the other hand, a
plate of zinc is made negative by the action of an acid on the greater part of
its surface, a detached drop of water has less cfl^iect on it, than in the natural
state: while a plate of iron, which touches the zinc, and forms a part of the
circle with it, is very readily oxidated at a distant point: such a plate must
therefore be considered, with regard to this eftect, as being made positive by
the electricity which it receives from the acid or the water; unless something-
like a compensation be supposed to take place, from the effects of
induced electricity. Instead of the extrication of. hydrogen, the same
causes will sometimes occasion a deposition of a metal which has been dis-
solved, will prevent the solution of a metal which would otherwise have been
corroded, or produce some effects which appear to indicate the presence of an
alkali, either volatile or fixed. All these operations may, however, be very
much impeded by the interposition of any considerable length of water, or of
any other imperfect conductor. (Plate XL. Fig. 556.)

It is obvious, that since the current of electricity, produced by a
galvanic circle, facilitates those actions from which its powers are derived, the
effect of a double series must be more than twice as great as that of a single
one: and hence arises the activity of the pile of Volta, the discovery of which
forms the most important era in the history of this department of natural
knowledge. The intensity of the electrical charge, and the chemical and
physiological eft'ects of a pile or battery, seem to depend principally on the
number of alternations of substances; the light and heat more on the joint mag-
nitude of the surfaces employed. In common electricity, the greatest heat

©N ELECTRICITT IN MOTION. ' 677

appears to be occasioned by a long continuation of a slow motion of the fluid;
and this is perhaps best furnislied in galvanism by a surface of large extent^
while some other effects may very naturally be expected to depend on the in-
tensity of the charge, independently of the quantity of charged surface. It
may easily be imagined, that the tension of the fluid must be nearly propor-
tional to the number of surfaces, imperfectly conducting, which are interposed
between the ends of a pile or battery, the density of the fluid becoming-
greater and greater by a limited quantity at each step; and it is easily un-
derstood, that any point of the pile may be rendered neutral, by a connexion
with the earth, while those parts, whichareaboveitorbelow it, will still preserve
their relations unaltered with respect to each other: the opposite extremi-
ties being, like the opposite surface of a charged jar, in contrary states, and a
partial discharge being produced, as often as they are connected by a con-
ducting substance. The various forms, in which the piles or troughs are con-
structed, are of little consequence to the theory of their operation : the most
convenient are the varnished troughs, in which plates of silvered zinc are ar-
ranged side by side, with intervening spaces for the reception of water, or of
an acid. (Plate XL. Fig. 55?.)

It is unquestionable that the torpedo, the gymnotus electricus, and some
other fishes, have organs appropriated to the excitation of electricity, and that
they have a power of comnmnicating this electricity at pleasure to conduct-
ing substances in their neighbourhood. These organs somewhat resemble in
their appearance the plates of the galvanic pile, although we know nothing
of the immediate arrangement, from which their electrical properties are de-
rived; but the effect of the shock, which they produce, resembles in all re-
spects that of the weak charge of a very large battery. It has also been shown
by the experiments of Galvani, Volta, and Aldini, that the nerves and muscles
of the human body possess some electrical powers, although they are so much
less concerned in the phenomena which were at first attributed to them by
Galvani, than he originally supposed, that many philosophers have been in-
clined to consider the excitation of electricity as always occasioned by the
inanimate substances employed, and the spasmodic contractions of the muscles
as merely very delicate tests of the influence of foreign electricity on the nerves.

Such is the general outline of the principal experiments and conclusions

4 p

678 LECTURE LIV.

which the subject of galvanism afforded before Mr. Davy's late ingenious and
interesting researches, which have thrown much light, not only on the foun-
dation of the whole of this class of phenomena, but also on the nature of
chemical actions and affinities in general. Mr. Davy is inclined to infer from
his experiments, that all the attractions, which are the causes of chemical com-
binations, depend on the opposite natural electricities of the bodies concerned;
since such bodies are always found, by delicate tests, to exhibit, when in con-
tact, marks of different species of electricity; and their mutual actions may
be either augmented or destroyed, by increasing their natural charges of elec-
tricity, or by electrifying them in a contrary Avay. Thus, an acid and a metal
are found to be negatively and positively electrical with respect to each other;
and by further electrifying the acid negatively, and the metal positively, their
combination is accelerated; but when the acid is positively electrified, or the
metal negatively, they have no effect whatever on each other. The acid is
also attracted, as a negative body; by another positively electrified, and the
metal by a body negatively electrified, so that a metallic salt may be decom-
posed in the circuit of Volta, the positive point attracting the acid, and the
negative point the metal: and these attractions are so strong, as to carry the
particles of the respective bodies through any intervening medium, which is in
a fluid state, or even through a moist solid; nor are they intercepted in their
passage, by substances which, in other cases, have the strongest elective attrac-
tions for them. Alkali, sulfur, and alkaline sulfurcts, are positive with respect
to the metals, and much more with respect to the acids: hence they have a
very strong natural tendency to combine with the acids and with oxygen:
and hydrogen must also be considered as belonging to the same class with the
alkalis.

Supposing now a plate of zinc to decompose a portion of water: the oxy-
gen, which has a negative property, unites with the zinc, and probably tends
to neutralise it, and to weaken its attractive force; the hydrogen is repelled
by the zinc, and carries to the opposite plate of silver its natural positive elec-
tricity; and if the two plates be made to touch, the energy of the plate of
zinc is restored, by the electricity which it receives from the silver: audit re-
ceives it the more readily, as the two metals, in any case of their contact,
have a tendency to become electrical, the zinc positively, and the silver ne-
gatively. Mr. Davy therefore considers this chemical action as destroying, or

ON ELECTRICITY IST MOTION.

679

at least counteracting, the natural tendency of the electric fluid to pass from
the water to the zinc, and from modifications of this counteraction he explains
the effects of galvanic combinations in all cases. Thus, in a circle composed
of copper, sulfurct, and iron, the fluid tends to pass from the iron towards
the sulfuret, and from the copper to the iron, in one direction, and in the
opposite direction from the copper to the sulfuret, with a force which must be
equal to both the others, since there would otherwise be a continual motion
without any mechanical cause, and without any chemical change; but the
action of the sulfuret on the copper tends to destroy its electromotive, or rather
electrophoric, power, of directing the current towards the sulfuret, and its
combination with the sulfur makes it either positively electrical, or negatively
electrical in a less considerable degree; consequently the fluid passes, accord-
ing to its natural tendency, from the copper to the iron, and from the iroa "REEsfT^
to the sulfuret. In a third case, when copper, an acid, and water, forra
a circle, the natural tendency is from the acid to the copper on one side, s^.'*'<j//.'. ''
and from the acid to the water, and from the water to the copper on the other; ^"<<^ '
here we must suppose the first force to be only a little weakened by the che-
mical action, while the third is destroyed, so that the first overcomes the sc
cond, and the circulation is determined, although very feebly, in such a direc-
tion, that the fluid passes from the acid to the copper. When, in the fourth
place, the combination consists of copper, sulfuret, and water, the tendencies
are, first, from the copper to the sulfuret, and from the water to the copperi
and secondly, from the water to the sulfuret : in this instance a chemical ac-
tion must be supposed between the oxygen of the water and the sulfuret,
which lessens the electromotive tendency, more than the action that takes
place between the sulfuret and the copper, so that the fluid passes from the
copper to the sulfuret; and the current has even force enough to prevent
any chemical action between tlie water and the copper, which would tend to
counteract that force, if it took place.

Mr. Davy has observed that the decomposition of the substances, employed
in the battery of Volta, is of much more consequence to their activity than
cither their conducting power, or their simple action on the other elements of the
series: thus, the sulfuric acid, which conducts electricity better, and dissolves
the metals more readily, than a neutral solution, is, notwithstanding, less
active in the batt-ery, because it is not easily decomposed. Mr. Davy lias also

680 LECTURE LIV.

extended his researches, and the application of his discoveries, to a vari-
ety of natural as well as artificial phenomena, and there can be no doubt but
that he will still make such additions to his experiments, as will be of the
greatest importance to this branch of science.

The operation of the most usual electrical machines depends first on the
excitation of electricity by the friction of glass on a cushion of leather,
covered with a metallic amalgam, usually made of mercury, zinc, and tin,
■which probably, besides being of use in supplying electricity readily to
different parts of the glass, undergoes hi general a chemical change, by means of
which some electricity is extricated. The fluid, thus excited, is received into an
insulated conductor by means of points, placed at a small distance from
the surface which has lately undergone the effects of friction, and from this
conductor it is conveyed by wires or chains to any other parts at pleasure.
Sometimes also the cushion, instead of being connected with the earth, is itself
fixed to a second conductor, which becomes negatively electrified; and either
conductor may contain within it ajar, which may be charged at once by the
operation of the machine, when its internal surface is connected cither with the
earth, or with that of the jar contained in the opposite conductor. The
glass may be either in the form of a circular plate or of a cylinder, and it is
uncertain which of the arrangements affords the greatest quantity of electri-
city from the same surface; but the cylinder is cheaper than the plate, and
less liable to accidents, and appears to be at least equally powerful. (Plate
XL. Fig. 558, 559.)

The plate machine in the Teylerian museum, employed by Van Marum,
when worked by two men, excited an electricity, of which the attraction was
sensible at the distance of 38 feet, and which made a point luminous at 27
feet, and afforded sparks nearly 24 inches long. A battery charged by it,
melted at once twenty five feet of fine iron wire. Mr. Wilson had also a few
years ago, in the Pantheon in London, an apparatus of singular extent; the
principal conductor was 150 feet long, and 16 inches in diameter, and he
employed a circuit of 4800 feet of wire.

The electrophorus derives its operation from the properties of induced elec-
tricity. A cake of a nonconducting substance, commonly of resin or of

ON ELECTRICITY IN MOTION. 681

sulfur, is first excited by friction, and becomes negatively electric: an in-
sulated plate of a conducting substance, being placed on it, does not come
sufficiently into contact with it to receive its electricity, but acquires by
induction an opposite state at its lower surface, and a similar state at its
upper; so that when this upper and negative surface is touched by a sub-
stance communicating with the earth, it receives enough of the electric fluid
to restore the equilibrium. The plate then being raised, the action of the
cake no longer continues, and the electricity, which the plate has received from
the earth, is imparted to a conductor or to ajar; and the operation may be
continually repeated, until the jar has received a charge, of an intensity equal
to that of the plate when raised. Although the quantity of electricity, re-
ceived by the plate, is exactly equal to that which is emitted from it at each
alternation, yet the spark is far less sensible; since the effect of the neighbour-
hood of the cake is to increase the capacity of the plate, while the tension or
force impelling the fluid is but weak; and at the same time the quantity re-
ceived is sufficient, when the capacity of the plate is again diminished, to pro-
duce a much greater tension, at a distance from the cake. (Plate XL.
Fig. 560.)

The condenser acts in some measure on the same principles with the elec-
trophorus, both instruments deriving their properties from the effects of induc-
tion. The use of the condenser is to collect a weak electricity from a large
substance into a smaller one, so as to make its density or tension sufficient to
be examined. A small plate, connected with the substance, is brought nearly
into contact with another plate communicating with the earth; in gene-
ral a thin stratum of air only is interposed ; but sometimes a nonconducting
varnish is employed ; this method is, however, liable to some uncertaiqty,
from the permanent electricity which the varnish sometimes contracts by fric-
tion. The electricity is accumulated by the attraction of the plate communi-
cating with the earth, into the plate of the condenser; and when this plate
is first separated from the substance to be examined, and then removed from
the opposite plate, its electricity is always of the same kind with that which
originally existed in the substance, but its tension is so much increased as to
render it more easily discoverable. This principle has been variously applied
by different electricians, and the employment of the instrument has been fa-
ciUtated by several subordinate arrangements. (Plate XL. Fig. 561.)'

682 LECTORE LIV.

JNfr. Cavallo's multiplier is a combination of two condensers; the second
or auxiliary plate of the first, like the plate of the electrophorus, is moveable,
and carries a charge of electricity, contrary to that of the substance to be ex-
amined, to the first or insulated plate of the second condenser, which receives
it repeatedly, until it has acquired an equal degree of tension; and when the
two plates of this condenser are separated, they both exhibit an electricity
much more powerful than that of the first condenser. The force is, however,
still more rapidly augmented by the instruments of Mr. Bennet and Mr.
Nicholson, although it has been supposed that these instruments are more
liable to inconvenience from the attachment of a greater portion of electri-
city to the first plate of the instrument, which leaves, for a very considerable
time, a certain quantity of the charge, not easily separable from it. Mr. Ben-
net employs three varnished plates laid on each other, but Mr. Nicholson has
substituted simple metallic plates, approachingonly very near together, so that
there can be no error from any accidental friction. In both of these instru-
ments, the second plate of a condenser acquires an electricity contrary and
nearly equal to that of the first, by means of which it brings a third plate
very nearly into the same state with the first; and when the first and third
plates are connected and insulated, they produce a charge nearly twice as
great in the second plate, while the first plate becomes at the same time
doubly charged; so that by each repetition of this process, the intensity of
the electricity is nearly doubled: it is therefore scarcely possible that any
quantity should be so small as to escape detection by its operation. (Plate
XL. Fig. 56<2, 563.)

The immediate intensity of the electricity may be measured, and its cha-
racter distinguished, by electrical balances, and by electrometers of difierent
constructions. The electrical balance measures the attraction or repulsion
exerted by two balls at a given distance, by tlie magnitude of the force re-
quired to counteract it; and the most convenient manner of applying this
force is by the torsion of a wire, which has been employed for the purpose by
Mr. Coulomb. The quadrant electrometer of Henley expresses the mutual
repulsion of a moveable ball and a fixed column, by the divisions of the arch
to which the ball rises. These divisions do not exactly denote the propor-
tional strength of the action, but they are still of utility in ascertaining the
identity of any two charges, and in informing us how far we may venture to

ON ELECTRICITV IN MOTION. 683

proceed in our experiments with safety; and the same purpose is answered, in
, a manner somewhat less accurate, by the electrometer, consisting of two pith
balls, or of two straws, Avhich are made to diverge by a smaller degree of
electricity. Mr, Eennet's electrometer is still more delicate; it consists of
two small portions of gold leaf, suspended from a plate, to whicli the electri-
city of any substance is communicated by contact: a very weak electricity is
sufficient to make them diverge, and it may easily be ascertained whether it
is positive or negative, by bringing an excited stick of sealing wax near the
plate, since its approach tends to produce by induction a state of negative
electricity in the remoter extremities of the leaves, so that their divergence is
either increased or diminished, accordingly as it was derived from negative or
from positive electricity : a strip of gold leaf or tin foil, fixed within the glass
which covers the electrometer, opposite to the extremities of the leaves, pre-
vents the communication of any electricity to the glass, which might interfere
with the action of the instrument. When the balls of an electrometer stand
at the distance of 4 degrees, they appear to indicate a charge nearly 8 times
as great as m hen they stand at one degree : a charge 8 times as great in each
ball producing a mutual action 64 times as great at any given distance, and
at a quadruple distance a quadruple force; in the same manner a separation of
9 degrees is probably derived from an intensity 27 times as great as at 1. In
Lane's electrometer the magnitude of a shock is determined by the quantity
of air through which it is obliged to pass, between two balls, of which the
distance may be varied at pleasure; and the power of the machine may be
estimated by the frequency of the sparks which pass at any given distance.
It appears from Mr. Lane's experiments, that the quantity of electricity re-
quired for a discharge is simply as the distance of the surfaces of the balls,
the shocks being twice as frequent when this distance is only ^ of an inch
as when it is -^. Mr. Volta says, that the indications of Lane's and
Henley's electrometer agree immediately with each other; but it seems diffi-
cult to reconcile this result with the general theory. Sometimes the force of
repulsion between two balls in contact is opposed by a counterpoise of given
magnitude, and as soon as this is overcome, they separate and form a circuit
which discharges a battery; whence the instrument is called a discharger.
(Plate XL. Fig. 564 . . 568. )

It must be confessed that the whole science of electricity is yet in a very

684 LECTURE IIV.

imperfect state: we know little or nothing of the intimate nature of the
substances and actions concerned in it: and we can never foresee, without
previous experiment, where or how it will be excited. We are wholly igno-
rant of the constitution of bodies, by Avhich they become possessed of differ-
ent conducting powers; and we have only been able to draw some general
conclusions respecting the distribution and equilibrium of the supposed electric
fhiid, from the laws of the attractions and repulsions that it appears to exert.
There seems to be some reason to suspect, from the phenomena of cohesion
and repulsion, that the pressure of an elastic medium is concerned in the ori-
gin of these forces; and if such a medium really exists, it is perhaps nearly
related to the electric fluid. The identity of the general causes of electrical
and of galvanic effects is now doubted by few ; and in this country the prin-
cipal phenomena of galvanism are universally considered as depending on che-
mical changes; perhaps, also, time may show, that electricity is very materi-
ally concerned in the essential properties, which distinguish the different kinds
of natural bodies, as well as in those minute mechanical actions and affections
■which are probably the foundation of all chemical operations ; but at present
it is scarcely safe to hazard a conjecture on a subject so obscure, although
Mr. Davy's experiments have already in some measure justified the boldness
of the suggestion.

68i

LECTURE LV.

ON MAGNETISM.

.llIE theory of magnetism bears a very strong resemblance to that of elec-
tricity, and it must therefore be placed near it in a system of natural philoso-
phy. We have seen the electric fluid not only exerting attractions and re-
pulsions, and causing a peculiar distribution of neighbouring portions of a fluid
similar to itself, but also excited in one body, and transferred to another, in
such a manner as to be perceptible to the senses, or at least to cause sensible
eft'ects, in its passage. The attraction and repulsion, and the peculiar distri-
bution of the neighbouring fluid, are found in tlie phenomena of magnetism;
but we do not perceive that there is ever any actual excitation, or any per-
ceptible transfer of the magnetic fluid from one body to another distinct body;
and it has also this striking peculiarity, that metallic iron is very nearly, if not
absolutely, the only substance capable of exhibiting any indications of its
presence or activity.

For explaining the phenomena of magnetism, we suppose the particles of a
peculiar fluid to repel each other, and to attract the particles of metallic iron
with equal forces, diminishing as the square of the distance increasqs; and
the particles of such iron must also be imagined to repel each other, in a si-
milar manner. Iron and steel, when soft, are conductors of the magnetic
fluid, and become less and less pervious to it as their hardness increases.
The ground work of this theory is due to Mr, Aepinus, but the forces have
been more particularly investigated by Coulomb and others. There are the
same objections to these hypotheses as to those which constitute the theory of
electricity, if considered as original and fundamental properties of matter:
and it is additionally difficult to imagine, why iron, and iron only, whether
apparently magnetic or not, should repel similar particles of iron with a pe-
culiar force, which happens to be precisely a balance to the attraction of the
magnetic fluid for iron. This is obviously improbable; but tlie hypotlieses

VOL. I. 4 Q

686 lectuhe lv.

are still of great utility in assisting us to generalise, and to retain in memory,
a number of particular facts wliicli would otherwise be insulated. The doc-
trine of the circulation of streams of the magnetic fluid has been justly and
universally abandoned, and some other theories, much more ingenious and
more probable, for instance that of Mr. Prevost, appear to be too compli-
cated, and too little supported by facts, to require much of our attention.

The distinction between conductors and nonconductors is, with respect to
the electric fluid, irregular and intricate: but in magnetism, the softness or
hardness of the iron or steel constitutes the only difference. Heat, as soft-
ening iron, must consequently render it a conductor; even the heat of boil-
ing water affects it in a certain degree, although it can scarcely be supposed
to alter its temper; but the effect of a moderate heat is not so considerable in
magnetism as in electricity. A strong degree of heat appears, from the expe-
riments of Gilbert, and of Mr. Cavallo, to destroy completely all magnetic
action.

It is perfectly certain that magnetic effects are produced by quantities of iron
incapable of being detected either by their weight or by any chemical tests.
Mr. Cavallo found that a few particles of steel, adhering to a hone, on which
the point of a needle was slightly rubbed, imparted to it magnetic properties;
and Mr. Coulomb has observed that there are scarcely any bodies in nature
which do not exhibit some marks of being subjected to the influence of mag-
netism, although its force is always proportional to the quantity of iron which
they contain, as far as that quantity can be ascertained; a single grain being
sufficient to make 20 pounds of another metal sensibly magnetic. A combi-
nation with a large proportion of oxygen deprives iron of the whole or the
greater part of its magnetic properties; finery cinder is still considerably
magnetic, but the more perfect oxids and the salts of iron only in a slight de-
gree; it is also said that antimony renders iron incapable of being attracted
by the magnet. Nickel, when freed from arsenic and from cobalt, is decid-
edly magnetic, and the more so as it contains less iron. Some of the older
chemists supposed nickel to be a compound metal containing iron, and we may
still venture to assume this opinion as a magnetical hypothesis. There is in-
deed no way of demonstrating that it is impossible for two substances to be so
united as to be incapable of separation by the art of the chemist; had nickel

4

ON MAGNETISM. 687

been as dense as platina, or as light as cork, we could not have supposed
that it contained any considerable quantity of iron, but in fact the specific
gravity of these metals is very nearly the same, and nickel is never found in
nature but in the neighbourhood of iron ; we may therefore suspect, with
some reason, that the hypothesis of the existence of iron in nickel may be
even chemically true. The aurora borealis is certainly in some measure a
raagnetical phenomenon, and if iron were the only substance capaple of
exhibiting magnetic effects, it would follow that some ferruginous particles
must exist in the upper regions of the atmosphere. The light usually attend-
ing this maguetical meteor may possibly be derived from electricity, which
may be the immediate cause of a change of the distribution of the magnetic
fluid, contained in the ferruginous vapours, that are imagined to float ia
the air.

We arc still less capable of distinguishing with certainty in magnetism,
than in electricity, a positive from a negative state, or a real redundancy of
the fluid from a deficiency. The north pole of a magnet may be considered
as the part in which the magnetic fluid is either redundant or deficient, pro-
vided that the south pole be understood in a contrary sense: thus, if the
north pole of a magnet be supposed to be positively charged, the south pole
must be imagined to be negative; and in hard iron or steel these poles may
be considered as unchangeable.

A north pole, therefore, always repels a north pole, and attracts a south
pole. And in a neutral piece of soft iron, near to the north pole of a
magnet, the fluid becomes so distributed by induction, as to form a
temporary south pole next to the magnet, and the whole piece is of course
attracted, from the greater proximity of the attracting pole. If the bar is
sufficiently soft, and not too long, the remoter end becomes a north pole,
and the whole bar a perfect temporary magnet. But when the bar is of
hard steel, the state of induction is imperfect, from the resistance opposed
to the motion of the fluid ; hence the attraction is less powerful, and an
opposite pole is formed, at a certain distance, within the bar; and beyond
this another pole, similar to the first; the alternation being sometimes re-
peated more than once. The distribution of the fluid within the magnet is
also affected by the neighbourhood of apiece of soft iron, the north pole

688 LECTURE LV.

becoming more powerful by the vicinity of the new south pole, and the
south pole being consequently strengthened in a certain degree; so that the
attractive power of the whole magnet is increased by the proximity of the
iron. A weak magnet is capable of receiving a temporary induction of a
contrary magnetism from the action of a more powerful one, its north pole
becoming a south pole on the approach of a stronger north pole; but the
original south pole still retains its situation at the opposite end, and
restores the magnet nearly to its original condition, after the removal of the
disturbing cause.

The polarity of magnets, or their disposition to assume a certain direction,
is of still greater importance than their attractive power. If a small magnet,
or simply a soft wire, be poised on a centre, it will arrange itself in such a
direction, as will produce an equilibrium of the attractions and repulsions of
the poles of a larger magnet; being a tangent to a certain oval figure, pass-
ino- through those poles, of which the properties have been calculated by
various mathematicians. This polarity may easily be imitated by electricity ;
a suspended wire being brought near to the ends of a positive and negative
conductor, which are placed parallel to each other, as in Nairne's electrical
machine, its position is perfectly similar to that of a needle attracted by a
magnet, of which those conductors represent the poles. (Plate XLI. Fig. 569. )

The same effect is observable in iron filings placed near a magnet, and they
adhere to each other in curved lines, by virtue of their induced magnetism,
the north pole of each particle being attached to the south pole of the par-
ticle next it. This arrangement may be seen by placing the filings either on
clean mercury, or on any surface that can be agitated; and it may be imitated
by strewing powder on a plate of glass, supported by two balls, which are
contrarily electrified. (Plate XLI. Fig. .570.)

The polarity of a needle may often be observed when it exhibits no sen-
sible attraction or repulsion as a whole ; and this may easily be understood
by considering that when one end of a needle is repelled from a given point,
and the other is attracted towards it, the two forces, if equal, will tend to
turn it round its centre, but will wholly destroy each other's effects with
respect to any progressive motion of the whole needle. Thus, when the end

ON MAGNETISM, GSQ

of a magnet is placed under a surface on which iron filings are spread, and
the surface is shaken, so as to leave the particles for a moment in the air,
they are not drawn sensibly towards the magnet, but their ends, which are
nearest to the point over the magnet, are turned a little downwards, so that
they strike the paper further and further from the magnet, and then fall out-
wards, as if they were repelled by it. (Plate XLI. Fig. 571.)

The magnets, which we have hitherto considered, are such as have a simple
and well determined form; but the great compound magnet, which directs
the mariner's compass, and which appears to consist principally of the me"
tallic and sfightly oxidated iron, contained in the internal parts of the earth,
is probably of a far more intricate structure, and we can only judge of its
nature from the various phenomena derived from its influence.

The accumulation and the deficiency of the magnetic fluid, which deter-
mine the place of the poles of this magnet, are probably in fact considerably
diffused, but they may generally be imagined, without much error in the
result, to centre in two points, one of them nearer to the north pole of the
earth, the other to the south pole. In consequence of their attractions
and repulsions, a needle, whether previously magnetic or not,assumes always,
if freely poised, the direction necessary for its equilibrium ; which, in
various parts of the globe, is variously inclined to the meridian and to the
horizon. Hence arises the use of the compass in navigation and in survey-
ing: a needle, whichis poised with a liberty of horizontal motion, assuming \
the direction of the magnetic meridian, which for a certain tiaie remains
almost invariable for the same place; and a similar property is also observa-
ble in the dipping needle, whichis moveable only in a vertical plane; for
when this plane is placed in the magnetic meridian, the needle acquires
an inclination to the horizon, which varies according to the situation of the
place with respect to the magnetic poles. (Plate XLI. Fig. 57'2, 57'o.)

The natural polarity of the needle may be in some measure illustrated by
inclosing an artificial magnet in a globe ; the direction of a small needle,
suspended over any part of its surface, being determined by the position of
the poles of the magnet, in the same manner as the direction of the compass
is determined by the magnetical poles of the earth, although \yith much
more regularity. In either case the whole needle is scarcely more or less

ggO ' LECTURE LV.

atttacted towards the globe than if the influence of magnetism were removed ;
except when the small needle is placed very near to one of the poles of the
artificial magnet, or, on the other hand, when the dipping needle is employed
in the neighbourhood of some strata of ferruginous substances, which, in
particular parts of the earth, interfere materially with the more general effects,
and alter the direction of the magnetic meridian.

A bar of soft iron, placed in the situation of the dipping needle, acquires
from the earth, by iuduction, a temporary state of magnetism, which may
be reversed at pleasure by reversing its direction; but bars of iron, which
have remained long in or near this direction, assume a permanent polarity ;
for iron, even when it has been at first quite soft, becomes in time a little
harder. A natural magnet is no more than a heavy iron ore, which, in the
course of ages, has acquired a strong i)olarity from the great primitive mag-
net. It must have lain in some degree detached, and must possess but
little conducting power, in order to have received and to retain its mag-
netism.

We cannot, from any assumed situation of two or more magnetic poles,
calculate the true position of the needle for all places; and even in the same
place, its direction is observed to change in the course of years, according
to a law which has never yet been generally determined, although the varia-
tion which has been observed, at any one place, since the discovery of the
compass, may perhaps be comprehended in some very intricate expressions;
but the less dependence can be placed on any calculations of this kind, as
there is reason to think, that the change" depends rather on chemical than on
physical causes. Dr. Halley indeed conjectured that the earth contained a
nucleus, or separate sphere, revolving freely within it, or rather floating in
a fluid contained in the intermediate space, and causing the variation of the
magnetic meridian ; and others have attributeil the efliect to the motions of
the celestial bodies: but in either case the changes produced would have
been much more regular and universal than those which have been actually
observed. Temporary changes of the terrestrial magnetism have certainly
been sometimes occasioned by other causes ; such causes are, therefore,
most likely to be concerned in the more permanent effects. Thus, the erup-
tion of Mount Hecla was found to derange the position of the needle consi-
derably; the aurora borealis has been observed to cause its north pole to move

ON MAGNETISM. 69I

6 or 7 degrees to the westward of its usual position; and a still more remark-
able change occurs continually in the diurnal variation. In these climates
the north pole of the needle moves slowly westwards from about 8 in the morn-
ing till 2, and in tiie evening returns again; a change which has with great
probability been attributed to the temporary elevation of the temperature of
the earth, eastwards of the place of observation, where the sun's action takes
place at an earlier hour in the morning, and to the diminution of the mag-
netic attraction in consequence of the heat thus communicated. In winter this
variation amounts to about 7 minutes, in summer to 13 or 14.

Important as the use of the compass is at present to navigation, it would be
still more valuable if its declination from the true meridian were constant for
the same place, or even if it varied according to any discoverable law; since
it would alford a ready mode of deternrniing the longitude of a place by a
comparison of an astronomical observation of its latitude with another of the
magnitude of the declination. And in some cases it may even now be applied
to this purpose, where we have a collection of late and numerous observations.
Such observations have from time to time been arranged in charts, furnished
with lines indicating the magnitude of the declination or variation at the
places through which they pass, beginning from the line of no variation,
and proceeding on the opposite sides of this line to show the magnitude of the
variation castor west. It is obvious that the intersection of a given parallel
of latitude, with the line showing the magnitude of the variation, will indicate
the precise situation of the place at which the observations have been made.

The line of no variation passed in 1657 through London, and in 1666 through
Paris: its northern extremity appears to have moved continually eastwards,
and its southern parts westwards ; and it now passes through the middle of
Asia. The opposite portion seems to liave moved more uniformly westwards;
it now runs from North America to the middle of the South Atlantic. On
the European side of these lines, the declination is westerly; on the South
American side, it is easterly. The variation in London has been for several
years a little more than 24 °. -In the West Indies it changes but slowly ; for
instance it was 6" near the island of Barbadoes, from. 1700 to 17^6. (Plate
XLI. Fig. 574 . . 576. Plate XLIL XLIII.)

692 LECTUllE LV.

Tlie dip of the nortli pole of the needle in the neighbourhood of London
is 72°. Hence the lower entl of a bar standing upright, as a poker, or a lamp
iron, becomes always a north pole, and the temporary south pole of apiece
of soft iron being uppermost, it is somewhat more strongly attracted by the
north pole of a magnet placed over it, than by its south pole ; the distribution
of tlie fluid in the magnet itself being also a little more favourable to the at-
traction, while its north pole is downwards. It is obvious that the magnetism
of the nortliern magnetic pole of the earth must resemble that of the south
pole of a magnet, since it attracts the north pole ; so that if we considered the
nature of the distribution of the fluid, rather than its situation in the earth,
we should call it a south pole. Although it is impossible to find any places
for two, or even for a greater number of magnetic poles, which will correctly
explain the direction of the needle in every part of the earth's surface, yet the
dip may be determined with tolerable accuracy, from the supposition of a
small magnet placed at the centre of the earth, and directed towards a point in
Baffin's Bay,about 75° north latitude, and 70° longitude west of London; and
the variation of the dip is so inconsiderable, that a very slow change of the po-
sition of this supposed magnet would probably be sufficient to produce it;
but the operation of such a magnet, according to the general laws of the forces
concerned, could not possibly account for the very irregular disposition of the
curves indicating the degree of variation or declination; a general idea of
these might perhaps be obtained from the supposition of two magnetic poles
situated in a line considerably distant from the centre of the earth ; but this
hypothesis is I)y no means sufficiently accurate to allow us to place any de-
pendence on it. (Plate XLL Fig. 577, 578)

The art of making magnets consists in a proper application of the attractions
and repulsions of the magnetic fluid, by means of the ditferent conducting
powers of different kinds of iron and steel, to the production and preservation
of such a distribution of the fluid in a magnet, as is the best fitted to the ex-
hibition of its peculiar properties.

We may begin with any bar of iron that has long stood in a vertical posi-
tion; but it is more common to employ an artificial magnet of greater
strength. When one pole of such a magnet touches the end of a bar of hard

ON MAGNETISM. GQS

iron or steel ; that end assumes in some degree the opposite character, and
the opposite end the same character: but in drawing the pole along the bar,
the first end becomes neutral, and afterwards has the opposite polarity; while
the second end has its force at first a little increased, then becomes neutral,
and afterwards is opposite to what it first was. When the operation is re-
peated, the effect is at first in some measure destroyed, and it is difficult to
understand why the repetition adds materially to the inequality of the distri-
bution of the fluid ; but the fact is certain, and the strength of the new mag-
net is for some time increased at each stroke, until it has acquired all that it
is capable of receiving. Several magnets, made in this manner, may be placed
side by side, and each of them being nearly equal in strength to the first,
the whole collection will produce together a much stronger effect; and in this
manner we may obtain from a weak magnet others continually stronger, until
we arrive at the greatest degree of polarity of which the metal is capable. It is,
however, more usual to employ the process called tlie double touch : placing
two magnets, with their opposite poles near to each other, or the opposite poles
of a single magnet, bent into the form of a horseshoe, in contact with the
middle of the bar: the opposite actions of these two poles then conspire in
their effort to displace the magnetic fluid, and the magnets having been
drawn backwards and forwards repeatedly, an equal number of times to and
from each end of the bar, with a considerable pressure, they are at last with-
drawn in the middle; in order to keep the poles at equal distances.

Iron filings, or the scoriae from a smith's forge, when finely levigated^,
and formed into a paste with linseed oil, are also capable of being made col-
lectively magnetic. A bar of steel, placed red hot between two magnets, and
suddenly quenched by cold water, becomes in some degree magnetic, but no4:
so powerfully as it may be rendered by other means. For preserving mag-
nets, it is usual to place their poles in contact with the opposite poles of other
magnets, or with pieces of soft iron, which, in consequence of their own in-
duced magnetism, tend to favour the accumulation of the magnetic power in
a greater quantity than the nietal can retain after they are removed. Hence
the ancients imagined that the magnet fed on u"on.

A single magnet may be made of two bars of steel, with their ends pressed
VOL. I. • 4 R

69^ LECTURE LV.

into close contact; and it might be expected that when these bars are sepa-
rated, or when a common magnet has been divided in the middle, the por-
tions should possess the properties of the respective poles only. But in fact
the ends which have been in contact are found to acquire the properties of
the poles opposite to those of their respective pieces, and a certain point in
each piece is neutral, which is at first nearer to the newly formed pole than
to the other end, but is removed by degrees to a more central situation. lii
this case we must suppose, contrarily to the general principles of the theory,
that the magnetic fluid has actually escaped by degrees from otie of the
])ieces, and has been received from the atmosphere by the other.

There is no reason to imagine any immediate connexion between magnet-
ism and electricity, except that electricity affects the conducting powers of
iron or steel for magnetism, in the same manner as heat or agitation. In some
cases a blow, an increase of temperature, or a slwck of electricity, may expe-
dite a little the acquisition of polarity ; but more commonly any one of these
causes impairs the magnetic power. Professor Robison found, that when a
good magnet was struck for three quarters of an hour, and allowed in the
mean time to ring, its efficacy was destroyed ; although the same operation
had little effect when the ringing was impeded; so that the continued exer-
tion of the cohesive and repulsive powers appears to favour the transmission
of the magnetic as well as of the electric fluid. The internal agitation, pro-
duced in bending a magnetic wire round a cylinder, also destroys its polarity,
and the operation of a file has the same effect. Mr. Cavallo has found that
brass becomes in general much more capable of beiri'g attracted when it has
been hammered, even between two flints; and that this property is again di-
minished by fire: in this case it may be conjectured that hammering increases
the conducting power of the iron contained in the brass, and thus renders it
more susceptible of magnetic action. I\Ir. Cavallo also observed that a mag-
netic needle was more powerfully attracted by iron filings during their solu-
tion in acids, especially in the sulfuric acid, than either before or after the
operation: others have not always succeeded in the experiment; but there is
nothing improbable in the circumstance, and there may have been some actual
difference in the results, dependent on causes too minute for observation. In
subjects so little understood as the theory of magnetism, we are obliged to ad-

ON MAGNETISM. 695

mit some paradoxical propositions, which are only surprising on account of the
imperfect state of our knowledge. Yet, little as we can understand the intimate
nature of magnetical actions, they exhibit to us a number of extremely amus-
ing as well as interesting phenomena; and the principles of crystallization,
and even of vital growth and reproduction, are no where so closely imitated,
as in the arrangement of the small particles of iron in the neighbourhood of
a magnet, and in the production of a multitude of complete magnets, from
the influence of a parent of the same kind.

696

LECTURE LVL

ON CLIMATES AND WINDS.

TL HE science of meteorology relates principally to the natural history of the air,
and to such temporary changes in the earth and sea as are produced by causes
not mechanical only. The subject is of a very con)plicated and intricate na-
ture; it comprehends many effects derived from such causes, as belong sepa-
rately to every department of physics which we have hitherto examined; and
although it has occupied the attention of several philosophers of considerable
eminence, we cannot yet boast of having made any great advancement in it.
Whether we shall ever be able to carry our theories to so high a degree of
perfection, as to furnish us with much information applicable to the purposes
of common life, to agriculture, or to medicine, is at present uncertain; al-
though some advantage has already been derived from the indications of me-
teorological instruments; and the philosophy of the science is in many re-
spects much more advanced than has commonly been supposed. We shall di-
vide this extensive subject into two parts, the first relating principally to the
effects of heat on the atmosphere, including the phenomena of winds; the
second to the nature and consequences of evaporation, comprehending atmo-
spherical electricity, and to the effects of subterraneous fires and igneous
meteors.

The variations of temperature, in different parts of the earth's surface, re-
quire to be examined in the first place; since they are not only of considera-
ble importance in themselves, but are also among the principal causes of other
changes in the state of the winds and weather. These changes are measured
by thermometers, of various kinds, which have already been described ;
but, for meteorological purposes, some additions are frequently made to the
simple thermometer. In Six's thermometer, the tube is twice bent, so as to
return in a parallel direction: the bulb is in the form of a long cylinder, and

ON CLIMATES AND WINTJS, 657

is usuall)' filled with spirit of wine, which is in contact with a portion of mer-
cury occupying the lower part of the tube; and this is succeeded by a second
portion of spirit. The mercury carries on each of its surfaces an index, which
is retained in its remotest situation by means of a weak spring; and conse-
quently shows the greatest degree of heat or of cold that has happened since
the last observation. The indexes are of iron or steel, and may be brought
back to the surface at pleasure by means of a magnet; they are carried up by
the mercury, more by its capillary action, than by the difference of the specific
gravities. A similar effect is obtained in Rutherford's arrangement of a pair
of thermometers, one with mercury, the other with spirit of wine, placed in a
horizontal position; one index being without the surface of the mercury, the
other within that of the spirit: the thermometers being in contrary direc-
tions, both indexes may be brought back to their places, by merely raising the
end of the instrument. Self registering thermometers have also sometimes
been constructed, for keeping a still more accurate account of all the varia-
tions of temperature that have occurred, by describing a line on a revolving
barrel, which shows the height for every instant during the whole time of
their operation. (Plate XLI. Fig. 579, 580.)

The climates of different parts of tlie earth's surface are unquestionably
owing in great measure to their position with respect to the sun. At the equa-
tor, where the sun is always nearly vertical, any given part of the surface re-
ceives a much greater (juantity of light and heat, than an equal portion near
the poles; and it is also still more affected by the sun's vertical rays, because
their passage through the atmosphere is shorter than that of the oblique rays.
As far as the sun's mean altitude only is concerned, it appears from Simpson's
calculations, that the heat received at the equator in the whole year, is nearly"
twice and a half as great as at the poles; this proportion being nearly tlie
same as that of the meridian heat of a vertical sun, to the heat derived, at the
altitude 234^°, in the middle of the long annual day at the poles. Hut the
difference is rendered still greater, by the effect of the atmosphere, which in-
terrupts a greater portion of the heat at the poles than elsewhere. IJouguer
has calculated, upon the supposition of the similarity of the affections of heat
and light, that in latitude 45°, 80 parts out of 100 are transmitted at noon
in July, and 55 only in December. The heat intercepted by the atmosphere
is perhaps not wholly, but very nearly, lost with respect to the climate of the

(t(9"8 lecture xv«.

neighbonring places. It is obvious that, at any individual j)lace, tlie climate ia
summer must approach in some degree to the equatorial climate, the sun's al-
titude being greater, and in winter to the climate of the polar regions.

While the earth is becoming warmer at any particular spot, the heat thrown
off by radiation into the atmosphere, and thence into the empty space beyond
it, together with that which is transmitted to the internal parts of the earth,
must be less than the heat received from the sun; and when the earth is
growing colder, more heat must pass off than is received: but whenever the
heat of the surface is stationary, neither increasing nor diminishing, as at the
times of the greatest and least heat, it is obvious that the heat received from
the sun must be precisely equal to the heat which is thrown off. Now this
quantity may be estimated by the degree of refrigeration in the night; and
hence Mr. Pr6vost has very ingeniously deduced the proportion of the sun's
beat arriving at the surface of the earth in the latitude of Geneva, in July,
and in December; which he finds to be as 7 or 8 to 1 ; and this result agrees
verj-^ well with a calculation deduced from the length of the day, the sun's
altitude, and the interception of his rays by the atmosphere.

In London the temperature generally varies, in the course of the day and
night, somewhat more than 5°, and less than 20°. In January, the mean di-
urnal variation of temperature is 6°, in March £0°, in July 10°, and in Sep-
tember, 18°. Hence, says Mr. Kirwan, we may understand the reason of
the great frequency of colds in spring and in autumn.-

Some philosophers have supposed the earth to become progressively warmer
in the course of ages, while others have imagined that its heat is exhausted.
Both these opinions appear in general improbable. The greater heat the
earth receives by day, the more it throws off, both by day and by night; so
that in the course of a few ages the heat must probably have attained its maxir
mum. Local changes may indeed arise from local circumstances; thus, the
climate of America is said to have become considerably warmer, since a large
part of its surface has been cleared from its dense forests by human labour:
and to judge from the descriptions of the ancients, it appears that even in
Europe the winters were formerly much colder than they are at present. If,
however, Dr. Herschel's opinion of the variation of the heat of the sun be

ON CLIMATES AND WINDS. ' 699

onfirmed, it will introduce a great uncertainty into all theories upon the
subject: since in these calculations the original heat of the sun has always
been supposed unalterable.

The sea is less heated than the land, partly because a greater quantity of
water evaporates from it, and partly because the sun's rays penetrate to a
considerable depth, and have less effect on the surface, while the water is
also mixed, by the agitation of its Waves and currents, with the colder water
below. It is also more slowly cooled than the land, since, when the tem-
perature of the superficial particles is depressed, they become heavier, and
sink to the bottom. For similar reasons, the sea is colder than the land in
hot climates, and by day, and warmer in cold climates, and by night.
These circumstances, however, nearly balance each other, so that the mean
temperatures of both are equal, that of the sea being only less variable.
Although the process of evaporation must cool the sea, yet when the vapours
are condensed without reaching the land, their condensation must compensate
for this effect by an equal extrication of heat.

There is another cause which perhaps contributes in some degree, in tem-
perate climates, to the production of cold ; that is, the alternation of freezing
and thawing. Mr. Prevost observes that congelation takes place much more
suddenly than the opposite process of liquefaction; and that of course the
same quantity of heat must be more rapidly extricated in freezing than it is
absorbed in thawing; that the heat, thus extricated, being disposed to fl}' off in
all directions, and little of it being retained by the neighbouring bodies,
more heat is lost than is gained by the alternation: so that where ice has once
been formed, its production is in this manner redoubled. This circumstance
must occur wherever it freezes, that is, on shore, in latitudes above 35°; and
it appears that from about 30° to the pole, the land is somewhat colder than
the sea, and the more as it is further distant from it; and nearer the equator
the land is warmer than the sea: but the process of congelation cannot by
any means be the principal cause of the difference, and it is probable that the
different capacity of earth and water for heat is materially concerned in it.

Since the atmosphere is very little heated by the passage of the
sun's rays through it, it is naturally colder than the earth's surface;

700 LECTUKE LVI.

and for this reason, the most elevated tracts of land, which are the most
prominent, and the most exposed to the effects of the atmosphere, are always
colder than situations nearer the level of the sea. The northern hemisphere
is somewhat warmer than the southern, perhaps because of the greater pro-
portion of land that it contains, and also in some measure on account of the
greater length of its summer than that of the southern; for although, as it
was long ago observed by Simpson, the different distance of the sun com-
pensates precisely for the different velocity of the earth in its orbit, with
respect to the whole quantity of heat received on either side of the equinoctial
points, yet Mr. Provost has shown, that in all probability the same quantity
of heat must produce a greater effect when it is more slowly applied; because
the portion lost by radiation from the heated body is greater, as the tempera-
ture is higher. Since, therefore, on account of the eccentricity of the earth's
orbit, the north pole is turned towards the sun 7 or 8 days longer than the
south pole, the northern winters must be milder than the southern : yet the
southern summers, though shorter, ought to be somewhat warmer than the
northern: but in fact they are colder, partly perhaps from the much greater
proportion of sea, which in some degree equalises the temperature, and
partly for other reasons. The comparative intensity of tlie southern summer
and winter is not exactly known; but in the island of New Georgia the
summer is said to be extremely cold.

The northern ice extends about 9° from the pole: the southern IB" or
S0° ; in some parts even 30°; and floating ice has occasionally teen found
in both hemispheres as far as 40° from the poles, and sometimes, as it has been
said, even in latitude 41° or 42°. Between 54° and 6o° south latitude, the
snow lies on the ground, at the sea side, throughout the summer. The line of
perpetual congelation is three miles above the surface at the equator, where the
mean heat is 84°; at Teneriffe, in latitude fe8°, two miles; in the latitude of
London, a little more than a mile; and in latitude 80° north, only 1200 feet.
At the pole, according to the analogy deduced by Mr. Kirwan, from a com-
parison of various observations, the mean temperature should be 31°. In
London the mean temperature is 50"* ; at Rome and at iNlontpelier, a little
more than 60° ; in the island of Madeira, 70°; and in Jamaica, 80°.

There are frequently some local causes of heat and coldM'hich are independ-

ON CLIMATES AND WINDS, 701

cnt of the sun's immediate action. Thus, it has been observed, that when
the weather has been clear, and a cloud passes over the place of observation, the
thermometer frequently rises a degree or two almost instantaneously. This
has been partly explained by considering the cloud as a vesture, preventing
the escape of the heat which is always radiating from the earth, and reflecting
it back to the surface : the cloud may also have been lately condensed, and
may itself be of ahigher temperature than the earth. Mr, Six has observed that in
clear weather, the air is usually some degrees colder at night, and warmer by day,
close to the ground, than a few feet above it; but that in cloudy weather there
is less difference: and it is possible that this circumstance may be derived
from the difference of the quantity of evaporation from the earth's surface,
which occasions a different degree of cold in different states of the atmosphere.

The motions of the air, which constitute winds, are in general dependent,
in the first instance, on variations of temperature. They are so accidental and
uncertain, as to be subjected to no universal laws ; as far however as any re-
gularity can be observed in their recurrence, it may in most cases be suffi-
ciently explained.

The principal phenomena of the periodical winds may be reduced to six
distinct heads: first the general tendency from north east and south east
towards the equator, in latitudes below 30°; secondly, the deviation of this
tendency from the precise situation of the equator; thirdly, the prevalence
of westerly winds between 30* and 40° or more, especially in the southern
hemisphere; fourthly, the local modifications to which these general effects
are subjected; fifthly the monsoons, which vary every half year; and lastly
the diurnal changes of land and sea breezes.

With respect to the general tendency of the trade winds to the west, it
may be sufficiently explained by Hadley's theory of the difference of the
rotatory motion of different parts of the atmosphere, combined with the
currents occasioned by the greater heat at the equator. For the sun's rays,
expanding the air in the neighbourhood of the equator, and causing it to
ascend, produce a current in the lower parts of the atmosphere, which rush
southwards and northwards towards the equator, in order to occupy the place
of the heated air as it rises: and since the rotatory motion of the earth is

VOL. I. 4s

^<S|^ I.KCTOllE XVI.

greatest at the equator, and is directed eastwards, the air coming- 'from thfc
poles has of course a relative motion westwards ; and 'hence the joint motion
of the current is directed, in the northern hemisphere, from north east to south
•west, and in the southern, from south -eaist to north west. Dr. Hjrlley sup-
posed that the air was made in some measure tofoilowthe son roimd rhecartA,
simply by means of the expansion of the atmosphere, which takes place im-
mediately under him, and accompanies him round the globe ; but it does
rot seem evident that the air could have any greater tendency to follow the
sun than to meet him. Astronomers have, however, deduced an additional
cause for an easterly wind from the attractions of the moon and of tlie sun,
■which -appeair, from the laws of gravitation, to liave a slight tendency to
retard the rotatory motion of the atmosphere: and a similar instance has
been observed in the motions of the atmosphere of the planet Jupiter, by
means of the appearances of spots of different kinds on his disc, some of
which seem to revolve less rapidly than the body of the planet. At so
great a distance, the influence of the sun's heat must be comparatively incon-
siderable, and the want of a tendency in the spots towards the equator appears
to show, that the atmosphere, iii which they float, is not put in motion by tlie
same causes, which we have supposed to be most concerned in the production
of our own trade winds. It has been remarked that the friction of the atmo-
sphere, thus retarded by the attraction of the sun and moon, must in the
course of ages have impaired the uniformity of the earth's diurnal motion ;
and it has been observed, on the other hand, that even this effect would be
partially counteracted by the gradual filling up of valleys, by means of the
descent of the superficial parts of mountains, which, at a greater distance
from the centre, were revolving with a rapidity somewhat |>reater than the
valleys in which they are deposited; but probably neither of these changes
would become sensible in millions of years.

The second circumstance is easily explained by the greater heat of the northern
than of the southern hemisphere ; so that instead of coinciding with the equator,
the neutral portion of the atmosphere lies between 3° and 5° of north latitude ;
the nor.h east wind not reaching the equator, and the south east continuing
about 3" beyond it. But the situation of the neutral portion varies with the
sun's declination, accordingly as different parallels of latitude become in
succession somewhat hotter than the neighbouring parts. Where the

ON CLIMATES AND VtKDS. 70f

northern and southern currents meet, their joint effect mu«t naturally be to
produce a due east wind; but in some parts of the ocean, temporary calms
and irregular squalls have been observed to take place of this easterly wind,
■which generally prevails in the neutral parts near the equator.

The tliird fact, that is, the frequency of westerly winds between the ^-^'^ESg ^
latitudes 30' and 40°, has not yet been sufficiently explained. The most
probable cause of this circumstance is, that the current of heated air, which ^*^/:/>r,
we have liitherto neglected, and which passes, in the upper parts of the
atmosphere, from the equator each way towards the poles, and whiJi, being
the converse of the trade wind, must be a south west and north west \viud>
in the different hemispheres, becomes here sufficiently cool to descend and mix
with tke lower parts of the atmosphere, or to carry them along by itslateral fric-
tion; and while it descends to complete the circle, necessary for supplying the
current to tlie equator, its motion with respect to tlie horizon nuist btcomeat a
certain time due M-est, since the cause which stops its progress n.rthwdnis, has
no tendency to impede its motion eastwards. The outN\ard bound East India
ships generally make their easting in about 36" south latitude. It is probably
also on account of the rotatory motion of the earth, that southwest winds are
more common in our latitudes than south east, and north east than northwest.

Among the local modifications to be considered in the fourth place, we
may reckon the greater indistinctness of the third effect in the northern than
in the southern hemisphere, a circumstance which is explained from the more
irregular distribution of sea and land: for between 30° and 40° south
latitude the ocean is scarcely any where interrupted. In lower latitudes also,
near the west coast of Africa, the winds are so much deflected towards the
land, as to become in general westerly instead of easterly.

The monsoons, which constitute the fifth remarkable circumstancey are
so called from a Malay word, denoting season. They are occasioned by the
peculiar situation of the continent of Asia, on the north side of the equator.
From April to September, the sun having north declination, the heat on this
continent, a little north of the tropic, is very intense, and the general
current is consequently towards the north. The air, therefore, coming
from douth latitudes towards the equator, becomes, on account of tlje defi-

704 • LECTURE LVI.

ciency of rotatory motion, a south east wind, as usual, which is found to
prevail between Madagascar and New Holland, as far as the equator. In
consequence perhaps of friction in its passage, it gradually loses its impetus
towards the west, and at the equator is nearly a south wind : but in proceed-
ing north from the equator, it becomes, from an excess of rotatory motion, a
south west wind, which blows into the Arabian gulf, and the bay of Bengal.
Both these winds are however variously modified by the particular situations
of the islands and continents. From October to March, on the contrary,
the sun having south declination, the south east trade wind stops at 10° south
latitude; the trade winds on the north side of the equator are as usual north
east; and beyond the equator they become for some degrees north west, the
circumstances being the reverse of those which happen in the summer months,
at greater distances, on the o»her side of the equator. (Plate XLII. XLIII. )

The last fact is the simplest of all. The land and sea breezes are produced
by the ascent of the air over the land in the day time, while the land is
hotter than the sea; and jits descent at night, when the land is become
colder: hence the breeze comes from the sea by day, and from the land by
night.

The violent agitations of the air, which constitute hurricanes and whirl-
winds, occur more commonly in tropical climates than in others. The
causes of these storms are little understood: their course is said to be
generally opposite to that of the trade winds ; but tornados, which are less
regular hurricanes, originate indift'erently from every quarter.

The variations of the weight of the air, which occasion the winds, and
other changes in its density, which are the effects of the winds themselves,
are indicated by the height of the barometer, which is in general the more
variable as the winds are more liable to sudden changes. Hence in the
neighbourhood of the equator the height of the barometer is scarcely ever a
quarter of an inch more or less than 30 inches, which is very nearly its mean
height on the level of the sea in every part of the globe: in Great Britain
it is sometimes as low as 28 inches, but never higher than 31. We have
already seen that the elevation of any place above the lea reduces the height
^f the barometer according to a law which is determined by the general

ON CLIMATES AND WINDS. 705

properties of elastic fluids : thus, at an elevation of 1 mile above the sea, the
mean height of the barometer is 244- inches, and at £ miles, 20 inches only.
The use of the barometer, in foretelling variations of weather, is perhaps more
limited than has sometimes been supposed; but by a careful observation, con-
clusions may be drawn from it, which may in many cases be of considerable
utility: and it has even been applied with success, by some late navigators, to
the prediction of changes of wind, sit times when they could not have been
suspected from any other circumstances.

yotf

LECTURE LVII.

ON AQtrEOFS AND IGNEOUS METEORS.

J- HE phenomena originating from the evaporation of water constitute a
large proportion of the subjects of meteorology: they are materially influenced
by the diversities of climates and winds, which we have lately considered; and
they appear to contribute to the electrical changes, which form a principal
part of luminous or igneous meteors : nor is the action of water wholly un-
concerned in many of the effects of subterraneous fires, which have also a
slight connexion with atmospherical electricity; and it has been conjectured
that the only igneous meteors, which appear wholly independent of any of
these phenomena, may originate from volcanic commotions in other worlds.

The action of heat appears to detach continually from the surface of water,
and perhaps of every other liquid, and even solid, a certain quantity of va-
pour, in the form of an invisible gas; but when the space above the liquid is
already charged with as much vapour as can exist in it at the actual tempe-
rature, the vapour, thus continually thrown off, either remains suspended in
the form of visible particles, or falls back immediately into the liquid. This
is the simplest mode of explaining the continuance of evaporation, under the
pressure of any dry gas, however dense, and its apparent suppression in the
presence of moist air, however rare. Sometimes also, when the temperature of
the liquid is elevated, so that minute globules either of steam or of air rise
through it, some visible particles are projected upwards by each globule, and
continue to float in the air ; this appears, however, to be an irregularity un-
connected with the principal process of slow evaporation.

The quantity of vapour, which can exist in the space above any portion of
water, has been supposed by Deluc, Volta, and Dalton, to be wliolly inde-
pendent of the nature, the density, or even the presence of the air or gas

ON AQUEOUS AKD IGNEOUS METEORS, 707

Av^lch that ■space contains: and we may easily imagine that the smallest dis-
taitce, at which the particles of water, constituting vapour, can exist, with-
ou't coming within the reach oftiieir mutual coliesion, is the same, whatever
Ocher ^particles .«ia\ be scattered through the intervening space. It appears,
howciver, more consistcnit with sofiie cx;perimcnts, to suppose, that the presence
of air of the usual density. allows the particles of water to approach a little
nearer together without coliering, so that the utmost quantity of moisture,
that can be contained iu a cubic foot of air at a given temperature, is not ex-
actly the same as would make a cubic foot of pure vapour, but always in a
certain proportion to it; and it seems to follow, from the experiments of
Saussure, compared with those of Pictet, ihat the weight of the vapour
contained in a cubic foot of air is about one half greater than that, of a cubic
foot of pure vapour- at the same temperature.

When the air, iu the neighbourhood of the surface of the water,has become
thus saturated with moisture, the evaporation proceeds very slowly, the va-
pour being precipitated as soon as it rises; but if the air be continually
changed, so that the moistened portion may be removed, and dry air substi-
tuted for it, the process will be greatly expedited ; and such a change may bp
effected cither by wind, or by the natural circulation, occasioned by any eleva-
tion of temperature crmmunieated by the water to the neighbouring air; but
when this circulation is jjievented, the evaporation is much diminished, al-
though the temperature may be considerably elevated. Iu moderate exposures,
theVlepth of the quantity of water, evaporating in 24 hours from any surface, is
'ex pressed, ^according to Mr. Dalton's experiments, by the height of the column
of mercury ccjuivalent to the force of steam at the given temperature, deduct-
ing, however, theeffect of the elasticity of the moisture already existing in the
air.

*Since the quantity of moisture, which the air is capable of receiving, is
■grta.tev ns iis .teiinperature is greater, we may obtain a natural measure of the
quantity which it contains, by reducing it to the temperature at which the
moisture begins to be r'epositfd. Thus, if we take a glass of cold water, and
add to it some common salt, or some muriate of lijrie, we may cool the air
near it so TnnciJ, as to cause it to deposit a pait of its moisture on the glass:
and by measuiing the temperature uf the water when the precipitation begins.

703 LECTURE LVir.

Mr. Dalton estimates the true state of the air with respect to moisture. Thus, if the
glass begins to be moistened when the water is at 40°, he infers from the known
elasticity of steam at that temperature, that the quantity of moisture contained in.
tlie air is equivalent to the pressure of a column of mercury about a quarter of
an inch in height; and if the actual temperature of the air be 50", the corre-
sponding elasticity of steam being a little more than one third of an inch,
the daily evaporation in such air will amount to about one ninth of an inch,
making 40 inches in the whole year. In fact, however, the air is usually
nioister than this, and the mean evaporation of all England is, according to
Air. Dalton, about 23 inches only.

In hotter climates, and in particular situations, the evaporation may be
considerably greater. The Mediterranean Sea, being surrounded by land, is
more heated than the ocean, and the winds which blow over it are drier; con-
sequently its evaporation is greater than that of the Atlantic, and its specific
gravity is increased by the increased proportion of salt; so that at the straights
of Gibraltar, a current runs inwards at the surface and outwards near the bot-
tom, for the same reason as the air, when it is denser in a passage than in the
adjoining room, blows a candle towards the room at the lower part of the
door, and draws it towards the passage at the upper. Had there been a con-
tinual current inwards through the Straights, at all parts, the Mediterranean
must in the course of ages have become a rock of salt. It is indeed remarka-
ble that all lakes, into which rivers run without any further discharge, are
more or less salt, as well as lakes in general near the sea: but where a river
runs through a lake into the sea, it must necessarily, in the course of time, have
carried the salt of the lake with it, if it had ever existed.

f»

Experiments on the deposition of moisture, like those of Mr. Dalton, arc
liable to a slight inaccuracy, on account of the effects of an apparent elective
attraction, by means of which, some substances seem to attract humidity at a
temperature a little higher than others. Thus, a surface of metal often re-
mains dry, in the neighbourhood of a piece of glass which is covered with
moisture. It is certain that some substances attract moisture from the air,
even when the quantity which it contains is incomparably less than that
which would saturate it, since it is on this circumstance that the construc-
tion of hygrometers depends; and it is probably by a property somewhat si-

ON AQUEOUS AND IGNEOUS METEORS. 70^

inilar, that even surfaces of different kinds possess different attractive powers
for moisture nearly ready to be deposited. It is, however, only necessary to
employ, for Mr. Dalton's experiment, a substance whicli has a very weak attrac-
tion for moisture; and any kind of metal will perhaps be found sufficiently
correct in its indications.

It has been observed, that a piece of metal, placed on glass, usually protects
also the opposite side of the glass from the deposition of dew; and Mr. Bene^
diet Provost has shown, that in general, whenever the metal is placed on the
M'armer side of the glass, the humidity is deposited more copiously either on
itself, or on the glass near it; that when it is on the colder side, it neither re-
ceives the humidity, nor permits its deposition on the glass; but that the ad-
dition of a second piece of glass, over the metal, destroys the effect, and a se-
cond piece of metal restores it. It appears that, from its properties with
respect to radiant heat, the metallic surface produces "these effects, by pre-
venting the ready communication either of heat or of cold to the glass.

The quantity of invisible moisture, contained in air,may be,in some degree,
estimated from the indications of hygrometers, although these instruments
'have hitherto remained in a state of great imperfection. A sponge,' a quan-
tity of caustic potash, or of sulfuric acid, or a stone of a peculiar nature, has
sometimes been employed for determining the degree of moisture of the air,
from which it acquires a certain augmentation of its weight. A cord dipped
in brine, or the beard of an oat, is also often used for the same purpose: the
degree in which it untwists, from the effect of moisture, being shown by an in-
dex. Buttheextensionofahair,orofaslipof whalebone, which have been employ-
ed by Saussure and Deluc, appear to be more certain and accurate in their indi-
cations. The hair hygrometer acquires more speedily the degree correspond-
ing to any given state of the air, but it seems to reach the utmost extent of
its scale before it arrives at perfect humidity ; while the whalebone hygrome-
ter appears to express a greater change upon immersion in water than from the
effect of the moistest transparent air, which has also been considered by some
as an imperfection. Both these instruments are impaired by time, and ac-
(juire contrary errors, so that a mean between both is more likely to be cor-
rect than either separately. Their indications are at all times widely different
from each other, and the mean appears to approach much nearer to a natural

VOL. I. 4t

710 lECTUBE LVII.

scale than eitlier of them. Mr. Leslie employs a very delicate thermometer, of
which the bulb is moistened, for measuring the dryness of the air, by the cold
produced during evaporation, when the thermometer is exposed to it; but this
mode of estimating the quantity of moisture appears to be liable to consider-
able uncertainty. (Plate XLI. Fig. 581.)

In order that the scale of a hygrometer should be perfectly natural, it ought
to express, at all temperatures, the proportion of the quantity of moisture in
the air to that which is required for its saturation; thus, at 100 degrees,
it should imply that the slightest depression of temperature would produce a
deposition; at .50 degrees, that the air contains only half as much water as
would saturate it, or, supposing the thermometer at 52°, that a deposition
would be produced in it by a depression of 17°. And if we know the actual
temperature, and the temperature at which the deposition takes place, we
may find the height of the natural hygrometer, by the proportion of the
corresponding elasticities of steam. The mean height of the natural hygro-
meter in London is probably about 80°; that of Deluc's hygrometer,' with
proper corrections, being nearly 70°: so that a depression of 6° must usually
be sufficient to cause a deposition of moisture.

The quantity of water actually contained in a cubic foot of air, saturated
with moisture, appears to be about 2 grains at the freezing point, 4 grains
at 48°, 6 at 60°, and 8 at 68°; and the density of the vapour, thus mixed
with air, is, according to Saussure's experiments, about three fourths as great as
that of the air itself; so that moist air is always a little lighter than dry air;
and the more so as the air is warmer, provided that it be saturated with mois-
ture by means of the presence of water. It follows from the properties of mois-
ture thus determined, that if any two portions of perfectly humid air, at differ-
ent temperatures, be mixed together, there must be a precipitation: thus, a cubic
foot of air at 32° being mixed with another at 60°, their common tempera-
ture must be 46°; if they are saturated with moisture, they must contain 8
grains of water when separate; but when mixed they will be too cold by 2° to
contain the same quantity; since air at 48° can only contain 4 grains for each
foot; and it has been supposed that such mixtures frequently occasion a pre-
cipitation in nature. Thus, it often happens that the breath of an animal,
which is in itself transparent, becomes visible when mixed with a cold atmo-

ON AQUEOUS AND IGNEOUS METEOKS, 711

Sphere; and in such cases the deposition may perhaps be facilitated by the
cooling of the warmer air to a certain degree, even before a perfect mixture
has taken place

When visible vapour has been thus deposited from transparent ^air, by means
either of cold or of mixture, it generally remains for some time suspended, in
the form of a mist or of a cloud : sometimes, however, it appears to be at once
deposited on the surface of a solid, in the form of dew or of hoar frost; for
it is not probable that the crystallized. form, in which hoar frost is arranged,
can be derived from the union of the particles already existing in the air g
distinct aggregates.

The dew, which is commonly deposited on vegetables, is paitly derived, TiL.^/f^nr;.^i^ -^ ■ i}'
the evening, from the vapours ascending from the heated earth, since it is then
found on the internal surface of a bell glass; and towards the morning, from
the moisture descending from the air above, as it begins to cool. Sometimes,
however, in warmer weather, the dew begins to descend in the evening; this
the French call serein: the humidity deposited by mists on trees, and by
moist air on windows, generally Avithin, but sometimes without, they call givre.

Mists are said to consist sometimes of other particles than pure water:
these are called dry mists, and they have been swpposed to blight vegetables.
Such mists are sometimes attended by a smell, resembling that which is occa-
sioned by an electric spark. Rain falling after a dry season deposits, when it
has been suffered to stand, some particles of foreign matter which it has
brought down from 4:he atmosphere. There must indeed frequently be a
multiplicity of substances of various kinds floating in the air; the wind has
been found to carry the farina of plants as far as 30 or 40 miles, and the
ashes of a volcano more than 200. It only requires that the magnitude of the
particles of any substance be sufficiently reduced in size, in order to render
them incapable of falling with any given velocity; and when this velocity
is very small, it may easily be overpowered by any accidental motions of the
air. The diameter of a sphere of water, falling at the rate of one inch only in
a second, ought to be one six hundred thousandth of an inch, which is about
the thickness of the upper part of a soap bubble at the instant when it bursts ;
but the particles of mists are incomparably larger than this, since they would
otherwise be perfectly iii visible as separate drops: the least particle, that could

712 LKCTURE rVII.

be discovered by the naked eye, being such as would fall with a velocity of about
a foot in asecond,if the air were perfectly at rest. But it is very probable that
the resistance, opposed to the motion of particles so small, may be considerably
greater, than would be expected from a calculation, derived from experiments
made on a much larger scale, and their descent consequently much slower.

When the particles of a mist are united into drops capable of descendino-
■with a considerable velocity, they constitute rain ; if they are frozen durino-
their deposition, they exhibit the appearance of a perfect crystallization, and
become snow: but if the drops already formed are frozen, either by means of
external cold, or on account of the great evaporation produced by a rapid de-
scent through very dry air, they acquire the character of hail, which is
often observed in weather much too hot for the formation of snow.

It cannot be doubled but that there is a connexion between the descent of
the barometer and the fall of rain; but no satisfactory reason has yet been as-
signed for the circumstance; nor is it possible to foretel, with certainty, that
rain will follow any changes in the height of the barometer that have been ob-
served. The immediate dependence of rain, or of any other atmospherical
phenomena, on the influence of the moon, appears to be rendered highly im-
, probable, not only by mathematical calculations of the effects of the moon's
attraction, but also by the irregularity of the very observations, which have
been adduced in favour of such a connexion. But however uncertain the
ultimate causes of rain'may be in general, their effects in some places are suf-
ficiently constant, to be attributed to permanent local circumstances, and in
particular to the periodical recurrence of similar winds:

In low and level countries, clouds may often begin to descend from the up-
per regions of the atmosphere, and may be redissolved by the warmer air be-
low; but when they descend in an equal degree among mountains, they fall
on the earth; and besides the quantity of water which they furnish for vege-
tation, and that which is carried off by evaporation, they afford, by means of
springs and rivers, a constant supply for the use of man and of other animals
in distant parts. The upper regions of the atmosphere are however by na
means the principal sources of rain in ordinary climates, since a gage placed
on a very high building seldom collects more than two thirds as much rain
as another standing on the ground below: and the effects of mountains in

ON AQUEOUS AND IGNEOUS METEOKS. 713

collecting rain are perhaps chiefly (derived from the ascending currents which
they occasion, and by which the air saturated with moisture is carried to a
higher and a colder region.

The Abyssinian rains arethecausesoftheinundationoftheNIle; theylastfrom
April to September ; but for the fiist three months the rain is only in the night-
The inundation, in Egypt, begins at present about the 17th of June; it increases
for 40 days, and subsides in the same time; but the ancient accounts, as well
as some modern ones, assign a longer duration to it. The river Laplata rises
and falls at the same times as the Nile. The Ganges, the Indus, the Euphrates,
the river of Ava or Pegu, and many other large rivers, have also considerable
inundations at regular periods. In many other countries there are seasons at
which the rains seldom fail to recur; and sometimes the periodical rains are
different in different parts pf the same country. Thus the coast of Malabar,
which is to the west of the Gate mountains, or Gauts, enjoys summer
weather, without rain, from September to April, while that of Coromandel*
which is on the eastern side, experiences all the rigours of its winter; being at
this time exposed to the influence of the north east trade wind. Vicissitudes
of a similar nature are also observed on the north and south sides of the island
of Jamaica. The mean fall of rain in London is about 23 inches; at Exeter,
which is nearer to the Atlantic, 33; the average of England and Wales is 31.

The evaporations and precipitations, and probably also the condensations
and expansions, which take place on a large scale in the atmosphere and in
the clouds, cannot fail of producing changes in their electrical qualities;
and these changes appear to be the principal sources of the phenomena of
thunder and lightning. The clouds, when electrified, being more or less
insulated by the interposition of the air, exhibit attractive and repulsive
effects, and are discharged by explosions, either among themselves, or com-
municating with the earth, in the same manner as bodies which have been
electrified by artificial means; they also sometimes produce, in the neighbour-
ing parts of the earth, and in the animals on its surface, a state of induced
electricity ; and in this case the returning stroke, or the sudden restoration
of the equilibrium, when the electricity of the nearest clouds is imparted t&
the more remote, may be fatal, without any appearance of an immediate
discharge, at the place where the animal stands.

Tl^ lECTUnjf LVII.

We can, however, by no means precisely ascertain in what manner all tlie
electrical phenomena of the atmosphere are produced. It appears from the
experiments of Beccaria and Cavallo that the air is in general positively
electrical, and most so in cold and clear weather; in cloudy weather more slight-
ly: and that during rain, the air is generally in a negative state. Mr. Read
has found that air charged with putrid vapours of any kind, and in particular
the air of close rooms, is almost always negatively electrified. The electri-
city is more readily communicated to an electrometer in an elevated situation,
and in damp weather, than in other circumstances; a candle is also very
useful in collecting it. When a wire is connected with a kite, being con-
tinued along the string, we may frequently obtain from it sparks a quarter
of an inch long.

We find a complete and interesting description of the effects of a violent
thunder storm in a paper by Mr. Brereton, insertf^d in the Philosophical
Transactions. The circumstance happened in September 1780, at East
liourn, in a house occupied by Mr. Adair: it was built of stone, and stood
facing the sea. About nine o'clock, in a very stormy morning, a black cloud
approached the house ; several balls of fire were seen to drop from it succes-
sively into the sea, and one in particular, appearing like an immense sky
rocket, broke against the front of the house in diiferent directions. Mr.
Adair was standing at a window on the first floor, with his hands clasped
together, and extended against the middle of the frame; his hands were
forced asunder, he was thrown several yards off on the floor, and remained
for some time speechless and motionless, although not insensible: his clothes
were much torn ; several articles of metal about his person were partially
melted, while others, apparently in similar circumstances, and in particular
a silver buckle, escaped; and his skin was in many parts much scorched and
lacerated. The whole of the glass in the window, and a pier glass near it,
were completely destroyed, and scattered about the room; most of the fur-
niture was broken to pieces, and all the bell wires were melted. In the
room above this, a lady and her maid were driven to a distant part, and
rendered insensible for some time, but not hurt; in the room below, two
servants, who were near the wnndows, were struck dead : both the bodies were
turned black; one of them had a wound near the heart; and neither of theih
became stilf after death; a third servant, who was a little behind one of them,

4

ON AQUEOUS AND IGNEOUS METEORS. 715

escaped with the loss of a telescope, which he held in his hand, and M'ith
the sensation of a violent pressure on his head and on his back. A large stone
was forced out of the wall near them, and thrown into the room, and some
other similar eflects were observed, which marked the progress of the explosion.

For guarding against accidents so dreadful, Dr. Franklin's great invention
of metallic conductors may be very advantageously employed: for, when pro-
perly fixed, they afford a degree of security which leaves very little room for
apprehension. A conductor ought to be continued deep into the earth, or con-
nected with some well or drain; it should be of ample dimensions, and where
smallest, of copper, since copper conducts electricity more readily than iron.
In one instance a conductor of iron, four inches wide,and half an inch thick,
appears to have been made red hot by a stroke of lightning. It seems to be
of some advantage that a conductor should be pointed, but the circumstance
is of less consequence than has often been supposed. Mr. Wilson exhibited
some experiments in which a point was struck at a greater distance than a
ball, and therefore argued against the employment of pointed conductors.
Mr. Nairne, on the contrary, showed that a ball is often struck in preference
to a point. But it has been observed, that if a poiat attracts the lightning from
a greater distance, it must protect a grea/ter extent of building. It is easy
to show, by hanging cotton or wool on a conductor, that a point repels light
electrical bodies, and that a pointed conductor may, therefore, drive away
some fleecy clouds; but this effect is principally derived from a current of
air repelled by the point; and such a current could scarcely be supposed to
have any perceptible efiect on clouds so distant as those which are concerned
in thunder storms. In order to escape personal danger in a thunder storm,
the best precautions are, to avoid eminences, and all exposed situations, as
well as a near approach to conductors. The neighbourhood of windows, look,
ing glasses, fire places, and trees, must always be considered as hazardous.

It has been supposed that a sudden condensation of the air, arising from
cold, accompanied by a deposition of moisture, and propagated by a con-
tinuation of the cause, by means of the cold occasioned by expansion, pro-
duces frequently the noise of thunder, without any lightning, and without
any electrical agitation; but it does not appear that the opinion is well
established.

716 LECTURE LVII.

The phenomena of waterspouts, if not of electrical origin, appear to have
some connexion with electrical causes. A waterspout generally consists of laro-e
drops, like a dense rain, much agitated, and descending or ascending with a
spiral motion, at the same time that the whole spout is carried along horizon-
tally, accompanied in general hy a sound like that of the dashing of waves.
Spouts are sometimes, although rarely, ohserved on shore, but generally in
the neighbourhood of water. They are commonly largest above ; sometimes
two cones project, the one from a cloud, the other from the sea below it, to meet
each other, the junction being accompanied by a flash of lightning: and
when the whole spout has exhibited a luminous appearance, it has perhaps
served to conduct electricity slowly from the clouds to the earth. Some of
these circumstances may be explained by considering the spout as a whirlwind*
carrying up drops of water, which it has separated from the surface of the
waves; and the remainder may perhaps be deduced from the cooperation of
electricity, already existing in a neighbouring cloud.

It is doubtful whether the light of the aurora borealis may not be of an elec-
trical nature: the phenomenon is certainly connected with the general cause
pf magnetisrn ; the primitive beams of light are supposed to be at an eleva-
tion of at least 50 or 100 miles above the earth, and every where in a direc-
tion parallel to that of the dipping needle ; but perhaps, although the sub-
stance is magnetical, the illumination, which renders it visible, may still be
derived from the passage of electricity, at too great a distance to be dis-
covered by any other test.

Earthquakes and volcanos appear to originate in chemical changes, which
take place within the substance of the earth: they have probably little
further connexion with electricity, than as causes which occasionally destroy
the electrical equilibrium ; for although some authors have inferred, from the
great velocity with which the shock of an earthquake is transmitted from
place to place, that its nature must be electrical, yet others have, with
greater probability, attributed the rapid, succession of the effects to the
operation of a single cause, acting at a great distance below the earth's sur-
face. There are however some circumstances, which indicate such a con-
nexion between the state of the atmosphere and the approach of an earthquake,
as cannot easily be explained by any hypothesis.

ON AQUEOUS AND IGNEOUS METEORS. 7J7

Tlife shocks of earthquakes, and the eruptions of volcanos, are in all pro-
bability modifications of the effects of one common cause; the same coutitrie*
are liable to both of them; and where the agitation produced by an earth*
quake extends further than there is any reason tosuspectasubterraneousconimo*
tion, it is probably propagated through the earth nearly in the same manner a* A
noise is conveyed through the air. Vokanos are found in almost all parts of
the world, * but most commonly in the neighbourhood of the sea; and espe-
cially in small islands; for instance, in Italy, Sicily, Iceland, Japan, the
Caribbees, the Cape Verd islands, the Canaries, and the Azores: there are
also numerous volcanos in Mexico and Peru, especially Pichincha and Coto-
paxi. The subterraneous fires, which are continually kept up in an open
volcano, depend perhaps in general on suU'ureous combinations and decom-
positions, like the heating of aheap of wet pyrites, or the union of sul-
fur and iron filings: but in other cases they may perhaps approach more
nearly to the nature of common fires. A mountain of coal has been burning
in Siberia for almost a century, and must probably have undermined in some
degree the neighbouring country. Tlie immediate cause of an eruption
appears to be very frequently an admission of water from the sea, or from
subterraneous reservoirs; it has often happened that boiling water has been
discharged in great quantities from a volcano; and the force of steam i»
perhaps more adequate to the production of violent explosions, than any
other power in nature. The consequence of such an admission of water, into
an immense collection of ignited materials, may in some measure be under-
stood, from the accidents which occasionally happen in founderies: thus a
whole furnace of melted iron was lately dissipated into the air in Colebrook
Dale, by the effect of a flood, which suddenly overflowed it.

The phenomena of earthquakes and volcanos are amply illustrated by
the particular accounts, transmitted to the Royal Society by Sir William
Hamilton, of those which have happened at different times in Italy. The
earthquake, which desolated Calabria, in 1783, was fatal to about 40000
persons, continuing its ravages for more than three months ; it destroyed
the towns and villages occupying a circle of nearly 50 miles in diame-
ter, lying between 33 and 39 degrees latitude, and extending almost
from the western to the eastern coast of the southernmost point of Italy,
besides doing considerable damage to places at much greater distances from
its origin, which is supposed to Imve been either immediately under the towa

VOL. I. 4 u

718 LECTURE LVII.

of Oppido, in the centre of this circle ; or under some part of the sea, be-
tween the west of Italy, and the volcanic island of Stromboli. This island^
as well as Mount Etna, had smoked less than usual before the earthquake,
but they both exhibited appearances of an eruption during its continuance;
Etna towards the beginning, and Stromboli at the end. Before each shock
the clouds were usually motionless for a certain time, and it rained violently;
frequently also lightning and sudden gusts of wind accompanied the rain.
The principal shocks appeared to consist in a sudden elevation of the ground
to a considerable height, which was propagated somewhat like a wave, from
■west to east: besides this, the ground had also a horizontal motion backwards
and forwards, and in some measure in a circular direction. This motion was
accompanied by a loud noise; it continued in one instance for ten seconds
without intermission: and it shook the trees so violently that their heads
nearly reached the ground. It affected the plains more strongly than the
hills. In some places luminous exhalations, which Sir William Hamilton
thinks rather electrical than igneous, were emitted by the earth : the^sea
boiled up near Messina, and was agitated as if by a copious discharge of
vapours from its bottom; and in several places water, mixed with sand, was
thrown up to a considerable height. The most general effect of these violent
commotions was the destruction of buildings of all kinds, except the light
barracks of wood or of reeds, into which the inhabitants retreated as soon as
they were aware of their danger: the beds of rivers were often left dry, while
the shock lasted, and the water on its return overflowed their banks : springs
were sometimes dried up, and new ones broke out in other places. The hills
"which formed the sides of steep vallies were often divided by deep chasms
parallel to the vallies; andin many cases large portions of them were separated,
and removed by the temporary deluge to places half a mile or a mile off;
with the buildings and trees still standing on them; and in this manner hills
were levelled, and vallies were filled up. But the most fatal accident of this
kind happened at Scilla, where so large a portion of a cliff" was thrown into
the sea, that it raised an immense wave, which carried off more than 2000
inhabitants who were collected on the beach, and even extended its formi-
dable effects to the opposite coast of Sicily, where several persons perished by
it in a similar manner.

The eruptions of volcanos are usually attended by some shocks like those
of earthquakes, although commonly Jeas violent. Open volcanos continually

4

ON AQUEOUS AND IGNEOUS METEORS, 7I9

throw out, in more or less abundance, smoke, ashes, and pumice stones, or
light cinders; but their most formidable effects are produced by a torrent of
ignited lava, which, like a vast deluge of liquid or semiliquid fire, lays
waste the country over which it runs, and buries all the works of human art.
In jNIarch, I767, Vesuvius began to throw out a considerable quantity of ashes
and stones, which raised its summit in the course of theyearnoless than 200 feet,
forming first a little mountain of pumice stones within the crater, which by
degrees became visible above its margin. The smoke, which was continually
emitted, was rendered luminous at night, by the light derived from the fire
burning below it. In August some lava had broken tlirough this mountain,
and in September it had filled the space left between it and the former crater.
On the 13th and 14th of October there were heavy rains, which perhaps
supplied the water concerned in the eruption that shortly followed. On the
morning of the 19th, clouds of smoke were forced, in continual succession,
out of the mouth of the volcano, forming a mass like a large pine tree, which
was lengthened into an arch, and extended to the island of Caprea, 28 miles
off: it was accompanied by much lightning, and by an appearance of meteors
like shooting stars. A mouth then opened below the crater, and discharged
a stream of lava, which Sir William Hamilton ventured to approach within a
short distance, imagining that the violence of the confined materials must
have been exhausted; but on a sudden the mountain opened with a great
noise at a much lower point, about a quarter of a mile from the place where
he stood, and threw out a torrent of lava, which advanced straight towards
him, while he was involved in a shower of small pumice stones and ashes, and
in a cloud of smoke. The force of the explosions was so great, that doors
and windows were thrown open by them at the distance of several miles: the
stream of lava was in some places two miles broad, and 60 or 70 feet deep; it
extended about six miles from the summit of the mountain, and remained hot
for several weeks. In 1794 a still more violent eruption occurred: it was
expected by the inhabitants of the neighbourhood, the crater being nearly
filled, and the water in the wells having subsided. Showers of immense
stones were projected to a great height; and ashes were thrown out so co-
piously, that they were very thick at Taranto, 250 miles off; some of them
also were wet with salt water. A heavy noxious vapour, supposed to be
carbonic acid, issued in many places from the earth, and destroyed the vine-
yards in which it was suffered to remain stagnant. A part of the town of
Torre del Greco was overwhelmed by a stream of lava, which ran through it

720 LECTUUE LVII.

into the sea; yet notwithstanding the frequency of such accidents, the in-
habitants had so strong a predilection for their native spot, that they refused
the offer of a safer situation for rebuilding their houses.

Convulsions of these kinds must have very materially influenced the dis"
position of the strata of the earth, as well as the form of its surface; but it
is by no means fully determined how far such causes have been concerned,
or how far the effects are to be attributed to the intermediation of water only.
Mineralogists and geologists have been principally divided into two classes
with respect to their theories of the earth, some maintaining the Vulcanian,
and some the Neptunian hypothesis. It appears to be impossible to decide
with any certainty between these opposite opinions; nor is it perhaps of
much consequence for any purpose of practice, or even of science. The
Neptunians are certainly able to establish their own theory positively, and
to prove that the fluid parts of the earth and sea must have been very materi-
ally concerned in producing the changes which have happened to the solid
parts; but it may be difficult for them to confute the assertion, that heat,
whether caused by volcanos or otherwise, has also been a very powerful
agent in these operations, and in some cases the joint effects of heat and of
increased pressure appear to have been concerned, in giving to minerals of dif-
ferent kinds tlieir actual form; although on the whole it seems probable that
the operation of heat has been much more limited than that of aqueous solu-
tions and precipitations. Mr. Davy has also very justly inferred, from his
experiments with the battery of Volta, that the effects of the electricity ex-
cited by means of chemical changes within the earth, have probably been
very materially concerned in the gradual formation of a variety of mineral
productions.

The arguments for establishing the general fact, that great convul
sions have actually happened to the earth, are too well known to require
minute examination : the variety of fossil substances, many of them ma-
rine productions, and some almost preserving a recent appearance, that are
found in mountains remote from the sea, are undeniable proofs that the
levels of the earth's surface must have undergone considerable changes; al-
though some philosophers are of opinion, that such of the primary mountains as
are above 6 or 7OO feet high, have never been wholly covered by the sea. It
is not at ail easy to explain the change of climate, which some of these cir-
1

ON AQUEOUS AND IGNEOUS METEOltS. 731.

r * ■ ■

cumstaiices appear to indicate; the remains of animals inhaijiting hot countries,
and the marine productions of hot climates, which are frequently found in -
high northern latitudes, would induce us to suspect, that the position of the '
earth's axis was at a former time very different from its present position { '
and we can scarcely assign any other probable cause for this change, than '
the casual interference, and perhaps incorporation, of a comet with the
earth. The probabilities of such an event, in the whole course of time, are
however so small, that we have no reason to be apprehensive of the chance
of its occurring in future, for it is not enough that a comet should approach •
so near to the earth as to be very powerfully attracted by it, its motion must
also be directed almost in a straight line towards the earth ; otherwise it might
only be inflected into a new orbit, and go off again, without having caused
any other disturbance than a partial overflow of the sea.

The face of the globe has also been very materially changed in the course
of ages, by the gradual operation of the sea and of rivers. The sea has in-
croached in particular parts, and retired from others; and the mouths of
large rivers, running through low countries, have often been variously modi-
fied, by a deposition and transfer of the matter washed down from the land.
At Havre the sea undermines the steep coast, and recedes at Dunkirk, where
the shore is flat: in Holland the Zuyder Zee was probably formed in the
middle ages by continual irruptions of the sea, where only the small lake
Flevo had before existed; and the mouths of the Rhine have been consider-
ably altered, both in their dimensions and in their directions. The
mud, deposited by large rivers, generally causes a Delta, or triangular
piece of land, to grow out into the sea; thus the mouth of the Missis-
sippi is said to have advanced above 50 miles since the discovery of"
America; and the sea has retired from Rosetta above a mile in 40 years.
The mouths of the Arno and of the Rhone consist also in great measure of
new land.

The meteors denominated shooting stars are observed to move in all direc-
tions, as well upwards as downwards, although they frequently seem to
have a tendency towards a particular quarter in the course of the same
evening. Their height is seldom less than 20 miles, and sometimes as
nmch as 100 or 200, but usually about 50; their velocity is commonly
about 20 miles in a second, wliich differs very little from that of the earth

72S lECTORE LVII.

in its orbit. The rapidity of their motion, as well as its occasional deviation
from a right line, has generally been considered as a reason for supposing
that they depend on electricity; but the opinion is by no means fully esta-
blished.

Other igneous meteors, which nearly resemble in their appearance the
largest of these, are sometimes observed to fall on the earth, either entire or
divided : and after their fall, certain stones have been found, which have
been supposed to have descended in an ignited state. Mr. Howard has ascer-
tained that almost all these stones agree in their general characters, and in
their chemical analysis, especially in the circumstance of containing nickel.
It has been conjectured, both in this country and on the continent, that they
have been emitted by lunar volcanos, and it has been observed, that since they
would find little or no resistance from the very rare atmosphere of the moon,
they would require a velocity of projection only four times as great as that
which a cannon ball sometimes receives, in order to rise into the sphere of
the earth's attraction. Their heat and combustion may not improbably be
derived from the great condensation which they must occasion in the air im-
mediately before them, and even their friction might easily produce enough
of electric light, to render them visible in the dark. Among many such sub-
stances projected from the moon, it is probable that a few only would be di-
rected towards the earth, and many more would be made to revolve in ellipses
round it, and become little satellites, too small for human observation, ex-
cept when they enter far enough into the atmosphere to produce an appear-
ance of light, resembling that of a shooting star ; but it is scarcely probable
that their velocity could ever be at all comparable with that which has been
attributed to these meteors. There is, however, no difficulty in supposing, on
the other hand, that the wandering substances, which may be moving through
empty space, with a velocity equal to that of the shooting stars, may be so
much retarded, when they penetrate deep into our atmosphere, as to make
but a moderate impression by their fall on the ground; and if we suppose
the meteors to be of one kind only, they must be referred rather to the de-
scription of shooting stars than to that of the productions of lunar volcanos;
although the undulatory motion, sometimes observed in these meteors seems to
be in some measure inconsistent with the progress of a heavy body, moving by
means of its natural inertia in a straight line.

72S

LECTURE LVIII.

ON VEGETATION.

It may appear idle to some persons, to attempt to reduce the outlines of na-
tural history into so small a compass, as is required for their becoming a part
of this course of lectures; and it would indeed be a fruitless undertaking to
endeavour to communicate a knowledge of the particular subjects of this sci-
ence, even in a much longer time than we shall bestow on it. But many na-
turalists have spent a great portion of their lives in learning the names of
plants and animals, and have known at last less of the philosophy of the sci-
ence, than might have been told them in a few hours, by persons who had ob-
served with more enlarged views, and who had reasoned on general principles.
And we shall perhaps find it possible to collect into a small compass the most
useful information, that has hitherto been obtained, respecting the laws of
animal and vegetable life, as well as the foundations of the methods, by which
the most received systematical classifications have been regulated.

The surface of the earth, as well sea as land, is occupied by innumerable
individuals, constituting an immense variety of distinct species of animated
and inanimate beings, comprehended in the three grand divisions of natural
bodies. The mineral kingdom consists of such substances, as are composed of
particles either united without any regular form, or collected together by ac-
cretion or external growth only. When mineral substances crystallize, they
often imitate the form, and almost assumetheexternalappearanceof vegetables:
but their particles are never extended to admit others between them, and to
be thus enlarged in all their dimensions ; their growth is only performed by
the addition of similar particles, upon the surface of those t' at have been al-
ready deposited.

Vegetables derive their existence, by seeds, or otherwise, from a parent

724 LECTURE LVni.

stock, their parts arc extended and evolved from within, and they imbibe their
nutriment by superficial absorption only. There is indeed in the crystalliza-
_tion of minerals a slight resemblance to a reproduction or generation, wlien a
small portion of the substance serves as a basis for the formation of subse-
quent crystals: but this portion becomes a constituent part of the crystal,
while it preserves its original form; a seed, on the contrary, is a substance
naturally and completely detached from the plant, and containing within it-
self the simplest rudiments of a new individual, which is afterwards evolved
and enlarged. Sometimes, however, vegetables are propagated by means of
bulbs, or by spreading roots, by slips, or by ingrafted scions, Avithout a seed de-
tached in the regular manner; but in these cases the new plant is much more
identical with the old one, than when it is raised from a seed, being as it were a
continuation of the same existence. Plants are nourished in great measure by
means of their roots; and sometimes, where they are without roots, their nu-
triment is probably absorbed by all parts of their surface.

Animals are distinguished from vegetables by the reception of their food,
for digestion and assimilation, into an internal cavity constituting a stomach.
The existence of a stomach, calculated for the digestion of food, appears to
be the best, if not the only criterion of an animal. Some vegetables, indeed,
have a power of catching and detaining animals, by curling up their leaves so
as to cover them, as the drosera or sundew, and the dionaea muscipula, or
catchfly; but this mechanism can scarcely be intended for their immediate
nutriment, at least the leaf can scarcely be supposed to assume the character
of a stomach. It is true that we imaaine all animals to have sensation, and
all plants to be without it; and if it were possible to discriminate decisively
between sensation and irritation, the distinction would supersede every other:
but in many cases it is extremely difficult to say where sensation is present,
and where irritation only produces the same apparent effects. We cannot be
sure that the hydra, or fresh water polypus, or the trichurus sol, an animal-
cule described by Dr. Shaw, suffers any sensation of pain when it is diviiled
into two parts; at least the pain seems to agree remarkably well with its con-
stitution, for it lives and thrives with increased vigour, as two distinct animals.
On the other hand, many plants are easily stimulated to perform motions,
which have the appearance of muscular actions, influenced by sensation: the
sensitive plants close or depress their leaves, in consequence of agitation or of

ox VEGETATION. 79,5

electricity; the stamina of the barberry and of the pellitory are thrown into
motion, when touched with a needle, and those of rue, and of the grass of
parnassus, have at times alternate motions without any apparent cause. A
zoophyte is an animal absolutely fixed to one place; and the vallisneria is a
vegetable possessed of a certain limited power of locomotion. A plant
chooses in preference to turn towards the light; and it has been known that
an ash tree on a wall, when incapable of being any longer supported by the
wall only, has concentrated all its force in tbe production of one large root,
descending to the ground. Some of these circumstances may be explained
without recurring to any thing like volition; but, as far as wc know, the
same explanations might be applied to some animal motions: and although it
is very possible that there may be a certain limit, where the influence of mind
and sensation terminates, and the laws of vegetable life only prevail; yet the
place of the division is not strongly enough marked, to allow it to form a
characteristic in an artificial system. It has, been asserted that some worms
are nourished by absorption only, without the assistance of a stomach; thus
hydatids, which are supposed to be of an animal nature, appear to be simply
bags of a fluid without any visible opening; but a few doubtful cases of this
kind can scarcely be sufficient, to invalidate the general position, that all bodies
decidedly animal have a cavity for the reception of food. There are usually
also some chemical distinctions in the component parts of animals and vege-
tables; animal substances commonly containing greater proportions of azote
or nitrogen, and of phosphoric acid; but there are some exceptions to this ob-
servation; thus the carica papaya, or papaw, contains nearly the same prin-
ciples as are usually found in substances of animal origin. In general we may,
readily distinguish a small portion of an animal from a vegetable substance,
by the smell produced in burning it. According to common language, W£
say, that minerals have growth only, but not always; that vegetables grow
and live also; and that animals have sensation, as well as life and increase of
magnitude.

Mineralogy is a branch of natural history so nearly allied to chemistry,
that it cannot be completely understood without a previous knowledge of that
science. It may therefore be more properly considered as belonging to a
course of chemical than of physical lectures.

VOL. I. 4 X

72^ LECTURE LVIII.

The vegetable kingdom presents to us a spectacle highly interesting by its
variety and by its elegance; but the economy of vegetation appears to be lit-
tle diversified, although little understood. With respect to the apparent per-
fection of their functions, and the complication of their structure, we may
consider all vegetables as belonging to two principal divisions, in one of
■which the seed is prepared with the assistance of a flower, having its stamina
and its pistils, with petals or a calyx; while in the other, the preparation
of the seed is less regular and conspicuous, and hence such plants are called
cryptogamous. In some of these there is a slight resemblance to the flowers of
other vegetables, but on the whole, the class appears to form one of the con-
necting links between the three kingdoms of nature; its physiology is proba-
bly simple, but it has been little examined. The herbs, palms, shrubs, and
trees, which constitute the numerous genera of flowering vegetables, exhibit
the greatest diversity in the forms and dispositions of the organs of fructifica-
tion, while they have all a general resemblance in their internal economy.

Every vegetable may be considered as a congeries of vessels, in which, by
some unknown means, the aqueous fluids, imbibed by its roots, are subjected
to peculiar chemical and vital actions, and exposed in the leaves to the in-
fluence of the light and air; so as to be rendered fit for becoming constituent
parts of the plant, or of the peculiar substances contained within it.

The first process in the germination of a seed is its imbibing moisture, and
undergoing a chemical fermentation, in which oxygen is ab*orbed, and a part
of the mucilage contained in the seed is converted into sugar; a substance
probably more nutritive to the young plant. The radicle shoots downwards,
and the seed leaves, or cotyledons, which are generally two, although some-
times more or less numerous, raise themselves above the ground, till in a
short time they die and drop off, being succeeded by the regular and more
adult leaves.

In every transverse section of a vegetable, we commonly discover at least

four different substances. The parts next to the, axis of the tree or branch

consist of medulla or pith, which is supposed by some to be the residence of

the vegetable life of the plant; but a tree may live for many years after be-

3

OK VEGETATION. 727

ing in great measure deprived of its medulla. The pith is of a loose and
light spongy texture ; it sends a ramification into each branch and each leaf,
where it appears to serve also as a reservoir of moisture. The pith is sur-
rounded by the woody part, composed of fibres more or less strongly com-
pacted together, but not actually ramifying into each other in any great
degree, although there is reason to suspect some lateral communications bcf
tween them. They are interrupted, at certain intervals, in many trees, by-
fibres, in a radiating direction, forming what is called the silver grain. Like
the bones in animals, the wood constitutes the strongest part of the vege--
table; and like them too it is in a certain degree furnished with vessels. It
has even been supposed by some, that the fibres themselves are distinct
tubes, and by others, that the interstices between them serve the purpose
of vessels, but neither of these opinions is at present generally received. Th«
wood consists of a number of concentric layers or strata, formed in succes-
sive years; the external part, which is last formed, is called the alburnum, or
white wood, and this part is the most vascular. The bark encompasses the
wood; and this also consists, in trees, of several layers, which are produced ia-
as many difterent years ; the external parts usually cracking, and allowing us
at their divisions to observe their number, the inner layer only being of
immediate use. This layer is called the liber, and since this material was
once used instead of paper, the Romans called a book also liber. The bark
consists of fibres of the same kind as the wood, but more loosely connected.
It is covered by the cuticle, which extends itself in a very great degree, as
the growth of the vegetable advances, but at last cracks, and has its ofiice
supplied by the outer layers of bark. Between the bark and the cuticle a
green pulpy substance, or parenchyma, is found, which seems to be analogous
to the rete mucosum, interposed between the true skin and the cuticle in
animals. Mr. Desfontaines has observed, that in palms, and in several other
natural orders of plants, the annual deposition of new matter is not confined to
the external surface, but that it takes place in various parts of the plant,
as if it were composed of a number of ordinary stems united together. -

There are three principal kinds of vessels in the different parts of vegeta-
bles: the sap vessels, which are found both in the wood and in the bark,
although their nature appears to require further examination: secondly, the
air vessels, or tracheae, which arc composed of single threads wound into a

728 iECTUKE LVIII.

spiral tube, like the spring of a bell, and capable of being easily uncoiled;
these, though they have been called air vessels, and supposed by some to
serve the purposes of respiration, are described by others as containing, during
the life of the plant, an aqueous fluid: and they are probably little more than
sap vessels, with an additional spiral coat : they are not found in the bark,
•nor in all species of plants; and it has thence been inferred that they are
not immediately necessary to the growth of the plant. The third kind are
the proper vessels of the plant, which are generally disposed in concentric
circles, and appear to be unconnected with the sap vessels, and to contain
the milky, resinous, and other peculiar juices, which are found in difterent
kinds of plants; for the sap is nearly the same in all, at least it is independ-
ent of the, gums and resin, which often distinguish particular plants; it con-
tains a certain portion of mucilage, and probably in some plants, as the
sugar maple, a considerable quantity of sugar. Mr. Mirbel has also made a
number of still more accurate distinctions respecting the structure of the dif-
ferent kinds of vessels. The circulation of the sap is not completely under-
stood; when an orifice is made near the root of a tree, it flows most copiously
from above : when near the summit, from below. Dr. Hope actually reverted
the natural course of the juices of a tree, without changing its position; by
inoculating a willow with two others, he completely united its existence with
theirs, and then, removing its roots, he found that its vegetation was sup-
ported by the juices of the two others. A tree may also be actually inverted,
and the upper part will strike root, the lower putting out branches and leaves.

Plants perspire very considerably, and also emit a quantity of gases of
different kinds; they generate a slight degree of heat, which may be observed
by means of the thermometer, and by the melting of snow in contact with
them. The growth of every tree takes place at the internal surface of the
bark, not only the bark itself being formed there, but the wood also being
deposited by the bark; for Pr. Hope Separated the whole of the bark of a
branch of willow from the wood, leaving it connected only at the ends, so as
to constitute a hollow cylinder, parallel to the wood ; and he found that new
layers were formed within the bark; and in another experiment a part of the
wood, deprived of the bark, although protected from the air, was only
covered with new bark as it grew over from, the old bark above and below.
The layers of wood, which are added in successive seasons, and keep a

ON VEGETATION. 729

register of the age of the tree, are very easily observed when it is cut across;
sometimes as many as 400 have been found in firs, and oaks are said to have
lived 1000 years.

Mr. Knight has inferred, from a great variety of experiments, that the sap,
either usually or universally, ascends through the wood into the leaves, and then
descends through the bark to nourish the plant. The leaves seem to be some-
what analogous to lungs, or rather to the gills of fishes: for plants have need
of air,and it has been found, that even seeds will not germinate in a vacuum.
As the lungs of animals appear to be concerned in forming the blood, so it
may be inferred from Mr, Knight's experiments, that the sap first ascends
to the leaves through the external i'resh wood or alburnum, and through the
central vessels of the young leaves and branches, derived from the alburnum,
and accompanied by the spiral tubes; and after being perfected by exposure
to light and air in the leaves, it descends in the bark, and serves for the secrcj-
tion of the alburnum, and of the internal la\ers of the bark, being conveyed
probably by two distinct sets of vessels. The sap, thus prepared by the leaves
in the summer and autumn, is supposed to leave its extractive matter in the
tree throughout the winter, in such a state as to be ready to unite with the
aqueous juices, which ascend from the root, in the succeeding spring. The in-
ternal parts of the wood, having served the purposes of vegetation, are hard-
ened, and perhaps dried up, so as to be afterwards principally subservient to
strength alone. By subsequent experiments, Mr. Knight has also found, that
when a branch hangs downwards, the sap still appears to proceed from the
part of the bark which is uppermost; so that the direction of the force of gra-
vity seems to be concerned in determining that of the motion of the sap.
There appears also to be some reason to suppose that mechanical means assist
in the protrusion of the sap, and the consequent growth of the tree; for if a
tree be more agitated by the wind in one direction than in another, its dia-
meter will be greatest in that direction.

The process of grafting depends on a remarkable property of 'the growth
of vegetables; if the cut surface of the inner bark of a small branch, or
cutting, be placed in contact with that of the branch of another tree, they
will unite sufficiently for the nourishment of the cutting; provided, however,
that the nature of the plants be not too diiTerent. Something of the same

73b LECTURE i.viir.

kind occurs in animal life, Avliere a tooth has been transplanted intb tht
socket of another, or where the spur of a cock has been inserted into his comb.

Plants have their natural periods of life, either of a few days, as in the case
of some of the fungi, of a year, of a few years, or of many centuries. They
have also their diseases ; they are often infested by insects, as in the gall of
the oak, and the woodruff of the rose, or by animalcules of a still lower order,
which are either the causes of the smut of corn, or constant attendants on it.
From unnatural and too luxuriant culture, they become sterile, and produce
double flowers instead of fruits and seeds. When deprived of sufficient mois-
ture, or nipped by frost, their leaves and branches often die^ and if the
plants recover their vigour, a separation is affected by a natural process, re-
sembling the sloughing of decayed parts of animals: but when the whole
plant sinks, the dead leaves continue to adhere to it. The annual fall of
leaves in autumn appears to be a natural separation nearly of the same kind,
which takes place when the leaves are no longer wanted; the growth of the
plant being discontinued, and their functions being no longer required.

Succulent plants generally die when the cuticle is removed, but not all
other plants. The air appears to be injurious to vegetables where it is not
natural; hence arises the benefit of Mr. Forsyth's method of completely ex-
cluding the air from the wounded parts of trees, by means of which their
losses are often in great measure repaired, and they acquire new strength and
vigour. Sometimes a diminution of the magnitude of a tree immediately in-
creases its fertihty ; its force being more concentrated, by lopping off its use-
less branches and leaves, it produces a larger quantity of fruit, with the juices
which would have been expended in their nourishment.

The Linnean system of vegetables is confessedly rather an artificial than a
natural one; but it is extremely well adapted for practice, and its universal
adoption has been productive of the most important improvements in the sci-
ence of botany. Of the 24 classes into which Linn^> has divided the vegeta-
ble kingdom, 23 are distinguished by the forms of the flowers and fruit, and
the 24th by the want of a regular florescence. The first 10 are named from
monandria, in order, to decandria; then follow dodecandria; icosandria, and
polyandria; the names expressing the niimber of the stamina, or filaments,
surrounding the seed vessel; and the orders are deduced in a similar manner

ON VFGETATIOV. 731

from the number of pistils, or little columns immediatefy connected Math the
seed vessel; and denominated nionogyaia, digynia, and so foith, as far as po-
lygynia. These classes dift'er little in general with respect to their natural habits,
except the twelfth, icosandria, which is characterized by the attachment of the
filaments to the green cup, surrounding the flower, and which comprehends
the most common fruit trees: this class has, however, been incorporated by
some later botanists M'ith the next. In the third class we find most of the
natural order of grasses ; the fifth, pentandria, is by far the most numerous
of any: the sixth contains the lilies, and many other bulbous plants. The
14th class, didynamia, is known by tvv^o longer and two shorter filaments;
it is perfectly natural, and comprehends flowers similar in their structure to
the foxglove and the deadnettle. The 15th also, tetradynaniia, is a class
of plants strongly characterized even by chemical properties; two of the fila-
ments are here shorter than the other four: cresses, radishes, and many other
acrid and ammoniacal vegetables belong to this class, as well as the turnip
and cabbage, which, when cultivated, become mild and nutritious. The class
monadelphia contains a few plants similar to the mallow; they are known by
the union of the filaments at their bases into a cylinder: those of the next
class have generally nine united, and one separate, whence the class is named,
diadelphia; it contains the papilionaceous flowers, somewhat resembling a
butterfly in their form, like the pea, and other leguminous plants, the broom,
the furze, and the acacia. The 18th class, polyadelphia, has the filaments of
its flowers united into several masses or bundles, as the hypericum or tutsan.
The next class is perfectly natural, and contains the composite flowers, which
have a peculiar union of the summits of the filaments; it is named syngenesiai
sunflowers, daisies, and artichokes, are familiar examples of the plants of this
class. The 20th class, gynandria, though it contains the natural family pf
the orchides, has been omitted by some late botanists; here the filaments arc
fixed on the pistil ; or more properly, in the arums, within the pistils. The
three following classes, monoecia, dioecia, and polygamia, difter from the
rest in having some flowers with filaments or chives, and some with pistils
only, either on the same plant, or on different plants, or mixed with flowers of
the mare common construction. Most of the forest trees belong to these
classes, but the distinctions which separate them from other classes are not
always very uniformly preserved, and, for this reason, many later botanists
have disused them. The plants of the last class, cryptogamia, are exceeilingly
numerous; the families of ferns, mosses, algae, or membranous weeds, and

732 IICTURE LVIII.

fungi or mushrooms, fill up its extensive departments; some have also sepa- *
rated a part of the algae under the name of hepaticae, or gelatinous weeds.
In this class the fructifications are extremely various; some of the fuci and
confervae approach so much in their general- appearance and mode of growth
to corallines and zoophytes, that they seem to form an obvious connexion
between the lowest ranks of the vegetable and animal kingdoms; Avhile other
plants of the class are scarcely distinguishable by their appearance from some
of the productions of the mineral kingdom.

The French have introduced into very general use the botanical system of
Jussieu. The most prominent feature in this system is the division of all the
genera into a hundred natural orders, which are also arranged in fifteen
classes. Jussieu begins, like Linne, with the separation of cryptogamic from
phanerogamic plants; the seeds of the cryptogamic plants, which form the
first class, being without cotyledons or seed leaves, and all other plants being
distinguished into such as have seeds with one and with two cotyledons.
Accordingly as the stamina or filaments are inserted below the pistil, on the
calyx, or on the seed vessel, the first description of seeds affords three dis-
tinct classes. The plants which have two cotyledons follow, and are divided
into apetalous, monopetalous, and polypetalous, from distinctions respect-
ing the corolla or flower leaves, which are somewhat arbitrarily understood;
and lastly diclinous, from the separation of the stamina and pistils. The
three first of these divisions are subdivided according to the insertion of the
stamina, and the union or separation of the antherae, which they support, into
ten classes, making, with the four already mentioned, fourteen, to which the
diclinous plants add a fifteenth. The orders are determined without any
particular limitation of the parts from which the characters are taken. This
system is of acknowledged merit as a philosophical classification of the natu-
ral orders of plants; such vegetables as nearly agree in their habits and ap-
pearances being brought more uniformly together than in the system of
Linne. Hence, in the arrangement of a botanical garden, or in a treatise on the
chemical or medical properties of plants, it might be employed with advan-
tage: but for the practical purposes of botanical investigation it appears to be
utterly unfit, since its author has sacrificed all logical and systematical laws
to the attempt to follow nature, in analogies, which are often discoverable only
with great difficulty, and which are seldom reducible to methodical defini-
tions.

753

LECTURE LIX.

ON ANIMAL LIFE.

The functions of animal life are not only more complicated in the sanu'
individual than those of vegetation, but also more diversified in the different
classes into which animals are divided; so that the physiology of each class
has its peculiar laws. We are indebted to Linnd for the first enlargement of
our views of the different classes of animals, and perhaps for the most conve-
nient arrangement, of the animal kingdom ; although his method has never
been universally adopted by our neighbours on the continent.

A considerable portion of the bulk of all animals is composed of tubular
vessels, which originate in a heart ; the heart propels through the arteries,
with the assistance of their own muscular powers, either a colourless transpar-
ent fluid, or a red blood, into the extremities of the veins ; through which it
again returns to the origin of its motion. Both insects, and vermes, or worms,
have their circulating fluids a little warmer than the surrounding medium, and
generally colourless ; but insects have legs furnished with joints, and worms
have nothing but simple tentacula at most in the place of legs. Fishes have
cold red blood, which is exposed to the influence of the air contained in water,
by means of their gills. The amphibia receive the air into their lungs, but
their blood is cold, like that of fishes, and in both these classes the heart has
only two regular cavities, while that of animals with warm blood has four ; the
whole contents of one pair being obliged to pass through the lungs, in order
to arrive at the other pair. Of animals with warm blood, the oviparous are
birds, and are generally covered with feathers, the viviparous are either
quadrupeds or cetaceous animals, and are furnished with organs for suckling
their young.

Each of these classes of animals is subdivided by Linn6 into different
VOL. I. 4y

734 LECTUBfe LIX.

orders, of which we shall only be able to take a very cursory view. The
first class, denominated mammalia, from the female's suckling its young,
comprehends all viviparous animals with warm blood. These, with very
few exceptions, have teeth fixed in their jaw bones; and from the form and
number of these teeth, the orders are distinguished, except that of cetaceous
fishes, which is known by the fins that are found in the place of feet. The
distinctions of the teeth are somewliat minute, but they appear to be con-
nected with the mode of life of the animal, and they are tolerably natural.
The first order, primates, contains man^ monkeys, and bats; the second,
bruta, among others, the elejihant, the rhinoceros, the ant cater, and the
ornithorhynchus, an extraordinary quadruped, lately discovered in New
Holland, with a bill like a duck, and sometimes teeth inserted behind it;
but there are some suspicions that the animal is oviparous. The order
ferae contains the seal, the dog, the cat, the lion, the tiger, the weasel,
and the mole, most of them beasts of prey; the opossum and the kan-
garoo also belong to this order, and the kangaroo feeds on vegetables,
although its teeth are like those of carnivorous animals. The fourth order,
glires, comprehends beavers, mice, s({uirrels, and hares, the fifth, pecora,
camels, goats, sheep, and horned cattle. The sixth order, belluae, contains
the horse, the hippopotamus, and the hog. The cetaceous fishes, or whales,
form the seventh and last order: they reside in the water, enveloped in a
thick clothing of fat, that is, of oily matter, deposited in cells, which enables
their blood to retain its temperature, notwithstanding the external contact
of a dense medium considerably colder.

Birds are distinguished from quadrupeds, by their laying eggs; they are also
generally feathered, although some few are rather hairy; and instead of hands
or fore legs they have wings. Their eggs are covered by a calcarious shell;
and they consist of a white, or albumen, which nourishes the chick during
incubation, and a yolk, which is so suspended within it, as to preserve the
side on which the little rudiment of a chicken is situated, continually up-
permost, and next to the mother that is sitting on it. The yolk is in great
measure received into the abdomen of the chicken a little before the time of
its being hatched, and serves for its support, like the milk of a (juadruped,
and like the cotyledons of young plants, until the system is become sulfi-

ON ANIMAL LIFE. 735

ckntly strong for extracting its own foot! oat of the ordinary nutriment of
the species.

Birds are divided, according to the form of their bills, into six orders:
accipitres, as eagles, vultures, and hawks; picae, as crows, jackdaws, hum-
ming birds, and parrots; anseres,, as ducks, swans, and gulls; grallae, as
herons, woodcocks, and ostriches; gallinae, as peacocks, pheasants, turkies,
and common fowls; and, lastly, passeres, comprehending sparrows, larks,
swallows, thrushes, and doves.

The amphibia are in some respects very nearly allied to birds: but their
blood is little warmer than the surrounding medium. Their respiration is
not necessarily performed in a continual succession of alternations, since
the whole of their blood does not pass through the lungs, and the circulation
may continue without interruption in other parts, although it may be im-
peded in these organs, for want of the motion of respiration. They are very
tenacious of life; it has been asserted on good authority that some of them
have lived many years without food, inclosed in hollow trees, and ev-en in
the middle of stones; and they often retain vestiges of life some days 'after
the loss of their hearts. Their eggs are generally covered with a membrane
only. They have sometimes an intermediate stage of existence, in which all
tlieir parts are not yet developed, as we observe in the tadpole; and in this
respect they resemble the class of insects. They are now universally consider-
ed as divided into two orders only ; reptilia, as the tortoise, the dragon, or
flying lizard, the frog and the toad ; all these have four feet : but the animals
which belong to the order serpen tes are without feet. Most of the serpentes
are perfectly innocent, but others have fangs,by which they instila poisonous
fluid into the wounds that they make. In England the viper is the only;
venomous serpent; it is known by its dark brown colour, and by a stiipe of
whitish spots running along its back ; but to mankind its bite is seldom, if-
ever, fatal.

The first three classes of animals have lungs, as we have already seen, for
respiration, and receive air by the mouth; those which have gills, and
red blood, are fishes, residing either in fresh or in salt water, or indiiferently

736 LECTURE LIX.

in both: their eggs are involved in a membrane, and have no albumen*
Of the six orders of fishes, four have regular gills, supported by little bones;
and they are distinguished, according to the place of their ventral fins, into
apodes, as the eel and lamprey; jugularis, as the cod; thoracici, as the
sole and perch, and abdominales, as the salmon and pjke : distinctions
which appear to be perfectly artificial, although useful in a systematic
' arrangement. Tiie two remaining orders are without bones in the gills,
those of the one being soft, and of the other cartilaginous or gristly.
These are the branchiostegi and chondropterygii of Artedi, which Linne,
from a mistake, classed among the amphibia. The sun fish, the lump fish,
the fishing frog, and the sea horse, are ofvthe former, and the sturgeon, the
skate, and the shark, of the latter order.

Insects derive their name from being almost always divided, into a head,
thorax, and abdomen, with very slender intervening portions: although
these divisions do not exist in all insects. They are usually oviparous : they
respire, but not by the mouth; they have a number of little orifices on each
side of the abdomen, by which the air is received into their ramified tracheae;
and if these are stopped with oil, they are suflfocated. Instead of bones, they
have a hard integument or shell. Their mouths are formed on constructions
extremel)- various, but generally very complicated : Fabriciushas made these
parts the basis of his classification; but from their minuteness in most species,
the method is, in practice, insuperably inconvenient; and the only way,
in Avhich such characters can be rendered really useful, is when they are
employed in the subdivision of the genera, as determined from more con-
spicuous distinctions. Insects have most frequently jaws, and often
several pairs, but they are always so placed as to open laterally or horizon-
tally. Sometimes, instead of jaws, they have a trunk, or proboscis. In
general, they pass through four stages of existence, the egg, the larva, or
stage of growth, the pupa, or chrysalis, which is usually in a state of torpor
or complete inactivity, and the imago, or perfect insect, in its nuptial,
capacity. After the last change, the insect most frequently takes no food
till its death.

The Linnean orders of insects are the coleoptera, with hard sheaths to tlieir

2 . '

ON ANIMAL LIFE.

IZ'T

wings, generally called beetles; the. hemiptera, of which the sheaths are of
a softer nature, and cross each other, as grasshoppers, bugs, and plant lice;
the lepidoptera, with dusty scales on their wings, as butterflies and moths;
the neuroptera, as the libellula, or dragon fly, the may fly, and other insects
with four transparent wings, but without stings; the hymenoptera, which
have stings, either poisonous or not, as bees, wasps, and ichneumons; the
diptera, with two wings, as common flies and gnats, which have halteres,
or balancing rods, instead of the second pair of wings; and lastly the aptera,
without any wings, which form the seventh order, comprehending crabs,
lobsters, shrimps and prawns, for these are properly insects; spiders, scor-
pions, millepeds, centipeds, mites, and monoculi. The monoculus is a genus
including the little active insects found in pond water, w'hich are scarcely
visible to the naked eye, as well as the Molucca crab, which is the largest
of all insects, being sometimes six feet long. Besides these there are several
genera of apterous insects which are parasitical, and infest the human race
as well as other animals.

The vermes are the last and lowest of animated beings, yet some of tbetti-^,^^>i^r, '^^■^
are not deficient either in magnitude or in beauty. The most natural divi--

■'?^w

sion of vermes is into five orders; the intestina, as earthworms and ascarides,
which are distinguished by the want of moveable appendages, or tentacula,
from the mollusca'; such as the dew snail,, the cuttle fish, the sea anemone,
and the hydra, or fresh water polype. The testacea have shells of one or
more pieces, and most of them inhabit the sea, and are called shell fish, as
the limpet, the periwinkle, the snail, the muscle, the oyster, and the
barnacle. The order zoophyta contains corallines, sponges, and other com-
pound animals, united by a common habitation, which has the general ap-
pearance of a vegetable, although of animal origin; each of the little inhabit-
ants, resembling a hydra, or polype, imitating by its extended arms the appear-
ance of an imperfect flower. The last order, infusoria, is scarcely distinguished
from the intestina and mollusca by any other character than the minuteness
of the individuals belonging to it, and their spontaneous appearance in
animal and vegetable infusions, where we can discover no traces of the man-
ner in which they are produced. The process, by which their numbers are
sometimes increased, is no less astonishing than their first production ; for
several of the genera often appear to divide spontaneously,, into two or more

738 LECTURE LIX.

parts, which become new and distinct animals, so that in such a case the
question respecting the identity of an individual would be very difficult
to determine. The volvox, and some of the vorticellae are remarkable for
their continual rotatory motion, probably intended for the purpose of strain-
ing their food out of the water: while some other species of the vorticella
resemble fungi or corallines in miniature.

Among the animals of these different classes, the more perfect are informed
of the qualities of external objects by the senses of touch, taste, smell, hear-
ing, and vision. A few quadrupeds are incapable of seeing: the mole has an
eye so small as to be with difficulty distinguishable; and the mus typhlus,
supposed to be the aspalax of Aristotle, has its eye completely covered by the
skin and integuments, without any perforation. Birds have hearing, but no
external ears, or auriculae. Insects appear to want the organs of smell; but
it is not impossible that their antennae may answer the purpose of hearing.
Many of the vermes are totally destitute of sight, and some of all the organs
of sense: none of them have either ears or nostrils. The external senses of
animals with warm blood are usually liable to a periodical state of inactivity
in the night time, denominated sleep. It is said that fishes never sleep; and
it is well known that some animals pass the whole of the severest part of the
winter in a state nearly resembling their usual sleep.

In animals which approach, in their economy, to that of the human system,
the process for supporting life by nutrition begins with the mastication of the
food, which has been received by the mouth- The food thus prepared is con-
veyed into the stomach by the operation of swallowing; but in ruminating
cattle, it is first lodged in a temporary receptacle, and more completely mas-
ticated at leisure. In the stomach, it undergoes digestion, and being af-
terwards mixed with the bile and other fluids, poured in by the liver and the
neighbouring glands, it becomes fit for affording the chyle, or nutritive juice,
which is separated from it by the absorbents of the intestines, in its passage
through the convolutions of a canal nearly forty feet in length. Together with
the chyle, all the aqueous fluids, which are swallowed, must also be absorbed,
and pass through the thoracic duct into the large veins entering the heart, and
thence into the general circulation, before they can arrive at the kidneys, by
which the superfluous parts are rejected. The chyle passes unaltered, with

ON ANIMAL LIFE. 739

the blood, through the right auricle and ventricle of the heart, and enters the
lungs, to be tliei e more intimately mixed with it, and perhaps to be rendered
animal and vital ; while the blood receives from the air, in the same place, a
supply of oxygen, with a small portion of nitrogen, and emits some superflu-
ous carbonic matter, in the form of carbonic acid. The blood, thus rendered
arterial, returuing to the left side of the heart, is distributed thence to every
part of the system, supplying nutriment throughout, while the glands and ar-
teries secrete from it such tluids,as are become redundant, and such as are required
for particular purposes subservient to the animal functions. It is probably in
these processes that heat is evolved; for by experiments on living animals, it has
been found, that the blood, returning from the lungs, is not warmer than be-
fore its entrance into them : we must therefore suppose, that when the tlorid
arterial blood is, by some unknown means, converted, in the extreme ramifica-
tions of the arteries, into the purple venous blood, to return to the heart by
the converging branches of the veins, there is a much more considerable ex-
trication of heat, than in the conversion of venous into arterial blood, by the
absorption of oxygen and nitrogen in the lungs. If the chyle is actually con-
verted into blood in the lungs, it is here that we must look for the formation
of the red globules, those singular corpuscles, to which the blood owes its
colour, as it docs its power of coagulation to a glutinous lymph, mixed with
a less coagulable scrum. The red particles in the human blood are about
•a-oW of an inch in diameter, somewhat. oblong, and flattened; they have
usually the appearance of a dark point in the centre; but there is tome
reason to suspect that this is merely an optical deception. In a few animals
they are a little smaller, but in most of the amphibia, much larger and flatter
than in man. While the lymph remains fluid, after the blood has been with-
drawn from the vessels, these globules tend to subside, and to leave it semi-
transparent: hence arises the appearance of a buff coat on blood left to co-
agulate, whicli is thinner or thicker, accordingly as the globules are sooner or
later arrested in their descent.

Themusclesareprobably furnished by the blood with a store of that unknown
principle, by which they are rendered ca])able of contracting, for producing
locomotion, or for other purposes, in obedience to the influence transmitted by
the nerves from the sensorium; the brain and nervous system in general arc
also sustained, by means of the vascular circulation, in a fit state for trans-
mitting the impressions, made by external objects on the senses, to the im-

740 LECTURE LTX.

mediate seat of thought and memory, in the sensorlum ; and for conveying
the dictates of the will, and the habitual impulses almost independent of vo-
lition, to the muscular parts of the whole frame.

In what manner these reciprocal impressions are transmitted by the nerves,
has never yet been fully determined : but it has long been conjectured, that
the medium of communication may bear a considerable analogy to the electrical
fluid; and the extreme sensibility of the nerves to the slightest portion of
electrical influence, as well as the real and apparently spontaneous excitation of
that influence in animal bodies, which have been of late years evinced by gal-
vanic experiments, have added very materially to the probability of the opi-
nion. An extremely slender fibre, of a substance capable of conducting elec-
tricity with perfect freedom, enveloped in a sheath of a perfect nonconductor,
would perhaps serve to communicate an impulse, very nearly in the same man-
ner, as the nerves appear to do. Indeed nothing can be more fit to constitute
a connecting link between material and immaterial beings, than some modi-
ficatiori of a fluid, which appears to difter very considerably, in its essential
properties, from the common gross matter of the universe, and to possess a
subtility and an activity, which entitle it to a superior rank in the order of
created substances.

When all the functions of animal life are carried on in their perfect and
natural manner, the animal is said to be in health: when they are disturbed,
a state of disease ensues. The diseases to which the human frame is liable
are so various and irregular, that they cannot easily be reduced to any sys-
tematical order. Dr. Cullen has divided them into four classes. Febrile dis-
eases, which constitute the first class, consist principally in an increase of
the frequency of the pulsations of the heart and arteries, together with an
elevation of the temperature, the whole animal economy being at the same
time in some measure impaired: they are often accompanied by unnatural or
irregular actions of the vessels of particular parts, constituting local inflamma-
tions, which were formerly considered as a derivation of diseased humours,
falling on those parts: thus, a pleurisy is a fever, with an inflammation of the
membrane lining the chest. The incapacity of a part to perform its functions,
upon the application of a natural stimulus, or perhaps more frequently the
incapacity of the nerves to transmit to it the dictates of the mind, constitutes
a palsy : such derangements, and others, by which the actions of the nervous

ON ANIMAL LIFI. 741

system are peculiarly in^paired, form the class of neuroses, including spasmo-
dic affections, madness, melancholy, and epilepsy, A general derangement
of the system, without fever, or any peculiar debility of the nerves, consti-
tutes the class of cachectic diseases, such as atrophy, consumption, scrofula,
and dropsy. Besides these diseases, we have a fourth class, consisting of lo-
cal affections only, such as blindness, deafness, tumors, and luxations.

Notwithstanding the labours of men of the greatest learning and genius,
continued for many centuries, it must be confessed that the art of healing dis-
eases is still in a state of great imperfection. Happily, however, for man-
kind, we may observe in almost all cases, where the offending cause is disco-
verable, and where the system is not at once overwhelmed by its magnitudcr a
wise and wonderful provision for removing it, by a mechanism admirably
simple and efficacious; and it is reasonable to conclude, where the cause is
more obscure, that the same benevolent Providence has employed agents
equally well adapted for counteracting it, although their operations are ut-
terly beyond the reach of human penetration.

VOL." I. 4 z

LECTURE LX.

ON THE HrSTORY OF TERllESTRIAL PHYSICS.

jLhROUGHOUT the whole of nature, we discover a tendency to the mul-
tiplication of life, of activity, and of enjoyment: man is placed at the head
of terrestrial beings, the only one that comprehends, and that can trace, in a faint
outline, the whole plan of the universe. We have seen the innumerable lumina-
ries which enliven the widely expanded regions of immeasurable space, with their
brilliant, but distant emanations of light and heat. Revolving round them at
lesser intervals, and cherished by their fostering influences, are their planets
and their comets; those preserving their distances nearly equal, and these,
ranging more widely from the upper to the lower regions, without limits to
their numbers or to their motions. Having conjectured what might possibly
exist on other planetary globes, we descended to our own, and examined its
structure and the proportions of its parts. Next we studied the general pro-
perties of the matter within our reach, and then the particular substances
or qualities that are either not material, or are distinguished by very
remarkable properties from other matter, as we found them concerned in
the phenomena of heat, of electricity, and of magnetism; and we after-
wards examined the combinations of all these, in the great atmospherical
apparatus of nature, which serves for the exhibition of meteorological phe -
nomena. The forms and the laws of animal and vegetable life have been tlie
last objects of our inquiries; but the magnitude of some departments of
natural history, and the obscurity of others, have prevented our entering
more than .superficially upon any of them.

Of the gradual advancement of astronomy we have already taken a his-
torical view. With respect to the other sciences comprehended under
the denomination of proper physics, the progress of discovery has generally
been slow, and frequently casual. The ancients had little or no substantial

ON THE HISTORY OF TERRESTRIAL PHYSICS. 743

knowledge of any part of physics, except astronomy and natural history:
their opinions were in general mere speculations, derived from fancy, and
inapplicable to the real phenomena of nature. Opinions such as these wvU
only require to be so far examined, as to enable us to trace the imperfect
rudiments of discoveries, which were only completed after intervals of many
ages.

The Chinese are said to have been acquainted with the use of the compass
above 3000 years ago; but in such accounts, it is impossible to ascertain how
far the spirit of national vanity may have induced a historian to falsify his
dates. It has been conjectured that the death of Numa, like that of Pro-
fessor llichniaun, ,was occasioned by some unguarded experiments on the
electricity of the atmosphere, which drew on him the effects of a thunderstorm
that was passing by. If, however, the fact was such, the experiments must
probably have been suggested rather by an accidental discovery of the light
on the point of a spear, than by any rational opinions respecting the nature
of the ethereal fire.

Thales is the most ancient of the Grecian philosophers, who appear to have
seriously studied the phenomena of nature. He supposed water to be the
general principle from which all material things are formed, and into which
they are resolved; an opinion which was without doubt suggested to him
by the obvious effects of water in the nutrition of plants and of animals. He
particularly noticed the properties of the magnet, which had been before
observed to attract iron, as well as the effect of friction in exciting the elec-
tricity of amber; and he attributed to both of these substances a certain
degree of animation, which he considered as the only original source of motion
of any kind.

Anaximander appears to have paid some attention to meteorology ; he
derived the winds from the rarefaction of the air, produced by the operation
of heat: thunder and lightning he attributed to the violent explosion or
bursting of the clouds, which he seems to have considered as bags, filled with
a mixture of wind and water. The same mistaken notion was entertained
by Anaximenes, who compared the light attending- the explosion, to
that which is frequently exhibited by the sea, when struck with an oar.

744 LECTUUE LX.

. Pythagoras, great as he was in some other departments of science, reasoned
r:speccing physical effects in a manner too mathematical and visionary, to
allow him much claim to he ranked among those, who have studied to inves-
tigate the minute operations of nature.

, Anaxagoras was so far from confining himself to the supposition of four
elements, which was most generally received by the philosophers of antiquity,
that he imagined the number of elements nearly if not absolutely infinite.
He conceived that the ultimate atoms, composing every substance, were of
the same kind with that substance, and his system was thence called the
homoeomeria; it erred perhaps less from the truth than many of the more
prevalent opinions. Dcmocritus, adopting the sentimentsofLeucippus, proposed
a still more correct theory of the constitution of matter, supposing it to be
ultimatel}' so far homogeneous, that the weight of its atoms was proportional
to their bulk. He asserted that the forms of these atoms were different and
unalterable; that they were always in motion, and that besides their primi-
tive difference of form, they were also susceptible of a variety in the mode

lof their arrangement. The space not occupied by the atoms of matter, he
considered as a perfect vacuum.

As Thales had supposed water to be the first principle of all things, and
Anaximenes air, so Heraclitus fixed on fire as the foundation of his system,
attributing to it the property of constant motion, and deriving all kinds of
grosser matter from its condensation in different degrees. This doctrine was
wholly unsupported by any thing like reason or observation.

Plato introduced into philosophy a variety of imaginations, which re-
sembled the fictions of poetry much more than the truths of science.
He maintained, for example, that ideas existed independently of the human
mind, and of the external world, and that they composed beings of different
kinds, by their union with an imperfect matter. It is observed by Bacon, in
his essay on the opinions of Parmenides, that the most ancient philosophers,
Empedocles, Anaxagoras, Anaximenes, Heraclitus, and Democritus, sub-
mitted their minds to things as they found them ; but that Plato made the
world subject to ideas, and Ajystotle made even ideas, as well as all other
things, subservient to words ; the minds of men beginning to be occupied, in

Oy THE HISTORY OF TERRESTRIAL PHYSICS. 745

those times, with idle discussions and verbal disputations, and the correct
investigation of nature being wholly neglected. Plato entertained, however,
some correct notions respecting the distinction of denser from rarer matter
by its greater inertia; and it would be extremely unjust to deny a very high
degree of merit to Aristotle's experimental researches, in various parts of
natural philosophy, and in particular to the vast collection of real information
contained in his works on natural history. Aristotle attributed absolute
levity to fire, and gravity to the earth, considering air and water as of an
intermediate nature. By gravity the ancients appear in general to have un-
derstood a tendency towards the centre of the earth, which they considered
as identical with that of the universe; and as long as they entertained this
opinion, it was almost impossible that they should suspect the operation of a
mutual attraction in all matter, as a cause of gravitation. The first traces
of this more correct opinion respecting it are found in the works of Plu-
tarch.

Epicurus appears to have reasoned as justly respecting many particular
subjects of natural philosophy, as he did absurdly respecting the origin of the
world, and of the animals which inhabit it. He adopted in great measure the
principles of Democritus respecting atoms; but attributed to them an innate
power of affecting each other's motions, and of declining, in such a manner,
as to constitute, by the diversity of their spontaneous arrangements, all the
varieties of natural bodies. He considered both heat and cold as material;
the heat emitted by the sun he thought not absolutely identical with light,
and even went so far as to conjecture that some of the sun's rays might
possibly possess the power of heating bodies, and yet not affect the sense of
v^ision. In order to explain the phenomena of magnetism, he supposed a
current of atoms, passing, in certain directions, through the magnet and
through iron, which produced all the effects by their interference with each
other. Earthquakes and volcanos he derived from the violent explosions of
imprisoned air.

Among all these opinions and conjectures, there is scarcely any one which
was scientifically established upon sure foundations. Some insulated observa-
tions had a certain degree of merit; and we find many interesting facts relating
to different departments of natural knowledge, not only in Aristotle, but also

746 ■ tF.CTURE LX.

in Theophrastus, Dioscorides, andPlmy,.as wellas in some of the historical writ-
ers of aatiquity. Protagorides of Cyziciim, who is quoted by Athenaeus, rehites
that in the time of king Antiochus, it was usual, as a luxury, to cool water by
evaporation ; and it is not impossible that the custom may have been introduced
from the east, where even ice is frequently made at present by a similar process;
others of the ancients had remarked, according to Dr. Falconer, that water
usually froze the more readily for having been boiled; and it is possible that
some other detached observations of a similar nature may occur to those who
have the curiosity to make them objects of research.

The thirteenth century may be considered as the date of the revival, if not
of the commencement, of physical discoveries. Our countryman, Roger
Bacon, was one of its principal ornaments: he appears to have anticipated in
his knowledge of chemistry, as well as of many other parts of natural phi-
losophy, the labours of later times. The polarity of the magnetic needle is
described in some lines which are attributed to Guyot, a French poet, who
lived about 1180; but some persons are of opinion that this description was
actually written by Hugo Bertius, in the middle of the succeeding- century;
and it is generally believed that the compass was first employed in navigation
by Gioja of Amalfi, about the year 1260; he is said to have marked the north
with a fleur de lis, in compliment to a branch of the royal familv of France,
then reigning at Naples. The declination of the needle from the true meri-
dian is mentioned by Petei* Adsiger, the author of a manuscript which bears
the date 1269. The poet Dante, who flourished at the close of this century,
distinguished himself not only by his literary, but also by his philosophical
pursuits; and we find among his numerous works an essay on the nature of
the elements.

The learned and voluminous labours, by which Gesncr and Aldrovandus
enriched the various departments of natural history, may be considered as
comprehending the greatest part of what had been done by the ancients in
the investigation of the economy of the animal world; but their works
have too much the appearance of collections of what others had asserted, rather
than of original observations of their own.

The first of the moderns, whose discoveries respecting the properties of

ON THE HISTORV OiF TERRESTRfAL PHYSICS. 747

natuial bodies excite our attention, by their novelty and importance, is Dr.
Gilbert, of Colchester: his work on magnetism, published in 1590, contains
a copious collection of valuable facts, and ingenious reasonings. He also
extended his researches to many other branches of science, and in particular
to the subject of electricity. It had been found, in the preceding century,
that sulfur, as vvell as amber, was capable of electric excitation, and Gilbert
made many further experiments on the natui*e of electric phenomena. The
change or variation of the declination of the needle is commonly said to have
been discovered by Gellibrand, a professor at Gresham college, in the
year \6Q5; but it must have been inferred from Gunter's observations,
made in 1622, if not from those of Mair, or of some other person, as early as
1612 ; for at this time the declination was considerably less than Burrows had
found it in I08O.

In the beginning of the seventeenth century. Lord Bacon acquired, by hH
laudable efforts to explode the incorrect modes of reasoning, which had oc-
cupied the schools, the just character of a reformer of philosophy: but his
immediate discoveries were neither striking nor numerous. In 1620, he
j)roposed, with respect to heat, an opinion which appears to have been at
'that time new, inferring, from a variety of considerations, which he has very
minutely detailed in his Novum organum, that it consisted in " an expan-
sive motion, confined and reflected within a body, so as to become alternate
and tremulous; having also a certain tendency to ascend". A similar opinion,
respecting the vibratory nature of heat, was also suggested, about the same
time, by David Gorlaeus, and it was afterwards adopted by Descartes, as a
part of his hypothesis respecting the constitution of matter; which he ima-
gined to consist of atoms of different forms, possessing no property besides
extension, and to derive all its other qualities from the operation of an
ethereal and infinitely elastic fluid, continually revolving in different orders
of vortices. -.

A much more important step, than the proposal of any hypothesis concern-
ing the nature of heat, was also made about the year 1620, by Cornelius Drebel,
who appears to have been the original inventor of the method of measuring the
degrees of heat by a thermometer. The utility of the instrument remained,
however, much limited, for want of an accurate method of adjusting its scale.

748 LECTURE LX.

and it was not till the close of the century, that Dr. Ilooke's discovery, of the
permanency of the temperature of boiling water, afftnded a correct and con-
venient limit to the scale on one side, M'hile the melting of snow served for
fixing a similar point on the other; although there would have been no
great difficulty in forming a scale sufficiently natural, from the proportion
of the expansion of the fluid contained in the thrrnomeeter to its whole
bulk. '

It was about the year 1628, that Dr. Harvey succeeded in demonstrating,
by a judicious and conclusive train of experiments, the true course of the
circulation of the blood, through the veins and arteries, both in the perfect
state of the animal, and during its existence as an embryo. Servetus had
explicitly asserted, in his work on the Trinity, as early as the year 1553,
that the blood performed, in its passage through the" lungs, a complete re-
volution, beginning and ending in the heart ; and Cisalpinus had even expressed,
in 1569, some suspicions that the circulation of the whole body was of a
similar nature; but neither of these authors had advanced any satisfactory
proofs in confirmation of his opinions.

In the middle of the seventeenth century, the barometer was invented by
Torricelli; the variation of the atmospheric pressure was discovered by
Descartes; and Pascal made several experiments on the difference of its
magnitude at different places, which tended to illustrate the principles, on
"which the method of determining heights by barometrical observations is
founded.

What Gesner and Aldrovandus had before done with regard to the animal
kingdom, was performed, a century later, for the vegetable world by John
and Caspar Bauhin, whose works, as collections of all that was to be found on
record respecting the distinctions and properties of plants, have not yet been
superseded by the latest publications. Our countrymen, Ray and Willughby,
contributed also to add much new matter to the stores of natural history,
in all its departments; and their labours, as well as those of Tournefort and
Reaumur, are of the more value, as they were far more studious than their
predecessors to discriminate truth from fiction.

ON THE HISTORY OF TERRESTRIAL PHYSICS. 74*)

The foundation of the most celebrated of the philosophical societies of Eu-
rope renders the latter half of the seventeenth century a very interesting pe-
riod in the history of natural knowledge. The Royal Society of London, and
the Academy of Sciences of Paris, have always been the most distinguished
of these: and the Florentine Academy del Cimento, although its labours were
not of long duration, produced at first in a short time a very copious and in-
teresting collection of experiments, relating to various subjects of physical re-
search. In the Royal Society, Boyle, Hooke, and Newton were the most industri-
ous, as well as the most successful investigators of natural phenomena : the ele-
mentary doctrines of chemistry, the nature of combustion, the effects of heatand
cold, and the laws of attraction, repulsion, and cohesion were attentively examin-
ed and discussed. The expansion ol water, by a reduction of its temperature, near
the freezing point, was first observed by Dr. Croune ; although his experi-
ments were considered by Dr. Hooke as inconclusive. The attention of the
society was directed by Newton to the phenomena of electricity, some of
which had been a short time before particularly noticed by Guericke'; the
mode of making electrical experiments was greatly improved by Hauksbee;
this accurate observer investigated also the nature of capillary attraction
with considerable success. Early in the succeeding century, many of the
members of the Academy of Petersburg followed the example of other so-
cieties with great industry; and the experiments of Richmann on heat were
among the first and best fruits of their researches.

Dr. Halley employed himself, with the most laudable zeal, in procuring in-
formation respecting the variation of the compass; he undertook a voyage
round the world, for the express purpose of making raagnetical observations ; and
he published a chart of variation, adapted to the year 1700. He also collected
many particulars respecting the trade winds and monsoons, and he endea-
voured to explain them by a theory which has been adopted by some of the
latest authors, but which is in reality nmch less satisfactory than the hy-
pothesis proposed some time afterwards by Hadley. His magnetical investi-
gations were continued with great diligence by Mountaine and Dodson, who
published, at different periods, two charts representing the successive states of
the variation. Euler, Mayer, and others have attempted, in later times, to
discover such general laws as might be sufficient to determine the magnitude

VOL. I. 5 a

750 LECTURE LX.

of the variation for every part of the globe ; but their success has been very
much limited.

The science of electricity was diligently cultivated in the middle of the
last century by Stephen Gray, Dufay, Winkler, Nollet, Musschenbroek, and
.Franklin. As early as 1735 it was remarked by Gray, that "the electric fire
seemed to be of the sanie nature as lightning," and their identity was after-
wards more strongly asserted by Winkler, and experimentally demonstrated by
Franklin. The shock of a charged jar was first discovered by Kleist, in 1745;
and the experiment was repeated by Lallamand and Musschenbroek, who de-
scribed its disagreeable effects on the sensations with an exaggeration not the
most philosophical. The theory of the nature of the charge was the second
gceat improvement made by Dr. Franklin in this science.

The introduction of the Linnean system of botany and zoology is to be
considered as bringing near to perfection the logic and phraseology of natu-
ral history; nor has its celebrated author wholly neglected the philosophy of
the science. The number and the diligence of his successors have already
furnished to the different departments of natural history a much ampler store
of observations than could easily have been expected from the short time
which their labours have occupied. Buffon had merit of a different kind,
and though his fancy was too little regulated by mathematical accuracy, the
elegance of his writings have made their subjects highly interesting to the
general reader. Among other modern naturalists of great respectability, Spal-
lanzani, Daubenton, Degeer, Geoffrey, Pennant, the Jussieus, Lacepede and
Haiiy, have particularly distinguished themselves by the importance of theit
discoveries, and the accuracy of their descriptions.

The absorption of heat, during the conversion of ice into water, appears to
have been separately observed by Deluc, Black, and Wilke, about the year
1755, On this experiment Dr. Black principally founded his doctrine of la-
tent heat, supposed to 'be retained in chemical combination by the particles
of fluids. Dr. Irvine and Dr. Crawford explained the circumstances some-
what, differently, by the theory of a change of capacity for heat only. Berg-
njann, Lavoisier, Laplace, Eifwan, Seguin, and many other philosophers have

2

ON THK BISTORT OF TERRESTRIAL PHYSICS. jT'SI

illustrated, by experiments and calculations, the various opinions which have
been entertained on this subject; and few chemists, from the times of Boer-
haave, Stahl, and Scheele to those of Priestley and other later authors, have
left the properties of heat wholly unnoticed.

The elegant hypothesis of Aepinus, respecting magnetism and electficitj-,
founded in great measure on the theory of Franklin, was advanced in 1759:
our venerable countryman, Mr. Cavendish, had invented a similar theory, and
had entered in many respects more minutely into the detail of its conse-
quences, without being acquainted with Aepinus's work ; although the publi-
cation of his paper on the subject was 12 years later. Lambert, Mayer,
Coulomb, and Robison have also pursued inquiries of a similar nature, both
theoretically and experimentally, with great success. The electrophorus of
Wilke, and the condenser of Volta, are among the earliest fruits of the cul-
tivation of a rational system of electricity, and Mr. Cavendish's investigation
of the properties of the torpedo may sei-ve as a model of accuracy and |)reci-
sion in tlie conduct of experimental researches. •

The speculations of Boscovich respecting the fundamental properties of
matter, and the general laws of the mutual action of bodies on each other,
have been considered by some candid judges as deserving the highest com-
mendation; they remain however almost in all cases speculations only; and
some of the most intricate of them, being calculated for the explanation of
some facts, which have perhaps been much misunderstood, must consequently
be both inaccurate and superfluous.

The attention of several experienced philosophers, who are now living, has
been devoted, with much perseverance, to the ditficult subject of hygrome-
try. Deluc's experiments have offered us a very useful comparison of the
feygrometrical qualities of various substances: Saussure has investigated, with
great labour, the indications of the hjgrometer and the thermometer, a^
connected with the presence of a certain portion of vapour, contained in air
of various densities; and Pictet has ascertained some similar circumstances
respecting vapours of different kinds wholly unmixed with any air. The hy-
potheses, which have usually accompanied the relation of most of these cxpe-

752 LECTURE tX.

riments, have however been in general too little supported by facts to be en-
titled to universal adoption.

For some years past, the philosophical, as well as the unphilosophical world,
has been much occupied and entertained by the discoveries of Galvani, Volta,
and others, respecting the operations of the electric fluid. The first circum-
stance, that attracted Galvani's attention to the subject of animal electricity,
was the agitation of a frog, that had a nerve armed, that is, laid bare and co-
vered with a metal, when a spark was taken in its neighbourhood. A person
acquainted with the well known laws of induced electricity might easily
have foreseen tliis effect: it proved, however, that a frog so prepared was a
very delicate electrometer, and it led Galvani to further experiments. It has
been shown by Volta, that an entire frog may be convulsed by a degree of
electricity which affects an electrometer but very weakly; but that when
prepared in Galvani's manner, it will be agitated by an electricity one fiftieth
part as great, which cannot be discovered, by any other means, without the
assistance of a condenser. Galvani, however, found that a communication
made between the armed nerve and its muscle, by means of any conducting
substance, was sufiScient to produce a convulsion, without the presence of
foreign 'electricity: hence he concluded that the nerve and muscle, like the
opposite surfaces of a charged jar, were in contrary states of electricity, and
that the communication produced a discharge between them. He observed,
however, a considerable difference in the effects, when different metals were
employed far forming the circuit; and this circumstance led to the discovery
of the excitation of electricity by means of a combination of different inani-
mate substances only, which Mr. Davy attributes to Fabroni, Creve, and Dr.
Ash. It was, however, stilt more satisfactorily demonstrated by Volta;
and he at first supposed that all the phenomeaa observed by Galvani were de-
rived from effects of this kind, but on further examination he was obliged to
allow the independent existence of animal electricity. This industrious and
ingenious philosopher has the sole merit of the invention of the pile or battery,
which has rendered every other mode of exciting the galvanic action compa-
ratively insignificant.

No sooner was VoUa's essay communicated to the Royal Society, than a

4

ON THE HISTOUY OF TEIlRESTItf A t PHVSICS. 753

■pile was constructed by j\fr. Carlisle, and its singular effects in tlie decompo-
^sition of water were jointly observed by himself and Mr. Nicholson. The
original existence of animal electricity, as asserted by Galvani and Volta,
has been in some degree confirmed by the experiments of Aldini, the nephew
of Galvani. A number of detached observations, of considerable merit, have
also been made by Pfaff, Ritter, Cruikshank, Wollaston, Fourcroy, and many
other chemists, both in this country and on the continent. But Mr. Davy's
late experiments must be considered as exceeding in importance every thing
that has been done upon the subject of electricity, since the discovery of
the pile of Volta. The conclusions which they have enabled him to form
respecting the electrical properties of such bodies as have the strongest ten-
dencies to act chemically on each other, and the power of modifying and
counteracting those tendencies which the electric fluid possesses, have
greatly extended our views of the minute operations of nature, and have
opened a new field for future investigations. I hope that I shall be par-
doned by astronomers for having inserted, on this occasion, in a vacant space
among the constellations, in the neighbourhood of Pegasus, the figure of a
galvanic battery ; which nuist now be allowed to have as great pretensions
to such a distinction as the electrical machine and the chemical furnace. ^

The late experiments and speculations of Mr. Dalton, on various subjects,
belonging to different branches of physics, have tended to place some parts
of the science of meteorology in a new light. It is true that many of his hy-
potheses are very arbitrarily assumed; some of them are manifestly contrary
to experiment, and others to analogy and probability; at the same time his
remarks appear in some cases to be either perfectly correct, or to lead to de-
terminations which are sufficiently accurate for every practical purpose. I have,
attempted to borrow from Mr. Dalton's ideas some hints, which I have incor-
porated with a less exceptionable system; and by a comparison of his experi-
ments with those of many other philosophers, I have deduced some methods
of calculation which may perhaps be practically useful; in particular a sim-
ple rule for determining the elasticity of steam, and a mode of reducing the
indications of hygrometers of different kinds to a natural scale.

Count Rumford's establishment of a prize medal, to be given every three

754 LECTURE LX.

years by the Royal Society to the author 6f the most valuable discovery re-
specting heat or light, forms an era less remarkable, than the first adjudication
of the medal to himself, and the second to Mr. Leslie. Count Rumford's nu-
merous experiments, on the production and communication of heat are highly
important, both for the utility which may be derived from their economical
application, and for the assistance which they afford us in the investigation
of the intimate nature of heat. Mr. Leslie's discovery of the different pro-
perties possessed by surfaces of different kinds, with regard to emitting and
receiving radiant heat, is in every respect highly interesting; and the multi-
plicity and diversity of his experiments would have entitled him to still
higher commendation than he has obtained, if they had been more simply and
circumstantially related. Perhaps, however, none of the modern improvements
in speculative science deserves a higher rank than Dr. Herschel's discovery of
the separation of heat from light by refraction. Mr. Prevost has made some
just remarks on the experiments of other philosophers respecting heat; and
his own theory of radiant heat, and his original investigations, on the effect of
the solar heat on the earth, have tended materially to illustrate the subject of
his researches.

The general laws of the ascent and descent of fluids in capillary tubes, and
between plates, of different kinds, had long ago been established by the ex-
periments of Hauksbee, Juvin, and Musschenbroek; many other circum-
stances, depending on the same principles, had been examined by Taylor,
Achard, and Guyton ; and some advances towards a theory of the forms as-
sumed by the surfaces of liquids, had been made by Clairaut, Segner, and
Monge. In an essay on the cohesion of fluids, read before the Royal Society
in the year 1804, I have reduced all effects of this nature to the joint opera-
tion of a cohesive and repulsive force, which balance each other; assuming
only that the repulsion is move augmented by the approach of the particles to
(?ach other than the cohesion ; and I have had the satisfaction of discovering
i^ this manner a perfect correspondence between many facts, which had not
l?een supposed to have the slightest coanexion with each other. Alinost a
year after the publication of this paper, Mr. Laplace Fcad to the National In-
stitute a memoir on capillary tubes, in which, as far as he has pursued the
subject, he has precisely confirm«d the most obvious of my concLusicns;

ON THE HISTORY OF TEItltfeSf RIAL PHYSICS. 755

although his mode of calculation appears to be by no means unexcep-
tionable, as it does not include the consideration of the effects of repul-
sion. Had my paper been so fortunate as to attract Mr. Laplace's attention
before his memoir was presented to the Institute, he would perhaps have
extended the results of my theory with the same success, which has uni-
formly distinguished his labours in every other department of natural philo-
sophy.

When we reflect on the state of the sciences in general, at the beginning
cf the seventeenth century, and compare it with the progress which has been
since made in all of them, we shall be convinced that the; last two hundred
years have done much more for the promotion of knowledge, than the two
thousand that preceded them : and we shall be still more encouraged by the
consideration, that perhaps the greater part of these acquisitions has been
made within fifty or sixty years only.. We have therefore the satisfaction of
viewing the knowledge of nature not only in a state of advancement, but
even advancing with increasing rapidity; and the universal diffusion, of a
taste for science appears to promise, that, as the number of its cultivators in-
creases, new facts will be continually discovered, and those,which are already
known, will be better uliderstood,^and more beneficially applied. The Royal In-
stitution, with other societies of a similar nature, will have tlie merit of assist-
ing in the dissemination of knowledge, and in the cultivation of a taste for
its pursuit ; and the advantages arising from the general introduction of
philosophical studies, and from the adoption of the practical improvements
depending on them, will amply repay the labours of those-, who have been ac-
tive in the establishment and support of associations so truly laudable.

rss

LECTURE IX.

CHRONOLOGY OF PHYSICAL AUTHORS.

700 B. C. e 00 i
.... 1 .... 1 .... 1 ... .

00 4 00 3
.... 1 1 . . . .

00 200
.... 1 ... .

V

.r H A

.AN

L E S. A
AXIMANDE.R

AN AXI MEN ES.
.VYTHAGORAS
H E R A C

NAXAGORAS.

.D E M O C R
. P L

LITUS

.TH EOPHRASl
I T U S. .EPIC
A T O.
.ARISTOTLE.

US.

U RUS.

200 B. C. I'OO BIRTH OF
.... I .... 1 .... 1 ... .

CHRIST. 1
.... 1 ... .

00 -J

00 300

.... 1 ... .

; ~ DIOSCORIDES

.PLINY.

300 4
.... 1 ... .

00 s

.... 1 ... .

00 6
.... 1 ... .

op 7

00 800

800 g

00 10

.... 1 ... .

00 11

00 la
.... 1 ... .

00 . 1300

.... 1 ... .

.R. BACON.
G I O J A

ADSIGE R

D A N

1300 14
.... 1 ... .

00 15
.... 1 ... .

00 16

00 i;
.... 1 ... .

00 1800
.... 1 ... .

T E.

.G E S N E R.

.ALDROVANDUS

.GILBERT

.J. B A U H I

G 0 R L A

.B A C

.C. B A L

.G A L I

.D R E

.R A y

.WILLU G.HBY
.H O O K E
N. .NEWT
EUS. C R O U
ON. .TOUR
H I N. .HAL
LEO. .S T A
BEL .BOER
DESCARTES. .J U
GELLIBR.AND S.
.G U E R I C K E. H
•.TORRIC. ELLI .R
PASCAL R
B O Y L E..

.PRIESTLEY

.BERGMANN

I R V I N E.

O N. .G A L V A N I

N E .R O B I S O N.

N.EFORT .SCHEELE.

L E Y .S A U S S U R E

H L. .LAVOISIER.

HAAVE. CRAWFORD.

R I N,
GRAY.
AUKSBEE
E A U M U R.
1 C H MA N N.
MUSSCHENBR.OEK
D U F A Y.

J U S S I E U.
N O L L E T.
.FRANKLIN.
-E U L E R.
.L I N N E.
.B O S C OV I C H.
.K L E I S T.
.D A U B E N T O N.
■D E G E E R
.MAYER.
.P E N N A NT.
•B L A C K.
W I L K E
A E P I N U S
.LAMB E Rt
.SPALLANZANI.

EXPLANATION OF THE PLATES.

5b

758

PLATE I.

Fig. 'I. The point A being supposed to move in a
right line to B, AB is the direction of its motion. P.
SI.

Fig. 9. The lines A B, B C, C D, are the successive
directions of the point A, moving from A to D in the
figure A BCD. P. 21.

Fig 3. The tangent A B is the direction of the mo-
tion of the point C, moving in the curve C D, when it
arrives at E. P. 21.

Fig. 4. The square AB, moving on the hoard C D,
so that the points E, F, describe the parallel lines E G,
J E H, with eqOal velocities, the plane A E F B is in rec-
tilinear motion with respect to the surface C D. P. 24.
Fig. 5. The cycloid A B C, and the trochoid D E F
are the resuits of the rotatory motion of the points B
and E round the centre of the wheel, combined with
^he progressive motion of the wheel along the base
AC. P. 24, 44.

Fig. 6. A B is a fixed bar, C D an arm which slides
on it, ECF a thread passing round the pulley at C,
and either fixed to the pin on the slider F, or passed
over the pulley G, and fixed again at II. The arm
turns round the same axis that carries the pulley at
C, and may be fixed by means of the screw which is
cut on the axis, while two other screws keep it steady
, by pressing on the slider below it. The point I de-
scribes, by its compound motion, the oblique line KI.
P. 24.

Fig. 7. The diagonal A B of the parallelogram C D
is the joint result of the motions, represented by its
sides AC, AD. P, 2a.

Fig. 8. The line A B may be either simply drawn
in the direction A B, or it may be traced by the equal
motions AC and AD of the arm and its slider, or by
the unequal motions A E and A F. P. 25.

Fig. 9. The body A, moving uniformly along the
line AB, first approaches to the point C, and then
recedes from it, as if repelled. P. 27.

Fig. 10. When A Band AC approach each other,
and coincide, the diagonal AD becomes equal to their
snm. P. 30.

Fig. 11. Atwood's machine. The boxes A, B, con-
taining equal weights, are connected by the thread
A C B, passing over the puUey C, which is supported ei-
ther on friction wheels, or by the points of screws, one
of which is seen at D. The box A is made to descend
either by a flat weight placed on it, or by the bar E,
which is intercepted by the ring F, and the box conti-
nues to descend till it strikes die stage G; the space
being measured on the scale H I, and the time by the
pendulum K, which may be kept in motion by a clock
scaperoent with a weight. The machine is levelled
by the screws L, M. P. 31.

Fig. 12. The time of the descent of a falling bodjr
being represented by any portion A B of the base of a
triangle, the velocity will be proportional to B C, which
is equal to A B, and the space described during the
time D E, supposed infinitely short, will be propor-
tional to the area D E F G, which is expressed by the
product of BC and D E; consequently the whole area
A E F will represent the space described in the time
AE, and A HI the space described in the time AH;
but A II I is half of the square H K, and A E F of
E L : the space is therefore always as the square of tlie
time, and is equal to half the space which would be de-
scribed in the same time with the final velocity. P. 32.

Fig. 13. The whirling table. The arms A B, C D,
are made to revolve on the axes E F, G II by the
string passing over the wheel I, the upper or under
pulley of either axis being employed at pleasure: the
stages K,L, with their weights, are placed at certain *
distances from the centre, by means of the racks or
teeth belovi them; they move along the arms by means
of friction wheels resting on wires, and they raise the
weights M,N, by rrieans of threads passing each over
two puUies. P. 35.

Fig. 14. If a body revolving in a curve ABC, by
means of a force directed to D, describe the portions
A E, B F, C G in equal times, the areas A D E, B D F,
CDG, will be equal, and the velocities in A,B, and
G, will be inversely as the perpendiculars D H, D I,
andDK. P. 36.

PLATE 1 .

Tie-. 5.

Tig-. 2.

Tig. 4-.

C

i; Hi

■■■■■l»iiilllfflliiillllliiiiiili|||^^ - l||||l«lllllii

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2'u/f . by J. Johnson, London. i July 1 8o6 .

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Plate H.

Piff. 16 .

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Pig;. 25.

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Ttih.by J.Johnson.ZonloTi xJiiiy26o&.

JojepTv ShfUon sci±>

759

PLATi; II.

■ 1 i JL I. I

Fig. 15. The ball A, revolving round the point B,
and being drawn towards it by means of the thread
BC, with a force variable at pleasure, its veldcity may
be observed to vary, abcording to itrdistancfe from the
point B. P. ST.

Fig. 16. The curve A B C D E is an ellipsis; E and
G are its f6ci, A D its greater axis, and C E ite lesser
axis. P. ST.

Fig. 17. The hol-izontal range, A B, Of a body pro-
jected at an elevation of 45", is greater than A C or
A D, the ranges of bodies projected with the same ve-
locity at a greater or less elevation. If the parallel
lines EF, G H, be always as the squares of A E, AG,
the curve A F H will be a parabola ; and such is the
path of a projectile. P. 39, 4o.

Fig. 18. The path of a ball moviilg swiftly through
the atmosphere nearly resembles the curve A B. P.
89.

Fig. IP. TheballA,having descended along the groove
A B, describes the parabola B C, passing through the
rings D, E. P. 40.

Fig. 20. The cylinder A, loaded at the axis, de-
scends along an inclined plane more rapidly than the
cylinder B, loaded with an equal weight at the circum-
ference. P. 42.

Fig. 21. The balls A, B,C descend along the planes
A D, B E, CF, of equal height, in times proportional

and the balls B, E, deicendiug from any two points of
the curve, will meet at E, in the same time that the'
Ijall G falls from a point nearly j of A E above A. The
space described by the pendulum in descending is al-
ways proportional to the height H I, to which a body
setting out fiom E, and revolving uniformly in a circle,
will rise in the same time. The circle E I lies without
the cycloid C E D, and is somewhat less incUncd to
the horizon at equal distances from E. P. 44, 45.

Fig. 25. The ball A, descending from B in the
curve B A, arrives at C before the ball D moving in a
right line on the plane B C. P. 46.

Fig. 26. The balls A, B, C, being made to revolve
by means of the whirling table, they are always found
in the same horizontal plane. The joint connecting
them with the axis is represented at D, as seen from
above, r. 47.

Fig. 27. The equal vibrations, represented by A B,
C D, compose, when united, the circular revolution
AEB: the unequal vibrations AB, FG, compose the
ellipsis AIIB; the place of the body being always as-
certained by combining the versed sines of two circu-
lar arcs increasing uniformly. P. 47.

Fig. 28. The biUls A, B, as their revolution be-
comes more rapid, fly out, and the point C is depressed.
P. 48.

Fig. 29. The mass of the body A being 1 and that

to their lengths. The upper surfaces of the slips AD, of B 2, and AC being twice BC, C is the centre of iu-

B E, C F, are slightly grooved. P. 43.

Fig. 22. The balls A,B,C, descend in equal times
along the chords A D, B D, C D. P. 43.

Fig. 23. The same ball, descending from equal
heights, at A, B, or C, by different paths, will rise to
the same height at D on the opposite side of E. P.
43.

Fig. 24. Tlic thread A B, playing between the cy-
cloidal checks AC, AD, desciibes the cycloid C ED,

ertia. P. 51.

Fig. 30. The balls A and B are suspended by long
threads, which allow them to move in tlie arcs AC,
B D ; the ball A is perforated in a horizontal direc-
tion, and contains aspiral spring, which is confined by
the thread E, and being set at , liberty by burning
this thread, strikes the ball B, so as to cause each of the
balls to move through an arc, of which the chord is pro-
portional to the weight of the other ball, P. 52.

760

PLATE III.

Fig. SI. The centre of inertia of the bodies A,B,
C,D, may be determinet) either by finding E the cen-
tre of inertia of A and B, and supposing a body equal
to their sura to be placed in it, then determining F
from E and C ; and G, the point required, from F and
D; or by finding first H and I from A, C, B, D, taken
in pairs, and dividing HI in due proportion in th?
same point G. P. 54.

Fig. 32. The point A being the centre of inertia of
the bodies B, C, D, E, the products obtained by multi-
plying B by B F, C by C G, D by D H, and E by E I,
»re equal, when added together, to the product of the
masses of all the bodies by the distance A K; all ihe
lines drawn to the plane F I being parallel. P. 55.

Fig. 33. The weights ABC will remain at rest
when they are in the same proportion to each other
as the respective sides of the triangle D EF; D Fbeing
parallel to EG. P. 61.

Fig. 34. The bodies A, B, remain in equilibrium
when their centre of inertia C is immediately below the
point of suspension D. P. 61.

Fig. 35. The system of bodies A, B, C, is at rest
, when the centre of inertia D is immediately below the
point of suspension E. P. 61.

Fig. 36. The bodies A,B, remain at rest when the
centre of inertia C is immediately above tlie point of
support D. P. 61.

Fig. 37. The bodies A, B, remain at rest when the
centre of inertia C coincides with the fulcrum or point
of support. P. 61.

Fig. 38. The irregular body A B, remains at rest
when the centre of inertia C is immediately below the
point of suspension D. P. 61.

Fig. 39. A being the centre of gravity of the board
B,C, the point ofsuspension being D,E, or F, the posi-
tion of the vertical line will be D A, E A, or F A. P. 62.

Fig. iO. The equilibrium of the vessel A is stable j

tiiat of the vessel B tottering, the path of the centre of
gravity having its concavity, upwards in the first, and
downwards in the second. P. 62.

Fig. 41. Paths of the centre of gravity of an oval.
P. 62.

Fig. 42. Paths of the centre of gravity of a body
resting on a sphere. P. 62.

Fig 4S. A, the path of the centre of gravity of k
body standing on a flat basis; B, the tottering equili-
brium of the same body inclined. P. 63.

Fig. 44. The effects of a certa'm inclination of a
waggon, loaded with light and heavy materials, are re-
presented at A and B respectively. P. 63.

Fig. 45. The suspension of a weight^om-aTp^ pro-
jecting over a table. P. 64. >' ,•,,,, ,,: p ,pf , :

Fig. 46. A shows the path of the centre of gravity
of a loaded cylinder on an inclined plaije, B that of
the centre of gravity of a double cone moving towards
the more elevated end of a triangular surface. C is an
elevation of the double tone. P. 64.

Fig. 47. A B is a lever of the first kind, tlie forces
acting on different sides of the fulcrum C; D E of tlie
second kind, the forces being applied at D and F, on
the same side of E. P. 65.

Fig. 48. A force applied at A may be held in equi-
librium by a triple force, applied in die direction B C
either at B or at C, or in a direction perpendicular to
the arm C D at E, D E and D B being each one third
of A D. P. 67.

Fig. 49. A force, acting at A on the lever A B, h^i
a great mechanical advantage in turning the lever C D ;
but when the levers are in the position B E, D F, the
force. acts witli a similar disadvantage. P. 67.

Fig. 50. The diameter of the cylinder A being three
times as great as that of B, the weight C, or an
equivalent force applied to the winch D, will support
a triple weight at £. P. 6T.

plaib m.

Fie-.3x.

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Kg". 3

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Fig^.34

Fig;-. 35

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Fig-. 36.

Fig;. 37

Fig;. 38

Tig-. 46.

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FiJy.'hy J. Johnson. .London i July 2S06.

Joj^K Skeltan .

Pub. by J. Johnson , London, i July iSoS.

JotspK Sl<dtm Jcitlp-

761

PLATE IV.

Ti-;. 51. The weiglit A, acting on the double cylin-
der H, supports the weight C by the pulley running in
the angle of the rope D C E, which is wound on the
larger cylinder nt D, while it is uncoiled from the
smaller at E, and the force is the same as if the weight
C were attached to the lineC F, acting on the axis F,
of which the diameter is equal to the difference of the
radii of the double cylinder. P. 63, 206.

Fig. 52. A single fixed pulley, supporting two equal
weights. P. 68.

Fig. 53. A single moveable pulley, by means of
whicfi a weight supports another twice as great. P.
68.

Fig. 51. The arrangement ofpuUies in ships' tackles,
with a force of six to one. P. 69.

Fig. 55. An arrangement of puUies in a vertical
line, with a force of six to one. P. 69.

Fig. 56. Mr. Smcaton's blocks, giving a force of
twenty to one, the rope being applied in the middle
of the outer series, and following the order of the fi-
gures from 1 to 21. P. 69, 207.

Fig. 5l. A system of puUies fixed on one axis in
each block; having a power of 8 to 1. P. 69.

Fig. 58. A system of pullies, each of which doubles
tlie effect; having a power of 8 to 1. P. 69.

Fjg. 59. A system of pullies with each rope fixed to
the weight, having a force of 7 to 1. P. 69.

Fig. 60. Two systems of pullies, of the kind dcuomi-

natcd Spanish bartons, in which two of the pullies arc
suspended by the same rope: the one has a power of
4, tlieother of5. P. 69.

Fig. 61. A. The depression of the middle weight be-
ing one third of its distance from tlie pullies, it sustains
two equal weiglits," which are together three times as
great as itself. B. The depression of the smaller
weight being one fourth of its distance from the pulley,
it supports a weight twice as great as itself. P. 70.

Fig. 63. A joiner's saw, stretched by twisting a
double cord, by means of a lever passing through it.

Fig; 63. The weight A, resting on an inclined plane
of which the height is to the oblique length as 3 to 5>
is sustained by a weight B three fifths as great as itself;
and if for the resistance of the plane we substitute the
action of the weight C, reduced to the direction AT)
perpendieular to the plane, this weight must be four
fifths of the weight A, the- horizontal length of the
wedge being four fifths of its oblique length. P. 70.

Fig. 64. The weights A, B, and C, acting, by means
of threads passing over pullies, wliich are fixed to any
required part of a horizontal table, on the rollers
which press against the sides of a wedge, proportional
in length to the respective weights, retain each other
in equilibrium, when their directions meet in one point.
In order that the threads may pass on each side of the
wedge, it may be supported by three or more balls..
P. 71.

7S2

PLATE V.

Fig. 65. Bjr means of the moveable inclined plane
AB, of which the height AC is one third of the hori-
zontal length BC, the weight D, acting horizontally,
sustains a triple weight E, acting iu a vertical direc-
tion. P. n.

Fig. 66. A B being one fourth of B C, the rope
A B must exert a force of tension equal to one fourth
of the weight C, in orderto support it, supposing the
»urfacesj to be without friction. But if the friction of
the end of the beam A C were equal to one fourth
of the pressure, it would support the weight C with-
out any other force, whatever might be its magnitude"
P. T2.

Fig. 67. AB being half of BC, or one fourth of
C D, the force extending the rope C D each way is
equal to the weight E. P. 72.

Fig. 68. The thin wedge AB, of which the height
is one fifth of the length, being rolled round the cy-
linder C, makes the screw D, by means of which the
weight E is capable of supporting a weight five times
as great as F. P. 72.

Fig. 69. A is a screw, and B the nut belonging to
it. P. 72.

Fig. 70. Tlie endless screw A B acts on the teeth
of the wheel CO. P. 72.

Fig. 71. The listance of the threads of the inte-
rior screw is four fifths of that of the exterior or per-
forated screw, and this distance is one thirtieth of the
circumference. Hence the weight A is capable of
sustaining a %veight B 150 times as great as itsell".
P. 73.

Fig. 72. The apparatus for experiments on collision.
Those balls which are not employed may be left be-
hind the graduated arc, as at A and B; some of tlie
strings have balls of half the weight of the rest, others
have a small dish C, on which balls of clay, or of wax
softened with one fourth its weight of oil, may he sup-
ported. P. 76.

Fi;;. 73. If the ball A strike the ball B iu the
oblique direction A C, the ball B will be impelled iu
the direction C D perpendicular to the surface of con-
tact; and the velocity EC being resolved into EF
and FC, t!io part FC will continue unaltered; and if
the bulls are equal, the part EF will be destroyed, so
that the ball A will move after the stroke in the direc-
tion C G, excepting the effect of any accidental dis-

4

turbance which may be derived from the resistance ot
the surrounding bodies. If we imagine a ball at C in
contact with B, in the direction D B, we may aim a
blow at the centre of this ball, in order to drive the
ball B toD ; and if B happen to be situated any where
in the semicircle D C G, the motion of A after the
impulse will be in the direction B G or G B, if there
be no resistance. When the ball H is reflected by a
fixed obstacle, as by the cushion of a billiard table, at
I, its velocity K I may be resolved into the parts K L,
LI; the partKLcontinues,and may be represented by
L M equal to K L, the part L I is converted into I L iu
a contrary direction, which when combined with LM
makes I M, the angle LI M being equal to LI K. We
may find the proper direction for striking any ball by
reflection if we suppose a ball N in contact with the near-
est point of the eushion, and making NO equal toMN,
aim at a ball supposed to be at O. In the same man-
ner if we wish to impel the ball P in the direction P Q
by a stroke of the ball 11 after reflection at S, we first
place a ball at T behind P, and determine the direc-
tion RS by aiming at a ball U, as if we wished to strike
a ball at T with a direct impulse. But in the case of a
billiard ball, the rotation of the ball round its axis, which
is not destroyed by the collision, will cause the ball to
move, on account of the friction of the table, in a direc-
tion difterent from its first direction: thus the ball C
will not go on to G, but will strike the cushion be-
tween C and D ; and the ball H, after reflection at I,
will proceed in a direction a little nearer to N than
IM; so that the imaginary ball O ought perhaps to be
placed as far from the cushion itself as M, in order that
the ball may be struck after reflection. P. 82.

Fig. 74. Mr. Stneaton's apparatusfor experiments on
rotatory motion. P. 84.

Fig. 75. The moveable centre of suspension being
fixed at the distance of 5 inches from one of the balls,
and 7 from the otlier, the vibration is performed at the
same time as that of a pendulum 37 inches long. P.
85.

Fig. 76. The three weights, supported on wheels,
being drawn up the three inclined planes at the same
time, by the action of three other equal weights, the
middle weight arrives first at the top, the length of its
plane being twice the height. P. 88.

Plate t .

Pig-.S5

Fig-. 69 .

Tig;. 74-

Fig;. 73,

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Joseph, Slcelton

Plate "vi.

Fig-. 77.

Fig;- .78.

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Tip. 84.

Fig. 85.

I^ub.hy J .Johnson .Zojldon 2 J'ldy %6o6 ,

Jiyfijrh Skeiten J< iJr

763

PLATE VI.

Fig. 7T. The proportions of the diameters of the
different parts of the double pullies being 3 to 2, 5 to
2, and 8 to 2, the middle weight may be observed to
rise the most rapidly. P. 88.

Fig. 78. A wheel supposed to be capable of pro-
ducing a perpetual motion; the descending balls, act-
ing at a greater distance from the centre, but being
fewer in number, than the ascending. In the model,
the balls may be kept in their places by a plate of
glass covering the wheel. P. 92.

Fig. 7^. A, the inclination of cross lines generally
most convenient for producing the effect of a tint, in
drawing, B shows the effect of lines crossing each
other perpendicularly, and C that of lines crossing too
obliquely. Where the surface to be shaded is large,
the separate lines or hatches should begin and end w ith
a point, in order that the junction of the different por-
tions may escape observation. P. 95.

Fig. 80. Dr. Hooke's telegraph, in which the cha-
racters are arranged behind a screen, and drawn out
as they are required. P. 100.

Fig. 81. Dr. Ilooke's alphabet, with some other
arbitrary characters for his telegraph. P. 100.

Fig. 82. A beam compass, witli a scale. P. 102.

Fig. 83 . . 85. Instruments for drawing arcs of
large circles. P. 102.

Fig. 86. A pair of triangular compasses. P. 102.

Fig, 87. Marquois's scales, for drawing parallel lines.
P. 103.

Fig. 88. A pen for ruling musical lines. P. 103.

Fig. 89. A pantograph. A being the centre of motion,
B the tracing point, and C the describing point, AB
is always to AC as A D to A E, and the copy F is si-
milar to tlie original G. P. 103.

Fig. 90. A pair of proportioaal compasses. P. 104.

r64

PLATE VII.

Fig. 91. A sector. The scale of equal parts is
marked L. As A B is to AC, so is B D to C E ; and
if any line R D be placed with its extremities in the
third division of the scale on each leg, tfie distance
C E between the seventh divisions will contain 7 equal
parts, of which B D contains 3 ; and the sam« is true
of any other numbers. P. 104.

Fig. 92. A vernier, indicating 38ot of the divisions
of its scale. P. 105.

Fig. 93. A sliding rule. The slider being drawn
out, so that the division marked 1 is opposite to 3 on
the rule ; all the other figures on the rule are triple of
tliose which stand opposite to them. P. 107.

Fij^. 9t. A circular logarithmic instrument. The
inner circle slides within the outer, and as it is represent-
ed in the figure, each number stands opposite to an-
other which is twice as great. P. 107.

Fig. 95. A steel chain, made by llarasden. A,«the
•crew for bringing the mark B precisely to the point
required; C a joint between the adjoining links; D,
a cross joint at every tenth link; E, a pulley and
weight for stretching the chain. P. 11?.

Fig. 9(5. A micronietrical scale made by Troughton.
The compound microscopes A and B are fixed nearly
»t the required distance on the scale C : A is the;i made
to point exactly to a division of the standard scale D
by means of the screw E, and B to another division,
at the required distance, by means of the screw F, the
fractiona parts being added by the turns of the screw
G. The scale D is then removed, and the object to
be compared with it is put in its place. P. 112.

Fig. 97. A diagonal scale. The line A B contains
S74 parts, of which the units of the scale contain 100.
P. 112.

Fig. 98. The statuary's compass, seen sideways.
The pin .IB is forced down, till it is stopped by th«

moveable stud C ; the screw D fixes it in its angular
position. It is also capable of motion round the axis
E F, which is fixed by the screw G. P. 113.

Fig. 99. An instrument for making drawings in
perspective; the perforated sight may be drawn out to
any required distance. The dotted lines show how a
cecond frame may be applied instead of the sight, so
as to answer the same purpose. P. 115.

Fig. 100. Illustration of the princij;les of pcrspec
vc. A being the place of the eye, and BC the plane
of proj ection, if A D be parallel to E F, G 11, and I K, D
will be their vanishing point, and E D, G 1), and I D,
thtir whole images : AL being parallel to EM and IN,
L will be their vanishing point, and EL,IL, their
whole images : and A O being parallel to P Q, O will
be its vanishing point. P. 115.

Fig. 101. A being the centre of the picture, A D the
horizontal vanishing line, AC the vertical line, and D the
point of distance, if a ground plan EFGHofany figure
on the horizontal plane be placed in its true position with
respect to I K, the bottom of the picture, the vanish-
ing points of all its lines will be found by drawing DL,
D M, D N, and D O, parallel to those lines respect-
ively; and the whole images of the lines will be PL,
QM, KN, and 10, determining, by their intersec-
tions, the figure IISTU, which will be the projec-
tion ofEFGH. The plan may also be drawn, in an
inverted position, below the line I K, and the point of
distance taken above A instead of below it. P. 115.

Fig. 102. A B being the whole image of the line re-
presented by A C as a ground plan, and D the point'
of distance, we may find E, the image of the point C,
by drawing CD; or we may make BF^rRD and
AG=AC, FG will then also cut AB in the point E.
P. 116.

Plate VK.

Tig. 91.

Tig-. 9

I'ig-S^

Of tfl

Fub. by J. Johnjori,. London, 1 July iSa6

Jufcph Skciii'i

L

PXAXB Tin.

Ti^.104

Tig-. 106 .

Pig-. 108

-J)

E E

Fig". 107 .

ig.iog.

Fig:. 110.

A D

Jhih.by J. Johns art, London iLJuly ido6 .

Jojcfli, JlcehtoTv jculp.

765

PLATE Vlir.

Fig. 103. Tlie heights of the housp5, -windows, doors,
»nd figures are determined by lines directed to the
centre of the picture ; tlio true height being measured
on the lines A B, C D, where the objects are supposed
to touch the plane of prnjection. The distance EF>
■and all other parts of lines perpendicular to the pic-
ture, are measured bj laying off the lengths of the
originals, as Gil, on the line AC, and drawing I EG
I EH, from I, the point of distance; which, inmost
cases, will be mbrc remote fi-om the centre of the pic-
ture than it is here made. The line K L, and others
parallel to A C, may be measured by the assistance
of any point M in the horizontal line, the distances,
NO, O P, being laid off on AC, or simply by reduc-
ing the scale in the proportion of M P to M L. P-
116.

Fig. 104. A circle thrown into perspective, by
means of the ■ circuiffscribfed square, the points of con-
tact being found by bisecting the sides. P. 116.

rig. 105, Two perspective delineations, and two
orthographical projections of a cube, in differen'
positions. For the orthograpliical projection, the
ground plan being A BCD, the image of any point
A,B, may be found by drawing A E, B F, perpendicu-
lar to the ground line, EG, FII, parallel to the line
assumed for the direction of the centre of the picture,
and AG, BlI parallel to the line of direction of the
point of distance; the interjections G and II will then
be the points corresponding to A and B. P. 116.

Fig. IOC. A is the orthographical projection of a
sphere, with some ofits circles; B the stcrcographical
projection of the same circles. P. 117.

Fi" 107. A balance made by Fidler for the Royal
Institution, nearly resembling those of Ramsden and
Troughton. The middle column A is raised at plea-
sure by the cock B, and carries the round ends of the
VOL. I.

axis in the forks at its upper part, iu order to rcmOTC
the pressure ou thfe sharp edges of the axis within the
forks. The scales are occasionally supported by the
pillars C and D, which are elevated or depressed by
turning the handle E. The screw F serves for rais-
ing or lowering a weight within the conical beam, by
means of which the place of the centre of gravity is
rculated. The extent of the vibrations is measured
on the graduated arc G. P. 125.

Fig. 108. A balance for the illustration of the dif-
ferent kinds of equilibrium. When the scales are hung
on the middle pins. A, B, which are in the same hori-
zontal line with the support of the beam, the equili-
brium is neutral, the weights acting as if the centre of
gravity coincided with the point of suspension. If the
scales be hung on the lowest pins C, D, the centre of
gravity will be nearly in the line C D, and its path the
curve E, which has its concavity upwards; but if the
scales are hung on the pins F, G, the path of the
centre of gravity will be convex upwards, and the beam
will overset. In reality the true paths of the centre of
gravity would be nearly in the curves II and I, situated
between the weights in the scales: but these are
similar to the other curves. P. 125.

Fig. 109. When the equilibrium of abalance is totter-
ing, the lower weight acts with the greatest advantage:
thus the effect of the weight A is reduced in the pro-
portion of BCtoDC, by the obliquity of tlie ann
C A, while the weight E acts on the whole length of
its arm CF. P. 125.

Fig. 110. If A BC be a semicircle, and BD repre-
sent a given weight, and A D its counterpoise in one
of the scales of an unequal balance D C will be the
counterpoise in the other scale. It is obvious that
AC is more than twice as great as BD. P. 126.

5 C

766

PLATE IX.

Fig. 111. A weighing machi»c. The platform sup.
porting the weight rests on the pins A,B,C, D, at
equal distances from the fulcra E,F,G,II; so that
wherever the weight may be placed, it presses equally
ou the lever IK, at L, and is counterpoised by a much
smaller weight placed in the scale M. P. 126.

Fig. 112. A steelyard resembling that of Mr. Paul,
in which different weights may be employed. A, a
loop to check the vibrations; B a scale to be sus"
pended by the hook C. If great delicacy be required
in the weiglits, the fractional parts may be expressed
by the turns of a micrometer screw D, furnished with
an index. P, 126.

Fig. 113. A bent lever balance. P. 127.

Fig. 1 14. A spring steelyard : half the case being
removed, to show the spring. P. 127.

Fig. 115. A B, the path of the centre of gravity of
the human body, such as it would be described in
walking, if the legs were inflexible. C D, the path de-
scribed in running, on the same supposition. P. ISO.

Fig. lie. The actual path of the centre of gravity,
•s it is usually described. P. 130.

Fig. 117. An elastic column, compressed by a weight
acting at the distance of one third of its depth from
the concave surface; the compression being every
where as the distance of the lines A B, A C. P. 139.

Fig. 118. An elastic column, extended by a weight
acting at the distance of one third of its depth from
the convex surface, the extension being every where
as the distance of A B, A C. P. 139. .

Fig. 119. An elastic column, compressed by a weight
acting immediately on the concave surface : the com-
pression extends only to the line A B, the parts beyond
this line being extended. P. 139.

Fig. 120. A column bent, by a weight acting lon-
gitudinally, into the form of a harmonic cur\e: the
line A B C D is the limit between the parts which are
compressed, and those which are extended. P. 139.

Fig. 121. An elastic plate or rod, considerably bent
by a weight acting at its extremity. P. 139.

Fig. 122. An elastic rod fixed at one end, and bent
by its own weight. P. 139.

Fig. 123. An elastic rod supported at each end, and
bent by its own weight. P. 139.

Plate IX.

Tie-.m.

Eg-.

g-.lL2

Tie- . 313 .

^tvi.T^y J.JoTtnsffn, ,ZonA0n iJuZy iSo(} .

Jt^s,-ph Skeh.'tt

v.-

PLATE X.

¥ig'.i24.. Tig-. 12 5.

Pig-. 126. Pig'.ia'].

Kg-.x36.

Fig-.x3i.

liiiiiiiiiiiiiiiiiiiiisiiiiiiiiiiiiiMiiiiiiiiiiiiiiiiiii

Fig.x32.

■

¥15.129. FigM^o

Tig-.iS-] .

iii|ipiiipipi*'«t"i*ri

Tig-.x39-

IjllllJjIlllllllilltllllillliillMmiiiiimmmJiaJuiiuumummm....,

Fig'. 140.

Fig-.X4-3.

«L «t. tJL -^ «A. ^ U.

T"" ,j;^|"fr'|nn|ini'|''in| | |n»ii ji-j^ijiai jiinM

Fig;. 145.

Fig". 146 .

Figr.i33.

"T"""II!JT

I I

Fig-.iH-

Fig:.i35.

,lllllllBI|llillliM«l

Qtmiatia-Q. <i. >a-<S- 2l ot a o

,„„„„„i,iiiiiiiiiiiii«ini iii«i«»«»" i»««»«i»"»"'i'r

piiiiiiiiii*"""

- Fig^.138.

iiiiiiiiiiii"^^

Fig. 141.

iMHmmiiiiiBimiiniiiiiiiiii

Fig. 1+4-

Puh.bv J. John^oti., X-ondert 1 July 1806 .

767

PLATE X.

Fig. 121. The mannci- in which a prismatic column
h crushed by pressure, supposing tlic hiteral adhesion
to be simply proportional to the surface concerned.
P. 1-1(3.

I'ig. 125. The manner in nhicli a. column is crush-
ed, supposing the lateral adhesion to be increased by
pressure. P. llti.

rig. I'i6. The circle is as strong as the circumscrib-
ing square, supposing the adiiesion proportional to
the surface, tlie relative force of all its chords being
equal. P. 116.

Fig. 127. The three circles are as strong as the cir-
cumscribing parallelogram. P. 146.

Fig. 128. A, the strongest form for a beam, cut out
ofa plank of uniform depth, for resisting a longitu-
dinal force; U, the form mto which it is bent; both
curves being circular. P. 150.

Fig. 129. A, the strongest form for a beam cut out
of a plank of ecpiablo breadth, for resisting a longitu-
dinal force which beads it into llie cycloidal cun'e
seen at B. P, 150.

Fig. 130. A, the strongest form for a square or turn-
ed beam or column, slightly bent by a longitudinal
force:, U, the form into which it is bent by such a
force. P. 150.

Fig. 131. The strongest form of a beam cut out of
ft horizontal plank, fixed at one end, and supporting a
weight at die other. P. 1 50.

Fig. 132. The strongest form of a beam cut out of
a vertical plank, fixed at one end, and supporting a
weight at the other; the outline being parabolic. In
practice the best method in such a case would be
simply to reduce the depth at the end to one half of
the whole, keeping the outline straight; in this
manner one fourth of the timber would he saved. P.
150.

Fig. 133. Tlie strongest form of a square or turned
beam, fixed at one end, and supporting a weight at
the other; the outline being a cubic parabola. P.
150.

Fig. 134. The sU'ongest form for the outline of a
compound spring, supporting a weight at the end.
P. 150.

Fig. 135. The strongest form for a beam cut out of
a horizontal plank, fixed at one end, and supporting
a weight equally distributed throughout its length ;
the outline being a parabola. P. 150.

Fig. 136. The strongest form for a beam cut out of
* ycrtical plank, fixed at one end, and supporting a

weight equally distributed throughout its length. P.
150.

Fig. 137. The strongest form for a square or turned
beam, fixed at one end, and supporting a weight equally
distributed throughout its length; the outline being
a seniicubic parabola, in which the cube of the thick-
ness is as the square of the distance from the end.
P. 150.

Fig. 133. The strongest form for a beam cut out
of a vertical plank, for supporting its own weight; the
outline being a parabola. P. 150.

Fig. 139. The strongest form for a turned beam,
for supporting its own weight; the outline being para-
bolic. P. 15<1.

Fig. 140. The strongest form of a beam calculated
to resist the pressure of its own weight by lateral ad-
hesion only. The outline is a logarithmic curve,
which iKjver comes into contact with the axis, and ia
order that the condition of equal strength may be
possible, the beam must be loaded with a weight, at
Its extremity, qqual to that of the portion which is
wanting to complete the figure. P. 150.

Fig. 141. The strongest form for a beam cut out of
a horizontal plank, supported at both ends, and bear-
ing a weight at the middle. P. 150.

Fig. 142. The strongest form for a beam cut out of
a horizontal plank, supported at both ends, and bear-
ing a weight equally distributed throughout its length;
the outhoe being p.vabolic. P. 150.

Fig. 143. The strongest form for a beam cut out
of a vertical plank, supported at both ends, and bear-
ing a weight equally distributed throughout, the ouC-
liiie being elliptic. P. 150.

Fig. 144. The strongest form for a beam cut out of
a horizontal plank, firmly fixed at both ends,'and sup-
porting a weight at the middle. P. 150.

I'ig. 145. ihc strongest form for a beam cut out of
a vertical plank, firmly fixed at both ends, and sup-
porting a weight at the middle, the curves being pai-
rabolic. P. l.iO.

Fig. 146. The strongest form for abeam cutout of
a vertical plank, and supporting every where a weight
proportional to tlie distance from the extremity : the
outline being a cubic parabola. P. 150.

Fig. 14T. The strongest form for a square or turned
beam, supporting every where a weight, proportional
to the distance from the extremity, and represented
by the section of the same figure, which is a pyramid
or a cone. P. 150.

768

PLATE XI.

Fig., 148. A machine Cor examining tlie strength of
materials. The force is applied by means of the
winch A, which winds up the rope BC, passing over
the first pulley, and under the second, which is directly
under the point D, at which the force acts on the piece
EFto be broken; the puUies slide on two parallel
bars, fixed in a frame, which is held down by a paint
projecting at G, from the lever Gil, which is gra-
duated like a steelyard, and measures the force. The
piece to be broken is held by a double vice, I,K, with
four screws, two of them hiding the other two in the
figure: if a wive is to be torn, it may be fixed to be
the cross bar LM; and a substance to be crushed
must be placed under the lever N O, the end N re-
ceiving the rope, and the end O being held down by
thejclick, which acts on the double ratchet O P. The
leve.r is double from O to Q, and acts on the substance
by a loop, fixed to it by a pin. P. 151.

Fig. 149. The outline of a column diminished one
^fth of its diameter, in two difierent Avays : the side A
being an arc of an ellipsis, of which the semidiameter
AB is the lesser semiaxis, joined at A to u right line
AC, of one third of the length of the column, the
part AD being cylindrical; the side D E is a cubic
pjiraboU, and may be drawn mechanically by fixing a
straight ruler EFjinsuchaposition that DF may be twice
the diminution at E, and then bending it to D : the dinii-
Qutiofi being every where as the cube of the distance
from D. These two methods are compared in a con-
tracted scale at G: the outer line represents the first
method, and the next line the second ; thq third,
which is nearest to, G the conclioid of Nicomedes, re-
commended by Chambers, said to be found in the
columns of the Pantiicon; the curve beginning at the
base. Palladio fixes the ruler at A, and bends it to H>
which makes the curvature abruptly greater at II. P.
158.

Fig. 150. A section of Mr. Smeaton's liglit house
at the Eddystone. P. 159.

Fig. 151. Mr. Smeaton's mode of uniting tiers o*^
stones by wooden pins and wedges. P. 160.

Fig. 152. A string of beads, suspended in equilibrium
from two points, and remaining in equilibrium in an
inverted position. The ends are supported by two
pieces, which slide backwards and forwards, and are
fixed by screws: the string is also tightened by turn
ing a pin. P. 161.

Fig. 153. A system of bars, hanging in equilibrium,
and supporting each other in the same form when in-
,,erted. P. 161.

Fig. 154. A, a chain loaded, at cqu^ distances,
with other chains of such a length, as to represent
the depth of the materials pressing on an arch of
the form shown by the first chain, and holding it in
equilibrium. B, an arch of a similar form. P. 161.

Fig. 155. A comparison of the curves which have
various advantages for the construction of an arch sup-
porting a horizontal road. TVie full line is an elliptic
arc, somewhat less than half the ellipsis. The outside
curve, which is also continued furthest down, is that
which iscalculated for resisting tlie pressure of materials
acting like a fluid, or in the manner of wedges : the second
dotted curve, for supporting the pressure of the mate-
rials above each part, supposed to act in a vertical di-
rection only: the third" is a circular arc, making one
third of a whole circle : the fourth is part of a logarith-
mic curve, whicli is nearly of equal strength with re-
spect to the tendency of the materials to give way for
want of lateral adhesion, and the fifth is composed
of parabolic curves, showing the outline which would
be strongest for supporting any additional weight placed
on the middle of the arch. If the height were greater
in proportion to the span, as usually happens in prac-
tice, there would be less difference between the curves.
The radius of curvature at the summit being AB, the
horizontal thrust is e'qual to the weight of the por-
tion A B C D of the materials.

PLAa-E XI .

Tig,- • 148 ■

Kg. 149.

Tig", i5o.

Piar. i5

rig.i55 .

Tig-. i5 4 .

S^

IPiih.by J. Johnson., London ^Jidy t8o6 .

Joseph Skcltan scuiv.

PLATE Xa.

rig.i56.

^ib . by y. Johnson .Zondon i Jufy :i.8o6 .

Ji'scph SAeit,/- .nt/)

7^9

PLATE XII.

Fig. 156, The middle areh of Black Friars Bridge,
P. 164.

Fig. 157. A spherical dome, of wliich the lower
parts are made thicker, in order that they may be of
equal stability throughout. From A to B the dome is
of equable thickness : below C and D the thickness can-*
not be increased sufficiently to procure an equilibrium,
without the application of a chain or hoop, of which
tlie section is represented at C, D. If the thickness
.were not at all increased, a hoop would be required
at E, F, or still higher. P. 165.

Fig. 158. A section of the roof of St. Paul's Cathe-
dral. The section of the dome consists of two circu-
lar arcs, of which the centres are a little beyond the
axis: it is supported by carpentry, resting on a cone of
brickwork. The internal dome is of brickwork only,
■ and is open at the summit. P. 165.

Fig. 159. A section of the dome of the Pantheon at
Kome, P. 165.

Fig. 160. A Tuscan column, with its pedestal, capi-
tal, and entablature. P. 165.

Fig. 161. A Doric column. P. 165.

Fig. 162. An Ionic column. P. 165.

Fig. 163. A Corinthian column. P. 165,

Fig. 164. A Composite column. P. 165.

Fig. 163. An elevation of the end of King's College
Chapel, Cambridge; showing on one side the buttresses,
the tower being supposed to be removed, and on the
other the tower, which not only supplies the place of a
buttress at the end, but assists also in supporting a
considerable portion of the thrust in the direction or
the length of the chapel ; the roof, which is of stone,
being vaulted in this direction as well as tranversely.
There is also a roof of carpentry, covered with lead
above the stone roof. P. 166.

770

PLATE XIII.

Fig. 166. Joints for a tie Insam. The joints at A and
n cannot be more than half as strong as the entire
beam, supposing the ^adhesion, produced by the pres-
sure of the bolts, as strong as could be required. The
joint at C is calied a dovetail joint; its strength is a
little less than chat of A and B, but the adhesion is
nvorc easily secured, since a force tending to separate
the beams must tighten the joint. P. 167.

Fig. 167. Joints for a lie beam. The joint A, if
sufliciently liglit, may possess t of the strength of tl)e
beam. The joint B might be as strong as the beam, if,
the adhesion were great enough, but it would be diffi-
cult to apply sufficient pressure to create such an ad-
hesion, and if the beam were subject to be much
sliakcn, the joint would be a very bad one. P. 167.

Fig. 168. A good joint for a tic beam; the adhe.
•ion being secured by a slight diminution of the
strength. P. 167.

Fig. 16?. A, a simple scarfed joint, which may be
tightened by a wedge at the centre; it is not strong.
B, a scarfed joint wliich is much stronger. P. 167.

Fig. 170. A joint for a beam supporting a weight
by its transverse strength. Thejunction might be made,
if it were necessary, by means of a third piece, of
which the limits are marked by the dotted line. The
strength is but little diminished by the joint, P. 168.

Fig. 171. A beam supporting a weight by its trans-
verse strength, joined to anotlier by means of a third
piece of half the depth, spliced or fished on, below
the beam, and secured by pins, and by blocks or jog-
gles. The strength is a little greater than that of the
original beam. The dotted lines show the proportion
in which the strata ate extended or compressed, the
lower part of the original beam remaining in its natu-
ral state, without sustaining any pressure, as far as one
fourth of the depth, and a little further. P. 158.

Fig. 172. A joint for a beam pressing obliquely
against another. The dotted lines show the form of
the tenon, which may occupy a considerable part of
the breadth of the beam. The uppers trap, A, is in the
most usual situatiou, but the lower one, B, appears
to afford greater strength, as it presses the beams more
closely together, yet without any danger of crippling
them; besides the advantage of having a firmer hold
of the lower beam. P. 169.

Fig. 173. A joint for a horizontal beam suspended
from a vertical one: the end of tlie tenon being di-
lated by wedges, and the whole secured by a strong
strap. The tenon ought not to be wide, since it dimi-
nishes the strength of the horizontal beam. P. 169.

Fig. 174. The straps, bent so as to deviate from
the right lines joining their extremities in the degree
that is here represented, have their strength reduced
to about one seventh of that which they would have
if straight. Thus, A B is only one seventli as strong
as C D, supposing the substance inflexible. P. 169.
Fig. 175. The simplest form of a roof AB, AC, are
the rafters, and B C the tie beam; the weight of each
half being i-eprcsented by AB, or A C, the thrust in the
direction of the rafters will be A D, and the horizontal
thrust each way BD or C D. It is obvious that A D
will be least when B AC is a right angle. P. 170.

Fig. 176. A common roof, with braces. A B is the
king post, and B C, B D the braces. P. 170.

Fig. 177. A kirb or mansard roof, the rafters of
which hold each other in equilibrium. A B and C D
ai-e queen posts helping to support the tie beam. The
piece A C acts as a strut, in supporting the pressure
occasioned by the weight of the tie beam. The heads of
the queen posts are not much thickened, in order to
avoid the change arising from the unequal contraction
cf the wood. P. 170.

Fi^.x66.

Plate UK

Fag.x6'5

Fig.x68

Fig,-.x69

rigr-^72- A

J*uo. hy J. Joluhs<m,,L{mdo7i 2 Ju]a' 1806.

Joseph SJcclti?n sctiip .

77'i

PLATE XV.

Fig. 189. The form of « wheel or pulley, on which a
'broad strap runs, the surface being convex : the wheel
wliich drives it is of a similar form, but its upper
part only is shown in the figure. P. 175.

Fig. 190. The teeth of two wheels, formed into epi-
cycloidal curves, acting on planes : the dotted lines
show the effective nnagnitude of the wheels. P. 176.

Fig. 191. The teeth of two wheels, formed into in-.
volutes of circles, described by uncoiling a thread
from the dotted circles; the point of contact of the
teeth being always in the straight line which touches
both circles. P. 176.

Fig. 192. Two surfaces formed into involutes of cir-
cles, revolving in contact with each other, the equi-
distant lines, drawn on them, continuing to meet each
other throughout the revolution. P. 176.

Fig. 193. The pinion A is of the kind called a spur
wheel ; B is a crown wheel, or a contrate wheel. P.
177.

Fig. 194. The wheel apd pinion are both bevilled :
the faces of the teeth being directed to the point A.
P. 177.

Fig. 195. Two wheels a little eccentric, acting on
each other. P. 178.
Fig. 196. An eccentric contrate wheel, acting on a

ong pinion. P. 178

Fig. 197. A machine for cutting the teeth of wheels.
A is the wheel, of which the teeth are formed by the
revolving saw B, turned by the wheel and pinion C,
D, by means of the handle E, while the frame, which
holds the saw, moving on hinges, and resting on a
spring, is depressed by the handle F, its place having
been ' previously adjusted by the screw G. The large
plate III contains a number of concentric circles, va-
riously divided by points, into which the end of the
spring I sinks at each step, so as to fix the apparatus
in the required position. P. 178.

Fig. 198. A chronometer for measuring minute por-
tions of time. The axis A B being turned, either by
the handle A or by the weight C, the balls'D, E fly oat,
and carry the weights F, G further ftdm the 'axis ; in
consequence of which the increased effect of friction
retards the motion, when it becomes too rapid. The
barrel H is turned in the mean time, with the axis, and
is allowed to descend as the thread at I is uncoiled, so
that the point K, which is pressed against it by a spring,
tiescribes on it a spiral, which is interrupted whenever
the pin K is touched. P. 191.

Fig. 199. The fusee of a watch or clock, the gene-
ral outline of which forms part of the hyperbola A B,
in which the distance of each point from the axis C D
is inversely as its distance from the line D E. P. 192.

PLA.TE Vf.

¥1^.189.

E%.X90.

i'isf.xgx.

Fig-. 19

¥1^.193.

lig-. 195.

''"^^^.:

J^ii.by jr..Jo7inso7v,Xond£fn J.Jidy ^So6 .

Jpsqyh Skeltan saJp.

PlATK XVI.

Fig'. 200.

Yie-. 201

R.g.202.

<iniinill«l!A;

\ i ^ \

Jij^.hy J. Johnson, .London. xJuly x8o6 .

Jasepk SkdU'n stM!^'

773

PLATE XVI.

Fiff. 200, A fusee n ith an auxiliary spring, for con-
tinuing the motion wlica the watcli is wound up. The
action of the main sprii-g turns the fusee in tlie direc-
tion A B; tlie ftisee nets on the ratchet wheel ABC
by means of tlic click B, and this wheel impels the
toothed wlieel D E by the spring C B A, which is sup-
posed to be seen through it. When tlie watch is
■wound up, this spring forces back the wheel ABC
against the click F, which serves as a fixed point, while
the other end continues to act on D E, and to main-
tain the motion. P. 193.

Fig. 201. The scape wheel A B, moving in the

direction AC B, impels the pallets \), E of llie crutch

or anchor, alternately in contrary directions. 1'. 191.

Fig. 202. A is the scape wheel, B and C the pallets

of the common watch scapement. P. 194.

Fig. 203. The dead beat scapement. 'J'he teelh
are first received on the flat or rather cylindrical sni--
faces A,B, on which they rest until the pendulum ar-
rives near the middle of its vibration, when the teeth
begin to act on the inclined surfaces terminating the
pallets. P. 195.

Fig. 201. The horizontal scapement, for a watch.
The tooth A rests first on the external surface of the
cylinder, BC, and then impels it by its inclined face,
in the direction BC; it afterwards falls on the con-
cave surface D K, and lastly impels the cylinder in the
contrary direction. P. 195.

Fig. 205. The duplex scapement. A B is the pallet,
through which the cylinder, and the tooth which rests
ou it, arc supposed to be seen, the point of the tooth
being about to escape from the notch towards C. The
short tooth D next nnpels the point of the pallet, and
the long tooth E falls on the cylinder. It first rests on
the convex surface, and then drops into tlie notch,
which causes a shght recoil in the wheel, and passes by,
the tooth F being beyond the reach of the pallet; but
on its return, the tooth falls again into the notch; and
when it escapes, the pallet is impelled as before. P.
196.

Fig. 200. Mr. Mudge's watch srai)cmcnt. A, the
scapewheel, and one of the subsidiary springs, seciV
from above; B a general view of the balance, with
both the subsidiary springs, seen from one side. The
point of one of the teeth rests at C on the end of the
pallet, which is bent so as to detain it until the pin D,
which is attached to the balance, sets it at liberty, bv
striking against the arm E: this arm is then carried
on by the balance, to the end of its vibration, and im-
pels it in its return, until the pall«;t meets the next
tooth. The other spring acts alternately in the same
tuunner, but in a couiriiry diicctioa. P. 19T,

Fig. 207. An improvement on Mr. Cumming's
scapement for a clock. The tooth A is seen resting
on a Hat surface at tlie end of the pallet B ; it is dis?
engaged by the descent of the opposite pallet into the
position in which it is represented, tlie pallet B being
impelled by it at C. This pallet continues resting on
the flat end of the tooth, until the pin U of the pendu-
lum strikes against the arm E, which is carried before
it, and impels the pendulum in its descent, until the
pallet B acquires the situation in which the opposita
pallet is represented, and sets that pallet at liberty
from the tooth E, which has raised it. The situation
and magnitude of the weights G, II, may be adjusted
at pleasure P. 197.

Fig. 208. Mr. Arnold's watch scapement. The
pill A, projecting from the verge or axis of the balance,
moving towards B, carries beiore it the spring B, and
with it the stifler spring C, so as to set at liberty the
tooth D, which rests on n pallet projecting frotri the
spring. The angle E of tlie principal pallet has then
just passed the tooth F, and is impelleil by it until the
tooth G arrives at the detent. In the return of the
balance, the pin A passes easily by the detent, by forc-
ing back the spring B. The screw II serves to adjust
the position of the detent, which presses asjaiiist it. P.
197."

Fig. 209. Mr. Eariishaw's scapement. A is the
unlocking pallet, B the spring on which it acts, C the
detent, holding the tooth D by a pin; E is the point
of the principal pallet first impelled by the tooth F,
G is the tooth next locked, and U the adjusting screw.
P. 197. ■ ■' ^

Fig. 210. A gridiron pendulum, consisting of three
bars of iron, and two ot a mixture of zinc and silver.
P. 200.

Fig. 211. A compensation balance, as employed ty
Arnold. The outside of the hoops A, B is of Irass,
the inside of sleeh the weights C, D are screwed
backwards and forwards, in order to obtain the reqiii-
siie degree of coiiipeiisutiun. I'he weights E, F, arc em-
ployed to regulate the mean rate of the watcli, and
G, U, and I, for adjusting it to all positions with re-
spect to the hori/on. P. 201.

Fig. 212. The compound plate A B rests on two
supports, which are adjusted to a proper distance by
luriihig the double screw C, the flexure of the plate
by heat raising the bar D, which supports the pendu-
lum, while its effective length is determined by a
fixed clip, whicfi is seen below the plate. P. 211.

VOL. r.

0 D

774

PLATE XVII.

Fig. 213, A jack for laisiag welglits by the alter-
nate motions of a lever, the clicks on each side being
detained in the teeth of the ratchets by the assistance
of the springs in which they terminate, and which are
coiinccied together. P. 204.

Fig. 214. The mode of supporting a tackle for
raising stones in building ; the summit of the triangle,
which is composed of three poles, being raised or
lowered by means of a rope and puUies. P. 907.

Fig. ai5. A method of raising weights obliquely,
by means of a rope, passing over a pulley, which is
drawn along horizontally. P. 207.

Fig. 216. AB, a section of an inclined plane, belong-
ing to the Duke of Bridgwater's canal: the boats are
drawn into the looks at A, which are then filled with
water ; C is the plan of the windlass, by which the de-
scending and ascending boats are connected together,
and which is turned by a winch ; D and E a"re the
locks. P. 308.

Fig. 217. A crane, with an oblique walking wheel,
for oxen or horses. The wheel is taken from a mill
of Leupold. P. 209.

Fig. 218. A crane with a wheel and break like Mr.
White's. The man wdlks at any required distance
from the axis of motion, and pushes forwards the lever

A, which moves the bar B C, connected to the same
axis, and removes the break CD from the ciicuiiife-
rence of the wliccl. P. 210.

Fig. 219. A lewis, for raising stones. P. 210.
Fig. 220. When the centre of gravity A is twice as
far from one of the porters B, as from the other C, the
first bears one third of the weight, the other two thirds.
P. 212.

Fig. 221. When the centre of gravity A is above the
line joining the points of support B, C, the load is di-
vided in the ratio of the segments CD, BD, termi-
nated by the vertical line AD; but it may be sup-
ported by two equal forces in the directions BE, C F,
found by makhig G H equal to BG, and joining C H;
the angle G B E being equal to G U F; the forces and
the weight may then be rtpreseutcd by the lines C I,
IK, andCK. P. 212.

Fig. 222. A roller with two wheels fixed on its ends,
by means of which tlie slab resting on it may be
moved to a considerable distance without leaving the
roller behind. P. 213.

Fig. 223. Mr. Garnet's roIlers,for diminishing fric-
tion : their axes being loosely connected by a ring, in
order to keep tliem in their places. P. 213.

Plate xvn .

Kg-. 219

:"ig'. 222.

Fig-. 220.

Fig;. 223.

Fi<" . 1

•■£ T •'

I'ub.by ^T.Johnjron , Lcrufvrt j July 1806.

Joseph Skclton, saJjp

Plate IVIIE.

Fig". 224 .

Fig". 22 5

Fig-. 226.

Fig:.

g:. 227

Fig-. 237. ^

Fi^.238

-^h. ^ J'. JoJmson , J. London, x July J.S06 .

Jo.fcph SlfAton .i3

ns

PLATE XVIII.

Fig. 224. A pair of friction wheels, supporting one
end of the axis of a wheel. 1'. 214.

Fig. 225. The centre of tiie wheel A B, passing
over the obstacle C, describes the path DE; that of
the larger wheel F G, the path II I, which i» less
»teep. P. 2 14.

Fig. 226, The centre of the wheel AB describes
the curved path C D, in passing over the obstacle E,
while that of the larger wheel FG has an angle at
H. P. 214.

Fig. 22T. The wheel AB, moving on a soft road
towards B, has to overcome the resistance of the ciirth
atC. P. 815.

Fig. 228. A section of the wheel of a carriage, a
little dished, or inclined outwards. P. 217.

Fig. 229. A B and G D being the straps or braces by
which a coach is suspended, if the centre of gravity be
at E, F, or G, it must move, when the carriage swings,
in the curve passing through the respective point. P.
818.

Fig. 230. The mode of harnessing two horses, so as
to make them draw conveniently together: when ei-
tlier horse advance»-sO far that the bar A B assumes
the position C D, the foremost horse has the disad-
vantage of acting on a lever equivalent only to K F,
while the other horse acts on EC. P. 218.

Fig. 231. A sugar mill. The axis K is turned cither
by animal force or by water: the liquor is collected in
the trongh B, and runs oft" in the channel C. Thex
openings D are for the purpose of adjusting the axes
of the rollers. The canes arc supplied by the liands
of the workmen. P. 221.

Fig. 232. A glazier's vice. The vacuity in the mid-
dle shows the form of the section of the lead which is
drawn through it, P. 223.

Fig. 233. A forge hammer, clevnted by the plugs,
projecting from an axis, either at A, or, more coiueni-
cnriy, at B, and thrown forcibly against the woode6
spring C. P. 224. - ■>

Fig. 234. An engine for driving piles, on Vauloue's
construction. - The horses, drawing at A, B, raise the

weight C, held by the tongs D, fixed in the follower
E, which are opened, when thty reach the summit, by
being pressed between the inclined planes F, G, so as
to let the weight fall. At the same tmie the lever 11
is raised by the rope I, and presses on the pin K L, so
as to depress the lever M N, and draw the pin O out
of the drum PQ; the follower then descends, and un-
coils the rope, its too rapid motion being prevented
by the counterpoise R, acting on the spiral barrel Q.
The motion is regulated by the fly S, ihe pinion of
which is turned by the great wheel T. P. 23G.

Fig. 235. The rollers of the slitting mill. P. 228.

I'ig. 23t3. A simple plough. A is the coulter, for
dividing the ground; B the share, fixed on the mould
board C, for turning it to the right hand; D is the rest,
and E,F,' the handles. P. 229.

Fig. 237. Sectimi of a threshing mill. The corn is
drawn in by the rollers or feeders A, B: it is beaten
by the rc\ ol\ ing beaters C, D, and the straw is drawn
out by the rakeu E F, which discharge it at G; the
grain fulling through tho arched bottoms II I, I G,
which are formed like sieves. P, 233.

lig. 238. A corn mill, with some of the improve-
ment* made in America, by Mr. I'Uicott and Mr.
Evans. The corn, being poured into ihc funnel A, is
conveyed, by the revolutions of a spiral B C, to C,
whence it is raised, by the chain of buckets C D, to be
cleaned by the revolving sievo E, and the fan F; it is
then deposited in the granary G, which supplies the
funnel or mill hopper 11; this being perpetually agitated
by the iron axis of the upper mill stone, shakes it by
degrees into the perforation of the stone; it escapes,
when ground, at I, and is conveyed, by means of the
carrier K I., RJid the elevator L M, to the cooler N,
where it is spread on a large surface :, it passes after-
terwards to the bolter O, and is received in tlie binn
P, from whence it is taken to bp packed in sacks or
barrels. Q represents the surface of a mill stone,
cut into furrows, in order to make it act more readily
on the corn. P. SS-i.

776

PLATE XIX.

Fig. 239. The surfaces of the fluid in the bent
tube A B lemBin on the same level, in the same man-
ner as if the tube were absent, and the fluid made a
part of that which is contained in the reservoir C D,
P. 260.

Fig. 240. The bucket A being suspended by the
rope B, and made to revolve rapidly round its axis, the
surface of the water assumes a panibolic form. P.
261.

Fig. 241. A heavier fluid being contained in the
upper part of the bent tube A li, which is immersed
in the lighter fluid filling the vessel CD, the fluid in
the tube remains in a state of tottering equilibiiura,
when its surfaces arc in the same level. P. 261.

Fig. 242. The fluid ABC presses on the bottom of
the vessel BC with the same force as if the vessel were
of the form B C D E. P. 261.

Fig. 243. The portion A B C D of the fluid being
supposed to be congealed, and then to fonn a part of
the vessel, the pressure oji the bottom would remain
unaltered. P. 263.

Fig. 244. The weight A may be supported by the
pressure of a small quantity of fluid, either by making
the surface of the vessel B C very large, and the height
of the tube D E moderate, or, while the vessel F re-
mains of a moderate size, by making the height of the
tube G H very great. P. 263.

• Fig. 245. The pressure on any small part of the side
of the vessel A B, at C or D may be represented by
the line C E,D F, and the whole pressure on the side
by the triangle BG, of which the centre of gravity is
at II; and if the side A I be supported by a single
prop, it must be placed at the point K, the height of
*hich is equal to that of II. P. 265.

Fig. 246. If the heiglit of the surface A above B he.
to BC as tlie specific gravity of tiie {iuid in BC to that
of the fluid in A B, the fluids will support each other.
r. 265.

Fig. 247. Two square beams floating at the depths

shown at A and B, will have a certain degree of sta-
bility, but if they sink, as at C, they will overset. But a
beam of the breadth shown at D will always float
securely. P. 26r. ^

Fig. 248. A jar containing images of fishes, with
bubbles of air in them, which sink when tlie cover of
the jar is pressed with the hand. P. 268.

Fig. 249. Dr. Ilookc's semicylindrical counter-
poise, by means of which a vessel is kept always full.
P. 268.

Fig. 250. The form into which the flexible bottom
of a cistern would be bent by the jjressure of the water:
the curve is the same as that into which an elastic rod
would be bent by forces acting at A and B. P. 269.

Fig. 251. TTiebottle A, containing air and mercury,
has the tube AB fitted into it: and when the jar
C D, in which it is enclosed, is exhausted by means of
the air pump, the elasticity of the air in the bottle
forces the mercury up the tube. P. 270.

Fig. 252. An instrument for showing the buovanS
effect of the iiir, called by Boyle a statical baroscope;
the index A shows, on the scale BC, tlie degree in
which the ball D is obliged to descend, by the di-
minution of the weight of the air. P. 272.

Fig. 253. The line 0 denoting the natural density
of the air, the line 1 A next above it shows the degree
in .which the air is expanded at the height of a mile,
and 1 B the density of the air at the same height: in
the same m.inncr 10 C shows the expansion of the air
at the height of 10 miles, .ind 10 D its density; and
51'", below the line, the density which it would acquire
at the depth of 5 miles below the earth's surface. The
lines AC,DBE, are of the kind called logarithmic
curves. P; 272.

Fig. 954. The box or bason, in which the mercury
of the common b:iromcter is contained : A is a float
for adjusting the luiglit, by means of the screw B,
operating on th(: leather which forms the bottom of
the cavity. P. 376.

PLATE XJX.

Fig;. 239.

ig.242.

Fig-. 243.

Ihih .by J. Johnson, T.ondxin j July J.806 .

Josrph Slcehon sctdr .

J

V-;.

El-ATE XS .

Fig. 2 55.

Pig. 2 56.

3 \W 1:1 I: J'?'//"

HA. by J. JdJmson JLcnion 3.Ju2y j.6oS .

Joseph Skeli

777

PLATE XX.

Fig. 255. A jet or vein of a fluid, passing through an
orifice in a tl)in plate in any direction, and contracted
after its escape, in consequence of tlie lateral motions
of the particles which flow towards the stream, nearly
in the directions of the lines here drawn. P. HBO.

Fig. 256. A stream flowing through a short cylin-
drical pipe, compared with another flowing through a
diverging conical pipe, the directions of the motions
of the particles appearing to be nearly similar in both
cases. P. 281. , ■ :

Fig. SST. In an experiment of D, Bernoulli, the
water flowing through the conical pipe A drew up
water through the tube B from the vessel C ; in another
of Venturi, the water flowing through the cylindrical
pipe D raised water througli the tube E. P. 281.
, Fig. 258. A siphon, through which a fluid rnns
from the higher vessel into the lower one. P. 283.

Fig. 259. A fluid flowing through a vertical pipe,
and filling a vessel to a height nearly equal to the
length of the pipes, while it is discharged through a si-
milar horizontal pipe. P. 284.

Fig. 260. Subterraneous cavities, with outlets in
tlie form of siphons, through which they do not begin
to discharge auy waliT till they are nearly full; tlie
lower one will then continue to nui liU it be empty.
In the mean time either of them may keep up a con-
stant stream by other passages. P. 285-

Fig. 261. A tube turned up and Contracted, sn as
to throw out the fluid contaiurd in it, in a jet, which
rises very nearly to the height of the fluid in tlic tube.
P. 286.

Fig. 262. The forms of jets issuing from various
parts of a reservoir, tlie amplitude A B being twice
C D, and AE four times F G. P. 280.

Fig. 263. A series of waves, moving in the direc-
tion A B, and reflected by the obstacle B, loses the
appearance of pi'ogrcssive motion, and vibrates up and
down within the limits of the curves A C D E B, and
F G II I K ; the elevation and depression become
however twice as gieat as before reflection. P. 289>

Fig. 26-1. A series of waves diverging from a centre
A, and striking a fixed obstacle B C, are reflected by it
into the same form as if they proceeded from the centre
D, at an equal distance on the opposite side of the sur-
face BC. P^2«9.

Fig. 265. An apparatus for observing the motions
of waves excited, in a fluid poured into the trough
A B, by the vibrations of the elastic wire C, loaded
with a moveable weight D; the shadow of the waves
being thrown on a screen E by the lamp F, through
the bottom of the trough, which is of glass. P. 290;

Fig. 2CC. A series of waves, diverging from the
centre A, and passing through the aperture BC, ex-
tend themselves on each side so as to fill the space
BCDE, while they alTect the parts without thi»
space much less sensibly. P. 290, 458.

Fig. 267. Two equal series of waves, diverging from
the centres A and B, and crossing eaeh other in sucii
a manner, that in the lines tending towards C,D,E,
and F, they counteract each other's cflVcts, and tlie
water remains nearly smooth, while in the interme-
diate spaces it is agitated. P. 290, 461.

778

PLATE XXI.

Fig. 2(53. A stream of air being forced through the
pipes A tind B, the mercury in the barometer C D
Calls from C to D. P. 29r.
- Vig. *ti9. A stream entering the reservoir A, by the
pipe B,carrics with it all the vvaterC,vvhich stands above
the level of its upper surface. P. 297.

Fig. 270. The ball A is permanently supported by
tJie jet B, because, when it fulls into the position here
represented, the centrifugal force of the water at A
cairics it back to the middle of the jet. P. 208.

Fig. 271. A plate, bent into the form A BC, turn-
in:; on the centre B, is impelled by a stream of air
D in the direction C D. I'. 298.
- Fig. 272. A cylinder moveable on an axis, with two
curved pipes inserted in its lower part, seen from
above. The stream A enters at the top of the cy-
linder, and is discharged by the orifices B, C, so as to
turn the vessel in the direction B D. P. 301.

Fig. V3. A jet of a Huid, striking on an obstacle
of equal diameter, and separated by it so as to con-
tinue its motion obliquely. P. 302.

Fig. 274. The whole resistance directly opposed
to tlie sutfacc A'B being represented by BC, the por-
tion which, according to Uie principles of the reso-
lution of forces, ought to at t on the wedge A B U, is re-
presented by B E; and in the same manner the resist-
ance on AB F is to the whoje as B G to BC. P. 303.

Fig. 275. The form of the dead water moving before
an obtuse body is nearly like that of ABC; and the
form adiiptcd for moving through the water with the
least possible resistance like A BDC. P. 804.

Fig. 276. The direction in wliirh the particles of a
fluid arc supposed to move when they strike against a
concave surface. P. 305.

Fig. 277. A hydrostatic balance. P. 309.

Fig. 278. Mr. Nicholson's hydrometer, to be em-
ployed with weights, for finding the specific gravity of
Muids or solids. P. 309.

Fig. 279. A spirit level. P. 311.

Fig. 20O. An overflowing lamp. The hemispheri-

cal counterpoise, wliich is so loaded, that its centre of
gravity is at A, raises the surface of the heavy fluid B
tlte higher as it is more exhausted, so that the oil C
is always forced up nearly to the level of the wick at D.
The oil is poured in by a pipe, in the middle of the
cylindrical column. The air holes may bo made
wherever it is most convenient. P. 311.

Fig. 281. A section of an embankment, of a proper
form to be opposed to the sea, with a drain passing
through it, and a valre at its opening. P. 312.

Fig. 282. The form recommended for the section
of a river or canal. P. 313.

Fij. 283. A B shows the strongest form for a'vertical
beam, fixed above and below, and calculated to resist
the pressure of a'fluid; the greatest thickness being at
C ; and D E is the outline of a series of horizontal
planks, of such a thickness as to afford equal strength
throughout the sluice or floodgate. P. 314.

F'ig. 281. A box, with a valve supported by a hol-
low ball, for letting out air from pipes, when it is be-
low the level of the reservoir. P. 310.

Fig. 285. Two methods of letting out air from pipes,
when it is above the level of the reservoir; A a valve
with a stopcock near it; B a vessel of water, screwed
on for receiving the air ; to be replenished with water
as it becomes empty. P. 317.

Fig. 286. A section of a compound stopcock, which
receives a fluid from either of the pipes A, B, or C,
into a cavity which descends a little in the direction
of the axis, and communicates with the pipe D, by
riicans of one of thfe 'bores represented by dotted lines,
according to the position into which the moveable cy-
linder is turned. P. 318.

Fig. 287. Valves of difterent kinds; A the commoA
clack valve; B a double clack valve, consisting of two
semicircular valves; C a pyramidical valve, consisting
of four triangular pieces; U a circular valve turning on
an axis; E, a stcain valve of metal, sometimes called
a T valve, F, a valve of oiled silk or bladder, support-
ed by a grating, for air. P. 318.

Plate :kxl.

Tig'. 268

Tub. by J. Johnson .Zondon 2. July 1806 .

Joseph Skehon srulp

Pr.ATE, Txn

-^uh .hy J. Johnson. JLenion iJidy 280&. .

J^os^h Skel:

779

PLATE XXir.

Fig. 288, Mr. Woltmann'g liydrometrical fly. Tlie
plates A,B, are so adjasted by experiment, as to move
exactly or very nearly with the velocity of the wind, a
few degrees being allow ed as a compensation for the
retardation of friction. The cord C is drawn up, and
the wheel D is caused to revolve, at a time observed
by a stop watch; and its surface is gnuluated so as to
number the revolutions of tlie fly. P. 319.

Fig. 289. An apparatus fur measuring a ship's way,
resembling Captain Ilamilton't. A is a funnel partly
covered, B a part of the ship's keel, C the upper part
of the pipe D, in which the smaller pipe El' slides in
a collar of leathers, so as to have the orifice F level
with the surface of the water. This pipe has a small
aperture at the bottom, wliich limits the magnitude
of the stream discharged into the vessel G, the end
F being considerably larger. The tube II serves as a
gage, to measure the velocity at any given time. P.
819.

Fig. 290. An overshot riheel, on which the water is
admitted in a retrograde direction, so as to run ofl" in
a continued stream ; at the lower part of the h heel it
is retained in the buckets partly by the assistance of a
sweep. P. 321.

Fig. 291. A breast wheel, witli a sweep. P. 322.

Fig. 292. An undershot wheel. P. 322.

Fig. 293. A the form of the sail of a windmill : B
the best inclination for each part of the sail A, accord-
ing to Smeaton's experiments. P. 32-1-.

Fig. 294. A kite supported by the wind, of which
the force acts nearly in the line A B, perpendicular to

tlie surface of the kitQ;.and this, compounded with the
force of the cord A C, produci^s the result A D, which
sustains the weight of the kite. P. 324.

Fig. 295. A ship working against a wind; the force
of the wMid acting nearly in the direction AB, per-
pendicular to the saijs, the sliip's real course is BC,
the angle C B D being the lee way. P. 320.

Fig. 296. The auoria, or noria, used in Spain, for
drawing, water, by a series of earthen pitchers, con-
nected by ropes, and passing over a sprocket wheel.
P. 327.

Fig. 297. An undershot waterwhecl, carrying fixed
buckets, which raise a portion of water, and deliver it
into a trough, furnished w ith a projection, which stands
under the buckets, at the upper part of the wheel.
P. 327.

I'ig. 298. A throwing wheel, for draining fens,
worked by a windmill or otlierwise, and cairying the
water upon a sweep from a lower to a higher level.
P. 327.

•Fig. 299. The rope pump of Vera, for raising water
by means of friction; the rope is kept stretched by a
pulley under the water, which is loaded with a weight,
and slides in a groove. P. 328.

Pig. 300. The screw of Archimedes, nearly as de-
scribed by Vitruvius. P. 399.

Fig. .001. The screw of Archimedes, as recom-
mended by I). Bernoulli. P. 329.

Fig. 302. A waterscrew, revolving within a fixed
cylinder. P. 329.

Fig. 303. the spiral i>ump of Wirtz. P. 330.

780

PLATE XXIII.

Fig. SD4. A centrifugal pump. The machine is
first filled through tlie fuiuiel A, and when it is made
to revolve, the water is discharged into a circular
trough, of which a section is seen at B and C. The
valve at U remains shut while the pump is filling. P.
331.

Fig. 303. A pump consisting of two plungers, con-
tinued nearly to the height at which the water is de-
livered. P. 332.

Fig. 306. Lahire's double forcing pump. When
the piston is depressed, the water enters the barrel at
the valve A, and goes out at B; when it is elevated, it
enters at C and escapes at D. P. 332.

Fig. 307. The common piston, coated with leather.
P. 332.

Fig. 308. Mr. Bramah's press. The pump A forces
tlie water throngh the jiipe B into the barrel C, in
which it acts very powerfully on the large piston D,
and raises tlie bottom of the press E. P. 332.

Fig. 309. Tlie common sucking pum)). P. 333.

Fig. 310. A bag pump, the bag or pufl" A being ex-
tended and contracted by the motion of the piston.
P. 333.

Fig. 311. A lifting pump, the piston rod A B being
drawn up by a frame. P. 333.

Fig. 312. A sucking pump, converted, by the addi-
tion of a collar of leathers at A, into a forcing pump.
P. 333.

F'ig. 313. A fire engine, on a construction similar to
some machines described by Raiuclli. A B is the pis-
ton, working within a cylindrical barrel, and moved
by the handles C 1). When the end C is depressed,
the water enters through the valves E and F, and is
discharged at O and II ; when D is depressed, the wa-
ter enters at I and K, and is discharged at L and M,
into the air vessel N, whence it is expelled by the pipe
O. The pipes P and Q may be united, if it be re-
quired. P. 334.

Fig. 314. I'rom Ramelli. The wheel A B, revolving
in the direction B A, carries a portion of water C be-
tween itself and the sweep D F,, which ii intercepted
by the shder F, and forced up the pipe FG. P. 335.

Fig. 815. From Ramelli. The roller A, revolving
within the reservoir B C, which is nearly cylindrical,
carries with it the slider D E, which is wade to sweep

the internal surface of the cylinder from C to F, by
means of a projecting surface acting on the end D, so
that the water G is forced through the pipe F. P. 335.

Fig. 316. From the cabinet of jMr. Serviere. The
wheels A and B carry, during their revolution, a quan-
tity of water from C to D, or from D to C, according
to the direction in which they are turned. P. 335.

Fig. 317. Mr. Gwynu's patent water engine. The
valve A is kept, partly by means of the spring B, bat
still more by the pressure of the water, in contact with
the roller or piston C, which revolves within the box
J) E, and sweeps it from E to F, so that the portion
of water G is forced, during each half of a revolution,
into the pipe F; or is drawn from F to E, when the
roller revolves in a contrary direction. P. 335.

F'ig. 318. A chain pump. P. 335.

F'ig. 319. The mechanism of Hull's acting pump.
In the position of the stopcock A B, here represented,
the water flows out of the barrel C, and the piston 1>
is allowed to descend. The rod E then turns the
stopcock, and the barrel C communicates only with
the pipe F, which fills it, and forces up the piston,
until the stopcock is turned back to its former posi-
tion. P. 336. *

t Fig. 320. The hydraulic air vessels of Schcranit2.
The reservoir A being filled with water, and B with
. air, and water being poured into the funnel C, the air
in B acts by the pipe D on the water in A, and forces
it up the pipe E. P. 337.

Fig. 321. A being the high water mark, and B the
low water mark, the vessels C and D are filled at high
water from below, the air being suft'ercd to escape by a
stopcock, which is opened by the fall of the ball F ; at
low water the air will enter the vessel D at B ; and be-
fore the next high water, the water C will be forced up
the pipe E. P. 337.

i'ig. 322. The fountain of Hero. Its operation re-
sembles that of the hydraulic air vessels, fig. 320; but
the pipe D here ascends. P. 337.

Fig. 323. The hydraulic ram of Montgolfier. When
the w ater in the pipe A B has acquired a sufficient ve-
locity, it raises the valve B, which stops its passage,
so that a part of it is forced through the valve C, into
the air vessel D, whence it rises through the pipe E,
P. 338.

Plate xxm.

Fig. 304.

Fig.3o6

Fig. 30/].

Fig-.3o8.

i_l

LB

Fig. 309. Fig.3io. Fig.Sn. Fig.Si

C J

rig.3i3. >^i3EL"-7.:^

Fuh.by J. Johnson, Lo?idi.'nt July 1806.

Joseph Skrlton Jrinf.

Pig-. 33o

Jii^ivX Johnson.. Zcrtdon j July 1S06.

JosepJv Sheltot

781
PLATE XXIV.

Fig. 824, Tlic cupping instrument of Hero. The
cavity A was partly exhausted by applying the mouth
repeatedly to the pipe D, the stopcock U being turned
after each application. When the stopcock C was
opened, the air at D in contact w ith the skin was also
rarefied, and the effect ot" suction was produced. P.
539,053.

Fig. 3H5. Mr. Cuthbertson's air pump. When the
piston rod A is depressed, it leaves the piston B a
little behind it, so as to make an opening betwetn two
conical parts which arc ground togetlier, and the air
escapes from the lower part of the barrel into the
Tipper part; when it is elevated, the whole piston is
raised, and a wire, which slides through the axis of the
rod, raises a small valve at the bottom of the barrel,
which leads to the receiver C, by the tube DE: the
air is forced from the upper part of the barrel through
a valve in the oil vessel F, wlience the oil runs back,
when it overflows, by a tube leading to the mouth of
the barrel; and if this tube be stopped by turning its
cock, the air may be condensed into a receiver fixed
at G. At U is a long gage, with a barometer im-
mersed in the same bason of mercury. The piston rod,
which is hollow, has a perforation a little above A, to
admit the oil, in order that the wire may work freely
in it. P. 340.

lig. 326. Tlie two flics A and B being caused to
revolve with equal velocities V)y the descent of the
weight C, they continue to move for an equal length
of time in the vacuum of the air pump. P. 341.

I'ig. 327. The air in the bottle A expands, when the
receiver B is exhausted, and causes the water to rise
in a jet, P. 341.

Fig. 328. A pear gage ; to be suspended in a receiver
by a book like that which is shown in fig. 325. P.
342.

Fig. 329. A condenser, with screws, for confining
the receiver. A is a gage for showing the degree of con-
densation; B the piston of tlie Syrinire, with a valve
of the best kind, which is conical, and is coiyfined by
a spiral spring. But iu common, the valves are made
of leather, wjth a phite of metal to strengthen it. P.
342.

Fig. SSO. A diving bell. A is the forcing pump,
B a stopcock for letting out the heated air, C a strong
glass for giv ing light, D a float for the security of tlie
diver. P. 343.

Fig. 331. Laurie's hydraulic bellows. When the
yessel A is raised, the air enters at the valve B; when
it is depressed, the valve B shuts, and the air is forced
through the pipeC D, which conducts it to the reser-
voir E,whei"e it is confined by the valve F, and forced by
the pressure of the water through the pipe G. P. 343.

Fig. 332. Mr. Watt's gasometer. The pressure is
regulated by the magnitude of the weights A and B,
which act by the spiral fusees C, D, so as to guslain a
part of the weight of the inverted vessel, represented
by the exterior dotted line. The gas is admitted at E
or F, and is delivered at 0. G H is a gage for show-

ing the height of the water within and without the
moveable vessel. I is a cock for lettii^ off the water
P. 344.

Fig. 333. The shower bellows. The stream A,
passing through the strainer B, carries with it a quantity
of air through the pipe C, which rises to the upper
pait of the air vessel D, and is discharged by the piue
E. P. 344.

Fig. 334. The centrifugal bellows. By the revolu-
tion of the fly, the air is caused to enter at A, and is
discharged at B. P. 345.

Fig. 335. The original steam engine of Savery. Tlie
vessel A being filled with steam from the boiler B, and
the stopcock being turned, the steam cools and is con-
densed, and water is forced into its place by the
pressure of the atmosphere, through the valve C :
the steam is then readmitted, and forces the water to
ascend through the valve D and the pipe U E. The
vessel F acts alternately with A. P. 317.

F'ig. 836. The common steam engine of Xcwcomen
and Beighton. The steam being admitted into the cy-
linder A below the piston, tlic weight B is allowed to
descend: a jet of water is then admitted by the pipe
C, which condenses the steam, and the pressure qf
the atmosjihere then depresses the pi^ton: a part of this
water is admitted by the pipe i) into the boiler, in
order to keep it suliiciently lull. P. 347.

Fig. 337. Mr. Watt's steam engine. The steam,
which is below the piston, is suffered to escape into
the condenser A by the cock B, which is opened by
tlie rod C, and at the same time the steam is admit-
ted by the cock D into the upper part of the cylinder;
when the piston has descended, the cocks 11 and F act
in a similar manner in letting out the steam from above
and admitting it below the piston. Tlie jet is suppli-
ed by the water of the cistern G, which is pumped
uj) at H from a reservoir : it is drawn out, togetlier
with the air that is extricated from it, by the air pump
I, which throws it into the cistern K, whence the
pump L raises it to the cistern M; and it enters the
boiler through a valve, which opens whenever the
float Jvi descends below its proper place. The pipes
O and P serve also to ascertain the quantity of water
in the boiler. The piston rod is confined to a motion"
nearly rectilinear by the frame Q; tlie fly wheel R is
turned by the sun and planet wheel S,T; and the strap
U turns the centrifugal regulator W, which governs
the supply of steam by the valve or stopcock X. P.
349. ,,

F'ig 338. Mr. Symington's steam boat. A is the
boiler, B the cylinder, C the piston, D the conden-
sation pipe, E the air pump, F stampers for break-
ing ice. V. 349.

Fig. 339. An air gun. The air is fiirced by the
syringe A into the cavity surrounding the barrel, whence
it is discharged by the valve B, which is opened either
immediately by the action of the trigger C, or by a
spring, which is bent by cocking the gun, and set at
liberty by the trigger. P. 351.

VOX. I.

5e

782

PLATE XXV.

rig. 340. A scries of waves or pulses of sound,
diverging frem one of the foci of an ellipsis, and re-
flected towards the other. P. 375.

rig. 341. Waves diverging from a point near the
centre of a circle, and converging after reflection to
a point at an equal distance on the other side of the
centre. P. 375.

rig. 342. A section of a speaking trumpet and of a
hearing trumpet: the lines representing the direction
of tlie sound before and after its reflections. P. 375.

Fig. 343. A string impelled by the bow of a violin,
and lightly touched at tl>e same time at a point one
third of its length from the end : the small pieces of
paper fly ofl' from the middle of tl>e vibrating portions,
while the pi^ce situated at the remaining point of
division retains its situation. P. 383.

Fi". 344. A vibration compounded with another
smaller vibration, three times as frequent, in a trans-
verse direction, the separate vibrations being such
that tl'.e points may be always opposite to a point
moving uniformly in a circle. Thus the vibrations in
the hnes AB and AC compose the complicated
figure D E. P. 384.

Fi" 345. A specimen of the manner in which the
-vibrations of a string are usually performed when it is
struck with a bow. P. 384.

Fig. 346. Specimens of the simplest manner iij
which sand is collected into lines, on a plate of glass
or metal, which is made to sound i)y means of the bow
4)f a violin. P. 385.

Fig. 847. A round plate, performing some of its
most complicated vibrations, the lines of division
being indicated by the place of the sand. From
Chladni. P. 385.

Fig. 348. A square plate divided into a diversity
of vibrating portions. From Chladni. P. 385.

Fig. 34!>. The small bones of the left ear, nearly
three times the natural size, supposed to be seen
through tUe membrane of the tympanum, by looking
directly into ilie auditory canal. A B is the membrane
of the tympanum, C the hammer, D the anvil, E its
attachment to the surrounding bone, F the stirrup, G
the round aperture in the bone leading to the cochlea.
P. 388.

Fig. 350. A view of the vestibule of the left ear,
with the semicircular canals and the cochlea, seen
with the eye a little more depressed than by looking
ktraight tlirough the canal, and exactly in the direc-

tion of the stirrup. ABC is the vestibule, imme<
diately behind the oval aperture, which is covered by
the basis of the stirrup, D are the canals, E the
cochlea, the upper spire terminating in the vestibule,
the lower in the round aperture at B. The projec-
tion of the membrane of the tympanum is marked by
an oval line. P. 388.

Fig. 351. The structure of the left ear, seen from
above, the upper part of the canal being supposed to
be removed. A is the auditory canal, B the membrane
of the tympanum, C the hammer, D the anvil, E the
stirrup; F the place of the canals, which are higher
than the parts represented, G the place of the cochlea,
H the round aperture. P. 388.

Fig. 352. A,B, C, a representation of the joint
effect of two equal vibrations variously combined, the
middle line being always half way between the two
outer ones, and showing the compound vibration re-
duced to half its real extent: D shows the mode of
finding the joint efliect of vibrations, by cutting a sur-
face into sliders, which are retained in their places
by a screw. P. 390.

Fig. 353. The uppermost and lowermost curves re-
present a series of vibrations, of which 12 occupy any
given period of time : the third and sixth lines two
series of which 15 and 16 occupy respectively the
same time: -the joint eflfcct of each pair is shown by
the dotted curves which are interposed between them,
the middle one representing the effect denominated
a beat. P. 391.

Fi". 354. The proportional lengths of a chord or
pipe, constituting the different notes of the simple dia-
tonic scale, with their mutual relations, shown by their
divisions into aliquot parts. P. 393.

Fi". 355. A good practical mode of temperament;
making all the fifths and the third in the first division
perfect concords; the three remaining fiULs equally
imperfect. P. 396.

Fig. 356. Tlie trumpet Marigni, with its bridge,
which is suppoited by the string AB nearly in contact
with the sounding board; this string being either
stretched by a pin at B, or by a cross string B C. Jte
places, at which the string is to be touched, may be
marketl by frets fixed un<^erthc*h, as they are here
shown by points. At D, tlie scale of this instrument
is exhibitcrl, resembling that of the trumpet and the
French horn. P. 399.

Kg" . S40.

jeiff. 34a,

TLATT. XXY.

Pigr. 342.

Kg-. 343 .

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Tig^. 346.

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Joseph Sk-L-lten .^cidp.

PlAIEXXVI.

Kg-.SS].

Rg:.3b9.

Pig. 364.

Fig. 367 .

Tig. 366.

Fig. 368. B
A.

I

Tig. 369.

Tig. 3^0

Fig.571

Pig. 37

Fig. 374-

£ub .l>y J. Jolinstm .^imdxfTi ijidy J-80S .

Joseph Sh:/t

783

PLATE XXVI.

Fig. 357. The right half of the human larynx.
ABC is the outline of the cricoid cartilage, DEFGH
of the thyreoid, and I K L of the arytaenoid cartilage;
M is the epiglottis,NK the upper ligament ot the glot-
tis, OP the lower ligament, and Q, the trachea. P. 400.

Fig. 358. A view of the ligaments of the glottis,
seen from above, the larynx being divided by a hori-
zontal section a little above them. P. 400.

Fig. 359. Sections of the pipes employed by Kratz-
ensteln for producing the sounds of the different vow-
els ; in general by means of a larynx resembling the
moutli piece of a reed organ pipe, but in the case of
the vowel I by simple inflation through the tube B.
The pipe for U produces the sound O, except when it
is very nearly shut up. P. 401.

Fig. 306. Tiie vox humana organ pipe, with the
mouth piece common to reed pipes in general ; the
lower part in contact with the tongue being nearly sc-
micylindrical : the tongue being adjusted to the pro-
per pitch by means of a sliding wire, which regulates
tlie length of the part that is at liberty to vibrate. P.
40i.

Fig. 361. The mouth piece proposed by Kratzen-
stein, for imitating the human voice, the tongue A
passing freely in and out of the tube, which is more
than half of a cylinder, as is seen at B. P. 401.

Fig. 362. The form of the regal organ pipe. P.
401.

Fig. 363. A front view and section of the open
diapason organ pipe of metal. It is tuned by open-
ing or contracting the upper orifice. P. 402.

Fig. 364. A a front vievr of the flute organ pipe,
of wood, which is tuned by a plug. B a section of
the pipe. P. 402.

Fig. 365. A stopped diapason organ pipe, of metal.
It is tuned by altering the position of the pieces on
each side of the mouth. P. 402.

Fig. 366. A chinmey pipe. P. 402.

Fig. 367. A spindle shaped organ pipe, contracted
above. P. 402.

Fig. 368. A the form of a cromorn pipe, B, of a
trumpet pipe, both having reed mouth pieces. P. 403.

Fig. 369. A ray or pencil of light A B, C B,.falUnjr
on the surface D E, a portion of tiie light in reflected,
and another portion is transmitted, in the direction
B F, B G, so tliat B G is equal to B C, and B H to B I,
C I K and G H L being lines perpendicular to D E at
any such distances, that BK may be to B L in a cer-
tain proportion, which is that of the sines of the angles
of incidence ABM, C;B M, to those of the angles of re-
fraction F B N, G B N. B O and B P are tlie reflected
portions of the rays. P. 411.

Fig. 370. A mode of determining the position of a
refracted ray, which is particularly convenient in the
case of refractions at spherical surfaces. ABC being
any circle, either touching the refractive surface at A,
or being itself a section of Uie refracting substance, if
another circle D E F be drawn on the same centre,
having its diameter to that of the first as the sine of
the angle of incidence to that of refraction, and a third
circle G H I, which is less than the first in the same
proportion as the second is greater; and if the direction
of the incident ray K A be continued to D, andLD be
drawn from the centre, cutting G H I in G, A G will be
the direction of the refracted ray: and if this ray
pass again out of tlie denser medium at B, its direc-
tion BM may be found by drawing LIF, and FBM
will be thus truly determined. P. 411.

Fig. 371. A ray or pencil A B, refracted at B to C,
and there reflected by a perpendicular surface into an
opposite direction C B, will return also in the direction
B A, a portion of it being reflected, in the first place to
D, and in the second to E. P. 412.

Fig. 372. A pencil A B passing through a substance
CD contained between parallel surfaces, continues its
course in the direction E F parallel to A B. P. 413.

Fig. 373, The ray AB, entering the medium CD
through the transparent substance E F, contained be-
tween parallel surfaces, acquires the direction Gil, pa-
rallel to IK, into which LI is at once refracted. P.
413.

Fig. 374. The appearance of a prism, of which the
lower surface is divided into a bright and a dark por-
tion, separated by a coloured arch A B C. P. 414.

784

• PLATE XXVII.

Fig. 375. A is an Actual focus of diverging rays, B
M actual focus both of couverging and of diverging rays,
C a virtual focus of converging rays, and D a virtual
focus of diverging rays; A and B, B and C, and C and
D are foci conjugate to each other, with respect to the
refractions of the three lenses. P. 415.

Fig. 376. The image of the point N, formed by the
plane mirror A B, is at an equal distance behind the
mirror; and in this manner the whole image of the
word is formed in an inverted position. P. 415.

Fig. S77. ABCD represents a pencil of parallfl
rays falling on the concave mirror C D, and collected
into the principal focus at E, wWch is half way be-
tween the surface and its centre. F is tlie principal
focus of the convex mirror G; and H that of the re-
fracting surface I. P. 416.

Fig. 378. A being the centre of the concave mirror
B, tlie image of an object at C will be found at D, and
the reverse. P. 416.

Fig. 379. A pencil of light, deflected from its path
by a prism of a denser substaiicc, in different posi-
tions. P. 416.

Fig. 380. A pencil of light scattered into various
directions by a multiplying glass. P. 416.

Fig. 381. A is a section of a double con vex lens, B of
a double conc«ve. C is a planoconvex, D a planocon-
cave; and E and V meniscus lenses; but a menis-
cus ot the form represented by F is sometimes called
a concavoconvex lens. P. 417.

Fig. S8'.J. The pencils of light A, B are refracted by
the convex lens tj in the same manner as lliey would
have been by the circumscribed double prism DE;
and in the same manner the concave lens F resembles
in its operation the prisms G, H. P. 417.

Fig. S83. A, a pencil of parallel rays, made to con-
verge, by a double convex lens of crown glass, to the
centre of cui-vature of one of its surfaces. B a double
concave lens, causing the rays to diverge from the
centre of curvature. C, D a planoconvex lens, of
which the principal focus is at the distance of a dia-
meter. P. 417.

Fig. 384. The lenses represented by the shaded
surfaces are equivalent in their effects to those of
which the sections are shown by the dotted lines; the
figures at A and B being of equal thickness in the
middle, and at C at the edges also. P. 417.

Fig. 385. At A, a r.idiant point and its image are
both situated at the distance of twice the focal length
from the lens; at B, the one is more remote, tlie other
nearer; and CD is to D E as EF to FG; D and F
being the principal foci of the lens. P. 418.

Fig. 386. Thie oblique pencils of rays A, B, and

the direct pencil C, are supposed to be brought to
their respective foci in the same plane D E. P. 419.

Fig. 387. The square A intercepts the whole light,
proceeding from the point B, which would fall on the
surface C D, four times as great, placed at a double
distance. P. 421.

Fig. 388. The box of Count Rumford's photome-
ter. The lights, being placed at proper distances on
the graduated arms or tables A, B, throw equally dark
shadows of the cylinders C, D on a white surface at
EF. The wings of the cylinders serve to make the
shadows of equal breadth. The shadows are viewed
through the aperture at G. P. 421.

F'ig. 389. Dr. Wollaston's instrument for the mea-
surement of refractive densities. A is a rectangular
prism of flint glass, under which the substance to be
examined is attached; BC is a rod, or ruler, 10
inches lone, C D and D E are each 15 ,»jji. Wlicn the
sights at B and C are so placed that the division be-
tween the light and dark portion of the lower surface
of the prism is seen through them, the rod F, which
carries a vernier, shows the index of the refractive
density, which, in the situation here represented,
would be 1.43. P. 421.

Fig. 390. A is the actual image of the candle B,
formed by the convex lens C. P. 422.

Fig. 391. A is the actual image of the candle B,
formed by the concave mirror C. P. 422.

Fig. 392. A is the actual image of the candle B,
formed by the convex lens C, being as much larger
than the object as it is more distant nom the lens. P.
422.

F'ig. 393. A is the virtual image of the Candle B,
placed within the focal distance of the concave mirror
C, the image remaining erect. P. 422.

Fig. 394. A is the virtual image of the candle B,
formed by the concave lens C, and less than the ob*
ject. P. 422.

Fig. 395. When the object A is placed in the prin-
cipal focus of the convex lens B, a virtual image i%
formed at an infinite distance, which subtends, when
viewed from C, or from any other point, the same an-
gle as the object subtends at the centre of the lens.
P. 422.

Fig. 396. The object A being placed a little within
the focus of the lens B, a virtual image C is fonned, at
such a distance as is most convenient to the eye, which
subtends the same angle a> the object, from theceotrC
of the lens, and therefore appears somewhat more
magnified than when the object is in the principal fo-
cus. P. 422.

Plate XXVn.

r.K.?,--.

FtA.hy J. Johnson. London i July 1806 .

Joseph. Skrltan sculp.

Pi ATE XXVffl..

Tig-. 357

Pub hy J. Johjhson .london i Juiy 1S06.

Joseph Skfhim SI

PLATE XXVIII.

Fig. Z9T. An imperfect image of an externa! object,
painted in a dark room, in an inverted position, by the
light coming in right lines tlirough a small aperture.
P. 425.

Fig. 398. A portable camera obscura. A is a lens,
B a mirror placed obliqnely, and throwing the image
on a plate of ground glass, CD. E is a moveable cover,
and FO a screen attached to it, for excluding foreign
light. P. 425.

Fig. 399. A camera oljscura, whicli throws down an
image, by means of the mirror A, and the Ions B, on
the surface C, where it may be seen through the aper-
ture D. The surface C has here the curvature best
adapted to receive every where a perfect image of a
distant object. P. 425.

Fig. 4o6. An arrangement proposed for a solar mi-
croscope, adapted to a window facing the souUi. I he
mirror A is moved by a hinge into the position required
for tlie day, and during the emph)ymeut of the instru-
ment is turned only round the axis .\ B, which is pa-
rallel to that of the earth. The mirror C is fixed: it
receives the beam of light from A, and throws it on the
object through the lenses D and E, of which the joint
focus is near the magnifying lens F; this lens paints
an image of the object in an inverted position on a
screen at G. If the focus of the condensing lenses
were behind the object, as at H, the light would be
liable to be condensed into a spot on the screen at I.
P. 426.

Fig. 401. An arrangement proposed for a phantas-
magoria. The light of the lamp A is thrown by the
mirror C and the lenses C and D on the painted slider
at E, and the magnifier F forms the image on the
screen at G. This lens is 6xed to a slider, which may
be drawn out of the general support or box H: and
when the box is drawn back on its wheels, the rod I
K lowers the point K, and by means of the rod K L
adjusts the slider in «urh a manner, tliat the image is
always distinctly painted on the screen G. When the
box advances towards the screen, in order that the
images may be diminished and appear to vanish, the
support of the lens F sutTers the screen M to fall and
intercept a part of the lijht. The rod K N must be
equal to I K, and the point I must be twice the focal
length of the lens F, before the object, L being iinmc-
<liatc!y under the focus of the lens. I'he screen M may
have a triangular opening, so as to uncover tlie middle
of the lens only, or the light may be intercepted in any
otlier manner. P. 427.

Fig. 402. The construction of the astronomical te-
lescope. ABC and D EC arc the central parts of the
pencils of rays, coming, from the c:i!tiemities of the visi-
ble field, through the middle of the object glass. P.
427.

Fig. 403. The extreme pencils of rays in the double
or compound microscoj-e. P..438.

Fig. 404. The extreme pencils in the Galilean tele-
€cope, or opera glass. P. 423.

Fig. 405. A, ilic directions of the extreme pencils
in the common daj telescope of lUicita. If only two
€ye glasses were employed, as at H, the field would
tibviously be more ccnUactLd. P. 428.

Fig. 406. Dr. Ilerschers forty fet t telescope. ABC
the path of a ray of light, reflected by the mirror at
B to the eye glass C. I) a chair in which the observer
sits. E a moveable gallery, on which several persons
may stand. F G a smooth surface, on which the bottom
of the telescope is made to roll along, while its opening

2

is raised or depressed by the pullies at II and I. K one
of two rooms or huts for the accommodation of the ob-
server's assistants. The wheels, under the frame, serve
to turn the whole instrument round its centre. P. 429.

Fig. 407. The Newtonian telescope, with the di-
rection of the central r.nys. These are not the rays by
which the object is actually seen, because they are
intercepted by the small .speculum, but they afford the
simplest determination of^ the magnitude of the field
of view. P. 429.

Fig. 408. The supposed path of the central rayl
in the Gregorian telescope. P. 429.

Fig. 409. The supposed path of the central rays in
Cassegrain's telescope. Here the rays actually repre-
sented would not only be intercepted by the small
mirror, but they would also fall on the perforation of
the great mirror. They, however, serve equally well
to determine the magnitude of the field. P. 429. ■

Fig. 410. The supposed path of the central rays ia
Dr. Smith's microscope. The rays running directly from
the object are intercepted by a screen. P. 429.

Fig. 411. A; the dotted line represents the curr*
called the caustic of a concave mirror, in which the
rays proceeding, in the section represented by the fi-
gure, from a distant point, would be collected. B; the
dotted line is the caustic of a convex mirror. The eye
being supposed to be at a great distance from the he-
mispherical mirrors C and 13, the images of distant ob-
jects ill all directions will be found between the dotted
curves, the distance of those curves sliowing the de-
gree of confusion. The images of distant objects ia
all directions formed by the small concave and convex
mirrors E and F, are found between the dotted circle
and the straight line touching it. P. 430.

Fig. 412. The effect of a field glass in a compound
microscope; the inner lines showing what would be
the magnitude of the field without it. P. 431.

Fig. 413. The manner in which Mr. Ilamsden em-
ployed a planoconvex lens in the eye pieces of his tele-
scopes and in his double magnifiers. The curved dot-
ted line shows the image of the straight line divided
into equal parts, which is formed by the larger lens, ia
the focus of the smaller, through which it is viewed.
P. 431.

Fig. 414. An achromatic telescope, with a triple
object glass, and with Boscovich's achromatic eve
piece, consisting of two similar lenses, one of which is
every w.-iy three times as groat as the other, their dis-
tance being twice the focal length of the smaller. P.
432.

Fig. 415. The dotted lines AB and CD represent
two images of the same object, formed by rays tliffer-
ently refrangible, passing through a simple object glass,
which are brought, Vjy the effect of the Ions or field glass
E, into such places and dimensions aslo subtend nearly
the same angle from the eye glass F. P- 432.

Fig. 410. A represents Mr. Ilamsden's divided eye
glass micrometer, the two portions being moved at
once in contrary directions by turning the pinion B,
until the two extremities of the distance to be mear-
sured appear to coincide. P. 433.

Fig. 417. Dr. Maskelyne's micrometer, made by a
double achromatic prism A, exhibiting two images B,
C, the different parts of which are made to coincide, by
moving the prism backwards and forwards in the direc-
tion of the axis of the telescope. Mr. Ramsden thinks
that any substance thus interposed must interfere
greatly with the perfection of the telescope. P. 4S3.

786

PLATE XXIX.

Fig. 418. If A B and AC represent tlie comparative
velocity of light and of the eartli, in their respective
directions, a telescope must be placed in the direction
BC, in order to see the star D, and the star v^ill ap-
pear at E. P. 437.

Fig. 419. The spectrum produced by lookingthrough
a prism at a narrow line of light. P. 438.

Fig. 420. The appearance of a portion of the blue
light at the bottom of a candle, viewed through a
prism. P. 438.

Fig. 421. The appearance of a circular aperture,
moderately large, when viewed through a prism. P.
439.

Fig. 422. A B and C D represent the appearance of
the two ends of a broad white surface, or a window,
'when viewed through a prism. The oblique stripes of
colour show the degrees by which the lights of different
kinds enter into the compound light. It follows from
this analysis, that the colours, horizontally opposite
each other in A B and C D, would always together
make up white light. P. 439.

Fig. 423. The colours on the circle A exhibit, when
whirled swiftly round, a whitish light resembling B.
P. 440.

Fig. 424 . . 426. The colours of the circle A pro-
duce, when made to revolve rapidly, the tints shown
atB. P. 440.

Fig. 427. A triangular figure, exhibiting in theory
all possible shades of colours. The red, the green, and
the violet, are single at their respective angles, and are
gradually shaded off towards the opposite sides: a
little yellow and blue only are added in their places,
in order to supply the want of brilliancy in the colours

which ought to compose them. The centre is grey, atvd
the lights of any two colours, which are found at equal
distaiices on opposite sides of it, would always very
nearly make up together white light, as yellow and
violet, greenish blue and red, or blue and orange. P.
441.

Fig. 428. The appearance of a pin, and of the word
POKER, when viewed by looking along the surface of a
red hot poker. From Dr. WoUaston. P. 442.

Fig. 429. The appearance of an oblique line, and of
the word spin it, viewed simply through rectified spi-
rit of wine, and through a portion of the spirit mixing
by degrees with the water on which it floats. From
Dr. WoUaston. P. 442.

Fig. 430. The colours of the primary and secondary
rainbow, as they usually appear. P. 443. !

Fig. 431. The most common form of halos and
parhelia. P. 444.

Fig. 432. Magnified figures of the simplest crystals
of snow, which are sufficient to account for the produc-
tion of halos. From Nettis. P. 444.

Fig. 433. A complicated system of halos. From
Lowitz. The arcs A, B, and C, were coloured, and,
like all the other coloured parts, bad the red towards
the sun. D and E are two anthelia. P. 444.

Fig. 434. The figures of two complicated flakes of
snow. From Nettis. P. 444.

Fig. 435. The ray of light AB, falling perpendicu-
larly on the surface of the piece of calcarious spar C D
atB, is divided into the portions BE and BF: the
portion B E passing to the point E, where the surface
of the spheroid EGH, inscribed in the greater angle
of the crystal, becomes parallel to C B. P. 44d.

Plate txtx .

Tig-. 419

Fig. 420. Fig^.421.

Fig-. 418

Fig-. 428 .

Fig-. 429

Fig-. 4^0 .

FuJb.by J. Johnjon .ZonAonj. Julyx8o6 .

JosefJv Skdtort jc

\

Plate XXX

Tig 438.

Fig. 443 .

Tig-. .1,16

illll Bli

^i?-447-

I'ig'- 444-

Pig. 440 ■

Eg-. 460 .

Tub.hy J. Johnson. LonSyOrt 2 July 1.S06 .

Joseph SkeiUn sadp .

787

PLATE XXX.

Fig. 436. A section of the human eye. A is the
cornea ; B the aqueous humour, in which the uvea
hangs; C the crystalline lens; the ciliary processes
being between it and the uvea; D the vitreous hu-
mour ; E F G is the choroid coat, lined by the retina;
li I K the sclerotica, and L the optic nerve. P, 447.

Fig. 43r. A picture painted on the retina in an
inverted position, seen by dissecting off tlie sclerotica
and choroid behind it. P. 448.

Fig. 438. The apparent figure of the heavens being
nearly like the curve ABC, the sun or moon at A
or C appears to be much larger than at B. P. 454.

Fig. 439. The red square A, inclosing a green square,
produces, if viewed attentively, in a strong light, a
spectrum resembUng B, which is red within and green
without, and which appears when we look soon after
cn any white object. P. 456.

Fig. 440. Tlie spot, wliich is tinted with blact lines
only, appears, upon the yellow grouud, of a purple
hue. P. 456.

Fig. 441. A grey spot on a purple ground appears
of a greenish yellow or olive hue. V. 456.

Fig. 442. The manner in which two portions of
coloured liglit, admitted through two small apertures,
produce light and dark stripes or friivges by their in-
terference, proceeding in the form of hyperbolas; the
middle ones are however usually a little dilated, as at
A. P. 465.

Fig. 443. A series of stripes of all colours, of their
appropriate breadths, placed side by side in the man-
ner in which they would be separated by refraction,
and combj^ncd together so as to form the fringes of
xolourB bcluw them, beginning from white. P. 465.

Fig 444. A series «fcoronae, seen round the sun sr
moon. P 466.

Fig. 445. The internal hyperbolic fringes of a rect-
angular shadow. P. 467.

Fig. 446. The external fringes seen on each side
of the shadow of a hair or wire, which is also divided
by its internal fringes. The dotted lines show the
natural magnitude of the shadow, independently of
diffraction. P. 468.

Fig. 447. Analysis of the colours of thin plates seen
by reflection, beginning from black. A line drawn
across the curved fringes would show the portions into
which the light of any part is divided when viewed
through a prism. P. 469.

Fig. 448. The coloured stripes of a film of soapy
water, covering a wine glass. P. 469.

Fig. 449. The colours of a thin plate of air or water,
contained between a convex and a plane glass, as seen
by reflection. P. 469.

Fig. 450. The colours of a mixed plate; as seen by
partially greasing a lens a little convex, and a flat glass,
and holding them together between the eye and the
edge of a dark object. One half of the series begins
from white, the other from black, and each colouris the
contrast to that of the opposite half of the ring. P. 470.

Fig. 451. The composition of the colours of the
primary rainbow, when attended by supernumerary
bows. P. 471.

Fig. 452. The colours of concave mirrors. The
small circles in the middle white ring represent the
aperture by which the light is adrnitted, and its image ;
the coloured rings are formed by the light irregularly
dissipated, before and after reflection. P. 471.

788

PLATE XXXI.

Fig. 453, 454. The appearance of the star Lyra,
viewed with telescopes magnifying 460 and «J450
times respectively. From Dr. Herschel. P. 491.

Fig. 455. The appearance of the nebula in Orion,
abont lialf a degree in length. From Messier. P. 492.

Fig. 456 . . 463. The appearances of different nebu-
lae. From Dr. Ilerschcl. P. 492.

Fig. 464. A section of the nebula to which the sun
is supposed to belong, its projection forming the milky
way ; taken in a plane perpendicular to its longest dia-
meter. From Dr. Herschel. The large stai in the
middle represents the sun, and the circle drawn round
itis at forty times the distance of the nearest fixed stars,
comprehending probably all the stars which are visible
to the naked eye. P. 493.

Fig. 465. A large spot, traced through different
forms in its path across the sun. From Dr. Wilson.
A is its place 23 Nov. 1769; B, 24 Nov. C, 11 Dec.
D, 12 Dec. and E, U Dec. P. 501.

Fig. 466. A, a large spot on the snn; B, the ar-
rangement of the luminous and opatjue strata of clouds
by which Dr. Herschel explains the appearance of the
spot. P. 501.

Fig. 467. A, a spot with a lighter portion in the
middle; B, the arrangement of the strata correspond-
ing to it. P. 501.

Fig, 468. The position assumed by the strata which
had formed the spot shown in the last figure, viewed
about an hour afterwards. P. 501.

Fig. 469. A and B are the forms of a solar spot,
at about two hours distance of time; C, D, and E,
are the successive forms of another spot. P. 501.

Fig. 470. The appearance of the zodiacal light, or
solar atmosphere, as it is seen in these climates, in the
evening, about the beginning of March ; A B being the
horizon, and C the supposed place of the sou. P.
SOS.

Plate jxkl.

Sg.453

Tig. 464.

Tig . 45 5 .

Kg. 466 .

Tab. by J. Johnson .J.ondon 1 July 1806.

Soscph Skehorh sa

'^\t. 0Jflu . ' tt^

/

Plate xxxn.

OJTie suTt. '^Miercvry ^ Venus.

© ITie ear0v. <S 2iars.

^ Jiaio . <^JPk3aj .

O Ceres. % Jupiter.

%j Satzcm .

O Geor^iaih
planet.

Fig. 475

£uh.lfy J.Johju<m,,X(mdorv d. JiJyx8o6 .

Joseph. Skeitmt scuT^

789

PLATE XXXir.

rig. 471. A representing the sun, B tlie eartli, and
C the planet Mars; supposing Mai's and the earth lo
net out to;;et!ier from D and E, the angle D A C was
letermined by Kepler from calculation, and the angles
BAD and ABC hy observation ; whence it was easy
to construct the triangle ABC, and to find the pro-
portion of A B to A C. P. .505.

Fig. 472. The solar system, representing the form
and proportions of the orbits of all the primary planets,
and of three of the comets. The parts of the orbits
represented by entire lines are on the north of the
ecliptic, the dotted parts on the south : the letters A
nnd P denote the aphelion and perihelion. The point
in the centre, which ought to be only 7J5 of an inch in
diameter, represents the sun. The figures of the re-
«pective planets show their comparative magnitude,
that of the sun being represented by the innermost of
the graduated circles which inclose the whole : they

are placed according to their actual situations on the
14th June, 1806. The letters M D show the mean
distance of the comet of 1759, being placed at the ex-
tremity of the lesser axis of the ellipsis in which it
must be supposed to revoWe. P. 514.

Fig. 473. The periodical times of the different pla-
nets, represented by lines of different lengths. P.
514.

Fig. 474. The comparative velocities of the dif-
ferent planets, represented by lines which show the
number of English miles described in a second, on tht
scale marked on the lowest line. P. 514.

Fig. 475. The places of the ascending nodes of all
the planets, marked on one half of the ecliptic, sup-
posed to be extended in a straight line ; together with
the inclinations of their orbits. The line marked
F. F. £. £, shows the situatioQ of the fixed ecliptic. P.
514.

VOL. I.

5 F

790

PLATE XXXIII.

Fig. 476. A. The appearance of Venus, from
Dr. Herschel: B,C, from Mr. Schroeter. P 514.

Fig. 47r. A . . D, the appearance of Mars, from
Dr. Herschel. The figures are inverted, as they
appear in the astronpmical telescope. P. 514.

Fig. 478. A,B. The appearance of Jupiter, witli
his belts, from Dr. Herscliel. P. 514.

Fig. 479. The appearance of Saturn, with his ring,
from Dr. Herschel. P. 514.

Fig. 480. The appearance of tlie moon, in an in-
verted position. The figure is copied from Mr.
Nicholson's plate, the references from Cassini and
Lalandc. Eq. is the place of the moon's equator. P.
514.

Names of the spots, according to
Riccioli, and Hevelius.

. 1 Grimaldus or
3 Galileus

3 Aristarchus

4 Keplerus

5 Gassendus

6 Schikardus

7 Harpalus

8 Hera elides
(J>) Vulcanus

9 Lansbergius

10 Reinoldus

11 Copernicus

12 Helicon

13 Capuanui

14 Buliialdus

15 Eratosthenes

16 Timocharis
IT Plato

18 Archimedes
(«) Aratus

19 Insula sinus medii
SO Pitatus

31 Tycho

Palus Mareotis
Mens Audus
Mons Porphyrites
Loca paludosa
Mons Cataractcs
Mons Troicus
Insula sinus hyperborej,
Caput mulieris

Insula Malta
Mons Ncptunus
Mons Aetna
Insula erroris
Itegio Cassiotis
Insula Cueta
Insula Vulcania
Insula Corsica
Locus niger major

Mare mortuum
Mont Sinai

Mons Carpathes
Mons .Serrorura
Insula Berbicus
Byzantium
Mons Bodinus

Promontorium Acherusia
Mons Moschi
Lacus Thospitis
Promontorium acutum

Promontorium Somnii
Mons Corax
Montes Riphaei
Mons Paropamisus
Petra Sogiliana
Insula major
Sinus Phasianus

22 Eudoxus

23 Aristoteles

24 Manilius

25 Menelaus

26 Hermes

27 Dionysius
(rf) Albatcgnius

29 Plinius

30 S. Thcophilu*

31 Fracastorius

32 Ccnsorinus

33 Mesisala
34

35 Proclus

36 Cleomedes

37 Snellius
83 Petavius

39 Langrenus

40 Taruntius
A Marc Humorum
B Mare Nubiura
C Mare Imbrium
D Mare Nectaris

£ MareTranquilitatis

F Mare Serenitatis

G Marc Foecunditatis

11 Mare Crisium »

Fig. 481 . . 483. The satellites of Jupiter, Saturn,
and the Geori;ian planet, at their proper distances, i"
proportion to the diameters of the planets, shown on
tiie same scale. P. 514.

Fig. 484. The figure of tlie tail of the comet of 1680,
represented in the plane of its orbit, from Newton.
A B is the earth's orbil, C and D arc the first and last
appearances of the tail, and E F is the line of tlie
nodes. P. 514, ■

Fig. 485. A, B, Two successive appearances of the
comet of 1723, from Lord Paisley. P. 314.

Plate XXXUL.

Fig-. 476.

Hg-.48i

Tuh.hy J.Jahruitn. .London 1 July 1806.

Joseph Skelion jctdp.

PLATE XXXIV .

Rg . 486 .

Fig;. 488

Figr- 499

Hth. by J. Johnson .London j July iSot*.

Joseph JX-cM'// sai{

791

PLATE XXXIV.

Fig. 486. Tlic gravitating body ABC, being sup-
posed to revolve on the axis A C, the fluid column
B D must be longer than ED, in order to support its
pressure. P. 510.

Fig. 487. If A represent the place of the sun, B
that of the earth, and C that of the moon, taking A 1)
to A C as tlie square of A C is to the square of A B,
AD will represent the sunV attraction acting on the
earth, and CD the disturbing force, wliich, together
with AD, makes up AC, the force actin;; on the
moon ; and it is obvious that, when the nodes are in
any oblique situation, as E F, the force being directed
to some point D, bclwcen B and A, while t!ie moon
moves from G to H, the force CD will tend to lesson
the inclination, while the moon is ascending from E
towards C, and to cause the node E to move back to-
wards G, and, when it is again de-cending towards
F, the inclination will he increased, and the node F
made to recede towards 11, until the nioon arrives at
II, and the force becomes directed to a point on the
other side of B; the nodes only advancing while the
moon is between II and F, or between G and E. P.
520.

Fip:. 488. A body attracted towards the centre A,
and descending from B in the ellipsis BCD, has the
inclination of its orbit to tlie revolving radius A B, A C,
AD, perpetually changed, until at D it becomes per-
pendicular to it ; but when the force increases more
rapidly, the radius does not become perpendicular to
the orbit till it arrives at E, and the line of the apsides
AD moves forwards to E. P. 521.

Fig. 489. A represents the position of the limit of
light and darkness on the earth's surface at the vernal
equinox, B at the summer solstice, and C at the win-
ter solstice: EQ denotes the equator, N the north
pole, and S the south. P. 525.

Fig. 400. NESW being the horizon, and Z the
7cnith, F' A W shows the sun's apparent path in Lon-
don at the time of the equinoxes, BCD at midsummer,
and F G II at midwinter, projected orthographically,
as if the circles were described on the surface of a
globe, and viewed from a great distance. The circle
I K L is the boundary of twilight, supposing it 18° be-
low the horizon, and its intersections with the sun's
path show the beginning and end of twihght, af at I
andK. P. 627.

Fig. 491. The rays of light, coming in the direction
AB, arc bent V)y the atmosphere so as to arrive at C^
and to illuminate a part of the atmosphere there,
which is visible, by mean.s of a second retraction, to a
upectator at D, and occasions the first and last twi-
gbt. • P. 527.

Fig. 492. Venus is at her greatest elongation or
angular distance from the sun A, when situated as at
B, with respei t to the earth at C ; and she is stationary
at D, when she is moving with the same velocity as the
earth, with respect to the dhection of the earth's mo-
tion, the line E D being then more oblique, with respect
to a fixed line, than either before or after. P. 627.

J'ig. 493. A BCD is the apparent path of Venusfor
the year 1806, supposing the sun E to revolve round
the earth F. "rhe place of the sun and planet is mark- '
cd for every four weeks. P. 527.

Fig. 494. The apparent path of Saturn in the hea-
vens for the year 1806, referred to its proper place
with respect to tbe eclijitic. The figures denote the
places at the beginning of eacii month. P. 527.

Fig. 495. I he small figures represent the phases of
the moon in different parts of her orbit. The smaller
detached fii'inf s show the appearance of the moon, as
seen from the earth ; the larger ones, those of the earth
at the same times, as seen from the moon, which are
always the reverse of the moon's appearance. At A
the moon is new; B is the first quarter, C the full
moon, and D the last quarter. A and C are some-
times called the syzygies, and B and D the quadra-
tures. P. 528.

Fig. 496. A, the moon passing through the earth's
sliadow ; which is distinguished into three parts, the
perfect shadow, the true shadow, and the penumbra.
At B and C the moon is shown passing through the
section of the shadow, P. 529.

F'ig. 497. The path of the moon's shadow passing
over the earth, in the solar eclipse of 1764, the earth
being supposed at the same time to revolve on its
axis. The line A B is the part in which ihe eclipse ap-
peared annular, CD being the breadth of the whole
shadow or penumbra. P. 529.

Fig. 498. The shadow of the moon falling on the
earth. The true shadow not extending here ta the
earth, the cone formed by tUe continuation of its out-
lines marks the extent of the parts in which the eclipse
appears annular. P. 529.

Fig. 499. The termination of the moon's disc in a
solar eclipse. From Dr. Ilerschel. P. .')29.

Fig. 500. The apparent mag^iiludes of the planets,
that of the sun or moon being supposed equal to a
circle a foot in diameter; whtrr there are two figures,
one of them shows the mean apparent niagnilude, and'
the other the greatest. P. 531.

F'ig. 501. "Vhe apparent n ngnitude of tlie sun, as
seen from the different planets ; for Mercury, the mag-
nitude is shown by that of the tarth in fig. ')07. P.
535.

792

PLATE XXXV.

Fig. 50'.!. AB btin s; the eRrth'3 axis, ll>c circle
A I'lj is tlie moridian o I tlu- pWe C,.aiid C E repre-
siiitii the [ilanc of its hori/oii. P. 537.

rig. 60:5. Tlie (tVtet ol tlu- obliqiiity of the ecliptic
ii.i llie equation of time i.s lovvii by tlie tlitTeniicc of
tilt unalch ABC and D BE, ^ubiended at tiie. jiole B
bj equal portions of the oblique circle A 1'.. P. 5;5i>.
riif. .504. A Hbciiiii paiaUfl to llie earlii's axis, the
12 pUiues passiiijitbrnugli it, at cqir.il angular distances,
mark, on the circle CD perpendicular to it, the liour .
lines of an equatoiiai dial, and on the liorizoiitid .sur-
face P. V those of a tiori/outal dial. P. o38.

Pig. 605. A method of coiistnictiug a dial on any
given plane. .'V li C is the eleviaion of the pole, or
more generally, the angle which the surface makes
with tlie i^nomon A B. J'he circles are divided into
equal parts, and 1,2,0,1,6,0 are the hour lines, B
tieiiig the place of the t;uonion. The reason of this
construction will appear by comparing the circle 111
the last figure with the ellipsis which is formed on the
horizontal surface. P. ^iliii.

Pig. 50(). A dial for a pointed gnomon, or obcliic,
drawn on a liorizontal surface. P. 538.

Fig. 507. A mural quadrant, with its telescope;
A P> is the plumb line, for adjusting the instrument,
and C the counterpoise for the telescope. P. 542.

I'ig. 503. A portable transit instrument. A and B
are screws for adjusting the axis by a vertical and a
horizontal motion ; C D is a spirit level, w hich may
occasionally he hung on the telescope by the pins E
and F. G is a small graduated arch, to be viewed
through the microscope H, for taking elevations of a
few degrees. P. 542.

Fig. 509. A transit circle, resembling Mr. Wollas-
ton's, with a horizontal circle, by means of which
both altitudes and azimuths may be measured. A is
a. microscope for viewing the plumb line, B anotlier
for reading ojT the divisions of tl>e horizonlid circle;
C and D are spirit levels. P. 642.

Fig. 510. A zenith sector, with its telescope, which
has usually a reflecting prism, like that of the Nev^-
tonian telescope, for its eyeglass. P. 542.

Pig. 511. The marine octant, introduced by lladley.
The mode of taking tlie common or front observation,
is shown by the lines drawn to the sun and moon : the
fcack observation by the two stars. A is a dark glass

to be used in observations of the sun, and.wluch may
be fixed at B, when required. P. 5 12.

Fig. 512. A B being the situation of the earth's ax-
is, if the angle C B U, or the altitude of the body D, be
measured, and wt subtract from it tlie elevation of the
equinoctial CHE, the remainder will be the decliua-
tion EBl). I'.aU, 543.

Fig. 513. The aiigle ABC is the moon's horizon-
tal parallax, and DBC the parallax when she is ele-
vated above the horizon D E in the angle BDE. P»
61,").

Fi:;. 514. The situation of the earth at the transit of
Venus in June 17d9. A spectator at the North Cape
was carried during the trimsit from A to B,and the tran-
sit apjieared to liim to last while Venus moved from
C to 1) : tlie island of Otaheite, on the contrary,
wliidi is situated on the lower part of the illuminated
hemisphere, was carried from E to F, and the duration
of the transit was there only while Venus moved from
G to il. Hence tiie rotatory motion of the earth was
compared with the excess of the motion of Venus in
its orbit above that of the earth. P. 514..

I'ig. 515. A planisphere ncaijly resembling tliat of
Professor Bode. The outer circle i.s fixed to the chart,
and is divided either according to tiie degrees of the
ecliptic, or the dajs of the month; the graduated cir-
cle immediately within it is divided into 2 li hours, and
is fixed to a circle of pasteboard, out of which the
circle NF^SW, representing the horizon, is cut, the
place being filled by thin varnished paper, with circles
of azimuth and altitude engraved on it, which is car-
ried round with the hour circle. P. "jtiT.

Fig. 516. A diagram showing the length of the day,
and the time of the sun's rising and setting in any part
of the globe, within a few minutes; the time of the
yoar being found in the graduated circle representing
portions of the ecliptic, and tlie latitude, on tjip mid-
dle line, by following the concentric circles of decli-
nation till they meet tiie horizon passing through the
given latitude, the line drawn from the pole ttiniugh
this point will cut the equator in the point showing
the length of the day or night. Thus, on the first of
March, in latitude 50" north, the length of the day
appears to be nearly 10 liours andJ, whence tiie sun
must rise about 37 minutes after six ; but in latitude
So'the sun never se ts on that day. P. 567. ,^ |

PLATES XXXVr, XXXVIL

Plate XXXVI. Fig. 517. Projection of the con-
stellations of the nortliern hemisphere ou the plane of
'fie equator. P. 498, 567.

Plate XXXVn. Fi^-. 518. Projection of the south
ern hemisphere. P. 498, 567.

Plate xxxv.

Pig' . 5o 2 .

A

^_\

■■

Fig;. 5o3.

Pig-. 504.

Tig'. 5o5 .

Pig-. Sog

Pub. by J. JoJuLSon, Londarv 2 July tdo6.

Joseph Skelt*}n, sculp-

Plate 5XXVi.T"ig. 5i'].

The place tt'dt^ hori-
zon at jmdni^ht shows
also its piacc at six lire
the cre/ii/iif ^e. foOuwaifl
quarter.

^Fuh.hv J.Jphnson.Lendtm tJulv^So^. ^

Joseph Skriton sculp.

Plate IIIVn.Fig.5i8.

-ft/^. ^v ./; Johnson .Zcndon x July ido!?.

Jasfffh S?arZtzm. scttlp.

PT.ATRTXXVm.

Bo- . Sag .

^ISfiles

oooTeet

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oooToisesI

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a6

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GftOp<LXi

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'Tic A Ossmw

n. .Tike of Xmeriffe
SEtna.

,-Buet
. JMonte Viso
JioTW CerUs
: z: GoTuiar ^byss-

, JMJmt d, or
'a 000; >

- -^^^^ Cenis,post house

^ JdffuiTt Jvra,
_ .1 Tuy de Dome
5- -^Tic MuifoJiiad/

,VUi>Ti. .

- ~Jrtgleborou^n,

Vtyui'itLT
^ ^Snowdorv
z-zs:-Sh<JuiUion

- ^v-j^U nwtmt
' \*' Ouujwiuiy i/tn

Skiddmv

, Bert Lomorid,

Saddleback

\Aosta>

JjoIcc of Geneviv

.^T'thurs scat
'Oiankhury rb^ Suss
vS^Teters irvrwi/ic t/rvu/ul/

SetL

jjau-piart SetL

IlllPirilnillH FTm\ .^^nr\ ifmifk -^fmrn l^ _Jiil!lli™Mnm.nn.r-,„„

Fig'. 522

■^

Fig'. 62a.

B D

Tiib.by J. Jofuison ..London jJuJ^ 1806 .

Joseph Skeltmi sad p.

793

PLATE. XXXVIII.

Fig. 510. A scale of tlic heiglit of different parts of
the earth's surface above tlie level of the sea, in
English feet and miles, and in French toises. P. .574.

Fig. ."iSO. A. Tiie dotted ellipsis shows the section
of a spheroid, which would be the form of the earth
and sea if it wcro always in a state of equilihriuni with
the attraction of a distant body, and the shaded ellip-
sis the actual form assumed in consequence of its ro-
tation round its centre, the depth of tlie sea being less
than l.*; miles. B. The surface of the sphere being
supposed to be flattened, and the tides spread on it,
they wo\rld assume the form of the waves here shown.
The dotted straight line shows the mean height,
which is a little above the surface in the principal
sections of the spheroid, although not universally. C.
The nature of the tides of lakes, the surface beiijg re-
gulated by that of the dotted line at B, nearly agree-
ing with it in direction, as at D, when the lake is nar-
row and deep, but differing from it, as at E, when sha.-
lower. P. 579.

Fig. 521. The progress of the tides from the At-
lantic through the channels surrounding the British
islands, the lunar tides happening in any part of the
shaded lines nearly at the hour, after the moon's south-
ing, which is indicated by the figure annexed to it.
P. 582.

Fig. 522. The lines AB and,BC, repreeentingithe
heights of the lunar and solar tides, find the angle
ABC twice their angular distance, or A DC being
simply the angular distance, the line A ;C shows, the

height of the compsand tide, and the angles B A C and
A C B its distance from the lunar and solar tides re-
spectively. P. 585.

F'ig. 523. Tlie two unequal tides represented by the
elevation of the ellipsis above the smaller circle may
be considered as composed of two equal tides cut off
by the dotted circle, and the single tide between the
two circles; as the tides B and C make the unequal
rides at D, P. 587.

Fig. 521. The first and second curves represeni
two equal semidiurnal and one diurnal tide, whicL
would make together two unequal tides : the third and
fourth the same tides six hours more advanced : and
when these are combined, the first and third destroy
each other, hut the second and fourth together com-
pose the fifth, or a large diurnal tide. P. 587.

Fig. 525. A tlie ancient system of the world,
adopted by Ptolemy. B th^ arrangement supposed
Lv some other astronomers. P. 590.

Fig. 526. The Egyptian system of the world. P.
590.

Fig. 527. The system of the Pythagoreans, and of
Copernicus. P; 592.

Fig. 528. The mode of representing the inequalities
of the celestial motions employed by Ptolemy, the
small circle being carried round the circumference of
the larger, while the lumiuary revolves in it, so as to
diescribe the dotted curve. P. 595.

Fig. 529. The Tychonic system of the world. P.
597. ■

794

PLATE XXXIX.

fii;. 530. '(lie repulsive force of two piirtides of
maiif !■, situated at tlie distance A H or AC, is rtpre-
sriiled liy the oidiirates or perpeiidicularfa B I), C E,
i)i:uvn to tile curve T) K, supposiiic; tlie force to be
inversely as the distance; but the law of the force
appears to be uiure nearly represented by a curve like
1' K. The line I) I" G shows the maguitudc of the
cohesive force, which (ivercomc? the repiiUioii at the
distance A G, and is balanced by it when the particles
arrive at the distance A U or A 11. The dotted lines
represent the nature of the changes made in the lines
V v., I) F (i, and FH, by aii elevation of temperature.
P. 619.

Fig. 531. The general direction of the cohesive force
acting on a particle of a liquid at A being represent-
ed by A B or AC, that of the repulsive force will
be 1) A or E A, and in order to maintain the equili-
brium, the forces B F and C G, making together H A,
must bo supplied by the pressure or reaction of the
internal parts. P. 620.

Fig. 532. A. The trarsverse section of a drop, sup-
posed to lie of considerable length, and flatatthe sides:
the curvature of the outline being every where propor-
tional to its distance from the horizontal line A B.
B, a round drop, the concavity at the horizontal line
being equal to the convexity which would be found
by cutting oft' the drop horizontally; the sum or differ-
ence of the curvatures being every where proportional
to the distance from this line. P. 621.

Fig. 533. The solid AB possessing }ialf the attrac-
tive power of the liquid CD, the surface of the liquid
will remain horizontal : for the attractions will be re
presented by D A, DE, and D C ; and of these D A
and D E make D B, and D B and D C make D F, which
IS in a vertical direction. If the solid be more attract-
ive, the forces will be combined nearly as at G, and
if less attractive, as at H. P. 622.

Fig. 534. The form of the surface of a liquid in
contactwith a pl.ane and vertical side of a solid which is
wetted by it. The height of the ascent of water is about
one fourth of that which is here represented. P. 622.
Fig. 535. The form of the surface of a liquid clerat-
ed between two plates which meet at A, and are at a
little distance from each other at B ; about one third
of an inch, supposing the liquid to be water. P. 623.
Fig. 536. The height at which water will stand in
tubes of the form and magnitude which arc here re-
presented. P. 623.

Fig. 537. The depression of niorcury, in contact
witli a large or Hat glass vessel, is one fourth as great
as that which is here represented. P. 623.

F'ig. 533. The depresKion of mercury within a small
tube of glass. P. CV3.

Fig. 530. The actual elevation of a portion of water
In contact with a horizontal surface which is wetted
by it. P. 624.

Fig. 540. The elevation of mercury in contact with
a horizontal surface of glass. P. 624.

Fig. 541. A, a wide drop of water standing on a dry
surface, not attracting it. B, a wide drop of mercury,
staiidhig on glass. P. 624.

Fig. 512. A magnified representation of the man-
ner in which the seeds of lycopodium prevent a drop
of water from wetting the substance od which it stands.
P. 624. ;

Fig. 543. The bodies A and B, and the bodies C
Snd D, appear to attract, and E and F to repel each
other. P. 625.

Fig. 544. The apparent cohesion of two plates, be-
tween which a fluid is interposed. P. 625.

Fig. 545. The apparent attraction of adrop between
two plates, tending to draw it towards the line of their
junction, causes the drop to rest in an inclined posi-
tion of the plates. P. 625.

Fig. 546. Dr. Ilerschel's figure, representing by tlie
distance of the curve ABC from the line .\ C the heat
thrown on different parts of A C by a |irism, while DC
ii the illuminated part, divided according to Newton's
experiments, tbr quantity of light being expressed by
the distance of the line D E C. P. 639.

Fig. 547. Dr. Ilerschel's figure of the distribution
of heat and light corrected ac«ording to the division
of the coloured spectrum, as ascertained by Dr. Wol-
laston. P. 639.

Fig. 548. Bernoulli's air thermometer. P. C50.
Fig. 549. A differential air thermometer, or tliermo-
scope, from which the pressure of the atmosphere is
excluded. From Kunze. P. 650.

Fig. 550. A differential thermometer on Mr.,Leslie's
construction. P. 650.

Fig. 551.The distribution of the electric fluid in spheres
of different sizes, and at different distances, and in a
conical point. The density is represented by the dis-
tance of^the dotted line from the surface. P. 603.

PLATE XXXIX

ng.s3i.

Fig.,53c

Fig.^Si.

R G B V D

Jos'. S/ceUon scu/p

Tub. by J. Johnson, LonJori . Julyj^/to6.

PLATE XL.

Vig. 56! .

Tig-. 553

Tig-. 564.

P<itlis?ud h^ J . Jrthrucn. J.iindcn.1 JiJv tfof

Joseph Skeitvn sculp.

795

PLATE XL.

Fig. 552. A. A spark passiiij; between a negti'ive
Slid a neutral h-M ; B, 'ictween a neutral and a positive
ball; C, beHveen a negative and a pobitive ball. D,
two spark* between a negative and a positive cy-
linder, each of tlie same form as if it were passing
sini:!^ frn:ii the end of ji charged to the side of a neu-
tral cylinder. From Mr. Nicholson. 1'. 671.

Fig. 553. A com|)Ound galvanic circuit, formed by
portionsof an acid, pieces of zinc, and wires of silver;
the arrows show the directions of the electric current.
P. 676.

Fit'. 55*. A compound galvanic circuit, formed by
•n acid, charcoal and watci , the water and the acid
coniaiuiiicatini!; by a small siphon. P. 676.

Fig. 555. A compoinid galvanic circuit, formed by
portioiis of an alkaline sulfurct, and water, and
{)ieces of c )pper: the liquids being connected by a
siphon, p. 676.

Fig. 556. A simple galvanic circuit, formed by wires
of zinc aijd sjU er, or platina, the lovwer ends being im-
mersed in an aci:i, and tlie upper being brought into
contact at pH asure. P. 676.

Fij. 557 A galvanic battery, in the form of a
trough, composed of plates of zinc, silvered on one
side, with vax;ant •ipaces f >r rhe reception of an acid :
the letters show the order of the elements, and the
arrows the dirt clion of the current, from Che positive
wire + to the negative wire — . P. 677.

Fig. 558. An electrical machine, on Xairnc's con-
struction. A, the cylinder of glass; B, the cushion,
or'rubber; C, the silk flap; D, the negative conduc-
tor; E, the i)ositive conductor; F, a ball connected
with the internal coating of a glass jar, contained in
the conductor. The conductors are insulated by var-
nished rods of glass. P. OiiO.

Fig. 559. A plate machine. A and B, the rubbers,
which .ire usually doubU; ; C I), double flaps of oiled
silk, for confining the electricity ; K, the conductor. P.
680.

Fig. 560. An rlcctrophorus. A, the cake of resin;
B, the plate of metal ; C, the ball for taking the spark :
D, the ha idle of glass. P. 681.

Fig. 561. A condenser, as arranged by Mr. Cavallo,
under the name of a collector : the middle plate is in-
sulated : the two outward platcp communicate with
the earth ; they stand near the first plate when the
electricity is imparted to it, and are afterwards re-
moved by means of their hinges. P. 681.

F^ 562. Mr. Cavallo's multiplier. The electri-

city being first communicated to the insulated piate A,
the moveable pLate B is brought near it, while the wire
C touches the pin D so as to form a communicatioo
with the earth; the plate B is then made to commu-
nicate with E, which is insulated, and stands near the
plate F, which enables it to receive ahnosr the whole
of the electricity brought at eacii alternation by B ;
and when the plate Fis removed from tlie neighbour-
hood of E, this plate becomes strongly charged. P.
682.

Fig. 563. A revolving deubler, on the principle of
Mr. Bcnnet's instrument. The fixed and insulated
plate A first receives the electricity, and "hen the
moveable piate B stands opposite to it, it receives by
a wire from the stand of the instrument C the opposite
electricity; wlien it is brought oppisitc to D, this
plate is made to communicate witii the stand by the
wire E, and acquires a charge similar and nearly equal
to^that of A. M'hen B comes again to A, the wire F
forming a communication between A, and D, nearly
the wliole charge of both these plates is brought into

A, and B receives a charge almost twice as great as at
first. P. 682.

Fig. 564. Mr. Coulomb's electrical balance. The
needle A is made of silk, covered with sealing wax; it,
supports, at the end B, a ball of the pith of elder'
another similar ball being fixed at C; the force of at-
traction or repulsion is. ascertained by the torsion of
the wire AD, which is measured by a graduated
circle E. P. 683.

Fig. 565. Mr. Henley's quadrant electrometer; it is
made of box wood, sui^i^orted by mttal; tlie ball is of
cork, the graduated arc of iviiry. P. 683.

Fig 566. A, Mr. Beniiet's gold leaf electrometer;

B, a piece of excited scaling wax held over it, for dis-
tinguishing the electricity. Instead of the pieces of
fiold leaf C,, we may substitute Mr. CavalloVpith balls
D, or the straws E, employed by Volta, r. 683. i ,:

Fig. 5fi7. ■ Mr. Lane's discharging electrometer."
The djstaiice ofthe fcalls A,JJ is trtt'asUrid by'thetufn^
of the screw on the scale C ; and the parts of a turn
are ascertainud by the graduated circle D. P. 683.

Fig. 568. A discharger for a battery. When the
repulsion of the balls A, B, becomes greater th.an the
weight (if a wire which passes through a perforation in
the ball-', tliey separate, and the ball C, descending
to D, forms a communication, ^vbich completes the
circn t, so that the shock passes tbrough any luhitancc
1 Uc€d at £, P. 083.

796

PLATE XLI.

fig. 569. The form of the curves which show the
jiirection of the magnetic needle, in cotisequence of
the attraction and repulsion of two poles, situated at
A and B. They are found by drawing the lines A C D,
BED, so that the sura or difterence of the parts AC'
BE, shall be always equal, ACEB being a semi-
circle : and the direction D F may be found by making
AF to BF as the cube of AD to that of DD. P.
688.

Fig. 570. The arrangement of iron filiogs in the
neighbourhood of a magnet. P. 688.

Fig. 571. The particle of iron A B, lying on a card
nearly over the magnet C, assumes, when the card in
shaken, first the position D, then, falling to E and E,
is left a little further from the magnet than at first.
P. 689.

Fig. 572. An azimuth compass. The box is turned
round, until the shadow of the thread A B or AC falls
on the . line C D : the position of the needle is then
ascertained by that of the card E, which is fixed on it.
The compass is kept always in a horizontal position,
by means of a double suspension On the gimbals E G.
Instead of this suspension, Mr. M'Cullbch makes the
bottom of the box in the form of a hollow cone, rest-
ing on a point, and loaded with a weight, which brings

the centre of gravity below the point of support, as at
H. P. 689.

Fig 573. A dipping needle. The piece A B is
brought into such a situation, that the line drawn on
it coincides with the middle of the vibrations of the
needle. The position of the needle may be chajiged,
either by turning the stand half round, or by turning the
needle within the stand. P. 689.

Fig. 574 . . 576. The situations of the lines of equal
declination in 1700, 1744, and 1794, in the hemi-
sphere, which is bisected by the meridian of London.
The first two from Mouiitaine's Tables, the last from
Churchman's Chart. P. 691.

Fig. 577. The actual situations of the lines of equal
dip. From Churchman's Chart. P. 69?.

Fig. 578. The lines of equal dip, calculated from
the supposition of a small magnet, situated at the
centre of the eartli, directed to a point in latitude
75° N. and longitude 70° W. P. 699.

Fig. 579. A, Six's thermometer; B, the wire with a
fine spring, which serves as an index. P. 697.

Fig. 580. Rutherford's double thermometer. P. 697.

Fig. 581. Deluc's whalebone hygrometer. A, the
slip of whalebone; B, a spiral spring, serving to kee{) it
stretched; C, the index. P. 710.

PLATES XLII, XLIIL

Fig. 582. A chart of the world, on Mercator's pro- year 1794; and with the trade winds and monsoons, P,
jection, from Arrowsmith ; with the dip and variation £71,691.
•f the coxapass, priacipally from Cburchman, for the

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principally irom Clnirtliimm_;for tlie year i*] 94.;
and Tvitli the Trade Winds and Monaoons.

/ Constaat "Winds . / S-ummjer and Autnnm.

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