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Received by bequest from
Albert H. Lybyer
Professor of History
University of Illinois
1916-1949
55
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Eighth Edition, with 26 pages of new matter, 7. Plates,
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NATURAL PHILOSOPHY
FOR GENERAL READERS AND YOUNG PERSONS.
A Course of Physics divested of Mathematical Formule,
expressed in the language of daily life.
Translated and Edited from GANov’s Cours Elémentatre de
Physique, by E. ATKINSON, Ph. D., F.C.S.
DOI FPP
LONGMANS, GREEN, & CO., 39 Paternoster Row, London
and Bombay.
TAIB IIE OF SIPIEGIIRA o
ti Ai
g
3
a
o
<<
eC]
a
E
wy
aoe 6
=e
g
oy
Z|
Peer vie DOs Rae lone AD Si E
ON
Pr YOLes
Teese ieee ViGEt IN ASEAN, DD) eA PP ee DD
HOKMMEMESOSE OH SCOLLEGES AND (SGHOOLS
TRANSLATED AND EDITED FROM
GANOT’SsELEMENTS DE PHYSIQUE
(with the Authors sanction)
BY
Dee CNS ON an EH). L OlS:
LATE PROFESSOR OF EXPERIMENTAL SCIENCE IN THE STAFF COLLEGE
FIFTEENTH EDITION, REVISED AND ENLARGED
ILLUSTRATED by 95 COLOURED PLATES and MAPS and 1037 WOODCUTS
We NG NLAIN Sai G RvE EON’) AN Da, CO:
sou PALE RNOS DORR O Ws) WON DON
AND BOMBAY
1898
All rights reserved
j ah | nl
t : % a) “a> be ad AG Pi ¥ 7Ae: ae We ty M ceerted i a a he
SSO
G Rona
1S9R
ADVERTISEMENT
iG)
brig wnt lel ds abe MIRE ab Di nlc LLOLN
THE additions made in the present edition have increased by twenty-
one pages the size of the work as it stood in the last edition, and by
thirty-six the number of illustrations, notwithstanding the omission
of matter which had become of minor importance ; and careful re-
vision throughout, has, it is hoped, improved the book beyond the
extent represented by a mere statement of the number of added pages
and cuts.
In issuing this new edition I have to express my acknowledgments
to Professor Reinold of the Royal Naval College, who made an inde-
pendent revision of the whole book. This has led to many valuable
corrections and additions, of which I have been glad to avail myself. I
- also have to thank Professor Foster of University College for several
valuable suggestions and additions.
The continued favour with which the work has been received,
as a Text-bock for Colleges and Schools, and also as a book of
reference for the general reader, perhaps renders any apology for
omissions unnecessary ; it may, however, be as well to point out
once more that the book is intended to be a general Elementary
_ Treatise on Physics, and that, while it accordingly aims at giving an
account of the most important facts and general laws of all branches
of Physics, an attempt to treat completely and exhaustively of any one
= branch would both be inconsistent with the general plan of the book
* and impossible within the available space.
| E. ATKINSON.
PORTESBERY HILL, CAMBERLEY : /z7e 1898.
TRANSLATOR S"PREPACE ORI S i eD /
Tur Eléments de Physique of Professor Ganot, of which the present
work is a translation, has acquired a high reputation as an Introduction
to Physical Science. In France it has passed through Nine large
editions in little more than as many years, and it has been translated
into German and Spanish.
This reputation it doubtless owes to the clearness and conciseness
with which the principal physical laws and phenomena are explained,
to its methodical arrangement, and to the excellence of its illustrations.
In undertaking a translation, I was influenced by the favourable opinion
which a previous use of it in teaching had enabled me to form.
I found that its principal defect consisted in its too close adaptation
to the French systems of instruction ; and accordingly, my chief labour,
beyond that of mere translation, has been expended in making such
alterations and additions as might render it more useful to the English
student.
I have retained throughout the use of the Centigrade thermometer,
and in some cases have expressed the smaller linear measures on the
metrical system. ‘These systems are now everywhere gaining ground,
and an apology is scarcely needed for an innovation which may help to
familiarise the English student with their use in the perusal of the larger
and more complete works on Physical Science to which this work may
serve as an introduction.
Lee e's
ROVAL MILITARY COLLEGE, SANDHURST :
1863.
TE IAT OT 6?
PAGE
ABSORBING powers. wedi s
Absorption of gases. 175, 180
heat by gases . 430
ee liquids 424
— vapours 426
hail jee ade various bodies
425, 431
Atmosphere, composition of . eae
BAROMETRIC variations 158
Boiling points 347
Breaking weight of substances 85
CAPILLARITY in barometers . 156
Capillary, constant 127
Combustion, heat of 486
Conducting as of solids for
heat 396
“a ees Bie liquids for heat 399
Conductors of electricity 726
DENSITIES of gases 322
—____— vapours . 383
Density of water . 313
Diamagnetism : 1002
Diathermanous power . 423
Diffusion of solutions 131
eee heats. 428
Dulong and Petit’s law 451
ELASTICITY : AT Gere
Electrical conductivity . . 1028
Electricity, positive and negative . 729
Electromotive force of different
elements . 827
Vas series 815
Endosmotic equivalents 129
Expansion, coefficients of solids 302, 303
(ee alee: liquids . 310
gases 318
Eye, dimensions of 618
——— refractive indices of media of . 618
FREEZING mixtures 333
Fusing points of bodies 323
TABLES
PAGE
GLAISHER’S factors 390
Gravity, force of, at various places 70
HARDNESS, scale of 86
LATENT heat, of evaporation 9350
—————— fusion a 456
Liquefied gases 370
MAGNETIC declination . 689
inclination . 696
PRESSURE of aqueous vapour 335, 342
LAST OF PPLAT ES ANDAR S'
TABLE OF SPECTRA
= — vapours of liquids 343
RADIATING powers 413
Radiation of powders 434
Reflecting powers ? 412
Refraction, angle of double 647
Refractive indices 548
of media of eye 618
SOUND, transmission of, in tubes . 215
' Specific gravity of liquids 113
solids. 110
ze heat of solids and alae H9, 450
ot Cee Bases 454
inductive capacities . 753
——-— striking distance 798
Surface tension 127
TANGENT galvanometer and volta-
meter, comparison between 874
Temperatures, various remarkable. 298
— at different latitudes . 1094
—_———_—— thermal springs 1095
easement Ail: 319
Thermo-electric series . 1005
UNDULATIONS, length of 642
VELOCITY of sound in gases. 218
La LIT 220
rocks. 222
< solids ceed
Vibrations of musical scale 236
Frontispiece
COLOURED RINGS PRODUCED BY POLARISED LIGHT IN DOUBLE REFRACT-
ING CRYSTALS
IsOGONIC LINES FOR THE VEAR 1882
IsOCLINIC LINES FOR THE YEAR 1882
LINES FOR THE YEAR 1882
AURORA BOREALIS
ISOTHERMAL FOR THE YEAR
ISOTHERMAL FOR JANUARY
ISOTHERMAL FOR JULY ‘
Zo face p. 668
ni 690
A 695
s 698
5» 1089
99 TO54
% TOy5
Lap Pee ae tah Tacks: 2 13 4|
LE: |2 [3 |4 15 16 [7 |3 ee:
Millimetres Centimetres
The area of the figure within the heavy lines is
that of a square decimetre. A cube, one of whose
sides is this area, is a cubic decimetre or “tre. A
litre of water at the temperature of 4° C. weighs a
kilogramme. fig. 23. RS represents the sec-
tion of a smooth piece of hard
wood hinged at R ; by means of
a screw it can be clamped at
any angle 2 against the arc-
shaped support, by which at the
same time the angle can be
measured; @ is a cylindrical
roller, to the axis of which is
attached a string passing over a
\ pulley to a scale-pan P.
It is thus easy to ascertain
P by direct experiments what
weights must be placed in the
pan P in order to balance a roller of any given weight, or to cause it to move
with a given angle of inclination.
\
Fig. 23
—43] Inclined Plane ag}
The line RS represents the /ength, ST the hezgh¢,and RT the dase of the
inclined plane.
In ascertaining the theoretical conditions of equilibrium we have a useful
application of the parallelogram of forces. Let the line a, fig. 23, represent
the force which the weight W of the cylinder exerts acting vertically down-
wards ; this may be decomposed into two others; one, ad, acting at right
angles against the plane, and representing the pressure which the weight
exerts against the plane, and which is counterbalanced by the reaction of
the plane ; the other, ac, represents the component which tends to move the
weight down the plane, and this component has to be held in equilibrium by
the weight P, equal to it, and acting in the opposite direction.
It can be readily shown that the triangle adc is similar to the triangle
SRT, and that the sides ac and aé are in the same proportion as the sides
ST and SR. But the line ac represents the power, and the line ad the
weight ; hence
SSR Paws
that is, on an inclined plane, equilibrium obtains when the power is to the
weight as the height of the tnclined plane to tts length.
Since the ration, is the sine of the angle x, we may also state the prin-
ciple thus eae ato
The component da or dc, which represents the actual pressure against
the plane, is equal to W cos 2; that is the pressure against the plane is to
the weight as the base is to the length of the inclined plane.
In the above case it has been considered that the power acts parallel to
the inclined plane. It may be applied so as to act horizontally. It will then
be seen from fig. 24 that the weight S
W may be decomposed into two es
forces, one of which, @é, acts at
right angles to the plane, and the
other, ac, parallel to the base. It
is this latter which is to be kept in
equilibrium by the power. From
the similarity of the two triangles
ach and STR, aciéc=ST:TR; #
but dc is equal to W, and ac is
equal to P ; hence the power which must be applied at 4 to hold the weight
W in equilibrium is as the height of the inclined plane is to the base or
as the tangent of the angle of inclination x; that is, P=Wtanx The
bc
pressure upon the plane in this case may be easily shown to be a= aaa
5)
af 4)
thatis R= _W _ where R is the pressure upon the plane. This is some-
cos +
times called the relative weighi on the plane.
If the force P which is to counterbalance W is not parallel to the plane,
but forms an angle, E, with it, this force can be decomposed into one which
is parallel to it, and one which is at right angles. Of these only the first is
operative, and is equal to P cos E.
28 On Matter, Force, and Motion [43—
In most cases of the use of the inclined plane, such as in moving carriages
and waggons along roads, in raising casks into waggons or warehouses, the
power is applied parallel to the inclined plane. An instance of a case in
which a force acts parallel to the base is met with in the screw.
Owing to the unevenness of the surfaces in actual use, and the conse-
quent frzctéon when one body moves over another, the laws of equilibrium
and of motion on an inclined plane undergo modification. Friction must be
looked upon as a hindrance to be continually overcome, and must be
deducted from the force required to keep a body from falling down an in-
clined plane, or must be added to it in the case in which a body is to be
moved up the plane. (See art. 47.)
Thus if we place on the plane a block of some material, by gradually
increasing the inclination it will begin to move at a certain angle, which
will depend on the nature of the material ; this angle zs the Limiting angle
of resistance, and its tangent is the coefficient of friction for that material.
This may serve as a rough illustration of determining this coefficient.
44. The wedge.—The ordinary form of the wedge is that of a three-
sided prism of iron or steel, one of whose angles is very acute. Its most
frequent use is in splitting stone, timber, &c. Fig.
25 represents in section the application of the
wedge to this purpose. The side @é is the back,
the vertex of the angle acé which the two faces ac -
and dc make with each other represents the edge, —
and the faces ac and dc the szdes of the wedge. The
power P is usually applied at right angles to the
back ; and we may look upon the cohesion be-
tween the fibres of the wood as representing the
resistance to be overcome; as corresponding to
what in other machines is the weight. Suppose
this to act at right angles to the two faces of
the wedge, and to be represented by the lines
fe and ge; complete the parallelogram gef, then
the diagonal /e will represent the resultant of
the reaction of the fibres tending to force the
wedge out ; the force which must be applied to
hold this wedge in equilibrium must therefore be
equal to ef. Now eff is similar to the triangle
ach, therefore ab:ac =ch:ef; but these lines represent the pressure applied
at the back of the wedge, and the pressure on the face ac, hence if P repre-
sent the former and Q the latter, there is equilibrium when P:Q=abd:ac,
that is, when the power is to the resistance in the same ratio as the back of
the wedge bears to one of the sides. The relation between power and re-
sistance is more favourable the sharper the edge, that is, the smaller the
angle which the sides make with each other.
The action of all sharp cutting instruments, such as chisels, knives,
scissors, &c., depends on the principle of the wedge. It is alsoapplied when
very heavy weights are to be raised through a short distance, as in launching
ships, and in bracing columns and walls to the vertical.
45. The screw.— Let us suppose a piece of paper in the shape of a
—46] Virtual Velocity 29
=
right-angled triangle ace’ to be applied with its vertical side ac’e’ against a
eylindes and peril! to the axis, and to be wrapped round the eultieeiae the
hypotenuse will describe a screw line or felzx on the surface of the cylinder
(fig. 26) ; the points adcde will occupy the positions respectively ad’c’d’e’
If the dimensions be so chosen that the base of the triangle, cc’, is equal
to the circumference of the cylinder, then the hypotenuse adc becomes an
inclined plane traced on the surface of the cylinder ; the distance ac’ being
the height of the plane.
An ordinary screw consists of an elevation on a solid cylinder ; this
elevation may be either square, as in fig. 27, or acute; and such screws are
called sguware or sharp screws accordingly.
When a corresponding groove is cut in the Hag lil aii : Sey
hollow cylinder or nut of the same diameter Tt 4 \= = nag ‘
as the bolt, this gives rise to an internal or s
companion screw or 7272, fig. 28.
The vertical distance between any two
threads of a screw measured parallel to the
axis is called the fzfch, and the angle acc’ or aee’ is called the zaclination of
the screw.
In practice, a raised screw is used with its companion in such a manner
that the elevations of the one fit into, and coincide with, the depressions of
the other. The screw isa Peigcstion of the inclined albeit and the condi-
tions of equilibrium are those which obtain in the case of the plane. The
resistance, which is either a weight to be raised, or a pressure to be exerted,
acts in the direction of the vertical, and the power acts parallel to the base ;
hence we have P:R=:4, and the length of the base is the Citeiateronee
of the cylinder ; whence P:R=A:2n7; 7 being the radius of the cylinder,
and / the pitch of the screw.
The power is usually applied to the screw by means of a lever, as in the
bookbinder’s press, the copying press, &c., and the principle of the screw
may be stated to be generally that the pow Le of the screw isto the resistance
in the same ratio as that of the pitch of the screw to the circumference of the
circle through which the power acts.
46. Virtual velocity.—If the point of application of a force be slightly
displaced, the resolved part of the displacement in the direction of the force
is termed the wzrtual velocity of the force, and is considered as positive or
negative, according as it is in the same direction as the force, or in the
opposite direction. Thus in fig. 29 let the point of application A of the force
P be displaced to A’, and draw A’a perpendicular to AP. Then Aa is the
30 On Matter, Force, and Motion [46—
virtual velocity of the force P, and being, in this case, in the direction of P, is
to be considered positive.
The principle of virtual velocities asserts that if any machine or system
be kept in equilibrium by any number of forces, and the machine or system
then receive any very small displacement, the algebraic sum of the products
formed by multiplying each force by its virtual velocity will be zero. Of
course, the displacement of the machine is supposed to be such as not to
break the connection of its parts ; thus in the wheel
and axle the only possible displacement is to turn it
round the fixed axle ; in the inclined plane the weight
must still continue to rest on the plane ; inthe various
systems of pulleys the strings must still continue
stretched, and must not alter in length, &c.
Fig. 29 The complete proof of this principle is beyond
the scope of the present work, but we may easily
establish its truth in any of the machines we have already considered. It
will be found in every case that, if the machine receive a small displace-
ment, the virtual velocities of P and W will be of opposite signs, and that,
neglecting the signs, Px P’s
virtual velocity = W x W’s vir-
tual velocity. Thus, to take the
case of a dent lever, let P and Q ~
be the forces acting at the ex-
tremities of the arms of the bent
lever AFB (fig. 30), and let the
lever be turned slightly round its
fulcrum F, bringing A to A’, and
B to B’.. Draw A’a and B’d
perpendicular to P and Q respec-
tively ; then Aa is the virtual
rises velocity of P, and Bé that of Q,
the former being positive and the
latter negative. Let F~, Fg be the perpendiculars from the fulcrum upon P
and Q, or what we have called (art. 40) the arms of P and Q. Now, as the
displacement is very small, the angles FAA’, FBB’ will be very nearly right
angles ; and, therefore, the right-angled triangles AaA’, BOB’ will ultimately
be similar to the triangles FAA, FgB respectively, whence eet
; AA’ FA
ae ae or eT EY ou = = eat But the triangles FAA’, FBB’ are
similar, as they are both isosceles, and their vertical angles are equal, so
that ao - whence Bp E pO as we may put it, Fp" Os Fy
Now the denominators of these two equal fractions are equal if the lever
be in equilibrium (art..40).. Hence the numerators are equal, or
P x P’s virtual velocity = Q x Q’s virtual velocity.
As a further and simpler example, take the case of the block and tackle
described in article 41. Suppose the weight to be raised through a space / ;
47] Friction 31
then the virtual velocity of the weight is #, and is negative. Now, as the
distance between the block and tackle is less than before by the space /, and
as the rope passes over this space z times, in order to keep the rope still
tight the power will have to move through a space equal to zZ. This is the
virtual velocity of P, and is positive, and as W=z2P, we see that
W x W’s virtual velocity = P x P’s virtual velocity.
47. Friction.—In the cases of the actions of machines which have hitherto
been described, the resistances which are offered to motion have not been
at all considered. The surfaces of bodies in contact are never perfectly
smooth ; even the smoothest present inequalities which can neither be
detected by the touch nor by ordinary sight ; hence when one body moves
over the surface of another, the elevations of one sink into the depressions
of the other, like the teeth of wheels, and thereby offer a certain resistance to
motion ; thisis what is called /rvzctzon. It must be regarded as a force which
continually acts in opposition to actual or possible motion.
Friction is of two kinds: sd¢ding, as when one body glides over another ;
this is least when the two surfaces in contact remain the same, as in the
motion of an axle in its bearing ; and vol/ing friction, which occurs when one
body rolls over another, as in the case of an ordinary wheel. The latter is
less than the former, for by the rolling the inequalities of one body are raised
over those of the other. As rolling friction is considerably less than sliding
friction, it is agreat saving of power to convert the latter into the former ; as
is done in the case of the casters of chairs and other furniture, and also in
that of friction wheels. This, however, is not always the case ; thus a sledge
experiences less friction on snow than a carriage, for in this case the wheels
sink and friction on the sides results. On the other hand, it is sometimes
useful to change rolling into sliding friction, as when drags are placed on
carriage wheels. ,
Friction is directly proportional to the pressure of the two surfaces
against each other. That fraction of the pressure which must act as moving
force merely to overcome friction is called the coefficzent of friction.
Friction is independent of the extent of the surfaces in contact if the pres-
sure is the same. Thus, suppose a board with a surface of a square deci-
metre resting on another board to be loaded with a weight of a kilogramme.
If this load be distributed over a similar board of two square decimetres’
surface, the total friction will be the same, while the friction per square
centimetre is one-half, for the pressure on each square centimetre is one-half
of what it was before. So, too, a rectangular stone experiences the same
friction whether it is laid on the narrow or on the broad side. Friction is
diminished by polishing and by smearing, but is increased by heat. It is
greater as a body passes from the state of rest to that of motion than during
motion, but seems independent of the velocity. The coefficient of friction
depends on the nature of the substances in contact ; similar bodies experience
in general greater friction than dissimilar ones, for with the former the in-
equalities fit more into one another ; thus for oak upon oak it is 0-418 when
the fibres are parallel, and 0:293 when they cross ; for beech upon beech it
is 0°36. Greasy substances, which are not absorbed by the body, diminish
friction, but increase it if they are absorbed. Thus moisture and oil increase,
32 On Matter, force, and Motion [47—
while tallow, soap, and graphite diminish, the friction of wooden surfaces.
In the sliding friction of cast iron upon bronze the coefficient was found to
be 0°25 wont grease ; with oil it was 0°17, fat o°1f, soap 0°03, and with a
mixture of fat and graphite 0-002. The coefficient of rolling friction for cast-
iron wheels on iron rails as in railways is about 0-004; for ordinary wheels
on an ordinary road it is o'o4, hence a horse can draw ten times as great a
load on rails as on an ordinary road, and this is indeed a main use of rail and
tram ways. The coefficient of steel upon smooth ice has been determined
by a skater holding in his hand a spring balance (89) attached to a cord by
which he was drawn along bya second skater. At starting the spiral showed
a pullof 5 to 6 kilos, but during the motion this varied between 1 and 2 kilos.
As the weight of the skater was 62 kilos, the coefficient of friction during
the motion was ,4 to 2, or 1°6 to 3°2 per cent.
Without friction on the ground, neither man nor animals, neither ordinary
carriages nor railway carriages, could move. Friction is necessary for the
transmission of power from one wheel to another by means of bands or
ropes ; and without friction we could hold nothing in the hands.
48. Resistance to motion in a fluid medium.—A body in moving through
any medium, such as air or water, experiences a certain resistance ; for the
moving body sets in motion those parts of the medium
with which it is.in contact, whereby it loses an equiva-
i lent amount of its own motion. .
| This resistance increases with the surface of the
i moving body ; thus a soap-bubble or a snow-flake falls
more slowly than does a drop of water of the same
weight. It also increases with the density of the
medium ; in rarefied air, therefore, it is less than in
air under the ordinary pressure ; and in this again it
is less than in water.
The influence of this resistance may be illustrated
by means of the apparatus represented in fig. 31,
which consists of two vanes, w w, fixed toa horizontal
axis, xx, to which is also attached a bobbin s. The
rotation of the vanes is effected by means of the falling
of a weight attached to the string coiled round the
bobbin. The vanes can be adjusted either at right
angles or parallel to the axis. In the former position
the vanes rotate rapidly when the weight is allowed to
act ; in the latter, however, where they press with their entire surface against
the air, the resistance greatly lessens the rapidity of rotation.
The resistance increases with the velocity of the moving body, and for
moderate velocities is proportional to the square ; for, supposing the velocity
of a body made twice as great, it must displace twice as much matter, and
must also impart to the displaced particles twice the velocity. For high
velocities the resistance in a medium increases in a more rapid ratio than
that of the square, for some of the medium is carried along with the moving
body, and this, by its friction against the other portions of the medium,
causes a loss of velocity.
It is this resistance which so greatly increases the difficulty and cost of
49] Uniformly Accelerated Rectilinear Motion 23
attaining very high speeds in steam-vessels, to which must be added the pro-
duction of waves on the surface, and of eddy currents. Use is made, on the
other hand, of this resistance in parachutes (fig. 183) and in the windvanes
for diminishing the velocity of falling bodies (fig. 57), the principle of which
is illustrated by the apparatus, fig. 31. Light bodies fall more slowly in air
than heavy ones of the same surface, for the moving force is smaller com-
pared with the resistance. The resistance to a falling body may ultimately
equal its weight ; it then moves uniformly forward with the velocity which
it has acquired. Thus, a raindrop falling from a height of 3,000 feet should,
when near the ground, have a velocity of nearly 440 feet, or that of a
musket-shot ; owing, however, to the resistance of the air, its actual velocity
is probably not more than 30 feet in a second. On railways the resistance
of the air is appreciable ; with a carriage exposing a surface of 22 square
feet, it amounts to 16 or 17 pounds when the speed of the train is 16 feet a
second, or 11 miles an hour.
By observing the rate of diminution in the number of oscillations of a
horizontal disc suspended by a thread when immersed in water, Meyer
determined the coefficient of the frictional or internal resistance of water,
and found that at 10° it was equal to 001567 gramme on a square centi-
metre ; and for air it was about 4 as much.
49. Uniformly accelerated rectilinear motion.—Let us suppose a body
containing 77 units of mass to move from rest under the action of a force of
F units ; the body will move in the line of action of the force, and will
acquire in each second an additional velocity / given by the equation
ay ke
consequently, if v is its velocity at the end of ¢ seconds, we have
v =f. (1)
To determine the space it will describe in ¢ seconds, we may reason as
follows :—The velocity at the time ¢ being /%, that at a time 7+7 will be
f (é+7). Ifthe body moved uniformly during the time 7 with the former
velocity, it would describe a space s squal to f¢r; if with the latter velocity,
a space s, equal to f(¢+7)r. Consequently,
Cees we Gace oe ee
therefore, when r is indefinitely small, the limiting values of s and s, are
equal. Now, since the body’s velocity is continually zzcreasing during the
time 7, the space actually described is greater
than s and less than s,. But since the limiting
values of s and s, are equal, the limiting value
of the space described is the same as that of s
or s, In other words, if we suppose the whole
time of the body’s motion to be divided into
any number of equal parts, if we determine the
velocity of the body at the beginning of each
of these parts, and if we ascertain the spaces
described on the supposition that the body
moves uniformly during each portion of time, the limiting value of the sum
of these spaces will be the space actually described by the body. Draw
D
34 On Matter, Force, and Motion [49-
a line AC (fig. 32), and at A construct an angle CAB, whose tangent equals
ff; divide AC into any number of equal parts in D, E, F,...and draw PD,
OE, RF;...BC at right angles to AC ; then smce PD=ADx/, QE=AEx 7,
RF=AF x f, BC=ACx f/f, &c., PD will represent the velocity of the body at
the end of the time represented by AD, and similarly QE, RF,...BC, will re-
present the velocity at the end of the times AE, AF,...AC. Complete the rect-
angles De, Ef, Fg... These rectangles represent the space described by the
body, on the above supposition, during the second, third, fourth,...portions of
the time. Consequently, the space actually described during the time AC is
the limit of the sum of the rectangles ; the limit being continually approached
as the number of parts into which AC is divided is continually increased.
But this limit is the area of the triangle ABC ; that is AC x CB or $AC
xACxf Therefore, if AC represents the time ¢ during which the body
describes a space s, we have
s=4/ft. | (2)
Since this equation can be written
PAREN ad
we find, on comparison with equation (1), that
U = 2fs. (3)
To illustrate these equations, let us suppose the accelerative effect of the
force to be 6 ; that 1s to say that, in virtue of the action of the force, the body
acquires in each successive second an additional velocity of 6 feet per second ;
and let it be asked what, on the supposition of the body moving from rest,
will be the velocity acquired, and the space described, at the end of 12
seconds ; equations I and 2 enable us to answer that at that instant it will be
moving at the rate of 72 feet per second, and will have described 432 feet.
The following important result follows from equation (2). At the end of
the first, second, third, fourth, &c., second of the motion, the body will have
described 3f, 3fx 4, f/x 9, 4fx 16, &c., feet ; and consequently durving the
first, second, third, fourth, &c., second of the motion will have described 3/7,
fx 3, 4f~x 5, 3/7, &c., feet, namely spaces in arithmetical progression.
The results of the above article can be stated in the form of laws which
apply to the condition of a body moving from a state of rest under the action
of a constant force :—
I. The velocities are proportional to the times during which the motion
has lasted.
Il. Zhe spaces described are proportional to the squares of the times em-
ployed tn thetr description.
III. The spaces described are proportional to the squares of the velocities
acquired during thetr description.
IV. Lhe spaces described in equal successive periods of time increase by a
constant quantity.
Instead of supposing the body to begin to move from a state of rest, we
may suppose it to have an initial velocity V, in the direction of the force. In
this case equations I, 2, and 3 can be easily shown to take the following
forms, respectively :—
—51] Motion of Projectiles 35
GaN STi,
S=Vi+s fe’,
UT? a VP 2 5
If the body move in a direction opposite to that of the force, f must be
reckoned negative.
The most important exemplification of the laws stated in the present
article is in the case of a body falling freely zz vacuo. Here the force causing
the acceleration is that of gravity, and the acceleration produced is denoted
by the letter @: it has already been stated (29) that the numerical value of
£ 1S 32°1912 at London, when the unit of time is a second and the unit of
length a foot. Adopting the metre as unit of length, the value of gat London
is 9°8117.
50. Motion on an inclined plane.—Referring to (43), suppose the force
P not to act ; then the mass M is acted on by an unbalanced force M g sin 2,
in the direction SR ; consequently the acceleration down the plane is ¢ sin x,
and the motion becomes a particular case of that discussed in the last article.
If it begins to move from rest, it will at the end of ¢ seconds acquire a
velocity v given by the equation
U= et sin x,
and will describe a length s of the plane given by the equation
Se-ec7 Sill 2.
Also, if v is the velocity acquired while describing s feet of the plane,
Vis OG Si Ye
Hence (fig. 23), if a body slides down the plane from S to R, the velocity
which it acquires at R is equal to ./ 2¢. RS sinRor V 2g¢.ST; that isto say,
the velocity which the body has at R does not depend on the angle x, but
only on the perpendicular height ST. The same would be true if for RS we
substituted any smooth curve ; and hence we may state generally that when
a body moves along any smooth line under the action of gravity, the change
of velocity it experiences in moving from one point to another is that due to —
the vertical height of the former point above the latter.
51. Motion of projectiles—The equations given in the above article
apply to the case of a body thrown vertically upwards or downwards with a
certain initial velocity. We will now consider the case of a heavy body
thrown in a horizontal direction. Let a, fig. 33, be such a body thrown with
an initial velocity of v feet in a second, and let the line ad represent the space
described in any interval ; then at the end of the 2nd, 3rd, 4th... equal interval,
the body, in virtue of its inertia, will have reached the points ¢, d, e, &c.
But during all this time the body is under the influence of gravity, which,
if it alone acted, would cause the body to fall through the distances repre-
sented on the vertical line; these are determined by the successive values
of 4g¢*, which is the formula for the space described by a freely falling body
(50). The effect of the combined action of the two forces is that at the end
of the first interval, &c., the body will be at 6’, at the end of the second
interval at c’, of the third at a’, &c., the spaces 00’ cc’ dd’... being propor-
D2
36 [51-
tional to the squares of ad, ac, ad, respectively, and the line joining these
points represents the path of the body. By taking the intervals of time
sufficiently small we get a regularly curved
line of the form known as the parabola.
In order to demonstrate motion with
horizontal and inclined direction the appa-
ratus represented in fig. 34 may be made
use of. It consists of a bottle from which
a steady stream of water issues through a
caoutchouc tube terminating ina jet. This
can be discharged in front of a slate or
blackboard on which the path of the curve in
each case can be chalked.
If the direction in which the body is
thrown makes an angle of a with the horizon
(fig. 35), then after ¢ seconds it would have
travelled a distance a=v7, where v is the
original velocity ; during this time, however,
it will have fallen through a distance dc = 4¢7? ;
the height which it will have actually reached
is =bd—bc=vt sin a—tgt?; and the hori-
zontal distance will be
ad=ab cos a=vt COS a.
The vange of the body,
or the greatest distance
through which itis thrown,
will be reached when the
On Matter, Force, and Motion
that
wi \! mi mil
Ht
iT f
ss
ii
_—SS SS
=
TT
}
Mn
ao NNT
q # i A |
1 | ‘ }
i ~ _ \\ I
SA St
vu itt
an if
|
\
—s
——
——
NN
height is again=o;
is, when v¢ sin a—4g¢? =0,
: 2U Si
from which ¢ = 2752 @,
Introducing this value of
¢# into the equation for
the distance, d, we have
is
da 2U" SiN @ COS a, Vey
Si
by a trigonometrical
: v* sin 2a
transformation = caine
The greatest height is
attained in half the time of
ysina
flight, or when 7= -
from which we_ get
9. Se,
v? sin* a
hk =—
wt
It follows from the
formula that the Aezgh¢ is greatest when sin a is greatest, which is the case
when it = 90°, or when the body is thrown vertically upwards ;
the range is
greatest where sin 2a is a maximum, that is, when 2a=90° or a= 45°.
-53] Motion in a Ctrcle—Centrifugal Force 37
In these formule it has been assumed that the air offers no resistance.
This is, however, far from the case, and in practice, particularly if the velocity
of projection is very great, the path differs from that of a parabola. - Fig. 35
approximately represents the path, allowing for the resistance of the air.
6b
Fig. 35
The divergence from the true theoretical path is affected by the fact that
in the modern rifled arms the projectiles are not spherical in shape ; and
also because, along with their motion of translation, they have, in consequence
of the rifling, a rotatory motion about their axis.
52. Composition of velocities.—The principle for the composition of
velocities is the same as that for the composition of forces: this follows evi-
dently from the fact that forces are measured by the momentum they com-
municate, and are therefore to one another in the same ratio as the velocities
they communicate to the same body. Thus (fig. 8, art. 33), if the point has
at any instant a velocity AB in the direction AP, and there is communicated
to it a velocity AC in the direction AQ, it will move in the direction AS with
a velocity represented by AD. And, conversely, the velocity of a body re-
presented by AD can be resolved into two component velocities AB and AC.
This suggests the method of determining the motion of a body when acted
on by a force in a direction transverse to the direction of its velocity ; namely,
suppose the time to be divided into a great number of intervals, and suppose
the velocity actually communicated by the force to be communicated at once ;
then by the composition of velocities we can determine the motion during
each interval, and therefore during the whole time ; the actual motion is the
limit to which the motion, thus determined, approaches when the number of
intervals is increased.
53. Motion in a circle—Centrifugal force.—When a body is once in
motion, unless it be acted upon by some force, it will move uniformly
forward in a straight line with unchanged velocity (26). If, therefore, a body
moves uniformly in any other path than a straight line—in a circle, for
instance—this must be because some force is constantly at work which
continuously deviates it from this straight line.
We have already seen an example of this in the case of the motion of
projectiles (51), and will now consider it in the case of central motion or
motion in a circle, of which we have an example in the motion of the
celestial bodies, or in the motion of a s/z7g.
In the latter case, if the string is cut, the stone, ceasing to be acted upon
by the tension of the string, will move in a straight line with the velocity
which it already possesses—that is, in the direction of the tangent to the
curve at the point where the stone was when the string was cut. The tension
38 On Matter, Force, ana Motion [53-
of the string, the effect of which is to pull the stone towards the centre of
the circle and to cause the stone to move in its circular path, is called the
centripetal or central force ; the reaction of the stone upon the string, which
is equal and opposite to this force, is called the centrifugal force. The
amount of the forces may be arrived at as follows :—
Let us suppose a body moving in a circle with given uniform velocity to
be at the point a (fig. 36); then, had it not been acted on by a force in the
direction ac, it would, in a small succeeding interval of
time Z, have continued to move in the direction of the
tangent at a,and have passed through a distance which
we will represent by ad. In consequence, however, of
this force, it has not followed this direction, but has
arrived at the point @ on the curve ; hence the force
has made it traverse the distance dd=ae in this
interval. If/fbe the acceleration with which the body
is drawn towards the centre ae=43/¢*, and if ad be very
small, it may be taken as equal to @6 or wé, where v
is the velocity of the moving body. Now if az is the
diameter of the circle, the triangle adz is inscribed in
a semicircle and is right-angled, whence ad! = ae x an
=aex2r. Substituting their values for ad and ae in
this equation, we find that v2? =4// x 27, from which
oye
iy == 5 that is, in order that a body with a certain
velocity may move in a circle, it must be drawn to
the centre by a force which is directly as the square
of the velocity with which the body moves, and
inversely as the radius of the circle. In‘order to
express this in the ordinary units of weight, we must
multiply the above expression by the mass, which
2
. V1 . .
ives vl c= ZANT G keep the body in a circle, an
r
attraction towards the centre is needed, which is
constantly equal to”, and this attraction is also
a
Fig. 36
constantly neutralised by the centrifugal force.
The above expression may be put in a form which is sometimes more
convenient. If T be the time in seconds aio to traverse the circum-
4mn*r
Tas
If a rigid body rotates about a fixed axis, all parts of the body describe
circumferences of various diameters, but all in the same time. The velocity
of the motion of individual particles increases with the distance from the axis
of rotation. By angular velocity is understood the velocity of a point at unit
distance from the axis of rotation. If this is denoted by a, na velocity v of a
ference 277 with the velocity wv, then v? = oor from which F =
3 : Bled : Uv
point at a distance from the axis is #7, from which o=< =~ and F=mro.
r 7
The existence of centrifugal force may be demonstrated by means of
numerous instructive experiments, such as the centrifugal railway. Ifasmall
—54] Motion in a Vertical Circle 39
can of water hung by the handle to a string be rapidly rotated in a vertical
circle, no water will fall out, for, at a suitable velocity, the liquid will press
against the bottom of the vessel with a force at right angles to the circle and
greater than its own weight.
Centrifugal force has been used in chemical laboratories to separate
crystals from the mother-liquors, and also to promote the deposition of fine
precipitates which under ordinary circumstances settle very slowly ; it is also
applied industrially in sugar factories to purify sugar from syrup, in dyeworks
to dry yarn and cloth rapidly, and in laundries.
54. Motion in a vertical circle.—Let ACBD (fig. 37) be a circle whose
plane is vertical and radius denoted by 7 Suppose a point placed at A, and
allowed to slide down the curve, what velocity will it
have acquired on reaching any given point P? Draw D
the vertical diameter CD, join CA, CP, and draw the
horizontal lines AMB and PNP’. Now, assuming the
curve to be smooth, the velocity acquired in falling
from A to P is that due to MN, the vertical height of
A above P (51); if therefore v denote the velocity of
the point at P, we shall have
U = 20 NIN"
Now by similar triangles DCP, PCN, we have
DONC? aCe EZ eines
consequently, if we denote by s the chord CP,
Z2rNC=s",
In like manner, if a denote the chord CA,
2MOA
therefore 27M N =a?—s”,
and y? =F (a? — 5s),
rv
Now wz will have equal values when s has the same value, whether positive
or negative, and for any one value of s there are two equal values of v, one
positive and one negative. That is to say, since CP’ is equal to CP, the
body will have the same velocity at P’ that it has at P, and at any point the
body will have the same velocity whether it is going up the curve or down
the curve. Of course it is included in this statement that if the body begins
to move from A it will just ascend to a point B on the other side of C, such
that A and B are in the same horizontal line. It will also be seen that at C
the value of sis zero; consequently, if Vis the velocity acquired by the
body in falling from A to C, we have
r
and, on the other hand, if the body begins to move from C with a velocity V,
40 On Matter, Force, and Motion [54-
it will reach a point A such that the chord AC or ais given by the same
equation. In other words, the velocity at the lowest point is proportional to
the chord of the are described.
55. Motion of a simple pendulum.—By a simple pendulum is meant a
heavy particle suspended by a fine thread from a fixed point, about which it
oscillates without friction. So far as its changes of velocity are concerned,
they will be the same as those of the point in the previous article, for the
tension of the thread, acting at each position in a direction at right angles to
that of the motion of the point, will no more affect its motion than the re-
action of the smooth curve affects that of the point in the last article. The
time of an oscillation—that is, the time in which the point moves from A to
B—can be easily ascertained when the arc of vibration is small; that is,
when the chord and the arc do not sensibly differ.
Thus, let AB (fig. 38) equal the arc or chord ACB (fig. 37) ; with centre
C and radius AC or a describe a circle, and suppose a point to describe the
circumference of that circle with a uniform velocity
am V ora J At any instant let the point be at Q,
r
L XQ
join CQ, draw the tangent QT, also draw QP at
right angles and QN parallel to AB, then the angles
NQT and CQP are equal. Now the velocity of Q
resolved parallel to AB is V cos TQN or ay/€
,
cos CQP;; that is,ifCP equals s, the velocity of Q
parallel to AB is
Fig. 38 A/£PQ oa Ae (a? -s°).
But if we suppose a point to move along AB in such a manner that its
velocity in each position is the same as that of the oscillating body, its
velocity at P would also equal Je &(a?—s*); and, therefore, this point
would describe AB in the same time that Q describes the sey UO he
AQB. If then 7 be the required time of an oscillation, we have
o Yr
fanasay /€ = raft.
r =
This result is independent of the length of the arc of vibration, provided its
amplitude, that is AB, be small—not exceeding 4 or 5 degrees, for instance.
It is evident from the formula that the time of a vibration is directly pro-
portional to the square root of the length of the pendulum, and inversely
proportional to the square root of the accelerating force of gravity.
As an example of the use of the formula we may take the following :—It
has been found that 39°13983 inches is the length of a single pendulum
whose time of oscillation at Greenwich is one second ; the formula at once
leads to an accurate determination of the accelerating force of gravity ¢ ; for
using feet and seconds as our units we have ¢=1, r= 3°26165, and w stands
for the known number 3°14159 ; therefore the formula gives us.
—57] Linpulstve Forces 41
PS(BTAT 59)? * 3°26165)= 3271012:
This is the value employed in (29).
Other examples will be met with in the Appendix.
56. Graphic representation of the changes of velocity of an oscil-
lating body.—The changes which the velocity of a vibrating body under-
goes may be graphically represented as follows :—Draw a line of indefinite
length and mark off AH (fig. 39) to represent the time of one vibration, HH’
to represent the time of the second vibration, and so on. During the first
vibration the velocity increases from zero toa maximum at the half-vibration,
and then decreases during the second half-vibration from the maximum to
zero. Consequently, a curved line or arc AQH may be drawn, whose
ordinate QM at any point Q will represent the velocity of the body at the
8—
ek Pye
ea iett M A
ig Eger
Fig. 39
time represented by AM. Ifa similar curved line or arc HPH’ be drawn,
the ordinate PN of any point P will represent the velocity at a time denoted
by AN. But since the arection of the velocity in the second oscillation is
contrary to that of the velocity in the first oscillation, the ordinate NP must
be drawn in the contrary direction to that of MQ. If then the curve be
continued ‘by a succession of equal arcs alternately on opposite sides of
AD, the variations of the velocity of the vibrating body will be completely
represented by the varying magnitudes of the ordinates of successive
points of the curve. The last article shows this to be the curve of sines for
a pendulum
57. Impulsive forces.—When a force acts on a body for an inappre-
ciably short time, and yet sensibly changes its velocity, it is termed an zmstan-
taneous or tmpulsive force. Such a force is called into play when one body
strikes against another. A force of this character is nothing but a finite
though very large force, acting for atime so short that its duration is nearly,
or quite, insensible. In fact, if M is the mass of the body, and the force
contains Mf units, it will, in a time 4 communicate a velocity /¢; now, how-
ever small ¢ may be, Mf and therefore f may be so large that /¢ may be of
sensible or even considerable magnitude. Thus if M containsa pound of
matter, and if the force contains ten thousand units, though ¢ were so short
as to be only the ;54, of a second, the velocity communicated by the force
would be one of ten feet per en It is also to be remarked that the body
will not sensibly move while this velocity is being communicated; thus in
the case supposed, the body would only move through 3/2 or the 345 of a
foot whilst the force acts upon it.
When one body impinges on another, it follows from the law of the
equality of action and reaction (39) that whatever force the first body exerts
upon the second, the second will exert an equal force upon the first in the
opposite direction. Now forces are proportional to the momenta generated
42 On Matter, Force, and Motion [57-
in the same time : consequently, these forces generate, during the whole or
any part of the time of impact, in the bodies respectively, equal momenta
K G ad k HH with contrary signs; and therefore the
sum of the ean ue of the two bodies
will remain constant during and at the
end ofthe. impact: It ist#éfi. Course
understood that if the two bodies move
in contrary directions, their momenta
have opposite signs, and their sum is an
algebraical sum. In order to test the
Fig. «oe physical validity of this conclusion,
Newton made a series of experiments,
which may be thus briefly described—Two balls A and B (fig. 40) are hung
from points C, D in the same horizontal line by threads in such a manner
that their centres A and B are in the same horizontal line. With centre C
and radius CA describe a semicircle EAF, and with centre D and radius
DB describe a semicircle GBH, on the wall in front of which the balls hang.
Let A be moved back to R, and be allowed to descend to A; it there
impinges on B; A and B will now move along the arcs AF and BH
respectively ; let A and B come to their highest points at and £ respectively.
Now if V denotes the velocity with which A reaches the lowest point, v and
wz the velocities with which A and B leave the lowest points after impact,
and 7 the radius AC, it follows from (54) that
=chd AR, /¥,v=chd Arq /$,and v= cha Bea /€ ;
rv
therefore if A and B are the masses of the two balls, the momentum at the
instant before impact was proportional to A x chd AR, and the momentum
after impact was proportional to Ax chd Ar+Bxchd B&. Now when the
position of the points R, ~, and & had been properly corrected for the
resistance of the air, it was found that these two expressions were equal to
within quantities so small that they could be properly referred to errors of
observation. The experiment succeeded equally under every modification,
whether A impinged on B at rest or in motion, and whatever the materials of
A and B might be.
58. Direct collision of two bodies.—Let A and B be two _ bodies
moving with velocities V and U respectively along the same line, and let
their mutual action take place in that line; if the one overtake the other,
what will be their respective velocities at the instant after impact? We will
answer this question in two extreme cases.
(i.) Let us suppose the bodies to be guz¢e znelastic. In this case, when A °
touches B, it will continue to press against B until their velocities are
equalised, when the mutual action ceases. For whatever deformation the .
bodies may have undergone, they have no tendency to recover their shapes.
If, therefore, x is their common velocity after impact, we shall have Ax + Br
their joint momentum at the end of impact ; but their momentum before
impact was AV + BU whence
(A+B)r=AV+BU,
an equation which determines »*.
—59] Work: Meaning of the Term 43
(i1.) Let us suppose the bodies Zerfectly elastic. In this case they recover
their shapes, with a force exactly equal to that with which they were com-
pressed, Consequently the whole momentum lost by the one and gained by
the other must be exactly double that lost while compression took place ;
that is, up to the instant at which their velocities were equalised. But these
are respectively AV — Ax and Ba— BU ; therefore if v and w are the required
final velocities,
Av=AV—-2(AV—-Ax) orv=—-Vt2r
Bu=BU+2(Br—BU) or w=2x—U ;
hence (A+ B)v=2BU +(A—B)V,
and (A + B)w=2AV—(A-—B)U.
The following conclusion from these equations may be noticed : suppose a
ball A, moving with a velocity V, to strike directly an equal ball B at rest.
In this case A=B and U =o, consequently v=o and z=V; that is, the
former ball A is brought to rest, and the latter B moves on with a velocity V.
If now B strike on a third equal ball C at rest, B will in turn be brought
to rest, and C will acquire the velocity V. And the same is true if there is
a fourth, or fifth, or indeed any number of balls. This result may be shown
with ivory balls, and is a very remarkable experiment.
59. Work: meaning of the term.—It has been pointed out (19, 26)
that a moving body has no power of itself to change either the direction or
the speed of its motion, and that, if any such change takes place, it is a proof
that the body is acted upon by some external force. But although change of
motion thus always implies the action of force, forces are often exerted with-
out causing any change in the motion of the bodies on which they act. For
instance, when a ship is sailing at a uniform speed, the force exerted on it by
the wind causes no change in its motion, but simply prevents such a change
being produced by the resistance of the water ; or, when a railway-train is
running with uniform velocity, the force of the engine does not change, but
only maintains its motion in opposition to the forces, such as friction and
the resistance of the air, which tend to destroy it.
These two classes of cases—namely, first, those in which forces cause a
change of motion ; and, secondly, those in which they prevent, wholly or in
part, such a change being produced by other forces—include all the effects
to which the action of forces can give rise. When acting in either of these
ways, a force is said to do work: an expression which is used scientifically
in a sense somewhat more precise, but closely accordant with that in which
it is used in common language. A little reflection will make it evident that,
in all cases in which we are accustomed to speak of work being done—
whether by men, horse-power, or steam-power, and however various the pro-
ducts may be in different cases—the physical part of the process consists
solely in producing or changing motion, or in keeping up motion in opposition
to resistance, or in a combination of these actions. The reader will easily
convince himself of this by calling to mind what the definite actions are which
constitute the work done by (say) a navvy, a joiner, a mechanic, a weaver ; that
done bya horse, whether employed in drawing a vehicle or in turning a gin ;
or that of a steam-engine, whether it be used to draw a railway-train or to
44 On Matter, Force, and Motion [59—
drive machinery. In all cases the work done is reducible, from a mechanical
point of view, to the elements that have been mentioned, although it may be
performed on different materials, with different tools, and with different
degrees of skill.
It is, moreover, easy to see (53) that any possible change or motion
may be represented as a gain by the moving body of an additional (positive
or negative) velocity either in the direction of its previous motion, or at
right angles to it; but a body which gains velocity is (27) said to be ac-
celerated. Hence, what has been said above may be summed up as
follows :—When a force produces acceleration, or when tt maintains motion
unchanged in opposition to reststance, tt 1s satd to do WORK.
60. Measure of work.—In considering how work is to be measured, or
how the relation between different quantities of work is to be expressed
numerically, we have, in accordance with the above, to consider, first, work
of acceleration; and, secondly, work against resistance. But in order to
make the evaluation of the two kinds of work consistent, we must bear in
mind that one and the same exertion of force will result in work of either
kind according to the conditions under which it takes place: thus, the force
of gravity acting on a weight let fall from the hand causes it to move with a
continually accelerated velocity until it strikes the ground ; but if the same
weight, instead of being allowed to fall freely through the air, be hung to a
cord passing round a cylinder by means of which various degrees of friction
can be applied to hinder its descent, it can be made to fall with a very small
and practically uniform velocity. Hence, speaking broadly, it may be said
that, in the former case, the work done by gravity upon the weight is work of
acceleration only, while in the latter case it is work against resistance (friction)
only. But it is very important to note that an essential condition, without
which a force, however great, cannot do work either of one kind or the other,
is that the thing acted on by it shall szove while the force continues to act.
This is obvious, for if no motion takes place it clearly cannot be either
accelerated or maintained against resistance. The motion of the body on
which a force acts being thus necessarily involved in our notion of work
being done by the force, it naturally follows that, in estimating how much
work is done, we should consider how much—that is to say, how far—the
body moves while the force acts upon it. This agrees with the mode of
estimating quantities of work in common life, as will be evident if we consider
a very simple case—for instance, that of a labourer employed to carry bricks
up to a scaffold : in such a case a double number of bricks carried would
represent a double quantity of work done, but so also would a double height
of the scaffold, for whatever amount of work is done in raising a certain
number to a height of twenty feet, the same amount must be done again to
raise them another twenty feet, or the amount of work done in raising the
bricks forty feet is twice as great as that done when they are raised only
twenty feet. It is also to be noted that no direct reference to é7me enters into
the conception of a quantity of work : if we want to know how much work a
labourer has done, we do not ask how long he has been at work, but what he
has done—for instance, how many bricks he has carried, and to what height ;
and our estimate of the total amount of work is the same whether the man
has spent hours or days in doing it.
—60] Measure of Work 45
The foregoing relations between force and work may be put into definite
mathematical language as follows :—-If the point of application of a force
moves ina straight line, and if the part of the force resolved along this line
acts in the direction of the motion, the product of that component and the
length of the line is the work done by the force. If the component acts in
the opposite direction to the motion, the component may be considered as
a resistance, and the product is work done against the resistance. Thus, in
(43), 1f we suppose @ to move up the plane from R to S, the work done by P
is Px RS: the work done against the resistance W is W sinx x RS. It
will be observed that if the forces are in equilibrium during the motion, so
that the velocity of ais uniform, P equals W sin x, and consequently the
work done by the power equals that done against the resistance. Also, since
RS sin x equals ST, the work done against the resistance equals W x ST.
In other words, to raise W from R to S requires the same amount of work
as to raise it from T to S.
If, however, the forces are not in equilibrium, the motion of a willnot be
uniform, but accelerated ; the work done upon it will nevertheless still be
represented by the product of the resultant force resolved along the direction
of motion into the distance through which it moves.
In order to ascertain the relation between the amount. of work done
and the change produced by it in the velocity of the moving mass, we must
recall one or two elementary mechanical principles. Let F be the resultant
force resolved along the direction of motion, and S. the distance through
which its point of application moves: then, according to what has been said,
the work done by the force=FS. Further, it has been pointed out (28) that
a constant force is measured by the momentum produced by it in a unit of
time : hence, if T be the time during which the force acts, V the velocity of
the mass M at the beginning of this period, and V, the velocity at the end,
the momentum produced during the time T is MV, — MV, and consequently
the momentum produced in a unit of time, or, in other words, the measure
of the force, is
MEV ea)
oe Pei
The distance S through which the mass M moves while its velocity
changes from the value V to the value V, is the same as if it had moved
during the whole period T with a velocity equal to the average value of the
varying velocity which it actually possesses. But a constant force acting
upon a constant mass causes its velocity to change at auniform rate; hence,
in the present case, the average velocity is simply the arithmetical mean of
the actual and final velocities :
S=4(V,+ V)T.
Combining this with the last equation, we get as the expression for the
work done by the force F :
FS=3$M(V2-V°);
or, in words, when a constant force acts on a mass so as to change tts velocity,
the work done by the force ts equal to half the uae of the mass into the
change of the square of the veloctty.
46 On Matter, Force, and Motion [60-
The foregoing conclusion has been arrived at by supposing the force F
to be constant, but it is easy to show that it holds good equally if F is the
average magnitude of a force which varies from one part to another of the
total distance through which it acts. To prove this, let the distance S be
subdivided into a very great number z of very small parts, each equal to s,
so that zs=S. Then, by supposing s to be sufficiently small, we may with-
out any appreciable error consider the force as.constant within each of these
intervals, and as changing suddenly as its point of application passes from
one interval, to’the’ next:; Let) F,) F7F,)2. .. Fy; be the forcessacting
throughout the 1st, 2nd, 3rd... . #th interval, and let the velocity at the
end of the same intervals be v,, U, Us . +--+ Un (=V,) respectively ; then,
for the work done in the successive intervals, we have :
Fis Pr +M(v,?— V?)
Fs =3M(uv,? —v,”*)
F,s=3M(v,’ —v,”)
£8 =3M(v," — Yn? -1) = 3M(V 1? — 9,2 — 1);
or, for the total work,
(eo to a ee + Fn)s=43M(V,?-V?);
where the quantity of the left-hand side of the equation may also be
e+ koto. FE
1
arithmetical mean) of the forces F,, F,, &c.
An important special case of the application of the above formula arises
when either the initial or the final velocity of the mass M is nothing ; that
is to say, when the effect of the force is to make a body pass from a state
of rest into one of motion, or from a state of motion into one of rest. The
general expression then assumes one of the following forms, namely :—
FS =4}MV,? or,
—FS=}MV?;
written
ms = FS, if we put F to stand for the average (or
the first of which denotes the quantity of work which must be done on a body
of mass M in order to give to it the velocity V,, while the second expresses
the work that must be done in order to bring the same mass to rest when it
is moving with the velocity V, the negative sign in the latter case showing
that the force here acts zz opposition to the actual motion, and is therefore
to be regarded as a resistance.
In practice, the case which most frequently occurs is where work of ac-
celeration and work against resistance are performed simultaneously. Thus,
recurring to the inclined plane already referred to in art. 43, let M be the
mass of a and W its weight. If the force P (where P is the constant force
with which the string pulls M up the plane) be greater than W sin x, the
mass M will move up the incline with a continually increasing velocity, and
—62] Unit of Work. Power 47
if the point of application of P be displaced from R to S, the total amount of
work done, namely, P x RS, consists of a portion= W sin x RS, done against
the resistance of the weight W, and of a portion=(P—W sin x) RS expended
in accelerating the weight. Hence, to determine the velocity wv with which
W arrives at the top of the incline, we have the equation
(P—W sin +) RS=4Mv’*;
for the portion of P which is in excess of what is required to produce equili-
brium with the weight W, namely, P— W sin x, corresponds to the resultant
force F supposed in the foregoing discussion, and RS to the distance through
which this resultant force acts.
61. Unit of work. Power.—-For strictly scientific purposes a unit of
work is taken to be the work done by a unit of force when its point of appli-
cation moves through the unit distance in the direction of its action ; but, as
a convenient and sufficiently accurate standard for practical purposes, the
quantity of work which is done in lifting 1 pound through the height of
1 foot is commonly adopted as the unit, and this quantity of work is spoken of
as one ‘foot-pound.’ It is, however, important to observe that the foot-pound
is not perfectly invariable, since the weight of a pound, and therefore the
work done in lifting it through a given height, differs at different places,
being a little greater near the Poles than near the Equator.
On the metrical system the clogrammetre is the unit; it is the work
done when a weight of a kilogramme is raised through a height of a
metre. This is equal to 7°23 foot-pounds, and one foot-pound = "1383 of a
kilogrammetre. .
In estimating the usefulness of any motor it becomes necessary to know
the time required by it for doing a given amount of work. The amount of
work per second is the ower of the motor. The unit of power is the
power required to do a unit of work in a unit of time. For measuring the
power of engines the unit used is the horse-fower, which represents a rate
of work of 33,000 foot-pounds per minute.
It is to be observed that in every case the unit is of the same denomina-
tion as the thing or quantity measured. The unit of length must bea length ;
the unit of value must be a definite quantity of some valuable commodity.
The numbers, to determine which is one of the objects of physical research,
are to be considered as abstract numbers, representing how many times the
unit is taken. |
62. Systems of units.—The units of mass, length, and time are said
to be fundamental units, as all other units, such as those of area, velocity,
acceleration, power, &c., are referred to them. These latter units are there-
fore called derived units. The magnitudes of the fundamental units are,
however, arbitrary. A large class of writers use the centimetre, gramme,
and second, and this system is usually called the C.G.S. system ; others
use the foot, pound,.and second. It thus becomes important to have a
systematic method of reducing measurements from one system of units to
another.
Let L, M, T represent respectively the magnitude or dmenszons of the
centimetre, the gramme, and the second, and L’, M’, T’ represent the
48 On Matter, Force, and Motion [62-
dimensions of the foot, the pound, and the minute. Then, if a wire is found
to be Z cm. or / ft. in length, its length may be represented either by ZL or
Ui /fwvand hence
Li orth - Os 7
UV de Ot. b= Th
The ratio 2 is the length of a foot in gute what and has been found
by direct comparison to be 30°4797.. Hence any measurement, Z’ in feet, is
converted into centimetres by multiplying 7” by this number.
In a similar manner, if #z and 7’ represent the number of units of mass
in a piece of matter in the two systems,
/
We ei
M
where the unit ratio is the number of grammes in a pound, or 453°59.
For converting a volume v’ into the equivalent v,
(/L’) = (IL), or 2 = fe ) ve
or Ux (-)~ ;
For density, a =D)
Yin WN Pies
7° 1373" 179
Dol’. (LY:
Here the ratio [3 is said to bea measure of the magnitude or dimensions
of the unit of density, in terms of the dimensions of the fundamental units
of mass and length. Ifa substance is saidto have a unit density, then if M
were the gramme and L? the cubic centimetre, the density of the substance
would be that of water. If, however, M were the kilogramme and L* the
cubic ‘centimetre, the density would be a thousand times that of water.
If, again, L® represent a cubic decimetre, and M the kilogramme, the
density would again be that of water. It appears, then, that the magnitude
of the unit of density is directly proportional to the magnitude of the unit
of mass, and inversely as the magnitude of the unit of volume or the cube
of the unit of length. As unit density is the density of a unit mass for
unit volume, it is clear that Ts meneures the dimensions of the unit of density.
Similar explanations apply in the succeeding cases.
For velocity, v 2
ie ca
‘dep d bua tinged Vg
1a iee as
VU=.- = POA
-62] 5 ‘ystems of Units
The ratio T _second _ 1
IT’ minute 60.
49
If the units of time were the same, the unit factor ae I, and the velocity
in centimetres would be
oi Nes o)/
0 = Se,
where w” is the velocity in feet per second.
el
for Momentum, mv = my
mie MUL_m'l’ M’L’
find ees
or MU = gee mv"
pew BL BRR one
for Acceleration, a=—= ca
dem Wiles 231) PEN
eT Ce
LL cee
a= (7): 4
where a’ is the acceleration in feet per minute.
ml
For Porte, F =ma= a
mel ML_ ml Nis
Pp.) pe pe?
ML /T\2
poML M67
M~LOA\T
In the C.G.S. system the unit is called the Dye.
For Work, W=Fl= a
TON Par Yip rem es LL?
Pe Ty? Pee ee
In the C.G.S. system the unit of work is called the Erg.
Rate of Work, or Power, ea
Le ANG NY Ca St Bi
ge Te”
ae
If work is expressed in foot-pounds or kilogramme-metres, the unit of
E
50 On Matter, Force, and Motion [62-
force being the weight of a pound or kilogramme, then to convert a certain
number of foot-pounds into kilogramme-metres we have
21) WL =r Wwe
“W’
Work (kgr.-m) = = work, foot-pounds,
W aL
W*" pound 7
h =
wltere 7 alee: ee
Ly foo ee
L metre pede:
the unit factor being thus 0°1383.
Similarly, to convert foot-pounds per minute into kilogr.-metres per second,
aye gee”:
where the conversion factor becomes 0°00230.
The units commonly used for measuring the power of engines are the
horse-power, which is 33,000 times as great as the unit in which P’ of the
last equation was measured, and the force de cheval, which is 75 times as
great as the unit in which P was measured. Hence, if P’ is to be in horse-
power, and P in force de cheval, the equation will become
P =0:00230 x 33:09 py
75
= 1°O120gh
and hence one British horse-power = 1°0139 force de cheval.
These examples will be sufficient to indicate the method of converting
measurements from one system of units to any other, and the treatment of
other derived units may be deferred until they are needed.
63. Energy.—The fact that any agent is capable of doing work is usually
expressed by saying that it possesses Hvergy, and the quantity of energy it
possesses is measured by the amount of work it can do. For example, in
the case of the inclined plane above referred to, the working power or energy
of the force P is Px RS; and if this force acts under the conditions last
supposed, by the time its own energy is exhausted (in consequence of its
point of application having arrived at S, the limit of the range through which
it is supposed able to act), it has one upon the mass M a quantity of
energy equal to that which has been expended ; for, in the first place, M
has been raised through a vertical height equal to ST, and could by falling
again through the same height do an amount of work represented by W x ST ;
and in the second place M can do work by virtue of the velocity that has
been imparted to it, and can continue moving in opposition to any given
resistance R through a distance s, such that
Rs=4Mv.
The energy possessed by the mass M in consequence of its having been
raised from the ground is commonly distinguished as exergy of position or
potential energy, and is measured by the product of the force tending to cause
motion into the distance through which the point of application of the force
—65] Transformation of Energy 51
is capable of being displaced in the direction in which the force acts. The
energy possessed by a body in consequence of its velocity is commonly dis-
tinguished as energy of motion, or kinetic energy : it is measured by half the
product of the moving mass into the square of its velocity.
64. Varieties of energy.—On considering the definition of work given
above, it will be seen that a force is said to do work when it produces any
change in the condition of bodies ; for the only changes which, according to
the definition of force given previously (26), a force is capable of producing,
are changes in the state of rest or motion of bodies, and changes of their
place in opposition to resistances tending to prevent motion or to produce
motion in an opposite direction. There are, however, many other kinds of
physical changes which can be produced under appropriate conditions, and
the recent progress of investigation has shown that the conditions under
which changes of all kinds occur are so far analogous to those required for
the production of work by mechanical forces that the term work has come
to be used in a more extended sense than formerly, and is now often used to
signify the production of any sort of physical change.
Thus work is said to be done when a body at a low temperature is raised
to a higher temperature, just as much as when a weight is raised from a
lower to a higher level ; or, again, work is done when an electrical, magnetic,
or chemical change is produced. This extension of the meaning of the
term work involves a similar extension of the meaning of exergy, which in
this wider sense may be defined as the capacity for producing physical
change.
As examples of energy in this more general sense, the following may be
mentioned :—(a@) The energy possessed by gunpowder in virtue of the mutual
chemical affinities of its constituents, whereby it is capable of doing work by
generating heat or by acting on a cannon-ball so as to change its state of
rest into one of rapid motion ; (8) the energy of a charged Leyden jar, which,
according to the way in which the jar is discharged, can give rise to changes’
of temperature, to changes of chemical composition, to mechanical changes,
or to changes of magnetic or electrical condition ; (c) the energy of a red-hot
ball, which, amongst other effects it 1s capable of producing, can raise the
temperature and increase the volume of bodies colder than itself, or can
change ice into water or water into steam; the energy of the stretched
string of a bow: here work has been consumed in stretching the string ;
when it is released the work reappears in the velocity imparted to the
arrow.
65. Transformation of energy.—It has been found by experiment that
when one kind of energy disappears or 1s expended, energy of some other
kind is produced, and that, under proper conditions, the disappearance of
any one of the known kinds of energy can be made to give rise to a greater
or less amount of any other kind. One of the simplest illustrations that can
be given of this transformation of energy is afforded by the oscillations of a
pendulum. When the pendulum is at rest in its lowest position it does not
possess any energy, for it has no power of setting either itself or other bodies
in motion, or of producing in them any kind of change. In order to set the
pendulum oscillating, work must be done upon it, and it thereafter possesses
an amount of energy corresponding to the work that has been expended.
E 2
U. OF ILL, LIB.
52 On Matter, Force, and Moton [65—
When it has reached either end of its path, the pendulum is for an instant at
rest ; but it possesses energy by virtue of its position, and can do an amount of
work while falling to its lowest position, which is represented by the product
of its weight into the vertical height through which its centre of gravity de-
scends. When at the middle of its path, the pendulum is passing through its
position of equilibrium, and has no power of doing work by falling lower ; but
it now possesses energy by virtue of the velocity which it has gained, and
this energy is able to carry it up on the second side of its lowest position to
a height equal to that from which it has descended on the first side. By
the time it reaches this position the pendulum has lost all its velocity, but it
has regained the power of falling ; this, in its turn, is lost as the pendulum
returns again to its lowest position, but at the same time it regains its pre-
vious velocity. Thus, during every quarter of an oscillation the energy of
the pendulum changes from potential energy of position into actual energy
or energy of motion, or wice versa.
A more complex case of the transformation of energy is afforded by a
thermo-electric pile, the terminals of which are connected by a conducting
wire ; the application of energy in the form of heat to one face of the pile
gives rise to an electric current in the wire, which, in its turn, reproduces
heat, or by proper arrangements can be made to produce chemical, magnetic,
or mechanical effects, such as those described below in the chapters on
Electricity.
It has also been found that the transformations of energy always take
place according to fixed proportions. For instance, when coal or any other
combustible is burned, its chemical energy, or power of combining with
oxygen, vanishes, and heat or thermal energy is produced, and the quantity
of heat produced by the combustion of a given amount of coal is fixed and
invariable. If the combustion takes place under the boiler of a steam-engine,
mechanical work can be obtained by the expenditure of part of the heat pro-
duced, and here again the quantitative relation between the heat expended
and the work gained in place of it is perfectly constant.
66. Conservation of energy.—Another result of great importance, which
has been arrived at by experiment, is that the total amount of energy possessed
by any system of bodies is unaltered by any transformations arising from the
action of one part of the system upon another, and can only be increased or
diminished by effects produced on the system by external agents. In this
statement it is of course understood that in reckoning the sum of the energy
of various kinds which the system may possess, those amounts of the
different forms of energy which are mutually convertible into each other are
taken as being numerically equal; or, what comes virtually to the same
thing, the total energy of the system is supposed to be reduced—either ac-
tually, or by calculation from the known ratio of transformation of the various
forms of energy—to energy of some one kind ; then the statement is equivalent
to this: that the total energy of any one form to which the energy of a given
system of bodies is reducible is unalterable so long as the system is not acted
on from without. Practically it is always possible, in one way or another, to
convert the whole of the energy possessed by any body or system of bodies
into heat, but it cannot be all converted without loss into any other form of
energy ; hence the principle stated at the beginning of this article can be
66] Conservation of Energy eis:
enunciated in the closest conformity with the direct results of experiment by
saying that, so long as any system of bodies is not acted on from without,
the total quantity of heat that can be obtained from it is unalterable by any
changes which may go on within the system itself. Forinstance, a quantity
of air compressed into the reservoir of an air-gun possesses energy which is
represented partly by the heat which gives to it its actual temperature above
the absolute zero (508), and partly by the work which the air can do in expand-
ing. This latter portion can be converted into heat in various ways, as, for
example, by allowing the air to escape through a system of capillary tubes
so fine that the air issues from them without any sensible velocity ; if, how-
ever, the expanding air be employed to propel a bullet from the gun, it
produces considerably less heat than in the case previously supposed, the
deficiency being represented for a time by the energy of the moving bullet,
but reappearing in the form of heat in the friction of the bullet against the
air, and, when the motion of the bullet is destroyed, by striking against an
inelastic obstacle at the same level as the gun. But whatever the mode and
however numerous the intermediate steps by which the energy of the com-
pressed air is converted into heat, the total quantity of heat finally obtainable
from it is the same.
54 Gravitation and Molecular Attraction [67—
BOOK II
GRAVITATION AND MOLECULAR ATTRACTION
CHAPTER TI
GRAVITY. CENTRE OF GRAVITY. THE BALANCE
67. Universal attraction: its laws.—Universal attraction is a force in
virtue of which the material particles of all bodies tend incessantly to
approach each other ; it is an action, however, which all bodies, at rest or
in motion, exert upon one another, no matter how great or how small the
space between them may be, or whether this space be occupied or un-
occupied by other matter.
A vague hypothesis of the tendency of the matter of the earth and stars
o a common centre was adopted even by Democritus and Epicurus. Kepler
assumed the existence of a mutual attraction between the sun, the earth, and
the other planets. Bacon, Galileo, and Hooke also recognised the existence
of universal attraction. But Newton was the first who established the law,
and the universality of gravitation.
After Newton’s time the attraction of matter by matter was experimentally
established by Cavendish. This eminent English physicist succeeded, by
means of a delicate'torsion balance (90), in rendering visible the attraction
between a large leaden and a small copper ball.
The attraction between any two bodies is the resultant of the attractions.
of each molecule of the one upon every molecule of the other according to
the law of Newton, which may be thus expressed: the attraction between
two material particles ts directly proportional to the product of their masses
and invers:ly broportional to the square of their distances asunder. To
‘illustrate this, we may take the case of two spheres, which, owing to their
symmetry, attract each other just as if their masses were concentrated in
their centres. If without other alteration the mass of one sphere were
doubled, tripled, &c., the attraction between them would be doubled, tripled,
&c. If, however, the mass of one sphere being doubled, that of the other
were increased three times, the distance between their centres remaining the
same, the attraction would be increased six times. Lastly, if, without alter-
ing their masses, the distance between their centres were zzcreased from I
to 2,3,4.... units, the attraction would be azmznished to the 4th, oth,
—68] Lerrestrial Gravitation 55
16th .... part of its former intensity. In short, if we define the unit of
attraction as that which would exist between two units of mass whose
distance asunder was the unit of length, the attraction of two molecules
having the masses #7 and m’, at the distance 7, would be expressed by
mene’
68. Terrestrial gravitation—The tendency of any body to fall towards
the earth is due to the mutual attraction of that body and the earth, or to
terrestrial gravitation, and is, in fact, merely a particular case of universal
attraction.
At any point of the earth’s surface, the direction of gravity—that is, the
line which a falling body describes—is called the ver¢zcal line. The vertical
lines drawn at different points of the earth’s surface converge very nearly to
the earth’s centre. For points situated on the same meridian the angle con-
tained between the vertical lines equals the difference between the latitudes
of those points.
The directions of the earth’s attraction upon neighbouring bodies, or upon
different molecules of one and the same body, must| therefore be considered
as parallel, for the two vertical lines form the sides of a triangle whose vertex
is near the earth’s centre, about 4,000 miles distant, and whose base is the
small distance between the molecules under consideration.
A plane or line is said to be horizontal when it 1s perpendicular to the
vertical line.
The vertical line at any point of the globe is generally Herermined by the
plumb-line (fig. 41), which consists of a weight attached to the end of a string.
It is evident that the weight cannot be in equilibrium
unless the direction of the earth’s attraction upon it
passes through the point of support, and therefore co-
incides with that of the string.
The horizontal plane is also determined with creat
ease, since it coincides, as will be afterwards shown, an
the /eve/ surface of every liquid when in a state of equili-
brium.
When the mean figure of the earth has been approxi-
mately determined, it becomes possible to compare the
direction of the plumb-line at any place with that of the
normal to the mean figure at that place. When any differ-
ence in these directions can be detected, it constitutes a
deviation of the plumb-line, and is due to the attraction of
some great mass of matter in the neighbourhood, such as
a mountain. Thus, in the case of the mountain of Schiehallion, in Perthshire,
it was found by Dr. Maskelyne that the angle between the directions of two
plumb-lines, one at a station to the north, and the other to the south, of the
mountain was greater by 11/6 than the angle between the normals of the
mean surface of the earth at those points ; in other words, each plumb-line
was deflected by about 6” towards the mountain. By calculating the volume
and mass of the mountain, it was inferred from this observation that the
mean density of the mountain was to that of the earth in the ratio of 5:9,
and that the mean density of the earth is about five times that of water—a
Ang
ANNI
Cf:
Fig. 41
56 Gravitation and Molecular Attraction [68—
result agreeing pretty closely with that deduced from Cavendish’s experi-
ment referred to in the last article.
69. Centre of gravity; its experimental determination.—Into what-
ever position a body may be turned with respect to the earth, there is a
certain point invariably situated with respect to the body, through which
the resultant of the attracting forces between the earth and its several mole-
cules always passes. This point is called the centre of gravity ; it may be
within or without the body, according to the form of the latter ; its existence,
however, is easily established by the following considerations : let 77 72’ m2’’
m’”’’. ... (fig. 42) be molecules of any body. The earth’s attraction upon
these molecules wlll constitute a system of parallel forces, having a common
vertical direction, whose resultant will be found by seeking first the resultant
of the forces which act on any two molecules, 7#z and 7’, then that of this
resultant and a third force acting on m’’, and so on until we arrive at the
final resultant W, representing the weight of the body and applied ata
certain point G. If the body be now turned into the position shown in
fig. 43, the molecules 7 m’ m’’. . . . will continue to be acted on by the
Ee eee
a=
---- -
Fig. 42
same forces as before, the resultant of the forces on 7 and wm’ will pass
through the same point o in the line mz’, the following resultant will again
- pass through the same point o’ in o72’’, and so on up to the final resultant
P, which will still pass through the same point C, which is the centre of
gravity.
To find the centre of gravity of a body is a purely geometrical problem ;
in many cases, however, it can be at once determined. For instance, the
centre of gravity of a right line of uniform density is the point which bisects
its length ; in the circle and sphere it coincides with the geometrical centre ;
in cylindrical bars it is the middle point of the axis. The centre of gravity
of a plane triangle is in the line which joins any vertex with the middle of
the opposite side, and at a distance from the vertex equal to two-thirds of
this line : in a cone or pyramid it is in the line which joins the vertex with
the centre of gravity of the base, and at a distance from the vertex equal to
three-fourths of this line. These rules, it must be remembered, presuppose
that the several bodies are of uniform density.
In order to determine experimentally the centre of gravity of a body, it
is suspended by a string in two different positions, as shown in figs. 44 and
45; the point where the directions AB and CD of the string in the two
—71] Different States of Equitibrium 57
experiments intersect each other is the centre of gravity required. For, the
resultant of the earth’s attraction being a vertical force applied at the centre
of gravity, the body can only be in equilibrium when the point lies vertically
under the point of suspension ; that is, in the prolongation of the suspended
string. But the centre of gravity,
being in AB as well as in CD, must
coincide with the point of intersec-
tion of these two lines.
The centre of gravity of a thin
piece of cardboard of irregular
shape, for instance, may be found
by balancing it in two positions on
a knife-edge ; the centre of gravity
will then lie in the intersection of
the two lines.
70. Equilibrium of heavy
bodies. —Since the action of gravity H
upon a body reduces itself to a
single vertical force applied at the
centre of gravity and directed to-
wards the earth’s centre, equili-
brium will be established only when this resultant is balanced by the
resultant of other forces and resistances acting on the body at the fixed point
through which it passes.
When only one point of the body is fixed, it will be in equilibrium if the
vertical line through its centre of gravity passes through the fixed point. If
more than one point is supported, the body will be in equilibrium if a vertical
line, through the centre of gravity, passes through a point within the polygon
formed by joining the points of support.
The Leaning Tower of Pisa continues to stand because the vertical line
drawn through its centre of gravity passes within its base.
It is easier to stand on our feet than on stilts, because in the latter case
the smallest motion is sufficient to cause the vertical line through the centre
of gravity of our bodies to pass outside the supporting base, which is here
reduced to a mere line joining the feet of the stilts. A man carrying a load
on his back must lean forward : if he carries it in the left hand he must incline
the upper part of his body to the right, for otherwise the centre of gravity of
the body and of the load would fall outside the line joining the feet and he
would fall. Again, it is impossible to stand on one leg if we keep one side
of the foot and head close to a vertical wall, because the latter prevents
us from throwing the body’s centre of gravity vertically above the supporting
base.
71. Different states of equilibrium.—Although a body supported by a
fixed point is in equilibrium whenever its centre of gravity is in the vertical
line through that point, the fact that the centre of gravity tends, incessantly
to occupy the lowest possible position leads us to distinguish between three
states of equilibrium—s/able, unstable, neutral.
A body is said to be in stadle equilibrium if it tends to return to its first
position after the equilibrium has been slightly disturbed. Every body is in
58 Gravitation and Molecular Attraction [71-
this state when its position is such that the slightest alteration of the same
elevates its centre of gravity; for the centre of gravity will descend again
when permitted, and after a few oscillations the body will return to its
original position.
The pendulum of a clock continually oscillates about its position of stable
equilibrium, and an egg on a level table is in this state when its long axis
is horizontal. We have another illustration in the
toy represented in the adjoining fig. 46. A small
figure cut in ivory is made to stand on one foot at the
top of a pedestal by being loaded with two leaden balls,
a, 6, placed sufficiently low to throw the centre of
gravity g of the whole compound body below the foot
of the figure. After being disturbed, the little figure
oscillates like a pendulum, having its point of sus-
pension at the toe, and its centre of gravity at a lower
point, &
A body is said to be in wsstable equilibrium when,
after the slightest disturbance, it tends to depart still
more from its original position. A body is in this state
when its centre of gravity is vertically above the point
of support, or higher than it would be in any adjacent
position of the body. An egg standing on its end, or
a stick balanced upright on the finger, is in this state.
Lastly, if in any adjacent position a body still remains in equilibrium,
its state of equilibrium is said to be zeztral or labile. In this case an altera-
tion in the position of the body neither raises nor lowers its centre of gravity.
A perfect sphere resting on a horizontal plane is in this state.
Fig. 47 represents three cones, A, B, C, placed respectively in stable,
unstable, and neutral equilibrium upon a horizontal plane. The letter g in
each shows the position
of the centre of gravity.
72. The balance.—
The balance is an in-
strument for determin-
ing the relative weights
or masses of bodies.
There are many varie-
ties.
The ordinary balance (fig. 48) consists of a lever of the first kind, called
the deam, AB, with its fulcrum in the middle ; at the extremities of the beam
are suspended two scale-pans, C and D, one intended to receive the object
to be weighed, and the other the counterpoise. The fulcrum consists of a
steel prism, 7, commonly called a kvzfe-edge, which passes through the beam,
and rests with its sharp edge, or axzs of susfenston, upon two supports ; these
are formed of agate, in order to diminish the friction. A needle or pointer
is fixed to the beam, and oscillates with it in front of a graduated arc, a:
when the beam is perfectly horizontal the needle points to the zero of the
graduated arc (fig. 51).
Since by (40) two equal forces in a lever of the first kind cannot be in
—73] Conditions to be satisfied by a Balance 59
equilibrium unless their leverages are equal, the length of the arms 7A and
2B ought to remain equal during the process of weighing. To secure this
the scales are suspended from hooks, whose curved parts have sharp edges,
ard rest on similar edges at the ends of the beam. In this manner the
scales are in effect supported on mere points, which remain unmoved during
the oscillations of the beam. This mode of suspension is represented in
fig. 48.
73. Conditions to be satisfied by a balance.—A good balance ought to
satisfy the following conditions :—
1. The two arms of the beam ought to be precisely equal; otherwise,
according to the principle of the lever, unequal weights will be required to
produce equilibrium. To test whether the arms of the beam are equal,
AU SYTAANYVANEETGDETUUTATVIUU TOMTOM SE HA AAA TO OT
Fig. 48
weights are placed in the two scales, until the beam becomes horizontal ;
the contents of the scales being then interchanged, the beam will remain
horizontal if its arms are equal, but if not, it will descend on the side of the
longer arm.
u. Lhe balance ought to be in equilibrium when the scales are empty, for
otherwise unequal weights must be placed in the scales in order to produce
equilibrium. It must be borne in mind, however, that the arms are not
necessarily equal, even if the beam remains horizontal when the scales are
empty ; for this result might also be produced by giving to the longer arm
the lighter scale.
ili. The beam being horizontal, its centre of gravity ought to be in the
same vertical line with the edge of the fulcrum, and a little below the latter,
for otherwise the beam would not be in stable equilibrium (71).
60 Gravitation and Molecular Attraction [73-
The effect of changing the position of the centre of gravity may be shown
by means of a beam (fig. 49), whose fulcrum, being the nut of a screw, a, can
be raised or lowered by turning the screw head, 0.
When the fulcrum is at the top of the groove c, in which it slides, the
centre of gravity of the beam is below its edge, and the latter oscillates
freely about a position of stable equilibrium. By gradually lowering the
fulcrum its edge may be made to pass through the centre of gravity of the
beam when the latter is in neutral equilibrium ; that is to say, it no longer
oscillates, but remains in equilibrium in all positions. When the fulcrum
is lowered still more, the centre of gravity passes above its edge, the
beam is in a state of unstable equilibrium, and is overturned by the least
displacement.
74. Delicacy of the balance.—A balance is said to be delicate or sensible
when a very small difference between the weights in the scales causes a per-
ceptible deflection of the pointer.
Let A and B (figs. 50 and 51) be the point from which the scale-pans
are suspended, and C the axis of suspension of the beam. A, B, and C are
assumed to be in the same straight line, according to the usual arrangement.
Suppose weights P and Q to be in the pans, suspended from A and B re-
spectively, and let G be the centre of gravity of the beam ; then the beam
will come to rest in the position shown in the figure, where the line DCN is
vertical, and ECG is the direction of the pointer. According to the above
statement, the greater the angle ECD for a given difference between P and
Q, the greater is the sensibility of the balance. Draw GN at right angles to
CG:
Let W be the weight of the beam ; then from the properties of the lever (40)
it follows that measuring moments with respect to C, the moment of P equals
the sum of the moments of Q and W—a condition which at once leads to the
relation
(P—OQ)AC=WxGN.
-75] Physical and Chemical Balances OI
e
Now it is clear that fora given value of CG the angle GCN (that is, ECD,
which measures the delicacy) is greater as GN is greater; and from the
formula it is clear that for a given value of P—Q we shall have GN greater
as AC is greater, and as W is less. Again, for a given value of GN the
angle GCN is greater as GC is less. Hence the means of rendering a
balance delicate are—
i. Zo make the arms of the balance long.
u. Zo make the weight of the beam as small as ts consistent with its
rigidity.
ii. Zo bring the centre of gravity of the beam a very little below the point
of support.
Moreover, since friction will always oppose the action of the force that
tends to preponderate, the balance will be rendered more delicate by diminish-
ing friction. To secure this advantage, the edges from which the beam and
scales are suspended are made as sharp and as hard as possible, and the
supports on which they rest are very smooth and hard. This is effected by
the use of agate knife-edges. And, further, the pointer is made long, since
its elongation renders a given deflection more perceptible by increasing the
arc which its end describes.
The sensitiveness of a balance is expressed by the ratio of the smallest
weight, which will produce a measurable deflection of the pointer, to the load.
75. Physical and chemical balances.—Fig. 52 represents one of the
accurate balances ordinarily used for chemical analysis. Its sensitiveness is
ir TMT Tm TTT
ATTN TT
Tui AAA rE
such that when charged with a kilogramme (1,000 grms.) in each scale an
excess of a tenth of a milligramme (z5455 of a grm.)in either scale produces
a very perceptible deflection of the index.
62 Gravitation and Molecular Attraction [75-
+
In order to protect the balance from air currents, dust, and moisture,
it is always, even when weighing, surrounded by a glass case, whose front
slides up and down, to enable the operator to introduce the objects to be
weighed. Where extreme accuracy is desired the case is constructed so
that the space may be exhausted, and the weighing made zz vacuo.
In order to preserve the edge of the fulcrum as much as possible, the
whole beam, BB, with its fulcrum K, can be raised from the support on
which the latter rests by simply turning the button O outside the case.
The horizontality of the beam is determined by means of a long index,
which points downwards to a graduated arc near the foot of the supporting
pillar. Lastly, the button C serves to alter the sensitiveness of the balance ;
by turning it, the centre of gravity of the beam can be made to approach or
recede from the fulcrum (73).
76. Method of double weighing.—Even if a balance be not perfectly
accurate, the true weight of a body may still be determined by its means. To
do so, the body to be weighed is placed in one
scale, and shot or sand poured into the other until
equilibrium is produced ; the body is then replaced
by known weights until equilibrium is re-esta-
blished. The sum of these weights will neces-
sarily be equal to the weight of the body, for, acting
under precisely the same circumstances, both have
produced precisely the same effect.
The exact weight of a body may also be deter-
mined by placing it successively in the two pans of
a balance, and then deducing its true weight.
For having~placed in one pan the body to be
weighed, whose true weight is #, and in the other
the weight Z, required to balance it, let a and 6
be the arms of levers corresponding to x and 7.
Then from the principle of the lever (40) we have
ax=pb. Similarly, if , is the weight when the body
is placed in the other pan, then dx=af,. Hence
abs =abpp,, from which x=,/ff,. This method
was invented by Pére Amiot, but is ordinarily
known as Borda's Method.
Jolly made use of a very sensible balance to
determine the constant of gravity. The balance
(fig. 53) was placed in a room in the tower of the
University of Miinich, and to each of the scale-pans
was attached, by a wire 21 metres in length, a second
scale-pan. A mass of mercury of 5 kilogrammes
contained in a glass vessel was first counterpoised
in the upper scale-pan ; it was then moved to the
lower one, and it was found necessary to add
31°683 mgr. to the upper pan in order to counterbalance the increase in
attractiveness due to the greater force in the lower pan.
Taking the radius of the earth at Munich at 6,365,722 metres, the number
—76] Method of Double Weighing 63
calculated from the formula in (83) is 33 mgr.; a sufficiently close result
when the difficulties of the experiments are taken into account.
A large lead sphere was then placed immediately below the mass in the
lower pan, and produced a measurable attraction. From the attraction thus
produced by the known mass of the lead it was possible to deduce the
mass and the mean density of the earth (68); the number obtained was
5°69. Similar experiments made by Prof. Poynting have led to the number
5°5:
64.
LAWS OF
Gravitation and Molecular Attraction [77-
CHAPTER
FALLING BODIES. INTENSITY OF TERRESTRIAL GRAVITY.
THE PENDULUM
77. Laws of falling bodies.—Since a _ body
falls to the ground in consequence of the earth’s
attraction on each of its molecules, it follows that,
everything else being the same, all bodies, great
and small, light and heavy, ought to fall with equal
rapidity, and a lump of sand without cohesion should
during its fall retain its original form as perfectly
as if it were compact stone. The fact that a stone
falls more rapidly than a feather is due solely to the
unequal resistances opposed by the air to the descent
of these bodies ; 27 a vacuum all bodies fall with
equal rapidity. To demonstrate this, by experiment
a glass tube about two yards long (fig. 54) may be
taken, having one of its ends completely closed,
and a brass cock fixed to the other. After having
introduced bodies of different weights and densities
(pieces of lead, paper, feathers, &c.) into the tube,
the air is withdrawn from it by an air-pump, and
the cock closed. If the tube be now suddenly re-
versed, all the bodies will fall equally quickly. On
introducing a little air and again inverting the tube,
the lighter bodies become slightly retarded, and
this retardation increases with the quantity of air
introduced.
The resistance opposed by the air to falling
bodies is especially remarkable in the case of
liquids. The Staubbach in Switzerland is a good
illustration ; an immense mass of water is seen fall-
ing over a high precipice, but before reaching the
bottom it is shattered by the air into the finest
mist. In a vacuum, however, liquids fall lke
solids without separation of their molecules. The
water-hammer illustrates this : the instrument con-
sists of a thick glass tube about a foot long, half
filled with water, the air having been expelled by
ebullition previous to closing one extremity with the
blowpipe. When such a tube is suddenly inverted,
the water falls in one undivided mass against the
~78] Atwood’s Machine 65
other extremity of the tube, and produces a sharp dry sound, resembling that
which accompanies the shock of two solid bodies.
From Newton’s law (67) it
follows that when a body falls
- to the earth the force of attrac-
tion which causes it to do
so increases as the body ap-
proaches the earth. Unless the
height from which the body
falls, however, be very great,
this increase will be altogether
inappreciable, and the force in
question may be considered as
constant and continuous. If
the resistance of the air were
removed, therefore, the motion
of all bodies falling to the earth
would be uniformly accelerated,
and would obey the laws already
explained (49).
78. Atwood’s machine.—
Severa! instruments have been
invented for illustrating and
experimentally verifying the
laws of falling bodies. Galileo,
who discovered these laws in
the early part of the seven-
teenth century, illustrated them
by means of bodies falling down
inclined planes. The great
object of all such instruments
is to diminish the rapidity of
the fall of bodies without
altering the character of their
motion, for by this means
their motion may not only be
_ better observed, but it will be
less modified by the resistance
of the air (48).
The most convenient instru-
ment of this kind is that invented
by Atwood at the end of the
last century, and represented in
fig. 55. It consists of a stout
pillar of wood, about 2} yards
high, at the top of which is a
brass pulley, whose axlerests and
turns upon four other wheels, called /r¢ctton wheels, inasmuch as they serve
to diminish friction. Two equal weights M and M’, are attached to the
F
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mya
X
a
|
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AN
i Alina
me ( i
i
||
Sena rani ana
Se ik
= UII =
“i
Teasers
ee ETE ST
Ernepoer eee
PRuEnp rnp SEPT j pay
Fo epee
(oe
66 Gravitation and Molecular Attractton [78-
extremities of a fine silk thread, which passes round the pulley ; a timepiece,
H, fixed to the pillar, is regulated by a seconds pendulum, P, in the usual
way ; that is to say, the oscillations of the pendulum are communicated to a
ratchet, whose two teeth, as seen in the figure, fit into those of the ratchet
wheel. The axle of this wheel gives motion tothe seconds hand of the dial,
and also to an eccentric behind the dial, as shown at E bya separate figure.
This eccentric plays against the extremity of a lever, D, which it pushes
until the latter no longer supports the small plate z; and thus the weight M,
which at first rested on this plate, is suddenly exposed to the free action of
gravity. The eccentric is so constructed that the little plate z falls precisely
when the hand of the dial points to zero.
The weights M and M’, being equal, hold each other in equilibrium ;
the weight M, however, is made to descend slowly by putting a small bar or
overweight 7z upon it ; and, to measure the spaces which it describes, the rod
or scale Q is divided into feet and inches, commencing from the plate z.
To complete the instrument there are a number of plates, A, A’, C, C’, and
a number of rings, B, B’, which may be fixed by screws at any part of the
scale. The plates arrest the descending weight M, the rings only arrest the
bar or overweight 77, which was the cause of motion, so that after passing
through them the weight M, in consequence of its inertia, will move on
uniformly with the velocity it had acquired on reaching the ring. The
several parts of the apparatus being described, a few words will suffice to
explain the method of experimenting.
Let the hand of the dial be placed behind the zero point, the lever D
adjusted to support the plate z, on which the weight M with its overweight
m rests, and the pendulum put in motion.. As soon as the hand of the dial
points to zero, the plate z will fall, the weights M and wz will descend, and by
a little attention and a few trials it will be easy to place a plate A so that M
may reach it exactly as the dial indicates the expiration of one second. To
make a second experiment let the weights M and 7, the plate z, and the
lever D be placed as at first ; remove the plate A, and in its place put aring,
B, so as to arrest the overweight 7 just when the weight M would have
reached A ; on putting the pendulum in motion again it will be easy, after a
few trials, to put a plate, C, so that the weight M may fall upon it precisely
when the hands of the dial point to two seconds. Since the overweight
in this experiment was arrested by the ring B at the expiration of one second,
the space BC was described by M in one second purely in virtue of its own
inertia, and consequently by (29). BC will indicate the velocity of the falling
mass at the expiration of one second.
Proceeding in the same manner as before, let a third experiment be made
in order to ascertain the point B’ at which the weights M and w arrive after
the lapse of two seconds, and putting a ring at B’, ascertain by a fourth
experiment the point C’ at which M arrives alone, three seconds after the
descent commenced ; B’C’ will then express the velocity acquired after a
descent of twoseconds. Ina similar manner, by a fifth and sixth experiment,
‘we may determine the space OB” described in three seconds, and the velo-
city B’C’” acquired during those three seconds, and so on; we shall find
that B’C’ is twice and B”’C” three times as great as BC—in other words,
that the velocities BC, B’C’, B’C” increase in the same proportion as the
~79] | Morin’s Apparatus a7
times (I, 2, 3, . . . seconds) employed in their acquirement. By the defi-
nition (49), therefore, the motion is uniformly accelerated. The same ex-
periments will also serve to verify and illustrate the four laws of uniformly
accelerated motion as enunciated in (49). For example, the spaces OB,
Of OB. 0 say.described froma, state of rest. in)J, 2,,3,.-, ...-..seconds,
will be found to be proportional to the numbers I, 4,9 ...; that is to say,
to the squares of those numbers of seconds, as stated in the third law.
Lastly, if the overweight 7z be changed, the acceleration or velocity BC
acquired per second will also be changed, and we may easily verify the
assertion in (27), that force is proportional to the product of the mass moved,
into the acceleration produced in a given time. For instance, assuming the
pulley to be so light that its inertia can be neglected, then if #z weighed half
an ounce, and M and M’ each 153 ounces, the acceleration BC would be found
to be six inches ; whilst.if #z weighed one ounce, and M and M’ each 633
ounces, the acceleration BC would be found to be three inches.
Now in these cases the forces producing motion, that is the overweights,
are in the ratio of 1:2; while the products of the masses and the accelera-
tions are in the ratio of ($+ 153+15%) x 6 to (1 + 634 + 634) x 3; that is, they
are also in the ratio 1:2. Now the same result is obtained in whatever
way the magnitudes of #, M, and M’ are varied, and consequently in all
cases the ratio of the forces producing motion equals the ratio of the mo-
menta generated.
79. Morin’s apparatus.—The principle of this apparatus, the original
idea of which is due to General Poncelet, is to make the falling body trace
its own path. Fig. 56 gives a view of the whole apparatus, and fig. 57
gives the details. The apparatus consists of a wooden framework, about
7 feet high, which holds in a vertical position a very light wooden cylinder,
M, which can turn freely about its axis. This cylinder is coated with
paper divided into squares by equidistant horizontal and vertical lines. The
latter measure the path traversed by the body falling along the cylinder,
while the horizontal lines are intended to divide the duration of the fall into
equal parts.
The falling body is a mass of iron, P, provided with a pencil, which is
pressed against the paper by a small spring. The iron is guided in its fall
by two light iron wires which pass through guide-holes on the two sides.
The top of this mass is provided with a tipper which catches against the end
of a bent lever, AC. This being pulled by the string K attached at A, the
weight falls. Ifthe cylinder M were fixed, the pencil would trace a Straight
line on it; but if the cylinder moves uniformly, the pencil traces the line
mn, which serves to deduce the law of the fall.
The cylinder is rotated by means of a weight, Q, suspended to a cord
which passes round the axle G. At the end of this are two toothed wheels,
c and 9, which turn two endless screws, a and 4, one’ of which turns the
cylinder, and the other two vanes, + and x’ (fig. 57). At the other end is a
ratchet wheel, in which fits the aa of a lever, B ; by pulling at a cord fixed
to the other end of B, the wheel is liberated, the weight Q descends, and the
whole system begins to turn. The motion ig at first accelerated, but as the
air offers a resistance to the vanes (48), which increases as the rotation
becomes more rapid, the resistance finally equals the acceleration which
F 2
68 Gravitation and Molecular Attraction [79—
gravity tends to impart. From this time the motion becomes uniform. This
is the case when the weight Q has traversed about three-quarters of its
course ; at this moment the weight P is detached by pulling the cord K, and
the pencil then traces the curve 777.
If, by means of this curve, we examine the double motion of the pencil
on the small squares which divide the paper, we see that for displacements
Oi:
i
a
mi) Eats
in
—=—=
SSS
—— :
Fig. 56
I, 2,3... in a horizontal direction, the displacemeénts are 1,4,9 4.5 ~= 5
in a vertical direction. This shows that the paths traversed in the direction
of the fall are directly as the squares of the lines in the direction of the
rotation, which verifies the second law of falling bodies.
From the relation which exists between the two dimensions of the curve
wn, it is concluded that this curve is a parabola (51).
—80] The Length of the Compound Pendulum 69
8o. The length of the compound pendulum.—The formula deduced in
article (55), and the conclusions which follow therefrom, refer to the case of
the simple or mathematical pendulum; that is, to a single heavy point
suspended by a thread without weight. Such a pendulum has only an
imaginary existence, and any pendulum which does not realise these con-
ditions is called a compound or physical pendulum. The laws for the time
of vibration of a compound pendulum are the same as those for the motion
of the simple pendulum, though it will be necessary to define accurately
what is meant by the /eneth of such a pendulum. A compound pendulum
being formed of a heavy rod terminated by a greater or less mass, it follows
that the several material points of the whole system will strive
to perform their oscillations in different times, their distances
from the axis of suspension being different, and the more distant
points requiring a longer time to complete an oscillation. From
this, and from the fact that being points of the same body they
must all oscillate together, it follows that the motion of the
points near the axis of suspension will be retarded, whilst that
of the more distant points will be accelerated, and between the
two extremities there will necessarily be a series of points whose
motion will be neither accelerated nor retarded, but which will
oscillate precisely as if they were perfectly free and unconnected
with the other points of the system. These points, being equi-
distant from the axis of suspension, constitute a parallel axis
known as the axzs of oscillation ; and it is to the distance be-
tween these two axes that the term length of the compound pen-
dulum is applied: we may say, therefore, that the length of a
compound pendulum ts that of the simple pendulum which would
describe tts oscillations in the same time.
Huyghens, the celebrated Dutch physicist, discovered that the
axes of suspension and oscillation are mutually convertible ;
that is to say, the time of oscillation will remain unaltered when
the pendulum is suspended from its axis of oscillation. This
enables us to determine experimentally the length of the com-
pound pendulum. For this purpose the reversible pendulum
devised by Bohnenberger and Kater may be used. One form of
this (fig. 58) is a rod with the knife-edges a and 6 turned towards
each other. W and V are lens-shaped masses the relative posi-
tions of which may be varied. By a series of trials a position
can be found such that the number of oscillations of the pemdu-
lum in a given time is the same whether it oscillates about the
axis @ or the axis 6. This being so, the distance aé represents
the length 7 of a simple pendulum which has the same time of
oscillation. From the value of /, thus obtained, it is easy to
determine the length of the seconds pendulum.
The length of the seconds pendulum—that is to say, of the pendulum
which makes one oscillation in a second—varies, of course, with the
force of gravity. The following table gives its value at the sea-level at
various places as determined by observation. The accelerative effect of
gravity at these places, according to formula (55). is obtained in feet and
70 Gravitation and Molecular Attraction [80—
metres, by multiplying the length of the seconds pendulum, reduced to feet
and metres respectively, by the square of 3°14159 or 9°8696.
| Acceleration of Gravity in :
; | Length of Pen- | ms 4
| Latitude = qulumininches ]
| | Feet Metres
| Hammerfest . S| 70" AO Nes 80 1040. a mann cea 50d 9°8258
| Aberdeen : , 57°9 Pm) Sor 55a" ) 432-3000 9°8164
_K6nigsberg . : 54°42 39°1507. | 32°2002 oSi42
_Manchester . bi hice) 39°1466 32°1968 9°8134 |
Dublin . : Tie At |. 39°1461 32°1963 yu) oSIsae a
| Berlin: -. : ; 52°30 | 39°1439 32°1945 9°8124
| Greenwich : : 51°29 eeO 1306 32°19012 g°8115
Paris : : . | 48°50 |. 207285 32°1819 9°8039
| Rome, . : eA TS 4 39° L145 | Wl. 32ye3 9°8053
New York : GAS 301012 | |) 32°) 504uuae 070010
Washington . ao 54 29°090S 4 321k So 9°8006
| Madras . arr SA 39°02608. 1’ 2°32°0082 "ENG 7530
Ascension ¢ Sn) Fats 39°0242 | 32°0961 9°7817
St homas) ir é O'25 43970207 A005 maz ORs 9°7826
Cape of Good Hope | 33°55S. | 39:0780 | 3271404 | 9°7962 -
Consequently, 4g or the space described in the first second of its motion
by a body falling zz vacuo from a state of rest (49) is
16'0466 feet or 4°891 metres at St. Thomas,
TO'00560) 4. 4514005 tay re eOnUOn cane
LO711827,, 05, 2018 we cate aminerics..
In all calculations, which are merely used for the sake of illustration, we
may take 32 feet, or 9°38 metres, as the accelerative effect due to gravity.
The metre (22) and the seconds pendulum differ in length at Greenwich,
by less than a quarter of an inch.
From observations with the pendulum, after applying the necessary
corrections, and taking into account the effect of rotation (83), the form of the
earth ‘can be deduced.
81. Verification of the laws of the pendulum.—In order to verify the laws
of the.simple pendulum (55) we are compelled to employ a compound one,
whose construction differs as little as possible from that of the former. For
this purpose a small sphere of a very dense substance, such as lead or
platinum, is suspended from a fixed point by means of a very fine metal wire.
A pendulum thus formed oscillates almost like a simple pendulum, whose
length is equal to the distance of the centre of the sphere from the point of
suspension.
In order to verify the isochronism of small oscillations, it is merely necessary
to count the number of oscillations made in equal times, as the amplitudes of
these oscillations diminish from 3 degrees to a fraction of a degree ; this
number is found to be constant.
That the time of vibration is proportional to the square root of the length
is verified by causing pendulums, whose lengths are as the numbers I, 4,
—82] Application of the Pendulum to Clocks. 71
9,.... to oscillate simultaneously. The corresponding numbers of oscil-
lations in a given time are then found to be proportional to the fractions
1, 3, 4, &c., . . . . which shows that the times of oscillation increase as the
Dim Weyvont. 2,93, tees ee:
By taking several pendulums of exactly equal length, B, C, D (fig 59),
but with spheres of different substances—lead, copper, ivory—it is found
that, neglecting the resistance of the air, these
pendulums oscillate in equal times, thereby show- :
ing that the accelerative effect of gravity on all (rt
bodies is the same at the same place. /
By means of an arrangement resembling the |
above, Newton verified the fact that the asses i
of bodies are determined by the balance; which, : Pe
it will be remarked, lies at the foundation of the |
measure of force (28). For it will be seen on /
comparing (54) and (55) with (49) that the law of |
the time of a small oscillation is obtained on the I
supposition that the force of gravity on all bodies |
is represented by Mg, in which M is determined
by the balance. In order to verify this, he had i
two round equal wooden boxes made ; one he i
filled with wood, and as nearly as possible in the |
centre of oscillation of the other he placed an |
equal weight of gold. He then suspended the j
boxes by threads eleven feet Jong, so that they
formed pendulums exactly equal so far as weight,
figure, and resistance of the air were concerned.
Their oscillations were performed in exactly the
same time. The same results were obtained
when other substances were used, such as silver,
lead, glass, sand, salt, wood, water, corn. Now Fig. 59
all these bodies had equal weights, and, being contained in the same boxes
they experienced the same resistance by the air, and if the inference that
therefore they had equal masses had been erroneous, by as little as the one-
thousandth part of the whole, the experiment would have detected it.
82. Application of the pendulum to clocks.—The regulation of the motion
of clocks is effected by means of pendulums, that of watches by dalance-
springs. Pendulums were first applied to this purpose by Huyghens in
1658, and in the same year Flooke applied a spiral spring to the balance of
a watch. The manner of employing the pendulum is shown in fig. 60.
The pendulum rod passing between the prongs of a fork, 2, communicates
its motion to a rod, 4, which oscillates on a horizontal axis, 0. To this axis
is fixed a piece, 727, called an escapement or crutch, terminated by two pro-
jections or fallefs, which work alternately with the teeth of the escadement
wheel R. This wheel being acted on by the weight tends to move con-
tinuously, let us say, in the direction indicated by the arrow-head. Now, if
the pendulum is at rest, the wheel is held at rest by the pallet 7, and with it
the whole of the clockwork and the weight. If, however, the pendulum
moves and takes the position shown by the dotted line wz is raised the
72 Gravitation and Molecular Attraction [82—
wheel escafes from the confinement in which it was held by the pallet, the
weight descends, and causes the wheel to turn until its motion is arrested by
the other pallet 7 ; which, in consequence of the motion of the pendulum,
will be brought into contact with another tooth of the
escapement wheel. In this manner the descent of the
weight is alternately permitted and arrested—or, in a
word, regulated—by the pendulum. By means of a
proper train of wheelwork the motion of the escape-
ment is communicated to the hands of the clock ; and
consequently their motion, also, is regulated by the
pendulum. In watches the watch-spring plays the
part of the weight in clocks.
The pendulum has also been used for measuring
great velocities. A large wooden box filled with sand
and weighing from 3 to 5 tons is coated with iron ;
against this arrangement, which is known as a daldistic
pendulum, a shot is fired, and the deflection thereby
produced is observed. From the laws of the impact
of inelastic bodies, and from those of the pendulum,
the velocity of the ball may be calculated from the -
amount of this deflection.
The gun may also be fastened to a pendulum
arrangement ; and, when fired, the reaction causes an
angular deflection, from which the pressure of the en-
closed gases can be deduced, and therefrom the initial
velocity of the shot.
An interesting application of the pendulum is to
the metronome, which consists of a short rod witha
fixed bob ; on the rod and above the axis is a sliding
weight. By raising this the rate of the pendulum is
Fig. 60 _ lengthened ; by lowering it accelerated ; and thus even
with a short pendulum the beats can be made pretty
long. Maelzel connected this with a clockwork arrangement so that the
beats are quite audible.
83. Causes which modify the intensity of terrestrial gravitation.—The
intensity of the force of gravity—-that is, the value of g—is not the same in
all parts of the earth. It is modified by several causes, of which the form.of
the earth and its rotation are the most important.
i. The attraction which the earth exerts upon a body at its surface is the
sum of the partial attractions which each part of the earth exerts upon that
body, and the resultant of all these attractions may be considered to act from
a single point—the centre. Hence, if the earth were a perfect sphere, a given
body would be equally attracted at any part of the earth’s surface. The
attraction would, however, vary with the height above the surface. For small
alterations of level the differences would be inappreciable ; but for greater
heights and in accurate measurements observations of the value of g must
be reduced to the sea-level. The attraction of gravitation being inversely
as the square of the distance from the centre (67), we shall have
—83] Causes which modify Terrestrial Gravitation 73
Peg = : EP where g 1s the value of the acceleration of gravity at
the sea-level, ¢, its value at any height Z, and R is the radius of the earth.
From this, seeing that / is very small compared with R, and that therefore
its square may be neglected, we get by simple algebraical transformation
ip Ae TERE
R
But even at the sea-level the force of gravity varies in different places in
consequence of the form of the earth. The earth is not a true sphere, but
an ellipsoid, the major axis of which is 12,754,796 metres, and the minor
12,712,160 metres. The distance, therefore, from the centre being greater at
the Equator than at the Poles, and the attraction on a body being inversely
as the square of these distances, calculation shows that the attraction due to
this cause is x4, greater at the Poles than at the Equator. This is what
would be true if, other things being the same, the earth were at rest.
i. In consequence of the earth’s rotation, the force of gravity is further
modified. If we imagine a body relatively at rest on the Equator, it really
shares the earth’s rotation, and describes, in the course of one day, a circle,
whose centre and radius are the centre and radius of the earth. Now, since
a body in motion tends by reason of its inertia to move in a straight line, it
follows that to make it move ina circle, a force must be employed at each
instant to deflect it from the tangent (53). Consequently, a certain portion
of the earth’s attraction must be employed in keeping the above body on the
surface of the earth, and only the remainder is sensible as weight. It
appears from calculation that at the Equator the s3,5th part of the earth’s
attraction on any body is thus employed, so that the magnitude of g at the
Equator is less by the 32,5th part of what it would be were the earth at rest.
iii. As the body goes nearer the Poles the force of gravity is less and less
diminished by the effect of centrifugal force. For in any given latitude it
will describe a circle coinciding with the parallel of
latitude in which it is placed; but as the radii of D
these circles diminish, so does the centrifugal force ey
up to the Pole, where the radius is null. Further, on NC
the Equator the centrifugal force is directly opposed
to gravitation: in any other latitude only a com- E E
ponent of the whole force is thus employed. This is
seen in fig. 61,in which PP’ represents the axis of
rotation of the earth, and EE’ the Equator. At any
given point Eon the Equator the centrifugal force Pp’
is directed along CE, and acts wholly in diminishing Biche:
the intensity of gravitation ; but on any other point,
a, nearer the Pole, the centrifugal force acting on a right line @é at right
angles to the axis PP’, while gravity acts along aC, gravity is no longer
directly diminished by centrifugal force, but only by its component ad, which
is less the nearer a is to the Pole.
The combined effect of these two causes—the flattening of the earth at
the Poles, and the centrifugal force—is to make the attraction of gravitation
at the Equator less by about the ;4,nd part of its value at the Poles.
74 Gravitation and Molecular Attraction [84-
CHAPTER wit
MOLECULAR FORCES
84. Nature of molecular forces.—The various phenomena which bodies
present show that their molecules are under the influence of two contrary
forces, one of which tends to bring them together, and the other to separate
them from each other. The first force, which is called molecular attraction,
varies in one and the same body with the distance only. The second force
is due to the vzs viva, or moving force, which the molecules possess. It is
the mutual relation between these forces, the preponderance of the one or
the other, which determines the molecular state of a body (4)—whether it be
solid, Jiquid, or gaseous.
Molecular attraction is only exerted at infinitely small distances. Its
effect is inappreciable when the distance between the molecules becomes
appreciable.
According to the manner in which it is regarded, molecular attraction is
designated by the terms cohesion, affinity, or adhesion.
85. Cohesion.—Coheston is the force which unites adjacent molecules
of the same nature ; for example, two molecules of water, or two molecules
of iron. Cohesion is strongly exerted in solids, less strongly in liquids, and
scarcely at all in gases. Itsstrength decreases as the temperature increases,
because then the wzs vzva of the molecules increases. Hence itis that when
solid bodies are heated they first liquefy, and are ultimately converted into
the gaseous state, provided that heat produces in them no chemical change.
Cohesion varies not only with the nature of bodies, but also with the
arrangement of their molecules ; thus, the difference between tempered and
untempered steel (95) is due to a difference in the molecular arrangement
produced by tempering. Many of the properties of bodies, such as tenacity,
hardness and ductility, are due to the modifications which this force
undergoes.
In large masses of liquids the force of gravity overcomes that of cohesion.
Hence liquids acted upon by the former force have no special shape ; they
take that of the vessel in which they are contained. But in smaller masses
cohesion gets the upper hand, and liquids assume then the spheroidal form.
This is seen in the drops of dew on the leaves of plants. It is also seen when
a liquid is placed ona solid which it does not moisten ; as, for example,
mercury upon wood. The experiment may also be made with water, by
sprinkling upon the surface of the wood some light powder such as lyco-
podium or lampblack, and then dropping a little water on it. The following
experiment is an illustration of the force of cohesion causing a liquid to as-
sume the spheroidalform. A saturated solution of zinc sulphate is placed ina
=87] Adhesion 75
narrow-necked bottle (fig. 62), and a small quantity of carbon bisulphide,
coloured with iodine, made to float on the surface. If pure water be now
carefully added, so as to rest on the surface of the zinc
sulphate solution, its specific gravity being less than that of
the saturated solution, the bisulphide collects in the form of a
flattened spheroid, which presents the appearance of blown
coloured glass, and is larger than the neck of the bottle, pro-
vided a sufficient quantity has been taken.
~ The force of cohesion of liquids may be illustrated and
even measured as follows. A plane, perfectly smooth disc, D jill
(fig. 63), is suspended horizontally to one scale-pan, Z, of a li
delicate balance, and is accurately equipoised. A some- —
what wide vessel of liquid is placed below, and the position
of the disc regulated by means of the sliding screw S until it just touches
the liquid. Weights are then carefully added to the other scale-pan until
the disc is detached from the liquid. In this way it has been found that
the weights required to detach the disc vary with the nature of the liquid ;
with a disc of 118 mm. diameter the numbers for waters, alcohol, and
turpentine were 59:4, 31, and 34 grammes respectively.
The results were the same whether the disc was of glass, of copper, or
of other metals, showing thus that they only depend on the nature of the
liquid. It is a measure of the cohesion of the liquid, for a layer remains
adhering to the disc ; hence the weight on the other side does not separate
the disc from the liquid, but separates the particles of liquid from each other.
86. Affinity.— Chemical affinity, or chemical attraction, is the force which
is exerted between molecules not of the same kind. Thus, in water, which
is composed of oxygen and hydrogen, it is affinity which unites these ele-
ments, but it is cohesion which binds together two molecules of water. In
compound bodies cohesion and affinity operate simultaneously, while in
simple bodies or elements cohesion has alone to be considered.
To affinity are due all the phenomena of combustion and of chemical
combination and decomposition.
Those causes which tend to weaken cohesion are most favourable to
affinity ; for instance, the action of affinity between substances is facilitated by
their division, and still more by reducing them to a liquid or gaseous state.
It is most powerfully exerted by a body in tts zascent state—that is, the state
in which the body exists at the moment it is disengaged from a compound ;
the body is then free and ready to obey the feeblest affinity. An increase
of temperature modifies affinity differently under different circumstances.
In some cases by diminishing cohesion, and increasing the distance between
the molecules, heat promotes combination ; thus, sulphur and oxygen, which
at the ordinary temperature are without action on each other, combine to form
sulphur dioxide when the temperature is raised. In other cases heat tends
to decompose compounds by imparting to their elements an unequal expan-
sibility ; hence it is that many metallic oxides—as, for example, those of silver
and mercury—are decomposed, by the action of heat, into gas and metal.
87. Adhesion.—The molecular attraction exerted between the szvrfaces
of bodies in contact is called adhesion.
i. Adhesion takes place between solids. If two leaden bullets are cut
Fig. 62
76 Gravitation and Motecular Attraction [87—
with a penknife so as to form two equal and brightly polished surfaces, and
the two faces are pressed and turned against each other, until they are in the
closest contact, they adhere so strongly as to require a force of more than
Ioo grammes to separate them. The same experiment may be made with
two equal pieces of glass which are polished and made perfectly plane.
When they are pressed one against the other, the adhesion is so powerful
that they cannot be separated without breaking. As the experiment succeeds
in vacuo, it cannot be due to atmospheric pressure, but must be attributed
to a reciprocal action between the two surfaces. The attraction also in-
creases as the contact is prolonged, and is greater in proportion as the con-
tact is closer.
It appears, however, from optical considerations that plates may be
separated from each other by a distance of o‘o001 mm. As this is greater
than the diameter of the sphere of molecular action (3), it is probable that
the connection of the platesis effected by layers of air condensedon the
surface (196).
In the operation of glueing the adhesion is complete, for the pores and
crevices of the fresh surfaces being filled with liquid glue, so that there is no
empty space on drying, wood and glue form one
compact whole. In some cases the adhesion of
cemented objects 1s so powerful that the mass
breaks more readily at other places than at the
cemented parts. Both in glueing and cementing
the layer should be thin.
Spring exposed various powders, such as salt-
petre, sawdust, fine sand, and chalk, to a pressure
of 10,000 atmospheres (166). He thus obtained
masses of greater hardness and tenacity than the
original substances possessed, and destitute of
crystalline form.
Soldering 1s due to adhesion ; the surface of
the metals must be quite clean, which is effected
by removing the layer of oxide, with which they
are usually coated, by acid or by borax. The
_solder when it solidifies only adheres to clean metal
surfaces,
There is no real difference between adhesion
- and cohesion; thus when two freshly cut surfaces
of caoutchouc are pressed together, they adhere
with considerable force, and ultimately form one
compact solid mass.
iu. Adhesion also takes place between solids
and liquids. If we dip a glass rod into water, and
then withdraw it, a drop will be found to collect at
its lower extremity, and remain suspended there. As the weight of the
drop tends to detach it, there must necessarily be some force superior to
this weight which maintains it there ; this force is the force of adhesion.
This is the cause why liquids when poured out of a vessel so easily run
—87] Adhesion a7
down the outside ; it is prevented by greasing the outer edge, and thus doing
away with the adhesion.
The adhesion between liquids and solids is more powerful than that
between solids. Thus, if in the above experiment a thin layer of oil is inter-
posed between the plates they adhere firmly, but when pulled asunder each
plate is moistened by the oil, showing therefore that in separating the plates
the cohesion of the liquid is overcome, but not the adhesion of the oil to the
metal.
In the above case the solid is wetted by the liquid ; that is, some remains
adhere even when the drop falls. But liquids adhere to solids even when
they are not wetted. Thus if a smooth glass plate be suspended horizontally
from one arm of a balance, and be counterpoised as in fig. 63 ; on sliding a
level surface of mercury under the plate, so that the plate touches the mercury,
a considerable weight must be placed in the other panso as to detach the
plate from the mercury. Small drops of mercury, too, adhere to the under
side of a glass or porcelain plate.
iii. The force of adhesion operates, lastly, between solids and gases.
If a glass or metal plate be immersed in water, bubbles will be found to
appear on the surface. As air cannot penetrate into the pores of the plate,
the bubbles could not arise from the air which has been expelled. It is
solely due to the layer of air which covered the plate and mozstened it like
a liquid. In many cases when gases are separated in the ascent state
on the surface of metals—as in electrolysis—the layer of gas which covers
the plate has such a density that it can produce chemical actions more
powerfu! than those which it can bring about in the free state.
The collection of dust on walls, writing and drawing with chalks and
pencils, depend on the adhesion of solids. Yet these are easily rubbed out,
for the adhesion is only to the surface layer. In writing with ink, and in
water-colour painting, the liquid penetrates into the pores, taking the solid
with it, which is left behind as the liquid evaporates, and hence the adhesion
of such writing and painting is far more complete.
78 Gravitation and Molecular Attraction [88-
CHAP They,
PROPERTIES PECULIAR TO SOLIDS
88. Various special properties.—After having described the principal
properties common to solids, liquids, and gases, we shall discuss the proper-
ties peculiar to solids.
They are elasticity, tenacity, ductility, and hardness.
With regard to elasticity we must distinguish between elasticity of volume,
longitudinal elasticity, and torsional elasticity or simple rigzdity.
Let us first define the terms s¢vess and strazm commonly used in the theory
of elasticity. A change in the size
or shape of a body due to the
application of force to the body is
called a strain, while the force in
the interior of the body producing
this strain is called a stvess. If the
displacements of the molecules of
a body due to the action of stress
are small, the strains produced are
proportional to the stresses pro-
ducing them, and hence the ratio
stress
strain
coefictent of elasticity of the body,
this coefficient being greatest in
those cases where a small displace-
ment requires a very large force to
produce it. Thus, steel and glass
are highly elastic bodies because
in them the application of evena
large force will produce only a
small change of shape or volume.
For by force of elasticity is under-
stood the force with which the dis-
placed particles tend to revert to
their original position, and which
force is equivalent to that which
has brought about the change.
Considered from this point of view,
is constant and is called the
gases have the least force of elasticity ; that of liquids is considerably greater,
and is, indeed, greater that that of many solids. Thus the force of elasticity
89] Volume Elastectty. Longitudinal Elasticity 79
of mercury is greater than that of caoutchouc, glass, wood, and stone. It is,
however, less than that of the other metals, with the exception of lead.
This mode of defining elasticity differs somewhat from ordinary ideas
according to which bodies, such as india-rubber, are considered highly
elastic which undergo considerable change of form on the application of a
small force. A body is perfectly elastic when any given stress produces no
permanent set, restitution being always complete. It is imperfectly elastic
when it does retain permanently such a set. Within the limits of elasticity
all bodies may be regarded as perfectly elastic.
89. Volume elasticity. Longitudinal elasticity.—Elasticity of volume is
the only kind of elasticity a liquid or a gas possesses, for liquids and gases
have no definite shape. A solid may by the application of stress have not
only its volume but also its shape altered. The volume elasticity of a body
is measured, as we have said, by the ratio stress/strain. The stress is the
force per unit area uniformly applied to the body to compress it ; the strain
is the resulting compression, that is the ratio of the change of volume to the
original volume. If the original volume V be reduced to V-v when sub-
jected to uniform pressure (force per unit area) P, the strain is v/V, and
U U
V
The dimensions (62) of P are those of a force divided by an area, Z.e.
iL’ or M/LT.? Since the strain is the ratio of a volume to a volume, its
dimensions are zero. Thus the dimensions of K, the coefficient of volume
elasticity, are the same as those of a pressure.
The reciprocal of £ is called the coefficient of compressibility or simply
the compressibility of the body.
In order to study the laws of longitudinal elasticity, Savart used the
apparatus represented in fig. 64. It consists of a wooden support from which
are suspended the rods or wires taken for experiment. At the lower ex-
tremity there is a scale-pan, and on the wire two points, A and B, are marked,
the distance between which is measured by means of the cathetometer before
the weights are added.
The cathetometer consists of a strong upright brass support, K, divided
nto millimetres, which can be adjusted in an exactly vertical position
by means of levelling screws and the plumb-line. A small telescope, exactly
at right angles to the scale, can be moved up and down, and is provided
with a vernier which measures fiftieths of a millimetre. By adjusting the
telescope successively on the two points A and B, as represented in the
figure, the distance between these points.is obtained on the graduated scale.
Placing, then, weights in the pan, and measuring again the distance from A
to B, the elongation is obtained.
By experiments of this kind it has been ascertained that—
The alteration in length within the limits of elasticity 7s in proportion to
the length and to the load acting on the body, and is inversely as the cross
Section
Let 7 be the radius of the wire, Z its length, and e the elongation produced
80 Gravitation and Molecular Attraction [89-
by the application of aload W. ‘Thestress, or force per unit of cross section
of the wire, is W/m7*, and since the length / is stretched by an amount g, the
strain is e/7. Thus by the definition,
errs Ley Ww wil
Co-efficient of longitudinal ‘Gale ae
Elasticity, or Young’s Modulus t
Z
We see from this expression that if the wire have unit cross section (77? = I)
and be stretched to double its length (e=7), »=W. In other words, we may
define Young’s Modulus as the stretching force which must be applied to a
wire of unit cross section to double its length. This cannot be directly
observed, for no substance has elastic limits so wide as to undergo stretching
to double its length without permanent set ; n, however, may be calculated
from any accurate observations by means of the above formula.
In the following table the values of » and e are given for a number of
substances, the units being 1 kilogramme, 1 millimetre, and 1 second. To
obtain the corresponding numbers in C.G.S. units (62) divide the values of p
by 981 and multiply by 10'! ; multiply the values of e by 981 and divide by
POW:
pe Py
Wrought-iron : 2 A a 20,869 0°000048
Steeliron |": : : ae 18,809 0°000053 _
Platinuin~ si: : ; 3 onl 17,044 0°000058
Copper : : ; : : ay 12,500 | 0'000080
Slate . : : , : : : 11,035 | 0000090
Zico ee ; : mA 8,734 | O'OOOI 14 |
Brass . é ‘ ; , | 8,543 O‘OOO1 17 |
Crown Glass : “ : A a 7,917 | 0'0001 26
Plate Glass . ; : , 3 cr 7,015 | O‘0001 42
Rock Salt. : 4,230 | 91000236 |
Marble : ‘ : : al 2,309 0°000382
Geaduar ; : , : : sid 1,803 | 07000555 |
Bonerg, ...: oy yp ae 1,635 | 0000612 |
Acacia . ; p : ; ; 2 Loe | 0°000792
Prac lee : , : : 5 ay Tbr | 0°000890
WON dl 1 ‘ : ; : : y g2I | O°001085
| Whalebone . ; se 700 | 0°001 428
ml Geet. : : Tenia hy 650 O°Ol1167
| Sandstone . ‘ a 631 | 0001521
| Fir : ; : : : ; | 564 | 0°001 768
| Gypsum ; ; ; | 400 | 0°002500 |
ie SS a Se at Ee fetes SS ee ee ee —___—— |
Thus, to double the length of a wrought-iron wire a square millimetre in
section would (if this were possible) require a weight of 19,000 kilogrammes ;
but a weight of 15 kilogrammes produces a permanent alteration in length
of +3'szth, and this is the limit of elasticity. The weight, which when applied
to a body of unit section just brings about an appreciable permanent change,
is a measure of the /z7z¢ of elasticity. _Whalebone has only a modulus of
-89] _ Elasticity of Traction 8I
700, and experiences a permanent elongation by a weight of 5 kilogrammes ;
its limit is, therefore, relatively greater than that of iron. Steel has a high
modulus, along with a wide limit.
Longitudinal stretching is accompanied by a lateral contraction, and
the ratio of the contraction to the proportional stretching is known as
Potsson’s coefficient. It was taken by him to be 0°25, but later experiments have
found the ratio to vary from o to o°5 ; it is about 0°25 for glass, and nearly o5
for caoutchouc. When a wire is stretched by a load to within the limit of
elasticity, some time often elapses before the full effect is produced, and
conversely when the load is removed the wire does not at once wholly
resume its original condition, but a small portion of the deformation remains,
and it only reverts to its initial state after the lapse of some time. This
phenomenon, first observed by Weber, which is met with in most elastic
changes of form, is called the elastic after-action or effect, or the elastic fatigue.
This phenomenon is probably due to the fact that the mole-
cules of bodies are not spherical, but are variously
extended in different directions, and in elastic deformation
are not only displaced in reference to each other, but
are also twisted.
This may be illustrated by the following experiment.
A piece of caoutchouc tube is closed by a glass plug at
the bottom, while the open end is passed over a piece
of glass tube. (oloured liquid is then poured in so that
it stands ata certain height in this tube. If then a weight
is suspended to the lower end of the india-rubber tube,
the liquid at once sinks to a considerable distance, and
afterwards very slowly a little further. Onremoving the
weight it rises again, but not immediately to the old
height. This it only reaches after some time. Both
calculation and experiment show that when bodies are
lengthened by traction their volume increases.
When weights are placed on a bar, the amount by
which it is shortened, or the coefficient of contraction, is
equal to the elongation which it would experience if the |
same weights were suspended to it, and is represented by
the above numbers.
The influence of temperature on the elasticity of iron,
copper, and brass was investigated by Kohlrausch and
Loomis. They found thatthe alteration in the coefficient
of elasticity by heat is the same as that which heat pro-
duces in the coefficient of expansion and in the refractive
power ; it is also much the same as the change in the .
permanent magnetism, and in the specific heat, while it :
is less than the alteration in the conductivity for elec-
tricity.
As an application of elasticity may be mentioned
Jolly’ s spring balance. This consists of a long steel wire, aé (fig. 65), wound
in the form of a spiral, which is suspended in front of an Accurately graduated
scale. To the lower end of the spiral two scale-pans, c and d, are hung by
G
Fig. 65
82 Gravitation and Molecular Attraction [89-
a thread, the lower one, d@, dipping in a small vessel of water on an adjust-
able support. The instrument is graduated empirically by observing what
displacement of the mark vz is produced by putting a known weight in the
scale-pan d@. Knowing then once for all the constant of the instrument, it
is easy to determine the weight of a body by reading the displacement
which it produces along the scale.
go. Elasticity of torsion.—The laws of the torsion of wires were deter-
mined by Coulomb, by means of an apparatus called the zorszon balance (fig.
66). It consists essentially of a metal wire, clamped at one end in a support,
A, and holding at the other a metal sphere, B, to which is affixed an index, C.
Immediately below this there is a graduated circle, CD. If the needle is
turned from its position of equilibrium through a certain angle, which is the
angle of torsion, the force necessary to produce this effect is the force of
torston. When, after this deflection, the sphere is left to itself, the reaction
of torsion produces its effect, the wire untwists itself, and the sphere rotates ©
about its vertical axis with increasing rapidity until it reaches its position of
equilibrium. It does not, however, rest there: in virtue of its inertia it
passes this position, and the wire undergoes a torsion in the opposite direc-
tion. The equilibrium being destroyed, the wire tends to untwist itself, the
same alterations are again produced, and the needle does not rest at zero
of the scale until after a certain number of oscillations about this point have
been completed.
By means of this apparatus, Coulomb found
that when the amplitude of the oscillations is
within certain limits, the oscillations are repre-
sented by the following laws :
I. Zhe oscillations are very nearly tsochronous.
Il. For the same wire, the angle of torsion ts
proportional to the moment of the force of torsion.
Ill. With the same force of torsion, and with
wires of the same diameter, the angles of torsion
are proportional to the length of the wires.
IV. Zhe same force of torsion being applied to
wzres of the same length, the angles of torsion are in-
versely proportional to the fourth powers of the dia-
meters.
Wertheim examined the elasticity of torsion in
the case of stout rods by means of a different appa-
ratus, and found that it 1s also subject to these laws.
He further found that, all dimensions being the same,
different substances undergo different degrees of tor-
sion for the same force, and each substance has its
own coefficient of torsion, which is usually denoted by
wm. The value of this coefficient is about 4 that of the modulus of elasticity.
The laws of torsion may be enunciated in the formula o = ae ; in which
mr
w is the angle of torsion, F the moment of the force of torsion, 7 the length
of the wire, 7 its radius, and z the torsion-coefficient or simple rigidity.
As the angle of torsion is inversely proportional to the fourth power of
-91} Determination of Young’s Modulus by Flexure 83
the radius, rods of some thickness require very great force to produce even
small twists. With very small diameters, such as those of a cocoon or glass
thread, the proportionality between the angle of torsion and the twisting
force holds even for several complete turns.
We may here mention a very ingenious method of obtaining very fine
threads of glass, and even of quartz and other minerals, which has been de-
vised by Professor Boys. It consists in attaching a stout thread of the sub-
stance in question to a small arrow of straw, melting the end so as to form a
small drop. When the arrow is shot from a small crossbow, the drop remains
behind in virtue of its inertia (19), and a thread practically uniform but of
excessive tenuity is spun out from it and carried along with the arrow. In
this way glass threads go feet in length and ;,/g5th of an inch in diameter
have been produced. By the same method, melting quartz with the oxy-
hydrogen blowpipe, threads of this substance have been produced which are
not more than o‘oooo! inch in diameter. Such threads are of great value
in torsion experiments, for, while they possess great tenacity, they are almost
destitute of the property of elastic fatigue (89).
gt. Determination of Young’s modulus by flexure.—A solid, when cut
into a rod or thin plate, and fixed at one end, after having been more or
less bent, strives to return to its original position when left to itself. This
property is known as the elasticity of flexure, and is very marked in steel,
caoutchouc, wood, and paper.
If a rectangular bar AB be clamped at one end and loaded at the other
end by a weight W (fig. 67), a flexure will be produced which may be ob-
served by the catheto-
meter. If the amount of
this flexure is denoted by
h, Young’s modulus 1s
given by the formula
_4WPR
ON
where W is the load, / the
length of the bar, @ its
breadth, % its depth or
thickness, and & a con-
stant, which depends on
the manner in which the
rod is supported, the three
principal cases _ being
represented in fig. 68 ; a is that in which the rod is supported at one end,
as in fig. 67 ; in 8 the rod rests on knife-edges, with both ends free ; while
ny both ends are rigid ; if one and the same a be fastened in these differ-
ent ways, the values of \ are respectively as 64:4:1.
If the section of the bar is a circle of radius 7, then
It will thus be seen that if for a given load the depression is not to be
greater with a long beam than with a short one, the height must increase in
the same ratio as the length.
‘ G2
84 Gravitation and Molecular Attraction [91-
The elasticity of flexure is applied in a vast variety of instances—for
example, in bows, watch-springs, carriage-springs ; in spring balances it is
used to determine weights, in dynamometers to determine the force of agents
in prime movers ; and, as a property of wool, hair, and feathers, it is applied
to domestic uses in cushions and mattresses.
Fig. 68
Whatever be the kind of elasticity, there is, as has been already said (89),
a limit to it—that is, there is a molecular displacement beyond which bodies
are broken, or at any rate do not regain their primitive form. This limit is
affected by various causes. The elasticity of many metals is increased by
hardening, whether by cold, by means of the draw-plate, by rolling, or by
hammering. Some substances, such as steel], cast iron, and glass, become
both harder and more elastic by tempering (95).
Elasticity, on the other hand, is diminished by azzealing, which consists
in raising the body to a temperature lower than that necessary for tempering,
and allowing it to cool slowly. By this means the elasticity of springs
may be regulated at pleasure. Glass, when it is heated, undergoes a
true tempering in being rapidly cooled, and hence, in order to lessen the
fragility of glass objects, they are reheated in a furnace, and are carefully
allowed to cool slowly, so that the particles have time to assume their most
stable position (95).
92. Tenacity.—7Zenacity is the resistance which a body opposes to the
total separation of its parts. According to the manner in which the external
force acts, we may have various kinds of tenacity ; ¢emaczty in the ordinary
sense, or resistance to traction ; ve/ative tenacity, or resistance to fracture ;
reactive tenacity, or resistance to crushing ; sheevzmg tenacity, or resistance
to displacement of particles in a lateral direction ; and ¢orszonal tenacity, or
resistance to twisting. Ordinary tenacity is determined in different bodies
by forming them into cylindrical or prismatic wires, and ascertaining the
weight necessary to break them.
Mere increase in length does not influence the breaking weight, for the
weight acts in the direction of the length, and stretches all parts as if it had
been directly applied to them.
Tenacity ts adtrectly proportional to the breaking weight, and inversely
proportional to the area of a transverse section of the wire.
Tenacity diminishes with the duration of the traction. A small force
continuously applied for a long time will often break a wire, which would not
at once be broken by a larger weight.
Not only does tenacity vary with different substances, but it also varies
with the form of the body. Thus, with the same sectional area, a cylinder
has greater tenacity than a prism. The quantity of matter being the same,
a hollow cylinder has greater tenacity than a solid one; and the tenacity of
this hollow cylinder is greatest when the external radius is to the internal
—92] Tenacity 85
one in the ratio of 11 to 5. The shape has also the same influence on the
resistance to crushing as it has on the resistance to traction. A hollow
cylinder with the same mass, and the same weight, offers a greater resistance
than a solid cylinder. Thus it is that the bones of animals, the feathers of
birds, the stems of corn and other plants, offer greater resistance than if they
were solid, the mass remaining the same.
Tenacity, like elasticity, is not the same in all directions in bodies. In
wood, for example, both the tenacity and the elasticity are greater in the direc-
tion of the fibres than in a transverse one. And this difference obtains in
general in all bodies, the texture of which is not uniform.
Wires by being worked acquire greater tenacity on the surface, and have
therefore a higher coefficient than even somewhat thicker rods of the same
material; and, according to some physicists, solids have a surface tension
analogous to that of liquids (135). 1,45 +T,,; hence
the two forces T,, and T,, cannot counter-
balance the force T,,, and the point A
must move in the direction of the pull
T,., until the whole surface is covered with a thin layer of oil. Although
oil zs spread over water by the pull T,., it is usual to say that oil spreads
itself on water.
That surface tension is only exhibited at the boundary of two liquids is
well seen by an experiment of Professor Boys: If a camel’s-hair brush is
dry the hairs are separately visible, and to make them come to a point they
must be wetted ; this adherence is not due to moisture, for if the Jencz7 is
wholly immersed in water the separate hairs are as visible as when the
pencil is dry.
140. Formation of drops in a capillary orifice.—When a liquid is con-
tained in a vessel terminating in a narrow capillary opening, such as a
dropping tube, a certain excess of pressure is
required to make the lquid flow out. If this
pressure is limited, the lower meniscus has
an invariable shape, and the drop does not
increase. But as the pressure increases the
drop gradually expands like a small elastic bag,
the tension of which is less in the degree in
which the surface increases, and when the drop
is so large that its weight exceeds the normal
component of the surface tension, it contracts
at the upper part, and finally breaks across
a circumference o0’o’, which is nearly equal to
that of the orifice oo. ty
Tate has found that the weights of drops
Sormed with different capillary tubes are for the ae
same liguid proportional to the diameters of the “eaue
orifice.
The weights of the drops are independent of the substance of the tube,
provided it is moistened ; they diminish with rise of temperature.
When a small but very hot flame is directed against the point of a fine
je TER el ie abet) Wek Wn
a
128 On Liquids [140-
metal wire, such as gold or platinum, the metal is melted and falls in drops,
the weight P of which is found to be very uniform. P is the greatest weight
which the melted mass can support, and is equal to 277T, where T is the
constant of capillarity and 27 the diameter of the wire. Quincke has applied
this method of determining the constant in cases where other methods are
not applicable, such as in the case of the noble metals, salts, selenium,
phosphorus, &c.
141. Osmose.—Other shares are observed when two different liquids
miscible with each other are separated by a porous diaphragm. This may
be best illustrated by means of the apparatus represented in fig. 123, in which
a vessel open at the bottom is tied round with a bladder. In the neck a
long narrow tube, @a, is fitted. This vessel is filled with solution of copper
sulphate, so that it stands at a certain height, 7, in the tube, and is then placed
in a larger vessel containing pure water, at the level
a mm. If the temperature remains stationary, it will be
seen that after some time the liquid in the tube aa,
which was originally at the level 7, has risen, while
the level of 77 has become somewhat lower ; it will
also be seen that the outer liquid has acquired a faint
bluish tinge. This process continues for some time
until the liquid has attained a certain height, It thus
appears that there is an interchange of the two liquids,
but the quantity of water which passes into the sulphate
of copper is greater than that of the solution which
passes out. If the experiment be reversed—that is, if
water is contained in 4, and copper sulphate in the
i outer vessel—the phenomena are reversed ; that is, the
| level in 7 sinks, while that in 77 rises. Dutrochet,
who first investigated these phenomena, applied the
term exosmose to the current which passes from the
denser liquid to the less dense, and ezdosmose to the
opposite current, and the apparatus itself he called an
endosmometer. The phenomena are now known as
those of dosmose or osmose.
For the occurrence of osmose the membrane must
be permeable to at least one of the liquids, and the
liquids must be different, but capable of mixing, such
as alcohol and water; there is none, for instance,
between water and oil. Osmose may occur between
two liquids of the same kind, but of different densities,
such as solutions of acids or salts of different strengths ;
here the current is from the weaker towards the stronger
solution, and this is general, osmose usually taking place towards the denser
liquid. Alcohol and ether form an exception ; although they are specifi-
cally lighter than water, they behave in this respect like liquids which are
denser.
If a tube filled with water is closed at both ends by a bladder (fig. 124),
and one end is placed in a vessel of water, the other being in contact with
the air, the water gradually evaporates through the bladder ; it is, however,
—141] Osmose 129
as rapidly replaced, so that, in consequence of evaporation, water moves
towards the place where this occurs. Hence osmose plays a part in the
motion. The evaporation from the skin of animals brings about a motion
of liquids from the interior towards the evaporating surface. In like manner,
the passage of water to the rootlets of plants, as well as the ascent of sap to
the highest points of the trees, is favoured by evaporation from branchlets,
leaves, flowers, and fruit.
The well-known fact that dilute alcohol kept in a porous vessel becomes
concentrated depends on osmose. If a mixture of alcohol and water be
kept for some time in a bladder, the volume diminishes, but the alcohol
becomes much more concentrated. The reason doubtless is that the bladder
absorbs water more readily than alcohol, and accordingly water evaporates
on the surface, and thus brings about a concentration of the residue.
Dutrochet’s method is not adapted for quantitative measurements, for it
does not take into account the hydrostatic pressure produced by the column,
Jolly examined the endosmose of various liquids by determining the weights
of the bodies diffused. He called the exdosmotic equivalent of a substance
the number which expresses how many parts by weight of water pass through
the bladder in exchange for one part by weight of the substance. The fol-
lowing are some of the endosmotic equivalents which he determined :—
Sulphuric acid : o'4 Copper sulphate. : 9°5
Alcohol . : i ‘ 4'2 Magnesium sulphate . I1'7
Sedium chloride . : 4°3 Caustic potash : er ZERO
Sugar. ; ; ; 7°1
He also found that the endosmotic equivalent increases with the temperature,
and that the quantities of substances which pass in equal times through the
bladder are proportional to the strengths of the solutions.
Porous diaphragms differ very greatly in the facility with which they
permit osmose ; of all substances goldbeater’s skin is the best, being twice
as good as vegetables, and sixty or seventy times as good as
porous earthenware, which, however, is necessary in some
cases, for organic membranes are apt to decompose.
Pfeffer has constructed what he calls sesmzpermeable
membranes, by immersing a porous cell, such as is used for
voltaic cells, in solution of copper sulphate, and then in one
of ferrocyanide of potassium. By double decomposition, a
coherent layer of ferrocyanide of copper is found, which is
permeable to the molecules of water, but not to those of sugar,
for instance. If a solution of sugar be exposed to pressure
in such a vessel, pure water filters through ; the membrane
acts asa molecular sieve.
The whole phenomena and laws of osmose have, in
recent times, acquired great importance from the theoretical considerations of
Van’t Hoff, on the nature of solutions, of which we may indicate the general
results.
If a one-per-cent. solution of sugar be placed in the vessel in such an
arrangement as that represented in fig. 123, when the semi-permeable dia-
K
130 On Liquids [141-—
phragm is of ferrocyanide of copper, it will be found that after the lapse of
some time the liquid will rise in the tube to a maximum height of 53°5 cm. 5
this height is a measure of the osmotic pressure. Dealing with dilute solutions,
it is found that this pressure is proportional to the concentration ; thus, with
solutions of 1, 2, 4, and 6 per cent. respectively, the corresponding osmotic
pressures are 53°5, 101°6, 2082, and 307°5, respectively. We shall afterwards
see (296) that we conceive a mass of gas as made up of a very large number
of molecules moving in all directions with extreme velocity, and that the
pressure of a gas is due to the impacts of these molecules against the sides of
the containing vessel. Now in what are called zdeal solutions—those, that
is to say, in which the dimensions of the molecules (3) of the body dis-
solved may be disregarded in comparison with the space in which they
are contained—Van ’t Hoff considers that the molecules of the body dis-
solved are animated by just such a motion as they possess in the case of
gases.
If the pressure on a given volume of gas be gradually increased its
volume will be diminished, and it is found that to reduce it to one-half, the
temperature remaining constant, the original pressure must be doubled.
For a given mass of gas, the product of pressure and volume is constant ;
this is what is known as Boyle’s law (183). Osmotic pressure in liquids is
exactly analogous to the pressure of gases; if we double the number of
molecules in a given volume of liquid, we double the pressure, just as we can
force two volumes of gas into the space occupied by one if we double the
pressure. . This analogy between osmotic and gaseous pressure is not a fanciful
one, but holds good in details so far asit has been tried. It can be shown, for
instance, that the osmotic pressure of sugar in solution is the same as would
be exerted by the same weight of sugar if it existed in the state of gas in
the same space as that occupied by the solution.
Gases, as will afterwards be shown, expand by a certain definite propor-
tion of their volume when heated, the pressure remaining constant ; or, if
the volume be kept constant, the increase of pressure is proportional to the
increase of temperature. This is also found to hold with the osmotic pres-
sure ; it increases in direct proportion to the temperature.
142. Diffusion of liquids.—If oil be poured on water, no tendency to
intermix is observed, and even if the two liquids be violently agitated to-
gether, two separate layers are formed on allowing them to stand. With
alcohol and water the case is different; if alcohol, which is specifically
lighter, be carefully poured upon water, so as to form two distinct layers,
it will be seen that the heavier water rises in opposition to gravity with the
lighter alcohol, which, in turn, passes into the denser liquid below; the liquids
gradually intermix, in spite of the difference of the specific gravities ; they
diffuse into one another.
This point may be illustrated by the experiment represented in fig. 125.
A tall jar contains water coloured by solution of blue litmus ; by means of
a funnel some dilute sulphuric acid is carefully poured in, so as to form a
layer at the bottom ; the colour of the solution is changed into red, pro-
gressing upwards, and after forty-eight hours the change is complete—a
result of the action of the acid, and a proof, therefore, that it has diffused
throughout the entire mass.
—142] Diffusion of Liquids 131
The laws of this diffusion, in which no porous diaphragm is used, were
completely investigated by Graham. The method by which his latest ex-
periments were made was the following :—A small wide-necked bottle, A
(fig. 126), filled with the liquid whose rate of diffusion was to be examined,
was closed by a thin glass disc and placed. in a larger vessel, B, in which
water was poured to a height of about an inch above the top of the bottle.
The disc was carefully removed, and then after a given time successive
layers were carefully drawn off by means of a siphon or pipette, and their
contents examined.
The general results of these investigations may be thus stated :—
i. When solutions of the same substance, but of different strengths, are
taken, the quantities diffused in equal times are proportional to the strengths
of the solutions.
ii. In the case of solutions containing equal weights of different substances,
the quantities diffused vary with the nature of the substances. Saline sub-
Fig. 125 Fig. 126
stances may be divided into a number of eguzdiffustve groups, the rates of
diffusion of each group being connected with the others by a simple numerical
relation.
ili, The quantity diffused varies with the temperature. Thus, taking the
rate of diffusion of hydrochloric acid at 15° C. as unity, at 49° C, it is 2°18.
iv. If two substances which do not combine be mixed in solution, they
may be partially separated by diffusion, the more diffusive one passing out
most rapidly. In some cases chemical decomposition even may be effected
by diffusion. Thus, potassium bisulphate is decomposed into free sulphuric
acid and neutral sulphate.
v. If liquids be dilute, a substance will diffuse into water containing
another substance Biceled as into pure water ; but the rate is materially
reduced if a portion of the same diffusing substance be already present.
The following table gives the approximate times of equal diffusion :—
Hydrochloric acid. LO Magnesium sulphate . 7:0
Sodium chloride ; 23 Albumen : . . 49°0
Sugar F : : oualy es: Caramel : ; 2050
K 2
132 On Ligutds [142—
It will be seen from the above table that the difference between the rates
of diffusion is very great. Thus magnesium sulphate, one of the least
diffusible saline substances, diffuses 7 times as rapidly as albumen and 14
times as rapidly as caramel. These last substances, like hydrated silicic
acid, starch, dextrine, gum, &c., constitute a class of substances which are
characterised by their incapacity for taking the crystalline form, and by the
mucilaginous character of their hydrates. Considering gelatine as the type
of this class, Graham called them colloids (kodXa, glue), in contradistinction
to the far more easily diffusible cvystallotd substances. Colloids are for
the most part bodies of high molecular weight, and it is probably the
larger size of their molecules which hinders their passing through minute
apertures.
Graham devised a method of separating bodies based on their unequal
diffusibility, which he called dialysts. His dialyser (fig. 127) consists of a
ring of gutta-percha, over which is stretched while wet a sheet of parchment
paper, forming thus a vessel about two inches high and ten inches in dia-
>
NX ‘uaa awe
sae oy
|
Fig. 127
meter, the bottom of which is of parchment paper. After pouring in the
mixed solution to be dialysed, the whole is floated on a vessel containing a
very large quantity of water (fig. 128). In the course of one or two days a
more or less complete separation will have been effected. Thus a solution
of arsenious acid mixed with various kinds of food readily diffuses out. The
process has received important applications to laboratory and pharmaceutical
purposes.
Emulsions, such as are of frequent use in medicine, are prepared by
intimately mixing oil with a solution of gum, albumen, or some other colloid,
and water. As stated above, the reason Bt the difficulty which a eelion
experiences in diffusing through the membrane of another colloid, is probably
that its molécules are too Jarge and too near each other—in other words,
that the pores are too small. Withan ordinary emulsion, the minute droplets
of oil are dispersed among the large and difficult mobile particles of the
colloid, which thus hinder their motion, and thereby prevent them from
uniting and forming a coherent layer.
~145] Direction of the Jet from Lateral Orifices 133
CHAPTER 1 El
HYDRODYNAMICS
143. Hydrodynamics.—The science which treats of the motion of liquids
is called hydrodynamics ; and the application of the principles of this science
to conducting and raising water in pipes and to the use of water as a motive
power is known by the name of hydraulics.
144. Velocity of efflux. Torricelli’s theorem.—Let us imagine an
aperture made in the bottom of any vessel, and consider the case of a particle
of liquid on the surface, without reference to those which are beneath. If
this particle fell freely, it would have a velocity on reaching the orifice equal
to that of any other body falling through the distance between the level of
the liquid and the orifice. This, from the laws of falling bodies, is ,/2g, in
which ¢ is the acceleration due to gravity, and /# the height. If the hquid
be maintained at the same level, for instance, by a stream of water running
into the vessel, sufficient to replace what has escaped, the particles will
follow one another with the same velocity, and will issue in the form of a
stream. Since pressure is transmitted equally in all directions, a liquid
would issue from an orifice in the side with the same velocity, provided the
depth were the same.
The law of the velocity of efflux was discovered by Torricelli. It may be
stated as follows :—TZhe velocity of efflux is the velocity which a freely
jalling body would have on reaching the orifice after having started from
a@ State of rest at the surface. It is expressed by the formula v=,/2¢h.
It follows directly from this law that the velocity of efflux depends on the
depth of the orifice below the surface, and not on the nature of the liquid.
Through orifices of equal size and of the same depth, water and mercury
would issue with the same velocity ; for although the density of the latter
liquid is greater, the weight of the column, and consequently the pressure,
are greater too. It follows further that the velocities of efflux are directly
proportional to the square roots of the depth of the orifices. Water could
issue from an orifice Too inches below the surface with ten times the velocity
with which it would issue from one an inch below the surface.
‘The quantities of water which issue from orifices of different areas are
very nearly proportional to the size of the orifice, provided the level remains
constant.
145. Direction of the jet from lateral orifices.—From the principle
of the equal transmission of pressure, water issues from an orifice in the side
of a vessel with the same velocity as from an aperture in the bottom of a
vessel at the same depth. Each particle of a jet issuing from the side of a
134! | On Liguzds [145-
vessel begins to move horizontally with the velocity above mentioned, but it
is at once drawn downward by the force of gravity in the same manner as a
bullet fired from a gun, with its barrel horizontal. It is well known that the
bullet describes a parabola (51) with a vertical axis, the vertex being the
muzzle of the gun. Now, since each particle of jet moves in the same
curve, the jet itself takes the para-
bolic form.
In every parabola there is a
certain point called the focus, and
the distance from the vertex to the
x focus fixes the magnitude of a para-
\ bola in much the same manner as
wae the distance from the centre to the
Ee circumference fixes the magnitude
~ of acircle. Now it can easily be
.. proved that the focus is as much
\ below as the surface of the water is
above the orifice. Accordingly, if
water issues through orifices which
are small in comparison with the contents of the vessel, the jets from orifices
at different depths below the surface take different forms, as shown in fig. 129.
If these are traced on paper held behind the jet, then, knowing the horizontal
and vertical distances of any point of the jet from the orifice, it is easy to
demonstrate that the jet forms a parabola.
146. Height of the jet.—If a jet issuing from an orifice in a vertical
direction has the same velocity as a body would have which fell from the
surface of the liquid to that orifice, the jet ought to rise to the level of the
liquid. It does not, however, reach this ; for the particles which fall hinder
it. But by inclining the jet at a small angle with the vertical it reaches
about 5%, of the theoretical height, the difference being due to friction and
to the resistance of the air. By experiments of this nature the truth of
Torricelli’s law has been demonstrated.
(47. Quantity of efflux. Vena contracta.—If we suppose the sides of
a vessel containing water to be thin, and the orifice to be a small circle whose
area is A, we might think that the quantity of water, E, discharged in a
second would be given by the expression A./2g¢%, since each
PR BP. particle has, on the average, a velocity equal to ./2gh, and
dhe particles issue from each point of the orifice. But this is by
\
A No B nomeans the case. This may be explained by reference to
!
| fig. 130, in which AB represents an orifice in the bottom of
| a vessel—what is true in this case being equally true of an
!
Fig. 129
to orifice in the side of the vessel. Every particle above AB
endeavours to pass out of the vessel, and in so doing exerts
a pressure on those near it. Those that issue near A and B
Wig 3 exert pressures in the directions MM and NN ; those near
the centre of the orifice in the direction RQ, those in the
intermediate parts in the directions PQP. In consequence, the water.
within the space PQP is unable to escape, and that which does escape,
instead of assuming a cylindrical form, at first contracts, and takes the form
-148] Jnfluence of Tubes on the Quantity of Effiux 135
of a truncated cone. It is found that the escaping jet continues to contract
until at a distance from the orifice about equal to the diameter of the orifice.
This part of the jet is called the vena contracta. It is found that the area
of its smallest section is about 3 or 0°625 of that of the orifice. Accord-
ingly, the true value of the efflux per second is given approximately by the
formula
E = 0°62A ./2¢h,
or the actual value of E is about 0°62 of its theoretical value.
148. Influence of tubes on the quantity of efflux.—The result given
in the last article has reference to an aperturein a thin wall. If a cylindrical
or conical efflux tube, or ajutage, is fitted to the aperture, the amount of the
efflux is considerably increased, and in some cases falls but little short of its
theoretical value.
A short cylindrical ajutage, whose length is from two to three times its dia-
meter, has been found to increase the efflux per second to about 0°82A,/2gh.
In this case the water on entering the ajutage forms a contracted vein (fig.
131), just as it would do on issuing freely into the air ; but afterwards it ex-
pands, and, in consequence of the adhesion of the water to the interior surface
of the tube, has, on leaving the ajutage, a section greater than that of the
contracted vein. The contraction of the jet within the ajutage causes a par-
tial vacuum. If an aperture is made in the ajutage, near the point of greatest
contraction, and is fitted with a vertical tube, the
other end of which dips into water (fig. 131), it is
found that water rises in the vertical tube, thereby
proving the formation of a partial vacuum.
If the ajutage has the form of a conic frustum
whose larger end is at the aperture, the efflux in
a second may be raised to 0'92A ./2¢%, provided
the dimensions are properly chosen. If the
smaller end of a frustum of a cone of suitable
dimensions be fitted to the orifice, the efflux
may be still further increased, and fall very little
short of the theoretical amount.
When the ajutage has more than a certain
length, a considerable diminution takes place in
the amount of the efflux ; for example, if its length
is 48 times its diameter, the efflux is reduced to 0°63A,/2gh. This arises from
the fact that, when water passes along cylindrical tubes, the resistance in-
creases with the length of the tube ; for a thin layer of liquid is attracted to
the walls by adhesion, and the internal flowing liquid rubs against this.
The resistance which gives rise to this result is called Aydraulic friction ; it
is independent of the material of the tube, provided it be not roughened ;
but depends in a considerable degree on the viscosity of the liquid; for
instance, ice-cold water experiences a greater resistance than lukewarm
water.
According to Prony, the mean velocity v of water in a cast-iron pipe of
the length /, and the diameter @, under the pressure Z, is in metres
I pe
|
136 On Liguzds [148—
This is on the assumption that the tubes are straight. Any angle or
curvature of the tube diminishes the velocity, seeing that part of the motion
is used up in pressure against the sides. Thus Venturi found the time
requisite to fill a small vessel by means of a tube 38 inches in length by 3°3
in diameter was 45, 50, or 70 seconds, according as the tube was straight,
curved, or bent at a right angle.
By means of hydraulic pressure Tresca submitted solids such as silver,
lead, iron and steel, powders like sand, soft plastic substances such as clay,
and brittle bodies like ice, to such enormous pressures as 100,000 kilo-
grammes per square cm, and has found that they then behave like fluid
bodies. His experiments show also that these bodies transmit pressure
equally in all directions when the pressure is considerable enough.
149. Efflux through capillary tubes.—This was investigated by
Poiseuille by means of the apparatus represented in fig. 132, in which the
capillary tube AB is sealed to a glass tube on which a bulb is blown. The
volume of the space between the marks M and N is accurately determined,
and the apparatus, having been filled with the liquid under examination
by suction, is connected at the end M with a reservoir of compressed
air, in which the pressure is measured by means of a mercury mano-
meter (186. The time is then noted which is required for the level of the
liquid to sink from M to N, the pressure remaining constant. It is thus found
that v, the volume which flows out in a given time, is, with close approxi-
mation, represented by the formula
mesa
8 Z
where / is the length and 7 the diameter of the tube, J the pressure, and 7 the
coeffictent of internal friction (48) ; which may be defined as the resistance to
motion offered by two layers
of the liquid of unit surface,
at unit distance, and moving
away from each other with
unit velocity. Knowing the
dimensions, a determination
of the volume which flows
OULU LIN Aaviven Unie moms
ready means of obtaining
this coefficient. If the liquid
which flows out through the
tube is one which moistens
it, a layer of liquid adheres
to the side ; and accordingly
the friction which the liquid
experiences is not that against
the sides, but is due to that of the particles against each other. The co-
efficient of internal friction is represented in the above formula by 7. Bodies
with a high coefficient of internal friction are said to be viscous (97). The
liquids ether, water, sulphuric acid, linseed oil, Venice turpentine, represent,
for instance, a series with increasing viscosity. The reciprocal of the
-150] Form of the Jet 137
viscosity, or ' , iscalled the fiuidity ; it appears probable that this increases
“i!
with the temperature in the same ratio as the conductivity for electricity.
The coefficient of internal friction is greater in the case of solution
of salts than with water, and increases with the strength of the solution. It
greatly diminishes with the temperature, and, for water, at 60° is one-third
what it is at zero.
A convenient apparatus for the purpose, more particularly for comparative
measurements, is that given by Ostwald (fig. 133). It consists essentially of
a tube, ac, which is narrowed at c, and opens into a
bulb, to which is. attached the capillary ad, which
again terminates in the wider tube de. The tube
is filled with liquid from the bottle up to the point c,
by aspiration through the caoutchouc tube ¢; the
liquid is then allowed to flow out, and the time
noted which its surface takes in falling from c toa
mark, a. If the experiment be made with water,
which is taken as standard, then, using the same
apparatus, other liquids may be compared with it ;
this has the advantage of dispensing with a deter-
mination of the dimensions of the tube, and par-
ticularly of the diameter—a matter of importance,
since its fourth power occurs in the formula, and thus
“any error in its determination greatly affects the
result.
If ¢ is the time required for the flow of the
given volume of water, and 2’ that of a liquid whose
coefficient is 7 and sp. gr. o, then
i
ball ni
il
i,
I
ee
Tl
|
|
ih
|
\
Wy ll
HT MATTIE:
I
|
HA
Ht
the coefficient of water and its specific gravity being each unity.
A lubricating substance applied between an axle and its bearing adheres
on the one hand to the axle, and on the other to the bearing, the outer layer
is at rest, the inner one rotates with the axle. The internal friction acts in
opposition to the motion, and the advantage of lubricators is that this internal
friction is far less than the sliding friction.
By observing the rate of diminution in the number of oscillations of a
horizontal disc suspended by a thread when immersed in water, Meyer de-
termined the coefficient of the frictional or internal resistance of water, and
found that at 10° it was equal to 001567 granime on a square centimetre :
. and for air it was about 34 as much.
150. Form of the jet.—After the contracted vein, the jet has the form
of a solid rod for a short distance, but then begins to separate into drops,
which present a peculiar appearance. Theyseem to form a series of ventral
and nodal segments (fig. 134). The ventral segments consist of drops extended
in a horizontal direction, and the nodal segments in a longitudinal direction.
And as the ventral and nodal segments have respectively a fixed position,
each drop must alternately become elongated and flattened while it is
138 On Liquids [150-
falling (fig. 135). Between any two drops there are smaller ones, so that the
whole jet has a tube-like appearance.
These alterations in form have been explained as being due to vibrations
in the mouth of the vessel itself. Their position is modified by extraneous
influences, such as musical and other sounds, but only when these influences
affect the edges themselves. When the vibrations of the vessel itself are
stopped, the enlargements and contractions in the jet cease also ; they are
strengthened, on the contrary, if a violoncello, for instance, is sounded.
If the jet is momentarily illuminated by the electric spark, its structure is
well seen ; the drops appear then to be stationary, and separate from each
other. Ifthe aperture is not circular, the form of the jet undergoes curious
changes.
0
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.
»
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.
7
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e
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ay ie) ———
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Fig. 136
When air issues from a gasholder under a pressure of 48 atmospheres,
the jet can be ascertained by photography to be resolved into a series of
drops of air following each other at equal intervals.
151. Barker’s mill—If water be contained in a vessel, and an aperture
be made in one of the sides, the pressure at this point is removed, for it is
expended in sending out the water ; but it remains on the other side ; and if
the vessel were movable in a horizontal direction, it would move in a direc-
tion opposite to that of the issuing jet. This is illustrated by the apparatus
known as the Aydraulic tourniquet or Barker's mili (fig. 136). It consists
of a glass vessel, M, containing water, and capable of moving about its
vertical axis. At the lower part there is a tube, C, bent horizontally in oppo-
site directions at the two ends. If the vessel were full of water and the tubes
closed, the pressure on the sides of C would balance each other, being equal
and acting in contrary directions ; but, being open, the water runs out, and the
—152] Water-wheels. Turbines 139
pressure is not exerted on the open part, but only on the opposite side, as
shown in the figure A. And this pressure, not being neutralised by an
opposite pressure imparts a rotatory motion in the direction of the arrow,
the velocity of which increases with the height of the liquid and the size of
the aperture.
The same principle may be illustrated by the following experiment. A
tall cylinder containing water, and provided with a lateral stopcock near the
bottom, is placed on a light shallow dish on water, so that it easily floats.
On opening the stopcock so as to allow water to flow out, the vessel
is observed to move in a direction diametrically opposite to that in which
the water is issuing. Similarly, if a vessel containing water be suspended
by a string on opening an aperture in one of the sides the water will jet out,
and the vessel be deflected away from the vertical in the opposite direction.
Segner water-wheel and the reaction machine depend on this principle.
So also do rotating fireworks; that is, an unbalanced reaction from the
heated gases which issue from openings in them gives them motion in the
opposite irection.
152. Water-wheels. Turbines.—When water is continuously flowing
from a_igher to a lower level, it may be made use of as a motive power.
The motive power of water is generally utilised either by means of wafer-
wheels, turbines, rams, or hydraulic engines.
Water-wheels are wheels provided with buckets or float-boards at the
circumference, on which the water acts either by pressure or by impact.
They are made to turn in a vertical plane round a horizontal axis, and are
of two principal kinds, wzdershot and overshot. In undershot wheels the
float boards are placed radially—that is, at right angles to the circumference
of the wheel. The lowest flat-boards are immersed in the water, which
flows with a velocity depending on the height of the fall. Such wheels are
applicable where the quantity of water is great but the fall inconsiderable.
Overshot wheels are used with a small quantity of water which has a high
fall, as with small mcuntain streams. On the circumference of the wheel
there are buckets of a peculiar shape. The water falls into the buckets on
the upper part of the wheel, which is thus moved by the weight of the water,
and as each bucket arrives at the lowest point of revolution it discharges all
the water, and ascends empty.
An overshot wheel driven by an extraneous force may be used for raising
water, as in dredging machines ; and an undershot one for moving a vessel
to which its axis is fixed, as in the paddles of steam-vessels.
The furbine is a horizontal water-wheel, and is similar in principle to the
hydraulic tourniquet or reaction wheel (151). It consists of a pair of discs,
one above the other, connected together by a number of specially shaped thin
-arms or blades, which divide the space between the discs into an equal
number of curved radial chambers. The wheel works generally upon a
vertical axis, and one of the discs is cut away at the centre. In an outward
Jlow turbine, the water enters through the opening so made into the space
between the discs, and passes outwards radially through the chambers above
mentioned, causing the wheel to rotate by its reaction upon their curved
walls. In order to prevent waste of energy in giving useless rotation to the
water, the peripheral openings of the wheel are surrounded by a series of
140 On Liquids [152-
corresponding fixed chambers, whose sides (gu¢de-b/ades) are so curved that
the water when it leaves them has lost all its rotational motion, and simply
flows away at right angles to the axis. In an zzward flow turbine the water
enters the peripheral opening of the wheel through the guide-blades, and
leaves the wheel at the centre.
The total theoretical effect of a fall of water is never realised ; for the
water, after acting on the wheel, still retains some velocity, and therefore
does not impart the whole of its energy to the wheel. In many cases water
flows past without acting at all; if the water acts by impact, vibrations are
produced which are transmitted to the earth and lost ; the same effect is
produced by the friction of water over an edge of the sluice, in the channel
which conveys it, or against the wheel itself, as well as by the friction of
this latter against the axle. A wheel working freely in a stream, as with the
corn-mills on the Rhine near Mainz, does not utilise more than 50 per cent.
of the theoretical effect. One of the most perfect forms of turbines will
work up to over 80 per cent. Turbines also, when properly designed, may
be made to have a very high efficiency either with high or low falls ; while, on
account of the great speed at which they run, they are very much smaller
than water-wheels in proportion to their power. They are thus more ‘ effi-
cient’ motors than steam engines, which, even if perfect, can only transform
into work from 25 to 30 per cent. of the energy represented by the coal they
burn, and seldom in practice utilise more than half of this percentage.
153. The hydraulic ram.—If a quantity of water flow through a pipe
open at one end, and if this aperture be quickly closed, a sudden impact will
be exerted on the closure as well as on the sides of the pipe. Some of the
energy of the falling water is thereby converted into heat, and some exerts a
dangerous pressure on the pipe. The existence of this pressure may be readily
observed in any town with a high-pressure water supply, by the sharp click
heard if the tap through which water is flowing is suddenly closed.
Le
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The hydraulic ram invented by Montgolfier is an arrangement by which
the energy of falling water is applied so as to raise a portion of it to a greater
height than the reservoir from which it is fed.
The principle of such an arrangement is represented in fig. 137, in which
E is the reservoir, A the pipe in which the water falls, B the channel, which
should be long and straight, a and 0 the valves, C the wind-chest, and D the
rising main. Water first flows out in quantity through the valve a, and as
-154] Hydraulic Ram 141
soon as it has acquired a certain velocity it raises that valve, and the
aperture is shut. The impact thus produced, acting on the sides of the pipe
and on the valve 4, raises this valve, and a quantity of water passes into the
wind-chest, shutting off air and compressing it in the space above the
mouth d@ of the rising main D. This air by its elastic force closes the
valve 6, and the water which has entered is raised in the main pipe D.
As soon as the impulsive action is over, and the water in the channel is
at rest, the valve a falls again by its own weight, the flow begins afresh,
and when it has acquired sufficient velocity the valve 6 is again closed,
and the whole process is repeated.
In this way water can be raised to a height several times as great as the
difference in level from E to the valve 6. If no energy were lost in
friction, and in raising the valves, the height of ascent would be to the fall
as the quantity of water which flows out at ais to that which is raised.
Thus + of the water flowing out of the channel could be raised to 4 times
the height of the available fall.
154. Hydraulic engine.—Historically, falling water was one of the
earliest sources of power ; but it is only in recent times that attention has been
called (first by Lord Armstrong) to the advantage of using hydraulic power in
towns and other places where there is no watwra/ fall of water for driving
certain classes of machines, in those cases more especially where the use of
the machinery is only intermittent.
——/ - ~
y yg |
SY A
ili
x Z \ (nu
La ff Z RQ N
NANA ASS SS S , uit \ ; WY
LHL i | i js! "
; \ HHT IT TAHT HP
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V4 waey dS ii SS
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Fig. 13%
For this purpose the most important docks and large warehouses are
now generally furnished with means of obtaining a water-supply at a very
high pressure, generally about 700 pounds to the square inch. Steam-
pumping engines are employed to pump water more or less continuously
into what are practically large cylinders with immensely heavy pistons loaded
to the required pressure. These vessels are called accumulators, and pipes
142 On Liquids f154-
from them are led away to the various places (lock gates, sluice valves,
cranes, capstans, &c.) where power may be wanted. At each of these places
there is some kind of hydraulic motor suitable to the particular work to be
done, and this motor can be instantaneously set to work by opening the
communication between it and the high-pressure water in the accumulator.
The motor used is not uncommonly a small engine similar in principle to
a steam engine, and one of the best of these engines is that illustrated in
fig. 138, which is the invention of Schmidt of Zitirich. It consists of a
cylinder fitted with a piston, c, whose rod is.connected directly to a crank
upon a horizontal shaft. The cylinder has two forts or passages, a and 4,
one at each end, both terminating below in openings upon a convex curved
face, which is kept continually pressed against a similar concave face upon
the framing of the engine. In this fixed face are also an inlet port or passage
A, and outlet passages B. When the cylinder is in the position shown
in the figure, the high-pressure water is passing through A and 4, forcing
the piston along, and driving out the already used water through a and
B. As the piston moves and turns the crank, the cylinder oscillates on
its bearings, and by the time the piston has got to the end of its stroke,
the cylinder then being horizontal, the process is just being reversed, water
passing in through A and a, and out through 4 and B. W is an air-vessel
for preventing shocks.
This motor utilises 90 per cent. of the available power ; in this respect it
far exceeds a steam-engine which does not utilise more than Io per cent. of
the power due to the consumption of the coal burnt.
The chief drawback to the use of water power, except where there is
a large natural supply under pressure, is its expense. For each revolution
of the crank shaft two complete cylinders full of water must be passed
through such an engine, as, whether the power be wanted or not, the water
cannot be expanded like steam.
With any given pressure it is easy to find out how much water will be
required for a given power. Ata pressure of 30 pounds per square inch,
for instance, one horse-power will require, supposing the effictency of the
33000 x 60
492), 30 x 144 x 0°7
gallons per hour, a quantity the cost of which would in most cases put the use
of this power out of the question. The pressure in town mains generally
lies between 20 and 4o pounds per square inch, and it is therefore only in
cases where a special high-pressure supply is available that the power can be
economically used.
In London, water is supplied to consumers by the Hydraulic Power Company
under a pressure of 700 pounds; and the quantity required for one horse-
power would be about 175 gallons. The cost of power supplied in this way
is about fourpence per horse-power per hour, which, although expensive for
continuous working, is not so when it is intermittently used, and when
only the quantity actually consumed is paid for.
Water-power is usually represented by the weight of the water multiplied
into the height of the available fall; or it may also be represented by half
the product of the mass into the square of the velocity. Both measurements
machine to be 70 per cent. ( = about 655 cubic feet or 4,000
~154] Hydraulic Engine 143
give the same result (60). The mass of water falling every hour over
Niagara is estimated at 100,000,000 tons ; taking the vertical depth at 150,
and adding to this 150 as representing the velocity, we have a total fall from
lake to lake of 300 feet. The force which the chief fall alone would furnish
represents 16,800,000 horse-power, which, if furnished by steam, would
require an annual consumption of 260,000 ooo tons of coal, taking 4 pounds
per hour for the horse-power. This is more than all the coal raised in the
year in the whole world.
144 On Gases [155-
BOOK LY.
ON GASES
CHAP Tivive!
PROPERTIES OF GASES. ATMOSPHERE. BAROMETERS
155. Physical properties of gases..-Gases are bodies which, unlike
solids, have no independent shape, and, unlike liquids, have no independent
volume. Their molecules possess almost perfect mobility ; they are con-
ceived as darting about in all directions, and are continually tending to
occupy a greater space. This property of gases is known by the names
expansibility, tenston, or elastic force, from which they are often called elastic
huids.
Gases and liquids have several properties in common, and some in which
they seem to differ are in reality only different degrees of the same property.
Thus, in both, the particles are capable of moving ; in gases with almost
perfect freedom ; in liquids not quite so freely, owing to a greater degree of
viscosity (149). Both are compressible, though in very different degrees.
If a liquid and a gas both exist under the pressure of one atmosphere, and
then the pressure be doubled, the water is compressed by about the zt y5
part, while the gas is compressed by one-half. In density there is a great
difference : water, which is the type of liquids, is 770 times as heavy as air,
the type of gaseous bodies, while under the pressure of one atmosphere. A
gas has no original volume ; it is always elastic, or, in other words, it is
always striving to attain a greater volume ; this tendency to indefinite ex-
pansion is the chief property by which gases are distinguished from liquids.
A spiral spring only shows elasticity when it is compressed; it loses its
tension when it has returned to its primitive condition.
By the aid of pressure and of low temperatures, the force of cohesion
may be so far increased in many gases that they are readily converted into
liquids, and we know now that with sufficient pressure and cold they may all
be liquefied. On the other hand, heat, which increases the vzs vzva of the
molecules, converts liquids, such as water, alcohol, and ether, into the aeriform
state in which they obey all the laws of gases. An aeriform substance is
called a vapour or a gas according as it can or cannot without change of
temperature be compressed into a liquid ; that is, it is a gas if its tempera-
—158] Weight of Gases 145
ture be above its critical temperature (374) and a vapour if below. Formerly, it
was usual to describe as a vapour a substance which at ordinary tempera-
tures is liquid (for instance, steam) and as a gas a substance which, at ordinary
temperatures and pressures, exists only in the gaseous state.
In describing the properties of gases we shall, for obvious reasons, refer
to atmospheric air as their type.
156. Expansibility of gases.—This property of gases, their tendency to
assume continually a greater volume, is exhibited by means of the following
experiment :—A bladder, closed by a stop-
cock and about half full of air, is placed under
the receiver of the air-pump (fig. 139), and a
vacuum is produced, on which the bladder
immediately distends. This arises from the
fact that the molecules of air flying about in
all directions (297) press against the sides of
the bladder. Under ordinary conditions,
this internal pressure is counterbalanced by
the air in the receiver, which exerts an equal
and contrary pressure. But when this pres-
sure is removed, by exhausting the receiver,
the internal pressure becomes evident. When
air is admitted into the receiver, the bladder
resumes its original form. ;
157. Compressibility of gases.—The
compressibility of gases is readily shown by
the pneumatic syringe (fig. 140). This con- Fieticd
sists of a stout glass tube closed at one end,
and provided with a tight-fitting solid piston. When the rod of the piston is
pressed it moves down in the tube, and the air becomes compressed into a
smaller volume; but as soon as the force is removed the air regains its
original volume, and the piston rises to its former position.
al cin |
zi , |
158. Weight of gases.—From their extreme fluidity and expansibility,
gases seem to be uninfluenced by the force of gravity: they nevertheless
possess weight like solids and liquids. To show this, a glass globe of 3 or 4
quarts capacity is taken (fig. 141), the neck of which is provided with a stop-
cock, which hermetically closes it, and by which it can be screwed to the
plate of the air-pump. The globe is then exhausted, and its weight deter-
mined by means of a delicate balance. Air is now allowed to enter, and the
L
146 On Gases [158-
globe again weighed. The weight in the second case will be found to be
greater than before, and if the capacity of the vessel is known, the increase
will obviously be the weight of that volume of air.
By a modification of this method, and with the adoption of certain pre-
cautions, the weight of air and of other gases has been determined. Perhaps
the most accurate are those of Regnault, who found that a
litre of dry air at o° C., and under a pressure of 760 milli-
metres, weighs 1°293187 gramme. Since a litre of water (or
1,000 cubic centimetres) at o° weighs ‘999877 gramme, the
density of air is 000129334 that of water under the same
circumstances ; that is, water is 773 times as heavy as air.
Expressed in English measures, 100 cubic inches of dry air
under the ordinary atmospheric pressure of 30 in. and at the
temperature of 16° C. weigh 31 grains ; the same volume of
carbonic acid gas under the same circumstances weighs
47°25 grains; 1oo cubic inches of hydrogen, the lightest of
all gases, weigh 2°14 grains; and too cubic inches of
hydriodic acid gas weigh 146 grains.
159. Pressure exerted by gases.—Gases exert on their
own molecules, and on the sides of vessels which contain
them, pressures which may be regarded from two points
of view. First, we may neglect the weight of the gas;
secondly, we may take account of its weight. It we neglect
Fig. 14x the weight of any gaseous mass at rest, and only consider its
expansive force, it will be seen that the pressures due to this
force act with the same strength on all points, both of the mass itself and of
the vessel in which it is contained. For itisanecessary consequence of the
elasticity and fluidity of gases that the repulsive force between the molecules
is the same at all points, and acts equally in all directions. This principle
of the equality of the pressure of gases in all directions may be shown ex-
perimentally by means of an apparatus resembling that by which the same
principle is demonstrated for liquids (fig. 71).
If we consider the weight of any gas, we shall see that it gives rise to
pressures which obey the same laws as those produced by the weight of
liquids. Let us imagine a cylinder, with its axis vertical, several miles high,
closed at both ends and full of air. Let us consider any small portion of
the air enclosed between two horizontal planes. This portion must sustain
the weight of all the air above it, and transmit that weight to the air beneath
it, and likewise to the curved surface of the cylinder which contains it, and
at each point in a direction at right angles to the surface. Thus the pressure
increases from the top of the column to the base; at any given layer it
acts equally on equal surfaces, and at right angles to them, whether they
are horizontal, vertical, or inclined. The pressure acts on the sides of
the vessel, and on any small surface it is equal to the weight of a column
of gas whose base is this surface, and whose height its distance from the
summit of the column, The pressure is also independent of the shape and
dimensions of the supposed cylinder, provided the height remain the same.
For a small quantity of gas the pressures due to its weight are quite
insignificant, and may be neglected ; but for large quantities, like the atmo-
sphere, the pressures are considerable, and must be allowed for.
~161] Atmospheric Pressure 14 7
160. The atmosphere: its composition. —The atmosphere is the layer
of air which surrounds our globe in every part. It partakes of the rotatory
motion of the globe, and would remain fixed relatively to terrestrial objects
but for local circumstances, which produce winds, and are constantly dis-
turbing its equilibrium.
It is essentially a mixture of oxygen and nitrogen gases ; its average
composition by volume being as follows :—
Nitrogen ; : ; : , 3 : : eo AG
Oxygen . : AES : , : : : re 08
Aqueous vapour. : : : ; : é nae Od,
Carbonic acid : ‘ : : : : ood
T00°00
The nitrogen of the atmosphere has recently been found by Lord
Rayleigh and Prof. Ramsay to contain about I per cent. of a new gaseous
element to which, in consequence of its extraordinary nertness, its discoverers
have given the name avgov. Argonisabout half as dense again as ordinary
nitrogen, and is condensed at a temperature of — 121° C., under a pressure of
51 atmospheres, to a colourless liquid. When cooled to —190° C. it solidifies.
The carbonic acid arises from the respiration of animals, from the pro-
cess of combustion, and from the decomposition of organic substances.
Boussingault estimated that in Paris the following quantities of carbonic
acid are produced every 24 hours :—
By the population and by animals . . 11,895,000 cubic feet
By processes of combustion . ; 492,101,000 i
103,996,000 i
Notwithstanding this enormous continual production of carbonic acid
the composition of the atmosphere does not vary ; for plants in the process
of vegetation decompose the carbonic acid, assimilating the carbon, and
restoring to the atmosphere the oxygen, which is being continually consumed
in the processes of respiration and combustion.
161. Atmospheric pressure.—If we neglect the perturbations to which
the atmosphere is subject, as being inconsiderable, we may consider it
as a fluid sea of a certain depth, surrounding the earth on all sides, and
exercising the same pressure as if it were a liquid of very small density.
Consequently, the pressure on the unit of area is constant at a given level,
being equal to the weight of the column of atmosphere above that level
whose horizontal section is the unit of area (Ioo). It will act at right angles
to the surface, whatever be its position. It will diminish as we ascend, and
‘Increase as we descend from that level. Consequently, at the same height,
the atmospheric pressures on unequal plane surfaces will be proportional to
the areas of those surfaces, provided they be small in proportion to the
height of the atmosphere.
In virtue of the expansive force of the air, it might be supposed that the
molecules would expand indefinitely into the planetary spaces. But, in pro-
portion as the air expands, its expansive force decreases, and is further
weakened by the low temperature of the upper regions of the atmosphere, so
ie
148 On Gases [161-
that, at a certain height, equilibrium is established between the expansive
force which separates the molecules and the action of gravity which draws
them towards the centre of the earth. It is therefore concluded that the
atmosphere is limited.
From the weight of the atmosphere, and its increase in density, and from
the observation of certain phenomena of twilight, its height has been esti-
mated at from 30 to 4omiles. Above that height the air is extremely rarefied,
and at a height of 60 miles it is assumed that there is a perfect vacuum. On
the other hand, meteorites have been seen at a height of 200 miles, and, as
their luminosity is undoubtedly due to friction against air, there must be air
at such a height. This higher estimate is supported by observations made
at Rio Janeiro on the twilight arc, by M. Liais, who estimated the height
of the atmosphere at between 198 and 212 miles. The question as to the
exact height of the atmosphere must therefore be considered as still awaiting
settlement.
As it has been previously stated that 100 cubic inches of air weigh 31
grains, it will readily be conceived that the whole atmosphere exercises a
considerable pressure on the surface of the earth. The existence of this
pressure is shown by the following experiments.
162. Crushing force of the atmosphere.—On one end of a stout glass
cylinder, about 5 inches high, and open at both ends, a piece of bladder is
tied quite air-tight. The other end, the edge of which is ground and well
greased, is pressed on the plate of the air-pump (fig. 142). As soon as the
air in the vessel is rarefied by working the air-pump, the bladder is depressed
by the weight of the atmosphere above it, and finally bursts with a loud
report caused by the sudden entrance of the air.
Mi
| i
163. Magdeburg hemispheres.—The preceding experiment only serves
to illustrate the downward pressure of the atmosphere. By means of the
-164] Torricelle’s Experiment 149
Magdeburg hemispheres (figs. 143 and 144), the invention of which is due to
Otto von Guericke, burgomaster of Magdeburg, it can be shown that the
pressure acts in all directions. This apparatus consists of two hollow brass
hemispheres of 4 to 43 inches diameter, the edges of which are made to fit
tightly, and are well greased. One of the hemispheres is provided with a
stopcock, by which it can be screwed on to the air-pump, and on the other there
isa handle. As long as the hemispheres contain air they can be separated
without any difficulty, for the external pressure of the atmosphere is counter-
balanced by the elastic force of the air in the interior. But when the air
in the interior is pumped out by means of the air-pump, the hemispheres
cannot be separated without a powerful effort: and as this is the case in
whatever position they are held, it follows that the atmospheric pressure is
transmitted in all directions.
DETERMINATION OF THE ATMOSPHERIC PRESSURE. BAROMETERS.
164. Torricelli’s experiment.—The above experiments demonstrate the
existence of the atmospheric pressure, but they give no precise indication
as to its amount. The following experiment, which was first made in 1643
by Torricelli, a pupil of Galileo, gives an
exact measure of the pressure of the
atmosphere.
A glass tube is taken, about a yard
long and a quarter of an inch internal
diameter (fig. 145). It is sealed at one
end, and is quite filled with mercury.
The aperture C being closed by the
thumb, the tube is inverted, the open end
placed in a small mercury trough, and
the thumb removed. The tube being in
a vertical position, the column of mercury
sinks, and, after oscillating some time, it
finally comes to rest at a height, A, about
301nches above the mercury in the trough.
The mercury is raised in the tube by the
pressure of the atmosphere on the mer-
cury in the trough. There is no contrary
pressure on the mercury in the tube,
because it is closed ; but, if the end of
the tube be opened, the atmosphere will
press equally inside and outside the tube,
and the mercury will sink to the level of
that in the trough. It has been shown in
Hydrostatics (108) that the heights of
two columns of liquid in communication
with each other are inversely as their
densities ; and hence it follows that the Fig. 145
pressure of the atmosphere is equal to
that of a column of mercury the height of which is 30 inches. If the
pressure of the atmosphere diminishes, the height of the column which it
can sustain must also diminish.
150 On Gases [165-
165. Pascal’s experiments.—Pascal, who wished to ascertain whether
the force which sustained the mercury in the tube was really the pressure
of the atmosphere, made the following experiments. (i.) If it were the case,
then the column of mercury ought to be lower in proportion as we ascend in
the atmosphere. He accordingly requested one of his relatives to repeat
Torricell’s experiment on the summit of Puy de Dome in Auvergne.
This was done, and it was found that the column of mercury was about 3
inches lower, thus proving that it is really the pressure due to the weight of the
atmosphere which supports the mercury, since, when this weight diminishes,
the height of the column also diminishes. (i1.) Pascal repeated Torricelli’s
experiment at Rouen in 1646, with other liquids. He closed a tube nearly
50 feet long at one end, and, having filled it with water, placed it vertically in
a vessel of water, and found that the water stood in the tube at a height of
34 feet ; that is, 13°6 times as high asmercury. SButsince the mercury is 13°6
times as heavy as water, the height of the column of water was exactly
equal to that of a column of mercury in Torricelli’s experiment, and it was
consequently the same force, the pressure of the atmosphere, which succes-
sively supported the two liquids. Pascal’s other experiments with oil and
with wine gave similar results.
166. Amount of the atmospheric pressure.—Let us assume that the
tube in the above experiment is a cylinder, the section of which is equal toa
square inch ; then, since the height of the column of mercury, in round num-
bers, is 30 inches, the column will contain 30 cubic inches ; and as a cubic
inch of mercury weighs 3,433°5 grains = 0°49 of a pound, the pressure of such
a column ona square inch of surface is equal to 14°7 pounds. In round
numbers, the pressure of the atmosphere is taken at 15 pounds on the square
inch. A surface of a foot square contains 144 square inches, and therefore
the pressure upon it is equal to 2,160 pounds, or nearly a ton. Expressed
in the metrical system the standard atmospheric pressure at o° and the sea-
level is 760 millimetres, which is equal to 29:9217 inches ; anda calculation
similar to the above shows that the pressure on a square centimetre is
= 1:032896 kilogramme, or 1°‘01327 x 10° dynes per sq. cm.
For convenience of calculation Everett has proposed to adopt the pressure
of a megadyne per sq. cm. or 10 C.G.S. units of pressure-intensity, as the
standard pressure ; this with a value of g=981'17 at Greenwich for this
country would represent a height of 74:96 cm. or 29°513 inches.
A gas or liquid which acts in such a manner that a square inch of surface
is exposed to a pressure of 15 pounds is called a pressure of one atmosphere.
If, for instance, the elastic force of the steam of a boiler isso great that each
square inch of the internal surface is exposed to a pressure of 90 pounds
(=6x 15), we say it is under a pressure of six atmospheres.
The surface of the body of a man of middle size is about 16 square feet ;
the pressure, therefore, which a man supports on the surface of his body is
35,560 pounds, or nearly 16 tons. Such an enormous pressure might seem
impossible to be borne ; but it must be remembered that, in all directions,
there are equal and contrary pressures which counterbalance one another.
It might also be supposed that the effect of this force, acting in all directions,
would be to press the body together and crush it. But the solid parts of the
skeleton could resist a far greater pressure ; and as to the air and liquids
-168] Cistern Barometer I51
contained in the organs and vessels, the air has the same density as the
external air, and cannot be further compressed by the atmospheric pressure ;
and from what has been said about liquids (98), it is clear that they are vir-
tually incompressible. Only by considerable variations in pressure is the
body affected, as by ascending great heights, or by divers in diving bells and
the like. When the external pressure is removed from any portion of the
body, either by means of a cupping-vessel or by the air-pump, the pressure
from within is seen by the distension of the surface.
167. Different kinds of barometers.—The instruments used for measur-
ing the atmospheric pressure are called darometers. In ordinary barometers
the pressure is measured by the height of a column of mercury, as in Torri-
celli’s experiment ; the barometers which we are about to describe are of this
kind. But there are barometers without any liquid, one of which, the aneroid
(190), is remarkable for its simplicity and portability.
168. Cistern barometer.—The céstern barometer consists of a straight
glass tube closed at one end, about 33 inches long, filled with mercury, and
dipping into a cistern also containing mercury. In order to render the
barometer more portable, and the variations of level in the cistern less
perceptible when the mercury rises or falls in the tube, several different
forms have been constructed.. Fig. 146 represents one form of the cistern
barometer. The apparatus is fixed to a mahogany stand, on the upper part
of which there is a scale graduated in millimetres or inches from the level
of the mercury in the cistern ; a movable index, z, shows on the scale the
level of the mercury. A thermometer on one side indicates the temperature.
There is one fault to which this barometer is liable, in common with all
others of the same kind. The zero of the scale does not always correspond
to the level of the mercury in the cistern. For, as the atmospheric pressure
is not always the same, the height of the mercurial column varies ; some-
times mercury is forced from the cistern into the tube, and sometimes from
the tube into the cistern, so that in the majority of cases the graduation of
the barometer does not indicate the true height. If the diameter of the
cistern is large, relatively to that of the tube, the error from this source, which
is known as the error of capacity, is lessened.
The height of the barometer is the distance between the levels of the
mercury in the tube and in the cistern. Hence the barometer should
always be perfectly vertical ; for if not, the tube being inclined, the column of
mercury is elongated (fig. 147), and the number read off on the scale is too
great. As the pressure which the mercury exerts by its weight at the base
of the tube is independent of the form of the tube and of its diameter (102),
provided it is not capillary, the height of the barometer is independent of
the diameter of the tube and of its shape, but is inversely as the density of
the liquid. With mercury the mean height at the level of the sea is 29°92,
Or, in round numbers, 30 inches ; in a water barometer it would be about
34 feet, or 10°33 metres.
In marine barometers the error of capacity is got rid of by graduating the
scale, not in the true measurements, but by an empirical correction depending
on the relative diameters of the tube and cistern. Thus if a rise of 1o mm.
in the tube produced a fall of 1 mm. in the cistern, the true change would not
be iIomm. but 11 mm. This is obviously allowed for by dividing the space
152 On Gases [168-
of 1o mm. on the scale into 11 mm: The correctness of such an instrument
depends on the accuracy with which the scale is laid off.
169. Fortin’s barometer.—/fortin’s barometer differs in the shape of
the cistern from that just described. The base of the cistern is made of
leather, and can be raised or lowered by means of a screw; this has the
advantage that a constant level can be obtained, and also that the instru-
ment is made more portable. For, in travelling, it is only necessary to raise
Fig. 146 Fig. 147
the leather until the mercury, which rises with it, quite fills the cistern and
the tube ; the barometer may then be inclined, and even inverted, without
any fear that a bubble of air may enter, or that the shock of the mercury
may crack the tube.
Fig. 148 represents the arrangement of the barometer, the tube of which
is placed in a brass case. At the top of this case there are two longitudinal
slits on opposite sides, so that the level of the mercury, B, is seen. The
scale on the case is graduated in millimetres. An index, A, moved by the
-169] Fortin’s Barometer 153
hand, gives by means of a vernier the height of the mercury to 4th of a
millimetre. At the bottom of a case is the cistern, 6, containing mercury, o.
Fig. 149 shows the details of the cistern on a larger scale. It consists of
a glass cylinder, 4, through which the mercury can be seen ; this is closed at
the top by a boxwood disc fitted on the under surface of the brass cover M.
Through this passes the barometer tube E, which is drawn out at the end,
and dips in the mercury ; the cistern and the tube are connected by a piece
of buckskin, ce, which is firmly tied at ¢ to a contraction in the tube, and at e
to a brass tubulure in the cover of the cistern. This mode of closing
prevents the mercury from escaping when the barometer is inverted, while
the pores of the leather transmit the atmospheric pressure. The bottom of
the cylinder 6 is cemented on a boxwood cylinder, zz, on a contraction in
which, 22, is firmly tied the buckskin, 77, which forms the base of the cistern.
On this skin is fastened a
wooden button, 1+, which rests
against the end of a screw, C.
According as this is turned
in one direction or the other
the skin sz is raised or
lowered, and with it the mer-
cury. In using this barometer
the mercury is first made ex-
actly level with the point a,
which is effected by turning
the screw C either in one
direction or the other. The
graduation of the scale is
counted from this point a,
and thus the distance of
the top of the column of
mercury from a gives the
height of the barometer.
The bottom of the cistern
is surrounded by a_ brass
case, which is fastened to
the cover M by screws, &,
k, k. We have already
seen (168) the importance
of having the barometer
quite vertical, which is
effected by the following
plan, known as Cardan’s
SUSPENSION.
The metal case containing the barometer is fixed in a copper sheath X
by two screws, a and 4 (fig. 150). This is provided with two axles (only one
of which, 9, is seen in the figure), which turn freely in two holes in a ring, Y.
In a direction at right angles to that of the axles, 00, the ring has also two
similar axles, #z and 2, resting on a support, Z. By means of this double
suspension the barometer can oscillate freely about the axes mm and vo, in
Fig. 149 Fig. 150
154 On Gases [169—
two directions at right angles to each other. But as care is taken that the
point at which these axes cross corresponds to the tube itself, the centre of
gravity of the system, which must always be lower than the axis of sus-
pension, is below the point of intersection, and the barometer is thus perfectly
vertical.
170. Gay-Lussac’s syphon barometer.—The syphon barometer is a
bent glass tube, one of the branches of which is much longer than the other.
Fig. 154 Fig. 155
The longer branch, which is closed at the top, is filled with mercury as in the
cistern barometer ; while the shorter branch, which is open, serves as a
cistern. The difference between the two levels is the height of the barometer.
Fig. 151 represents the syphon barometer as modified by Gay-Lussac.
In order to render it more available for travelling, by preventing the entrance
of air, he joined the two branches by a capillary tube (fig. 152); when the
~171] Precautions in reference to Barometers 155
instrument is inverted (fig. 153) the tube always remains full in virtue of its
capillarity, and air cannot penetrate into the longer branch. A sudden
shock, however, might separate the mercury and admit some air. To avoid
this, Bunten introduced an ingenious modification into the apparatus. The
longer branch is drawn out to a fine point, and is joined to a tube, B, of the
form represented in fig. 154. This arrangement forms an az-trap ; for if air
passes through the capillary tube it cannot penetrate the drawn-out extremity
of the longer branch, but lodges in the upper part of the enlargement B.
In this position it does not affect the observations, since the vacuum is
always at the upper part of the tube ; it is, moreover, easily removed.
In the syphon barometer the shorter branch is closed, but there is a
capillary aperture in the side z, through which the atmospheric pressure is
transmitted.
The barometric height is determined by means of a o scales, which have
a common zero at O, towards the middle of the longer branch, ed are gra-
duated in contrary directions, the one from O to FE, and the other from O to
B, either on the tube itself, or on brass rules fixed parallel to the tube. Two
sliding verniers, 7 and , indicate tenths of a millimetre. The total height of
the barometer, AB, is the sum of the distances from O to A and from O to B.
Fig. 155 represents a very convenient mode of arranging the open end of
a syphon barometer for transport. The quantity of mercury is so arranged
that when the Torricellian space is quite filled with mercury, by inclining the
tube the enlargement is just filled to d@. This is closed by a carefully fitted
cork, fixed on the end of a glass tube, do, about a millimetre in diameter,
which allows for the expansion of mercury by heat. When the barometer is
to be used, the cork and tube are raised.
171. Precautions in reference to barometers.—In the construction of
barometers mercury is chosen in preference to any other liquid, since, being
the densest of all liquids, it stands at the least height. When the mercury
barometer stands at 30 inches, the water barometer would stand at about
34 feet (168). It also deserves preference because it does not moisten the
glass. It is necessary that the mercury be pure and free from oxide, other-
wise it adheres to the glass and tarnishes it. Moreover, if it is impure, its
density is changed, and the height of the barometer is too great or too small.
Mercury is purified, before being used for barometers, by treatment with
dilute nitric acid, and by distillation.
The space at the top of the tube (figs. 146 and 151), which is called the
Lorricellian vacuum, must be quite free from air and from aqueous vapour,
for otherwise either would depress the mercurial column by its elastic force.
To obtain this result, a small quantity of pure mercury is placed in the tube
and boiled for some time. It is then allowed to cool, and a further quantity,
previously warmed, added, which is boiled, and so on, until the tube is quite
full ; in this manner the moisture and the air which adhere to the sides of the
tube (196) pass off with the mercurial vapour. A barometer tube should not
be too narrow, for otherwise the mercury is moved with difficulty ; and before
a reading is taken, the barometer should be tapped so as to get rid of the
Be esion, to the glass.
A Paina | is free from air and moisture if, when it is inclined, the
150 On Gases _ [171-
mercury strikes with a sharp metallic sound against the top of the tube. If
there is air or moisture in it, the sound is deadened.
172. Correction for capillarity.x—In cistern barometers
there is always a certain depression of the mercurial column
due to capillarity, unless the internal diameter of the tube
exceeds o'8 inch. To make the correction due to this
depression, it is not enough to know the diameter of the
tube ; we must also know the height of the meniscus, od (fig.
156), which varies according as the meniscus has been
formed during an ascending or descending motion of the
mercury in the tube. Consequently, the height of the
meniscus must be determined by bringing the pointer to
the level a4, and then to the level d, when the difference of the readings will
give the height, od, required. These two terms—namely, the internal
diameter of the tube and the height of the meniscus—being known, the
resulting correction can be taken out of the following table :
Fig. 156
Height of sagitta of meniscus in inches
|
Internal
| diameter | 5 rh
| in inches | | | |
O‘OIO O°OI5 | 0°020 0°025 | 0'030 0°035 0040
O°157 0'0293 | 070431 | 0°0555 | 00677 | 0:0780 | 0:0870 | 0°0948
0'236 | OOIIQ | O°0176 | 0°O231 | 0°0294 | 0°0342 | 0°0398 | 0°0432
0°315 | 010060 | 0:0088 | o-0118 | 00144 | 00175 | 0°0196 | 0:0221
07394 | 0°0039 | 0°0048 | 0:0063 | 0°0078 | 070095 | O;OIIO O'0I25
0°472 | 0°0020 | 00029 | 0°0036 | 00045 | 0°0053 | 0°0063 0°0073
O°550 | O'001O | O'00I7 | 0'0024 | 00029 | 0°0034 0°0039 0°0044
\
In the syphon barometer the two tubes are of the same diameter, so
that the error caused by the depression in the one tube very nearly corrects
that caused by the depression in the other. As, however, the meniscus in
the one tube is formed by a column of mercury with an ascending motion,
while that in the other is formed by a column with a descending motion,
their heights will not be the same, and the reciprocal correction will not be
quite exact.
173. Correction for temperature.—In all observations with barometers,
whatever be their construction, a correction must be made for temperature.
Mercury contracts and expands with change of temperature, hence its
density changes, and consequently the barometric height for a given pressure
is inversely as the density of the mercury, so that for different atmospheric
pressures the mercurial column might have the same height. Accordingly,
in each observation the height observed must be reduced to a standard
temperature. The choice of this is quite arbitrary, but that of melting ice is
always adopted in practice. It will be seen in the book on Heat how this
correction is made.
174. Variations in the height of the barometer.—When the barometer
is observed for several days, its height, corrected for temperature, is found
—175] Causes of Barometric Variations Tse
to vary in the same place, not only from one day to another, but also during
the same day.
The extent of these variations—thatis, the difference between the greatest
and the least height—is different in different places. It increases from the
equator towards the poles. Except under extraordinary circumstances, the
greatest variations do not exceed six millimetres under the equator, 30 under
the tropic of Cancer, 40 in France, and 60 at 25 degrees from the pole. The
greatest variations are observed in winter.
The mean datly height is the height obtained by dividing the sum of 24
successive hourly observations by 24. In our latitudes the barometric height
at noon corresponds to the mean daily height. The mean monthly height
is obtained by adding together the mean daily heights for a month and
dividing by 30. The sean yearly height is similarly obtained.
Under the equator the mean annual height at the level of the sea is
o™-758, or 29°84 inches. It increases from the equator, and between the
latitudes 30° and 4o° it attains a maximum of 0™°763, or 30°04 inches. In
lower latitudes it decreases, and in Paris it does not exceed 0o™°7568.
The general mean at the level of the sea is o™-761, or 29°96 inches.
The mean monthly height is greater in winter than in summer, in conse-
quence of the cooler atmosphere.
Two kinds of variations are observed in the barometer :—Ist, the acc7-
dental variations, which present no regularity ; they depend on the seasons,
the direction of the winds, and the geographical position, and are common
in our climates ; 2nd, the dazly variations, which are produced periodically
at certain hours of the day.
At the equator, and between the tropics, no accidental variations are
observed ; but the daily variations take place with such regularity that a
barometer may serve to a certain extent as a clock. The barometer sinks
from midday till towards four o’clock ; it then rises, and reaches its maximum
at about ten o’clock in the evening. It then again sinks, and reaches a
second minimum towards four o’clock in the morning, and a second maxi-
mum at ten o’clock. In the temperate zones there are also daily variations,
but they are detected with difficulty, since they occur in conjunction with
accidental variations.
The hours of the maxima and minima appear to be the same in all
climates, whatever be the latitude ; they merely vary a little with the seasons.
175. Causes of barometric variations.—It is observed that the course
of the barometer is generally in the opposite direction to that of the thermo-
meter ; that is, that when the temperature rises the barometer falls, and vzce
versa ; which indicates that the barometric variations at any given place are
produced by the expansion or contraction of the air, and therefore by its
change in density. If the temperature were the same throughout the whole
extent of the atmosphere, no currents would be produced, and at the same
height atmospheric pressure would be everywhere the same. But when
any portion of the atmosphere becomes warmer than the neighbouring parts
its specific gravity is diminished, and it rises and passes away through
the upper regions of the air, whence it follows that the pressure is
diminished and the barometer falls. If any portion of the atmosphere
retains its temperature, while the neighbouring parts become cooler, the same
158 On Gases [175-
effect is produced ; for in this case, too, the density of the first-mentioned
portion is less than that of the others. Hence, also, it usually happens that
an extraordinary fall of the barometer at one place is counterbalanced by
an extraordinary rise at another place. The daily variations appear to
result from the expansions and contractions which are periodically pro-
duced in the atmosphere by the heat of the sun during the rotation of the
earth.
176. Relation of barometric variations to the state of the weather.—
It has been observed that, in our climate, the barometer in fine weather is
generally above 30 inches, and is below this point when there is rain, snow,
wind, or storm ; and also, that for any given number of days at which the
barometer stands at 30 inches there are as many fine as rainy days. From
this coincidence between the height of the barometer and the state of the
weather, the following indications have been marked on the barometer,
counting by thirds of an inch above and below 30 inches :—
Height State of the weather
31 inches . : ; : Very "dary:
502 CEUs : } ; . Settled weather,
BOTY , | Fine weather.
30.) Sees ; ; . Variable.
aoe 0) ee : é . Rain or wind.
5 Loy Ee : ; ; . Much rain.
ete ky dls : ; ; .- Tempest:
In using the barometer as an indicator of the state of the weather, we
must not forget that it really only serves to measure the pressure of the atmo-
sphere, and that it only rises or falls as the pressure in-
creases or diminishes; and although a change of
weather frequently coincides with a change in the
pressure, they are not necessarily connected. This
coincidence arises from meteorological conditions
peculiar to our climate, and does not occur every-
where. That a fall in the barometer usually precedes
rain in our latitudes is caused by the position of
Europe. The prevailing winds here are the south-
west and north-east. The former, coming to us from
the equatorial regions, are warmer and lighter. They
often, therefore, biow for hours or even days in the
higher regions of the atmosphere before manifesting
themselves on the surface of the earth. The air is
therefore lighter, and the pressure lower. Hence a
fall of the barometer is a probable indication of the
south-west winds, which gradually extend downwards,
and, reaching us, after having traversed large tracts
of water, are charged with moisture, and bring us rain.
The north-east wind blows simultaneously aboveand
below, but the hindrances to the motion of the current
on the earth, by hills, forests, and houses, cause the
upper current to be somewhat in Bitanee of the lower ones, fought not so
much so as the south-west wind. The air is therefore LSE heavier
4
178] Fixed Barometer 159
even before we perceive the north-east, and a rise in the barometer affords
a forecast of the occurrence of this wind, which, as it reaches us after having
passed over the immense tracts of dry land in Central and Northern Europe,
is mostly dry and fine.
When the barometer rises or sinks slowly, that is, for two or three days,
towards fine weather or towards rain, it has been found from a great number
of observations that the indications are then extremely probable. Sudden
variations in either direction indicate bad weather or wind.
177. Wheel barometer.—The wheel barometer, which was invented by
Hooke, is a syphon barometer, and is especially intended to indicate good
and bad weather (fig. 157). In the shorter leg of the syphon there is a float
which rises and falls with the mercury. 1, OG PV, =I+e, the gas
—184] Boyle's Law 169
: ‘ ; id is
ismore compressible than Boyle’s law requires. If ey << 1b OF ay
BV Pay.
the gas is less compressible than it would be in accordance with the law.
The following table gives the results of a series of experiments made on
ait, nitrogen, carbonic acid, and hydrogen :—
sae ALES
Air Nitrogen Carbonic acid Hydrogen
Pav, Pay PoV
12 ovo P ov%o P ACR) Pp SON
P,V, ‘ P.V, A PVG 5 PV,
mm mm mm mm
738°72 | YZ'oor414 75346 r°000988 764°03 I°007597 = oe
2II2°53 I°002765 495392 | 1°002952 3486°13 1°028698 2211°18 0°998584
4140°82 1°003253 8628°54 1°004768 4879°77 1°045625 5845718 o’996121
9330°41 1°006366 10g81"42 1'000456 9619°97 1155865 g176°50 =| 0°992933
Regnault’s conclusions were :—
1. That no gas rigorously obeys Boyle’s law. The divergence is small
for small pressures, but increases with the pressure.
2. That «¢ is positive for all the gases experimented on except hydrogen.
Hydrogen then is less compressible, all the other gases more compressible,
than Boyle’s law requires.
3. The divergence from the law is greater for the easily liquefiable gases,
such as carbonic acid, sulphurous acid, ammonia, and cyanogen, than for
the gases called in Regnault’s time permanent gases, viz. oxygen, nitrogen,
methane, nitric oxide, and carbon monoxide. F
Thus to reduce air to 345 of its original volume, a pressure of 19°7199 atm.
was required instead of 20; and while carbonic acid only required 16°705,
hydrogen required 20:269 atmospheres.
Very much higher pressures have been employed in similar experiments
by Natterer, who applied.pressures of 2,900 atmospheres, and by Andrews.
Natterer’s experiments’ showed that air, oxygen, nitrogen, and carbonic
oxide are for moderate pressures more compressible and for high pressures
less compressible than in accordance with Boyle’s law. Andrews’s experi-
ments will be described later (374). Cailletet used a special apparatus by
which the pressure could be raised to 600 atmospheres.
Amagat made a remarkable series of experiments by a method based
on Boyle’s experiment. The pressure could be applied directly by means
of mercury in a steel tube about 1,300 feet: in length, arranged in the shaft
of a deep coalpit, and suitably connected at the bottom with a carefully
calibrated glass compression tube. In this way pressures of as much as 500
atmospheres could be applied ; the temperatures were kept constant by sur-
rounding the compression tube by a jacket through which water circulated.
The general result of these experiments is exhibited by the curves in
fig. 166, which are plotted with pressures as abscissz and the products PV
as ordinates. Were Boyle’s law true for these gases, the curves would be
straight lines parallel to the axis of pressures. The curves show that PV
diminishes at first for all the gases examined (except hydrogen). The
deviation from Boyle’s law reaches a maximum, different for different gases,
and then diminishes ; further, that at a certain pressure, which for atmo-
170 On Gases [184-
spheric air is 175 atmospheres, or a little over one ton weight per square
inch, each gas accurately obeys Boyle’s law. From this point the devia-
tion from the law is in the same direction as that exhibited by hydrogen,
and appears to increase indefinitely with the pressure.
\ome
ENR a da
ERNNK
fe
ia
=
Rezeakt
=
FENCN:
aL eR
ENG CAcmaa
A
bn intnt
>
"&
S
Le
Fig. 166
Experiments have been made as to the validity of Boyle’s law for pres-
sures much lower than one atmosphere, but the variations observed are
within the errors of observation.
185. Van der Waals’ formula.—Under high pressures gases do not, as
we have seen, follow Boyle’s law with strictness. In order to account for these
discrepancies, Van der Waals has introduced a modification into the formula
PV =const. (183) which is based on the following considerations. We shall
afterwards see (296) that Boyle’s law may be deduced from the dynamical
theory of gases, which assumes that they are made up of infinitely small
particles moving with great velocities ;, it is also assumed that these particles
have no cohesion or specificattraction for each other, and further, that they are
mere mathematical points. )
Van der Waals takes account of these limitations. He considers that the
cohesion a, which the particles possess, though small, has still a certain value,
the effect of which is to add itself to the pressure ; its force will be proportional
to the number of acting and attracting particles, and will be directly propor-
tional to the square of the density, or inversely proportional to the square of
the volume. The other correction is for the volume of the particles them-
selves, 6, which, though exceedingly small, has a certain value. The pressure
of a given mass of gas being due to the number of impacts which take place
186] Manometers 171
in a given time, it is clear that if the particles have a certain magnitude they
must collide against each other more frequently than if they are mere mathe-
matical points ; the influence on the formula will be that the volume V
will be diminished by an amount which represents a multiple of the molecular
volume, or the space actually occupied by the particles.
The formula of Boyle’s law, as thus modified by Van der Waals, becomes
( + vi) (V — 6) = const.
It will thus be seen that the two influences mentioned affect Boyle’s law
in opposite directions. With hydrogen, where the molecules have little or
no attraction, there is no cohesion, and accordingly the pro-
duct PV increases continuously with the pressure, and there
is NO maximum of compressibility.
With other gases @ has a definite value ; at low pres-
sures the product PV is less than that required by Boyle’s
law, and the influence of @ preponderates ; but asthe pressure
continuously increases this diminishes in comparison with
the influence of 4, and the product now increases, and at |,,;
high pressures the gases behave as does hydrogen at low :
ones. Between these a maximum compressibility is seen,
which varies with different gases according to the values of |
a and 6 in each case.
Van der Waals deduced from the experimental results
obtained by Regnault for the comparison of various gases
and for their expansion by heat, values for a@ and 4 for the
respective gases, which when introduced into the formula
satisfactorily represent the numbers obtained by experiment.
Thus for 4 in the case of hydrogen he obtained the
number 0:00069 ; this is confirmed by Budde, who obtained
0°0007 by an entirely different method.
186. Manometers.—Manometers are instruments for
measuring the pressure of gases or vapours. In all such in-
struments the unit chosen is the pressure of one atmosphere,
or thirty inches of mercury at the standard temperature,
which, as we have seen, is nearly ‘15 Ib. to the square inch.
The open-air manometer consists of a bent glass tube BD
(fig. 167), fastened to‘ the bottom of a reservoir AC, of. the
same material, containing mercury, which is connected with
the closed recipient containing the gas or vapour the pres-
sure of which is to be measured. The whole is fixed on a
long plank kept in a vertical position.
In graduating this manometer, C is left open, and the
number 1 marked at the level of the mercury, for this repre-
sents one atmosphere. From this point the numbers 2, 3, 4,
5, 6, are marked at each 30 inches, indicating so many atmo-
spheres, since a column of mercury 30 inches represents a
pressure of one atmosphere. The intervals from 1 to 2, and from 2 to 3,
&c., are divided into tenths. C -being then placed in connection with
a boiler, for example, the mercury rises in the tube BD to a herght
mol
a
3
trol
fn
5
utitsols
bo
ts|>
on
3
wu)
oo
—)
dob
«
Se)
ae
=
toot
S
=
ith
=
sy ois
o i
&
totus by botortorites
=
binitibyit
Ed co
Fig. 167
172
On Gases [186—
which measures the tension of the vapour. In the figure the manometer
marks 2 atmospheres, which represents a height of 30 inches or 76 cm.,
RWW WS
SS
SSG
TTR HL 7,
Fig. 169
plus the atmospheric pressure exerted at the top of the
column through the aperture D.
This manometer is only used where the pressures do
not exceed 5 to 6 atmospheres. Beyond this, the length of
tube necessary makes it very inconvenient, and the following
apparatus is commonly used.
187. Manometer with compressed air.—The manometer
with conipressed air is founded on Boyle’s law: one form is
represented in fig. 168, which may be screwed into a boiler
or steam-pipe where pressure is to be measured. The pres-
sure is transmitted through the opening @ into the closed
space 6. In this is an iron vessel containing mercury, in
which dips the open end of the manometer tube, which is
screwed airtight in the tubulure.
In the graduation of this manometer, the quantity of air
contained in the tube is such that when the aperture @ com-
municates freely with the atmosphere, the level of the
mercury is the same in the tube and in the tubulure.
Consequently, at this level, the number 1 is marked on the
scale to which the tube is affixed. As the pressure acting
through the tubulure @ increases, the mercury rises' in the
tube, until its weight, added to the pressure of the compressed
air, is equal to the external pressure. It would consequently
be incorrect to mark two atmospheres in the middle of the
tube ; for since the volume of the air is reduced to one-half,
its pressure is equal to two atmospheres, and, together with
the weight of the mercury raised in the tube, is therefore
more than two atmospheres. The position of the number is
at such a height that the elastic force of the compressed air,
together with the weight of the column of mercury in the
tube, is equal to two atmospheres. The exact position of
the numbers 2, 3, 4, &c. on the manometer scale can only
be determined by calculation.
188. Volumenometer.—An interesting application of
Boyle’s law is met with in the volumenometer, which is used in
determinations of the specific gravity of solids which cannot be
brought into contact with water or other liquids.: A simple
form consists of a glass tube with a cylinder G at the top
(fig. 169), the edges of which are carefully ground, and which
can be closed hermetically by means of a ground-glass plate
D. The top being open, the tube is immersed until the
level of the mercury inside and outside is the same ; this is
represented by the mark Z. The apparatus is then closed
airtight by the plate, and is raised until the mercury stands
at a height 4, above the level Q in the bath. The original
volume of the enclosed air V, which was under the pressure of the atmosphere,
1 now increased to V + v, since the pressure has diminished by the height of
3 ~190] Anerod Barometer 173
the column of mercury /. Calling the height of the barometer at the time
of observation 4, we shall have V : V+ ee hii :
Placing now in the cylinder a body Kk, whose volume x is unknown, the
same operations are repeated; the tube is raised until the mercury again
stands at the same mark as before, but its height above the bath is now
different ; a second reading, /,, is obtained and we have (V —%) : (V—2).+v
=b—h,:6. Combining and reducing, we getx = (V+ v) (1 - é j= The
volume V+v is constant, and is determined numerically, once for all, by
making the experiment with a substance of known volume, such as a glass
bulb.
This apparatus is also known as the stereometer. It is of great value in
determining the geometrical or true density of gunpowder ; this averages
from 1°67 to 1°84, and is thus materially different from its apparent density,
or the weight of a given volume compared with that of an equal volume of
water, which is from 0°89 to 0-94. “
189. Regnault’s barometric manometer.—For measuring pressures of
less than one atmosphere, Regnault devised the following arrangement,
which is a modification of his fixed barometer (fig. 158). In the barometer
cistern dips a second tube a of the same diameter, open at both ends, and
provided at the top with a three-way cock, one aperture of which is connected
with an air-pump and the other with the space to be exhausted. | The
further the exhaustion is carried the higher the mercury rises in the tube a.
_ The differences of level in the tubes 4 and a give the pressures.. Hence, by
measuring the height a4, by means of the cathetometer, the pressure in the
space that is being exhausted is accurately given. This apparatus is also
called a differential barometer or a barometer gauge.
190. Aneroid barometer.—This instrument derives its name from the
circumstance that no liquid is used in its construction (d, without ; »mpds,
moist). Fig. 170 represents one of the forms of this instrument ; it
consists of a cylindrical metal box, exhausted of air, the top of which is
made of thin corrugated metal, so elastic that it readily yields to alterations
in-the pressure of the atmosphere.
When the pressure increases, the top is pressed inwards ; when, on the
contrary, it decreases, the elasticity of the lid, aided by a spring, tends to
move it inthe opposite direction. These motions are transmitted by delicate
multiplying levers to an index which moves on a scale. The instrument is
graduated empirically by comparing its indications, under different pressures,
with those of an ordinary mercury barometer.
The aneroid has the advantage of being portable, and can be constructed
of such delicacy as to indicate the difference in pressure between the height
of an ordinary table and the ground. It is hence much used in determining
heights in mountain ascents. But it is somewhat liable to get out of order,
especially when it has been subjected to great sudden variations of pressure ;
and its indications must from time to time be controlled by comparison with
those of a standard barometer.
The errors arising from the use of the aneroid are mainly due to the trans-
mission of the motion of the lid by the multiplying arrangement. Goldschmid
of Ziirich devised a form in which the motion of the lid is directly observed.
174 On Gases | [190-
In this instrument, as in other aneroids, the lid of a box a@ (fig. 171), in
which the alterations of pressure are determined, is of fine corrugated sheet
metal. To this is fixed a horizontal metal strip 4, on the front end of which
is a small square e, acting as index. This rises and falls with the movement
of the lid, and indicates on a scale 7’, on the sides of the slit dd’, alterations
of pressure in centimetres. To this strip a second and more delicate one, ¢,
is attached, on the front end of which is also fixed an indexe’. Before making
an observation, the horizontal line of this index is made to coincide with that
st . a;
re aja 5 6 2 i
* NOR wa ia 1 20
or ’ «Bhs
Sp
mun ck
= OLS
GOee SCHMID,
iN
We of
ao KA The whole subject of gas absorption has been investigated by Bunsen.
The general rules are the following :— .
I. For the same gas, the same liquid, and the same temperature, the
weight of gas absorbed is proportional to the pressure. This may also be
expressed by saying that at all pressures the volume dissolved is the same ;
or that the density of the gas absorbed is in constant relation with that of
the external gas which is not absorbed.
Accordinels when the pressure diminishes, the quantity of dissolved
gas decreases. Ifa solution of gas be placed ander the receiver of an air-
pump and the pressure be chenimasaed) the gas ale its expansive force, and
escapes with effervescence.
Il. Lhe guantity of gas absorbed decreases with zncrease of the tempera-
ture; that is to say, when the elastic force of the gas is greater. Thus at
15% water absorbs only 1:00 of carbonic acid.
Ill. Zhe quantity of gas which a liquid can dissolve zs independent of
the nature and of the quantity ike Sunes gases which tt may already hold in
solution.
This absorption of gases may be determined by the absorptiometer re-
presented in fig. 173, yhien consists of a graduated measuring tube, A,
connected by a caoutchouc tube with a tube of
equal diameter, B. The absorption vessel, C, is
connected with A by means of a thin flexible
capillary lead tube ; @ and @ are three-way stop-
cocks, and ¢ an ordinary one. The vessel C is
fitted with air-free liquid, and A with the gas,
which by means of the two three-way stopcocks
is easily effected. The tube B is raised or
lowered until the level of the mercury is the
same as in A, and the volume of gas is read off.
A is now put in connection with C, and, the
stopcock c having been opened, B is raised so
that a determinate volume of liquid runs out.
An equal volume of the gas then passes into C,
and the absorption proceeds, C being constantly
shaken. In order to work at constant tempera-
ture, A and C may be surrounded by water.
In every gaseous mixture each gas exercises
the same pressure as it would if its volume occu-
pied the whole space ; and the total pressure is
equal to the sum of the individual pressures, When a liquid is in contact
with a gaseous mixture, it absorbs a certain part of each gas, but less than
it would if the whole space were occupied by each gas. The quantity of
each gas dissolved is proportional to the pressure which the unabsorbed gas
exercises alone. For instance, oxygen forms only about + the quantity of
air ; and water under ordinary conditions absorbs exactly the same quantity
of oxygen as it would if the atmosphere were entirely formed of this gas
under a pressure equal to # that of the atmosphere.
193. Diffusion of gases, —Phenomena analogous to those of endosmose
(141) are seen in a high degree in the case of gases. When two different
Fig. 173
-193] Diffusion of Gases 177
gases are separated by a porous diaphragm, an interchange takes place
between them, and ultimately the composition of the gas on both sides of the
diaphragm is the same ; but the rapidity with which different gases diffuse
into each other under these circumstances varies considerably. There is,
however, an essential difference between the phenomena of endosmose and
those of diffusion ; for while the inequality in the currents in the former case
is due to the different attraction of the material of the diaphragm for the con-
stituents, in the diffusion of gases the nature of this material has no influence ;
from the smallness of the pores the actions are molecular, and not molar,
and the rate of interchange depends only on the size of the molecules,
that is on the specific gravities of the gases. The laws of the diffusion of
gases were investigated by Graham. Numerous experiments illustrate them,
some of the most interesting of which are the following :—
A glass cylinder closed at one end is filled with carbonic acid gas, its
open end tied over with a bladder, and the whole placed under a jar of
hydrogen. Diffusion takes place between them through the porous dia-
phragm, and after the lapse of a certain time hydrogen has passed through
Fig. 174
the bladder into the cylindrical vessel in much greater quantity than the
carbonic acid which has passed out, so that the bladder becomes very much
distended outwards (fig. 174). If the cylinder be filled with hydrogen and
the bell-jar with carbonic acid, the reverse phenomenon will be produced—
the bladder will be pressed inwards (fig. 175).
A tube about 12 inches long, closed at one end by a plug of dry plaster
of Paris, is filled with dry hydrogen, and its open end then immersed in a
mercury bath. Diffusion of the hydrogen towards the air takes place so
rapidly that a partial vacuum is produced, and mercury rises in the tube to a
height of several inches (fig. 176). If several such tubes are filled with
different gases, and allowed to diffuse into the air in a similar manner, in the
same time, different quantities of the various gases will diffuse, and Graham
found that the law regulating these diffusions is that ‘re guantity of a gas
which passes through a porous diaphragm in a given time ts inversely as
the square root of the density of the gas. Thus, if two vessels of equal
capacity, containing oxygen and hydrogen, be separated by a porous plug,
diffusion takes place ; and after the lapse of some time, for every one part of
N
178 On Gases [193-
oxygen which has passed into the hydrogen, four parts of hydrogen have
passed into the oxygen. Now, the density of hydrogen being 1, that of
oxygen is 16 ; hence the force of diffusion is inversely as the square roots of
these numbers. It is four times as great in the one which has ;% the density
of the other.
Let the stem of an ordinary tobacco pipe be cemented, so that its ends
project, in an outer glass tube, which can be connected with an air-pump
and thus exhausted. On allowing then a slow current of air to enter one
end of the pipe, its nitrogen diffuses more rapidly on its way through the
porous pipe than the heavier oxygen, so that the gas which emerges at the
‘other end of the porous pipe, and which can be collected, is richer in
oxygen, and by repeating the operation on the gas which has passed through,
the proportion of oxygen is so much increased that the gas can relight a
semi-extinguished taper. To this process, in
which one gas can be separated from another by
diffusion, the term azmolyszs is given.
Fig. 177 is an excellent illustration of the
action of diffusion. A porous pot, A, such as is
used for voltaic cells, is fixed by means of a cork
to the glass tube, which contains water up to the
bulb, C, the upper part containing air. Whena
beaker containing hydrogen, B, is placed over the
| pot, the diffusion of the hydrogen into it is so
SRI rapid that the water is at once driven down and
! jets out. When the beaker is removed, the gas
inside the pot, being richer in hydrogen, now
diffuses out with great rapidity, and the water
rises in the tube much higher than its original
level.
194. Effusion of gases.—A gas can only
flow from one space to another space occupied
by the same gas when the pressure in the one
is greater than in the other. fusion is the
term applied to the phenomenon of the passage
of gases into vacuum, through a minute aperture
not much more or less than o’o13 millimetre in
diameter, in a thin plate of metal or of glass ;
for in a tube we are dealing with masses of
gases, and friction comes into play, and in a
larger aperture the particles would strike against
one another, and form eddies and whirlpools.
The velocity of the efflux is measured by the
formula v=.4/2gh, in which / represents the
pressure under which the gas flows, expressed in terms of the height of a
column of the gas which would exert the same pressure as that of the effluent
gas. Thus for air under the ordinary pressure flowing into a vacuum the
pressure is equivalent to a column of mercury 76 centimetres high ; and as
mercury is approximately 10,500 times as dense as air, the equivalent column
of air will be 76 x 10,500= 7,980 metres. Hence the velocity of efflux of air
~195] ' Transpiration of Gases 179
into vacuum is = 1/2 x 9°8 x 7980= 395°5 metres. ‘This velocity into vacuum
only holds, however, for the first moment, for the space contains a continu-
ally increasing quantity of air, so that the velocity becomes continually
smaller, and is null when the pressure on each side is the same. If the height
of the column of air, corresponding to the' external pressure, is known, the
velocity may be calculated by the formula v= ./2¢ (h-/,).
For gases lighter than aira greater height must be inserted in the formula,
and for heavier gases a lower height ; and this change must be inversely as
the change of density. Hence the veloctties of efflux of various gases must
be tnversely as the square roots of their densitzes. A simple inversion of this
statement is that the demszties of two gases are inversely as the squares of
their velocities of effusion. On this law Bunsen has based an interesting
method of determining the densities of gases and vapours, which is of great
service where only small quantities of the substances are available.
The gas in question is contained (fig. 178) in
a glass tube A, closed at the top with a stopper,
S,in the neck, B. Inalittle enlargement here a
thin platinum plate V is fixed, in which is a fine
capillary aperture. The tube is depressed in a
deep mercury trough, CC, until the top 7 of a
glass float D is level with the mercury. The
stopper S having been removed, the gas issues
through the capillary aperture, and the time is
noted which elapses until a mark ¢ in the float
is level with the mercury. Working in this
way with different gases, Bunsen found that
the ratios of the times of effusion are directly
as the sguare roots of the densities, which is
another form of the above statement.
By this method it may often be ascertained
whether a gas is a mixture or not. Thus marsh
gas (CH,) has the same specific gravity (07554)
as a mixture in equal volumes of dimethyl
(C,H,, sp. gr. 1°039) and hydrogen (sp. gr.
0'069), and would furnish the same results on
chemical analysis. But if the composition of
the gas which had been subjected to effusion
were examined in the two cases, it would be
found that the residual marsh gas would retain
the same composition, while that of the mixture
would be different, for a relatively larger
volume of the specifically lighter hydrogen
would have passed out.
195. Transpiration of gases.—If gases issue
through long, fine capillary tubes into a vacuum, the phenomenon is called
transpiration ; and the rate of efflux, or the velocity of transpiration, is not
the same as the rate of diffusion, either through a single aperture or through
a series of fine capillary tubes, as in a porous diaphragm.
This property of gases may be investigated by means of an apparatus
N 2
180 On Gases f[195-—
analogous to that represented in fig. 133, and consisting essentially of an
arrangement by which gas under known pressure is allowed to flow through
a capillary tube of known length and diameter.
The volume which flows out in a given time, or the rate of transpiration, is
represented by a formula which is identical with that for liquids (149) namely,
s _(p—-p,)7*
SSAA Sp lal
where # is the pressure of the gas on entering, and 7, that on leaving the
capillary tube ; ~ is the diameter, and / the length of the tube, and 7 is the
coefficient of internal friction of the gas.
This furnishes an easy method of determining the value of y in this formula,
as all the other magnitudes are capable of direct accurate measurement.
This is a most important physical constant, as it occurs in many formulze by
which molecular magnitudes are determined, such as the length of the mean
free path of gases (298), the number of impacts in a second, and even the
dimensions of the molecules themselves. Expressed in CGS units, the value
of n for air 1s 0°0,18.
196. Absorption of gases by solids.—The surfaces of all solid bodies
exert an attraction on the molecules of gases with which they are in contact
of such a nature that they become covered with a
more or less thick layer of condensed gas. When a
porous body, such as a piece of charcoal, which conse-
quently presents an immensely increased surface in
proportion to its size, is placed in a vessel of ammonia
gas over mercury (fig. 179), the great diminution of
volume which ensues indicates that considerable quan-
tities of gas are absorbed.
Now, although there is no absorption such as arises ~
from chemical combination between the solid and the
gas (as with phosphorus and oxygen), still the quan-
tity of gas absorbed is not entirely dependent on the
physical conditions of the solid body ; it is influenced
in some measure by the chemical nature both of the
solid and the gas. Boxwood charcoal has very great
absorptive power. The following table gives the
volumes of gas, under standard conditions of tempera-
ture and pressure, absorbed by one volume of boxwood charcoal and of
meerschaum respectively :—
Charcoal Meerschaum
Ammonia . : : . : { : go 15
Hydrochloric acid . . é ‘ ; £ 85 —
Sulphurous acid. : ‘ : : ; 65 <4
Sulphuretted hydrogen . : , ‘ ; 55 II
Carbonic acid : } ‘ : : 35 553
Carbonic oxide. : s : 4 9°4 Le
Oxygen ; F ; ’ : 2 I°5
Nitrogen : : : : : 7°4 1°6
Hydrogen. ; F : ‘ : see ehdo765 0'5
197] Occlusion of Gases ISI
The absorption of gases is in general greatest in the case of those which are
most easily liquefied.
Cocoa-nut charcoal is even more highly absorbent; it absorbs 171 of
ammonia, 73 of carbonic acid, and 108 of cyanogen at the ordinary pressure ;
the amount of absorption increases with the pressure. The absorptive
power of pine charcoal is about half as much as that of boxwood. The
charcoal made from cork wood, which is very porous, is not absorbent ;
neither is graphite. Platinum, in the finely divided form known as platinum
sponge, is said to absorb 250 times its volume of oxygen gas. Many other
porous substances, such as gypsum, silk, &c., are also highly absorbent.
If a coin is laid on a plate of glass or metal, after some time, when
the plate is breathed on, an image of the coin appears. If a figure is traced
on a glass plate with the finger, nothing appears until the plate is breathed
on, when the figure is at once seen. Indeed, the traces of an engraving
which has long lain on a glass plate may be produced in this way.
These phenomena are known as Moser’s zmages, for they were first in-
vestigated by Moser, although he explained them erroneously. The correct
explanation was given by Waidele, who ascribed them to alterations in the
layer of gas, vapour, and fine dust which is condensed on the surface of all
solids. If this layer is removed by wiping, on afterwards breathing against
the surface more vapour is condensed on the marks in question, which then
present a different appearance from the rest.
; If a die or a stamp is Jaid on a freshly polished metal plate, one
‘therefore which has been deprived of its atmosphere, the layer of vapour
from the coin will diffuse on to the metal plate, which thereby becomes
altered ; so that when this is breathed on an impression is seen.
Conversely, if a coin is polished and placed on an ordinary glass plate,
it will partially remove the layer of gas from the parts in contact, so that on
breathing on the plate the image is visible.
Ordinary glass kept in moist air becomes covered with a layer of water,
which can be weighed. This is due to an action of the alkali in glass which
attracts moisture, and is absent in glass free from alkali ; it can be consider-
ably diminished by boiling with water, by which the alkali on the surface is
removed. In addition to this layer, which appears rather to be chemically
than physically attracted, there is a temporary one which escapes in a vacuum
at the ordinary temperature.
197. Occlusion of gases.—Graham found that at a high temperature
platinum and iron allow hydrogen to traverse them even more readily than
does caoutchouc in the cold. Thus, while a square metre of caoutchouc o-or4
millimetre in thickness allowed 129 cubic centimetres of hydrogen at 20° to
_ traverse it in a minute, a platinum tube 11 millimetre in thickness and of the
same surface allowed 489 cubic centimetres to traverse it at a bright red heat.
This is probably connected with the property which some metals, though
destitute of physical pores, possess of absorbing gases either on their surface
or in their mass, and to which Graham has applied the term occlusion. It
is best observed by allowing the heated metal to cool in contact with the
gas. The gas cannot then be extracted by the air-pump, but is disengaged
on heating. In this way Graham found that platinum occluded four times
its volume of hydrogen ; iron wire 0°44 its volume of hydrogen, and 4°15
182 On Gases [197-
volumes of carbonic oxide ; silver, reduced from the oxide, absorbed about
seven volumes of oxygen, and nearly one volume of hydrogen when heated
to dull redness in these gases. This property is most remarkable in palla-
dium, which absorbs hydrogen not only in cooling after being heated, but
also in the cold. When, for instance, a palladium electrode is used in the
decomposition of water, one volume of the metal can absorb 98o times its
volume of the gas. This gas is again driven out on being heated, in which
respect there is a resemblance to the solution of gases in liquids. By the
occlusion of hydrogen the volume of palladium is increased by 0°09827 of
its original amount, from which it follows that the hydrogen, which under
ordinary circumstances has a density of 0:000089546 that of water, has herea
density nearly 9,868 times as great, or about 0°88 that of water. Hence the
hydrogen must be in the liquid or even solid state ; it probably forms thus
an alloy with palladium, like a true metal—a view of this gas which is
strongly supported by independent chemical considerations. The physical
properties, too, in so far as they have been examined, support this view of its
being an alloy.
The phenomenon of occlusion may be illustrated by the following experi-
ment (fig. 180). A platinum wire, dc, is stretched between supports on a
glass plate; one end of a _ palladium
@ @ ~ wire, jg, is also fixed, the other end
being attached to the short arm of a light
lever movable about 0, the long arm of
which is loaded with a weight (not repre-
sented in the figure) to keep the wire tight.
The platinum wire is connected with the
positive pole a, and the palladium with the
negative pole @, of a voltaic battery, and
the apparatus is partially immersed in
acidulated water; the water is thereby
decomposed into its constituent gases ;
oxygen is liberated in bubbles from the
platinum wire, but there is no visible dis-
Pigs sso engagement atthe palladium. The latter
becomes longer, however, as is seen by the
motion of the lever. If the current is reversed, the wire again contracts, and
the lever resumes its original position.
~198] Archimedes Principle applied to Gases 183
CHAPTER: IT!
PRESSURE ON BODIES IN AIR. BALLOONS
198. Archimedes’ principle applied to gases.—The pressure exerted
by gases on bodies immersed in them is transmitted equally in all directions,
as has been shown by the experiment
with the Magdeburg hemispheres (163).
It therefore follows that all which has
been said about the equilibrium of
bodies in liquids applies to bodies in
air; they lose apparently a part of
their weight equal-to that of the air
which they displace.
The loss of weight in air is demon-
strated by means of the Jdavoscofe,
which consists of a scalebeam, at one
end of which a small leaden weight
is supported, and at the other there
is a hollow copper sphere (fig. 181).
In the air they exactly balance each
other; but when they are placed
under the receiver of an air-pump, = ies :
and a vacuum is produced, the sphere —————————————
sinks, thereby showing that in reality Pittey
it is heavier than the smaller leaden r
weight. Before the air is exhausted each body is buoyed up by the weight
of the air which it displaces. But as the sphere is much the larger of the
two, its weight undergoes most apparent diminution, and thus, though in
reality the heavier body, it is balanced by the small leaden weight. It may
be proved by means of the same apparatus that this loss is equal to the
weight of the displaced air. Suppose the volume of the sphere is 10 cubic
inches. The weight of this volume of air is 3°1 grains. If now this weight
be added to the leaden weight, it will overbalance the sphere in air, but will
exactly balance it in vacuo. .
The principle of Archimedes is true for bodies in air; all that has been
said about bodies immersed in liquids apples to them ; that is, that when a
body is heavier than air it will sink, owing to the excess of its weight over
the buoyancy. If it is as heavy as air, its weight will exactly counterbalance
the buoyancy, and the body will float in the atmosphere. If the body is
lighter than air, the buoyancy of the air will prevail and the body will rise
184 On Gases [198-
in the atmosphere until it reaches ‘a layer of the same density as its own.
' The force causing ascent is equal to the excess of the buoyancy over the
weight of the body. This is the reason why smoke, vapours, clouds, and air-
balloons rise in the air. It will be understood that by dueyancy is meant the
weight of the medium displaced whatever that medium may be.
AIR-BALLOONS
199. Air-balloons.—H-—A’, if k’>h. Thus water will flow from the
vessel if AB is greater than DC. If AB=DC, there will be no flow ; and if
AB is less than DC, the liquid will flow in the opposite direction.
It follows from the explanation of the siphon that it would not work in
vacuo, nor if the height CD were greater than that of a column of liquid which
counterbalances the atmospheric pressure.
217. The intermittent siphon.—In the zz¢termizttent siphon the flow is
not continuous. It is arranged in a vessel, so that the shorter leg is near the
bottom of the vessel, while the longer leg passes
through it (fig. 209). Being fed by a constant
supply of water, the level gradually rises both
in. the vessel and in the tube to the top of the
siphon, which it fills, and water begins to flow
out. But the apparatus is arranged so that the
flow of the siphon is more rapid than that of the
tube which supplies the vessel, and consequently
the level sinks in the vessel until the shorter
branch no longer dips in the liquid ; the siphon
is then empty, and the flow ceases. But as the
vessel is continually fed from the same source
the level again rises, and the same series of phenomena is reproduced.
The theory of the intermittent siphon explains the natural intermittent
springs which are found in many countries, and of which there is an excel-
lent example near Giggleswick in Yorkshire. Many of these springs fur-
nish water for several days or months, and then, after stopping for a certain
interval, again recommence. In others the flow stops and recommences
several times in an hour.
These phenomena are explained by assuming that there are subterranean
fountains, which are more or less slowly filled by springs, and which are then
emptied by fissures so occurring in the ground as to form an intermittent
siphon.
218. Different kinds of pumps.—/zzszfs are machines which serve to
raise water either by suction, by pressure, or by both effects combined ; they
Fig. 209
—219] Suction-pump 205
are consequently divided into szction or lift pumps, force-pumps, and suction
and forcing pumps.
The various parts entering into the construction of a pump are the barrel,
the piston, the valves, and the pipes. The éarre/ is a cylinder of metal or
of wood, in which is the fzstom. The latter is a metal or wooden cylinder
wrapped with tow, and work- ,
ing with gentle friction the ul TN Ih}
whole length of the barrel. LAS |
The valves are discs of
metal or leather, which alter-
nately close the apertures
which connect the barrel with
the pipes. The most usual
valves are the clack valve (fig. 210) and the conzcal valve (fig. 211). The former
is a metal disc fixed to a hinge on the edge of the orifice to be closed. In order
more effectually to close it, the lower part of the disc is covered with thick
leather. Sometimes the valve consists merely of a leather disc, of larger
diameter than the orifice, nailed on the edge of the orifice. Its flexibility
enables it to act as a hinge.
The conical valve consists of a metal cone fitting in an aperture of the
same shape. Below this is aniron hoop,
through which passes a bolt-head . Afi
fixed to the valve. The object of this es
is to limit the play of the valve when i
it is raised by the water, and to pre- i
vent its removal. | |
WU
pe
TOM Na
Fig. 210 Fig. 211
muta)
TC gnaw me i}
219. Suction-pump.—Fig. 212 re-
presents a model of a suction-pump i
such as is used in lectures, but which |
has essentially the same arrangement
| s
Ne
Win
Hi)
)
mui
ATETEGE
HH! a
is
|||
\
|
as the pumps in common use. It |
consists, Ist, of a glass cylinder, B,
at the bottom of which is a valve, S, /
opening upwards ; 2nd, of a szction- / |
tube, A, which dips into the reservoir WJ
from which water is to be raised ; 3rd,
of a gzston, which is moved up and
down by a rod worked by a handle,
P. The piston is perforated by a hole ;
the upper aperture is closed by a valve,
O, opening upwards.
When the piston rises from the
bottom of the cylinder B, a vacuum is =
produced below, and the valve O is SSS
kept closed by the atmospheric pres- == ——
sure, while the air in the pipe A, in SSS SSS SS
consequence of its elasticity, raises the
valve S, and partially passes into the
cylinder. The air being thus rarefied, water rises in the pipe until the pres-
(G
—
i =
/ =
if i
iN , bse
on =a: uw E
=|
. ba) —
SSS ATI
Tn
Fig. 212
206 On Gases [219-
sure of the liquid column, together with the pressure of the rarefied air
which remains in the tube, counterbalances the pressure of the atmosphere
on the water of the reservoir.
When the piston descends, the valve S closes by its own weight, and prevents
the return of the air from the cylinder into the tube A. The air compressed
by the piston opens the valve O, and escapes into the atmosphere by the
pipe C. With a second stroke of the piston the same series of phenomena
is produced, and after a few strokes the water reaches the cylinder. The
effect is now somewhat modified ; during the descent of the piston the valve
S closes, and the water raises the valve O, and passes above the piston by
which it is lifted into the upper reservoir D. There is now no more air in
the pump, and the water forced by the atmospheric pressure rises with the
piston. It is essential for the action of the pump that the valve S should
be less than 34 feet above the level of the water in which the tube A
dips, for we have seen (165) that a column of water of this height is equal to
the pressure of the atmosphere.
In practice the height of the tube A does not exceed 26 to 28 feet ; for
although the atmospheric pressure can support a higher column, the vacuum
produced in the barrel is
qos not perfect, owing to the
ge —— | fact that the piston does
eu | ! not fit exactly on the
| sd bottom ofthe barrel. But
when the water has passed
the piston, itis the ascend-
ing force ofthe latter which
raises it, and the height
to which it can be brought
depends on the power
which works the piston.
220. Suction- and
force-pump.—The action
of this pump, a model of
which is represented in
fig. 213, depends both on
exhaustion and on _pres-
sure. At the base of the
barrel, where it is cone
nected with the tube A,
there is a valve, S, which
opens upwards. Another
valve, O, opening in the
same direction, closes the
aperture of a conduit,
which passes from a hole,
o, near the valve S, into
a vessel, M, which is called the az7-chamber. From this chamber there is
another tube, D, up which the water is forced.
At each ascent of the piston B, which is solid, the water rises through the
221] Load which the Piston supports 207
tube A into the barrel. When the piston sinks the valve S closes, and the
water is forced through the valve O into the reservoir M, and thence into
the tube D. The height to which it can be raised in this tube depends
solely on the motive force which works the pump.
If the tube D were a prolongation of the tube Jao, the flow would be
intermittent ; it would take place when the piston descended, and would
cease as soon as it ascended. But between these tubes there is an
interval, which, by means of the air in the reservoir M, ensures a continuous
flow. The water forced into the reservoir M divides into two parts, one of
which, rising in D, presses on the water in the reservoir by its weight ; while
the other, in virtue of this pressure, rises in the reservoir above the lower
orifice of the tube D, compressing the air above. Consequently, when the
piston ascends, and no longer forces the water into M, the air of the reser-
voir expands, and raises the liquid in the tube D, until the piston again
descends, so that the jet is continuous.
aed
thy
il
221. Load which the piston supports.—In the suction-pump, when
once the water fills the pipe, and the barrel, as far as the spout, the effort
necessary to raise the piston is equal to the weight of a column of water
the base of which ts this piston, and the height the vertical distance tn the
Spout from the level of the water tn the reservotr; that ts, the height to
which the water ts ratsed. For if H is the atmospheric pressure, / the
height of the water above the piston, and 4%’ the height of the column
which fills the suction-tube A (fig. 213), and the lower part of the barrel, the
pressure above the piston is obviously H+, and that below is H—/’, since
the weight of the column /’ tends to counterbalance the atmospheric pressure.
208 On Gases [221
But as the pressure H —/’ tends to raise the piston, the effective resistance
is equal to the excess of H+ over H—/’; that is to say, to +h’.
In the suction- and force-pump it is readily seen that the pressure which
the piston supports is also equal to the weight of a column of water the base
of which is the section of the piston, and the height that to which the water
is raised.
222. Fire-engine._--The /ive-engine is a force-pump in which a steady jet
is obtained by the aid of an air-chamber, and also by two pumps working
alternately (fig. 214). The two pumps 7z and , worked by the same lever,
PQ, are immersed in a tank, which is kept filled with water as long as the
pump works. From the arrangement of the valves it will be seen that when
one pump, 7, draws water from the tank, the other, 7, forces it into the az7-
chamber, R.; whence, by an orifice, Z, it passes into the delivery tube, by
which it can be sent in any direction.
Without the air-chamber the jet would be intermittent. But as the velo-
city of the water on entering the reservoir is less than on emerging, the level
of the water rises above the orifice Z, compressing the air which fills the
reservoir. Hence, whenever the piston stops, the air thus compressed,
reacting on the liquid, forces itout during its momentary stoppage, and thus
keeps up a constant flow.
—225] Cause of Sound 209
BOOK V
ON SOUND j
CHAPTER I
PRODUCTION, PROPAGATION, AND REFLECTION OF SOUND
223. Province of acoustics.—The study of sounds and that of the vibra-
tions of elastic bodies form the province of the science of sownds, or
ACOUSTICS. «
Music considers sounds with reference to the pleasurable feeling they are
calculated to excite. Acoustics is concerned with the questions of the pro-
duction, transmission, and comparison of sounds ; to which may be added
the physiological question of the perception of sounds,
224. Sound and noise.—Sowzd is the peculiar sensation excited in the
organ of hearing by the vibratory motion of bodies, when this motion is
transmitted to the ear through an elastic medium.
Sounds are distinguished from zozses. Sound properly so called,
or musical sound, is that which produces a continuous sensation, the
musical value of which can be estimated; while noise is either a sound
of too short a duration to be determined, like the report of a cannon ; or
else it is a confused mixture of many discordant sounds, like the rolling
_ of thunder or the noise of the waves. Nevertheless, the difference between
sound and noise is by no means precise; Savart showed that there are
relations of height in the case of noise, as well as in that of sound; and
there are said to be certain ears sufficiently well organised to determine
the musical value of the sound produced by a carriage rolling on the
pavement.
225. Cause of sound.—Sound is always the result of rapid oscillations
- imparted to the molecules of elastic bodies, when the state of equilibrium of
these bodies has been disturbed either bya shock or by friction. Such bodies
tend to retain their first position of equilibrium, but only reach it after per-
forming, on each side of that position, very rapid vibratory movements, the
amplitude of which quickly decreases. A body which is capable of pro-
ducing a sound is called a sonorous or sounding body.
As understood in England and Germany, a vibration comprises a motion
to and fro ; in France, on the contrary, a vibration means a movement to 07
P
210 On Sound [225-
fro. ‘The French vibrations are with us semi-vibrations ; an osczllation or
vibration is the movement of the vibrating molecule in only one direction ;
a double or complete vibration comprises the oscillation both backwards and
forwards. Vibrations of sounding bodies are very readily observed. If a
light powder is sprinkled on a body which is in the act of yielding a musical
sound, a rapid motion is imparted
to the powder, which renders visible
the vibrations of the body ; and, in
the same manner, if a stretched
cord is smartly pulled and let go,
its vibrations are apparent to the
eye.
A bell-jar is held horizontally
Fig. 215 in one hand (fig. 215), and made
' to vibrate by being struck with the
other; if then a piece of meta! is placed in it, it is rapidly raised by the
vibrations of the side ; touching the bell-jar with the hand, the sound ceases,
and with it the motion of the metal.
226. Sounds not propagated in vacuo.—The vibrations of elastic bodies
can only produce the sensation of sound in us by the intervention of a
medium interposed between the air and the
sonorous body and vibrating with.it. This
medium is usually the air; but all gases,
vapours, liquids, and solids also transmit
sounds. .
The following experiment shows that the
presence of a ponderable medium is neces-
sary for the propagation of sound. A small
metal bell, which is continually struck by a
small hammer by means of clockwork, or
else an ordinary musical box, is placed under
the receiver of an air-pump (fig. 216). So
long as the receiver is full of air at the ordi-
nary pressure the sound is transmitted ; but
in proportion as the air is exhausted the
sound becomes feebler, and cannot be heard
in a vacuum.
To ensure the success of the experiment,
the bellwork or the musical box must be
placed on wadding or on a block of vulcan-
ised rubber; for otherwise the vibrations
would be transmitted to the air through the
| plate of the pump.
227. Sound is propagated in all elastic bodies.—If, in the above
experiment, any vapour or gas be admitted after the vacuum has been made,
the sound of the bell will be heard, showing that sound is propagated in this
medium as in air.
Sound is also propagated in liquids. When two stones are struck against
each other under water, the shock is distinctly heard ; and a diver at the
Fig. 216
—228] Propagation of Sound in Atr 211
bottom of the water can hear the sound of voices on the bank. The sound
is, however, enfeebled, as a considerable portion is reflected at the boundary
of the two media.
The conductibility of solids is such that the faint scratching of a pen or
the ticking of a watch at one end of a long horizontal wooden rod is heard
much more distinctly when the ear is directly applied against the other end
of the rod than when it is at the same distance in the air. Sound may even
reach the ear through solids alone without passing through the air ; for if the
ears be closed, and the rod be put between the teeth, the ticking is distinctly
heard. The earth conducts sound so well that at night, when the ear is
applied to the ground, the stepping of horses, or any other noise at a great
distance, is heard.
228. Propagation of sound in air.—In order to simplify the theory of
the propagation of sound in air, we shall first consider the case in which it
is propagated in a cylindrical tube of indefinite length. Let MN (fig. 217)
be a tube filled with air at a constant pressure and temperature, and let P
be a piston oscillating rapidly from A toa. When the piston starts from A,
it compresses the air in front of it and the compression increases until P
Fig. 217
reaches the position halfway between A and a, when it is a maximum, after
which it diminishes as P reaches a. Suppose that as the piston moves from
A to a, the disturbance of the air in the tube travels to H. Thus in @H the
pressure of the airis greater than normal, the compression being greatest at
the centre. When the piston returns in the direction aA, the pressure
behind it is diminished and the diminution of pressure is a maximum when
P is halfway back. This reduction of pressure or rarefaction travels along
the tube in the same way and at the same rate as the compression, so that
when the piston has reached A, the point from which it started, the compres-
sion has advanced to the position HH’, and its place has been taken by the
rarefied portion. Thus after one complete oscillation of the piston the
beginning of the air disturbance is at H’and theend at a. The whole length
aH’ is a wave or undulation. It consists of two equal parts in one of which
the air is more compressed and in the other is more rarefied than in the
undisturbed tube.
__ When the piston has made another complete oscillation, the wave aH’
will have advanced by a distance equal to itself, and its place will have been
taken by another wave, and so on. The velocity with which the disturbance
travels is the velocity of sound in the air of the tube. If A denote the length
of a wave, and z be the number of oscillations of the piston per second, 7A
is equal to the total distance travelled by the beginning of the distance in one
second. If this distance is vw, the velocity of sound, then v= za.
It is important to remark that if we consider a single row of particles,
which when at rest occupy a line parallel to the axis of the cylinder—for
P2
212 On Sound [228—
instance, those along AH” (fig. 217)—we shall find they will have respectively
at the same instant all the various velocities which the piston has had suc-
cessively while oscillating from A to @ and back to A. Sothat ifin fig. 39 -
AH’ represents the length of one undulation, the curved line H’PQA will
represent the several velocities which all the points in the line AH’ have
simultaneously ; for instance, at the instant the piston has returned to A,
the particle at M will be moving to the right with a velocity represented by
QM ; the particle at N will be moving to the left with a velocity represented
by PN, and so on of the other particles.
When an undulatory motion is transmitted through a medium, the
motions of any two particles are said to be in the same phase when those
particles move with equal velocities in the same direction ; the motions are
said to be in opposite phases when the particles move with the same velocities
in opposite directions. It is plain from an inspection of fig. 39 that when
any two particles are separated by a distance equal to half an undulation,
their motions are always in opposite phases, but if their distance equals the
length of a complete undulation their motions are in the same phase.
‘It is an easy transition from the explanation of the motion of sound-
waves in acylinder to that of their motion in an unenclosed medium. It is
simply necessary to apply in all directions to each molecule of the vibrating
body what has been said about a piston movable ina tube. A series of
spherical waves alternately condensed and rarefied is produced around each
centre of disturbance. As these waves are contained within two concentrical
spherical surfaces, whose radii gradually increase while the length of the
undulation remains the same, their mass increases with the distance from
the centre of disturbance, so that the amplitude of the vibration of the mole-
cules gradually lessens, and the intensity of the sound diminishes.
It is these spherical waves, consisting of portions alternately condensed
and expanded, which in being propagated transmit sound. If many points
are disturbed at the same time, a system of waves is produced around each
point. But all these waves are transmitted one through the other without
modifying either their lengths or their velocities. When two waves meet
each other the effect will be an augmentation or diminution of sound accord-
ing to the relative phases in which the waves meet. If the surface of still
water is disturbed at two or more points, the co-existence of waves becomes
sensible to the eye. |
229. Causes which influence the intensity of sound.—Many causes
modify the force or the zzfensity of sound. These are the distance of the
sounding body, the amplitude of the vibrations, the density of the air at the
place where the sound is produced, the direction of the currents of air, and,
lastly, the neighbourhood of other sounding bodies.
i. The intensity of sound ts inversely as the square of the distance of the
sounding body from the ear. This law has been deduced by calculation, but
it may be also demonstrated experimentally. Let us suppose several sounds
of equal intensity—for instance, bells of the same kind, struck by hammers
of the same weight, falling from equal heights. If four of these bells are
placed at a distance of 20 yards from the ear, and one at a distance of Io
yards, it is found that the single bell produces a sound of the same intensity
as the four bells struck simultaneously. Consequently, for double the dis-
—230] Apparatus to strengthen Sound BER
tance the intensity of the sound is only one-fourth. A method of com-
paring the intensities of different sounds will be described afterwards (293).
The distance at which sounds can be heard depends on their intensity.
The report of a volcano at St. Vincent was heard at Demerara, 300 miles
off, and the firing at Waterloo was heard at Dover.
u. Lhe intensity of sound increases with the amplitude of the vibrations
of the sonorous body. The connection between the intensity of the sound
and the amplitude of the vibrations is readily observed by means of vibrating
strings (269). For, if the strings are somewhat long, the oscillations are per-
ceptible to the eye, and it is seen that the sound is feebler in proportion as
the amplitude of the oscillations decreases. The intensity varies as the square
of the amplitude of oscillation.
ui. Zhe tntensity of sound depends on the density of the air in the place tn
which tt ts produced. As we have already seen (226), when an alarum actuated
by clockwork is placed under the bell-jar of an air-pump, the sound becomes
weaker in proportion as the air is rarefied.
In hydrogen, which is about 4 the density of air, sounds are much
feebler, although the pressure is the same. In carbonic acid on the con-
trary, whose density is 1°529, sounds are more intense. On high mountains,
where the air is much rarefied, it is necessary to speak with some effort in
order to be heard, and the discharge of a gun produces only a feeble sound.
The ticking of a watch is heard in water ata distance of 23 feet, in oil of 163,
in alcohol of 13, and in air of only Io feet.
iv. Zhe intensity of sound ts modified by the motion of the atmosphere
and the direction of the wind. \n calm weather sound is always better
propagated than when there is wind ; in the latter case, for an equal distance,
sound is more intense in the direction of the wind than in the contrary
direction.
v. Lastly, sound ts strengthened by the netghbourhood of a sonorous body.
A string made to vibrate in free air has but a very feeble sound ; but when it
vibrates above a sounding-box, as in the case of the violin, guitar, or violon-
cello, its sound is much stronger. This arises from the fact that the box and
the air which it contains vibrate in unison with the string. Hence the use of
Ssounding-boxes in stringed instruments.
Attempts have been made to get a measure of the loudness of sound
which should serve as a standard, by allowing leaden bullets to fall from
various heights on an iron plate of some size. It appears that within
certain limits the loudness is nearly proportional to the square root of the
height from which the bullet falls, and not to the height itself. It thus
appears that only a portion of the energy of the falling body is expended in
producing vibrations of the plate.
230. Apparatus to strengthen sound.—The apparatus represented .in
fig. 218 was used by Savart to show the influence of boxes in strengthening
sound. It consists of a hemispherical brass vessel, A, which is set in vibra
tion by means of a violin bow. Near it isa hollow cardboard cylinder, B,
closed at the further end. By means of a handle this cylinder can be
turned on its support, so as to be inclined at any given degree towards the
vessel. The cylinder is fixed on a slide, C, by which means it can be placed
at any distance from A. When the vessel is made to vibrate, the strengthen-
214 On Sound [230-
ing of the sound is very remarkable. But the sound loses almost all its
intensity if the cylinder is turned away, and it becomes gradually weaker
when the cylinder is re-
moved to a greater dis-
tance, showing that the
strengthening is due to
the vibration of the air in
the cylinder.
The air in the cylinder
B is made to vibrate in
Zp si unison with the brass
vessel by adjusting it toa
bi, AS ss certain depth, which is
py ity 6 ~—s effected by making one
; part of the cylinder slide
into the other.
Vitruvius states that
in the theatres of the
ancients resonant brass
vessels were placed to
strengthen the voices of
the actors.
231. Influence of tubes on the transmission of sound.—The law that the
intensity of sound decreases in proportion to the square of the distance does
not apply to the case of tubes, especially if they are straight and cylindrical.
The sound-waves in that case are not propagated in the form of increasing
concentric spheres, and sound can be transmitted to a great distance with-
out any perceptible alteration. Biot found that in one of the Paris water-
pipes, 1,040 yards long, the voice lost so little of its intensity that a con-
versation could be kept up at the ends of a tube ina very low tone. The
weakening of sound becomes, however, perceptible in tubes of large
diameter, or where the sides are rough. This property of transmitting
sounds was first used in England for sfeaking tubes. They consist of caout-
chouc or metal tubes of small diameter passing from one room to another.
If a person speaks at one end of the tube, he is distinctly heard by a person
with his ear at the other end.
From Biot’s experiments it is evident that a communication might be
made between two towns by means of speaking tubes. The velocity of
sound is 1,125 feet in a second at 16°°6 C., so that a distance of 50 miles
would be traversed in four minutes.
232. Regnault’s experiments.—Theoretically, a sound-wave should be.
propagated in a straight cylindrical tube witha constant intensity. Regnault
found, however, that in these circumstances the intensity of sound gradually
diminishes with the distance, and that the distance at which it ceases to be
audible is nearly proportional to the diameter of the tube.
He reproduced sound-waves of equal strength by means of a small pistal
charged with a gramme of powder, and fired at the open ends of tubes of
various diameters ; and he then ascertained the distance at which the sound
could no longer be heard, or at which it ceased to act on what he calls a
—233] Velocity of Sound in Aur 215
sensitive membrane. This was a very flexible membrane which could be
fixed across the tube at various distances, and was provided with a small
metal disc in its centre. When the membrane begins to vibrate, this disc
struck against a metallic contact, and thereby closed a voltaic circuit, which
traced on a chronograph the exact moment at which the membrane received
the sound-wave.
Experimenting in this manner, Regnault found that the report of a pistol
charged as stated is no longer audible at a distance of
moso metres in.a.tube of, .. , : : . o@108 diameter
3,810 = dane . ‘ : : mt 2 ZOO pe
9,540 be _ . . ; : Pe eda OO 3
These numbers represent the limit of distance at which the sound-wave is
no longer heard, but it still acts on the membrane at the distances of 4,156,
11,430, and 19,851 metres respectively.
According to Regnault the principal cause of this diminution of intensity
is the loss of vzs vzva against the sides of the tube ; he found also that sounds
of high pitch are propagated in tubes less easily than those of low pitch: a
bass voice would be heard at a greater distance than a treble voice.
233. Velocity of sound in air.—Since the propagation of sound-waves is
gradual, sound requires a certain time for its transmission from one place to
another, as is seen in numerous phenomena. For example, the sound of
thunder is only heard some time after the flash of lightning has been seen,
although both the sound and the light are produced simultaneously ; and in
like manner we see a mason at a distance in the act of striking a stone, or a
man felling a tree, before we hear the sound.
The velocity of sound in air has often been the subject of experimental
research. One of the most accurate of the direct measurements was made
by Moll and Van Beck in 1823. Two hills, near Amsterdam, Kooltjesberg
and Zevenboomen, were chosen as stations: their distance from each other
as determined trigonometrically was 57,971 feet, or nearly eleven miles.
Cannons were fired at stated intervals simultaneously at each station, and
the time which elapsed between seeing the flash and hearing the sound was
noted by chronometers. This time could be taken as that which the sound
required to travel between the two stations ; for it will be subsequently seen
that light takes an inappreciable time to traverse the above distance. In-
troducing corrections for the barometric pressure, temperature, and hygro-
metric state, and eliminating the influence of the wind, Molland Van Beck’s
results as recalculated by Schréder van der Kolk gave 1,092°78 feet as the
velocity of sound in one second in dry air at o° C., and under a pressure of
760 mm. Kendall, in a North Pole expedition, found that the velocity of
sound at a temperature of — 40° was 314 metres or 103074 feet. Stone’s
_ determinations, made at the Cape of Good Hope with very great care, gave
1,090°57 or 332°4 metres, as the velocity of sound at 0°,
The velocity of sound at o° may be taken at 1,093 feet, or 333 metres.
It increases with increase of temperature, and may be calculated for a tem-
perature 7° from the formula
UV = 1093.V/(1 + 0'0036057)
216 On Sound [233-
where 1,093 is the velocity in feet at 0° C., and 0'003665 the coefficient of
expansion for 1° C. This amounts to an increase of nearly two feet for
every degree Centigrade. For the same temperature it is independent of
the density of the air, and consequently of the pressure. It is the same for
the same temperature with all sounds, whether they be strong or weak, deep
or acute. Biot found, in his experiments on the conductivity of sound. in
tubes, that when a well-known air was played on a flute at one end of a tube
1,040 yards long, it was heard without alteration at the other end, from which
he concluded that the velocity of different sounds is the same. For the
same reason the tune played by a band is heard at a great distance without
alteration, except in loudness, which could not ,be the case if sounds differ-
ing in pitch and intensity travelled with different velocities.
This cannot, however, be admitted as universally true. Earnshaw, as
the result of a mathematical investigation of the laws of the propagation of
sound, concluded that the velocity of a sound depends on its strength ; and,
accordingly, that a violent sound ought to be propagated with greater
velocity than a gentler one. This conclusion is confirmed by an observation
made by Captain Parry on his Arctic expedition. During artillery practice
it was found, by persons stationed at a considerable distance from the guns,
that the report of the cannon was heard before the command to fire given
by the officer. And, more recently, Mallet made a series of experiments on
the velocity with which sound is propagated in rocks, by observing the times
_ which elapsed before blastings, made at Holyhead, were heard at a distance.
He found that the larger the charge of gunpowder, and therefore the louder
the report, the more rapid was the transmission. With a charge of 2,000
pounds of gunpowder the velocity was 967 feet in a second, while with a
charge of 12,000 it was 1,210 feet in the same time.
Jacques made a series of experiments by firing different weights of
powder from a cannon, and determining the velocity of the report at different
distances from the gun by means of an electrical arrangement. He thus
found that, close to the gun, the velocity is least, and that it increases to a
certain maximum which is considerably greater than the average velocity.
The velocity is also greater with the heavier charge. ‘Thus with a charge of
13 pound the velocity was 1187, and with a charge of } pound it was 1032
at a distance of from 30 to 50 feet ; while at a distance of 70 to 80 it was
1267 and 1120: and at 90 to 100 feet it was 1262 and 1114 respectively.
Bravais and Martins found, in 1844, that sound travelled with the same
velocity from the base to the summit of the Faulhorn as from the summit to
the base.
A laboratory method of determining the velocity of sounds consists in
using a metronome (82) which is beating slowly, and is approached to a
wall until a position is found at which the echo of one beat coincides with
the sound of another heard directly. The distance from the wall is then
half the distance, which sound traverses in the interval between two beats
of the metrono me. ;
234. Calculation of the velocity of sound in gases.—From theoretical
considerations Newton gave a rule for calculating the velocity of sound in
gases, which may be represented by the formula
ay dhe fe
a 5
—234] Calculation of the Velocity of Sound in Gases 217
in which v represents the velocity of the sound, or the distance it travels in
a second, ¢ the elasticity of the gas, and d its density.
This formula expresses that the velocity of the propagation of sound in
gases ts directly as the square voot of the elasticity of the gas, and tnversely
as the square root of tts density. It follows that the velocity of sound is the
same under any pressure ; for although the elasticity increases with increased
pressure, according to Boyle’s law, the density increases in the same ratio.
At Quito, where the mean pressure is only 21°8 inches, the velocity is the
same as at the sea-level, provided the temperature is the same.
Now the elasticity of a gas is measured by the ratio of a small applied
pressure to the compression thereby produced, and it may be easily proved
that, supposing the changes of pressure and volume to take place isotherm-
ally—that is, supposing Boyle’s law to hold—the elasticity of the gas is equal to
the pressure P to which it is subjected. If Z be the height of the barometer,
6 the density of mercury, and g the acceleration due to gravity, the pressure
= 96h ; further, if Z be the density of the gas at 7°C. and d, the density at
o°C., d,=d (1 +aZ), where a is the coefficient of expansion of the gas (335).
Thus Newton’s formula becomes
oer + at)
10)
a =>
< é
Substituting in this formula the values in centimetres and grammes,
=981, = 76, d+0°001293, we get for the value v a number 29,795 centi-
metres = 297°95 metres, which is about one-sixth less than the experimental
result. The reason for this discrepancy was given by Laplace, who pointed
out that when sound waves are travelling through air the heat which is pro-
duced by the increase of pressure in the compressed part of any wave does
not rapidly escape into the surrounding air. Similarly the cold- due to the
diminution of pressure in the rarefied portion of the wave is not at once
compensated by the ingress of heat from the surrounding space. Con-
sequently the temperature in the two parts of any wave cannot be regarded
as constant, and therefore Boyle’s law does not hold. Although the average
temperature of the air is unaltered, its elasticity is increased and is no longer
measured by the pressure P. It may be shown that the elasticity is greater
than the isothermal elasticity P in the proportion in which the specific
heat of the gas at constant pressure is greater than the specific heat at
constant volume. If these specific heats are denoted by ¢, c’ respectively,
¢ the elasticity = P _ Py, and the expression for the velocity of sound in
Oe °
the gas is
(pe Ve po ay (I+at)y
he =\/' ne aee 4
The value of y for air is 1°41, and if the value of the velocity obtained above,
viz. 297°95 metres, be multiplied by ./1‘41 or 1° 187 5, the calculated numbers
agree with the Experimental results.
Knowing the velocity of sound, we can calculate. approximately the dis-
tance at which it is produced. Light travels with such velocity that the
flash or the smoke accompanying the report of a gun may be considered to
218 On Sound [234—
be seen simultaneously with the occurrence of the explosion. Counting
then the number of seconds which elapse between seeing the flash and
hearing the sound, and multiplying this number by 1,125, we get the distance
in feet at which the gun is discharged. In the same way the distance of
thunder may be estimated.
235. Velocity of sound in various gases.—Approximately the same
results have been obtained for the velocity of sound in air by another method,
by which the velocity in other gases could be determined. As the wave-
length X is the distance which sound travels during the time of one oscillation,
that is, Sotaa second, the velocity of sound or the distance traversed in a
nt
second is v=, (233). Now the length of an open pipe is half the wave-
length of the fundamental note of that pipe ; and that of a closed pipe is a
quarter of the wave-length (279). Hence, if we know the number of vibra-
tions of the note emitted by any particular pipe, which can be easily ascer-
tained by means of a sirene, and we know the length of this pipe, we can
calculate v. Taking the temperature into account, Wertheim found in this
way 1,086 feet for the velocity of sound in air at zero.
Further, since in gases which differ in density, but are subjected to the
same pressure, the velocity of sound varies inversely as the square root of
the density, knowing the velocity of sound in air, we may calculate it for
other gases ; thus in hydrogen it will be
100 Dies feet.
/0°'0688 creed
Velocities calculated in this way cannot be universally accurate, for the
coefficient £,or y differs somewhat in different gases. And when pipes were
C
sounded with different gases, and the number of vibrations of the notes
multiplied with twice the length of the pipe, numbers were obtained which
differed for those calculated by the above formula. When, however, the
proper value of y for each gas was introduced into the calculation, the theo-
retical results agreed very well with the observed ones.
By the above method the following values have been obtained :—
Chlorine : s : : : : 677 feet in a second
Carbonic acid 5 : : ; ; 856 ys
Oxygen : ; : : : . 1040 #
Air ; ; : ; : : 1003 i
Carbonic oxide. ; Peri toOG a
Hydrogen . : ‘ : : Se ato3 és
236. Doppler’s principle—When a sounding body approaches the ear,
the note perceived is somewhat higher than the true one; but if the source
of sound recedes from the ear, the note perceived is lower. The truth of
this, which is known as Dopfler’s principle, will be apparent from the follow-
ing considerations :—When the source of sound and the ear are relatively
at rest, the ear receives 7 waves in a second; but if the ear approaches the
sound, or the sound approaches the ear, it receives more; just as a ship
237] Doppler's Principle 219
meets more waves when it ploughs through them than if it is at rest.
Conversely, the ear receives a smaller number when it recedes from the
source of sound. The effect in the first case is as if the sounding body
emitted more vibrations in a second than it really does, and in the second
case fewer. Hence in the first case the note appears higher ; in the second
case lower.
If the distance which the ear traverses in a second towards the source of
sound (supposed to be stationary) is s feet, and the wave-length of the par-
ticular note is A feet, then there are ~ waves ina second; this is equal to
nS U :
for A=—, where vis the velocity of sound (233). Hence the. ear re-
c m0
* . Fewias ne
ceives not only the z original waves, but also —— in addition. Therefore the
YU
number of waves per second which enter the ear is
Wi I oan (I+ Se
On, U
for an ear which approaches the sound ; and by similar reasoning it is
/
Wap 2H (1 a)
U v
for an ear receding from the sound.
To test Doppler’s theory Buys Ballot stationed trumpeters on the Utrecht
railway and also upon locomotives, and had the height of the approaching
or receding notes compared with stationary ones by musicians. He thus
found both the principle and the formula fully confirmed. Similar conclu-
sive experiments were made by Scott Russell on English railways. The
observation may often be made as a fast train passes a station in which
an electrical alarum is sounding. Independently of the difference in loud-
ness, an attentive ear can detect a difference in pitch on approaching and on
leaving the station. A speed of about 4o miles an hour sharpens the note
of the whistle of an approaching train by a semitone, and flattens it to that
extent as the train recedes.
Doppler’s principle may also be established by direct laboratory ex-
periments. Rollmann fixed a long rod on a turning table, at the end
of which was a large glass bulb with a slit in it, which sounded like a
humming-top when a tangential current of air was blown against the slit.
The uniform and sufficiently rapid rotation of the sphere developed such
a current, and produced a steady note, the pitch of which was higher or
lower in each rotation according as the bulb came nearer, or receded from,
the observer.
The principle may also be illustrated by means of a tuning-fork with wide
branches, and producing a very high note of 2,046 vibrations. When this is
loudly sounded, and, being held in front of a smooth wall, is moved towards
it with a velocity of a metre in a second, the direct note and that reflected.
from the wall undergo opposite changes, so that an observer hears distinctly
twelve beats in a second (266).
237. Velocity of sound in liquids.—The velocity of sound in water was
220 Ox Sound [237-
experimentally determined in 1827 by Colladon and Sturm. They moored
two boats at a known distance apart in the Lake of Geneva. The first
supported a bell immersed in water, and a bent lever provided at one end
with a hammer which struck the bell, and at the other with a lighted wick,
so arranged that it ignited some powder the moment the hammer struck the
bell. To the second boat was affixed an ear-trumpet, the bell of which was
in water, while the mouth was applied to the ear of the observer, so that he
could measure the time between the flash of light and the arrival of sound by
the water. By this method the velocity was found to be 4,708 feet in a second
at the temperature 8°'1, or four times as great as in air.
The velocity of sound, which is different in different liquids, can be cal-
culated by a formula identical with that given above (234) as applicable to
gases—that is, v= IN / In this formula, ¢ is the volume elasticity of the
liquid—that is, the ratio of pressure applied to the compression produced—
and @ the density. The compression per unit of volume due to the applica-
tion of a pressure of one atmosphere is called the compressibility of
the liquid. The numbers given in the following table were computed from
the above formula. As in the case of gases, the velocity varies with the tem-
perature, which is therefore appended in each case.
River water (Seine) ‘ : . 13°C. = 4714 feet in a second
” ” ” : ‘ Dies ohed on Ee ”
Artificial sea water : : SRO S761 :
Mercury ; i : : Awe bs) = 4866 -
Solution of common salt , eA lbs: = MS132 i
Absolute alcohol . : : pos = 3854 He
Turpentine . . : ; Sey = 30976 xs
Hihera oe } : ; t ‘ =n 3801 mis
It will be seen how close is the agreement between the two values for
the velocity of sound in water, the only case in which they have been
directly compared. There is considerable uncertainty about the values for
other liquids, owing to the doubt as to the values for their compressibility.
238. Velocity of sound in solids.—As a general rule, the elasticity of
solids, as compared with the density, is greater than that of liquids, and
consequently the propagation of sound is more rapid.
The difference is well seen in an experiment by Biot, who found that when
a bell was struck by a hammer, at one end of an iron tube 3,120 feet long,
two sounds were distinctly heard at the other end. The first of these was
transmitted by the tube itself with a velocity, +; and the second by the en-
closed air with a known velocity, a. The interval between the sounds was
2°5 seconds. The value of x obtained from the equation
SEAS LP
a x
shows that the velocity of sound in the tube is nearly 9 times as great as that
in air.
-238] Velocity of Sound in Solids 221
That the report of the firing of cannon is heard at far greater distances
than peals of thunder is doubtless owing to the fact that the sound in the
former case is mainly transmitted through the earth.
To this class of phenomena belongs the fact that if the ear is held against
a rock in which a blasting is being made at a distance, two distinct reports
are heard—one transmitted through the rock to the ear, and the other trans-
mitted through the air. The propagation of sound in solids is also well
illustrated by the fact that in manufacturing telegraph wires the filing at any
particular part can be heard at distances bf miles by placing one end of the
wire in the ear. The Zoy telephone also is based on this fact.
The velocity of sound in wires has also been determined theoretically,
by Wertheim and others, by the formula v= Fin which pis the longi-
y » DY A, a ‘ed 5
tudinal elasticity (Young’s modulus) of the material (89), while @ is the
density.
This may be illustrated from a determination by Wertheim of the velocity
of sound in a specimen of annealed steel wire, the density s of which was
7631 and longitudinal elasticity 21,000 (89). That is, a weight of 21,000
kilogrammes would double the length of a wire I sq. mm. in cross section,
if this were possible, without exceeding the limit of elasticity. This is equal to
2,100,000,000, or 21 x IO* grammes on a wire I sq. cm. in cross section.
fence
U= Neo oe = 519581 cm, =17047 feet.
3}
The following table gives the velocity in various bodies, expressed in feet
per second, mostly from the experimental determinations of Wertheim and
of Stefan :—
Caoutchouc . - 100 to 200 Copper : : . 12194
Tallow : : ; 1180 Oak . : : ae D022
Wax . : : 2394 Cedar. ; ; re £20
Paraffine . é 4250 i ove : ; Peet S510
Lead . : : : 4653 Asha ; : PP Ls 3i4
Membranes . 2300 to 6560 Die : j SAGs
Gold . ‘ : ; 7021 Walnut : ; ts 744
Paper . x . 5250 to 8860 Glass . 4 : mr LCOS 7
Silver . : : ; 8806 Steel wire . ‘ 16336
ae. : : 8 TOQOO Wrought iron and Sod 16498
The numbers for caoutchouc are of the same order of magnitude as those
for the propagation of a nervous impulse, and suggest that such an EDU
is transmitted by longitudinal vibrations (285) like those of sound.
In the case of wood these velocities are in the directions of the fibres,
and are considerably greater than across the rings or along the rings ; thus
with fir the velocities are 4,382 and 2,572 for these directions respectively.’
From a recent determination of the elasticity of ice, Trowbridge and
Macrae deduced the velocity of sound in it to be 9,600 feet per second, or
about 9 times that of air. |
222 On Sound [238—
Mallet investigated the velocity of the transmission of sound in various
rocks, and found that it is as follows :—-
Wet sand. j ; . 825 feet in a second
Contorted, euaiined Guaere and slate TOGKs |) «lOen *
Discontinuous granite : ‘ . : tk 300) *
Solid granite , A ; : : * 16604 2
A direct experimental method of determining the velocity of sound in
solids, gases, and vapours will be described subsequently (281).
If a medium through which sound passes is heterogeneous, the waves of
sound are reflected on the different surfaces, and the sound becomes rapidly
enfeebled. Thus a soft earth conducts sound badly, while a hard ground
which forms a compact mass conducts it well. So also we hear badly
through air-spaces which are filled with porous materials, such as shavings,
sawdust, cinders, and the like.
239. Reflection of sound.—So long as sound-waves are not obstructed
in their motion they are propagated in the form of concentric spheres ; but
when they meet with an obstacle they follow the general law of elastic
bodies ; that is, they return upon themselves, forming new concentric waves,
which seem to emanate from a second centre on the other side of the obstacle.
This phenomenon constitutes the reflection of sound.
Fig. 219 represents a series of incident waves reflected from an obstacle,
PQ. Taking for example the incident wave MCDN, emitted from the
centre A, the corresponding reflected wave is represented by the arc CKD
of a circle whose centre a is as far behind the obstacle PQ as A is before it.
If any point, C, of the reflecting surface be joined to the centre of sound,
and if the perpendicular CH be let fall on the surface of this body, the angle
ACH is called the angle of incidence, and the angle BCH, formed by the
prolongation of aC, is the angle of reflection.
The reflection of sound is subject to the two following laws :—
I. The angle of reflection ts equal to the angle of incidence.
—240] Echoes and Resonances 228
Il. Zhe cnctdent sonorous ray and the reflected ray are in the same plane
perpendicular to the reflecting surface.
From these laws it follows that the wave, which in the figure is propa-
gated in the direction AC, takes the direction CB after reflection, so that an
observer placed at B hears a second sound, which appears to come from C,
besides the sound proceeding from the point A.
The laws of the reflection of sound are the same as those for light and
radiant heat, and may be demonstrated by similar experiments. One of the
simplest of these is made with conjugate mirrors (see chapter on Radiant
Heat) ; if in the focus of one of these mirrors, which should be rather large,
a watch is placed, the ear placed in the focus of the second mirror hears the
ticking very distinctly even when the mirrors are at a distance of, 12 or 13
yards. The mirrors should be large, so that the head does not prevent too
large a proportion of the waves from the first mirror from falling on the
other. With smaller mirrors the bell of an ear trumpet is held at the focus,
and the tube end is placed in the ear, which is held on one side of the
mirror.
In like manner, the explosion of fulminating mercury in the focus of one
mirror causes that of iodide of nitrogen placed in that of the other.
240. Echoes and resonances.—An echo is the repetition of a sound in
the air, caused by its reflection from some obstacle.
A very sharp quick sound can produce an echo when the reflecting
surface is 55 feet distant ; but for articulate sounds at least double that
distance is necessary, for it may be easily shown that no one can pronounce
or hear distinctly more than five syllables in a second. Now, as the velo-
city of sound at ordinary temperatures may be taken at 1,125 feet ina second,
in a fifth of that time sound would travel 225 feet. If the reflecting surface
is 112°5 feet distant, in going and returning sound would travel through 225
feet. The time which elapses between the articulated and the reflected
sound would, therefore, be a fifth of a second, the two sounds would not
interfere, and the reflected sound would be distinctly heard. A person
speaking with a loud voice in front of a reflector, at a distance of 112°5 feet,
can only distinguish the last reflected syllable: such an echo is said to be
monosyllabic. If the reflector were at a distance of two or three times 112°5
feet, the echo would be a@syllabic, trisyllabic, and so on.
When the distance of the reflecting surface is less than 1125 feet, the
direct and the reflected sound are confounded. They cannot be heard
separately, but the sound is strengthened. This is what is often called
resonance, and is frequently observed in large rooms. Bare walls ; and par-
ticularly woodwork, are very resonant ; they reflect the sound and add to it
the effect of their own vibrations, so that the sound is prolonged and
enforced. In a large meeting-room this may considerably aid a speaker’s
voice ; too great resonance, however, hinders the distinct perception of the
words. Tapestry and hangings, on the contrary, which are bad reflectors,
deaden the sound. To control or eliminate the effects of resonance is a
difficult problem in the acoustics of the building art.
Multiple echoes are those which repeat the same sound several times ;
this is the case when two opposite surfaces (for example, two parallel walls)
successively reflect sound. There are echoes which repeat the same sound
224 On Sound [240-
20 or 30 times. Anecho in the chateau of Simonetta, in Italy, repeats a
sound 30 times. At Woodstock there is one which repeats from 17 to 20
syllables.
As the laws of reflection of sound are the same as those of light and
heat, curved surfaces produce acoustic foc? like the luminous and calorific
foci produced by concave reflectors. Ifa person standing under the arch of
a bridge speaks with his face turned towards one of the piers, the sound is
reproduced near the other pier with such distinctness that a conversation
can be kept up in a low tone, which is not heard by anyone standing in the
intermediate spaces.
There is a square room with an elliptical ceiling on the ground floor of the
Conservatoire des Arts et Métiers in Paris which presents this phenomenon
in a remarkable degree to persons standing in the two foci of the ellipse.
Whispering galleries are formed of smooth walls having a continuous
curved form. The mouth of the speaker is presented at one point, and
the ear of the hearer at another and distant point. In this case the
sound is successively reflected from one. point to the other until it reaches
the ear.
In the whispering gallery of St. Paul’s the faintest sound is thus conveyed
from one side to the other of the dome, but it is not heard at any intermediate
points. Placing himself close to the upper wall of the Colosseum, a circular
building 130 feet in diameter, Wheatstone found a word to be repeated a
great many times. A single exclamation sounded like a peal of laughter,
while the tearing of a piece of paper resembled the patter of hail.
It is not merely by solid surfaces, such as walls, rocks, ships’ sails, &c.,
that sound is reflected. It is also reflected by clouds, and it has even been
shown by direct experiment that a sound in passing from a gas of one density
into another is reflected at the surface of separation as it would be against
a solid surface. Now, different parts of the earth’s surface are unequally
heated by the sun, owing to the shades of trees, evaporation of water, and
other causes, so that in the atmosphere there are numerous ascending and
descending currents of air of different density. Whenever a sound-wave
passes from a medium of one density into another it undergoes partial reflec-
tion, which, though not strong enough to form an echo, distinctly weakens
the direct sound. This is doubtless the reason, as Humboldt remarked, why
sound travels further at night than at daytime, even in the South American
forests, where the animals, which are silent by day, fill the atmosphere at
night with thousands of confused sounds. To this may be added that at
night and in repose, when other senses are at rest, that of hearing becomes
more acute. This is the case with persons who have become blind.
It has generally been considered that fog in the atmosphere is a great
deadener of sound ; it being a mixture of air and globules of water, at each
of the innumerable surfaces of contact a portion of the vibration is lost.
The evidence as to the influence of this property is conflicting ; Tyndall’s
researches show that a white fog, or snow, or hail, is not an important
obstacle to the transmission of sound, but that aqueous vapour is. Expe-
riments made on a large scale, in order to ascertain the best form of fog
signals, gave some remarkable resus
On some days, which optically were quite clear, certain sounds could not
241] Refraction of Sound 225
be heard at a distance far inferior to that at which they could be heard even
during a thick haze. Tyndall ascribed this result to the presence in the
atmosphere of aqueous vapour, which forms in the air innumerable strize
that do not interfere with its optical clearness, but render it acoustically
turbid, the sound being reflected by this invisible vapour just as light is by
the visible cloud.
These conclusions, first drawn from observations, have been verified by
laboratory experiments. Tyndall showed that a medium consisting of
alternate layers of hght and heavy gas, such as coal gas and carbonic
acid, deadens sound, and also that a medium consisting of alternate strata
of heated and ordinary air exerts a similar influence. The same is the case
with an atmosphere containing the vapours of volatile liquids. So long as
the continuity of air is preserved, sound has great power of passing through
the interstices of solids ; thus it will pass through twelve folds of a dry silk
handkerchief, but is stopped by a single layer if it is wetted.
241. Refraction of sound.—lIt will be found afterwards (547) that ve/rac-
tion is the change of direction which light and heat experience on passing from
one medium to another. It has been shown by Hajech that the laws of the
refraction of sound are the same as those for light and heat : he used tubes
filled with various gases and liquids, and closed by membranes ; the mem-
brane at one end was at right angles to the axis of the tube, while the other
made an angle with it. When
these tubes were placed in
an aperture in the wall be-
tween two rooms, a sound
produced in front of the
tube in one room, that of a
tuning-fork for instance, was
heard in directions in the
other varying with the in-
clination of the second mem-
brane, and with the nature
of the substance with which |
the tube was filled. Accurate Bez: -— a
measurements showed that aug
the law held that the sines
of the angle of incidence
and of refraction are in a constant ratio, and that this ratio is equal to that
of the velocity of sound in the two media.
Thus the velocity of sound in water is not very different from that in
hydrogen, and they produce deviations which are nearly equal.
Sondhauss confirmed the analogy of the refraction of sound-waves to
those of light and heat. He constructed lenses of gas by cutting equal
segments out of a large collodion balloon, and fastening them on the two
sides of a sheet-iron ring a foot in diameter, so as to form a double convex
lens about 4 inches thick in the centre (fig. 220). This was filled with car-
bonic acid, and a watch A was placed in the direction of the axis ; the point
was then sought on the other side of the lens at which the sound was most
Q
226 . On Sound [241—
distinctly heard. It was found that when the ear was removed from the
axis the sound was scarcely perceptible, but that at a certain point B on the
axial line it was very distinctly heard. Consequently, the sound-waves in
passing from the lens had converged towards the axis ; their direction had
been changed ; in other words, they had been refracted.
The refraction of sound may be easily demonstrated by means of one of
the very thin india-rubber balloons used as children’s toys, inflated by
carbonic acid. If, however, the balloon be filled with
hydrogen, no focus is detected; it acts like a
concave lens, and, the divergence of the rays is
increased, instead of their being converged to the
ear.
A direct proof of the refraction of sound is
given by the experiments of Schellbach and Bohm.
The source of sound was a film of collodion
stretched across a ring, ad (fig. 221), which was
put in vibration by electrical sparks at 0. A disc
of paper, #, sprinkled with fine charcoal powder,
was suspended in the vessel BB’. When this
vessel contained air, rings of dust were formed, the
centre of which was at f in the direction of the
propagation of the sound. But if the vessel was
filled with carbonic acid the centre of the rings
was found to be at 7, showing that the sound had been refracted towards the
perpendicular on passing from air into the denser medium ; and measure-
ments showed that the position of the point /” was in accordance with the
law of refraction for light. Experiments suitably modified showed that,
when hydrogen was substituted for carbonic acid, the sound was bent away
from the perpendicular.
It has long been known that sound is propagated in a direction against
that of the wind with less velocity than with the wind. This is probably
due to a refraction of sound.on a large scale. The velocity of wind along
the ground is always considerably less than at a greater height ; thus, the
velocity at a height of 8 feet has been observed to be double what it is at a
height of one foot above the ground. Hence a wave-front (fig. 219),
originally vertical, becomes tilted upwards, with the lower part forward ;
and, as the direction of the wave-motion is at right angles to the front of
the wave, the effect of the coalescence of a number of these rays, thus
directed upwards, is to produce an increase of the sound in the higher
regions. The rays which travel with the wind will, for similar reasons, be
refracted downwards, and thus the sound be better heard.
242. Speaking trumpet. Ear trumpet. —These instruments depend on
the reflection of sound in tubes.
The speaking trumpet, as its name implies, is used to render the voice
audible at great distances, more especially on board ship. It consists of a.
slightly conical tin or brass tube (fig. 222), very much wider at one end (which
is called the de//), and provided with a mouthpiece at the other. They are
as much as 7 feet in length, the bell being 1 foot in diameter.
The larger the dimensions of this instrument the greater is the distanee
Fig. 221
-243] | Stethoscope 227
at which the voice is heard. Its action is usually ascribed to the successive
reflections of sound-waves from the sides of the tube, by which the waves
tend more and more to pass in a direction parallel to the axis of the
instrument. It has, however, been objected to this explanation that the
sounds emitted by the speaking trumpet are not stronger solely in the
direction of the axis, but in all directions ; that the bell would not tend to
produce parallelism in the sound-wave, whereas it certainly exerts consider-
able influence in strengthening the sound. According to Hassenfratz, the bell
acts by causing a large mass of air to be set in consonant vibration before
Fig. 222
it begins to be diffused. This is probably also the reason why sound travels
best in the chief direction of the sounding body ; thus the report of a cannon,
the sound of a wind instrument in the line of the tube, the voice of the
direction of the mouth, &c.
The ear trumpet is used by persons who are hard of hearing. It is
essentially an inverted speaking trumpet, and consists of a conical metallic
tube, one of whose ends, terminating in a de//, receives the sound, while
the other end is introduced into the ear. This instrument is the reverse of
the speaking trumpet. The bell serves as a mouthpiece ; that is, it receives
the sound coming from the mouth of the person who speaks. ‘These sounds
are transmitted by a series of reflections to the interior of the trumpet, so
that the waves, which would become greatly diffused, are concentrated on
the ear, and produce a far greater effect than divergent waves would have
done. : iettts
243. Stethoscope.—One of the most useful applications of acoustical
principles is the stethoscope. Figs. 223, 224, represent an improved form of
this instrument devised by Kénig. Two sheets of caoutchouc, c and a, are
fixed to the circular edge of a hollow metal hemisphere ; the edge is provided
with a stopcock, so that the sheets can be jnflated, and then present the ap-
pearance of a double convex lens, as represented in section in fig. 223. To
Q2
228 On Sound [243—
a tubulure on the hemisphere is fixed a caoutchouc tube terminated by horn
or ivory, 4, which is placed in the ear (fig. 224).
When the membrane c of the stethoscope is applied to the chest of a sick
person, the beating of the heart and the sounds of respiration are trans-
mitted to the air in the chamber a, and thence to the ear by means of the
flexible tube. If several tubes are fixed to the instrument, as many observers
may simultaneously auscultate the same patient.
A recent application—that to the water stethoscofe—has been found of
great service. It consists of a steel rod about three feet in length, with an
enlargement at each end; one of these is so shaped that it fits against a
water-pipe, while the other is applied to the ear. The taps having been
turned off, a skilled observer can detect the slight sound due to any flow of
water, which, in the circumstances, must be due to leakage.
} The audiphone, invented by Mr. Rhodes, of Chicago, is of considerable
service to people hard of hearing ; in its most simple form (fig. 225) it con-
sists of a thin rectangular piece of fine cardboard, the square end of which
Fig. 225
is held in one hand while the opposite and convex edge is pressed against
the teeth of the upper jaw so that it is slightly bent: it receives the sounds
which are produced in the air, and transmits them to the auditory nerves
through the bones of the head.
—245] Szrene 229
CHAPTER II
MEASUREMENT OF THE NUMBER OF VIBRATIONS
244. Savart’s apparatus.—Savart’s toothed wheel, so called from the
name of its inventor, is an apparatus by which the absolute number of vibra-
tions corresponding to a given note can be determined. It consists of a
solid oak frame in which are two wheels, A and B (fig. 226); the larger
wheel, A, is connected with the toothed wheel by means of a strap and a
multiplying wheel, thereby causing the toothed wheel to revolve with great
velocity ; a card, E, is fixed on the frame, and, in revolving, the toothed
wheel strikes against it and causes it to vibrate. The card, being struck by
each tooth, makes as many vibrations as there are teeth. At the side of the
apparatus is an indicator, H, which gives the number of revolutions of the
wheel, and consequently the number of vibrations in a given time.
Fig. 226
When the wheel is moved slowly, the separate shocks against the card
are distinctly heard ; but if the velocity is gradually increased, the sound
becomes higher and higher. Having obtained the sound whose number of
vibrations is to be determined, the revolution of the wheel is continued with
the same velocity for a certain number of seconds. The number of turns of
the toothed wheel B is then read off on the indicator, and this multiplied
by the number of teeth in the wheel gives the total number of vibrations.
Dividing this by the corresponding number of seconds, the quotient gives
the number of vibrations per second for the given sound.
245. Sirene.—The szvene is an apparatus which, like Savart’s wheel, is
used to measure the number of vibrations of a body in a given time. The
230 On Sound [245—
name ‘sirene’ was given to it by its inventor, Cagniard Latour, because it
yields sounds under water.
It is made entirely of brass. Fig. 227 represents it fixed on the table of
a bellows, by which a continuous current of air can be sent through it. Figs.
228 and 229 show the internal details. The lower part consists of a cylin-
drical box, O, closed by a fixed plate, B. On this plate a vertical rod, T, rests,
to which is fixed a disc, A, moving with the rod. In the plate B there are
equidistant circular holes, and in the disc A an equal number of holes of
the same size,‘and at the same distance from the centre as those of the plate.
These holes are not perpendicular to the disc ; they are all inclined to the
same extent in the same direction in the plate, and are inclined to the same
extent in the opposite direction in the disc, so that when they are opposite
each other they have the appearance represented in 7m, fig. 228. Conse-
quently, when a current of air from the bellows reaches the hole 7, it strikes
=
obliquely against the sides of the hole 7, and makes the disc A rotate in
the direction 7A.
For the sake of simplicity, let us first suppose that in the movable disc
A there are eighteen holes, and in the fixed plate B only one, which faces
one of the upper holes. The wind from the bellows striking against the
sides of the latter, the movable disc begins to rotate, and the space between
two of its consecutive holes closes the hole in the lower plate. But as the
disc continues to turn from its acquired velocity, two holes are again opposite
each other, a new impulse is produced, and so on. During a complete
revolution of the disc the lower hole is eighteen times open and eighteen
times closed. A series of effluxes and stoppages is thus produced, which
makes the air vibrate, and ultimately produces a sound when the successive
impulses are sufficiently rapid. If the fixed plate, like the moving disc, had
eighteen holes, each hole would separately produce the same effect as a
~247] Limit of Perceptible Sounds 231
separate one, the sound would be eighteen times as intense, but the number
of vibrations would not be increased.
In order to know the number of vibrations corresponding to the sound
produced, it is necessary to know the number of revolutions of the disc A in
a second. For this purpose an endless screw on the rod T transmits the
motion to a wheel, a, with 100 teeth. On this wheel, which moves by one
tooth for every turn of the disc, there is a catch, P, which at each complete
revolution moves one tooth of a second wheel, 6 (fig. 229). On the axis of
these wheels there are two needles, which move round dials represented in
fig. 227. One of these indices gives the number of turns of the disc A, the
other the number of hundreds of turns. Ry means of two screws, D and C,
the wheel @ can be uncoupled from the endless screw.
Since the pitch of the sound rises in proportion to the velocity of the disc
A, the wind is forced until the desired sound is produced. The same current
is kept up for a certain time—two minutes, for example—and the number of
turns read off. This number, multiplied by 18 and divided by 120, gives
the number of vibrations in a second. For the same velocity of rotation the
sirene gives the same sound in air as in water ; the same is the case with
all gases ; and it appears, therefore, that any given sound depends on the
number of vibrations produced, and not on the nature of the sounding
body.
The buzzing and humming noise of certain insects is not vocal, but is
produced by very rapid flapping of the wings against the air or the body.
The sirene has been ingeniously applied to count the rate per second of the
undulations thus produced, which is effected by bringing it into unison with
the sound. It has thus been found that the wings of a gnat flap at the rate
of 1,500 times in a second. If a report is produced in a space with two
parallel walls at no great distance apart, the sound is reflected from one to
the other, and reaches the ear at regular and frequent intervals ; that is, the
repetition of the echo acts as a note.
A modification of the sirene known as Brown’s steam-horn, in which high-
pressure steam is employed instead of compressed air, is used as a fog-ségnal.
Its shrill and penetrating note is better adapted than an ordinary fog-horn,
or even cannon, for being heard over the noise of breakers.
246. Bellows.—In acoustics a dellows is an apparatus by which wind
instruments, such as the sirene and organ-pipes, are worked. Between the
four legs of a table there is a pair of bellows, S (fig. 230), which is worked
by means of a pedal, P. Disa reservoir of flexible leather, in which is stored
the air forced in by the bellows. If this reservoir is pressed by means of
weights on a rod, T, moved by the hand, the air is driven through a pipe, E,
into a chest, C, fixed on thetable. In this chest there are small holes closed
_ by leather valves, which can be opened by pressing on keys in front of the
box. The sirene or sounding pipe is placed in one of these holes.
247. Limit of perceptible sounds.—Previous to Savart’s researches,
physicists assumed that the ear could not perceive asound when the number
of vibrations was below 16 for deep sounds, or above 9,000 for acute sounds.
But he showed that these limits were too close, and that the faculty of per-
ceiving sounds depends rather on their intensity than on their height; so
that when extremely acute sounds are not heard it arises from the fact.that
232 On Sound [247—
they have not been produced with sufficient intensity to affect the organ of
hearing.
By increasing the diameter of the toothed wheel, and consequently the
amplitude and intensity of the vibrations, Savart pushed the limit of acute
sounds to 24,000 vibrations in a second.
For deep sounds he substituted for the toothed wheel an iron bar about
two feet long, which revolved on a horizontal axis between two thin wooden
plates, about 0'08 of an inch from the bar. As often as the bar passed a
grave sound was produced, due to the displacement of the air. As the
motion was accelerated the sound became continuous, very grave, and
deafening. By this means Savart found that, with 7 to 8 vibrations in a
second, the ear perceived a
distinct but very deep sound.
Despretz, however, who
investigated the same sub-
nA ii mall ject, disputed Savart’s results
oe as to the limits of deep
eee ZA sounds, and considers that
me HN no sound is audible that is
made by less than 16 vibra-
tions per second. Von Helm-
holtz holds that the percep-
tion of a sound begins at 30
vibrations, and only has a
definite musical value when
the number is more than 4o.
Below 30 the impression of
a number of separate beats
is produced. On the other
hand, acute sounds are aud-
ible up to those correspond-
ing to 38,000 vibrations ina
second. Such sounds, how-
ever, are far from pleasur-
able: they affect the ear as
if it had been pricked with a
pin or needle.
The discordant results obtained by these and other observers for the
limit of audibility of higher notes are no doubt due to the circumstance
that different observers have different capacities for the perception of
sounds. Preyer has investigated this subject by means of experimental
methods of greater precision than any that have hitherto been applied
for this purpose. The minimum limit for the normal ear he found to lie
between 16 and 24 single vibrations in a second ; the maximum limit reached
41,000 ; but many persons with average powers of hearing were found to be
absolutely deaf to notes of 16,000, 12,000, or even fewer vibrations.
It appears that the limit of .audibility for any particular ear is increased
with the strength of the sound. Paucher examined this by sounding a
powerful sirene by steam ; he found that with steam of $ an atmosphere pres-
Fig. 230
~248] Duhamel’s Graphic Method 233
sure the upper limit was at 48,o0o vibrations, with 1} atmosphere it was
60,000, while with steam of 23} atmospheres, it had not been attained with
72,000 vibrations.
248. Duhamel’s graphic method.—When the sirene or Savart’s wheel is
used to determine the exact number of vibrations corresponding to a given
note, it is necessary to bring the sounds which they produce into unison
with the given note, and this cannot be done exactly unless the experi-
menter has a practised ear. Duhamel’s graphic method is very simple and
exact, and free from this difficulty. It consists in fixing a fine point to the
body emitting the note, and causing it to trace the vibrations on a properly
prepared surface.
The apparatus consists of a wood or metal cylinder, A (fig. 231), fixed to
a vertical axis, O, and turned by a handle. The lower part of the axis is a
screw working in a fixed nut, so that according as the handle is turned from
left to right, or from right to left, the cylinder is raised or depressed. Round
_the cylinder is rolled a sheet of paper covered with an inadhesive film of
lampblack. On this film the vibrations register themselves. This is effected
as follows. Suppose the body emitting the note to be a steel rod. Itis held
firmly at one end, and carries at the other a fine point which grazes the sur-
faces of the cylinder. If the rod is made to vibrate and the cylinder is at rest,
the point would describe a short line ; but if the cylinder is turned, the point
produces an wuadulating line, containing as many undulations as the point
has made vibrations. Consequently, the number of vibrations can be counted.
It remains only to determine the time in which the vibrations were made.
234 On Sound , [248-
There are several ways of doing this. The simplest is to compare the
curve traced by the vibrating rod with that traced by a tuning-fork (254),
-which gives a known number of vibrations per second —for example, 500.
The prong of the fork is furnished with a point, which is placed in contact
with the lampblack. The fork and the rod are then set vibrating together,
and each produces its own undulating trace. When the paper is unrolled,
it is easy, by counting the number of vibrations each has made in the same
distance, to determine the number of vibrations made per second by the
elastic rod. Suppose, for instance, that the tuning-fork made 150 vibrations,
while the rod made 165 vibrations. Now we already know that the tuning-
fork makes one vibration in the 545 part of a second, and therefore 150
vibrations in 43° of a second. But in the same time the rod makes 165
vibrations ; therefore, it makes one vibration in the NS?
500 x 165
of a second,
. 00 x 16 :
and hence it makes per second 5 SE se or 550 vibrations.
150
-250] Musical Intervals 235
CHAPTER III
THE PHYSICAL THEORY OF MUSIC
249. Properties of musical notes._-A simple musical note results from
continuous rapid isochronous vibrations, provided the number of the vibra-
tions falls within the very wide limits mentioned in the last chapter (247).
Musical notes are in most cases compound. The distinction between a
simple and a compound musical note will be explained later in the chapter.
The tone yielded by a tuning-fork furnished with a proper resonance-box is
simple ; that yielded by a wide-stopped organ pipe, or by a flute, is. zearly
simple ; that yielded by a musical string 1s compound.
Musical notes have three leading qualities, namely, Aztch, znfensity, and
timbre or quality.
i, The fztch of a musical note is determined by the number of vibrations
per second yielded by the body producing the note.
i. The zztenszty of the note depends on the eavent¢ of the vibrations. | It
is greater when the extent is greater, and less when it is less. It is, in fact,
proportional to the square of the extent, or amplitude of the vibrations which
produce the note.
ii. The “bre or stamp or gialzty is that peculiar property of note which
distinguishes a note when sounded on one instrument from the same note
when sounded on another, and which by some is called the colour. Thus
when the C of the treble stave is sounded on a violin and on a flute, the two
notes will have the same pitch ; that is, they are produced by the same number
of vibrations per second, and they may have the same intensity, and yet the
two notes will have very distinct qualities ; that is, their timbre is different.
The cause of the peculiar timbre of notes will be considered later in the
chapter.
250. Musical intervals.—Let us suppose that a musical note, which for
the sake of future reference we will denote by the letter C, is produced by
m vibrations per second ; and let us further suppose that any other musical
note, X, is produced by z vibrations per second, z being greater than 7 ;
then the interval from the note C to the note X is the ratio 7 : #7, the interval
between two notes being obtained by azvzszon, not by subtraction. Although
two or more notes may be separately musical, it by no means follows that
when sounded together they produce a pleasant sensation. On the con-
trary, unless they are concordant, the result is harsh, and usually unpleasing.
We have, therefore, to inquire what zofes are fit to be sounded together.
Now, when musical notes are compared, it is found that if they are separated
by an interval of 2:1, 4:1, &c. they so closely resemble one another that
they may for most purposes of music be considered as the samenote. Thus
236 On Sound [250-
suppose ¢ to stand for a musical note produced by 27 vibrations per second,
then C and ¢ so closely resemble each other as to be called in music by
the same name. The interval from C to ¢ is called an octave, and c is
said to be an octave above C, and conversely C an octave below c. If we now
consider musical sounds that do not differ by an octave, it is found that
if we take three notes, X, Y, and Z, resulting respectively from 7, g, and +
vibrations per second, these three notes when sounded together will be con-
cordant if the ratio of f:¢:7r equals 4:5:6. Three such notes form an
harmonic triad, and if sounded with a fourth note, which is the octave of
X, constitute what is called in music a sajor chord. Any of the notes of a
chord may be altered by one or more octaves without changing its distinc-
tive character ; for instance, C, E, G, and ¢ are a chord, and C, ¢, e, ¢ form
the same chord.
If, however, the ratiof:g:r7 equals 10:12:15, the three sounds are
slightly dissonant, but not so much so as to disqualify them for producing
a pleasing sensation. When these three notes and the octave to the lower
are sounded together, they constitute what in music is called a wnor chord.
251. The musical scale-—The series of sounds which connects a given
note C with its octave ¢c is called the dzatonic scale or gamut. The notes
composing it arevindicated by the letters C) Dy) F/G, Ay Bt ihescale
is then continued by taking the octaves of these notes, namely, CfA, Of Pa
and again the octaves of these last, and so on.
The notes are also known by names—viz. do or ut, re, mit, fa, sol, ta 34
do. The relations existing between the notes are these :—C, E, G ae
a major Zvzad, G, B, d form a: major ¢riad, and F, A, c form a ee: triad.
C, G, and F have, for this reason, special names, being called respectively
the ¢onic, dominant, and subdominant, and the three triads the ‘onic,
dominant, and subdominant triads or chords respectively. Consequently,
the numerical relations between the notes of the scale will be given by the
three proportions—
pe Ges GPs a Sr
Ga Busi erase as
Bf Arede vane aaeee EG
wa Ut
Hence, if #z denotes the number of double vibrations corresponding to
the note C, the number of vibrations corresponding to the remaining notes
will be given by the following table—
ado re Mite? Aa sol la St do
C D E i G a B C
m Sm = =2m 4770 37 Bm oS 2m
The intervals between the successive notes being respectively—
Cte DP eD tok Eto) We neoneree Or. tO A atc meee ees
9 10 16 9 10 9 16
8 9 15 8 9 8 1d
It will be observed here that there are three kinds of intervals, 2, 4°, and
i835 of these the first two are called a Zone, the last a semzttone, because it
is about half as great as the interval of atone. The two tones, however, are
not identical, but differ by an interval of $4, which is called a comma. Two
-253] On Musical Temperament 237
notes which differ by a comma can be readily distinguished by a trained
ear. The interval between the tonic and any note is denominated by the
position of the latter note in the scale ; thus the interval from C to G is a
fifth. The scale we have now considered is called the zajor scale, as being
formed of wzajor triads. If the minor triad were substituted for the major,
a scale would be formed that could be strictly called a mznor scale. As
scales are usually written, however, the ascending scale is so formed that
the tonic bears a minor triad, the dominant and subdominant bear major
triads, while in the descending scale they all bear mzzor triads. Practically,
in musical composition, the dominant triad is always major. If the ratios
given above are examined, it will be found that in the major scale the
interval from C to E equals 3, while in the minor scale it equals $. The
former interval is called a major third, the latter a szzzor third. Hence the
major third exceeds the minor third by an interval of 3%. This interval is
called a semitone, though very different from the interval above called by
that name. .
252. On semitones and on scales with different keynotes.—It will be seen
from the last article that the term ‘semitone’ does not denote a constant
interval, being in one case equivalent to $£ and in another to 33. It is found
convenient for the purposes of music to introduce notes intermediate to the
seven notes of the gamut ; this is done by raising or lowering these notes
by an interval of 22, When a note (say C) is increased by this interval, it
is said to be sharpened, and is denoted by the symbol Cf, called ‘C sharp ;’
that is, Cf +C=3%. When it is lowered by the same interval, it is said
to be flattened, and is represented thus—Bb, called ‘B flat ;’ that is,
B+Bb =33. If the effect of this be examined, it will be found that the
number of notes in the scale from C up to ¢ has been increased from seven
to twenty-one notes, all of which can be easily distinguished by the ear.
Thus, reckoning C to equal I, we have---
ee Ct Db D Dt Eb E &c.
I 25 $ # 8 &e.
Hitherto we have made the note C the tonic or keynote. Any other of
the twenty-one distinct notes above mentioned, e.g. G, or F, or Cr, &c.,
may be made the keynote, and a scale of notes constructed with reference
to it. This will be found to give rise in each case to a series of notes, some
of which are identical with those contained in the series of which C is the
keynote, but most of them different. And of course the same would be true
for the minor scale as well as for the major scale, and indeed for other scales
which may be constructed by means of the fundamental triads.
253. On musical temperament.—The number of notes that arise from the
construction of the scales described in the last article is so great as to prove
quite unmanageable in the practice of music; and particularly for music
designed for instruments with fixed notes, such as the pianoforte or harp.
Accordingly it becomes practically important to reduce the number of notes,
which is done by slightly altering their just proportions. This process is
called ¢emperament, and the scale is called the tempered scale. By tempering
the notes, however, more or less dissonance is introduced, and accordingly
several different systems of temperament have been devised for rendering
238 On Sound [253-
this dissonance as slight as possible. The system usually adopted is called
the system of egwal temperament. It consists in retaining the octaves pure,
and in substituting between C and c eleven notes at equal intervals, each
interval being, of course, the twelfth root of 2, or 1'05946. By this means
the distinction between the semitones is abolished, so that, for example, Ct
and Db become the same note. The scale of twelve notes thus formed is
called the chromatic scale. It follows, of course, that major triads become
slightly dissonant. Thus, in the diatonic scale, if we reckon C to be 1, E is
denoted by 1:25000, and G by 1°50000. On the system of equal tempera-
ment, if C is denoted by 1, E is denoted by 1°25992 and G by 1°49831.
If individual intervals are made pure while the errors are distributed over
the others, such a system is called that of wmegual temperament. Of this
class is Kzrnberger’s, in which nine of the tones are pure.
Although the system of equal temperament has the advantage of afford-
ing the greatest variety of tones with as small a number of notes as possible,
yet it has the drawback that no chord of an equally tempered instrument,
such as the piano, is perfectly pure. And as musical education mostly has
its basis on the piano, even singers and instrumentalists usually give equally
tempered intervals. Only in the case of string quartet players, who have
freed themselves from school rules, and in that of vocal quartet singers, who
sing frequently without accompaniment, does the natural pure temperament
assert itself, and thus produce the highest musical effect.
254. The number of vibrations producing each note. The tuning-fork.
Hitherto we have denoted the number of vibrations corresponding to the
note C by wm, and have not assigned any
numerical .value to that symbol. In the theory
of music it is frequently assumed that the middle
C corresponds to 256 double vibrations in a
second. This 1s. the note which, on a pianoforte
of seven octaves, is produced by the white key
on the left of the two black keys close to the
centre of the keyboard. This number is con-
venient as being continually divisible by two,
and is therefore frequently used in numerical
illustrations. It is, however, arbitrary. An
instrument is in tune provided the intervals
between the notes are correct, when c is yielded
by any number of vibrations per second not
differing much from 256. Moreover, two instru-
ments are in tune with each other if, being
separately in tune, they have any one note, for
instance C, yielded by the same number of vibra-
tions.. Consequently, if two instruments have
one note in common, they can then be brought
into tune jointly by having their remaining notes
jae separately adjusted with reference to the funda-
mental note. BBOB?
poe V5 508 1He
Z 5508+¢
I + 5508
In this calculation, the coefficient of absolute expansion of mercury is
taken, and not that of apparent expansion ; for the value H is the same as
if the glass did not expand, the barometric height being independent of the
diameter of the tube, and therefore of its expansion.
332. Correction of thermometric readings.—If the whole column of
mercury of a thermometer is not immersed in the space whose temperature
is to be determined, it is necessary to make a correction, which in the
accurate determination of boiling points, for instance, is of great import-
ance, in order to arrive at the true temperature which the thermometer
should show. That part of the stem which projects will have a tempera-
ture which must be estimated, and which may roughly be taken as some-
thing over that of the surrounding air.
Suppose, for instance, that the actual reading is 160° and that the whole of
the part over 80° is outside the vessel, while the temperature of the surround-
ing air is 15°. Wewill assume that the mean temperature of the stem is 25°,
and that a length of 160°— 80° is to be heated through 160—25 = 135°; this
gives 80x ae 1°66 (taking the coefficient of apparent expansion of
mercury) ; so that the true reading is 161°66.
333. Force exerted by liquids in expanding.—The force which liquids
exert in expanding is very great, and equal to that which would be required
in order to bring the expanded liquid back to its original volume. Now we
know what an enormous force is required to compress a liquid to even a
very small extent (98). Thus between 0° and 10°, mercury expands by
0°0015790 of its volume at 0° ; its compressibility is 0700000295 of its volume
for one atmosphere ; hence a pressure of more than 600 atmospheres would
be requisite to prevent mercury expanding when it is heated from 0° to 10°.
In like manner a pressure of 140 atmospheres would be required to prevent
water from expanding when its temperature was raised from 4° to 14°.
312 On Feat [334—
334. Maximum density of water.—Water presents the remarkable pheno-
menon that when its temperature sinks it:contracts down to 4°; but from
that point, although the cooling continues, it expands to the freezing point,
so that 4° represents the point of greatest contraction of water.
Many methods have been used to determine the temperature of the maxi-
mum density of water. Hope made the following experiment :— He took adeep
vessel with two apertures in the sides, in which he fixed thermometers, and
having filled the vessel with water at 0°, he placed it in a room at a tem-
perature of 15°. As the layers of liquid at the sides of the vessel became
heated they sank to the bottom, and the lower thermometer marked 4° while
the upper one was still at zero. Hope then made the inverse experiment ;
having filled the vessel with water at 15°, he placed it in a room at zero.
The lower thermometer having sunk to 4° remained stationary for some
time, while the upper one cooled down until it reached zero. Both these
experiments prove that water is heavier at 4° than at 0°, for in both cases the
water at 4° sinks to the lower part of the vessel.
This last experiment may be adapted for lecture illustration by using a
cylinder containing water at 15° C., partially surrounded by a jacket contain-
ing bruised ice (fig. 317).
Hallstr6m made a determination of the maximum density of water in the
following manner :—He took a glass bulb, loaded with sand, and weighed it
in water of different temperatures. Allow-
ing for the expansion of glass, he found
that 4°1° was the temperature at which it
lost most weight, and consequently this
was the temperature of the maximum
density of water.
Despretz arrived at the temperature
4° by another method. He took a water
thermometer—that is to say, a bulbed
tube containing water-—and, placing it in
a bath, the temperature of which was in-
dicated by an ordinary mercury thermo-
meter, found that the water contracted to
the greatest extent at 4°, and that this
therefore is the point of greatest density.
This phenomenon is of great import-
ance in the economy of nature. In winter
the temperature of lakes and rivers falls,
from being in contact with the cold air
and from other causes, such as radiation.
The cold water sinks to the bottom, and
a continual series of currents goes on until the whole has a temperature of
°, The cooling on the surface still continues, but the cooled layers, being
an
lighter than those below, remain on the surface, and ultimately freeze. The
ice formed thus protects the water below, the lower portions of which remain
at a temperature of 4°, even in the most severe winters, a temperature at
which fish and other inhabitants of the water are not destroyed.
Salt dissolved in water lowers the temperature of the maximum density,
334]
and sea water exhibits a maximum. According to Rosetti, this temperature
is between 3°2° and 3°9° in the Adriatic.
The following table of the density of pure water at various temperatures
is based on several sets of observations :—
Tempe-
ratures
Maximum Density of Water
Density of water between 0° and 30°.
Densities
Tempe- |
m OO ON DAuifHO N HO
HOH
0°99988
099993
0°99997
099999
I ‘OOO00O
099999
0°99997
0°99994
099988
099982
0°99974
0°99965
NNN
Go NS &
Densities Ee aah Densities
0°99955 24 0°99738
0°99943 25 099714
0°99930 26 099689
O'99915 a7 0'99662
0°99900 28 0°99635
0.99884 29 0°99607
0°99870 30 0°99579
0°99847 40 - 0°99226
0°99827 50 0'98820
0.99806 60 0°98232
0°99785 70 0°97796
0'99762 80 o'9g719I
314 On Heat [335—
CHARTER SIV
EXPANSION AND DENSITY OF GASES
335. Gay-Lussac’s method.—Gases are the most expansible of all bodies,
and at the same time the most regular in their expansion. The coefficients
of expansion, too, of the several gases differ ‘only by very small quantities.
The cubical expansion of gases need alone be considered.
Gay-Lussac first determined the coefficient of the expansion of gases by
means of the apparatus represented in fig. 318.
In a rectangular metal bath, about 16 inches long, was fitted an air
thermometer, which consisted of a capillary tube, AB, with a bulb, A, at one:
end: "The tube)
was divided into
parts of equal
capacity, and the
contents of the
bulb ascertained
| in terms of these
ee T parts. This was
cn
cay)! a aes
2 = 4b tube full of mer-
———
=
(=
[z= [a
|| ==> el cury * at) zero,
and then heating
slightly to expel
a small quantity
of mercury, which was weighed. The apparatus being again cooled down
to zero, the vacant space in the tube corresponded to the weight of mercury
which had overflowed ; the volume of mercury remaining in the apparatus,
and consequently the volume of the bulb, was determined by calculations
analogous to those made for the’piezometer (98).
In order to fill the thermometer with dry air it was first filled with
mercury, which was boiled in the bulb itself. A tube, C, filled with calcium
chloride, was then fixed on to its end by means of a cork. A fine platinum
wire having then been introduced into-:the stem AB through-the tube C, and
the apparatus being slightly inclined and agitated from time to time, air
entered, having been previously well dried by passing through the calcium
chloride tube. The whole of the mercury was displaced, with the excep-
tion of a small thread, which remained in the tube AB as an index.
The air thermometer was then placed in the box filled with melting ice,
the index moved towards A, and the point was. noted at which it became:
Fig. 318
—336] Problems on the Expansion of Gases 315
stationary. This gave the volume of air at zero, since the capacity of the
bulb was known. Water or oil was then substituted for the ice, and the
bath successively heated to different temperatures. The air expanded and
moved the index from A towards B. The position of the index in each case
was noted, and the corresponding temperature was indicated by means of
the thermometers D and E.
Assuming that the atmospheric pressure did not vary during the experi-
ment, and neglecting the expansion of the glass as being small in comparison
with that of the air, the total expansion of the air is obtained by subtracting
from its volume at a given temperature its volume at zero. Dividing this by
the given temperature, and then by the number of units contained in the
volume at zero, the quotient is the expansion for a single unit of volume and
a single degree ; that is, the coefficient of expansion. It will be seen further
on how corrections for pressure and temperature may be introduced ; by
this method Gay-Lussac found that the coefficient of expansion of air was
0°00375.
The two following laws hold in reference to the expansion of gases :—
I. All gases have the same coefficient of expanston as atr.
Il. This coefficient ts the same whatever be the pressure supported by
the gas.
These simple laws are not, however, rigorously exact (337); they only
express the expansion of gases in an approximate manner. They were
discovered independently by Dalton and by Gay-Lussac, and are usually
ascribed to them. The first discoverer of the former law was, however,
Charles.
336. Problems on the expansion of gases.—Many of the problems
relative to the expansion of gases are similar to those on the expansion of
liquids. With obvious modification, they are solved in a similar manner.
In most cases the pressure of the atmosphere must be taken into account
in considering the expansion of gases. The following is an example of the
manner in which this correction is made :—
i. The volume of a gas at ¢°, and under the pressure H, is V’: what will
be the volume V of the same gas at zero, and under the normal pressure
760 millimetres ?
Here there are two corrections to be made; one relative to the tempera-
ture and the other to the pressure. It is quite immaterial which is taken
first. If a be the coefficient of cubical expansion for a single degree, by
reasoning similar to that in the case of linear expansion (317), the volume of
/
the gas at zero, but still under the pressure H, will be- ey . This pressure
Trac
is reduced to the pressure 760 in accordance with Boyle’s law (183), by
peas ye VA
tting Vx 760 = leben a Raa
ees bi sk ad meee 760 (1 + aé)
i. A volume of gas weighs P’ at 7°: what will be the-weight of an equal
volume at zero?
Let P be the desired weight, a the coefficient of |expansion of the gas,
@ its density at 7°, and d its density at ‘zero. As the weights of equal
Hi 7
volumes are proportional to the densities, we have Baie lit, besthe
316 On Fleat [336—
volume of a gas at zero, its volume at ¢ will be 1+ az: but as the densities
a’ I
are inversely.as the’ volumes, —-=—__4
a@ i+at
i I ; ; ‘
and therefore = =———_, ; whence P=P”(1 + a7).
Pap dete?
From this equation we get P’=
K ee which gives the weight at 4, know-
ing the weight at zero, and which further shows that the weight P’ is inversely
as the binomial of expansion 1 + aé.
337. Regnault’s method.—Regnault used successfully four different
methods for determining the expansion of gases. In some of them the
pressure was constant and the volume variable, as in Gay-Lussac’s method ;
in others the volume remained the same while the pressure varied. The
first method will be described. It is the same as that used by Rudberg and
Dulong, but is distinguished by the care with which all sources of error are
avoided.
The apparatus consisted of a pretty large cylindrical reservoir, B (fig.
319), terminating in a bent capillary tube. In order to fill the reservoir with
ye
Son eS See SS
SSS
dry air, it was placed in a hot-water bath, and the capillary tube connected
by a caoutchouc tube with a series of drying [tubes. These tubes were
joined to a small air-pump, B, by which a vacuum could be produced in the
reservoir while at a temperature of 100°. The reservoir was first exhausted,
and air afterwards admitted slowly ; this operation was repeated a great
many times, so that the air in the reservoir became quite dry, for the mois-
ture adhering to the sides passed off in vapour at 100°, and the air which
entered became dry in its passage through the U tubes.
The reservoir was then kept for half an hour at the temperature of boil-
ing water; the air-pump having been detached, the drying tubes were then
disconnected, and the end of the tube hermetically sealed, the height H of
the barometer being noted. When the reservoir B was cool, it was placed
337] — Regnault’s Method aly,
in the apparatus represented in fig. 320. It was there quite surrounded
with ice, and the end of the tube dipped in the mercury bath, C. After the
air in the reservoir B had sunk to zero, the
point 6 was broken off by means of a pair of
forceps ; the air in the interior became con-
densed by atmospheric pressure, the mercury
rising to a height 0G. In order to measure
the height of this column, Go, which will be
called %, a movable rod, go, was lowered until
its point, 9, was flush with the surface of the
mercury in the bath ; the distance between the
point o and the level of the mercury G was
measured by means of the cathetometer. The
point & was finally closed with wax by means of
the spoon a, and the barometric pressure noted
at this moment. If this pressure be H’, the
pressure in the reservoir is H’—4.
The reservoir was now weighed to ascertain
P, the weight:of the mercury which it con-
tained. It was then completely filled with mer-
cury at zero, in order to have the weight P’ of
the mercury in the reservoir and in the tube.
If 5 be the coefficient of the cubical expan-
sion of glass, and D the density of mercury at zero, the coefficient a of
the cubical expansion of air is determined in the following manner :—
Fig. 320
The volume of the reservoir and of the tube at zero is ae from the formula
P=VD (126) ; consequently, this volume is
/
RS osu diclall | 2k xe
at the temperature 7°, assuming, as is the case, that the reservoir and tube
expand as if they were solid glass (325). But from the formula P = VD, the
volume of air in the reservoir at zero, and under the pressure H’—4, is
P’—P
At the same pressure, but at 2°, its volume would be
Lt abet +at),
and by Boyle’s law (183), at the pressure H, at which the tube was sealed,
this volume must have been
CPT) (it ad) Tae (2)
time 3 —s ib) H 4 = . . . . . . . . * e —_
Now the volumes represented by these formulze (1) and (2) are each
equal to the volume of the reservoir and the tube at 7°: they are therefore
equal. Removing the denominators, we have
P’ (1 + 64) H=(P’—P) (1 +a/) (H’—4) MEEEORIO ET
from which the value of a is deduced.
318 On Heat [337-
The means of a great number of experiments between zero and 100? and
for pressure between 300 millimetres and 500 millimetres, gave the following
numbers for the coefficients of expansion for a single degree :—
AIT , : . 0°003667 Carbonic acid. 3) °O°003710
Hydrogen : . 0'003661 Nitrous oxide . . - 0°003719
‘Nitrogen . , . 0'003661 Cyanogen . 0°003877
‘Carbonic oxide » 0°003667 Sulphurous acid . 0°003903
‘These numbers, with which the results obtained by Magnus closely agree,
show that the coefficients of expansion of the permanent gases differ very
little; but that they are somewhat greater in the case of the more easily
‘condensable gases, such as carbonic and sulphurous acids. Regnault has
further found that, at the same temperature, the coefficient of expansion of
any gas increases with the pressure which it supports. Thus, while the
coefficient of expansion of air under a pressure of 110 mm. is 0°003648, under
a pressure of 3655 mm., or nearly five atmospheres, it is 0°003709.
The ‘number found by Regnault for the coefficient of the expansion of
air, 0°003667, is equal to ee x+g nearly ; and if we take the coefficient of
expansion at 0'0036666 . . . it may be represented by the fraction 544,
which is convenient for many purposes of calculation.
The small differences in the expansibility of various gases may be ascribed
‘to the circumstance that when a gas is heated the relative positions of the
atoms in the molecules are thereby altered ; and a certain amount of internal
work is required for this, which is different for different gases (296).
338. Air thermometer.—The azr thermometer is based on the expan-
sion of air. When it is used to measure small differences of temperature, it
thas the same form as the tube used by Gay-Lussac in determining the
expansion of air (fig. 318), that is, a capillary tube with a bulb at the end.
The reservoir being filled with dry air, an index of coloured sulphuric acid
or a drop of mercury is passed into the tube ; the apparatus is then graduated
in Centigrade degrees by comparing the positions of the index with the
indications of a mercurial thermometer. Of course the end of the tube
must remain open ; otherwise, the air above the index condensing or ex-
panding at the same time as that in the bulb, the index would remain
stationary. A correction must be made at each observation for the atmo-
‘spheric pressure.
When considerable variations of temperature are to be measured, the
tube has a form like that used in Regnault’s experiments (figs. 319 and 320).
By experiments, made ‘as described invart. 933742, 1P’, H, Hand Zmmay
be found, and the coefficients a and 5 being known, the temperature 7 to
which the tube has been raised is readily reduced from the equation (3).
Regnault found that the air and the mercury thermometer agree up to
260°, but above that point mercury expands relatively more than air. In
cases where very high temperatures are to be measured, the reservoir is
made of-platinum. - The use of an air thermometer is seen in Dulong and
Petit’s experiment (326) ; it was by such an apparatus that Pouillet measured
the temperature corresponding to the colours which metals take when heated
in a fire, and found them to be as follows :—
—339] Density of Gases 319
Incipient red ; 825° Cet Darkerange . : 2 Tico? G:
Pullkredy +: : e700 White ™. : : . 1300
Gheétry redex a. fe) Dazzling white. . 1500
In the measurement of high temperatures Deville and Troost used with
advantage the vapour of iodine instead of air, and, as platinum has been
found to be permeable to gases at high temperatures, they employed porce-
lain instead of that metal.
The expansion of gases has been determined by Jolly by means of a
form of apparatus which is also a convenient form of air thermometer (fig.
321). A quadrangular post rests on a tripod ; on one side
of this post is a graduated glass scale, while in the two
others are grooves in which screw-blocks A and A’ can
be slid up and down and adjusted at any height.
A glass bulb a is prolonged in a tube bent twice, the
end of which is provided with a stopcock, not shown in
the figure, and in which can be fitted a glass tube R sup-
ported by the block A. This again is fitted to a flexible
india-rubber tube, at the other end of which is an open
glass tube R’ fixed to the block A’. This tube contains
mercury.
The bulb a having been filled with dry air, the stopcock
is closed, the tube R fixed, and the stopcock opened.
The bulb a@ is then immersed to the stem in melting ice,
and when it is supposed that the temperature is stationary,
the tube R’ is moved up and down until the mercury in
the other limb is ata mark S. The difference between
the levels of the mercury at S and at R’ is noted. If the
latter is higher the difference is added to, and if lower
subtracted from, the barometric height at the time, to give
the pressure / in the vessel a.
The bulb a is then placed in a space at any constant
temperature, and the same operation repeated to get the
pressure /,, From the ratio of the total pressures in the two cases we get
the coefficient of expansion a from the formula £:4,=1+atf:1+at’. By
means of this apparatus Jolly found 0°00366957 for the value of a.
339. Density of gases.—The relative density of a gas, or its specific
gravity, is the ratio of the weight of a certain volume of the gas to that of
the same volume of air ; both the gas and the air being at zero and under
a pressure of 760 millimetres.
In order, therefore, to find the specific gravity of a gas, it is necessary to
determine the weight of a certain volume of this gas at a pressure of 760
millimetres, and a’ temperature of zero, and then the weight of the same
volume of air under the same conditions. For this purpose a large globe of
about two gallons capacity is used, the neck of which is provided with a
stopcock, which can be screwed to the air-pump. The globe is first weighed
empty, and then full of air, and afterwards full of the gas in question. The
weights of the gas and of the air are obtained by subtracting the weight of
the exhausted globe from the weight of the globe filled, respectively, with
320 On Heat -[389-
air and gas. The quotient, obtained by dividing the latter by the former,
gives the specific gravity of the gas. It is difficult to make these determina-
tions at the same temperature and pressure, and therefore all the weights
are reduced to zero and the normal pressure of 760 millimetres.
The gases are dried by causing them to pass through drying tubes before
they enter the globe, and air must also be passed over potash to free it from
carbonic acid. And as even the best air-pumps never produce a perfect
vacuum, it is necessary to exhaust the globe until the manometer in each
case marks the same pressure.
The globe having been exhausted, dried air is allowed to enter, and the
process is repeated several times until the globe is perfectly dried. It is
then finally exhausted until the residual pressure in millimetres is e. The
weight of the exhausted globe is gZ. Air, which has been dried and purified by
passing through potash and calcium chloride tubes, is then allowed to enter
slowly. The weight of the globe full of airis P. If H is the barometric
height in millimetres, and 2° the temperature at the time of weighing, P—/is
the weight of the air in the globe at the temperature ¢, and the pressure H —e.
To reduce this weight to the pressure 760 millimetres and the tempera-
ture zero, let a be the coefficient of the expansion of air, and 6 the coefficient
of the cubical expansion of glass. From Boyle’s law the weight, which is
P—f/at 7° and a pressure of H —e, would be Gir se under the pressure
—eé
760 millimetres and at the same temperature 7°. If the temperature is 0°,
the capacity of the globe will diminish in the ratio 1+6¢ to 1, while the
weight of the gas increases in the ratio 1 : 1+ a¢,as follows from the problems
in art. 336. Consequently, the weight of the air in the globe at 0° and at the
‘pressure 760 millimetres will be
(P =f)
760 (I + aZ)
SEAN CHEER Tale : ; : (1)
Further, let a’ be the coefficient of expansion of the gas in question ; let
P’ be the weight of the globe full of gas at the temperature 7 and the pres-
sure H’, and let #’ be the weight of the globe when it is exhausted to the
pressure e; the weight of the gas in the salts at the pressure 760 and the
temperature zero will be
760 (I sat” : (2)
Ge PD oy H’—2) (1+ 62)
Dividing the latter formula by the former we obtain the density
bo na A ) (H —e) (1+a’Z) (1 + 62)
(P —f) (H’ -e) (1 +a?) (1 + 82’)
If the temperature and the pressure do not vary during the experiment,
H =H’ and ¢=/; whence D= Oe ea and, if a=a’, D=~, a
340. Regnault’s method of determining the density of gases.—Regnault
so modified the above method that many of the corrections may be dispensed
with. The globe in which the gas is weighed is suspended from one pan of
ee |
-340] Method of determining the Density of Gases 321
eed
a balance, and is counterpoised by means of a second globe of the same
dimensions, and hermetically sealed, suspended from the other. These two
globes, expanding at the same time, always displace the same quantity of air,
‘and consequently variations in the temperature and pressure of the atmo-
sphere do not influence the weighing. The globe, too, is filled with air or
with the gas, at the temperature of zero. This is effected by placing it ina
vessel full of ice, as shown in fig. 322. It is then connected witha three-way
cock, A, by which it may be put into communication either with an air-pump,
or with the tubes M and N, which are connected with the reservoir of gas.
The tubes M and N contain substances which by their action on the gas
dry and also purify it.
The stopcock A being so turned that the globe is only connected with
the air-pump, a vacuum is produced ; by means of the same cock, the con-
nection with the pump being cut off, but established with M and N the
SSS Ea ——————
BG —s =
gas soon fills the globe. But, as the exhaustion could not have been com-
plete, and some air must have been left, the globe is again exhausted and
the gas allowed to enter, and the process is repeated until it is thought that
all airis removed. The vacuum being once more produced, a differential
barometer (fig. 158), connected with the apparatus by the tube E, indicates
the pressure of the residual rarefied gas ¢. Closing the cock B and de-
taching A, the globe is removed from the ice, and after being cleaned. is
weighed.
This gives the weight of the empty globe 4; it is again replaced in the
ice,-the stopcock A adjusted, and the gas allowed to enter, care being taken
to leave the stopcocks open long enough to allow the gas in the globe to ac-
quire the pressure of the atmosphere, H, which is marked by the barometer.
The stopcock A is then closed, A removed, and the globe weighed with the
same precautions as before. This gives the weight P’ of the gas and globe.
Y
322 On Heat [340-
The same operations are then repeated on this globe with air, and two
corresponding weights # and P are obtained. The only correction necessary
is to reduce the weights in the two cases to the standard pressure by the
method described in the preceding paragraph.- The correction for temperature
is not needed, as the gas is at the temperature of melting ice. The ratio of
the weight of the gas to that of the air is thus obtained by the formula
je Se
Vet
341. Density of gases which attack metals.—For gases which attack
the ordinary metals, such as chlorine, a metal stopcock cannot be used, and
vessels with ground-glass stoppers (fig. 323) are substituted.
The gas is introduced by a bent glass tube, the vessel being held
either upright or inverted, according as the gas is heavier or
lighter than air ; when the vessel is supposed to be full, the tube
is withdrawn, the stopper inserted, and the weight taken. This
gives the weight of the vessel and gas. If the capacity of the
vessel be measured by means of water, the weight of the air
which it contains is deduced, for the density of air at 0° C. and
760 millimetres pressure is +4, that of distilled water under the
same circumstances. The weight of the vessel full of air, less
the weight of the contained air, gives the weight of the vessel
itself. From these three data—the weight of the vessel full of
the gas, the weight of the air which it contains, and the weight
of the vessel alone—the specific gravity of the gas is readily deduced, the
necessary corrections being made for temperature and pressure.
Relative density of gases at zero and at a pressure of 760 millimetres, that
of atr being taken as untty.
Alted f : . 1°0000 Sulphuretted hydrogen I'1912
Hydrogen . . 0'0693 Hydrochloric acid et 2540
Ammoniacal gas. LOS 8On Protoxide of nitrogen . 1°5270
Marsh gas . 1a 035590 Carbonic acid . oP gles 2or
Carbonic oxide . . 09670 Cyanogen . : . 1'8600
Nitrogen ; eO'O7.14 Sulphurous acid . 1 Basra
Binoxide of nitrogen . 1°0360 Chlorine ee eye ee,
Oxygen : ; » PISLOgy Hydriodic acid . ie Bn ke)
Regnault made the following determinations of the weight of a litre of
the most important gases at o° C. and 760 mm. :—
Air. . 1°293187 grms. Nitrogen . 1°256157 grms.
Oxygen . UO EEAZOGO? wats, Carbonic acid 1°977414 ,,
Hydrogen’ 2 7oo8otyo = s.
~342] Fusion. lis Laws 323
CHAP TRG.
CHANGES OF CONDITION. VAPOUR
342. Fusion. Its laws.—The only phenomena of heat with which we
have hitherto been engaged have been those of expansion. In the case of
solids it is easy to see that this expansion is limited. For in proportion as
a body absorbs a larger quantity of heat, the kinetic energy of the molecules
is increased, and ultimately a point is reached at which the molecular attrac-
tion is not sufficient to retain the body in the solid state. A new phenomenon
is then produced ; melting or fuston takes place; that is, the body passes
from the solid into the liquid state.
Some substances, however, such as paper, wood, wool, and certain salts,
do not fuse at a high temperature, but are decomposed. Many bodies have
long been considered vefractory—that is, incapable of fusion ; but, in pro-
portion as it has been possible to produce higher temperatures, their number
has diminished. Gaudin succeeded in fusing rock crystal by means of a
lamp fed by a jet of oxygen ; and Despretz, by combining the effects of the
sun, the voltaic battery, and the oxy-hydrogen blowpipe, melted alumina
and magnesia, and softened carbon so as to be flexible, which is a condition
near that of fusion.
It has been found experimentally that the fusion of bodies is governed
by the two following laws :-—
I. Every substance begins to fuse at a certain temperature, which ts
invariable for each substance, tf the pressure be constant.
Il. Whatever be the intensity of the source of heat, from the moment
fuston begins, the temperature of the body ceases to rise, and remains constant
until the fusion ts complete.
Melting points of certain substances.
Ethylene . : .—169° Phosphorus. : ee Ae
Ammonia. : . 75 Spermaceti ; : phd
Mercury . é . —38°8 Potassium : : ae 55
Oil of turpentine. . —27 Margaric acid . ; bn
Bromine . d ; . -12 Stearine . : : dts 00)
ier ay O White wax smi hOS
Nitrobenzene . ; . +3°0 Wood’s fusible metal RAO s)
Formic acid . : Ose eAT CACC «4. : 7G
Acetic acid. . Pea, Sodium . ; ; WO nOO
Butter! 3): Htc Rose’s fusible metal. a On.
Rubidium ; PERO Sulphur . : . ee!
324 On. Heat [342—
Benzoic acid . 920%" NMagwiesium 2); ; Li F5or
Indium. : S > BEZO Aluminium. SSO
Tink: 228 Sodium chloride Anos
Bismuth . ’ . 246 vers © : : . 980
Cadmium. B wUReT Gold : : : . 1060
Lead : : : iy As Copper”. : : “7068
Zinc. : ‘ : y yAze Potassium sulphate . . O73
Antimony ; ; eerie Iron. : : s . 1500
Arsenic . hw iV 590 Platinum . ; Lega
Potassium iodide . ft. 023 Iridium . : : . 1950
Some substances pass from the solid to the liquid state without showing
any definite melting point ; for example, glass and iron become gradually
softer and softer when heated, and pass by imperceptible stages from the
solidi-to the liquid condition. This inter-
mediate condition is spoken of as the state
of vitreous fusion. Such substances may be
said to melt at the lowest temperature at
which perceptible softening occurs, and to be
fully melted when the further elevation of
temperature does not make them more fluid ;
but no precise temperature can be given as
that of their melting points.
The determination of the melting point
of a body is a matter of considerable im-
portance in fixing the identity of many
chemical compounds, and is moreover of —
frequent practical application in determin-
ing the commercial value of tallow and other
fats.
It is done as follows :—A portion of the
substance is melted in a watch-glass, and a
small quantity of it sucked into a fine capil-
lary tube, which is then placed in a bath
of clear water (fig. 324) attached to a ther-
mometer, and the temperature of the bath
is gradually raised until the substance is
completely melted, which from its small mass
is very easily observed. The bath is then allowed to cool, and the solidi-
fying point noted ; and the mean of the two is taken as the true melting point.
343. Influence of pressure on the melting point.—Lord Kelvin and
Clausius deduced from the principles of the mechanical theory of heat that,
with an increase of pressure, the melting point of a body must be raised.
All bodies which expand on passing from the solid to the liquid state have
to perform external work—namely, to raise the pressure of the atmosphere
by the amount of this expansion. Under ordinary circumstances, the
amount of external work which solids and liquids thus perform is so small
that it may be neglected. But, if the external pressure be increased, the
power of overcoming it can only be obtained by an increase of the kinetic
Fig. 324.
4
-343] Lnfiuence of Pressure on the Melting Point 325
energy of the molecules. More external work is thereby done ; the tempera-
ture of fusion and the heat of fusion are both increased. Bunsen examined
the influence of pressure on the melting point by means of the apparatus
represented in fig. 325, somewhat resembling in appearance a siphon
barometer. The tube is closed at bothends. The part from @ to c contains
mercury except at the end J, where the substance under examination is put.
Air occupies the portion which is carefully calibrated. The lower part of the
apparatus is placed in a water bath, the mercury being heated as well as the
substance. The expansion of the mercury compresses the air, the elastic
force of which reacts on the substance and exerts on it a gradually increasing
pressure. It only then remains to observe the temperature at which the
es TM
Fig. 326.
substance solidifies, and the corresponding pressure at that moment. In
this way Bunsen found that spermaceti, which melts at 48° under a pressure
of 1 atmosphere, melts at 51° under a pressure of 156 atmospheres. Hopkins
found that spermaceti melted at 60° under a pressure of 519 atmospheres
and at 80° under 792 atmospheres; the melting point of sulphur under these
pressures was respectively 135° and 141°
But with regard to those bodies which contract on passing from the solid
to the liquid state, and of which water is the best example, the reverse is
the case. Melting ice has no {external work to perform, since it has no
external pressure to overcome; on the contrary, in melting, it absorbs
external work, which, transformed into heat, renders a smaller quantity of
heat necessary; the external work acts in the same direction as the internal
heat—namely, in breaking up the crystalline aggregates. Yet these differ-
ences of temperature must be but small for the molecular forces in solids
326 On Fleat [343—
preponderate far over the external pressure ; the internal work is far greater
than the external.
Lord Kelvin found that increase of pressure lowered the melting point of
ice. The apparatus consisted of a piezometer (fig. 326); a thick leaden
ring divided the vessel into two compartments, the upper
one of which contained water and the lower one crushed ice,
which was thus prevented from rising. This also served to
support a thermometer enclosed in a very stout tube, and a
manometer with compressed air. The pressures were
exerted by means of a screw piston V.
Lord Kelvin thus found that pressures of 81 and 16°8
atmospheres lowered the melting point of ice by o-059° and
o'126° respectively. These results justify the theoretical
previsions of his brother, Professor J. Thomson, according to
which an increase of pressure of 7 atmospheres lowers the
melting point of ice by 0:00747° C.,so that a pressure of 135 atmospheres, or
about 2,000 pounds to the square inch, would lower the melting point 1° C.
This lowering of the melting point is also shown by the experiment of
Mousson. The apparatus consists of a stout steel tube closed at one end by
a screw and with a screw piston at the other (fig. 327). The tube is filled
with water and a metal bullet
lo ™ introduced. When the apparatus
f 4 is closed it is inverted so that the
f (Pi)
i ul bullet rests on the piston, and
|
unarare
placed thus in a freezing mixture ;
the water freezes and presses the
ball against the piston. This is
then turned again, and pressure is
gradually applied by turning the
handle of the screw. When the
lower screw is opened the copper
ball falls out, and is followed by a
thick cylinder of ice which must
have been formed at the moment
of opening. Hence the ice must,
by a pressure estimated at 13,000
atmospheres, have been converted
into water at about — 18° C.
This influence is likewise readily
demonstrated by an experiment of von Helmholtz (fig. 328). Water is boiled
in a flask until all air is expelled,and it is then closed. It is afterwards
placed in a freezing mixture so that some ice forms inside. This is then
allowed to melt again in great part, and the flask is placed in a vessel of
water containing lumps of ice. It is then found that the still unfrozen water
inside the flask freezes while that of the outside is melting.
344. Alloys. Fluxes.—Alloys are generally more fusible than any of the
metals of which they are composed ; for instance, an alloy of 5 parts of tin
and 1 of lead fuses at 194°. The alloy known as Rose’s fusible metal, which
consists of 4 parts of bismuth, 1 part of lead, and 1 of tin, melts at 94°, and
Fig. 328.
—-346] Solution Car:
an alloy of 1 or 2 parts of cadmium with 2 parts of tin, 4 parts of lead, and
7 or 8 parts of bismuth, known as Wood's fusible Devel, melts peceea 66°
and 71° C. An alloy of potassium and sodium in equivalent proportions is
liquid at the ordinary temperature. Fusible alloys are of extended use in
soldering and in taking casts. Steel melts at a lower temperature than iron,
though it contains carbon, which is almost completely infusible.
Mixtures of the fatty acids melt at lower temperatures than the pure acids.
A mixture of potassium and sodium chlorides fuses at a lower temperature
than either of its constituents ; this is also the case with a mixture of
potassium and sodium carbonates, especially when they are mixed in the
proportion of their chemical equivalents.
An application of this property is met with in the case of jfwxes, which
are much used in metallurgical operations. They consist of substances
which, when added to an ore, partly by their chemical action, help the
reduction of the substance to the metallic state, and, partly, by presenting a
readily fusible medium, promote the agglomeration of the individual particles
with the formation of a mass of metal or regudits.
345. Latent heat.—Since, during the passage of a body from the solid to
the liquid state, the temperature remains constant until the fusion 1s com-
plete, whatever be the intensity of the source of heat, it must be concluded
that, in changing their condition, bodies absorb a considerable amount of
heat, the only effect of which is to maintain them in the liquid state. This
heat, which is not indicated by the thermometer, is called /atent heat or
latent heat of fusion, an expression which, though not in strict accordance
with modern ideas, is convenient from the fact of its universal recognition
and employment (470).
An idea of what is meant by latent heat may be obtained from the follow-
ing experiment :—If a pound of water at 80° is mixed with a pound of water
at zero, the temperature of the mixture is 40°. But if a pound of pounded
zce at zero is mixed with a pound of water at 80°, the ice melts and two
pounds of water at zero are obtained. Consequently the mere change of a
pound of ice to a pound of water at the same temperature requires as much
heat as will raise a pound of water through 80°. This quantity of heat
represents the latent heat of the fusion of ice, or the latent heat of water.
Every liquid has its own latent heat, and in the chapter on Calorimetry
we shall show how this is determined.
346. Solution._-A body is said to a@ssolve when it becomes liquid in
consequence of an attraction between its molecules and those of a liquid.
Gum arabic, sugar, and most salts dissolve in water. The weight dissolved
in a given quantity of water generally increases with the temperature, as is
seen.from the following table :—
Common Salt Nitre Sodium Sulphate Copper Sulphate| Zinc Sulphate
°
O 35 13 32 115
20 37 21 53 42 131
100 40 247 42 203 654
Fost On Heat ‘[346-
When a liquid has dissolved as much as it can at a particular tempera-
ture, it is said to be saturated.
The belief formerly held that the properties of a liquid were altered when
a body was dissolved in it nearly in proportion to the quantity dissolved is
not confirmed by the results of electrolysis. The first small quantity dis-
solved produces a far greater change than a subsequent equal quantity.
When a salt dissolves in water it may be supposed that the vibrations of
its bounding molecules, which are in contact with the solvent, possibly owing
to the attraction of the solvent, or owing to capillarity, increase their amplitude
so that they get beyond the sphere of action of the other molecules of the
salt, and thereby assume a progressive motion like the molecules of a gas.
Like them they then exert a pressure against the sides of the containing
vessel, which is called osmotic Dressure (141).
During solution, as well asduring fusion, a certain quantity of heat always
becomes latent, and hence it is that the solution of a substance usually
produces a diminution of temperature. In certain cases, however, instead
of the temperature being lowered, it actually rises, as when caustic potash is
dissolved in water. This depends upon the fact that two simultaneous
and contrary phenomena are produced. The first is the passage from the
solid to the liquid condition, which always lowers the temperature. The
second is the chemical combination of the body dissolved with the liquid,
which, as in the case of all chemical combinations, produces an increase
of temperature. Consequently, as the one or the other of these effects pre-
dominates, or as they are equal, the temperature either rises or sinks, or
remains constant.
347. Solidification — Solidification or congelation is the passage of a
body from the liquid to the solid state. This phenomenon is expressed by
the two following laws :—
I. Every body, under the same pressure, solidifies ata fixed temperature,
which ts the same as that of fusion.
Il. From the commencement to the end of the solidification, the tempera-
ture of a liguid remains constant.
Certain bodies, more especially some of the fats, present an exception to
the first law, in so far that by repeated fusions they seem to undergo a
molecular change which alters their melting point.
The second law is the consequence of the fact that the latent heat
absorbed during fusion becomes free at the moment of solidification.
The application of the very low temperatures which can now be so readily
procured has lessened the number of those liquids which it was formerly
thought could not be solidified. By allowing liquid ethylene (388) to boil in
a vacuum, Wroblewski and Olszewski obtained a temperature of — 136°.
They observed that carbon disulphide solidified at —116° and fused again at
about —110°. Absolute alcohol became viscid at —129° and solidified at
—130°5°. Pure ether solidifies at — 1297,
Water containing a salt dissolved always solidifies below zero ; the de-
pression of the freezing point is proportional to the weight of salt dissolved,
at any rate for weak solutions. This is known as Blagden’s law.
. If several salts which have no chemical action on each other be dis-
solved in a given weight of water, the lowering of the freezing point is the
—347] Solidification 329
sum of the depressions which each of them would produce separately if
dissolved in the same quantity of water.
When the numbers observed in any experiment of this kind do not agree
with those calculated, this points to the occurrence of some chemical action
between the substances dissolved,
and the observation of such devia- »
tions has been of use in questions
of chemical statics.
The elaborate researches of
Raoult on the temperature of
solidification of solutions of bodies
in water and other solvents have
led to important conclusions. The
temperature at which a solution
solidifies, or its freezing point, is
always lower than that of the pure
solvent. If P be the weight in
grammes of any substance dis-
solved in 100 grammes of a solvent,
and C be the depression in the freez-
ing point observed, then : SHAM is
the depression which would be pro-
duced by dissolving ove gramme of
the substance in Ioo grammes of
the solvent, and is known as the
coefficient of depression.
A comparison of the values for
A for various substances and the
same solvent shows that they differ
considerably ; this 1s not so if we
compare the depressions produced
by molecular weights of the sub-
stances. That is, if we multiply the
value of A in the above equation by
M, the molecular weight of the sub-
stance dissolved, we obtain the de-
pression which would be produced
by dissolving one gramme-mniole-
cule of a body in 100 grammes of
the solvent, or the coefficient of
molecular depression ; this is called
T, and we have T = oe
Now it is found that in a very large number of cases the value of T, for
one and the same solvent, is a constant number; it has the value 19 for
water, 39 for glacial acetic acid, and 49 for benzene.
_ This relation is of great value ; by means of a simple determination of the
freezing point of a solid we can calculate the molecular weight of substances
330 On Heat [347—
which cannot be obtained in the gaseous state without being decomposed.
This is conveniently effected by means of the apparatus represented in
fig. 329. The solvent is contained in the vessel A, and the substance to
be investigated is introduced by the lateral aperture A’. A is surrounded
by a wide glass tube B containing air, and this again is placed in a wider
vessel C which contains the freezing mixture ; for experiments with benzene
or glacial acetic acid as a solvent, this is bruised ice, and with water a mixture
of ice and salt. The liquid from these may be drawn off by a siphon placed
.through 4. In A is a platinum stirrer 7, and a delicate thermometer D,
indicating the +45 of a degree. C is also a Stirrer.
Since C and P are known, M is determined from the formula
ee
where T is the constant for the particular solvent employed, which is ordinary
glacial acetic acid in the majority of cases.
Van ‘t Hoff has shown that the coefficient of depression ¢ may be
| calculated by means of the formula ¢ = Siete
@
j fusion, and T the temperature of fusion in absolute degrees (507).
: In the case of such salts as potassium chloride the molecular
depressions are greater than is required by the law, being nearly twice
F as much as in indifferent bodies like sugar; this is probably due
: to the fact that a greater or less proportion of the salt is a@ssoctated
where wis heat of
40
cha into its constituents, a phenomenon analogous to the dissociation
is of vapours, to which are due abnormal vapour densities (394).
f 348. Crystallisation.— Generally speaking, bodies which pass
[| 20 ’ i
: slowly from the liquid to the solid state assume regular geometri-
i cal forms, such as the cube, prism, rhombohedron, &c. ; these are
Ho called crystals. Ifthe crystals are formed from a body in fusion,
such as sulphur or bismuth, the crystallisation is said to take
place by the dry way. The crystallisation is said to be by the
moist way when it takes place owing to the slow evaporation
of a solution of a salt, or when a solution saturated at a
higher temperature is allowed to cool slowly. Snow, ice, and
many salts present examples of crystallisation.
349. Retardation of the point of solidification.—The freezing .
point of pure water can be diminished by several degrees, if the
water be previously freed from air by boiling and be then kept
in a perfectly still place. In fact, it may be cooled to —15° C.,
and even lower, without freezing. But when it is slightly agitated,
the liquid at once solidifies. This may be conveniently shown by
means of the apparatus represented in fig. 330, which consists of
a delicate thermometer, round the bulb of which is a wider one
containing some water. Before sealing at a the whole outside
bulb was filled with water, which was then boiled out and sealed
so that over the water the space is quite empty. This is clamped in a retort
stand, and ether is dropped on it, that which has dropped off, and become
colder, being used over and over again. In this way the temperature may
soon be reduced to —6°, and if then the bulb be shaken, part of the water
Fig 330.
—349] Retardation of the Point of Solidification 331
freezes and the temperature rises to zero. The smaller the quantity of liquid,
the lower is the temperature to which it can be cooled, and the greater the
mechanical disturbance it supports without freezing. Fournet has observed
the frequent occurrence of mists formed of particles of liquid matter sus-
pended in an atmosphere whose temperature was 10° or even 15° below zero.
A very rapid agitation also prevents the formation of ice. Thisis also the
case with all actions which, hindering the molecules in their movements, do
not permit them to arrange themselves in the conditions necessary for the
solid state. Despretz was able to lower the temperature of water contained
in fine capillary tubes to —20° without their solidifying. This experiment
shows how it is that plants in many cases do not become frozen even during
severe cold, as the sap is contained in very fine capillary vessels.
If water contains salts, or other foreign bodies, its freezing point is
lowered. Sea water freezes at —2°5° to —3°.C.; the ice which forms is
quite pure, and a saturated solution remains. In Finland advantage is taken
of this property to concentrate sea water for the purpose of extracting salt
from it. If water contains alcohol, precisely analogous phenomena are
observed ; the ice formed is pure, and practically all the alcohol is contained
in the residue. ;
Dufour has observed some very curious cases of liquids cooled out of
contact with solid bodies. His mode of experimenting was to place the
liquid in another of the same specific gravity but of lower melting point,
in which it is insoluble. Drops of water, for instance, suspended in a
mixture of chloroform and oil, usually solidified between —4° and —12°,
while still smaller globules cooled down
to —18° or —20°. Contact with a frag-
ment of ice immediately set up congela-
tion. Globules of sulphur (which solidifies
at 115°) remained liquid at 40° ; and glo-
bules of phosphorus (solidifying point 42°)
at 20°.
The superfusion of phosphorus may
be illustrated by the experiment repre-
sented by fig. 331. A long test tube
containing phosphorus, A, and covered
‘with a layer of water, is fixed along with
a thermometer T in a large flask con-
taining water. This flask is raised to a
temperature of about 44° at which the
phosphorus fuses, and is then withdrawn
from the source of heat; as its mass is
considerable, it cools very slowly, and
the phosphorus remains liquid even at
ordinary temperatures. A glass rod may
even be dipped into it without change ;
but if the rod be rubbed along solid Fig. 331.
phosphorus so as to detach a small par-
ticle it at once brings about solidification if dipped in the melted mass.
When a liquid solidifies after being cooled below its normal freezing point
332 On Heat [349—
the solidification takes place very rapidly, and is accompanied by a disen-
gagement of heat, which is sufficient to raise its temperature from the point
at which solidification begins up to its ordinary freezing point. This is
well seen in the case of sodium hyposulphite, which melts in its own water
of crystallisation at 45°, and when carefully cooled will remain liquid at the
ordinary temperature of the atmosphere. If it then be made to solidify by
agitation, or by adding a small fragment of the solid salt, the rise of tems
perature is distinctly felt by the hand. In this case the heat, which had
become latent in the process of liquefaction, again becomes free, and a
portion of the substance remains melted ; for it is kept hauig by the heat of
solidification of that which has solidified.
350. Change of volume on solidification and liquefaction.—The rate
of expansion of bodies generally increases as they approach their
melting points, and is in most cases followed by a further expansion at the
moment of liquefaction, so that the liquid occupies a greater volume than
the solid from which it is formed. The apparatus represented in fig. 332 is
well adapted for exhibiting this phenomenon. It consists of a
glass tube, aé, containing water or some other suitable liquid, to
which is carefully fitted a cork with a graduated glass tube c.
This forms, in fact, a thermometer, and the values of the divisions
on the tube ¢ are determined in terms of the capacity of the whole
apparatus. A known volume of the substance is placed in the
tube aa and the cork inserted ; the apparatus is then, placed in a
space at a temperature very little below the melting point of the
body in question, until it has acquired its temperature, and the
position of the liquid in ¢ is noted. The temperature is then
allowed to rise slowly, and the position noted when the melting is
complete. Knowing then the difference in the two readings and
the volume of the substance under experiment, and making a
correction for the expansion of the liquid and of the glass, it is
easy to deduce the increase due to the melting alone. Phos-
phorus, for instance, increases about 3°4 per cent. on liquefaction ;
that is, 100 volumes of solid phosphorus at 44° (the melting point)
become 103°4 at the same temperature when melted. Sulphur
expands about 5 per cent. on liquefying, and stearic acid about
II per cent.
Water presents a remarkable exception ; it expands at the
moment of solidifying, or contracts on melting, by about Io per
cent. One volume of ice at 0° gives 09178 of water at 0°, or I
volume of water at 0° gives I‘102 of ice at the same temperature.
In consequence of this expansion, ice floats on the surface of water. Accord-
ing to Dufour, the specific gravity of ice is 0°9178; Bunsen found for ice
which had been made from water freed from air by boiling the somewhat
smaller number 0°91674.
The increase of volume in the formation of ice is accompanied by an
expansive force which sometimes produces powerful mechanical effects, of
which the bursting of water-pipes and the breaking of jugs containing water
are familiar examples. The splitting of stones, rocks, and the swelling up
of moist ground during frost, are caused by the fact that water penetrates
Fig. 332.
~851] Freezing Mixtures 333
into the pores and there becomes frozen ; in short, the great expansion of
water on freezing is the most active and powerful agent of disintegration on
the earth’s surface.
The expansive force of ice was strikingly shown by some experiments of
Major Williams in Canada. Having quite filled a 13-inch iron bomb-shell
with water, he firmly closed the touch-hole with an iron
plug weighing three pounds and exposed it in this state
to the frost. After some time the iron plug was forced
out with a loud explosion, and thrown. to a distance of
415 feet, and a cylinder of ice 8 inches long issued from
the opening. In another case the shell burst before the
plug was driven out, and in this case a sheet of ice spread
out all round the crack (fig. 333). It is probable that
under the great pressure some of the water still remained liquid (343) up to
the time at which the resistance was overcome ; that it then issued from the
shell in a liquid state, but at a temperature below 0°, and therefore instantly
began to solidify when the pressure was removed, and thus retained the
shape of the orifice whence it issued.
Cast-iron, bismuth, and antimony expand on solidifying, like water, and
can thus be used for casting ; but gold, silver, and copper contract, and
hence coins of these metals cannot be cast, but must be stamped with a die.
An iron tube filled with molten bismuth and closed by a screw, is broken
as the bismuth becomes solid.
This increase of volume when liquids solidify, and the correlated decrease
on melting again, in the case of water and some other crystalline substances
such as bismuth, are probably due to the fact that such bodies are aggregates
of small crystalline masses, which are grouped in such a way that small
interstices are formed. When the liquid melts these interstices fill up owing
to the mobility of the molecules, and, notwithstanding the greater space
which each individual group takes up, owing to expansion, there is on the
whole a decrease of volume.
351. Freezing mixtures.—The absorption of heat in the passage of
bodies from the solid to the liquid state has been used to produce artificial
cold. This is effected by mixing together bodies which have an affinity for
each other, and of which one at least is solid, such as water and a salt, ice
and a salt, or an acid and a salt. Chemical affinity accelerates the fusion or
solution ; the portion which melts or dissolves robs the rest of the mixture of
a large quantity of sensible heat, which thus becomes latent. In many cases
a very considerable diminution of temperature is produced.
The following table gives the names of the substances mixed, their pro-
portions, and the corresponding diminutions of temperature :—
Parts Reduction of
Substances by weight temperature
Sodium sulphate . , , ; 8
P l + 10° to —17°
Hydrochloric acid .
Pounded ice or snow
5)
2) :
Common salt : : F ; I}
3)
2)
rlO AO =a1o
Sodium sulphate
Dilute nitric acid
+ 10° to —19°
On Heat [351-
334
Parts Reduction of
Substances by weight temperature
Sodium sulphate . : ‘ ; 6)
Ammonium nitrate 5. + 10° to — 26°
Dilute nitric acid . . y,
Sodium phosphate : 9) 3 ‘
Dilute nitric acid . ; 4) Tiare ae eae
If the substances taken be themselves previously cooled down, a still
more considerable diminution of temperature is occasioned.
Freezing mixtures are frequently used in chemistry, in physics, and in
domestic economy. One form of the portable ice-making machines which
have come into use during the last few years consists of a cylindrical
metallic vessel divided into four concentric compartments. In the central
one is placed the water to be frozen; in the next there is the freezing
mixture, which usually consists of sulphate of sodium and hydrochloric acid ;
6 pounds of the former and 5 of the latter will make 5 to 6 pounds of ice in
an hour. The third compartment also contains water, and the outside one
‘contains some badly conducting substance, such as cotton, to cut off the
influence of the external temperature. The best effect is obtained when
pretty large quantities (2 or 3 pounds) of the mixture are used, and when
the ingredients are intimately mixed. It is also advantageous to use the
machines for a succession of operations.
352. Guthrie's researches.—It appears from the experiments of the late
Dr. Guthrie that what are called freezing mixtures may be divided into two
classes—namely, those in which one of the constituents is liquid and those
in which both are solid. The temperature indicated by the thermometer
placed in a freezing mixture 1s, of course, due to the loss of heat by the
thermometer in the liquefying freezing mixture, and is measured by the rate
of such loss. The quantity of heat absorbed by the freezing mixture is
obviously the heat required to melt the constituents, together with (+) the
heat of combination of the constituents. When one constituent is liquid,
as when hydrochloric acid is added to ice, then a lower temperature is got
by previously cooling the hydrochloric acid. There is no advantage in
cooling the ice. But when both constituents are solid, as in the case of the
ice-salt freezing mixture, there is no advantage to be gained by cooling one or
both constituents. Within very wide limits it is also in the latter case a matter
of indifference as to the ratio between the constituents. Nor does it matter
whether the ice is finely powdered as snow or in pieces as large as a pea.
The different powers of various salts when used in conjunction with ice
as freezing mixtures appear to have remained unexplained until Guthrie
showed that, with each salt, there is always a minimum temperature below
which it is impossible for an aqueous solution of any strength of that salt to
exist in the liquid form ; that there is a certain strength of solution for each
salt which resists solidification the longest, that is, to the lowest temperature.
Weaker solutions give up ice on being cooled, stronger solutions give up the
salt either in the anhydrous state or in Sombuiation built water. A solution
of such a strength as to resist solidification to the lowest temperature, was
called by Guthrie a cryohydrate. It is of such a strength that when cooled
~355] Elastic Force of Vapour 335
below o° C. it solidifies as a whole; that is, the ice and the salt solidify
together and form crystals of constant composition and constant melting
and the same solidifying temperatures. The liquid portion of a freezing
mixture, as long as the temperature is at its lowest, is, indeed, a melted
cryohydrate. The slightest depression of temperature below this causes
solidification of the cryohydrate, and hence the temperature can never sink
below the solidifying temperature of the cryohydrate.
Guthrie also showed that colloid bodies, such as gum and gelatine, neither
raise the boiling point of water nor depress the solidifying point, nor can
they act as elements in freezing mixtures.
VAPOURS. MEASUREMENT OF THEIR PRESSURE.
353. Vapours.—We have already seen (155) that vapours are the aériform
fluids into which volatile substances, such as ether, alcohol, water, and
mercury, are changed by the absorption of heat. Volatile liguids are those
which thus possess the property of passing into the aériform state, and fixed
liguids are those which do not form vapour at any temperature without
undergoing chemical decomposition, such as the fatty oils. Ice and snow
volatilise in closed spaces, forming crystals on the cooled parts. The forma-
tion of vapour is thus not restricted to the liquid state, and in some bodies,
such as arsenic, the boiling point is below the freezing point. As the boiling
point is raised by pressure it is possible to liquefy such bodies also, by
applying sufficient pressure.
Iodine melts at 104° and boils at 175° under ordi-
nary pressure. It therefore evaporates after melting ; |
but at a pressure of 250 mm. its boiling point is below
its melting point, and it then evaporates without melt-
ing. Even at ordinary temperatures a considerable
quantity volatilises without melting.
Vapours are transparent, like gases, and generally
colourless ; there are only a few coloured liquids which
also give coloured vapours.
354. Vaporisation.—The passage of a liquid into
the gaseous state is designated by the general term
vaporisation; the term evaporation especially
refers to the slow production of vapour at the
free surface of a liquid, and doz/ig to its rapid pro-
duction in the mass of the lquid itself. We shall
presently see (367) that at the ordinary atmospheric
pressure, ebullition, like fusion, takes place at a definite
temperature. This is not the case with evaporation,
which occurs even with the same liquid at very different
temperatures, although the formation of a vapour
seems to cease below a certain point. Mercury, for
example, is stated to give no vapour below — 10°, nor
sulphuric acid below 30°.
355. Elastic force of vapour.—Like gases, vapours have a certain elastic
force, in virtue of which they exert pressures on the sides of vessels in
which they are contained. The elastic force of vapour may be demonstrated
336 On Heat | (355-
by the following experiment :—A quantity of mercury is placed in a bent
glass tube (fig. 334), the shorter leg of which is closed; a few drops of
ether are then passed into the closed leg and the tube is immersed in a
water bath at a temperature of about 45°. The mercury then sinks slowly
in the short branch, and the space aé is filled with a gas which has all the
appearance of air, and whose elastic force counterbalances the pressure of
the column of mercury cd, and the atmospheric pressure on @. This gas
is the vapour of ether. If the water be cooled, or if the tube be removed
from the bath, the vapour which fills the space aé disappears, and the drop of
ttt i AO
fe ‘4
ether is reproduced. If, on the contrary, the bath be heated still higher, the
level of the mercury descends below 4, indicating an increase in the elastic
force of the vapour.
356. Formation of vapour in a vacuum.—The change from liquid to
vapour takes place very slowly when the liquid is freely exposed to the air.
The atmosphere is an obstacle to the vaporisation. In a vacuum there is
no resistance, and the formation of vapour is instantaneous, as is seen in the
following experiment :—Four barometer tubes, filled with mercury, are im-
mersed in the same trough, fig. 335. One of them, A, serves as a barometer,
~358] Unsaturated Vapours 337
and a few drops of water, alcohol, and ether are respectively introduced into
the tubes B, C, D. When the liquids reach the vacuum, a depression of the
mercury is at once produced. And as this depression cannot be caused by
the weight of the liquid, which is an extremely small fraction of the weight
of the displaced mercury, it must be due to the formation of some vapour
whose elastic force has depressed the column of mercury.
The experiment also shows that the depression is not the same in all the
tubes ; it is greater in the case of alcohol than of water, and greater again
with ether than with alcohol. We consequently obtain the two following
laws of the formation of vapours :—
I. In a vacuum all volatile liguids are instantaneously converted into
vapour.
Il. Ad the same temperature the vapours of different liquids have different
pressures.
For example, at 20° the pressure of ether vapour is 25 times as great as
that of aqueous vapour.
357. Saturated vapour. Maximum of pressure.—When a very small
quantity of a volatile liquid, such as ether, is introduced into a barometer
tube, it is at once completely vaporised, and the column of mercury is not
‘depressed to its full extent; for if some more ether be introduced -the
depression increases. The ether, if still more be added, finally ceases to
vaporise, and remains in the liquid state. There is, therefore, for a certain
temperature, a limit to the quantity of vapour which can be formed in a
given space. This space is accordingly said to be saturated. Further,
when the vaporisation of the ether ceases, the depression of the mercurial
column stops. And hence there is a limit to the pressure of the vapour, a
limit which, as we shall presently see (358), varies with the temperature.
To show that, in a closed space, saturated with vapour and containing
liquid 27 excess, the temperature remaining constant, there is a maximum of
pressure which the vapour cannot exceed, a barometric tube is used which
dips in a deep bath (fig. 336). This tube is filled with mercury, and then so
much ether is added as to be in excess after the Torricellian vacuum is
saturated. The height of the column of mercury is next noted by means of
the scale graduated on the tube itself. Now, whether the tube be depressed,
which tends to compress the vapour, or whether it be raised, which tends to
expand it, the height of the column of mercury is constant. The pressure of
the vapour remains constant in the two cases, for the depression neither
increases nor diminishes it. Hence it is concluded that when the saturated
vapour is compressed, a portion returns to the liquid state ; that when, on
the other hand, the pressure is diminished, a portion of the excess of liquid
vaporises, and the space occupied by the vapour is again saturated ; but in
both cases the pressure and the density of the vapour remain constant.
358. Unsaturated vapours.—It will be seen from what has been said,
that vapours present two very different states, according as they are saturated
or not. In the first case, where they are saturated and in contact with the
liquid, they differ completely from gases, since for a given temperature they
can neither be compressed nor expanded ; their elastic force and their density
remain constant.
In the second case, on the contrary, where they are not saturated, they
z
338 On Heat [358--
exactly resemble gases. For if the experiments (fig. 336) be repeated, only
a small quantity of ether being introduced, so that the vapour is not saturated,
and if the tube be then slightly raised, the level of the mercury is seen to rise,
which shows that the elastic force of the vapour has diminished. Similarly,
by immersing the tube still more, the level of the mercury sinks. The vapour
consequently behaves just as a gas would do, its pressure diminishing
when the volume increases, and vice versa ; and as in both cases the volume
of the vapour is inversely as the pressure, it is concluded that umsaturated
vapours obey Boyle's law.
When an unsaturated vapour is heated, its volume increases like that of
a gas ; and the number 000367, which is the coefficient of the expansion of
air, may be taken for that of unsaturated vapours.
Hence we see that the physical properties of unsaturated vapours are
comparable with those of gases, and that the formulz for the compressibility
and expansibility of gases (184 and 336) also apply to unsaturated vapours.
359. Pressure of aqueous vapour below zero.—In order to measure
the elastic force of aqueous vapour below zero, Gay-Lussac used two baro-
meter tubes filled with mercury, and placed in the same reservoir (fig. 337).
The straight tube, A, serves as a barometer ; the other, C, is bent, so that part
of the Torricellian vacuum can be surrounded
by a freezing mixture, B (351). When a little
water is admitted into the bent tube, the level of
the mercury sinks below that in the tube A, to
an extent which varies with the temperature of
the freezing mixture.
At o° the depression is . 4°54 millimetres
9 ee ” ” » 4°25 ”
2). ee ” ” : 3°63 ”
ey Oe 5° ” 2a oh) » ZI ”
2) ee Tie ” ” 2 2°67 ”
3) gaa! 10° ” ” . 2°08 ”
” 310" ” ” 2 0°84 ”
” = 307 ” ” : 0°36 ”
These depressions, which must be due to
the pressure of aqueous vapour in the space BC,
show that even at very low temperatures there
is always some aqueous vapour in the atmo-
sphere.
Although in the above experiment the part B
and the part C are not both immersed in the
freezing mixture, we shall presently see that
when two communicating vessels are at different
temperatures, the tension of the vapour is the
same in both, and always corresponds to that of
the lower temperature.
That water evaporates even below zero
follows from the fact that wet linen exposed to the air during frost becomes
first stiff and then dry, showing that the particles of water evaporate even
after the latter has been converted into ice.
~360] Pressure of Aqueous Vapour 339
360. Pressure of aqueous vapour between zero and one hundred
degrees.—i. Dalton’s method. Dalton measured the elastic force of aqueous
vapour between o° and 100° by means of the apparatus represented in
fig. 338. Two barometer tubes, A and B, are filled with mercury, and inverted
in an iron bath full of mercury, which is placed on a furnace. The tube A
contains a small quantity of water. The tubes are supported in a cylindrical
vessel, open top and bottom and full of water, the temperature of which is
indicated by the thermometer. The bath being gradually heated, the water
in the cylinder becomes heated too; the water which is in the tube A
: Ls
Ra
mH nl
WAT =
l yy TTT TT =
==
ZA
\" z: | |
ih ie||/>s
oe
———e
Fig. 338.
vaporises, and in proportion as the pressure of its vapour increases, the
mercury sinks. The depressions of the mercury corresponding to each degree
of the thermometer are indicated on the scale E, and in this manner a table
of the elastic forces between zero and 100° has been constructed.
ii. Regnaul’s method.—Dalton’s method is wanting in precision, for the
temperature of the liquid in the cylinder is not everywhere the same, and
consequently the exact temperature of the aqueous vapour is not shown.
Regnault’s apparatus is a modification of that of Dalton. The cylindrical
glass vessel is replaced by a large cylindrical zinc drum, MN (fig. 339), in the
Z2
340 On Heat [3860-
bottom of which are two tubulures. The tubes A and B pass through these
tubulures, and are fixed by caoutchouc collars. The tube containing vapour,
B, is connected with a flask, a, by means of a brass three-way tube, O. The
third limb of this tube is connected with a drying tube, D, containing
pumice charged with sulphuric acid, which is connected with the air-pump.
When the flask @ contains some water, a small portion is distilled into B
by gently heating the flask. Exhausting, then, by means of the air-pump,
the water distils continuously from the flask and from the barometric tube
towards D, which condenses the vapour. After having vaporised some
quantity of water, and when it is thought that the air in the tube is with-
drawn, the capillary tube which connects B with the three-way tube is
sealed. The tube B being thus closed, it is experimented with asin Dalton’s
method.
The drum, MN, being filled with water, is heated by a spirit lamp,
i}
i!
|
YAWN yyy, pen
which is screened from the tubes by a wooden board. By means of a
stirrer, K, all parts of the liquid are kept at the same temperature. In the
side of the drum is a glass window, through which the height of the mercury
in the tubes can be read off by means of a cathetometer ; from the difference
in these heights, reduced to zero, the tension of vapour is deduced. By
means of this apparatus, the elastic force of vapour between o° and 50° has
been determined with accuracy. )
361. Pressure of aqueous vapour above 100° C.—Two methods have
principally been employed for determining the pressure of aqueous vapour
at temperatures above 100° ; the one by Dulong and Arago in 1830, and the
other by Regnault in 1844.
Fig. 338 represents a vertical section of the apparatus used by Dulong
and Arago. It consisted of a copper boiler, 4, with very thick sides, and of
about 20 gallons’ capacity. Two gun-barrels, a, of which only one is seen in
—-362] Pressure of Aqueous Vapour 341
‘ the drawing, were firmly fixed in the sides of the boiler, and plunged in the
water. The gun-barrels were closed below, and contained mercury, in which
were placed thermometers, 7, indicating the temperature of the water and of
the vapour. The pressure of the vapour was measured by means of a mano-
meter with compressed air, 7, previously graduated (187) and fitted into
an iron vessel, @, filled with mercury. In order to see the height of the
mercury in the vessel, it was connected above and below with a glass tube, z,
in which the level was always the same as in the bath. A copper tube, z,
connected the upper part of the vessel, ¢, with a vertical tube, ¢, fitted in the
boiler. The tube z and the upper part of the bath d@ were filled with water,
which was kept cool by means of a current of cold water flowing from a
reservoir, and circulating through the tube 4.
The vapour which was disengaged from the tube ¢ exerted a pressure
on the water of the tube z; this pressure was transmitted to the water and
to the mercury in thé bath d@, and the mercury rose in the manometer. By
noting on the manometer the pressures corresponding to each degree of the
thermometer, Dulong and Arago were able to make a direct measurement
of the pressure up to 24 atmospheres, and the pressure to 50 atmospheres
was determined by calculation.
362. Pressure of vapour below and above 100° C.—Regnault devised
a method by which the Heese of vapour may be measured at temperatures
either below or above 100° It depends on the principle that when a liquid
boils, the pressure of the vapour is equal to the pressure the liquid sup-
ports:(367).. (lf therefore, the temperature and the corresponding pressure
342 On Feat [362—
are known, the question is solved, and the method merely consists in causing *
water to boil in a vessel under a given pressure, and measuring the corre-
sponding temperature.
The apparatus consists of a copper retort, C (fig. 341), hermetically closed
and about two-thirds full of water. In the cover are four thermometers,
two of which just dip into the water, and two descend almost to the bottom.
By means of a tube, AB, the retort C is connected with a glass globe, M, of
about 6 gallons’ capacity, and full of air. The tube AB passes through a
metal cylinder, D, through which a current of cold water is constantly
flowing from the reservoir E. To the upper part of the globe a tube with
two branches is attached, one of which is connected with a manometer, O ;
the other tube, HH’, which is of lead, can be attached to either an exhaust-
ing or a condensing air-pump, according as the air in the globe is to be rare-
fied or condensed. ‘The reservoir K, in which is the globe, contains water
at the temperature of the surrounding air.
If the elastic force of aqueous vapour below 100° is to be measured, the
end H’ of the lead pipe is connected with the plate of the air-pump, and
the air in the globe M, and consequently that in the retort C, is rarefied.
The retort being gently heated, the water begins to boil at a temperature
below 100°, in consequence of the diminished pressure. And since the vapour
is condensed in the tube AB, which is always cool, the pressure originally
indicated by the manometer does not increase, and therefore the pressure of
the vapour during ebullition remains equal to the pressure on the liquid.
A little air is then allowed to enter; this alters the pressure, and the
liquid boils at a new temperature ; both these are read off, and the experi-
ment repeated as often as desired up to 100°.
In order to measure the pressure above I00°, the tube H’ is connected
Pressures of aqueous vapour from —i0° to 104° C.
Tempe-| Pressure in | Tempe-| Pressure in Tempe. Pressure in Terps | Pressure in |
ratures | millimetres | ratures | millimetres |) ratures | millimetres || ratures millimetres
Se Wa eer 2) | alae DS aR) Sean 1
— 10° 2°078 | 12° 10°457 29° 29782. |e OO" 1 ak 25 oie
8 2250 ga els I1°062 30 315450 1) Ol a e545 7omm
6 2890 || 14 11-906 a1 33405 || 92 | 560°76 |
4 3387, || 15 | 12°699 32 35°359 || 93 | 588-41 |
2 31985 Otte a3 33 37°410 . || 94 | 610°74 |
fe) 4°600 ||P 17 | 14421 34 39°565 || 95 | 633°78
ee 49940 | 18 | 15°357 35 41°827 || 96 | 657°54
z 5°302 || «19 16°346 40 54°906 || 97 .| 682°03
Br Gr W75'087.-) Boll ahi asOn 45 | 71391 || 98 | 707°26
4 G:i007.) (iil) 21g yeas 50 | 91982 || 985; 720715
Soin 25345. in i22.u) pekOiORe 55 \1 117479 | 99:0). 733791
6 6:998 23. |) 420°886 60 | 148791 | 99°5, 746°50
7 7-492 ||. 24 22°184 65 | 186.945 | 100°0 760'00
8 BOL7 sai 26 | 237550) a0 2330034 OOS me vaao7. 5
9 eS 7 ae NiueeG 24°998 75 288°517 Iolo, 787°63
fe) S105 27 Fess 80 354°643 102°0| 816°17
II O17921 ier e8') | 28-TOD 85 43341 | 10470) 875°69
-364] Pressure of Aqueous Vapour 343
with a condensing pump, by means of which the air in the globe M and that
in the vessel C are exposed to successive pressures, higher than the atmo-
sphere. The ebullition is retarded (371), and it is only necessary to observe
the difference in the height of the mercury in the two tubes of the mano-
meter O, and the corresponding temperature, in order to obtain the pressure
for a given temperature. The table on the preceding page by Regnault gives
the pressure of aqueous vapour from — 10° to 104°.
In the following table the numbers were obtained by direct observation
up to 24 atmospheres ; the others were calculated by the aid of a formula of
interpolation. This table and the one next following show that the elastic
force increases much more rapidly than the temperature. It has been
attempted to express the relation between them by formule, but none of the
formulze seems to have the simplicity which characterises a true law.
Pressures in atmospheres from 100° to 230°9°
|
|
i 7 | |
|| Number Number'| Number Number
|
Temperatures | ofatmo- Temperatures of atmo-| Temperatures of atmo- | Temperatures of atmo-
| spheres spheres | spheres | spheres
RO eet | | NPS Nee Ns Z|
| | |
100'0° ie eae FRO ve he 1 sTepedre aan hielo ay = a7 Ou 22 |
by 2 eeees te Id polienk'75:8 Oi 2019 16 29079 23 |
120°6 he 180°3 10 204°9 17 22275 Pyne
| 133'9 6 184°5 LI 207°7 18 224°7 25 |
| 144°0 Ae ERT OS AL oll) 12 210°4 19 226°8 20:4
BN ih oad all an 07 8 13 27 3:00 20 228°'9 oY a |
T59'21 Gs) 4 mirg dss 14 QT SiSMnniy "aT 230°9 28 |
15 tame 97 | |
363. Pressure of the vapours of different liquids.—Regnault deter-
mined the elastic force, at various temperatures, of the vapours of a certain
number of liquids which are given in the following table :
ea leiae | Tempe- Pressures in | Polat Tempe- Pressures in |
Liquids | eee cre Liquids ratures millimetres
if | 0° 0°02 (| —20° GS ie
Mercury . Se eail-fe) Ort in tian O Too «|
| r
a LOOusa| o'74 | Uae 60 1728
| fe) U3 ot 100 | 4950 |
Alcohol | BO. | 220 | — 20 Azo e |
: x | Sulphurou |
too | : . —181°4° Butyric acid . . UT eOe
Nitrous oxide : - —-92 Turpentine. : ei hy;
Carbonic acid ; f, 00, Aniline > : yh key
Ammonia A - —39 #.Methylene ‘eilae: : Selo
Methyl chloride . pee) tien LOCINGmay : ; 12200
Cyanogen . : . -—20 +x.Naphthaline . ; Bae 7
Sulphurous acid . . -—I10 Diphenyl / ; ue ie
Ethyl] chloride : Pees Dii benzOlc acicume: ‘ se ee
Aldehyde. : : 21 Phosphorus. : eer 200:
Ether ‘ : 370) Wiphenyiaminem aa ae STO
Carbon Becenide : 47 Strong sulphuricacid . 318
Acetone. : ; : 56 Phenanthrene : g4O
Bromine : : : 58 Mercury : Me cht
Methylic alcohol . ; 66 Phenyl Bhocenate ; gy vio
Alcohol . : : - 78 ASSORICY a ‘ aay
Benzole. s : é SI Sulphur . : 444
Distilled water . . 100 Phosphorus pentasulphide 530
Acetic acid . : ne Sd Ry: Selenium . ‘ 665
Amylic alcohol . Pedic Cadmium ‘ : eat a0
Propionic acid ; ByiA bev ehie : : : png Oia)
Kopp pointed out that in homologous chemical compounds the same
difference in chemical composition frequently involves the same difference
of boiling points; and he showed that in an extensive series of com-
348 On Heat [367—
pounds, the fatty acids for instance, the difference of CH, is attended by
a difference of 19° C. in the boiling point. In other series of homologous
compounds, the corresponding difference in the boiling point is 30°, and in
others again 24°.
368. Theoretical explanation of evaporation and ebullition.— From what
has been said about the nature of the motion of the molecules in liquids
(296), it may readily be conceived that in the great variety of these motions,
the case occurs in which, by a fortuitous concurrence of the progressive,
vibratory, and rotatory motions, a molecule is projected from the surface of
the liquid with such force that it overleaps the sphere of the action of its cir-
cumjacent molecules, before, by their attraction, it has lost its initial velocity ;
and that it then flies into the space above the liquid.
Let us first suppose this space limited and originally vacuous ; it gradu-
ally fills with the propelled molecules, which act like a gas and in their
motion are driven against the sides of the envelope. One of these sides,
however, is the surface of the liquid itself, and a molecule when it strikes
against this surface will not in general be repelled, but will be retained by the
attraction which the adjacent ones exert. Equilibrium will be established
when as many molecules are dispersed in the surrounding space as, on the
average, impinge against the surface and are retained by it in the unit of
time. This state of equilibrium is not, however, one of rest, in which eva-
poration has ceased, but a condition in which evaporation and condensation,
which are equally strong, continually compensate each other. °
The density of a vapour depends on the number of molecules which are
repelled in a given time, and this manifestly depends on the motion of the
molecules in the liquid, and therefore on the temperature.
What has been said respecting the surface of the liquid clearly applies to
the other sides of the vessel within which the vapour is formed ; some vapour
is condensed, this 1s subject to evaporation, and a condition ultimately occurs
in which evaporation and condensation are equal. The quantity of vapour
necessary for this depends on the density of vapour in the closed space, on
the temperature of the vapour and of the sides of the vessel, and on the force
with which this attracts the molecules. The maximum will be reached when
the sides are covered with a layer of liquid, which then acts like the free
surface of a liquid.
In the interior of a liquid it may happen that the molecules repel each
other with such force as momentarily to destroy the coherence of the mass.
The small vacuous space which is thereby formed is entirely surrounded by
a medium which does not allow of the passage of the repelled molecules.
Hence it cannot increase and maintain itself as a bubble of vapour, unless so
many molecules are projected from the inner sides that the internal pressure
which thereby results can balance the external pressure which tends to
condense the bubble. The expansive force of the enclosed vapour must
therefore be so much the greater, the higher the external pressure on the
liquid, and we can thus understand the influence of pressure on the tempera-
ture of boiling.
369. Influence of substances in solution on the boiling point.—The
ebullition of a liquid is the more retarded the greater the quantity of any
substance it may contain in solution, provided that the substance be not
-369] Influence of Substances 349
volatile, or, at all events, be less volatile than the liquid itself. Water, which
boils at 100° when pure, boils at the following temperatures when saturated
with different salts :—
Water saturated with common salt ‘ : boils at 102°
oh potassium nitrate : aL io
" + potassium carbonate . 5 135
_ be calcium chloride : Hee cia)
Acids in solution present analogous results; but substances merely
mechanically suspended, such as earthy matters, bran, wooden shavings, &c.,
do not affect the boiling point.
Absorbed air exerts a very marked influence on the boiling point of
water. Deluc first observed that water freed from air by ebullition, and
placed in a flask with a long neck, could be raised to 112° without boiling.
Donny examined this phenomenon by means of the apparatus depicted in
figure 345. It consists of a glass tube CAB, bent at one end and closed at
C, while the other is blown into a pear-shaped bulb, B, drawn out to a
point. The tube contains water which is boiled until all air is expelled, and
the open end is hermetically sealed. By inclining the tube the water passes
into the bent end CA ; this end being placed in a bath of chloride of calcium,
the temperature may be raised to 130° without any signs of boiling. At 238°
the liquid is suddenly converted into steam, and the water is thrown over
into the bulb, which is smashed if it is not sufficiently strong.
Boiled-out water, covered with a layer of oil, may be raised to 120° with-
out boiling, but above this temperature it suddenly begins to boil, and with
almost explosive violence.
When a liquid is suspended in another of the same specific gravity, but
of higher boiling point, with which it does not mix, it may be raised far be-
yond its boiling point without the formation of a trace of vapour. Dufour
made a number of valuable experiments on this subject ; he used in the
case of water a mixture of oil of cloves and linseed oil, and placed in it
globules of water, and then gradually heated the oil ; in this way ebullition
rarely set in below 110° or 115°; globules of to millimetres’ diameter very
commonly reached a temperature of 120° or 130°, while very small globules of
1 to 3 millimetres reached the temperature of 175°, a temperature at which
the pressure of vapour on a free surface is 8 or 9 atmospheres.
At these high temperatures the contact of a solid body, or the production
of gas bubbles in the liquid, occasioned a sudden vaporisation of the globule,
accompanied by a sound like the hissing of a hot iron in water.
Saturated aqueous solutions of copper sulphate, sodium chloride, &c.,
remain liquid at a temperature far beyond their boiling point, when
immersed in melted stearic acid. In like manner, globules of chloroform
350 On Heat [369-
(which boils at 61°), suspended in a solution of chloride of zinc, could be
heated to 97° or 98° without boiling.
It is a disputed question as to what is the temperature of the vapour
from boiling saturated saline solutions. It has been stated by Rudberg to
be that of pure water boiling under the same pressure. The experiments
of Magnus seem to show, however, that this is not the case, but that the
vapour of boiling solutions is hotter than that of pure water ; and that the
temperature rises as the solutions become more concentrated, and therefore
boil at higher temperatures. Nevertheless, the vapour was always found
somewhat cooler than the mass of the boiling solution, and the difference
was greater at high than at low temperatures.
The boiling point of a liquid is usually lowered when it is mixed with a
more volatile liquid than itself, but raised when it contains one which is less
volatile. Thus a mixture of two parts alcohol and one of water boils at 83°,
a mixture of two parts of carbon bisulphide and one part of ether boils
at 38°. In some cases the boiling point of a mixture is lower than that of
either of its constituents. A mixture of water and bisulphide boils at 43°,
the boiling point of the latter being 46°. On this depends the following
curious experiment. If water and carbon bisulphide, both at the tempe-
rature 45°, are mixed together, the mixture at once begins to boil briskly.
370. Influence of the nature of the vessel on the boiling point.—
Gay-Lussac observed that water in a glass vessel required a higher tempera-
ture for ebullition than in a metal one. Taking the temperature of boiling
water in a copper vessel at 100%, its boiling point in a glass vessel was
found to be ro1°; and if the glass vessel had been previously cleaned by
means of sulphuric acid and of potash, the temperature would rise to 105°
or even to 106°, before ebullition commenced. A piece of metal placed in
the bottom of the vessel was always sufficient to lower the temperature to
100°, and at the same time to prevent the violent concussions which accom-
pany the ebullition of saline or acid solutions in glass vessels. Whatever
be the boiling point of water, the temperature of its vapour is uninfluenced
by the substance of the vessels.
371. Influence of pressure on the boiling point.—We see from the
table of pressures (362) that at 100°, the temperature at which water boils
under a pressure of 760 millimetres, which is that of the atmosphere,
aqueous vapour has a pressure exactly equal to this pressure. This principle
is general, and may be thus enunciated : A Uiguid boils when the pressure of
its vapour ts equal to the pressure tt supports. Consequently, as the superin-
cumbent pressure increases or diminishes, the pressure of the vapour, and
therefore the temperature necessary for ebullition, must increase or diminish.
Hence a liquid has, strictly speaking, an indefinite number of boiling points.
In order to show that the boiling point is lower under diminished pres-
sure, a small dish containing water at 30° is placed under the receiver of an
air-pump, which is then exhausted. The liquid soon begins to boil, the
vapour formed being pumped out as rapidly as it is generated.
A paradoxical but very simple experiment also well illustrates the de-
pendence of the boiling point on the pressure. In a glass flask, water is
boiled for some time, and when all air has been expelled by the steam, the
flask is closed by a cork and inverted, as shown in fig. 346. Ifthe bottom
—373] Measurement of Heights 351
is then cocled by a stream of cold water from a sponge, the water begins
to boil again. This arises from the condensation of the steam above the
surface of the water, by whicha partial
vacuum is produced.
It is in consequence of this dimi-
nution of pressure that liquids boil on
high mountains at lower temperatures.
On Mont Blanc, for example, water
boils at 84°, and at Quito at go°.
On the more rapid evaporation of
water under feeble pressures is based
the use of the air-pump in concentrat-
ing those solutions which either cannot
bear a high temperature, or which
can be more cheaply evaporated in an
exhaustedspace. Howard madea most
important and useful application of
this principle in the manufacture of
sugar. The syrup, in his method, is
enclosed in an air-tight vessel, which is
exhausted by a steam-engine. The
evaporation consequently goes on at
a lower temperature, which secures the
syrup from injury. The same plan is
adopted in evaporating the juice of
certain plants used in preparing medicinal extracts.
On the other hand, boiling is retarded by increasing the pressure ; under
the pressure of two atmospheres,
for example, water only boils at
1297°6.
372. Franklin’s experiment.—
The influence of pressure on boiling
raay further be illustrated by means
of an experiment originally made
by Franklin. The apparatus con-
sists of a bulb, a, and a tube, J,
joined by a tube of smaller dimen-
Sionse e804 7).6 el Demtube (2) 1s
drawn out, and the apparatus filled with water, which is then in part boiled
away by means of a spirit lamp. When it has been boiled sufficiently long
to expel all the air, the tube J is sealed. There is then a vacuum in the
apparatus, or rather there is a pressure due to the elastic force of aqueous
vapour, which at ordinary temperatures is very small. Consequently, if
the bulb, a, be placed in the hand, the heat is sufficient to produce a pres-
sure which drives the water into the tube, 4, and causes a brisk ebullition.
373. Measurement of heights by the boiling point.— From the connection
between the boiling point of water and the pressure, the heights of
mountains may be measured by the thermometer instead of by the baro-
meter. Suppose, for example, it is found that water boils on the summit:
352 On Heat [373-
of amountain at 90°, and at its base at 98° ; at these temperatures the elastic
force of the vapour is equal to the pressure on the liquid ; that is, to the pressure
of the atmosphere at the two places respectively.
Now, the pressures of aqueous vapour for various
temperatures have been determined, and accord-
ingly the pressures corresponding to the above
temperatures are sought in the tables. These
numbers represent the atmospheric pressures
at the two places ; in other words, they give the
barometric heights, and from these the height
of the mountain may be calculated by the method
already given (181). An ascent of about 1‘o80
feet produces a diminution of 1°C. in the boiling
point.
The instruments used for this purpose are
called thermo-barometers or hypsometers, and
were first supplied by Wollaston. They consist
essentially of a small metallic vessel for boiling
water (fig. 348), fitted with very delicate thermo-
meters, which are only graduated from 80° to
100° ; so that, as each degree occupies a con-
siderable space on the scale, the roths, and even
the rooths, of a degree may be estimated, and
thus it is possible to determine the height of
a place by means of the boiling point to within
about Io feet.
374. Formation of vapour in closed tubes.—
We have hitherto considered vapours as being
produced in an indefinite space, or where they
could expand freely, and it is only under this
condition that boiling can take place. In a closed vessel, the vapours pro-
duced finding no issue, their pressure and their density increase with the tem-
perature, but that rapid disengagement of vapour which constitutes boiling
is impossible. Hence, while the temperature of a liquid in an open vessel
can never exceed that of boiling, in a closed vessel it may be much higher.
The liquid state has, nevertheless, a limit ; for, according to experiments by
‘Cagniard-Latour and others, if either water, alcohol, or ether be placed
in strong glass tubes, which are hermetically sealed after the air has been ex-
pelled by boiling, and if then these tubes are exposed to a sufficiently high
temperature, a moment is reached at which the liquid suddenly disappears,
and is converted into vapour. With ether this occurs at 200° ; the vapour
then occupies a space less than double its volume in the liquid state, its
pressure being then 38 atmospheres.
Alcohol which half fills a tube is converted into vapour at 207° C. If
a glass tube about half filled with water, in which some carbonate of soda
has been dissolved, to diminish the action of the water on the glass, be
heated, it is completely vaporised at about the temperature of melting zinc.
When ethyl chloride is heated in a stout sealed tube, the upper
surface ceases to be distinct at 170°, and is replaced by an ill-defined
—374] Formation of Vapour in Closed Tubes 353
nebulous zone. As the temperafure rises this zone increases in width in
both directions, becoming at the same time more transparent ; after a time
the liquid is completely vaporised, and the tube becomes transparent and
seemingly empty. On cooling, the phenomena are
reproduced in opposite order. Similar appearances
are observed on heating ether in a sealed tube
at OOo,
Andrews made a series of observations on the
behaviour of condensed gases at different tem-
peratures, by means of an apparatus the principal
features of which are represented in fig. 349.
The pure and dry gas is contained in a tube
g, which is sealed at one end, and the gas is shut
in by a thread of mercury. The tube is inserted
in a brass end-piece, E, which is firmly screwed
on a strong copper tube, R. At the other end is
a similar piece, in which a steel screw works,
perfect tightness being ensured by good packing.
The tube is full of water, so that by turning this
screw the pressure on the enclosed gas can be
increased up to 500 atmospheres. In some cases
the projecting capillary tube is bent downwards,
so that it can be placed in a freezing mixture.
Andrews found on raising liquid carbonic acid
in such a tube to a temperature of 31° C. that the
surface of demarcation between the liquid.and the
gas became fainter, lost its curvature, and gradually
disappeared. The space was then occupied by a
homogeneous fluid, which, when the pressure was
suddenly diminished, or the temperature slightly
lowered, exhibited a peculiar appearance of moving
or flickering striz throughout its whole mass.
Above 31° no apparent liquefaction of carbonic
anhydride, or separation into two distinct forms of
matter, could be effected, not even when the pres-
sure of 400 atmospheres was applied.
From similar observations made with other substances it seems that
there exists for every liquid a temperature, the critical point or critical tem-
perature. While below this critical point a sudden transition from gas to
liquid is accompanied by a sudden diminution of volume, and liquid and
gas are separated by a sharp line of demarcation, above this critical point
the change is connected with a gradual diminution of volume, and is quite
imperceptible. The condensation can, indeed, only be recognised by a
sudden ebullition when the pressure is lessened. Hence, ordinary condensa-
tion is only possible at a temperature below the critical point, and it is not
surprising, therefore, that mere pressure, however great, should have failed
to liquefy many of the gases.
These relations are shown in the case of carbonic acid by fig 351, in
which the horizontal lines, the abscissze, represent volumes, and the vertical
AA
Fig. 350
354 ) On Heat | [374-
lines, the ordinates, pressures in atmospheres. Suppose now at the particular
temperature 13°1° a given volume of gas is subjected to gradually increasing
pressure : the volume diminishes until it reaches 48 atmospheres, the gas
begins to liquefy, and the continued
application of this pressure completes
the liquefaction (this state is repre-
sented by the line AB), after which
any further increase of pressure only
diminishes the volume to much the
same extent as any other liquid (98).
At a higher temperature, 21°5°, the
same general results are obtained, ex-
cept that a pressure of 61 atmospheres
is required for the liquefaction, the line
A’B’ is shorter. On continuing the ex-.
periments it is found that at a tem-
perature of 30°9° there is no horizontal
part, the lines merge into each other,
and at no higher temperature is there
a separation into liquid and gas. This
is the critical temperature, and the higher the temperature the more nearly
does the curve show the behaviour of a perfect gas.
The phenomenon of the critical temperature may be conveniently illus-
trated by the following arrangement (fig. 350), which is also well adapted
for projection on a screen by means of a magic-lantern for lecture purposes.
A stout glass tube about 2°5™™ wide and 4o™™ long, contains liquid sulphurous
acid, and is supported, with the drawn-out end downwards, in a test-tube by
means of a wire frame. Pure melted paraffin is added to about 10°" above
the inner tube. The whole arrangement is suspended in a retort-holder,
and heat applied with a spirit lamp. With careful manipulation there is no
danger, and the course of the phenomenon is readily seen through the clear
paraffin.
The boiling point of a body may be defined as the temperature above
which a body passes into the state of gas, not only on the surface but in the
body of the liquid ; this temperature is therefore different for different pres-
sures, and is accordingly a velatzve magnitude. The absolute boiling point
is the temperature at which a body is converted into gas, whatever be the
pressure ; it is identical with the critical temperature. Mendelejeff found
that a relation existed between the absolute temperature and the capillarity
of liquids. Increase of temperature diminishes the cohesion, and therefore
the elevation of a liquid in a capillary tube. The elevation ultimately
vanishes, and the temperature at which this takes place is the absolute
boiling point. For some it is very low ; in the case of air, for instance, it is
iba
The critical pressure is that at which condensation takes place at the
critical temperature, and the volume of the saturated vapour at the
critical temperature, and under the critical pressure, is called the critical
volunte.
A vapour may be defined as being a gas at any temperature below its
Fig. 351
—376] Papin’s Digester—Latent Heat of Vapour 355
critical point. Hence a vapour can be converted into a liquid by pressure
alone, and can therefore exist at the pressure of its own liquid, while a. gas
requires cooling as well as pressure to ,
convert it into a liquid ; that is, to alter
its arrangement in such a manner that a
liquid can be seen to be separated from
a gas by a distinctly bounded surface.
375. Papin’s digester.— Papin appears
to have been the first to investigate the
effects of the production of jvapour ,jin
closed vessels. The apparatus* which
bears his name consists of a cylindrical
iron vessel M (fig. 352) provided with a
cover, which is firmly fastened down by
the screw B. In order to close the vessel
hermetically, sheet lead is placed between
the edges of the cover and the vessel. A
cylindrical channel through the cover is
closed by a valve to which a rod wz is
attached.’ This rod presses against a
lever ab, movable at a, and the pressure
may be regulated by means of a weight
f movable on this lever. The lever is
so weighted that when the pressure in
the interior is equal to six atmospheres,
for example, the valve rises and the vapour escapes. The destruction of the
apparatus is thus avoided, and this mechanism has hence received the name
of safety-valve. The digester is filled about two-thirds with water, and is
heated on a furnace. The water may thus be raised to a temperature far
above 100°, and the pressure of the vapour increased to several atmospheres,
according to the weight on the lever. |
We have seen that water boils at much lower temperatures on high
mountains (371) ; the temperature‘of water boiling in open vessels in such
localities is not sufficient to soften animal fibre completely and extract the
nutriment, and hence Papin’s digester is used in the preparation of food.
It is also used in extracting gelatine. When bones are digested in this
apparatus they are softened, so that the gelatine which they contain is
dissolved: the part through which the screw B passes is made of such
elasticity that it yields, and the lid opens when the pressure of the vapour
becomes dangerous. e
376. Latent heat of vapour.—As the temperature of a liquid remains
constant during boiling, whatever be the source of heat (367), it follows
that a considerable quantity of heat becomes absorbed in boiling, the only
effect of which is to transform the body from the liquid to the gaseous con-
dition. And, conversely, when a saturated vapour passes into the state of
liquid, it gives out a definite amount of heat. .
These phenomena were first observed by Black, and he described them
by saying that during vaporisation a quantity of sensible heat became latent,
-and that the latent heat again became free during condensation. The
AA2
356 On Heat [376—
quantity of heat which a liquid must absorb in passing from the liquid to
the gaseous state, and which it gives out in passing from the state of vapour
to that of liquid, is spoken of as the latent heat of evaporation.
The analogy of these phenomena to those of fusion will be at once seen ;
the modes of determining them will be described in the chapter on Calori-
metry ; but the following results, which have been obtained for the latent
heats of evaporation at 0°, may be here given :—
Water : , ROOT, Carbon bisulphide . «! OO
Alcohol . : : = 230 Turpentine : : Nive
Benzole. : : Le 109 Chloroform . : sy Oy
Acetic acid : nlo2 Bromine . tee. 249
Ether ; : ‘ aod Iodine. : : et
The meaning of these numbers 1s, in the case of water, for instance, that
it requires as much heat to convert a pound of water from the state of liquid
at o° C. to that of vapour at the same temperature, as would raise a pound
of water through 607 degrees, or 607 pounds of water through one degree ;
or that the conversion of one pound of vapour of alcohol at o° into liquid
alcohol of the same temperature would heat 236 pounds of water through
one degree.
Watt, who investigated the subject, held that the whole quantity of heat
necessary to raise a given weight of water from zero to any temperature,
and then to evaporate it entirely, or what is called the heat of evaporation,
is a constant quantity. His experiments showed that this quantity is 640.
Hence the lower the temperature the greater the latent heat, and, on the
other hand, the higher the temperature the less the latent heat. The latent
heat of the vapour of water evaporated at 100° would be 540, while at 50°
it would be 590. At higher temperatures the latent heat of aqueous
vapour would go on diminishing. Water evaporated under a pressure of
15 atmospheres at a temperature of 200° would have a latent heat of 440,
and if it could be evaporated at 640° it would have no latent heat at all.
Regnault, who examined this question with great care, found that the
total quantity of heat necessary for the evaporation of water increases with
the temperature, and is not constant, as Watt had supposed. It is repre-
sented by the formula
Q = 606'5 + 0°305/,
in which Q is the total quantity of heat, and ¢ the temperature of the water
during evaporation, while the numbers are constant quantities. The total
quantity of heat necessary to evaporate water at 100° is 606°5 + (0°305 x 100)
= 6373 at 120° it 15,643 ; at.150° it is 651 ;,and at 180° 1t/1s 66%.
The total heat of the evaporation of ether is expressed by a formula
similar to that of water, namely, Q=94+0'045/; and that for chloroform
Q =67 + 013752.
The heat which is expended simply in evaporating a liquid, and which is
spoken of as the latent heat, produces no rise of temperature, and only
appears as doing the work of a change of state. One portion of this work
is expended in overcoming the cohesion of the particles in the liquid state,
—377] Cold due to Evaporation. Mercury Frozen '357
and enabling them to assume the gaseous form—this is the zzéermal work,
and is by much the greater ; the other, the external work, is expended ‘in
overcoming the external pressure on the vapour formed.
Knowing the increase of volume, and the pressure, the external work may
be readily calculated ; for if the volumes of unit weight of the substance in the
state of liquid and of vapour are respectively s and o, and the pressure for
unit surface is #, then the external work is Ap (o —s), A being the mechanical
equivalent of heat. So that, if ~ is the total heat of evaporation,
r=p+Ap (a—s)
in which p is the internal work. From the values of ~ and of AD (a —S), it is
easy to deduce that of p, and it is found that this value decreases as the
temperature increases.
Thus for the temperatures 0°, 50°, 100°, and 150° the values are 576, 536,
496, and 457 respectively ; that is, that when water at o° is converted into
vapour, a greater in-
ternal work is required
to overcome the cohe-
sion, than at 100° for
instance.
377. Cold due to
evaporation. Mercury
frozen.—Whatever be
the temperature at
which a vapour is pro-
duced, an absorption |
of heat always takes TT
2 MRACUPRUEDAMUPOR RCP RRRERS 1) |
place. If, therefore, a i i ai
liquid evaporates, and IN
does not receive from Fig. 353 Fig. 354
without a quantity of
heat equal to that which is expended in producing the vapour, its tempera-
ture sinks, and the cooling is greater in proportion as the evaporation is more
rapid, :
Leslie succeeded in freezing water by means of its own rapid evaporation.
Under the receiver of the air-pump is placed a vessel containing strong
sulphuric acid, and above it a thin metal capsule, A (fig. 353), containing a
small quantity of water. By exhausting the receiver the water begins to
boil (367), and since the vapour is absorbed by the sulphuric acid as fast as
it is formed, a rapid evaporation is produced, which quickly effects the freezing
of the water.
This experiment is best performed by using, instead of a thin metal dish,
a watch-glass coated with lampblack and resting on acork. The advantage
of this is twofold: firstly, the lampblack is a very bad conductor ; and,
secondly, it is not moistened by the liquid, which remains in the form of a
globule not in contact with the glass. A small porous dish may also ad-
vantageously be used,
The same result is obtained by means of Wollaston’s cryophorus (fig. 354),
358 On Feat [377—
which consists of a bent glass tube provided with a bulb at each end.
The apparatus is prepared by introducing a small quantity of water, which
is then boiled so as to expel all air. It is then hermetically sealed, so that
on-cooling it contains only water and the vapour of water. The water being
passed into the bulb A by tilting the apparatus, the other bulb is immersed
in a freezing mixture. The vapour in the tube is thus condensed ; the water
in A rapidly yields more. But this rapid production of vapour requires a
large amount of heat, which is abstracted from the water in A, and its tem-
perature is so much reduced that it freezes.
By using liquids more volatile than water, more particularly liquid sul-
phurous acid, which boils at — 10°, or, still better, methyl chloride, which
is now prepared industrially in large quantities, a degree of cold is obtained
sufficiently low to freeze mercury. This experiment may be made on a
small scale by covering the bulb of a thermometer with cotton wool, and,
after having moistened it with the liquid in question, placing it under the
receiver of the air-pump. When a vacuum is produced the mercury is
quickly frozen.
By passing a current of air, previously cooled, through liquid methyl
chloride, temperatures of from —23° to —70° C. may be maintained with
great constancy for several hours. Thilorier, by directing a jet of liquid
carbonic acid on the bulb of an alcohol thermometer, obtained a tempera-
ture of — 100° without freezing the alcohol (347).
By means of the evaporation of carbon bisulphide the formation of ice
may be illustrated without the aid of an air-pump. A little water is dropped
on a board, and a capsule of thin copper foil, containing carbon bisulphide,
is placed on the water. The evaporation of the bisulphide is accelerated by
means of a pair of bellows, and after a few minutes the water freezes round
the capsule so that the latter adheres to the wood.
In like manner, if some water be placed in a test-tube, which is then
dipped in a glass containing some ether, and a current of air be blown
through the ether by means of a glass tube fitted to the nozzle of a pair of
bellows, the rapid evaporation of the ether very soon freezes the water in
the tube. Richardson’s apparatus for producing local anesthesia also de-
pends on the cold produced by the evaporation of ether.
The cold produced by evaporation is used in hot climates to cool water
by means of alcarrazas. These are porous earthen vessels, through which
water percolates, so that on the outside there is a continual evaporation,
which is accelerated when the vessels are placed in a current of air. For
the same reason wine is cooled by wrapping the bottles in wet cloths and
placing them in a draught.
In Harrison’s method of making ice artificially, a steam-engine is used
to work an air-pump which produces a rapid evaporation of some ether, in
which is immersed the vessel containing the water to be frozen. The
apparatus is so constructed that the vaporised ether can be condensed and
used again.
_ The cooling effect produced by a wind or draught does not necessarily
arise from the wind being cooler, for it may, as shown by the thermometer,
be actually warmer, but arises from the rapid evaporation it causes from the
surface of the skin. We have the feeling of oppression even at moderate
—378] Carré’s Apparatus for Freesing Water 359
temperatures, when we are in an atmosphere saturated by moisture, in which
no evaporation takes place.
378. Carré’s apparatus for freezing water.—We have already seen
that when any liquid is converted into vapour it absorbs a considerable
quantity of sensible heat ; this furnishes a source of cold which is more
abundant the more volatile the liquid, and the greater its heat of vaporisa-
tion.
This property of liquids has been utilised by Carré, in freezing water
by the distillation of ammonia. The apparatus consists of a cylindrical
boiler C (figs. 355, 356), and of a slightly conical vessel A, which is the
freezer. These two vessels are connected by a tube, 7z, and a brace, 7, binds
them firmly. They are made of strong galvanised iron plate, and can resist
a pressure of seven atmospheres.
a
Fig. 355 Fig. 356
The boiler C, which holds about two gallons, is three parts filled with a
strong solution of ammonia. In a tubulure in the upper part of the boiler
‘some oil is placed, and in this a thermometer 4 The freezer A consists of
two concentric envelopes, in such a manner that, its centre being hollow, a
metal vessel, G, containing the water to be frozen, can be placed in this
space. Hence only the annular space between the sides of the freezer is
in communication with the boiler by means of the tube.7z. In the upper
part of the freezer there is a small tubulure which can be closed by a metal
stopper, and by which the solution of ammonia is introduced.
The formation of ice comprises two distinct operations. In the first,
the boiler is placed in a furnace F, and the freezer in a bath of cold water of
about 12°. The boiler being heated to 130°, the ammoniacal gas dissolved
in the water of the boiler is disengaged, and, in virtue of its own pressure, is
liquefied in the freezer A, along with about a tenth of its weight of water. This
360 | On feat . [378-
distillation of C towards A lasts about an hour and a quarter, and when it is
finished the second operation commences ; this consists in placing the boiler
in the cold-water
bath (fig. 356), and
the freezer A out-
side, care being
taken to surround
it with dry flannel.
The vessel G, about
three-quarters full
of water, is placed
in the freezer. As
the boiler cools, the
ammoniacal gas
with which it is
filled is again dis-
solved ; the pressure
thus being di-
minished, the am-
monia which has
been liquefied in
the freezer is con-
verted into the
gaseous form, and
now distils from A
towards C, to re-
dissolve in the water
which has remained
in the boiler. During this distillation the ammonia which is gasified absorbs
a great quantity of heat, which is withdrawn from the vessel G and the water
it contains. Hence it is that this water freezes. In order to have better
contact between the sides of the vessel G and the freezer, alcohol is poured
between them. In about an hour and a quarter a perfectly compact cylin-
drical block of ice can be taken from the vessel G.
This apparatus gives about four pounds of ice in an hour, at a price of
about a farthing per pound; large continuously working apparatus have,
however, been constructed, which produce as much as 800 pounds of ice in
an hour.
Carré constructed an ice-making machine which is an industrial appli-
cation of Leslie’s experiment (377), and by which considerable quantities
of water may be frozen in a short time. It consists of a cylinder, R, about
15 inches long by 4 in diameter, made of an alloy of lead and antimony (fig.
357). At one end is a funnel E, by which strong sulphuric acid can be in-
troduced ; at the other is a tubulure 7, to which is screwed a dome d that
supports a series of obstacles intended to prevent any sulphuric acid from
spirting into # and 6. There are, moreover, on the receiver a wide tube, z,
closed by a thick glass disc O, and a long tube 4, to the top of which is fitted
the bottle C containing water to be frozen. The dome d, the disc O, and the
stopper z of the funnel E are all sealed with wax.
—880] Liquefaction of Vapours 361
On the side of the receiver is an air-pump P, connected with it bya tube
6, and worked bya handle M. To this handle is attached a rod 4, which,
by the mechanism represented on the left of the figure, works a stirrer A
in the sulphuric acid. A lever x connected with a horizontal axis which
traverses a small stuffing-box , transmits its backward and forward motion
to the rod e and to the stirrer. This and the stuffing-box z are fitted in a
tubulure on the side of the tubulure zz.
The smallest size which Carré makes contains 2°5 kilogrammes of sul-
phuric acid, and the water-bottle about 400 grammes, when it is one-third full.
After about 70 strokes of the piston the water begins to boil ; the acid being
in continued agitation, the vapour is rapidly absorbed by it, and the pump is
worked until freezing begins. For this purpose it is merely necessary to
give a few strokes every five minutes. The rate of freezing depends on the
strength of the acid ; when this gets very dilute it requires renewal ; but 12
water-bottles can be frozen with the same quantity of acid.
LIQUEFACTION OF VAPOURS AND GASES
379. Liquefaction of vapours.-—The “guwefaction or condensation of
vapours is their passage from the aériform to the liquid state. Condensa-
tion may be due to three causes—cooling, compression, or chemical action.
For the first two causes the vapours must be saturated (357), while the
latter produces the liquefaction of the most rarefied vapours. Thus, a large
number of salts absorb and condense the aqueous vapours in the atmo-
sphere, however small its quantity.
When vapours are condensed, their latent heat becomes free ; that is, it
affects the thermometer. This is readily seen when a current of steam at
100° is passed into a vessel of water at {the ordinary temperature. The
liquid becomes rapidly heated, and soon reaches 100°. The quantity of
heat given up in liquefaction is equal to the quantity absorbed in producing
the vapour.
380. Distillation. Stills.—D¢zstillation is an operation by which a
volatile liquid| may be separated from substances which it holds in solution,
or by which two liquids o. different volatilities may be separated. The
operation depends on!}the transformation of liquids .nto vapour by the action
of heat, and on the condensation ot this vapour by cooling.
The apparatus used in distillation is called a s¢/Z. Its form may vary
* greatly, but it consists essentially of three parts: rst, the dody, A (fig. 358),
a copper vessel containing the liquid, the lower part of which fits in the
furnace ; 2nd, the head, B, which fits on the body, and from which a lateral
tube, C, leads to ; 3rd, the worm, S, a long spiral tin or copper tube placed
in a cistern kept constantly full of cold water. The object of the worm is to
condense the vapour by exposing a greater extent of cold surface.
To free ordinary water from the many impurities which it contains, it is
placed in a still and heated. The vapours disengaged are condensed in the
worm, and the distilled water arising from the condensation is collected in
the receiver D. The vapours in condensing rapidly heat the water in the
cistern, which must therefore be constantly renewed. For this purpose a
362 On Feat , [380—.
continual supply of cold water passes into the bottom of the'cistern, while
the lighter heated water rises to the surface and escapes by a tube in the
top of the cistern.
Fig. 358
381. Liebig’s Condenser.—In distilling smaller quantities of liquids, the:
apparatus known as Lzebig’s Condenser ts extremely useful. It consists of
a glass tube, ¢¢ (fig. 359), about thirty inches long, fitted in a copper or tin
eat ines
megan"
Fig. 359
tube by means of perforated corks. A constant supply of cold water from
the vessel a passes into the space between the two tubes, being conveyed to:
—383] Apparatus for determining Alcoholic Value of Wines 363
the lower part of the condenser by a funnel and tube g, flowing out from the
upper part of the tube £ The liquid to be distilled is contained: in a retort,
the neck of which is placed in the tube ; the condensed liquid drops quite
cold into a vessel placed to receive it at the other end of the condensing
tube.
382. Apparatus for determining the alcoholic value of wines.—One of
the forms of this apparatus consists of a glass flask resting on a tripod,
and heated bya
spirit lamp (fig.
360). By means
of a caoutchouc
tube this is con-
nected with a
worm placed in
a copper vessel
filled with cold
water, below
which is a test
glass for collect- ©
ing the distillate.
On this are three
divisions, one a,
which measures
the quantity of
wine taken ; the
two others indi-
cating one-half and one-third of this volume.
The test glass is filled with the wine up to a; this is then poured into
the flask, which having been connected with the worm, the distillation is
commenced. The liquid which distils overis a mixture of alcohol and water ;
for ordinary wines, such as clarets and hocks, about one-third is distilled
over, and for wines richer in spirit, such as sherries and ports, one-half must
be distilled ; experiment has shown that in these circumstances practically
all the alcohol passes over in the distillate. The measure is then filled up
with distilled water to a ; this gives the mixture of alcohol and water of the
same volume as the wine taken, free from all solid matters, such as sugar,
colouring matter, and acid, but containing all the alcohol. The specific
gravity of this distillate is then taken by means of an alcoholometer (129),
and the number thus obtained corresponds to a certain strength of alcohol
as indicated by the tables.
383. Safety-tube.—In preparing gases and collecting them over mercury
or water, it occasionally happens that these liquids rush back into the
generating vessel, and destroy the operation. This arises from an excess of
atmospheric pressure over the elastic force in the vessel. Ifa gas—sulphurous
acid for example—be generated in the flask 7 (fig. 361), and be passed into
water in the vessel A, as long as the gas is given off freely, its elastic force
exceeds the atmospheric pressure, and the weight of the column of water,
on, so that the water in the vessel cannot rise in the tube, and absorption is
impossible. But if the tension decreases, either through the flask becoming
Fig. 360
304 On Heat [383—
cooled or the gas being disengaged too slowly, the external pressure pre-
vails, and when it exceeds the internal pressure by more than the weight of
the column of water co, the water rises into the flask, and the operation is
spoiled. This accident is prevented by means of safety-tubes.
These are tubes which prevent absorption by allowing the air to enter in
proportion as the internal pressure decreases. The simplest is a tube C
(fig. 362), passing through the cork which closes the flask M, in which the
gas is generated, and dipping in the liquid. When the pressure of the
Fig 362
gas diminishes in M, the atmospheric pressure on the water in the bath E
causes it to rise to a certain height in the tube DA ; but this pressure, acting
also on the liquid in the tube C, depresses it to the same depth, assuming
that the liquid has the same density as the water in E. Now, as this
depth is less than the height DH, air enters by the aperture, before the water
in the bath can rise to A, and no absorption takes place.
384. Liquefaction of gases.—We have already seen that a saturated
vapour, the temperature of which is constant, is liquefied by decreasing the
volume, and that, the volume remaining constant, it is brought into the liquid
state by diminishing the temperature.
Unsaturated vapours behave in all respects hke gases. For the gaseous
form is accidental, and is not inherent in the nature of the substance. At
ordinary temperatures sulphurous anhydride is a vapour, while in countries
near the poles it is a liquid ; in temperate climates ether is a liquid, at a tropical
heat it is a vapour. And just as unsaturated vapours may be brought to
the state of saturation, and then liquefied, by suitably diminishing the tempe-
rature or increasing the pressure, so by the same means gases may be
liquefied. But as they are mostly very far removed from this state of satura-
tion, great cold and pressure are required. Some of them may indeed be
liquefied either by cold or by pressure ; for the majority, however, both
agencies must be simultaneously employed. Recent researches have shown
that the distinction fermanent gas no longer exists, now that all have been
liquefied.
We have seen that there is for each gas a critical temperature (374), so
that no pressure, however great, can liquefy a gas which is above this tempe-
rature. If a gas is below this point, then the nearer it is to it the greater is
—385] Apparatus to Liguefy and Solidify Gases 365
the pressure required ; conversely, if the temperature is very low, the pressure
required to liquefy it may be low too.
Faraday was the first to liquefy some of the gases. His method con-
sists in enclosing in a bent glass tube (fig. 363) substances by whose
chemical action the gas to be liquefied is produced, and then sealing the
shorter leg. In proportion as the gas is dis-
engaged its pressure increases, and it ultimately
liquefies and collects in the shorter leg, more
especially if its condensation is assisted by
placing the shorter leg in a freezing mixture.
A small manometer may be placed in the appa-
ratus to indicate the pressure.
Cyanogen gas is readily liquefied by heating
cyanide of mercury in a bent tube of this de-
scription ; other gases have been condensed by &
taking advantage of special reactions, the con- Fig. 363
sideration of which belongs rather to chemistry
than to physics. For example, silver chloride absorbs about 200 times
its volume of ammonia; when the compound thus formed is placed in the
long leg of a bent tube and gently heated, while the shorter leg is immersed
in a freezing mixture, a quantity of liquid ammonia speedily collects in
the shorter leg.
385. Apparatus to liquefy and solidify gases.—Thilorier first constructed
an apparatus by which considerable quantities of carbonic acid could be
liquefied. Its principle is the same as that used by Faraday in working with
glass tubes ; the gas is generated in an iron cylinder, and passes through a
metal tube into another similar cylinder, where it condenses. The use of
this apparatus is not free from danger; many accidents have already
happened with it, and it has been superseded by an apparatus constructed
by Natterer, of Vienna, which is both convenient and safe.
A perspective view of the apparatus, as modified by Bianchi, is repre-
sented in fig. 365, and a section on a larger scale in fig. 364. It consists of
a wrought-iron reservoir A, of something less than a quart capacity, which
can resist a pressure of more than 600 atmospheres. A small force-pump is
screwed on the lower part of this reservoir. The piston rod ¢is moved by
the crank-rod E, which is worked by the handle M. As the compression of
the gas and the friction of the piston produce a considerable disengagement
of heat, the reservoir A is surrounded by a copper vessel, in which ice or a
freezing mixture is placed. The water arising from the melting of the ice
passes by a tube 77 into a cylindrical copper case C, which surrounds the
force-pump, whence it escapes through the tube z and the stopcock 0. The
whole arrangement rests on an iron frame, PQ.
The gas to be liquefied is previously collected in airtight bags R,.
whence it passes into a bottle V, containing some suitable drying substance ;
it then passes into the condensing pump through the vulcanised indiarubber
tube H. After the apparatus has been worked for some time the reservoir
A can be unscrewed from the pump without any escape of the liquid, for it is.
closed below by a valve S (fig. 364). In order to collect some of the liquid
gas, the reservoir is inverted, and on turning the stopcock 7 the liquid escapes,
by a small tubulure x. The specific gravity of liquid CO, is 0°88.
366 : On teat [385-
When carbonic acid has been liquefied and is allowed to escape into the
air, a portion only of the liquid volatilises ; in consequence of the ‘heat ab-
sorbed by this evaporation, the rest is so much cooled as to solidify'in white
flakes like snow or anhydrous phosphoric acid. This may be collected by
placing a stout woollen bag like a tobacco pouch over a pipe attached to the
tube x; if the porous mass is compressed or hammered in stout wooden
cylinders, sticks of solid carbonic acid are obtained, very lke chalk in
appearance. Its specific gravity is 1:2.
We ZZ
Solid carbonic acid evaporates very slowly. By means ot an alcohol
thermometer its temperature has been found to be about —90° C. A small
quantity placed on the hand does not produce the sensation of such great
cold as might be expected. This,arises from the imperfect contact. But if
the solid be mixed with ether the cold produced is so intense that when a
little is placed on the skin all the effects of a severe burn are produced. A
mixture of these two substances solidifies four times its weight of mercury in
386] Cailletet’s Researches 367
a few minutes. When a tube containing liquid carbonic acid is placed in
this mixture, the liquid becomes solid and looks like a transparent piece
of ice.
The most remarkable liquefaction obtained by this apparatus is that of
nitrous oxide. The gas once liquefied only evaporates slowly, and produces
a temperature of —88° C. Mercury placed in it in small quantities instantly
solidifies. The same is the case with water ; it must be added drop by
drop, otherwise, its latent heat being much greater than that of mercury, the
heat given up by the water in solidifying would be sufficient to cause an
explosion of the nitrous oxide.
Nitrous oxide is readily decomposed by heat, and has the property of
supporting the combustion of bodies with almost as much brilliancy as
oxygen ; and even at low temperatures it preserves this property. When a
piece of incandescent charcoal is thrown on liquid nitrous oxide, it continues
to burn with a brillant light.
The cold produced by the evaporation of ether (377) has been used by
Loir and Drion in the liquefaction of gases on a small scale. By passing
a current of air from a blowpipe bellows through several tubes into a few
ounces of ether,.a temperature of — 34° C. can be reached in five or six
minutes, and may be kept up for fifteen or twenty minutes. By evaporating
liquid sulphurous acid in the same manner a great degree of cold, -— 50° C.
is obtained. At this temperature ammonia may be liquefied. By rapidly
evaporating liquid ammonia under the air-pump, in the presence of sulphuric
acid, a temperature of — 87° is attained, which is found sufficient to liquefy
carbonic acid under the ordinary pressure of the atmosphere.
386. Cailletet’s researches.—Cailletet and Pictet, working independently,
but simultaneously, have effaced the old distinction between permanent and
non-permanent gases, by effecting the liquefaction of oxygen, and other gases
which it was supposed could not be condensed. This has been accomplished
by means of powerful material appliances directed with great skill and
ingenuity. The critical temperature of these gases is mostly below — 100°,
while their critical pressure is somewhat less than that of carbonic acid,
excepting in the case of hydrogen, which is over 100 atmospheres.
The essential parts of Cailletet’s apparatus are represented in fig. 366.
BB’ is a strong wrought-iron bath containing mercury ; in this is placed the
tube TO, the upper part of which is capillary and contains the gas to be
liquefied. ‘This tube is supported bya screw z, in which it is fixed by marine
glue. In the side of BB’ is a second screw, through which passes a tube 4,
giving passage to the water forced by the pump. The valves of this, one for
suction and one for compression, are placed under the screws S and S’. A
screw plunger worked by the wheel X-serves to force the pressure, while by
a stopcock worked by a wheel X’ the compressed gas can be suddenly
allowed to expand. A manometer. zz fixed on the case indicates the
pressure.
To fill the tube TO it is placed horizontally, the capillary end being still
open, and pure well-dried gas is admitted at the other end (fig. 367) by a
caoutchouc tube. When all air is expelled, the end O is sealed, the tube held
vertically so that a drop of mercury @ previously introduced closes the tube.
It is then placed.in the bath BB’, z being firmly screwed. On this is fixed the
368 On Heat [386—
plate Q, to which is attached a cylinder M, which can be filled with water
from 7 or a freezing mixture. This is surrounded by a safety bell-jar, C.
By working the force pump a pressure of 400 atmospheres can be pro-
duced, which can be increased to 2,500 atmospheres by means of the screw
Ss
W
SS AZ.
LA,
Fig. 366
piston. When a suitable pressure has been applied, and after waiting until
the heat due to the compression has disappeared, if the screw worked by
the wheel X is suddenly opened, the pressure being diminished to one
Fig. 367
atmosphere, the cold produced by the sudden expansion of the gas in the
tube TP is so great as to liquefy a portion of it, as is shown by the produc-
tion of a mist.
This observation was first made with nitric oxide, but similar results
have been obtained with marsh gas, carbonic acid, and oxygen.
~387] Pictet’s Method 369
387. Pictet’s method.—The principle of Pictet’s method is that of liberating
the gas under great pressure, combined with the application of a very low
temperature. The essential parts of the apparatus are the following :—Two
double-acting pumps, A and B (fig. 368), are so ‘coupled together that they
cause the evaporation of liquid sulphurous acid contained in the annular
receiver C. By the action of the pumps the gas thus evaporated is forced into
the receiver D, where it is cooled by a current of water, and again liquefied
under a pressure of three atmospheres. Thence it passes again by the
narrow tube d to the receiver C, to replace that which is evaporated.
In this way the temperature of the liquid sulphurous acid is reduced to
—65°. Its function is to produce a sufficient quantity of liquid carbonic acid,
which is then sub-
mitted to a perfect-
ly analogous pro-
cess of rarefaction
and condensation.
This is effected by
means of two simi-
lar pumps, E and
Pb. > The, carbonic
acid gas, perfectly
pure and dry, is
drawn from a reser-
voir through a tube
not represented in
the figure, and is
forced into the con-
denser K, which is
cooled by the liquid
ssulphurous acid to
eo
a temperature of
-— 65°, and is there =="
liquefied. S D
Miss astube.of ae v
ig. 368
stout copper con-
nected with the condenser K by anarrow tube &. Whena sufficient quantity
of carbonic acid has been liquefied, the connection with the gasholder is cut
off, and by working the pumps E and F a vacuum is created over the liquid
carbonic acid in H, which produces so great a cold as to solidify it.
L is a stout wrought-iron retort capable of standing a pressure of 1,500
atmospheres. In it are placed the substances by whose chemical actions
the gas is produced: potassium chlorate in the case of oxygen. The retort
is connected with a strong copper tube in which the actual condensation is
effected. This tube, the pressure in which is indicated by a specially con-
structed manometer R, is closed by a stopcock N,
When the four pumps are set in action, for which a steam-engine of 15
horse-power is required, heat is applied to the retort. Oxygen is liberated
in a calculated quantity, the temperature of the retort being about 485°.
Towards the close of the decomposition the manometer indicates a pressure
BB
370 On Fleat [387—
of 500 atmospheres, and then sinks to 320. This diminution is due to the
condensation of gas, and at this stage the tube contains liquefied oxygen
If the cock N is opened, the liquid issues with violence, having the appear-
ance of a dazzling white pencil. This lasts three or four seconds. On closing
the stopcock the pressure, which had diminished to 400 atmospheres, now
rises, and again becomes stationary, proving that the gas is once more being
condensed.
The phenomena presented by the jet of oxygen when viewed by the
electric light showed that the light it emits was partially polarised, indicating
a probable transient crystallisation of the liquid.
The following table, given by Olszewski (January 1895), exhibits some of
the physical properties of substances, gaseous at ordinary teniperatures, when
reduced to very low temperatures :—
Boiling
Critical | ‘point at Petene Density of the
Name tempera- | atmo- | dices: liquid at the Colour of liquid
ture spheric ie boiling point
pressure
fo) | fo) °
Hydrogen . —235 .|-244 | — a Colourless
Nitrogen . |-146'°0 | —194 —214'0 | 0°885 .
Carbonic oxide . |—139°5 | -—190 | —207°0 (?) i
Argon —I12I‘0 | --187. | —190 I°5 (about) 5
Oxygen —1188 }»-183 £4x— ried Bluish
Nitric oxide —93°5 | -154 —167°0 ~ Colourless
Methane —81°8 —164 — 186 O45 ‘
388. Later researches.—Wroblewski and Olszewski made use of the
apparatus represented in fig. 369. The gas to be liquefied is contained in
the tube gv, and is compressed by means of a sort of Cailletet pump
coupled up with 4. Liquid ethylene is contained in the reservoir x, which
is surrounded by a freezing mixture of ice and salt ; it passes thence through
the tube 6’, which is surrounded by a paste of solid carbonic acid and ether,
and then reaches s, cooled down to a temperature of — 100°.
By means of an air-pump to which is connected the lead tube vw this.
cooled liquid can be caused to evaporate under a pressure of 25 mm., so that
the temperature as indicated by the hydrogen thermometer ¢ is -136°. The
vessel in which this is effected contains calcium chloride y, the object of which
is to prevent any deposition of dew on the tube.
At a temperature of — 136° oxygen at once liquefies under a pressure of 20
atmospheres. By still further reducing the pressure so that ethylene evapo-
rates at a pressure of I mm. the temperature sinks to—152° C., and now nitro-
gen and carbonic oxide can be directly condensed.
If again the space above these lige is rarefied, carbonic oxide becomes.
solid at -190°, and nitrogen at — 203°.
Dewar has carried out extensive researches on the liquefaction of gases,
and has liquefied and even solidified air. The methods adopted do not
differ in principle from those which have been mentioned ; the cold is pro-
duced by the evaporation of liquid ethylene.
-388] Later Researches 371
He has introduced an important improvement in surrounding the
vessel in which the liquefied gas is contained by a single or double vacuum
jacket, that is, a space from which the air is exhausted ; in this way liquid
air may be kept and manipulated in open vessels, or, in other words, at the
ordinary atmospheric pressure.
o&~
JACQUET
Fig. 369 Fig. 370
Fig. 370 illustrates an arrangement by which liquid air may be kept
in an open glass vessel virtually without evaporation. The smaller tube
is a glass one surrounded by a second one, from which the air has been
exhausted ; this tube contains liquid air, and, after the insertion of a glass
tube and stopper, it is immersed in liquid air contained in a similar outer
vacuum tube ; A is connected with the inner and B with the outer tube. As
the latter receives all the radiant and conducted heat, air is continuously
boiling off from the outer tube ; but as no heat reaches the inner tube there
is no escape from A. By connecting B with an air-pump so as to reduce
the pressure to about Io mm., and simultaneously connecting A with an air-
pump which is worked, the temperature of the liquid air is so reduced that
it solidifies to a jelly-like mass.
These experiments have made it possible to examine physical properties
of various substances at temperatures which approach absolute zero. It is
impossible here to give an account of the results obtained, but some of the
most important will be mentioned in their places. One interesting experi-
BB2
372 On Feat [388—
ment may be mentioned. Ifa barometer is prepared in the usual way, and
a sponge dipped in liquid air is applied to a portion of the outer surface of
the Torricellian vacuum space, a mirror of metallic mercury is immediately
deposited on the inside.
Linde has constructed an apparatus for the liquefaction of gases, which
works continuously and depends essentially on the cooling produced when a
gas expands ; it may be looked upon as the reverse of a regenerative furnace.
The main features of this apparatus are represented in fig. 371.
Consider, in the first case, a single round of operations. Air supplied
through the intake z, at the pressure Z, and temperature 7,, is brought by
the compressor F to the pressure #,, say of 50 atmospheres, thereby becoming
heated, but by passing through the cooler K is restored to the temperature
z,; from this it passes through the inner tube of C, which is the character-
istic feature of the apparatus ; meeting there a current of cooled gas pro-
Ry
Fig. 371
ceeding in the opposite direction through the annular space of C, its
temperature is lowered to ¢,.
If the throttle valve v is opened for a moment the gas suddenly expands,
its pressure is reduced to J,, and its temperature falls to Z,. With this latter
temperature it passes through the annular space of C, and so back to the
compressor F’, cooling, as already stated, the current passing in the opposite
direction through the inner tube and itself becoming raised to the tempe-
rature Z,.
The gas thus reduced to this latter temperature, and at the original
pressure 7, again goes through the same round of operations, again experi-
encing a further reduction of temperature until liquefaction sets in. The
operations are, in fact, continuous, and with a large apparatus of this kind
several litres of liquid air have been prepared in an hour.
-389] Mixture of Gases and Vapours 373
MIXTURE OF GASES AND VAPOURS
389. Laws of the mixture of gases and vapours.—Every mixture of a
gas and a vapour obeys the two following laws :—
I. The pressure, and, consequently, the quantity, of vapour which saturates
a given space are the same for the same temperature, whether this space con-
tains a gas or ts a vacuum.
Il. Zhe pressure of the mixture of a gas and a vapour ts equal to the
sum of the pressures which each would exert tf tt occupied the same space
alone.
These are known as Dalton’s laws, from their discoverer, and are de-
monstrated by the following apparatus, which was invented by Gay-Lussac :—
It consists of a glass tube A (fig. 372), to which
two stopcocks, 4 and d@, are cemented. The
lower stopcock is provided with a tubulure which
connects the tube A with a tube B of smaller
diameter. A scale between the two tubes serves
to measure the heights of the mercurial columns
in these tubes.
The tube A is filled with mercury, and the
stopcocks 6 and dare closed. A glass globe M,
filled with dry air or any other gas, is screwed
on by means of a stopcock in the place of the
funnel C. All three stopcocks are then opened,
and a little mercury is allowed to escape, which
is replaced by the dry air of the globe. The
stopcocks are then closed, and as the air in the
tube expands on leaving the globe, the pressure
on it is less than that of the atmosphere. Mer-
cury is accordingly poured into the tube B until
it is at the same level in bothtubes. The globe
is then removed, and replaced by the funnel C,
provided with a stopcock a@ of a peculiar con-
struction. It is not perforated, but has a small
cavity, as represented in 7, on the left of the
figure. Some of the liquid to be vaporised is
poured into C, and the height of the mercury &
having been noted, the stopcock 6 is opened,
and a@ turned so that its cavity becomes filled
with. liquid ; being again turned, the liquid
enters the space A and vaporises. The liquid nie: 272
is allowed to fall drop by drop until the air in the tube is saturated, which is
the case when the level £ of the mercury ceases to sink (357).
As the pressure of the vapour produced in the space A is added to that
of the air already present, the total volume of gas is increased. It may
easily be restored to its original volume by pouring mercury into B. When
the mercury in the large tube has been raised to the level 4, there is a
difference Bo in the level of the mercury in the two tubes which obviously
374 On Heat [389-
represents the pressure of the vapour ; for as the air has resumed its original
volume, its pressure has not changed. Now, if a few drops of the same
liquid be passed into the vacuum of a barometric tube, a depression exactly
equal to Bo is produced, which proves that, for the same temperature, the
pressure of a saturated vapour is the same in a gas as in a vacuum; from
which it is concluded that at the same temperature the quantity of vapour
is also the same.
The second law is likewise proved by this experiment, for, when the
mercury has regained its level, the mixture supports the atmospheric pressure
on the top of the column B, in addition to the weight of the column of mer-
cury Bo. But of these two pressures, one represents that of the dry air, and
the other that of the vapour. The second law is, moreover, a necessary
consequence of the first.
Experiments can only be made with this apparatus at ordinary tempera-
tures ; but Regnault, by means of an apparatus which can be used at different
temperatures, investigated the pressures of the vapours of water, ether,
bisulphide of carbon, and benzole, both in a vacuum and in air. He found
that the pressure in air is less than it is in a vacuum, but the differences are
so small as not to invalidate Dalton’s law. Regnault was even inclined to
consider this law as theoretically true, attributing the differences which he
observed to the hygroscopic properties of the sides of the tubes.
390. Problems on mixtures of gases and vapours.—i. A volume of dry
air V, at the pressure H, being given, what will be its volume V’, when it is
saturated with vapour, the temperature and the pressure remaining the same?
If F be the elastic force of the vapour which saturates the air, the latter,
in the mixture, only supports a pressure equal to H — F (356). But by Boyle’s
law the volumes V and V’ are inversely as their pressures, consequently
Vv = ashe whence V’/= te
ii. Let V be a given volume of saturated air at the pressure H and the
temperature ¢; what will be its volume V’, also saturated, at the pressure H’
and the temperature 7?
If f be the maximum pressure of aqueous vapour at 2°, and /” its maximum
pressure at 2’°, the air alone in each of the mixtures V and V’ will be respec-
tively under the pressures H—f and H’~—/’; consequently, assuming first
that the temperature is constant, we obtain
Meoaties 7.
Wi H’ —f
But as the volumes V’ and V of air, at the temperatures / and 4, are in the .
ratio of 1 +a?’ to 1+a¢, a being the coefficient of the expansion of air, the
equation becomes W Hf 1+ at’
Vie WEL? eal az
iil. What is the weight P of a volume of air V saturated with aqueous
vapour at the temperature ¢ and pressure H ?
If F be the maximum pressure of the vapour at 7°, the pressure of
the air alone will be H-F, and the problem reduces itself to finding: Ist,
—891] © Spheroidal State 375
the weight of V cubic inches of dry air at ¢ and under the pressure H-F ;
and 2nd, the weight of V cubic inches of saturated vapour at 7° under the
pressure F.
To solve the first part of the problem, we know that a cubic inch of dry
air at o° and the pressure 760 millimetres weighs 0°31 grain, and that at 7°,
and the pressure H - F, it weighs > ay vee (335) ; consequently V cubic
inches of dry air weigh 031 (H-F) V
(1 A at) 760 ° . 4 ° ° : (1)
To obtain the weight of the vapour, the weight of the same volume of
dry air at the same temperature and pressure must be sought, and this is to
be multiplied by the relative density of the vapour. Now,as V cubic inches
O3U 4 ie
(14 + at) 760°
aqueous vapour, whose density is 3 that of air (339), weigh
of dry air at 7°, and the pressure F, weigh V cubic inches of
ci a ae : : ; ; aria (2)
(1+ at) 760 8
and as the weight P is equal to the sum of the weights (1) and (2) we have
Prog nN og te VE) 5 OBR ea
/ (H —2 F).
(1 + at) 760 (1+at) 760 8 (1+ fi
Suu Wun ii )
“a (|
———SSSSSS—aaaaaaasasasaeE SS =
Sins
i ——
Fig. 389
400 On Feat [416—
layer as metals have ; but certainly when they are restrained in their motion
their conductivity is very small. All substances, for instance, between whose
particles air remains stationary, offer great resistance to the propagation of
heat. This is well seen in straw, eider-down, and furs. The propagation of
heat in a gaseous mass is effected by means of the ascending and descending
currents formed in it, as is the case with liquids.
The following experiment, a modification of one originally devised by
the late Sir W. Grove, is considered to prove that gases have a certain
conductivity.
A glass tube, fig. 390, with two lateral tubes @ and e opening into it at
one end, is closed in the middle by a cork, J, through which a stout copper
wire passes. This is connected by thin platinum wires with similar stout
copper wires passing through the corks a and c. Whena sufficiently strong
electric current is passed through the wires, both platinums are equally
incandescent. If, now, one half of the tube is filled with hydrogen by con-
necting one of the small tubes with a supply of that gas, and the current is
again passed, the wire in the hydrogen is scarcely luminous, while that in
air is still brightly incandescent.
This greater chilling of the wire in hydrogen than in air was considered
by Magnus to be an effect of conduction ; while Tyndall ascribed it to the
greater mobility of the particles of hydrogen.
Stefan found the value of & for air to be 070000558 in CGS units, so
that its conductivity is only ;545,5 that of copper, and 3,5; that of iron. He
also found that hydrogen conducts seven times as well as air, and that
difference of density seems to have no influence on the conductivity.
Maxwell deduced from purely theoretical considerations, based on the
kinetic theory of gases, that the conductivity of air must be 5:4, that of iron.
417. Applications.—The greater or less conductivity of bodies meets
with numerous applications. Ifa liquid is to be kept warm for a long time,
it is placed in a vessel and packed round with non-conducting substances,
such as shavings, straw, or bruised charcoal. For this purpose water-pipes
and pumps are wrapped in straw at the approach of frost. The same means
are used to hinder a body from becoming heated. Ice is transported in
summer by packing it in bran or folding it in flannel.
Double walls constructed of thick planks having between them any finely
divided materials, such as shavings, sawdust, dry leaves, &c., retain heat
extremely well ; and are likewise advantageous in hot countries, for they
prevent its access. Pure silica in the state of rock crystal is a better con-
ductor than lead, but in a state of powder it conducts very badly. If a layer
of asbestos is placed on the hand, a red-hot iron ball can be held without
inconvenience. Red-hot cannon-balls can be wheeled to the gun’s mouth in
—417] Applications 401
wooden barrows partially filled with sand. Lava has been known to flow
over a layer of ashes underneath which was a bed of ice, and the non-
conducting power of the ashes has prevented the ice from melting.
The clothes which we wear are not warm in themselves; they only
hinder the body from losing heat, in consequence of their spongy texture
and the air they enclose. The warmth of bed-covers and of counterpanes
is explained in a similar manner. Double windows are frequently used in
cold climates to keep a room warm—they do this by the non-conducting
layer of air interposed between them. It is for the same reason that two
shirts are warmer than one of the same material but of double the thickness.
Hence, too, the warmth of furs, eider-down, &c.
The small conducting power of felt is used in the North of Europe in the
construction of the Morwegian stove, which consists merely of a wooden
‘box with a thick lining of felt on the inside. In the centre is a cavity in
which can be placed a stew-pan provided with a cover. On the top of this
is a lid, also made of felt, so that the pan is surrounded by a very badly
conducting envelope. Meat, with water and suitable additions, is placed in
the pan, and the contents are then raised to boiling point. The whole is then
enclosed in the box and left to itself; the cooking will go on without fire,
and after the lapse of several hours it will be quite finished. The cooling
down is very slow, owing to the bad conducting power of the lining ; at the
end of three hours the temperature is usually not found to have sunk more
than from 10° to 15°.
That water boils more rapidly in a metallic vessel than in one of porcelain
of the same thickness ; that a burning piece of wood can be held close to
the burning part with the naked hand, while a piece of iron heated at one
end can only be held at a great distance, are easily explained by reference
to their various conductivities.
The sensation of heat or cold which we feel when in contact with certain
bodies is materially influenced by their conductivity. If their temperature is
lower than ours, they appear colder than they really are, because from their
conductivity heat passes away from us. If, onthe contrary, their temperature
is higher than that of our body, they appear warmer from the heat which
they give up at different parts of their mass. Hence it is clear why carpets,
for example, are warmer than wooden floors, and why the latter again are
warmer than stone floors.
The closer the contact of the hand with a substance, the greater is the
difference of temperature felt. With smooth surfaces there are more points
of contact than with rough ones. A hot glass rod feels hotter than a piece
of rusted iron of the same temperature, although the latter is a better con-
‘ductor. The closer the substance is pressed, the more intimate the contact ;
an ignited piece of charcoal can be lifted by the fingers if it is not closely
pressed.
AOSi) |)” On Feat [418—
CHAPTERS VAT!
RADIATION OF HEAT
418. Radiant heat.—It has been already stated (410) that heat can be
transmitted from one body to another without altering the temperature of the
intervening medium. If we stand in front of a fire we experience a sensation
of warmth which is not due to the temperature of the air, for if a screen be
interposed the sensation immediately disappears, which would not be the
case if the surrounding air had a high temperature. Hence bodies can send
out rays which excite heat, and which penetrate through the air without
heating it, as rays of light through transparent bodies. Heat thus propagated
is said to be radiated ; and we shall use the terms ray of heat, or thermad,
or calorific ray, in a similar sense to that in which we use the term vay of
light, or luminous ray.
We shall find that the property of radiating heat is not confined to
luminous bodies, such as a fire or a red-hot ball, but that bodies of all tem-
peratures radiate heat. It will be convenient to make a distinction between
luminous and obscure rays of heat.
419. Detection and measurement of radiant heat.—In demonstrating
the phenomena of radiant heat, very delicate thermometers are required, and
the thermo-electrical multiplier of Melloni is used for this purpose with great
advantage ; for it not only indicates minute differences of temperature, but
it also measures them with accuracy.
This instrument cannot be properly understood without a knowledge of
the principles of thermo-electricity, for which Book X. must be consulted.
It may, however, be stated here that when two different metals A and B are
soldered together at one end (figs. 391, 392), the free ends being joined by a
wire, when the soldering
C is heated, a current
of electricity circulates
through the system; if,
on.'+ they jcontraryagorhe
soldering be cooled, a
current is also produced,
Bivesor Rivteoe but it circulates in exactly
the opposite direction.
This is called a thermo-electric couple or pair. If a number of such pairs be
alternately soldered together, as represented in fig. 392, the strength of the
current produced by heating the ends is increased ; or, what amounts to the
same thing, a smaller quantity of heat will produce the same effect. Such an.
—420] Laws of Radiation 403
arrangement of a number of thermo-electric pairs is called a ¢thermo-electric
battery or pile.
Melloni’s thermomultiplier consists of a thermo-electric pile connected
with a delicate galvanometer. The thermo-electric pile is constructed of a
number of thin bars of bismuth and antimony soldered together alternately,
though kept insulated from each other, and contained in a rectangular box
P (fig. 393). The terminal bars are connected with two binding screws m
and 7, which in turn are connected with the galvanometer G by means of the
wires a and 6.
The galvanometer consists of a quantity of fine insulated copper wire
coiled round a frame, in the centre of which a delicate magnetic needle is
suspended by means of a silk thread. When an electric current is passed
through this coil, the needle is deflected through an angle which depends on
the strength of the current. The angle is measured ona dial by an index
connected with the needle.
It may then be sufficient to state that the thermo-electric pile being con-
nected with the galvanometer by means of the wires a and J, an excess of
Fig. 393
temperature at one end of the pile causes the needle to be deflected through
an angle which depends on the extent of this excess ; and similarly if the
temperature is depressed below that of the other end, a corresponding
deflection is produced in the opposite direction. With an instrument of
this kind Melloni was able to measure differences of temperature of sj4oth
of a degree. The object of the cone C is to concentrate the thermal rays on
the face of the pile.
420. Laws of radiation.—The radiation of heat is represented by three
laws :— . |
I. Radiation takes place tn all directions from a body. \f a thermometer
be placed in different positions round a heated body, it indicates everywhere
a rise in temperature.
Il. J a homogeneous medium radiation takes place in a right line. For,
if a screen be placed in the right line which joins the source of heat and the
thermometer, the latter is not affected.
DD2
404 On Feat [420-
But in passing obliquely from one medium into another, as from air into
glass, thermal like luminous rays become deviated, an effect known as
refraction. The laws of this phenomenon are the same for heat as for light,
and they will be more fully discussed under the latter subject.
Ill. Radiant heat ts propagated in vacuo as well as in
aiy. This is demonstrated by the following experiment :—
In the bottom of a glass flask a thermometer is fixed in
such a manner that its bulb occupies the centre of the flask
(fig. 394). The neck of the flask is carefully narrowed by
means of the blowpipe, and then the apparatus having been
suitably attached to an air-pump, a vacuum is produced in
the interior. This having been done, the tube is sealed at
the narrow part. On immersing this apparatus in hot water,
or on bringing near it some hot charcoal, the thermometer is
at once seen to rise. This could only be due to radiation
through the vacuum in the interior, for glass is so bad a
conductor that the heat could not travel with this rapidity
through the sides of the flask and the stem of the ther-
mometer.
421. Causes which modify the intensity of radiant heat.—By the zx/enszty
of radiant heat is understood the quantity of heat received on the unit of
surface. Three causes are found to modify this intensity : the temperature
of the source of heat, its distance, and the obliquity of the calorific rays in
reference to the surface which emits them. The laws which regulate these
modifications may be thus stated :—
I. Zhe intensity of radiant heat ts proportional to the temperature of the
source.
Il. Zhe intensity ts inversely as the square of the distance.
Ill. Zhe intenstty ts less, the greater the obliquity of the rays with respect
to the radiating surface.
The first law is demonstrated by placing a metal box containing water
at 10°, 20°, or 30° successively at equal distances from the bulb of a differen-
tial thermometer. The temperatures indicated
by the latter are then found to be in the same
ratio as those of the box: for instance, if the
temperature of that corresponding to the box at
10° be 2°, those of others will be 4° and 6° re-
spectively.
The truth of the second law follows from the
geometrical principle that the surface of a sphere
increases as the square of its radius. Suppose
a hollow sphere aé (fig. 395) of any given radius
and a source of heat, C, in its centre ; each unit
of surface in the interior receives a certain quan-
tity of heat. Nowa sphere, ef, of double the radius will present a surface
four times as great ; its internal surface contains, therefore, four times as
many units of surface, and as the quantity of heat emitted is the same, each
unit must receive one-fourth the quantity.
To demonstrate the same law experimentally, a narrow tin-plate box is
Fig. 304
Fig. 395
—421] Causes which modify the Intensity of Radiant Heat 405
taken (fig. 396), filled with hot water, and coated on one side with lampblack.
The thermopile with its conical cap, which in this experiment is lined with
black paper to absorb any radiation that falls upon it, is placed so that its
face is at a certain definite distance, co, say 9 inches, from this box, and the
cover having been lowered, the needle of the galvanometer is observed to be
deflected, through 80° for example.
—— sil
- Sa
SS
Fig. 396
If now the pile is removed to a distance, CO (fig. 397), double that of co,
the deflection of the galvanometer remains the same, which shows that
the pile receives the same amount of heat; the same is the case if the
pile is removed to three or four times the distance. This result, though
a
‘|
Fig. 397
apparently in opposition to the second law, really confirms it. For at first
the pile only receives heat from the circular portion ad of the side of the
box, while, in the second case, the circular portion AB radiates towards it:
But, as the two cones ACB and acé are similar, and the height of ACB is
double that of acé, the diameter AB is double that of ad, and therefore the
406 On Feat [421-
area AB is four times as great as that of ad, for the areas of circles are pro-
portional to the squares of the radii. But since the radiating surface increases
as the square of the distance, while the galvanometer remains stationary, the
heat received by the battery must be inversely as this same square.
The third law is demonstrated by means of the following experiment,
which is a modification of one originally devised by Leslie (fig. 398) :—P
represents the thermomultiplier which is connected with its galvanometer,
and A a metal cube full of hot water. The cube being first placed in such
Fig. 398
a position, A, that its front face, ac, is vertical, the deflection of the galvano-
meter is noted. Supposing it amounts to 45°, this represents the radiation
from ac. If this now be turned in the direction represented by A’, the
galvanometer is still found to mark 45°.
The second surface is larger than the first, and it therefore sends more
rays to the mirror. But as the action on the thermometer is no greater
than in the first case, it follows that in the second case, where the rays
are oblique, the intensity is less than in the first case, where they are per-
pendicular.
In order to express this in a formula, let z be the intensity of the rays
emitted perpendicularly to the surface, and z’ that of the oblique rays.
These intensities are necessarily inversely as the surfaces ac and a’c’, for the
effect is the same in both cases, and therefore z’ x surface a’c’ =z x surface ac ;
surf, .@¢_ 4, ac
SUti7 aa
of oblique rays ts proportional to the cosine of the anglewhich these rays form
wzth the normal to the surface ; for this angle is equal to the angle aoa’.
This law is known as the law of the cosine ; it is, however, not general ;
Desains and De la Provostaye have shown that it is only true within very
narrow limits ; that is, only with bodies which, like lampblack, are entirely
destitute of reflecting power (430).
422. Mobile equilibrium. Theory of exchanges.—Prévost of Geneva
suggested the following hypothesis in reference to radiant heat, known as
Prévost’s theory of exchanges, which is now universally admitted. All bodies,
whatever their temperatures, constantly radiate heat in all directions. If
we imagine two bodies at different temperatures placed near each other,
the one at a higher temperature will experience a loss of heat, its temperature
will sink, because the radiation it emits is greater than that which it
receives ; the colder body, on the contrary, will rise in temperature, because
it receives more radiation than it emits. Ultimately the temperature of both
bodies becomes the same, but heat is still exchanged between them, only
hence z’=2z =7 cos. aoa’; which signifies that the znzensity
—424] Reflection of Heat 407
each receives as much as it emits, and the temperature remains constant.
This state is called the modzle eguzlibrium of temperature.
423. Newton’s law of cooling.—A body placed in a vacuum is only
cooled or heated by radiation. In the atmosphere it becomes cooled or
heated by its contact with the air, according as the latter is colder or hotter
than the radiating body. In both cases the velocity of cooling or of heating
—that is, the guantity of heat lost or gained in a second—is greater accord-
ing as the difference of temperature is greater.
Newton enunciated the following law in reference to the cooling or
heating of a body :— The quantity of heat lost or gained by a body in a second
zs proportional to the difference between tts temperature and that of the sur-
rounding medium. Dulong and Petit have proved that this law is not so
general as Newton supposed, and only applies where the differences of
temperature do not exceed 15° to 20°. Beyond that, the quantity of heat
lost or gained is greater than what is required by this law.
Two consequences follow from Newton’s law :—
I. When a body is exposed to a constant source of heat, its temperature
does not increase indefinitely, for the quantity which it receives in the same
time is always the same ; while that which it loses increases with the excess
of its temperature over that of the surrounding medium. Consequently a
point is reached at which the quantity of heat emitted is equal to that ab-
sorbed, and the temperature then remains stationary.
II. Newton’s law, as applied to the differential thermometer, shows that
its indications are proportional to the quantities of heat which it receives.
If one of the bulbs of a differential thermometer receives rays of heat from
a constant source, the instrument exhibits, first, increasing temperature, but
afterwards becomes stationary. In this case, the quantity of heat which it
receives is equal to that which it emits. But the latter is proportional to the
excess of the temperature of the bulb above that of the surrounding atmo-
sphere—that is, to the number of degrees indicated by the thermometer :
consequently, the temperature indicated by the differential thermometer is
proportional to the quantity of heat it receives.
REFLECTION OF HEAT.
424. Laws of reflection.— When thermal rays fall upon a body they are,
speaking generally, divided into two portions, one of which penetrates the
body while the other rebounds as if repelled
from the surface like an elastic ball. This is D
said to be reflected.
If 7m be a plane reflecting surface (fig. 399),
CB an zucident ray, DB a line perpendicular to
the surface called the zormal, and BA the ,re-
flected ray, the angle CBD is called the angle
of incidence, and DBA the angle of reflection.
The reflection of heat, like that of lhght, is Fig. 399
governed by the two following laws :—
I. The angle of reflection ts equal to the angle of incidence.
Il. Both the incident and the reflected ray are in the same plane with the
perpendicular to the reflecting surface.
408 On Feat [425—
425. Experimental demonstration of the laws of reflection of heat.—
This may be effected by means of Melloni’s thermopile and also by the con-
jugate mirrors (427). Fig. 400 represents the arrangement adopted in the
former case. MN isa horizontal bar, about a metre in length, graduated in
millimetres, on which slide various parts, which can be clamped by means
of screws. The source of heat, S,isa platinum spiral, kept at a white heat in
a spiritlamp. A screen K, when raised, cuts off the radiation from the source ;
a second screen, F, with an aperture in the centre, cuts off all rays except a
pencil which falls upon the mirror 7. At the other end is an upright rod, I,
with a graduated dial, the zero of which is in the direction of MN, and
therefore parallel to the pencil S7z. In the centre of the dial is an aperture,
in which turns an axis that supports a metallic mirror 7. About this axis
turns an arm, R, on which is fixed the thermopile, P, in connection with
the galvanometer G ; H is a screen, the object of which is to cut off any
direct radiation from the source of heat towards the pile. In order not to mask
the pile, it is not represented in the position it occupies in the experiment.
Fig. 400
By lowering the screen K, a pencil of parallel rays, passing through the
aperture F, falls upon the mirror 7z, and is there reflected. If the arm R
is not in the direction of the reflected pencil, this latter does not fall on
the pile, and the needle of the galvanometer remains stationary ; but by
slowly turning the arm R, a position is found at which the galvanometer
attains its greatest deviation, which is the case when the pile receives the
reflected pencil perpendicularly to its surface. Reading off then on the dial
the position of a small needle perpendicular to the mirror, we observe that
this bisects the angle formed by the incident and the reflected pencils, which
demonstrates the first law. 7F
The second law is also proved by the same experiment, for the various
pieces of the apparatus are arranged so that the incident and reflected rays
are in the same horizontal plane, and therefore at right angles to the reflect-
ing surface, which is vertical.
~427] Verification of the Laws of Reflection 409
426. Reflection from concave mirrors.—Concave mirrors ox reflectors are
polished spherical or parabolic surfaces of metal or of glass, which are used
to concentrate luminous or calorific rays in the same point.
We shall only consider the case of spherical mirrors. Fig. 402 represents
two of these mirrors; fig. 401 gives a medial section, which is called the
principal section.
The, centre C of M
the sphere to
whichthemirror
belongsis called Miso
the centre ofcur- , jes See
vature;thepoint , Coma ene
A, the middleof \4-~
the refiector, 1s
LNG Mere en Oy
the petra, Ae Fig. 401
straight line AB |
passing through these points, is the principal axis of the mirror.
In order to apply to spherical mirrors the laws of reflection from plane
surfaces, they are considered to be composed of an infinite number of in-
finitely small plane surfaces, each belonging to the corresponding tangent
plane; the normals to these small surfaces are all radii of the same sphere,
and therefore meet at its centre, the centre of curvature of the mirror.
Suppose now, on the axis AB of the mirror MN, a source of heat so
distant that the rays EK, PH . . . . which start from it may be considered
as parallel. From the hypothesis that the mirror 1s composed of an infini-
tude of small planes, the ray EK is reflected from the plane K just as from
a plane mirror ; that is to say, CK being the normal to this plane, the
reflected ray takes a direction such that the angle CKF is equal to the
angle CKE. ‘The other rays, PH, GI... . are reflected in the same
manner, and all converge approximately towards the same point F, on the
line AC. There is then a concentration of the rays in this point, and conse-
quently a higher temperature than at any other point. This point is called
the focus, and the distance from the focus to the mirror at A is the focal
distance.
In the above figure the heat is propagated along the lines EKF, LDF, in
the direction of the arrows ; but, conversely, if the heated body be placed at
_F, the heat is propagated along the lines FKE, FDL, so that the rays
emitted from the focus are nearly parallel after reflection.
427. Verification of the laws of reflection.—The following experiment,
which was made for the first time by Pictet and Saussure, and which is
known as the experiment of the conjugate mirrors, demonstrates not only
the existence of the foci, but also the laws of reflection. Two reflectors,
M and N (fig. 402), are arranged at a distance of 4 to 5 yards, and so that
their axes coincide. In the focus of one of them, A, is placed a small wire
basket containing a red-hot iron ball. In the focus of the other is placed
B, an easily inflammable body, such as gun-cotton or phosphorus. The rays
emitted from the focus A are first reflected from the mirror M, in a direction
parallel to the axis (426), and falling on the other mirror, N, are reflected
Eaw&n B&B
410 On Fleat [427-
so that they coincide in the focus B. That this is so, is proved by the fact
that the gun-cotton at this point takes fire, which is not the case if it is above
or below it.
The experiment also serves to show that light and heat are reflected in
the same manner. For this purpose a lighted candle is placed in the focus
of A, and a ground-glass screen in the focus of B, when a luminous focus is
seen on it exactly in the spot where the gun-cotton ignites. Hence the
luminous and the calorific foci are produced at the same point, and the
reflection takes place in both cases according to the same laws, for it will be
afterwards shown that for light, the angle of reflection is equal to the angle
of incidence, and that both the incident and the reflected rays are in the same
plane perpendicular to the plane reflecting surface.
From the high temperature produced in the foci of concave mirrors
they have been called durning mirrors. It is stated that Archimedes
burnt the Roman vessels before Syracuse by means of such mirrors. |
Buffon constructed burning mirrors of such power as to prove that the feat
attributed to Archimedes was not impossible. The mirrors were made up of
a number of silver plane mirrors about 8 inches long by 5 broad. They
could be turned independently of each other in such a manner that the rays
reflected from each coincided in the same point. With 128 mirrors anda
hot summer’s sun Buffon ignited a plank of tarred wood at a distance of 70
yards.
428. Reflection in a vacuum.—Heat is reflected in a vacuum asjwell as
in air, as is seen from the following experiment (fig. 403), due to Sir Hum-
phry Davy. Two small concave reflectors were placed opposite each other
under the receiver of an air pump. In the focus of one was placed a delicate
—430] Reflecting Power 4LI
thermometer, and in the focus of the other a platinum wire made incandescent
by means of a galvanic current. The thermometer was immediately seen to
rise several degrees, which could only be due to reflected heat, for the ther-
mometer did not show any increase of
temperature if it were not exactly in the
focus of the second reflector.
429. Apparent reflection of cold.—
If two mirrors are arranged as repre-
sented in fig. 400, and a piece of ice is
placed in one of the foci instead of the
red-hot ball, the surrounding tempera-
ture being greater than zero, a differ-
ential thermometer placed in the focus
of the second reflector would exhibit a
decrease in temperature of several de-
grees. This appears at first to be
caused by the emission of /rigorific rays
from ice. It is, however, easily explained
A I NE
from what has been said about the ii iii Heat
Hh
Fig. 403
mobile equilibrium of temperature (422).
There is still an interchange of tempera-
ture, but here the thermometer is the
warmer body. As the radiation from the thermometer is greater than that
emitted by the ice, the former gives out more heat than it receives, and hence
its temperature sinks.
The sensation of cold experienced when we stand near a plaster or stone
wall whose temperature is lower than that of our body, or when we stand in
front of a wall of ice, is explained in the same way.
430. Reflecting power.—The veflecting power of a substance is its pro-
perty of throwing off a greater or less proportion of incident heat.
This power varies in different substances. In order to study this power
in different bodies without having recourse to as many reflectors, Leslie
arranged his experiment as shown in fig. 404. The source of heat is a
cubical canister, M, now known as Leséze’s cube, filled with hot water. A
plate, a, of the substance to be experimented upon is placed on the axis of a
reflecting mirror between the focus and the mirror. In this manner the rays
emitted by the source are first reflected from the mirror and impinge on the
plate a, where they are again reflected and converge to the focus between the
plate and the mirror, at which point a differential thermometer is placed.
The reflector and the thermometer are always in the same position, and the
water of the cube is always kept at 100°, but it is found that the temperature
indicated by the thermometer varies with the nature of the plate. This
method gives a means of determining, not the absolute reflecting power of a
body, but its power relatively to that of some body taken‘ as a standard of
comparison. For from whatjhas been said on the application of Newton’s law
to the differential thermometer (423), the temperatures which this instrument
indicates are proportional to the quantities of heat which it receives. Hence,
if in the above experiment a plate of glass causes the temperature to rise 1°
and a plate of lead 6°, it follows that the quantity of heat reflected by the
412 On Fleat [430-
latter is six times as great as that reflected by the former. For the heat
emitted by the source remains the same, the concave reflector receives the
same portion, and the difference can only arise from the reflecting power of
the plate a.
By this method Leslie determined the reflecting powers of the following
substances, relatively to that of brass, taken as Ioo :—
Polished brass . , 4-100 Indian ink : 2 ae
Silver ; : ; fiot9o Glass , ; : “BIO
Steel , ; SO Oiled glass. , Se
Lead ; . ‘ + NGO Lampblack ; 91, FHD
The numbers only represent the relative reflecting powers. Their absolute
power is the relation of the quantity of heat reflected to the guantity of heat
received. Desains and De la Provostaye obtained the following results for
the absolute reflecting power by means of Melloni’s thermomultiplier (419),
the heat being reflected at an angle of 50° :—
Silver plate. : LOO? Steel : 1 Loge
Gold : ¢ FOROS Zinc : ; OSE
Brass: *; : , EQOA Iron ; : MIO g a
Platinum + FO'S3 Cast iron ; i Ok
431. Absorbing power.—The absorbing power of a body is its property
of allowing a greater or less quantity of the heat which falls upon it to pass.
into its mass. Its absolute value is the ratio of the quantity of heat absorbed
to the quantity of heat received.
The absorbing power of a body is always inversely as its reflecting
power : a body which is a good absorbent is a bad reflector, and vice versd..
—432] Radiating Power 413
It was formerly supposed that the two powers were exactly complementary,
that the sum of the reflected and absorbed heat was equal to the total quan-
tity of incident heat. This is not the case; it is always less: the incident
heat is divided into three parts—tIst, one which is absorbed ; 2nd, another
which is reflected regularly—that is, according to laws previously demon-
strated (424); and a third, which is irregularly reflected in all directions,
and which is called scattered or diffused heat.
In order to determine the absorbing power of bodies, Leslie used the
apparatus which he employed in determining the reflecting powers (430).
But he suppressed the plate a, and placed the bulb of the thermometer in
the focus of the reflector. This bulb being then covered successively with
lampblack, or varnish, or with gold, silver, or copper foil, &c., the thermo-
meter exhibited a higher temperature under the influence of the source of
heat, M, according as the substance with which the bulb was covered
absorbed more heat. Leslie found in this way that the absorbing power of
a body is greater the less its reflecting power. In these experiments, how-
ever, the relation of the absorbing powers cannot be deduced from that of
the temperatures indicated by the thermometer, for Newton’s law is not
exactly applicable in this case, as it only prevails for bodies whose substance
does not vary, and here the covering of the bulb varied with each observa-
tion. But we shall presently show (433) how the comparative absorbing
powers may be deduced from the ratios of the emissive powers.
Taking, as a source of heat, a canister filled with water at 100°, Melloni
found, by means of the thermomultiplier, the following relative absorbing
powers :-—
Lampblack . , . 100 Indian ink . ; es
White lead . EL OO Shellac : é ie
Isinglass : : eet Metals : : ; le
432. Radiating power.—The vadiating or emisstve power of a body is
its capability of emitting, at the same temperature, and with the same extent
‘of surface, greater or less quantities of heat.
The apparatus represented in fig. 405 was also used by Leslie in deter-
mining the radiating power of bodies. For this purpose the bulb of the
thermometer was placed in the focus of the reflector, and the faces of the
canister M were formed of different metals, or covered with different
substances such as lampblack, paper, &c. The cube being filled with hot
water, at 100°, and all other conditions remaining the same, Leslie turned
each face of the cube successively towards the reflectors, and noted the
temperature each time. That face which was coated with lampblack caused
the greatest elevation of temperature, and the metal faces the least. Applying
Newton’s law, Leslie found the following table of radiating powers :—
Lampblack . Sis Tarnished lead . PAs
White lead, : TOS Mercury . : . che? 15)
Paper 98 Polished lead. ’ Sass
Ordinary white glass . 90 Polished iron. 15
Isinglass : : 224880 Tin, gold, silver, copper, &c. 12
414 On Heat [432-
It will be seen that, in this table, the order of the bodies is exactly the
reverse of that in the tables of reflecting powers.
The radiating powers of several substances were determined by Desains
and De la Provostaye, who used the thermomultiplier. They found, in this
manner, the following numbers compared with lampblack as 1oo :—
Platinum foil . ; : . 10°80
Burnished platinum ‘ s ghOrRgO
Silver deposited chemically. . . : 2 5936
Copper foil Wi . ; : ; free A10G
Gold leaf F : , : ‘ : : -=RAZS
Pure silver laminated ; : : : ir 13°08
r, deposited chemically and burnished - 2°25
The radiating power found by Leslie for the metals is thus too large.
433. Identity of the absorbing and radiating powers.—The absorbing
power of a body cannot be accurately deduced from its reflecting power,
because the two are not exactly complementary. But the absorbing power
would be determined if it could be shown that in the same body it is equal
to the radiating power. This conclusion has been drawn by Dulong and
Petit from the following experiments :—In a large glass globe, blackened on
the inside, was placed a thermometer at a certain temperature, 15° for ex-
ample; the globe was kept at zero by surrounding it with ice, and having
been exhausted by means of atubulure connected with an air-pump, the time
was noted which elapsed while the thermometer fell through 5°. The experi-
ment was then made in the contrary direction ; that is, the sides of the globe
were heated to 15°, while the thermometer was cooled to zero ; the time was
then observed which the thermometer occupied in rising through 5°. It was
found that this time was exactly the same as that which the thermometer
had taken in sinking through 5°, and it was thence concluded that the
radiating power is equal to the absorbing power for the same body, and for
the same difference between its temperature and the temperature of the sure
rounding medium, because the quantities of heat emitted or absorbed in the
same time are equal.
This point may also be demonstrated by means of the following apparatus
devised by Ritchie. Fig. 405 represents what is virtually a differential
thermometer, the two glass bulbs of which are replaced by two cylindrical
reservoirs B and C, of metal, and full of air. Between them is a third and
larger one A, which can be filled with hot water by means of a tubulure,
The ends of B and of A, which face the right, are coated with lampblack ;
those of C and of A, which face the left, are either painted white, or are
coated with silver foil. Thus one of the two faces opposite each other is
black, and the other white ; hence when the cylinder A is filled with hot
water, its white face radiates towards the black face of B, and its black face
towards the white face of C. In these circumstances the liquid in the
stem does not move, indicating that the two reservoirs are at the same
temperature. On the one hand, the greater emissive power of the black
face of A is compensated by the smaller absorptive power of the white face
—434] Causes which modify the different Powers 415
of C ; while, on the other hand, the feebler radiating power of the white face
of A is compensated by the greater absorbing power of the black face of B.
The experiment .may be varied by re- fA,
placing the two white faces by discs of paper, = =
glass, porcelain, &c.
434. Causes which modify the reflecting,
absorbing, and radiating powers.—As the
radiating and absorbing powers are equal,
any cause which affects the one affects the
other also. And as the reflecting power
varies in an inverse manner, whatever in-
creases it diminishes the radiating and
absorbing powers, and vice versa.
It has been already stated that these dif-
ferent powers vary with different bodies, and
that metals have the greatest reflecting power,
and lampblack the least. In the same body
these powers are modified by the degree of
polish, the density, the thickness of the
radiating substance, the obliquity of the
incident or emitted rays, and, lastly, by the j
nature of the source of heat. ie 4s
It has been usually assumed that the reflecting power increases with the
polish of the surface, and that the other powers diminish therewith. But
Melloni showed that by scratching a polished metallic surface its reflecting
power was sometimes diminished and sometimes increased. This pheno-
menon he attributed to the greater or less density of the reflecting surface.
If the plate had been originally hammered, its homogeneity would be
destroyed by this process, the molecules would be closer together on the
surface than in the interior, and the reflecting power would be increased.
But if the surface is scratched, the interior and less dense mass becomes
exposed, and the reflecting power diminished. On the contrary, in a plate
which has not been hammered, and which is homogeneous, the reflecting
power is increased when the plate is scratched, because the density at the
surface is increased by the scratches.
Melloni found that when the faces of a cube filled with water at a constant
temperature were varnished, the emissive power increased with the number
of layers up to 16 layers, while above that point it remained constant, what-
ever the number. The thickness of the 16 layers was calculated to be
o70o4 mm. With reference to metals, gold leaves of 0.008, o’004, and 0-002
of a millimetre in thickness, having been successfully applied on the sides
of a cube of glass, the diminution of radiant heat was the same in each case.
It appears, therefore, that, beyond certain limits, the thickness of the
radiating layer of metal is without influence.
The absorbing power is greatest when the rays are at right angles to the
surface, and it diminishes in proportion as the incident rays deviate from the
normal. This is one reason why the sun is hotter in summer than in winter,
because, in the former case, the sun’s rays are less oblique.
The radiating power of gaseous bodies in a state of combustion is very
Mt ——
ila Mt
416 On Heat [434—
weak, as is seen by bringing the bulb of a thermometer near a hydrogen
flame, the temperature of which is very high. But if a platinum spiral be
placed in this flame, it assumes the temperature of the flame, and radiates
a great amount of heat, as is shown by the thermometer. For a similar
reason the flames of oil and of gas lamps radiate more than a hydrogen
flame in consequence of the excess of carbon which they contain, and
which, not being entirely burned, becomes incandescent in the flame.
435. Melloni’s researches on radiant heat._-For our knowledge of the
phenomena of the reflection, emission, and absorption of heat which have up
to now been de-
scribed, science
is indebted
mainly to Leslie.
But since his
time the dis-
covery of other
and far more
delicate modes
of detecting and
measuring heat
th has not only
— extended and
Mi ll
corrected our
previous know-
ledge, but has led to the discovery of other phenomena of radiant heat, which
‘without such improved means must have remained unknown.
This advance in science is due to an Italian philosopher, Melloni, who
first applied the thermo-electric pile, invented by Nobili, to the measurement
of very small differences of temperature ; a method of which a preliminary
account has already been given (419).
In his experiments Melloni used five sources of heat—trst, a Locatelli’s
lamp—one, that is, without a glass chimney, but provided with a reflector
(fig. 406) ; 2nd, an Argand lamp, that is, one with a chimney and a double
draught ; 3rd, a platinum spiral, kept red-hot by a spirit lamp (fig. 407) ;
4th, a blackened copper plate, kept at a temperature of about 400° by a spirit
lamp (fig. 408) ; 5th, a copper tube, blackened on the outside and filled with
water at 100° (fig. 409).
436. Dynamical theory of heat.—Before describing the results arrived
‘at by Melloni and others, it will be convenient to explain here the view now
generally taken as to the mode in which heat is propagated. For additional
information the chapter on the Mechanical Theory of Heat and the book on
Light should be read. According to what has already been stated (296), a
hot body is nothing more than one whose particles are ina state of vibration.
The higher the temperature of the body, the more rapid are these vibrations,
and a diminution in temperature is but a diminished rapidity of vibration of
the particles. The propagation of heat through a bar is due to a gradual
communication of this vibratory motion from the heated part to the rest of
the bar. A good conductor is one which readily takes up and transmits the
vibratory motion from particle to particle, while a bad conductor is one which
mk
UTI PANASEY
Fig. 409
—436] Dynamical Theory of Heat 417
takes up and transmits the motion with difficulty. But even through the best
conductors the propagation of this motion is comparatively slow. How then
are we to explain the instantaneous perception of heat experienced when a
screen is removed from a fire, or when a cloud drifts from the face of the
sun? In this case the heat passes from one body to another without affect-
ing the temperature of the space through which it passes. In order to ex-
plain these phenomena, it is imagined that all space, the interplanetary spaces
as well as the interstices in the hardest crystal or the heaviest metal—in
short, matter of any kind—is permeated by a medium having the properties
of a fluid of infinite tenuity, called eter (511). The particles of a heated
body, being in a state of intensely rapid vibration, communicate their motion
to the ether around them, throwing it into a system of waves which travel
through space and pass from one body to another with the velocity of light.
When the undulations of the ether reach a given body, the motion is again
delivered up to the particles of that body, which in turn begin to vibrate:
that is, the body becomes heated. This process of motion through the
hypothetical ether is termed radiation, and what is called a ‘ ray of heat’ is
merely a series of waves moving in a certain direction.
It will facilitate the understanding of this to consider the analogous mode
in which sound is produced and propagated. A sounding body is one whose
entire mass is in a state of vibration (228) ; the more rapid the rate of vibra-
tion, the more acute the sound ; the slower the rate of vibration, the deeper
thesound. This vibratory motion is communicated to the surrounding air, by
means of which the vibrations reach the auditory nerve, and there produce
the sensation of sound. If a metal ball be heated, say, to the temperature
of boiling water, we can ascertain that it radiates heat, although we cannot
see any luminosity; and if its temperature be gradually raised, we see it
becomes successively of a dull red, bright red, and dazzling white. At each
particular temperature the heated body emits waves of a definite length ; in
other words, its particles vibrate in a certain period. As its temperature
rises it sends out other and more rapid vibrations, which coexist, however,
with all those which it had previously emitted. Thus the motion at each
successive temperature is compounded of all preceding ones.
It has been seen that vibrations of the air below and above a certain rate
do not affect the auditory nerve (247) ; it can only take up and transmit to the
brain vibrations of a certain periodicity. So too with the vibrations which
produce light. The optic nerve is insensible to a large number of wave-
lengths. It can apprehend only those waves that form the visible spectrum.
If the rate of undulation be slower than the red or faster than the violet,
though intense motion may pass through the humours of the eye and fall
upon the retina, yet we shall be utterly unconscious of the fact, for the
optic nerve cannot take up and respond to the rate of vibrations which exist
beyond the visible spectrum in both directions. Hence, these are termed
inuistble or obscure rays. A vast quantity of these obscure rays is emitted
by flames which, though intensely hot, are yet almost non-luminous, such
as the oxy-hydrogen flame, or that of a Bunsen’s burner ; for the vibra-
tions which these emit, though capable in part of penetrating the media
of the eye, are incapable of exciting in the optic nerve the sensation of
light.
EE
418 On Ffeat [437—
437. Thermal analysis of sunlight.—When a beam of sunlight (fig.
410), admitted through an aperture in a dark room, is concentrated on a
prism of rock salt by means of a lens of the same material, and then, after
emerging from the prism, is received on a screen, it will be found to present
a band of colours in the following order: red, orange, yellow, green, blue,
and violet. This is called the sfectrum (576).
If now a narrow and delicate thermopile be placed successively on the
space occupied by each of the colours, it will be scarcely affected on the
violet, but in passing over the other colours it will indicate a gradual rise of
temperature, which is greatest at the red. Painters, thus guided by a cor-
rect but unconscious feeling, always speak of blue and green colours as cold,
and of red and orange as warm tones. If the pile be now moved in the
same direction beyond the limits of the luminous spectrum, the temperature
will gradually rise up to CP, at which it attains its maximum. From this
point the pile indicates a decrease of temperature until it reaches a point, O,
where it ceases to be affected. This point is about as distant from R as the
latter is from V ; that is, there is a region in which thermal effects are pro-
Riba
Fig. 410
duced extending as far beyond the red end of the spectrum in one direction
as the entire length of the visible spectrum in the other. In accordance
with what we have stated, the sun’s light consists of rays of different rates of
vibration. By their passage through the prism they are unequally broken or
refracted ; those of greatest wave-length or slowest vibrating period are least
bent aside, or are said to be the least refrangible, while those with shorter
wave-lengths are the most refrangible.
These non-luminous rays outside the red are called the ultra-red rays, or
sometimes the Werschelian rays, from Sir W. Herschel, who first discovered
their existence.
If, in the above case, prisms of other materials than rock salt be used,
the position of the maximum heat will be found to vary with the nature of
the prism, a fact first noticed by Seebeck. Thus with a prism of water it is
in the yellow, with one of crown glass in the middle of the red, and so on.
These changes are due to the circumstance that prisms of different materials
absorb rays of different refrangibility to unequal extents. But rock salt
practically allows heat of all kinds to pass with equal facility, and thus gives
a normal spectrum.
—438 | Lyndalls Researches 419
438. Tyndall’s researches.—Tyndall investigated the spectrum pro-
duced by the electric light, by the following method :—The beam of
electric light, rendered parallel by a rock-salt lens, was caused to pass
through a narrow slit, and then through a second lens of rock salt ; the
slices of white light thus obtained being decomposed by a prism of the same
material. To investigate the thermal conditions of the spectrum a “near
thermo-electric pile was used ; that is, one consisting of a number of ele-
ments arranged ‘B
in a line, in
front of which
was a slit that
could be nar-
rowed to any
extent mnie ite
strument was c \
mounted on a
movable bar
connected with » D
a fine screw, so
that by turning
a handle the
pile could be ‘
moved through the smallest space. On placing this apparatus successively
in each part of the spectrum of the electric light, the heating effected at
various points near each other was determined by a delicate galvanometer.
As in the case of the solar spectrum, the heating effect gradually increased
from the violet end towards the red, and was greatest in the dark space
beyond the red. The position of the greatest heat was about as far
from the limit of the visible red as the latter was from the green, and the
total extent of the invisible spectrum was found to be twice that of the
visible.
The increase of temperature in the dark space is very considerable. If
thermal intensities are represented by perpendicular lines of proportionate
length, erected at those parts of the spectrum to which they correspond, on
passing beyond the red end these lines increase rapidly and greatly in
length, reach a maximum, and then fall somewhat more suddenly. If these
lines are connected, they form a curve (fig. 411), which beyond the red
represents a peak, quite dwarfing that of the visible spectrum. In fig. 410,
the dark parts at the end represent the obscure radiation. The curve is
based, in the manner above stated, on the results obtained by Tyndall with
the electric light. The upper curve in fig.\412 represents the spectrum of
sunlight with a rock-salt prism, while the lower curve represents the results
obtained with a flint-glass prism, which is thus seen to absorb some of the
ultra-red radiation.
By interposing various substances, more especially water, in certain
thicknesses, in the path of the electric hight, the ultra-red radiation was
greatly diminished. Now aqueous vapour, like water, absorbs the obscure
rays. And probably the reason why the obscure part of the spectrum of
sunlight is not so intense as in the case of the electric light is that the
EB 2
Fig, 411
420 On Heat [438-
obscure rays have been already partially absorbed by the aqueous vapour of
the atmosphere. If a solar spectrum could be produced outside the atmo-
sphere, it would probably give a spectrum more like that of the electric
light, which is unaffected by the atmospheric absorption.
This has been confirmed in other ways. Melloni observed that the
position of the maximum in the solar spectrum differs on different days ;
which is probably due to the varying absorption of the atmosphere, in con-
sequence of its varying hygrometric state. Secchi, in Kome, found the
red than in sum-
same shifting of
a i the maximum to
mer, when the
aqueous vapour in the air is most abundant. Cooke.jfound that the faint
occur in the dif-
black lines in the selar spectrum attributed to the absorption of light by our
ferent seasons
atmosphere (see book on Optics) are chiefly caused by the presence of
of the year ; for
in winter, when ©
aqueous vapour.
there is least
moisture in the
atmosphere, the
maximum is far-
ther from the
Fig. 412
| Use 1 1 n Aa —— oma
i HbDCA | i i ui
OY ivisiic: 1% 2h 5 Zea ae ar
i] ‘ t
: Fig. 413
439. Langley’s observations.—The most accurate and complete investiga-
tions of the heat spectrum of the sun have been those made by Langley ; he
—440] Luminous and Obscure Radiation 421
used for this purpose a Rowland’s grating (666) so as to avoid effects due to
absorption, and the heat in the various parts in the spectrum thus produced
was measured by a dolometer which showed differences in temperature of
o‘oooo1°® F. He obtained in this way a spectrum invisible to the eye
extending beyond the red to 20 times the length of the visible spectrum.
Fig. 413 represents about two-thirds of this length, extending to a wave length
of 54=0'005 mm. The thermal action begins just outside the violet at a wave
length of about 0°25 uw, and is at a maximum between yellow and orange at a
wave length of 0°65 ». The depressions in the curve represent the dark lines,
or what are called Fraunhofers lines (585).
For details of the experiments and interpretation of the results the
student should consult the original paper, Phil. Mag. [v] vol. 26, p. 505.
440. Luminous and obscure radiation.—The radiation from a luminous
object, a gas flame, for example, is of a composite character ; a portion con-
sists of what we term light, but a far greater part consists of heat rays,
which are insensible to our eyes, being unable to affect the optic nerve.
When this mixed radiation falls upon the blackened face of a thermo-electric
pile, the whole of it is taken to be absorbed, the light by this act being
converted into heat, and affecting the instrument proportionally with the
purely calorific rays. The total radiation of a luminous source, expressed
in units of heat, can thus be measured. By introducing into the path of the
rays a body capable of stopping either the luminous or the obscure radiation,
we can ascertain by the comparative action on the pile the relative quanti-
ties of heat and hght radiated from the source. Melloni sought to do this
by passing a luminous beam through a layer of water containing alum
in solution, a liquid which he found in previous experiments absorbed
all the radiation from bodies heated under incandescence. Comparing
the transmission through this liquid—which allowed the luminous but not
the obscure part of the beam to pass—with the transmission through a
plate of rock salt—which affected neither the luminous nor the obscure
radiation, but gave the loss due to reflection—Melloni found that 90 per cent.
of the radiation from an oil flame and 99 per cent. of the radiation from
an alcohol flame consist of invisible calorific rays. Tyndall employed a
solution of iodine in carbon bisulphide, which he found to be impervious
to the brightest light, but very pervious to radiant heat; only a slight
absorption being effected by the bisulphide. By comparing the transmission
through the transparent bisulphide, and that through the same liquid
rendered opaque by iodine, the value of the luminous radiation from various
sources was found to be as follows :—
Source Luminous Obscure
Red-hot spiral ; ; : EO 100
Hydrogen flame . : ; ORK: 100
Oil flame mike 97
Gas flame : : : : ; cet 96
White-hot spiral ; : Seacliae, 95°4
Electric ight . . : . ; Jnl, go
Here by direct experiment the ratio of luminous to obscure rays in the
electric light is found to be ro per cent. of the total radiation. By prismatic
422 On Fleat [440-
analysis, the curve shown in fig. 411 was obtained, graphically representing
the proportion of luminous to obscure rays in the electric light ; by calculating
the areas of the two spaces in the diagram, the obscure portion, DCBA, is
found to be nearly to times as large as the luminous one, DCE.
441. Transmutation of obscure rays.—We shall find, in speaking of the
luminous spectrum (575), that beyond the violet there are rays which are in-
visible to the eye, but which are distinguished by their chemical action, and
are spoken of as the actinic or chemical rays ; they are also known as the
Ritteric rays, from the philosopher who first discovered their existence.
Stokes, as we shall afterwards see in the book on Optics, succeeded in
converting these rays into visible rays of lower refrangibility ; so Tyndall
effected the corresponding but inverse change, and increasing the refrangi-
bility of the ultra-red rays, rendered them visible. The charcoal points of
the electric light were placed in front of a concave silvered glass mirror
so that the rays after reflection were concentrated to a focus about
6 inches distant. On the path of the beam was interposed a cell full of
a solution of iodine in carbon bisulphide, which (440) has the power of
completely stopping all luminous radiation, but gives free passage to
the non-luminous rays. A piece of platinum placed in the focus of the
beam, thus sifted, was raised to incandescence by the perfectly invisible
rays. In like manner a piece of charcoal zz vacuo was heated to red-
ness.
By a proper arrangement of the charcoal points a metal may be raised
to whiteness, and the light now emitted by the metal yields on prismatic
analysis a brilliant luminous spectrum, which is thus entirely derived from
the invisible rays beyond the red. This transmutation of non-luminous into
luminous heat Tyndall called calorescence.
When the eye was cautiously placed in the focus, guarded by a small
hole pierced in a metal screen, so that the converged rays should only enter
the pupil and not affect the surrounding part of the eye, no impression of
light was produced, and there was scarcely any sensation of heat. A con-
siderable portion was absorbed by the humours of the eye, but yet a power-
ful beam undoubtedly reached the retina; for, as Tyndall showed by a
separate experiment, about 18 per cent. of the obscure radiation from the
electric light passed through the humours of an ox’s eye.
442. Transmission of thermal rays.—Melloni examined the absorption of
heat by solids and liquids by;the apparatus represented in fig. 414, where AB
is the thermo-electric pile ; a is a support for the source of heat, in this case
a Locatelli’s lamp ; F and E are screens, and C is a support ; while 7z is the
pile, and D the galvanometer.
To express the power which bodies have of transmitting heat, Melloni
used the term diathermancy: diathermancy bears the same relation to
radiant heat that transparency does to light ; and in like manner the power
of stopping radiant heat is called athermancy, which thus corresponds to
opacity for ight. In experimenting on the diathermancy of liquids, Melloni
used glass troughs with parallel sides, the thickness of the liquid layer being
0°36 in. The radiant heat of an Argand lamp was first allowed to fall directly
on the face of the pile, and the deflection produced in the galvanometer taken
as measuring the total radiation 7’, the substance under examination was then
—442] Transmission of Thermal Rays 4.23
interposed, and the deflection noted. This corresponded to the quantity of
heat, ¢, which is transmitted by the substance. Hence
POUT TOO" a
the percentage of rays transmitted. Thus calling the total radiation 100,
Melloni found that
Carbon bisulphide transmitted : : : ; who xs
Olive oil Be : ‘ ; : ; » Xe
Ether . : : : : : tea
Sulphuric acid a : “ ; : ; 2 flys
Alcohol -* : : : 5 ; Jets
Solution of alum or sugar
@ ; : ; : : yA:
Distilled water
9 ; : J : : eats
In experimenting with solids they were cut into plates o‘1 inch in thick-
ness, and it was found that of every Ioo rays there was transmitted by
Rock salt ws , : =e 92 Selenite : A220
Smoky quartz } : m7, Adore : . Vek?
Transparent lead carbonate . 52 Copper sulphate . 2 ke.
The transmission of heat through liquids was re-examined by Tyndall,
who used a cell consisting of parallel plates of rock salt separated by a ring
of brass with an aperture on the top through which the liquid could be
poured. As this ring could be changed at will, liquid layers of various
thicknesses were easily obtainable, the apparatus being merely screwed
together and made liquid-tight by paper washers. The instrument was
mounted on a support before an opening in a brass screen placed in front
of the pile. The source of heat employed was a spiral of platinum wire
raised to incandescence by an electric current, the spiral being enclosed ina
small glass globe with an aperture in front, through which the radiation
424 On Heat [442—
passed unchanged in its character, a point of essential importance overlooked
by Melloni. The following table contains the results of experiments made
with liquids in the various thicknesses indicated, the numbers expressing
the absorption per cent. of the total radiation. The ¢vansmisston per cent.
can be found in each case by subtracting the absorption from too. Thus a
layer of water o'2 inch thick absorbs 80°7 and transmits 19°3 per cent. of the
radiation from a red-hot spiral.
Absorption of heat by liquids
| Thickness of liquids in parts of an inch
Liquid |
0°02 | 0°04 0°07 : O'14 0°27
-Carbon bisulphide . OE seg Gin lll Se BIS eee | 1632 bie eee
Chloroform . ‘ Al TO Gr ine 2570 35:0 the doro: (aia asones
Methyl iodide . ; SPROUT ee 84035 cag 65°20) [aes G
iebenzolé.. ‘ HiRAS A; ABS. 55 7A ots 715 nee
| Amylene . ; . ch S'S ee heOSr eu shth7s0 TI Fh, AROOBES
| Ether : ; : veh te 3" 3 Mew 73 Sie sh GO the ehieaeu lee tama
| Alcohol . : ; O7 Bent 0 Om on ro Te Se Lela Phot
| Water. ; ch. 80°77. W ASO at boo Oo. nO UO salsa tear
It thus appears that there is no connection between diathermancy and
transparency. Liquids, except olive oil, are all colourless and transparent;
and yet vary as much as 75 per cent. in the amount of heat transmitted.
Smoky quartz, which is nearly opaque to light, transmits heat very well ;
while alum, which is perfectly transparent, cuts off 88 per cent. of heat
rays. As there are different degrees of transparency, so there are different
degrees of diathermancy ; and the one cannot be predicated from the
other.
By studying the transmission of heat from different parts of the spec-
trum separately, the connection between light and heat becomes manifest.
With this view Masson and Jamin received the spectrum of the solar light
given by a prism of rock salt on a movable screen provided with an aperture,
so that by raising or lowering the screen the action of any given part of the
spectrum on different plates could be investigated. They thus found—
That glass, rock crystal, ice, and generally substances transparent for
light, are also diathermanous for all kinds of /umznous heat ;
That a coloured glass, red, for instance, which only transmits the red rays
of the spectrum, and extinguishes the others, also extinguishes every kind of
luminous heat, excepting that of the red rays ;
That glass and rock crystal, which are diathermanous for luminous heat,
also transmit the obscure heat near the red—that is, the most refrangible of
the ultra-red rays—but extinguish the extreme obscure rays, or those which
are the least deflected by the prism. Alum extinguishes a still greater pro-
portion of the obscure spectrum, and ice stops it altogether.
Knoblauch has shown that very thin layers of gold, silver, and platinum,
which are known to transmit luminous rays of a definite colour, also allow
—443] Jnfluence of the Nature of the Source of Heat 425
rays of heat to pass ; so that these substances are diathermanous, though in
a small degree. This is also the case with thin sheets of ebonite.
443. Influence of the nature of the source of heat.—The diathermanous
power differs greatly with the radiation from different sources, as is seen from
the following table, in which the numbers express what proportion of every
Ioo rays from the different sources of heat incident on the plates is trans-
mitted :—
| Locatelli’s
| lamp sae | Copper at 400° | Copper at 100°
| |
| Rock salt . ; hy 92 92 92 92
| Fluor spar : a 78 69 42 a |
| Plate glass ma 39 24 6 )
| Black glass : i 26 55 I2 O
| Selenite .. 14 5 O O
' Alum : ; Aa 9 | 3 re) O
iv Leer: pa SAe A 6 | O'5 | fe) fe) |
These different sources of heat correspond to light from different sources.
‘Rock salt is here stated to transmit all kinds of heat with equal facility, and
to be the only substance which does so. It is analogous to white glass,
which is transparent for light from all sources. Fluor spar transmits 78 per
cent. of the rays from a lamp, but only 33 of those from a blackened surface
at 100°. A piece of plate glass only one-tenth of an inch thick, and perfectly
transparent to light, is opaque to all the radiation from a source of 100°,
transmits only 6 per cent. of the heat from a source at 400°, and but 39 of
the radiation from the lamp. Black glass, on the contrary, though it cuts
off all heat from a source at 100°, allows 12 per cent. of the heat at 400° ta
pass, and is equally transparent to the heat from the spiral, but on account
of its blackness is more opaque to the heat from the lamp. As we have
already seen, every luminous ray is a heat ray ; now as several of the sub-
stances in this table are pervious to all the luminous rays, and yet, as in the
case of ice, transmit about 6 per cent. of luminous heat, we have an apparent
anomaly ; which, however, is only a confirmation of the remarkably small
ratio which the luminous rays of a lamp bear to the obscure.
From these experiments Melloni concluded that as the temperature of
the source rose, more heat was transmitted. This was confirmed by
Tyndall. The platinum lamp (438) was used as the source, the temperature
of which could be varied from a dark to a brilliant white heat, by a gradual
augmentation of the strength of the electric current which heated the platinum
spiral. Instead of liquids, vapours were examined in a manner to be de-
scribed subsequently ; the results of experiments are given in the table on
next page.
The percentage of rays absorbed is here seen to diminish in each case
as the temperature of the source rises. Mere rise of temperature does
not, however, invariably produce a high penetrative power in the rays
emitted : the rays from sources of far higher temperature than any of the
foregoing are more largely absorbed by certain substances than are the rays
426 On Fleat [443—
Absorption of heat by vapour
Source, platinum spiral
Name of vapour 5 a
Barely visible | Bright red White hot Near fusion
| Carbon bisulphide 6°5 4°7 2°9 2%
Chloroform . g'l 6°3 Si, 3°9
Methyl iodide . i2°5 ) 9°6 7°8
Benzole 26.4 20°6 165
Ether 43°4 314 25°9 237
Formic ether 45°2 31°9 FA 21-3
Acetic ether 49°6 34°65 27o
emitted from any one of the sources as yet mentioned. Thus, the radia-
tion from a hydrogen flame was completely intercepted by a layer of water
only 0:27 of.an inch thick, the same layer transmitting 9 per cent. of the
radiation from the red-hot spiral, a source of much lower temperature. The
explanation of this is, that those rays which heated water emits (and water
the product of combustion is the main radiant in a hydrogen flame) are the
very ones which this substance most largely absorbs. This statement, which
will become clearer after considering the analogous phenomena in the case
of light, was exemplified by the powerful absorption of the heat from a
carbonic oxide flame by carbonic acid gas. It will be seen presently (446)
that of the rays from a heated plate of copper, ethylene absorbs Io times
the quantity intercepted by carbonic acid, whilst of the rays from a carbonic
oxide flame Tyndall found carbonic acid absorbed twice as much as ethylene.
Carbonic acid, at a pressure of a tenth of an atmosphere, enclosed in a
tube 4 feet long, absorbs 60 per cent. of the radiation from a carbonic oxide
flame. Radiant heat of this character can thus be used as a delicate test for
the presence of carbonic acid, the amount of which may even be accurately
measured by the same means. Prof.: Barrett made in this way a physical
analysis of the human breath. In one experiment, the carbonic acid con-
tained in breath physically analysed was found to be 4°65 per cent., whilst
the same breath chemically analysed gave 4°66 per cent.
444. Influence of the thickness and nature of screens.—It will pee seen
from the table (443) that of every 100 rays rock salt transmits 92. The
other 8 may either have been absorbed or reflected from the surface of the
plate. According to Melloni, the latter is the case ; for if, instead of on one
plate, heat be allowed to fall on two or more plates whose total thickness
does not exceed that of the one, the quantity of heat arrested will be propor-
tional to the number of reflecting surfaces. He therefore concluded that
rock salt was quite diathermanous. Later experiments show that this con-
clusion is not strictly correct ; rock salt does absorb a very small proportion
of obscure rays.
The quantity of heat transmitted through rock salt is practically the
same, whether the plate be 1, 2, or 4 millimetres thick. But with other bodies
absorption increases with the thickness, although by no means in direct
proportion. This is seen to be the case in the table of absorption by liquids
—445] Influence of the Thickness and Nature OF Screens A427
at different thicknesses. The following table tells what proportion of
1,000 rays from a Locatelli’s lamp pass through a glass plate of the given
thickness :—
MDickness Intiiinmerces. 0,5 ff 2 @ueetemse O75)! S
Rays transmitted . - 775 733 682 653 634 620 609 600 592
The absorption takes place in the first layers ; the rays which have passed
these possess the property of passing through other layers ina higher degree,
so that beyond the first layers the heat transmitted approaches a certain
constant value. If a thin glass plate be placed behind another glass plate
a centimetre thick, the former diminishes the transmission by little more
than the reflection from its surface. But if a plate of alum were placed
behind the glass plate, the result would be different, for the latter is opaque
for much of the heat transmitted by glass.
Heat, therefore, which has traversed a glass plate traverses another plate
of the same material with very slight loss, but is very greatly diminished by
a plate of alum. Of I00 rays which had passed through green glass or
tourmaline, only 5 and 7 were respectively transmitted by a similar plate of -
alum. A plate of blackened rock salt only transmits obscure rays, while
alum extinguishes them. Consequently, when these two substances are
superposed, a system impervious to light and heat is obtained.
These phenomena find their exact analogies in the case of hight. The
different sources of heat correspond to flames of different colours, and the
screens of various materials to glasses of different colours. A red flame
looked at through a red glass appears quite bright, but through a green glass
it appears dim or is scarcely visible. So in like manner heat which has
traversed a red glass passes through another red glass with little diminu-
tion, but it is almost completely stopped by a green glass. Rock salt at
150° emits only one kind of heat ; it is »zonothermadl, just as sodium vapour
is monochromatic.
Different luminous rays being distinguished by their colours, Melloni
gave the name of ‘¢hermocrose or heat coloration to these different obscure
calorific rays. The invisible portion of the spectrum is accordingly mapped
out into a series of spaces, each possessing its own peculiar feature corre-
sponding to the coloured spaces which are seen in that portion of the spec-
trum visible to our eyes.
Besides thickness and colour, the polish of a substance influences the
transmission. Glass plates of the same size and thickness transmit more
heat as their surface is more polished. Bodies which transmit heat of any
kind very readily are not heated. Thus a window pane is not much heated
by the strongest sun’s heat ; but a glass screen held before a common fire
stops most of the heat, and is itself heated thereby. The reason of this is
that by far the greater part of the heat from a fire is obscure, and glass is
opaque to this kind of heat. |
445. Diffusion of heat.—When}a ray of light falls upon an unpolished
surface in a definite direction, it is decomposed into a variety of rays which
are reflected from the surface in all directions. This irregular reflection is
called afuston, and it is in virtue of it that bodies are visible when light
falls up6n them. A further peculiarity is, that all solar rays are not equally
428 On Heat : [445-
diffused from the surface of bodies. Certain bodies diffuse certain rays and
absorb others, and accordingly appear coloured. The red colour of a gera-
nium is caused by its absorbing all the rays, excepting the red, which are
irregularly reflected. Just as is the case with transmitted light in transparent
bodies, so with diffused hight in opaque ones ; for if a red body is illuminated
by red light it appears of a bright red colour, but if green light fall upon it
it is almost black. We shall now see that here again analogous phenomena
prevail with heat.
Various substances diffuse different thermal rays to a different extent ;
each possesses a peculiar thermocrose. Melloni placed a number of strips
of brass foil between the source of heat and the thermopile. They were
coated on the side opposite to the pile with lampblack, and on the other
side with the substances to be investigated. Representing the quantity of
heat absorbed by the lampblack by too, the absorption of the other bodies
was as follows :—
arisen eal | Copper at 400° | Copper at 100° |
| |
Lampblack : : : i 100 | 100 100
White lead : . : 56 | 89 100 |
Isinglass . ; 54 | 64 gI |
Indian ink : ‘ : ae 95 | 87 85 |
| Shellac . : F : ~ 47 70 D |
| Polished metal | Tas peer 13 3
Hence white lead absorbs far less of the heat radiated from incandescent
platinum than lampblack, but it absorbs the obscure rays from copper at
100° as completely as lampblack. Indian ink is the reverse of this; it
absorbs obscure rays less completely than luminous rays. Lampblack
absorbs the heat from all sources in equal quantities, and very nearly com-
pletely. In consequence of this property all thermoscopes which are used
for investigating radiant heat are covered with lampblack, as it is the best-
known absorbent of heat. The behaviour of metals is the reverse of that of
lampblack. They reflect the heat of different sources in the same degree.
They are to heat what wz¢e bodies are to light.
As coloured light is altered by diffusion from several bodies, so Knoblauch
has shown that the different kinds of heat are altered by reflection from dif-
ferent surfaces. The heat of an Argand lamp diffused from white paper
passes more easily through calcspar than when it has been diffused from
black paper.
The rays of heat, like the rays of light, are susceptible of polarisation
and double refraction. These properties will be better understood after the
subject of light has been treated.
446. Relation of gases and vapours to radiant heat.—This subject was
investigated by Tyndall ; the apparatus he used is represented in the adja-
cent figure, the arrangement being looked upon from above.
A (fig. 415) is a cylinder about 4 feet in length and 24 inches in diameter,
placed horizontally, the ends of which can be closed with rock salt plates ;
—446] Relation of Gases and Vapours to Radiant Heat 429
by means of a lateral tube at 7 it can be connected with an air-pump and
exhausted ; while at ¢ is another tube which serves for the introduction of
gases and vapours. T is a sensitive thermopile connected with an extremely
delicate galvanometer, M.
The deflections of this galvanometer were proportional to the differences of
temperature of the faces of the thermopile up to about 30° ; beyond this
point the proportionality no longer held good, and accordingly, for greater
differences, a table was empirically constructed, in which the value of the
higher deflections was expressed in units; the unit being the difference of
temperature necessary to move the needle through one of the lower degrees.
C was a source of heat, which usually was either a Leslie’s cube filled
with boiling water, or else a sheet of blackened copper heated by gas. Now,
when the source of heat was permitted to radiate through the exhausted
ube, the needle made a great deflection ; and in this position a very con-
siderable degree of absorption would have been needed to produce an
alteration of 1° of the galvanometer. Andif to lessen this deflection a source
of heat of lower temperature had been used, the fraction absorbed would be
correspondingly less, and might well have been insensible. Hence Tyndall
adopted the following device, by which he was enabled to use a powerful
flux of heat, and at the same time to discover small variations in the quantity
falling on the pile.
Cc
ey)
Fig. 415
The source of heat at C was allowed to radiate through the tube at the
end of which the pile was placed ; a deflection was produced of, say, 70° ;
a second source of heat, D, was then placed near the other face of the pile,
the amount of heat falling on the pile from this compensating cube being
regulated by means of a movable screen S. Since the strength of the thermo-
electric current, and therefore the deflection of the galvanometer needle,
depends upon the difference of temperature of the two faces.of the thermo-
pile, it is clear that when the compensation by D is perfect there will be no
deflection, however high may be the temperature on both sides. In the
arrangement just described, by means of the screen S, the radiation from
the compensating cube was caused to neutralise exactly the radiation from
the source C ; the needle consequently was brought down from 70° to zero,
and remained there so long as both sources were equal. If now a gas or
vapour be admitted into the exhausted tube, any power of absorption it may
possess will be indicated by the destruction of this equilibrium, and pre-
ponderance of the radiation from the compensating cube by an amount
corresponding to the heat cut off by the gas. Examined in this way, air,
hydrogen, and nitrogen, when dried by passing through sulphuric acid, were
found to exert an almost inappreciable effect; their presence as regards
430 On Fleat [446-
radiant heat being but little different fromavacuum. But with ethylene and
other complex gases the case was entirely different. Representing by the
number 1 the quantity of radiant heat absorbed by air, ethylene absorbs
g70 times, and ammoniacal gas 1,195 times, this amount. In the following
table is given the absorption of obscure heat by various gases, referred to
air as unity :—
Absorption |! Absorption
Name of gas ‘under 30 inches|| Name of gas ‘under 30 inches
i of pressure | of pressure
Air I | Carbonic acid . a go
| Oxygen I || Nitrous oxide. os
Nitrogen I | Marsh gas . ‘ 403
Hydrogen , I | Sulphurous acid . . 710 .
Chlorine ; é fe 39 |) Ethylene. ~. ; . 970
Hydrochloric acid a 62 | Ammonia . : VINE SiO5
If, instead of comparing the gases at a common pressure of one atmo-
sphere, they are compared at a common pressure of an inch, their differences
in absorption are still more strikingly seen. Thus, assuming the absorption
by 1 inch of dry air to be 1, the absorption by 1 inch of ethylene is 7,950,
and by the same amount of sulphurous acid 8,800.
447. Influence of pressure and thickness on the absorption of heat by
gases.—The absorption of heat by gases varies with the pressure; this
variation is best seen in the case of those gases which have considerable
absorptive power. Taking the total absorption by atmospheric air under
ordinary pressure at unity, the numbers of ethylene under a pressure of 1,
3, 5, 7, and ro inches of mercury are respectively 90, 142, 168, 182, and 193.
Thus ethylene, at a pressure of one-thirtieth of an atmosphere, exerts go
times the absorption of air at ordinary pressure. And the absorption, it is
seen, increases with the density, though not in a direct ratio. Tyndall showed,
however, by special experiments, that for very low pressures the absorption
does increase with the density. Employing as unit volume of the gas a
quantity which measured only »4 of a cubic inch, and admitting succes-
sive measures of ethylene into the experimental tube, it was found that up
to 15 measures the absorption was directly proportionate to the density in
each case.
In these experiments the length of the experimental tube remained the
same, whilst the pressure of the gas within it was caused to vary ; in subse-
quent experiments the pressure of the gas was kept constant, whilst the
length of the tube was, by suitable means, varied from o:o! of an inch up to
so inches. The source was a heated plate of copper ; of the total radiation
from this nearly 2 per cent. was absorbed by a film of ethylene -o1 of an
inch thick, upwards of 9 per cent. by a layer of the same gas ol of an inch
thick, 33 per cent. by a layer 2 inches thick, 68 per cent. by a column 20
inches long, and 77 per cent. by a column rather more than 4 feet long.
448. Absorptive power of vapours.—The absorptive power of ethy-
lene is exceeded by that of-several vapours. The liquid from which the
—448] Absorptive Power of Vapours 431
vapours were to be produced was enclosed in a small flask, which could be
attached with a stop-cock to the exhausted experimental tube. The absorp-
tion was then determined after admitting the vapours into the tube in
quantities measured by the pressure of the barometer gauge attached to the
air-pump.
The following table shows the absorption of vapours under pressures
varying from o'l to 4 inch of mercury :—
Absorption under pressure in inches of mercury
Name of vapours
| o'r | ou T‘o
| Carbon bisulphide. 15 47 | 62
Benzole : : : Saul 66 182 | 267
| Chloroform . ! ; 28 85 182 | 236
ieEther =! f é 2 300 710 | 870
| Alcohol . , ‘ . hy 325 622 |
Acetic ether . ; : : 590 986 ie MEIOS
These numbers refer to the absorption of a whole atmosphere of dry air
as their unit, and it is thus seen that a quantity of carbon bisulphide
vapour, the feeblest absorbent yet examined, which only exerts a pressure of
the 34, of an atmosphere, gave fifteen times the absorption of an entire
atmosphere of air ; and acetic ether, under the same conditions, 590 times
as much. Comparing air at a pressure of o'r with acetic ether of the same
pressure, the absorption of the latter would be more than 17,500 times as
great as that of the former.
Odours from the essential oils exercised a marked influence on radiant
heat. Dry air was allowed to pass through a tube containing dried paper
impregnated with various essential oils, and then admitted into the experi-
mental tube. Taking the absorption of dry air as unity, the following were
the numbers respectively obtained for air scented with various oils :—
Patchouli 31, otto of roses 37, lavender 60, thyme 68, rosemary 74, cassia 109,
aniseed 372. Thus the perfume of a flower-bed absorbs a large percentage
of the heat of low refrangibility emitted from it.
Ozone prepared by electrolysing water was also found to have a remark-
able absorptive effect. The small quantity of ozone present in electrolytic
oxygen was found in one experiment to exercise 136 times the absorption
of the entire mass of the oxygen itself.
But the most important results are those which follow from Tyndall’s
experiments on the behaviour of aqueous vapour to radiant heat. The experi-
mental tube was filled with perfectly dry air, and the absorption was found to
be one unit. Exhausting the tube, and admitting the ordinary undried, but not
specially moist, air from the laboratory, the absorption now rose to 72 units.
The ‘difference between dried and undried air can only be ascribed to the
aqueous vapour the latter contains. Thus on a day of average humidity the
absorption due to the transparent aqueous vapour present in the atmosphere
is 72 times as great as that of the air itself, though in quantity the latter is
about 200 times greater than the former. Analogous results were obtained
432 On Heat [448—
on different days, and with specimens of air taken from various localities.
When air which had been specially purified and dried was allowed to pass
through a tube filled with fragments of moistened glass and examined, it
was found to exert an absorption 90 times that of dry air. In other experi-
ments Tyndall suppressed the use of rock salt plates in his experimental
tube, and even the tube itself, and yet in every case the results were such as
to show the great power which aqueous vapour possesy2s as an absorbent of
radiant heat.
The absorptive action which the aqueous vapour in the atmosphere exerts
on the sun’s heat has been established by a series of actinometrical observa-
tions made by Soret at Genevaand on the summit of Mont Blanc ; he found
that the intensity of the solar heat on the top of Mont Blanc is £ of that
at Geneva; in other words, that of the heat which is radiated at the height
of Mont Blanc, about 4 is absorbed in passing through a vertical layer of
the atmosphere 14,436 feet in thickness. The same observer has found that
with the sun at heights which are virtually equal there is the smallest trans-
mission of heat on those days on which the pressure of aqueous vapour is
greatest ; that is, when there is most moisture in the atmosphere.
449. Radiating power of gases.—Tyndall also examined the radiating
power of gases. A red-hot copper ball was placed so that the current of
heated air which rose from it acted on one face of a thermopile ; this action
was compensated by a cube of hot water placed in front of the opposite face.
On then allowing a current of dry ethylene from a gasholder to stream
through a ring burner over the heated ball and thus supplant the ascending
current of hot air, it was found that the gas radiated energetically. By com-
paring in this manner the action of many gases it was discovered that, as is
the case with solids, those gases which are the best absorbers are also those
which radiate most freely.
450. Dynamic radiation and absorption.—A gas when permitted to
enter an exhausted tube is heated in consequence of the collision of its par-
ticles against the sides of the vessel ; it thus becomes a source of heat, which
is perfectly capable of being measured. Tyndall calls this dynamic heating.
In like manner, when a tube full of gas or vapour is rapidly exhausted, a
chilling takes place owing to the loss of heat in the production of motion ;
this he calls dynamic chilling or absorption.
He could thus determine the radiation or absorption of a gas without
any source of heat external to the gas itself. An experimental tube was
taken, one end of which was closed with a polished metal plate, and the
other with a plate of rock salt ; in front of the latter was the face of the pile.
The needle being at zero, and the tube exhausted, a gas was allowed quickly
to enter until the tube was full, the effect on the galvanometer being noted.
This being only a transitory effect, the needle soon returned to zero; the
tube was then rapidly pumped out, by which a sudden chilling was produced,
and the needle exhibited a deflection in the opposite direction. Comparing
in this way the dynamic heating and chilling of various gases, those gases
which are the best absorbers were also found to be the best radiators.
Polished metallic surfaces are, as we have seen (432), bad radiators,
but radiate freely when covered with varnish. Tyndall made the curious
experiment of varnishing a metallic surface by a film of gas.. A Leslie’s
—451] Relation of Absorption to Molecular State 433
cube was placed with its polished metal side in front of the pile, and its effect
neutralised by a second cube placed before the other face of the pile. On
allowing a stream of ethylene or of coal gas to flow over the metal face of
the first cube, a copious radiation from that side was produced as long as
the flow of gas continued. Acting on the principle indicated in the fore-
going experiment, Tyndall determined the dynamic radiation and absorp-
tion of vapours. The experimental tube containing a vapour under a
small known pressure, air was allowed to enter until the pressure inside
the tube was the same as that of the atmosphere. In this way the enter-
ing air, by its impact against the tube, became heated ; and its particles
mixing with those of the minute quantity of vapour present, each of them
became, so to speak, coated with a layer of the vapour. The entering air
was in this case a source of heat, just as in the above experiments the
Leslie’s cube was. Here, however, one gas varnished another ; the radia-
tion and subsequently the absorption of various vapours could thus be
determined.
Vapours were found to differ very materially in their power of radiating
under these circumstances ; of those tried carbon bisulphide was the worst
and boracic ether the best radiator. In all cases the best absorbents were
also the best radiators.
451. Relation of absorption to molecular state.—After examining the
absorption of heat by vapours, Tyndall tried the same substances in a liquid
form in the same conditions of experiment. Thesource of heat was a spiral
of platinum heated to redness by an electric current of known strength ; and
plates of rock salt were invariably employed in the case of both vapours and
liquids. Finally, the absorption by the vapours was re-measured ; in this
case by introducing into the experimental tube, not, as before, equal quanti-
ties of vapour, but amounts proportional to the density of the liquid. When
this last condition had been attained, it was found that the order of absorp-
tion by a series of liquids, and by the same series when turned into vapour,
was precisely the same. Thus the substances tried stood in the following
order as liquid and as vapour, beginning with the feeblest absorbent, and
ending with the most powerful :—
Liquids Vapours
Carbon bisulphide . . Carbon bisulphide.
Chloroform . : : ; : . Chloroform.
Ethyl iodide. ¢ : : ; . Ethyl iodide.
Benzole ; J : ‘ 5 . Benzole.
Ether ©. ; : . 4 L/P Ether
Alcohol : : : : é . Alcohol.
Water
A direct determination of aqueous vapour could not be made, on account
of its small elastic force and the hygroscopic nature of the rock salt. But the
undeviating regularity of the absorption by all the other substances in the list,
both as liquids and vapour, establishes the fact, which is corroborated by
the experiments already mentioned, that aqueous vapour is one of the most
energetic absorbents of heat.
In this table it will be noticed that those substances which have the
¥ F
434 On Feat [451—
simplest chemical constitution stand first in the list, with one anomalous
exception, namely, that of water. Inthe absorption of heat by gases, Tyndall
found that the elementary gases were the feeblest absorbents, while the
gases of most complex constitution were the most powerful absorbents. Thus
it may be inferred that absorption is mainly dependent on chemical consti-
tution; that is to say, that absorption and radiation are molecular acts
independent of the physical condition of the body.
Tyndall discovered that the radiation of powders is similar to that of the
solids from which they were derived, and therefore differs greatly zzfer se.
The absorbent power of powders was also found to correspond with their
radiative power—which, as we have shown, is the case with solids and gases,
and is doubtless also true for liquids. The powders were attached to the tin
surfaces of a Leslie’s cube, in such a manner that radiation took place from
the surface of the powder alone. The following table gives the radiation in
units from some of the powders examined by Tyndall; the metal surface of
the cube giving a deflection of 15 units :—
Radiation from powders.
Rock salt 2 : ges Calcium sulphate. nitager
Mercury biniodide. sor, Red oxide of iron . LSA
Sulphur . i yoo Hydrated zinc oxide . 804
Calcium carbonate wo? Iron sulphide . f on fey
Dead ‘oxide. : ne we. Lampblack . ; BAO
These substances are of various colours. Some are white, such as rock
salt, calcium carbonate and sulphate, and hydrated zinc oxide; some are
red, such as mercury biniodide and lead oxide; whilst others are black,
as iron sulphide and lampblack. The colours, therefore, have no influence
on the radiating power: rock salt, for example, is the feeblest of radiators,
and hydrated zinc oxide one of the most powerful.
Nearly a century ago Franklin made experiments on coloured pieces of
cloth, and found their absorption, indicated by their sinking into snow on
which they were placed, to increase with the darkness of the colour. But
all the cloths were equally powerful absorbents of obscure heat, and the
effects noticed were only produced by their relative absorptions of light. In
fact, the conclusions to be drawn from Franklin’s experiments only hold good
for luminous heat, especially sunlight such as he employed.
452. Applications.—The properties which bodies possess of absorbing,
emitting, and reflecting heat meet with numerous applications in domestic
economy and in the arts. Leshe stated in a general manner that white
bodies reflect heat very well, and absorb very little, and the contrary is
the case with black substances. As we have seen, this principle is not
generally true, as Leslie supposed ; for example, white lead has as great an
absorbing power for non-luminous rays as lampblack (445). Leslie’s principle
applies to powerful absorbents like cloth, cotton, wool, and other organic
substances when exposed to luminous heat. Accordingly, the most suitable
coloured clothing for summer is just that which experience has taught us to
use, namely, white, for it absorbs less of the sun’s rays than black clothing,
and hence feels cooler.
~453] } Applications 435
The polished fire-irons before a fire are cold, whilst the black fender is
often unbearably hot. If, on the contrary, a liquid is to be kept hot as long
as possible, it must be placed in a brightly polished metallic vessel, for
then, the emissive power being less, the cooling is slower. Hence it is
advantageous that the steam pipes, &c., of locomotives should be kept
bright. In the Alps, the mountaineers accelerate the fusion of the snow by
covering it with earth, which increases the absorbing power.
‘In our dwellings, the outside of stoves and of hot-water apparatus ought
to be black, and the insides of fireplaces ought to be lined with firebrick, in
order to increase the radiating power towards the apartment.
It is owing to the great diathermancy of dry atmospheric air that the
higher regions of the atmosphere are so cold, notwithstanding the great heat
which traverses them; whilst the intense heat of the sun’s rays on high
mountains is probably due to the comparative absence of aqueous vapour at
these elevations.
As nearly all the luminous rays of the sun pass through water, and the
sun’s radiation as we receive it on the surface of the earth consists of a
large proportion of luminous rays, accidents have often arisen from the con-
vergence of these luminous rays by bottles of water which act as lenses. In _
this way gunpowder could be fired by the heat of the sun’s rays concen-
trated by a water lens; and the drops of water on leaves in greenhouses
have been found to act as lenses, and burn the leaves on which they
Tesh.
Certain bodies can be used (440) to separate the heat and light radiated
from the same source. Rock salt coated with lampblack, or still better
with iodine, transmits heat, but completely stops light. On the other hand,
alum, either as a plate or in solution, or a thin layer of water, is permeable
to light, but stops all the heat from obscure sources. This property is made
use of in apparatus illuminated by the sun’s rays, in order to sift the
rays of their heating power; a vessel full of water or a solution of alum
is used with the electric light when it is desirable to avoid too intense a
heat.
In gardens, the use of shades to protect plants depends partly on the
diathermancy of glass for heat from luminous rays and its athermancy for
obscure rays. The heat which radiates from the sun is largely of the former
quality, but by contact with the earth it is changed into obscure heat, which,
as such, cannot retraverse the glass. This explains the manner in which
greenhouses accumulate their warmth, and also the great heat experienced
in summer in rooms having glass roofs, for the glass in both cases acts, as
it were, as a valve which effectually entraps the solar rays. On the same
principle plates of glass are frequently used as screens to protect us from the
heat of a fire ; the glass allows us to see the cheerful light of the fire, but
intercepts the larger part of the heat radiated from the fire. Though the
screens thus become warm by the heat they have absorbed, yet, as they
radiate this heat in all directions towards the fire as well as towards us, we
finally receive less heat when they are interposed.
453. Attraction and repulsion arising from radiation.—Crookes dis-
covered a highly remarkable class of phenomena which are due to the
radiant action of heated and of luminous bodies. These phenomena are
FF 2
436 On Feat [453—
most conveniently illustrated by means of an instrument which he has
devised, and which is called the ~adtometer, the construction of which 1s as
follows :—A glass tube (fig. 416), with a bulb blown on it, is fused at the
bottom to a glass tube which at one end serves to rest the whole apparatus
in a wooden support. In the other end is fused a fine steel point. On this
rests a small vane or fly, consisting of
four arms of aluminium wire fixed at one
end to a small cap, while at the others
are fixed small discs or lozenges of thin
mica, coated on one side with lampblack.
The weight of the fly is not more than
two grains.
In order to keep the fly on the pivot
a tube is fused in the upper part of the
bulb which reaches down to and just sur-
rounds the top of the cap, without, how-
ever, touching it; the other end of this
tube is drawn out and connected with an
arrangement for exhausting the air by the
Sprengel pump (208) or by chemical
means : when the desired degree of ex-
haustion has been attained this can be
sealed. By keeping the apparatus during
exhaustion in a hot-air bath at a tempera-
ture of 300°, the gases occluded on the
inner surface of the glass, and by the
vanes, are got rid of.
If a source of light or of heat, a
candle for instance, is brought near the
fly, it is attracted, and the fly rotates
slowly in a direction showing that the
blackened side moves towards the light ;
this movement, indicating an attraction,
depends on a certain state of rarefaction.
If, however, the apparatus be connected
with an arrangement which allows the
pressure to be varied, this rotation gradu-
ally diminishes in rapidity as the air
= within is further rarefied, until a certain
Fig. 416 ) point is reached at which it ceases. If
now the rarefaction is pushed further, the
highly remarkable phenomenon is observed that repulsion succeeds to
attraction, and that the fly now rotates in the direction away from the source
of heat. In a double radiometer, in which two flies are pivoted indepen-
dently one over the other, having their blackened sides opposite each
other, the flies rotate in opposite directions on the approach of a lighted
candle. When a cold body, such as a piece of ice, is brought near, instead
of a hot one, exactly the opposite effects are observed; when the vessel
contains air a pith ball svspended at one end of a light arm is repelled, the
—453] dia iv; Z, RS
SSSA GAA AAAS SS SS SSN SS SSS SNS SN SSS NS SSS SITS SN ISS INSISTENT
SNWH
FS RE BSRIAWSG
¥ NISRA SSS SSS SIS SSISSISS SSIS SS SS SS SSSI SSSI INSS SSN SAQAA,/
Fig. 433
encircling the boiler with flues it is endeavoured to get all the heat possible
from the gases before they are allowed to pass away up the chimney. The
principal f¢tings or mountings of the boiler are indicated in the figures, and
are as follows : G is a dome on which stands the s¢op-valve N through which
the steam is carried to the engine. The object of the dome is to take the
steam from a point far away from the water
line, so that it may be as dry as possible. P
is a safety valve, held down on its seat by
the action of a weighted lever, and so ad-
justed that as soon as the pressure of steam
reaches its intended maximum and tends to
rise beyond it, the valve is lifted and the steam
: rushes away into the air. Q isa man-hole
Edy door by which access is had to the interior
: of the boiler, when it is empty and out of
use, for cleaning and repair. Ris a pressure
gauge or indicator, standing in front of the
shell, showing, by a hand working in front ofa
dial plate, the ‘ boiler pressure’ or amount by
which the pressure of steam inside the boiler
exceeds that of the atmosphere surrounding it. S is a water gauge, a glass
tube connected at top and bottom to the boiler, its upper end to the steam
space, and the lower end to the water space. The water stands in the glass
tube at the same level as in the boiler, and the fireman can see at a glance
whether it is at the right height. This matter is of great importance,
because an accidental fall of water-level is a frequent cause of boiler explo-
sions. If, for instance, the water fell so low as to leave the top of the furnace
B uncovered, the plates would get red-hot and soften so much as to collapse
Ss
SSSGEVN
Fig. 434
477] Cornish Engine 465
under the action of the steam pressure, with consequences that might be
most serious. :
In marine boilers, when it is of the greatest importance to get as much
heating surface as possible into a small space, and similarly in the locomotive
boiler to be presently described, the hot gases after leaving the furnace are
made to pass through a number of small tubes instead of one large one as in
fig. 433. Such boilers are called szzltitubular botlers.
Of late years the shells of large boilers have frequently been made of
“mild steel,’ produced by the Bessemer or Siemens- Martin processes, rather
than of wrought iron. In locomotive boilers, where the combustion is very
rapid and intense, the fire-boxes are frequen made of copper, a mnych
better conductor a heat than either iron or steel.
477. Cornish engine.—Fig. 435 shows the oldest of all the types of
engines still in use, the Cornish pumping engine, which is worth examina-
Spear
SSB
== Oe
2)
SOOAD
AS
w
\\
AA
A
a
~~
mr i | I | | NX
pe Seba pa i M ie it mt | l Tee Hl IN
a ul) le le
ECC ll.
ao \~ \
Be : ~
SAR Xr CS 9 WR
Fig. 435
tion both for its historical interest and on account of the special way in
which it works. (In the figure all details except those absolutely necessary
to illustrate the action of the engine are omitted.) The engine has a vertical
cylinder A (often of very great size, and with as much as Io or I! ft. stroke),
in which works a piston P, whose rod is connected by a chain to a sector on
the end of a beam B. Beside the cylinder is a chamber C containing the
valves for admitting and discharging steam, whose mode of working will be
presently described. At the further end of the beam a second sector is
HH
466 On Feat [477—
connected with the pump-rod, at the upper end of which is placed a heavy
counterweight Q. Below the cylinder a pipe M leads to a chamber N called
the condenser, into which a jet of water from the tank in which it stands
continually plays. The condenser in its turn is connected with a pump
called an air-pump, worked from the beam by the rod E, and fitted with
suction and discharge valves, and valves in its piston in the usual way.
We can follow the working of the engine easily by supposing the piston
to start at the top of its stroke. The valves are then in the position shown,
uz open, 7 and o closed. Steam passes from the boiler through the pipe T
to the top of the piston, and forces it down against the small pressure of the
steam below it, this steam escaping into the condenser through the valve o
and the pipe M. The pump-rods or fzt work, and the weight Q, are thus
lifted to the top of their stroke. When the piston arrives at the bottom of
its stroke the valves #7 and o are shut and wz is opened. This allows free
communication between the two sides of the piston, and so puts it into
equilibrium. The counter-weight Q, together with the pump-rods, is made
somewhat heavier than the piston and rod plus the whole weight of the
column of water to be lifted. It therefore falls slowly (the whole affair thus
becoming an Atwood’s machine (78) on an enormous scale), and forces
up the water through the pumps. As soon as the piston has once more
got to the top of its stroke, by which time of course all the steam has been
transferred to its under side, the position of the valves is again reversed,
and the piston once more begins to fall. The steam below the piston is
suddenly put into communication with the condenser N, into which a jet of
cold water is always playing. It is therefore reduced in temperature almost
instantaneously, much of it is condensed into water, and the rest, which still
fills the space below the piston, is necessarily reduced to a pressure of only
about 3 pounds per square inch or about 4 of an atmosphere. As the pres-
sure of the steam coming direct from the boiler in such engines is often 50
pounds per square inch above that of the atmosphere, it follows that the differ-
ence of pressure on the two sides of the piston in such a case is 50+ 15 —3
=62 pounds per square inch, and it is this difference of pressure which
compels the piston to move downwards and lift all the weight at the other
end of the beam. The condensed steam and the condensing water fall
together at the bottom of the condenser, and are continually removed (along
with the uncondensed steam and any air that may be present) by the azr
pump, which is a simple lift pump with a valve in its piston (220).
In all modern Cornish engines the beams are of iron and the sector and
chains are replaced by an arrangement of iron links forming a parallel motion
which it is not necessary here to describe. The simple arrangement for
working the valves, shown in outline in the figure, is also replaced by a much
more complicated apparatus in which, by means of cataracts, any required
length of pause can be made between the strokes of the engine, a matter
which is sometimes of importance in heavy pumping work. It will be
noticed that by the peculiar single-acting method of working adopted in
the Cornish engine, the velocity of the down stroke (also called the steamer
stroke, or the zndoor stroke) depends—other things being equal—upon the
steam pressure, but the velocity of the up stroke (eguzl¢brium or outdoor
stroke) depends solely on the overplus weight put on the outer end of the
—479] Distribution of Steam. Slide Valves 467
beam. In this way a slow and quiet upward motion can be given to the
water, no matter how quickly the steam may move the piston.
478. Ordinary horizontal engine.—The engines now most largely
used in factories for driving machinery differ altogether in their action from
the Cornish engine. In them the cylinder is generally horizontal, and the
crank is driven through a connecting rod only, without the intervention of
any beam. Such an engine is shown in fig. 436. Here A is the steam
cylinder, B the valve chest, or chamber in which works the valve whose mode
of action is described in the next article. D is the main shaft, on the inner
end of which is the crank driven by the connecting rod E. C is an eccentric
(fig. 438), which works the valve by the rod N._ F is a governor controlling
the admission of steam to the cylinder by the valve H. M 1s the dedplate
or frame of the engine, and L the flywheel.
A few words are necessary about the governor. This apparatus, an
invention of James Watt’s, consists of two weighted arms hinged at the top,
iN
(
oo = mn [iw i i i
eT nl Tm i il il TT me
which fly outward when the speed of rotation is increased and drop together
when it is reduced. The outward or inward motion of the arms is caused
by a simple arrangement to turn the spindle G and so to close or open the
valve H, which admits steam through K to the cylinder. In this way the
engine automatically controls its own speed (480).
479. Distribution of steam. Slide valves.—Figs. 437 and 438 show
details as to the working of the valve and the distribution of the steam
in the engine just described. The former is a longitudinal section of the
cylinder shown in fig. 436. A is the cylinder itself, B the piston, C the
piston-rod, D the stuffing box through which the piston passes steam-tight.
It will be seen that a fort or passage L communicates between each end of
the cylinder and the surface on which the valve works, or valve face. On
this face, and between the two steam-ports, comes a third point M, communi-
cating directly with the atmosphere or with a condenser as the case may be.
The valve G is shaped in section something like an irregular D, and is often.
H H 2
468 On Feat [479-
called a ‘D’ valve in consequence. It is moved continuously backwards
and forwards upon the valve face by the valve rod H working in the stuffing-
box K. When in the position, shown in the figure, the steam enters by F,
and passes into the left-hand end of the cylinder (past the edge of the
valve) and pushes the piston from left to right. The steam at present in
the cylinder (as shown by the arrows) passes out at L, and through the
under part of the valve G to the exhaust port M. As the piston moves on,
the valve at first moves in the same direction, opening the port a little wider,
then gradually moves back again and closes the admission port altogether.
The point at which this occurs is called the point of cut of Nomore steam
is allowed to enter the cylinder for that stroke, the piston being pushed
forward by the pressure of the elastic steam expanding behind it. By the
time the piston has got to the end of its stroke, the position of the valve is
just reversed from that in which it is shown, and steam passes into the
cylinder through the right-hand port, driving the piston from right to left,
while the steam which has already done duty in the left-hand end of the
cylinder passes away, in its turn, through the exhaust.
BN
bs AN
WHETEEEEEHEEELEpLLfltli~
Up
YM MM
LM/;
WH
Fig. 437 Fig. 438
The eccentric from which the valve receives its motion (lettered C in fig.
437) is shown in detail in fig. 438. Here D is the crankshaft and A a disc
(solid or ribbed) fixed eccentrically on it so asto revolve with it. Encircling
this disc (which is the eccentric) is a strap or ring B (made in two pieces for
the sake of getting on and off), rigidly connected with a rod C, which is
coupled by a pin to the valve-rod E. .In each revolution of the eccentric
the valve-rod is moved backwards and forwards through a space equal to
twice the eccentricity of the eccentric, or distance between the centres of D
and of A. The eccentric is thus equivalent exactly to a crank having a
radius equal to its eccentricity. It is used instead of a crank because it
does not require any gap to be left in the shaft, as a crank would do, but
allows it to be carried continuously on.
In locomotive or marine engines two eccentrics are commonly used, one
so placed as to give the valve the right motion when the shaft rotates in
one direction, and one rightly placed for the other. By apparatus called
reversing gear either one or the other can be caused to move the valve, so
that the engine can be made, at pleasure, to turn the shaft in one or the
other direction.
—480] Locomotives 409
480. Locomotives.—Locomotive engines, or simply locomotives, are
steam engines which, mounted on a carriage, propel themselves by trans-
mitting their motion to wheels. The whole machine, fig. 439, boiler and
engine, is fixed to a wrought-iron /yvame, which, therefore, is made strong
Fig. 439
enough to carry the whole weight, and which in turn transmits that weight
to the axle-boxes (or bearings in which the ax/es turn), by means of springs,
and thence through the wheels to the rails. The doz/er is of a special type,
adopted in order to get the greatest possible heating surface in a very limited
470 On Heat [480-
space. It consists of three parts—the five-dox, barrel, and smoke-box. The
fire-box, in the left of the engraving, is generally a more or less rectangular
box, with a flat top, placed inside a second box of somewhat similar shape,
but with a semi-cylindrical, or, as in the figure, domed top. In the inner
fire-box are the fire-bars, on which the fuel is placed through a door in front.
The space between the inner and outer boxes is filled with water to a height
considerably over the top of the inner one, and communicates freely with a
long cylindrical darre/, closed at the other end by the soke-box. This
barrel, which forms the main bulk of the boiler, is filled with water to within
nine or ten inches of its upper side. It is traversed from end to end by a
great number of small tubes (about 14 inch in diameter) which communicate
with the inner fire-box at the one end, and with the smoke-box at the other.
They, therefore, are entirely immersed in the water from end to end. The
gases of combustion, formed in the inner fire-box, pass through these tubes
to the smoke-box, and thence up the chimney, and impart most of their heat
to the water as they pass along. There are two steam cylinders, one on each
side of the frame, each one with its piston and connecting rod, etc., being
simply an ordinary high-pressure horizontal engine. Their exhaust steam
is discharged through a d/ast pipe into a nozzle inside the chimney near its
base, and this serves to excite the fierce draught which is required in order
that the necessary heat may be developed by the very small furnace. The
two cylinders work cranks at right angles to each other, so that one may be
in full action when the other is'at its dead point.
A locomotive such as that shown in the figure is called an outside
cylinder engine, on account of the position of its cylinders. In England
many engines have cylinders placed inside the frames, which are then called
inside cylinder locomotives. In express ‘engines the cylinders frequently
drive only one very large pair of wheels, as is shown in the figure. These
are called driving wheels, those on the front axle being leading wheels, and
on the rear axle ¢razling wheels. In the case of goods engines, however (as
well as in many other instances), when less speed but a greater pull is re-
quired, two or more pairs of wheels of the same diameter are connected
together by coupling rods, so that two or more axles may be directly or
indirectly actually driven by the engine. Such engines are called coupled
engines.
The action of the engine upon the wheels may cause them either to slip
round on the rails (in which case the engine, of course, does not move
onwards) or to roll on themin the usual way. To prevent slipping occurring
it is necessary to make the friction between the wheels and the rails as great
as possible. This is done by making as large a proportion of the whole
weight as possible rest on the driving or the coupled wheels, and also—when
bad weather causes the rails to be greasy or otherwise unusually slippery—
by increasing the coefficient of friction (47) between the wheels and the rails
by pouring sand on the latter. All locomotives are furnished with a sand-
box for this purpose.
The steam pressure in locomotives is greater than that commonly used
in any other engines, being often 120 to 130 Ibs. per square inch above the
atmosphere. In marine engines 70 to 80 Ibs. 1s often used, in stationary
engines seldom quite so much.
—481] Vartous Kinds of Steam Engine 471
The following is an explanation of the reference letters in fig. 439 :—A,
the main steam-pipe, conveying steam to the cylinder F, in which works a
piston P, driving the crank M through the connecting-rod K, rv are the
piston-rod guides, V the stuffing-box. The ‘exhaust steam is discharged
through the pipe E. (It will be remembered that the cylinder and all this
gear are duplicated on the other side of the engine.) DZ is the outer fire-
box and X the barrel of the boiler, both covered with felt and wood or sheet
iron to prevent loss of heat by radiation. The small tubes are seen at a,
Y is the smoke-box, and Q the chimney or funnel. TT are the springs
which transmit the weight of the frame to the axle-boxes. Of the smaller
details, GI is the arrangement for closing or opening the steam-admission
valve, BéC the reversing gear, RR feed-water pipes, N coupling rod for
attaching tender and rest of train, ez safety valves, 2 whistle, #z steps, 72
water gauge, ¢ cocks for blowing water out of cylinders, H cock for blowing
out boiler when necessary.
It is perhaps hardly necessary to explain that the breaking away of part
of the fire-box, cylinder, etc., is done in the drawing only for the sake of
showing clearly the internal construction.
481. Various kinds of steam engine.—Three types of steam engine
have been described: the Cornish engine, the ordinary horizontal engine,
and the locomotive engine. Others ought to be mentioned, although they
cannot be here described in detail. Compound engines are those in which
the steam is first used in the ordinary way in one cylinder and then trans-
ferred—of course at a comparatively low pressure—to another cylinder and
used in it before being sent away to the condenser. This type is practically
universal for marine purposes, and is very common for stationary engines.
Its main advantage is a thermodynamic one. In an ordinary engine the
cylinder walls are exposed alternately to the hot steam from the boiler
and the cool vapour passing to the condenser. The latter so reduces the
temperature of the iron, that when the first rush of fresh steam comes into
the cylinder, much of it is immediately condensed on the cool metal, and an
enormous quantity of heat is thereby lost. By passing the steam through
an intermediate, or low-pressure, cylinder on its way to the condenser, the
sides of the first or A¢gh-pressure cylinder are never exposed to condenser
temperature, but only to that of the steam as it passes to the low-pressure
cylinder ; they therefore are not so much cooled, and the loss of steam by
condensation on them is very much reduced. There is no mechanical gain,
as has sometimes been stated, in the use of two cylinders instead of one.
Sometimes the cylinder of an engine is enclosed ina second, slightly
larger, cylinder, and fresh steam at boiler pressure admitted to the annular
space so formed outside the working cylinder. The object of this is to re-
duce still further the condensation in the cylinder just alluded to. Such an
engine is said to be steam-jacketed.
A surface-condensing engine is one in which the steam is condensed by
contact with the surface of a number of small tubes through which cold
water is kept continually circulating without being itself actually mixed with
the condensing water. By this arrangement the condensed steam is kept
by itself, and being distilled water it can be used very advantageously to feed
the boiler again. Compound marine engines are almost invariably surface.
472 On Ffeat [481—
condensing. In this case the air-pump only takes away the condensed
steam, a separate pump, called a c¢vculating pump, being used to force the
condensing water through the tubes.
Engines without any condenser, like that shown in fig. 439, in which the
steam is exhausted directly into the atmosphere after it has done its work,
are often called high-pressure engines, but high pressures (of 80 to 90 pounds.
per square inch) are now frequently used in condensing engines, so that the
name may be somewhat misleading.
In such an engine as is shown in fig. 439 we have seen that the governor
keeps the speed constant, by closing or opening an exterior valve through
which the steam passes on its way to the main valve. An artificial resist-
ance is in this way opposed to the passage of the steam, by increasing
which the pressure can be reduced, and therefore the work done by the
steam, so that the engine will not run too fast if the resistance to its motion
be diminished (as by disconnecting some of the machines it is driving,
etc.). The actual weight of steam passing into the cylinder at each stroke
remains unchanged, but the amount of wsefu/ work the steam can do is.
diminished anincely by giving it some wseless work to do in addition, in
forcing its way through a constricted passage. This is now known to Se a
wasteful way of controlling speed. In modern engines, therefore, the
governor is frequently made to act by regulating the quantity of steam ad-
mitted by each stroke, and thus making the consumption of steam as nearly
as possible proportional to the work done. Engines so arranged, of which
the Corliss engine is one of the best known examples, are said to be fitted
with automatic cut-off gear.
There is a popular misconception, that somehow or other work is lost in
an engine of the ordinary type between the piston and the crank, the latter
receiving less work than is done on the former in consequence of the nature
of the mechanism connecting them. It is probably unnecessary to point
out here the fallacy of this notion, but it has received sufficient acceptance
to lead to the invention of a host of vofavry engines, in which it is endeavoured
to obtain the desired rotary motion in a somewhat more direct fashion.
Reuleaux has shown that in almost every case the mechanisms used in the
rotary engines are the same as those of ordinary engines, although disguised
in form, so that the idea of mechanical advantage is doubly a mistake, while
in almost every case the rotary engines possess such grave mechanical
defects that none of them have practically come into use.
482. Work of an engine. Horse-power.—The unit of work by which
the performance of an engine is measured is in this country always the foot-
pound. The number of foot-pounds of work done by the engine in any
given time is equal to the average effective pressure upon its piston during
that time, multiplied by the total distance through which the piston has
moved under that pressure. By average effective pressure is meant the
average value of the difference between the pressures on its two sides.
Taking the time as one minute, this quantity of work in foot-pounds is
equal to :—
Area of piston x mean intensity of pressure on piston x length of stroke
x number of strokes per minute.
The stroke must be taken in feet. If the area is in square feet, the
483] Indicator. Brake 473
pressure must be in pounds per square foot ; if the area is in square inches,
the pressure must be in pounds per square inch. If the strokes are doudble
strokes, each corresponding, that is, to one whole revolution of the shaft, the
length of stroke must be multiplied by 2. To find, for example, the work
done in one minute by an engine with cylinder 16 inches diameter and 24
inches stroke, making 50 (double) strokes per minute with a mean pressure
of 52 pounds per square inch, we have
(GISCRLIALO) x5 2: x (Chke 2) x 50 = 2,091,000 ft.-lbs.
The rate at which an engine does work is often measured in horse-fower of
33,000 ft.-Ilbs. per minute, an arbitrary unit supposed to represent the maxi-
mum rate at which work could actually be done by a horse. In the case
supposed the horse-power would be 2107000 = 63°4.
33,000
On the Continent the unit of work is a kilogrammetre, which is very
closely equal to 77 {ft.-lbs. The horse-power used abroad, of 75 kilo-
grammetres per second, is nearly 2 per cent. smaller than that in use in this
country.
483. Indicator. Brake.—By the expression work done by an engine we
may mean either of two things, viz.—the Zofa/ work done by the engine, or
what is called its useful, or effective, work. The total work is the actual work
done by the steam on the piston and obtained by calculation, as described
in the last paragraph. The useful work is what remains of this total after
deduction has been made of the work necessary to drive the engine itself
against its own frictional resistances. The total work of an engine is mea-
sured by means of an apparatus called an zwzdtcator, invented by Watt, of
which fig. 440 shows one of the most recent forms (Richard’s), omitting a
number of constructional details. The steam-engine indicator consists of a
small cylinder A, half a square inch in area, in which works a piston B, the
under side of which can be put into full communication with the cylinder
of the engine by opening the cock C. Between the top side of the piston
and the under side of the cylinder-cover is a spiral spring. The motion
of the piston-rod is transferred to a parallel motion DD, and so causes a
point E to move in a straight line up and down, its stroke being about
four times as great as that of the small piston. The indicator is fixed on to
the cylinder of the steam-engine near one end, so that when the cock C is
opened, there is the same pressure of steam on the indicator piston as on the
engine piston. This pressure forces up the piston, and the amount of com-
pression of the spring so caused is proportionate to the pressure causing it.
The upward motion of E, therefore, is proportional to the steam pressure.
In front of E is a vertical drum F, on which a strip of paper can be fixed,
and this drum is caused to rotate about its axis by attaching the cord G
to any suitable part of the engine. The paper thus moves horizontally
under the pencil, with a motion proportional to the stroke of the engine,
while the pencil moves up and down on the paper with a motion proportional
to the steam pressure on the piston. The two motions occurring simul-
taneously, the pencil traces on the paper a curve whose horizontal and
vertical ordinates are proportional to the two quantities just named, and
474 On Heat [483-
whose area is therefore proportional to the product of these quantities, or,
which is the same thing, to the work done by the piston as defined in the
last paragraph. The curve is called an indicator card, or zzditcator diagram,
and while its avea shows the whole work done by the steam, its fori shows
the engineer what is happening within the cylinder at each point of the
stroke, which he may often require to know.
Figs. 441 and 442 show two forms of indicator diagram. The curves
themselves, as drawn by the indicators, are lettered ABCD. Beside them
a scale of pressure in atmospheres is placed. In fig. 441 the steam is ex-
panded about seven times, and the back pressure is about 4 of an atmo-
sphere, the pressure during admission being five atmospheres. The engine
is a condensing one, and the diagram is fairly good. Fig. 442 is for a non-
condensing engine, the back pressure being above that of the atmosphere.
Ce
eo
oH
A:
3:
Ze
U7
SZ
=
—
i}
i}
INQ
4 bea
)
I:
Gini; Ti 7 i i‘ i i
Pressure tin Albmospheres
Fig. 441
Pressure tn Atmospheres
Fig. 440 Fig. 442
The steam is cut off (at B) only at about 3 of the stroke, so that it is not
working economically, and from the roundness of its corners the diagram
would be considered a poor one.
The wseful work of an engine is measured by an entirely different piece
of apparatus, called a dynamometer. This is used in many forms, but
fig. 443 shows the principle upon which the majority act. The apparatus
shown in the figure is known as a Prony’s friction brake. A is the shaft,
the usual work transmitted by which we require to find. Upon the shaft is
a fixed pulley B, embraced by two blocks B, and B,, which can be tightened
up by the screws at C, and C,. ‘To the lower block is fixed a lever D, from
which hangs a weight, and which has at its extremity a small pointer work-
ing against a short scale F. If such an apparatus be set in motion by
turning the shaft A, one of two things must happen: either the pulley must
—484] Efficiency of Heat Engines 475
slip round in the blocks, or it must so grip them as to carry both them and
the lever D round its own axis. The moment of resistance to the former is
x F, if ~ be the radius of the pulley and F the frictional resistance at its
p
Fig. 443
periphery ; that of the latter is RW, where R is the radius of the weight
and W the weight itself. In practice the screw C, is loosened just suffi-
ciently to keep the weight just lifted from the ground, while the pulley is
always turning round in the blocks, so that, therefore,
7 = RW.
The work done at the brake per minute is equal to the frictional resistance
multiplied by the distance through which it is overcome in the same time,
or, if 2 be the number of revolutions per minute,
= 2nrFu=27rRW2.
It is therefore just the same as if a resistance = W were continually being
overcome at the periphery of a wheel of radius R, making z turns per minute.
As the values of all the quantities in the expression 27RWz7 are very readily
determined, it will be seen that this brake affords a very simple way of
measuring the net work transmitted through the shaft of an engine.
The ratio ane mae gone shOw mapa Re , is called the efi-
total work’ work shown by indicator
ciency of the engine as a machine, or its mechanical efficiency. It is often as
much as 0°85, and sometimes even higher than o-9 or go per cent., being
generally greatest in large engines.
484. Efficiency of heat engines.—There is another ratio of efficiency
connected with the steam-engine, namely the ratio
Total work done by engine
Total heat expended -
what is called the effictency of the engine as a heat engine or its thermo-
dynamic efficiency. lf T, and T, be respectively the absolute temperatures
(508) of the steam and the feed water in any engine, then it can be shown
476 On Heat [484—
that such an engine, if working quite perfectly, could transform no more
than(“1—*2) of the heat which it receives into work. This fraction in the
t
case of a steam engine is seldom more than about 0°25. The value of the
actual efficiency of the engine is often from o'lo to o'14; while, therefore,
an ordinary steam engine, with such an efficiency, turns into work only from
z5 to 4 of the whole heat it receives, yet it may be turning into work 4 or
more of the whole heat which it could possibly transform into work if it
were perfect.
To increase the economy of steam engines we require to make the value
ot (222 larger. This is done either by raising T, or by lowering T,, or
1
both. The chief difficulty is that we cannot raise T, without increasing the
steam pressure, which it is often not convenient to do, while we cannot lower
T, below such a temperature, 50° to 60° F., as can readily be obtained
naturally at all seasons of the year.
485. Hot-air engines.—The difficulty as to T, just mentioned is got over
by the use of some fluid whose pressure is not a function of its temperature,
and naturally azv is the most convenient fluid for the purpose. Many ‘hot-
air’ engines have been designed, and some have found a considerable
measure of success commercially, as Rider’s, Hock’s, and Lehmann’s. In
all cases the engines consist essentially of one (or two) chambers placed so
that one end can be heated by a furnace and the other cooled by a refrige-
rator. The air is compelled to move from the cold space to the hot and back
again continually. When hot it is allowed to expand and push forward a
piston, when cold it is compressed by pushing back the piston again to its
original position. The difference between these two quantities of work is
the whole work done by the engine. By making T, avery high temperature,
the theoretical efficiency( “17 ny of an air engine may be made much
1
higher than that of a steam engine. But it is so much more difficult to attain
the theoretical efficiency in the air than in the steam engine, that its actual
efficiency is generally much lower than that of a steam engine. There are
constructive difficulties connected with the hot-air chambers, and with the
regulation of the speed, and these, as well as with the large bulk of most air
engines in proportion to their power, have stood greatly in the: way of their
development. No doubt, however, much more improvement would have
taken place in these engines had not gas engines come into prominence of
late years and proved much more convenient.
486. Gas engines.—Gas engines, like steam engines and air engines, are
heat engines, but in them the working fluid is ordinary coal gas mixed with
air, in«the proportion of about 1 to 11 by volume. The principle of action
is very simple :—The explosive mixture after being drawn into the cylinder
is set light to, the heat generated by the very rapid combustion, which
we call an explosion, causes the mixed gases to expand and drive forward
the piston. The great difficulty for many years was that the explosion was
so rapid that the comparatively slow-going piston could not keep up with it,
and the greater part of the energy of the explosion was lost by radiation and
conduction. In the more modern gas engines, however (Otto’s and Clerk’s.
—486] Gas Engines 477
and others), this difficulty is got over by compressing the charge before
igniting it, a treatment which is found to decrease very much the rapidity
of the explosion and so greatly increase the actual efficiency of the engine.
Fig. 444 shows the principal parts of an Otto ‘ Silent’ gas engine, as now made.
A is the cylinder, open at front and single-acting, in which works a deep
piston F, driving a crank in the usual manner. The cylinder is surrounded
by a water jacket, to prevent it from getting too hot. At the back of the
cylinder is a slide valve B, worked by a cam, not shown in drawing, on the
lay shaft G. The valve B is kept up against its face by spiral springs E.
D is a chamber in which a small jet of gas for igniting the mixture is con-
tinually burning. C, is the cock for admission of gas, and C, an india-
rubber bag to equalise the gas pressure. The working of the engine is as
follows :—the piston moves from left to right and draws into the cylinder the
explosive mixture. On the return stroke it compresses the mixture to about
3 atmospheres. The igniting flame is then allowed to come for an instant
ll TE il — = mi)
Fig. 444
into contact with the compressed mixture, which burns very rapidly (or
explodes slowly, whichever expression be preferred) and pushes the piston
forward again, the pressure rising to Io or 12 atmospheres. On the next
return stroke the burnt gases are pushed out through the opening shown in
the drawing, and the process begins again once more. There are many
ingenious arrangements about this type of engine which our space will not
allow us to mention in detail. It must suffice to say that the engine has
proved distinctly economical, and has such very great conveniences as may
fairly account for the rapid way in which its use (and that of other gas
engines) has extended.
In conclusion, it is as well to point out that, as long as they work between
the same temperatures, there is no difference between steam, air, and gas
engines as to theoretical economy. The last two gain by the possibility of
using higher limits of temperature than can be employed in a steam engine,
but, so far, have lost by constructive and mechanical difficulties which pre-
vent their theoretical efficiency from being attained.
478 On Ffeat [487 .
CHAT TTGRT TA!
SOURCES OF HEAT AND COLD
487. Different sources of heat.—The following different sources of
heat may be distinguished: i. the szechantcal sources, comprising friction,
percussion, and pressure ; ii. the Pxystcal sources—that is, solar radiation,
terrestrial heat, molecular actions, change of conditions, and electricity ;
iii. the chemical sources, or molecular combinations, and more especially
combustion.
In what follows it will be seen that heat may be produced by reversing
its effects ; as, for instance, when a liquid is solidified or a gas compressed
(489) ; though it does not necessarily follow that in all cases the reversal of
its effects causes heat to be produced—uinstead of it, an equivalent of some
other form of energy may be generated.
In like manner heat may be forced to disappear, or cold be produced
when a change such as heat can produce is brought about by other means,
as when a liquid is vaporised or a solid liquefied by solution ; though here
also the disappearance of heat is not always a necessary consequence of
the production, by other means, of changes such as might be effected by
heat.
MECHANICAL SOURCES
488. Heat due to friction.—The friction of two bodies, one against the
other, produces heat, which is greater the greater the pressure and the more
rapid the motion. For example, the axles of carriage wheels, by their fric-
tion against the boxes, often become so strongly heated as to take fire. By
rubbing together two pieces of ice in a vacuum below zero, Sir H. Davy
partially melted them. In boring a brass cannon Rumford found that the
heat developed in the course of 2} hours was sufficient to raise 263} pounds
of water from zero to 100°, which represents 2,650 thermal units (456). Mayer
raised water from 12° to 13° by shaking it. At the Paris Exhibition, in 1855,
Beaumont and Mayer exhibited an apparatus, which consisted of a wooden
cone covered with hemp, and moving with a velocity of 400 revolutions in a
minute, in a hollow copper cone, which was fixed and immersed in the water
of an hermetically closed boiler. The surfaces were kept covered with oil.
By means of this apparatus 88 gallons of water were raised from Io to 130
degrees in the course of a few hours.
In the case of flint and steel, the friction of the flint against the steel
raises the temperature of the metallic particles, which fly off, heated to such
an extent that they take fire in the air.
-489] Hleat due to Pressure and Percussion 479
The luminosity of aerolites is considered to be due to their friction
against the air, and to their condensation of the air in front of them (489),
their velocity attaining as much as I50 miles in a second.
Tyndall devised an experiment by which the great heat developed by
friction is illustrated in a striking manner. A small brass tube closed at one
end (fig. 445) is fixed on a small wheel. The tube, three parts full of water,
is closed by a cork, and is pressed between a wooden clamp, while the
wheel is rotated with some rapidity. The water rapidly becomes heated
by the friction, and its temperature soon exceeding the boiling-point, the
cork is projected to a height of several yards by the elastic force of the
steam.
489. Heat due to pressure and percussion.—If a body be so com-
pressed that its density is increased, its temperature rises according as the
volume diminishes. Joule verified this in the case of water and of oil,
which were exposed to pressures of 15 to 25 atmospheres. In the case of
water at 1'2° C., increase of pressure caused lowering of temperature—a result
which agrees with the fact that water contracts by heat at this temperature.
Similarly, when weights are laid on metal pillars, heat is evolved, and
absorbed when they are removed. So in like manner the stretching of a
metal wire is attended with a diminution of temperature.
The production of heat by the compression of gases is easily shown by
means of the pueumatic syringe (fig. 446). This consists of a glass tube
with thick sides, closed hermetically by a leather piston. At the bottom of
this there is a cavity in which a small piece of cotton, moistened with
ether or bisulphide of carbon, is placed. The tube being full of air, the
piston is suddenly plunged downwards ; the air thus compressed disengages
so much heat as to ignite the cotton, which is seen to burn when the piston
is rapidly withdrawn. ‘The ignition of the cotton in this experiment indicates
a temperature of at least 300°.
The rise of temperature produced by the compression in the above
480 On Fleat [489 -
experiment is sufficient to effect the combination, and therefore the detonation,
of a mixture of hydrogen and oxygen.
A curious application of the principle of the pneumatic syringe is met
with in the American powder ram for pile-driving. On the pile to be driven
is fixed a powder mortar, above which is suspended at a suitable distance an
iron rammer, shaped like a gigantic stopper, which just fits in the mortar.
Gunpowder is placed in the mortar, and when the rammer is detached it
falls into the mortar, compresses the air, producing so much heat that the
powder is exploded. The force of the gases projects the rammer into its
original position, where it is caught by a suitable arrangement ; at the same
time the reaction of the mortar on the pile drives this in with far greater
force than the fall of the rammer. After adding a fresh charge of powder,
the rammer is again allowed to fall, again produces heat, explosion, and so
forth, so that the driving is effected in a surprisingly short time.
Percussion is also a source of heat. In firing shot at an iron target, a
sheet of flame is frequently seen at the moment of impact ; and Sir J. Whit-
worth used iron shells which are exploded by the concussion on striking
an iron target. A small piece of iron hammered on the anvil becomes very
hot.
Fig. 446
The heat due to the impact of bodies is not difficult to calculate. When-
ever a body moving with a velocity v is suddenly arrested in its motion, its
kinetic energy is converted into heat.. This holds equally whatever be the
cause to which the motion is due: whether it be that acquired bya stone
falling from a height, by a bullet fired from a gun, or the rotation of a
copper disc by means of a turning table. The energy of any moving body
is expressed by ““”" or in foot-pounds by Pv", where p is the weight in
2 2
pounds, zv the velocity in feet per second, and g¢ is about 32 (29) ; and if the
whole of this be converted into heat, its equivalent in thermal units will be
2
Be 2: Suppose, for instance, a lead ball weighing a pound be fired
from a gun, and strike against a target, what amount of heat will it produce?
We may assume that its velocity will be about 1,600 feet per second ; then
its kinetic energy will be ~~ - 1600°
=o on 40,000 foot-pounds. Some of this will
.
have been consumed in producing the vibrations which represent the sound
of the shock, some of it also in its change of shape ; but neglecting these two
as being small, and assuming that the heat is equally divided between the ball
—490] Solar Radiation 481
and the target, then, since 40,000 foot-pounds is the equivalent of 28:7
thermal units, the share of the ball will be 14:3 thermal units ; and if, for
simplicity’s sake, we assume that its initial temperature is zero, then, taking
its specific heat at 0'0314, we shall have
Weoo3t4x7=14'3 or £= 457 =
which is a temperature considerably above that of the melting point of
lead (342). .
By allowing a lead ball to fall from various heights on an iron plate, both
experience an increase of temperature which may be measured by the
thermopile ; and from these increases it may be easily shown that the heat
is directly proportional to the height of fall, and therefore to the square of
the velocity.
By similar methods Mayer calculated that if the motion of the earth
were suddenly arrested the temperature produced would be sufficient.to melt
and even volatilise it ; while, if it fell into the sun, as much heat would be
produced as results from the combustion of 5,000 spheres of carbon the size
of our globe.
PHYSICAL SOURCES
490. Solar radiation..-The most intense of all sources of heat is the
sun. Pouillet made the first accurate measurements of the heat of the sun
by means of an instrument called the
pyroheliometer. The form represented
in fig. 447 consists of a flat cylindrical
metal box 3 inches in diameter and $
an inch deep, containing a known
weight of water. To it is fitted a metal
tube which contains the stem of a deli-
cate thermometer, the bulb of which
dips in the liquid of the box, being fitted
by means of acork. The tube works
in two collars, so that by means of a
milled head it can be turned, and with
it the vessel, and the liquid thus be
uniformly mixed. The face of the
vessel is coated with lampblack, and is
so adjusted that the sun’s rays fall
perpendicularly upon it. This can be
ascertained by observing when the
shadow exactly covers the lower disc
which is fitted to the same axis.
The instrument was exposed for
five minutes at a time to the sun’s
rays ; knowing the weight of the water,
and the rise of temperature, we may
easily calculate the heat absorbed by
it. Corrections were necessary for the heat reflected by the lampblack, and
also for the heat absorbed by the air.
The solar constant Q is the quantity of heat in gramme degrees which a
im
482 . On Feat [490-
square centimetre of a perfect absorbent would receive in a minute from the
vertical sun’s rays at the limit of the atmosphere. On the surface of the
earth the value Q is less, but by determining it at various heights and
combining the observations, the absorption by the atmosphere can be deter-
mined and Q ascertained.
The most trustworthy experiments give for this value 3 gramme
calories. When the sun is in the zenith about one-third is absorbed and
two-thirds reach the earth.
Of older data, Pouillet calculated from the results of experiments with his
apparatus that if the total quantity of heat which the earth receives from the
sun in the course of a year were employed to melt ice, it would be capable
of melting a layer of ice all round the earth of 35 yards in thickness. Another
statement is that the heat emitted by the sun is equal to that produced by the
combustion of 1,500 pounds of coal in an hour on each square foot of its
surface. But from the surface which the earth exposes to the sun’s radia-
tion, and from the distance which separates the earth from the sun, the
quantity of heat which the earth receives can only be esau of the heat
emitted by the sun. Violle calculated the thickness of ice melted by the
sun’s heat at the equator, apart from absorption by the atmosphere, at 55
metres in thickness ; and, deducting this absorption, at 37 metres.
Faraday calculated that the average amount of heat radiated in a day on
each acre of ground in the latitude of London is equal to that which would
be produced by the combustion of sixty sacks of coal.
The heat of the sun cannot be due to combustion, for even if the sun
consisted of hydrogen, which of all substances gives the most heat in com-
bining with oxygen, it can be calculated that the heat thus produced would
not last more than 3,000 years. Another supposition is that originally put
forth by Mayer, according to which the heat which the sun loses by radiation
is replaced by the fall of aerolites against its surface. One class of these is
what we know as shooting stars, which often appear in the heavens with
great brilliancy, especially on August 14 and November 15 ; the term seteoric
stone or aerolite being properly restricted to the bodies which fall on
the earth. They are often of considerable size, and are even met with
in the form of dust. Although some of the sun’s heat may be restored
by the impact of such bodies against the sun, the amount must be very
small, for Lord Kelvin has proved that a fall of o°3 gramme of matter
in a second on each square metre of surface would be necessary for this
purpose. The effect of this would.be that the mass of the sun would
increase, and the velocity of the earth’s rotation about the sun would be
accelerated to an extent which would be detected by astronomical observa-
tions.
Helmholtz considers that the heat of the sun was produced originally by
the condensation of a nebulous mass, and is kept up by a continuance of
this contraction. A sudden contraction of the primitive nebular mass of the
sun to its present volume would produce a temperature of 28 millions ot
degrees Centigrade ; and a contraction of z;5}5p of its mass would be
sufficient to supply the heat radiated by the sun in 2,000 years. This amount
of contraction could not be detected even by the most refined astronomical
methods.
492] Heat produced by Absorption and Imbtbition 483
491. Terrestrial heat.—Our globe possesses heat peculiar to it, which is
called terrestrial heat. ‘The heat from the sun penetrates slowly by conduc-
tion into the interior, and accordingly the maximum temperature will be at
different depths at different times. Thus with four thermometers sunk at
depths of 3, 6, 12 and 25°5 feet in the porphyry rock of the Calton Hill, Edin-
burgh, the registered maximum temperatures were on August 19,September 8,
October 19, and January 4 respectively. But some of the heat is retained in
each layer and raises the temperature so that the yearly variations diminish
with the depth. For the above thermometers these were 8°2°, 5°6°, 2°7°,
and o'7°._ From observations of this kind it is concluded that the solar heat
does not penetrate below a certain internal layer, which is called the /ayer
of constant annual temperature ; its depth below the earth’s external surface
varies, of course, in different parts of the globe ; at Paris, itis about 30 yards,
and the temperature is constant at 11°8° C.
Below the layer of constant temperature, the temperature is observed to
increase, on the average, 1° C. for every 90 feet. The most rapid increase
is at Irkutsk in Siberia, where it is 1° for 20 feet, and the slowest in the mines
at Mansfield, where it is about 1° C. for 330 feet. This increase has been
verified in mines and artesian wells. According to this at a depth of 3,000
yards, the teniperature of a corresponding layer would be I00°, and at a
depth of 20 to 30 miles there would be a temperature sufficient to melt all
substances which exist on the surface. Hot springs and volcanoes confirm
the existence of this central heat.
Various hypotheses have been proposed to account for the existence of
this central heat. The one usually admitted by physicists is that the earth
was originally in a liquid state in consequence of
the high temperature, and that by radiation the
surface has gradually solidified, so as to form a
solid crust. The cooling must be very slow, owing
to the small conductivity of the crust. For the
same reason the central heat does not appear to
raise the temperature of the surface more than 34 of
a degree.
Fourier calculated that the heat given off by the
earth in 100 years would be sufficient to melt a
layer of ice 3 metres in thickness, which therefore
is only zg455 Of that received by the sun in the same
time.
492. Heat produced by absorption and imbibi-
tion.— Molecular phenomena, such as imbibition,
absorption, capillary actions, are usually accom-
panied by disengagement of heat. Pouillet found = 2 Se
that whenever a liquid is poured on a finely divided ——
solid, an increase of temperature is produced which Fig. 448
varies with the nature of the substances. With in-
organic substances, such as metal, the oxides, the earths, the increase is 345
of a degree ; but with organic substances, such as sponge, flour, starch roots,
dried membranes, the increase varies from I to 10 degrees.
The absorption of gases by solid bodies presents the same phenomena.
W1i2
Cie > ;
4“ Ui! ==
484 On Heat | [492--
Débereiner found that when platinum, in the fine state of division known as
platinum black, is placed in oxygen, it absorbs many hundred times its
volume, and that the gas is then in such a state of density, and the tempera-
ture so high, as to give rise to strong combustion. Spongy platinum pro-
duces the same effect. A jet of hydrogen directed on it takes fire.
The apparatus known as Dodereiner’s Lamp depends on this property of
finely divided platinum. It consists of two glass vessels (fig. 448). The first,
A, fits in the lower vessel by means of a tubulure which closes it hermetically.
At the end of the tubulure is a lump of zinc, Z, immersed in dilute sulphuric
acid. By the chemical action of the zinc on the dilute acid hydrogen gas is
generated, which, finding no issue, forces the liquid out of the vessel B into
the vessel A, so that the zinc is not in contact with the liquid. The stopper
of the upper vessel is raised to give exit to the air in proportion as the water
rises. Ona copper tube, H, fixed in the side of the vessel B, there is a small
cone, a, perforated by an orifice ; above this there is some spongy platinum
in the capsule, c. As soon now as the cock, which closes the tube H, is
opened, the hydrogen escapes, and, coming in contact with the spongy
platinum, is ignited.
The condensation of vapours by solids often produces an appreciable
rise of temperature. This is particularly the case with humus, which, to the
benefit of plants, is warmer in moist air than the air itself.
Favre found that when a gas is absorbed by charcoal the amount of
heat produced by the absorption of a given weight of sulphurous acid, or of
nitrous oxide, greatly exceeds that which is disengaged in the lique-
faction of the same weight of gas ; for carbonic acid, the heat produced by
absorption exceeds even the heat which would be disengaged by the solidi-
fication of the gas. The heat produced by the absorption of these gases
cannot, therefore, be explained by assuming that the gas is liquefied, or even
solidified in the pores of the charcoal. It is probable that it is in part due to
that produced by the liquefaction of the gas, and in part to the heat due to
the imbibition in the charcoal of the liquid so produced.
CHEMICAL SOURCES
493. Chemical combination. Combustion.—-Chemical combinations are
usually accompanied by a rise of temperature. When these combinations
take place slowly, as when iron oxidises in the air, the heat produced is im-
perceptible ; but if they take place rapidly, the disengagement of heat is very
intense. The same quantity of heat is produced in both cases, but when
evolved slowly it is dissipated as fast as formed.
Combustion is chemical combination attended with the evolution i light
and heat. In ordinary combustion in lamps, fires, candles, the carbon and
hydrogen of the coal, or of the oil, etc., combine au the oxygen of the air.
But combustion does not necessarily involve the presence of oxygen. If
either powdered antimony or a fragment of phosphorus be placed in a vessel
of chlorine, it unites with chlorine, producing thereby heat and flame.
Many combustibles burn with flame. A flame is a gas or vapour raised
to a high temperature by combustion. Its illuminating power varies with
the nature of the product formed. The presence of a solid body in the fame
—494] feat disengaged during Chemical Action 485
increases the illuminating power. The flames of hydrogen, carbonic oxide,
and alcohol are pale, because they only contain gaseous products of com-
bustion. But the flames of candles, lamps, coal gas, havea high illuminating
power. They owe this to the fact that the high temperature produced de-
composes certain of the gases, with the production of carbon, which, not
being perfectly burnt, becomes incandescent in the flame. Coal-gas, when
burnt in an arrangemerft by which it obtains an adequate supply of air, such
as a Bunsen’s burner, is almost entirely devoid of luminosity. A non-lumi-
nous flame may be made luminous by placing in it platinum wire or asbestos.
The temperature of a flame does not depend on its illuminating power.
A hydrogen flame, which is the palest of all flames, is the hottest.
Chemical decomposition, in which the attraction of heterogeneous mole-
cules for each other is overcome, and they are moved further apart, is an
operation requiring an expenditure of work or an equivalent consumption of
heat ; and conversely, in chemical combination, motion is transformed into
heat. When bodies attract each other chemically their molecules move
towards each other with gradually increasing velocity, and when impact has
taken place the progressive motion of the molecules ceases, and is converted
into a rotating, vibrating, or progressive motion of the molecules of the new
body.
The heat produced by chemical combination of two elements may be
compared to that due to the impact of bodies against each other. Thus the
action of the atoms of oxygen,
which in virtue of their progressive
motion, and of chemical attraction,
rush against ignited carbon, has
been lhkened by Tyndall to the
action of meteorites which fall into
the sun.
494. Heat disengaged during
chemical action.— Many physicists,
more especially Lavoisier, Rum- -| sean |
lords Dulong, Despretz)* Hess, 2 a
Favre and Silbermann, Berthelot, =
Thomsen, and Andrews, have in-
vestigated the quantity of heat dis-
engaged by various bodies in
chemical actions. ——
Lavoisier used in his experi- Sage ES | ;
ments the ice calorimeter already a Oe
described. Rumford used a calori-
meter known by his name, which
consists of a rectangular copper Joe Eee
canister filled with water. In this RAIA III
canister there is a worm which
passes through the bottom of the
box, and terminates below in an inverted funnel. Under this funnel is burnt
the substance experimented upon. The products of combustion, in passing
through the worm, heat the water of the canister. and from the increase of
Fig. 449
486 ? On Feat [494-
its temperature the quantity of heat evolved is calculated. Despretz and
Dulong successively modified Rumford’s calorimeter by allowing the com-
bustion to take place, not outside the canister, but in a chamber placed in
the liquid itself; the oxygen necessary for the combustion entered by a
tube in the lower part of the chamber, and the products of combustion
escaped by another tube placed at the upper part and twisted in a ser-
pentine form in the mass of the liquid to be heated. * Favre and Silbermann
improved this calorimeter very greatly (473), not only by avoiding or taking
account of all possible sources of error, but by arranging it for the deter-
mination of the heat evolved in such chemical actions as take place between
gases and vapours. The gases enter by tubes BB’ and CC’, fig. 448, into a
metal chamber A, where the reaction takes place, the course of which can
be watched through a glass plate which closes a wider tube FK. The
gaseous products before passing into the air traverse a long serpentine tube
H, at the lower end of which is a small box G which receives the liquids
arising from the condensation of the vapours. The cylinder A and the
serpentine are contained in a known mass of water contained in a calori-
meter, and from the rise in temperature of this water the heat developed
can be calculated. To avoid any loss of heat this is placed within a metal
case, MM, containing swan’s down. The whole is contained in a vessel of
water NN in which is a thermometer, to eliminate the influence of changes
in the temperature of the air.
The experiments of Favre and Silbermann are the most trustworthy, as
having been executed with the greatest care. They agree very closely with
those of Dulong. Taking as thermal unit the heat necessary to raise the
temperature of a pound of water through ove degree Centigrade, the following
table gives the thermal units in round numbers disengaged by a pound of
each of the substances while burning in oxygen :—
Hydrogen . s 134,402 Diamond : ; n4t%, 778
Marsh gas . ; wr El 3,003 Absolute alcohol . Weak oo
Ethylenea a : 1 t,055 Cokeay : ‘ pe TZ000
Petroleum . : . 1,000 Phosphorus . ; 53750
Oil of turpentine PalO, 652 Coal gas ; : , ) 5,600
Olive oil : yt O,d00 Wood, dried at-120° t7.. 3,619
Ether . : : re O30 Carbon bisulphide . .- 3,401
Anthracite . ; eet 0,400 Wood, ordinary . ub 23750
Charcoal ; Se OOO Carbonic oxide ; -, 2,400
Oodle : : HO, G00. Sulphur . : : sH12,220
Tallow : . . «8,000 Zinc : ; ; s+ 1g300
Graphite . : ti Bray Se Iron ¢ ; f P ahehod
Bunsen’s calorimeter (460) has been used with advantage for studying
the heat produced in chemical reactions, in cases in which only very small
quantities are available.
For experiments on the heat of neutralisation of acids and bases the
apparatus represented in fig. 450 may be used. Wis a large vessel of water
of constant temperature ; the beaker glass, B, which is the calorimeter, rests
on a cork in the outer one, A. On the wooden lid, H, are two weights, S,
—496] Berthelot’'s Calorimetrical Bomb 487
and S,, to keep A down in the water; c and dare tubes placed in holes in
the lid, and contain weighed quantities of the two liquids; 4 is a delicate
thermometer. After the tubes c and d@ have acquired the temperature of
the water ¢, their contents are poured into B through an aperture in the lid
for this purpose. When the reaction is complete, the temperature indicated
by the thermometer, which reaches to the middle of B, rises to ¢,, so that,
when we know the weight of the substances, and the rise of temperature
z,—7 the quantity of heat produced in the reaction is easily determined.
mT
Fig. 451
495. Berthelot’s calorimetrical bomb.—This apparatus, represented in
section in fig. 451, is small enough to be inserted in the water of a calori-
meter. It consists of a steel reservoir C lined with platinum, which can
be hermetically closed by a screwed cover B. At thecentre is a cylinder in
which a tube can be turned, serving to admit the gases to be worked with.
Near this is a carefully insulated platinum wire, which ends near the side of
the apparatus ; when an electric spark is passed it sets up the chemical
reaction, the heat due to which is to be measured. For this purpose the
bomb before the experiment is placed in a calorimeter, and from the rise in
temperature of the known weight of water the quantity of heat can be
deduced.
If a solid is to be burned it is placed in a platinum capsule, and the
combustion set up by passing a current through a very fine platinum wire in
contact with it.
496. Endothermic and exothermic actions.—All chemical actions whether
458 On Heat [496—
of combination or of decomposition, are attended by a disturbance of the
thermal equilibrium ; and the quantity of heat disengaged is a measure of
the physical and chemical work.
In most cases the act of chemical combination is attended by a rise of
temperature, and the quantity of heat is a measure of the energy developed
in the reaction. Thus in the formation of one szolecule of water there are:
liberated 68,924 thermal units, which may be written thus,
H, +O=H,0 + 68,924.
Those reactions which take place with disengagement of heat are said to:
be exothermic ; there are, however, cases where bodies do not directly com-
bine without the intervention of extraneous heat—for instance, iodine and
hydrogen to form hydriodic acid ; the equation for this is
I+H+6,000=I1H.
Such reactions are called endothermic.
Those bodies are most stable in the formation of which most heat is.
developed ; thus the iron and zinc oxides, in the formation of which 1,181
and 1,300 units are respectively developed, are much more stable than
silver oxide, in the formation of which only 27 units are developed. The
heat of decomposition is the reciprocal of that of combination ; those
bodies which develop most heat in their formation require conversely an
equivalent quantity to decompose them; decompositions which require an
expenditure of heat to produce them are called endothermic. Those com-
pounds, on the contrary, which absorb heat in their formation, develop an
equivalent quantity in being decomposed, and the reactions are exothermic ;
they often take place with explosive violence, as in the case of the nitrogen
chlorides and iodide. An exothermic reaction gives rise to an endothermic
compound ; and, conversely, an endothermic reaction forms an exothermic
compound.
The oxidising compounds in ‘most ordinary explosives, potassium chlorate
and nitrate, are endothermic, evolving heat during decomposition which thus
helps the reactions.
If there be any system of bodies which act on each other without the
supply of extraneous energy, then that body or set of bodies results, in the
formation of which most heat is produced. This is called the principle of
greatest chemical action.
The heat developed in any chemical reaction depends on the relation
between the initial and the final products, and is independent of the nature
and succession of the intermediate stages. It is equal to the sum of the
quantities of heat produced in each stage, regard being had to the negative
quantities due to such processes as solution and gasification.
Thus a unit weight of carbon in burning to carbonic acid produces 8,080
units. If the same weight of carbon burns so as to form carbonic oxide, it
forms 2,473 ; and the combustion of the carbonic oxide resulting from this
reaction yields 5,607, making together 8,080.
Potassium combines directly with chlorine to form potassium chloride,
the heat of formation of which is 15,000 and is equal to that produced by the
same weight of salt, whether this be forméd by the direct union of hydro-
497] Animal Heat 489
chloric acid and potash, or whether it be produced by the action of potassium
on aqueous solution of hydrochloric acid. .
The heat of combustion of a compound is not always equal to the sum of
that of each of its constituents. The heat of combustion of carbon bisulphide
iS 3,401, while that calculated from its constituents is 3,145 ; the compound
accordingly possesses more energy than its constituents, and its formation
is due to an endothermic reaction.
Metameric bodies are those which contain the same number of elements
but in different groupings ; thus acetic acid and methylic formate have
each the composition C,H,O,; but the heat of combustion of the latter
1s 4,157, and that of the former 3,505 ; from this it is to be inferred that the
grouping of the atoms to form acetic acid has been attended with the expendi-
ture of more energy than in the case of methylic formate.
Polymeric bodies are those which have the same elements and the same
percentage composition but differ in the number-of atoms which form a
molecule. Thus the more complex the molecule the smaller is the quantity
of heat. That of amylene, for instance, C,H,,, is 11,401, and that of
metamylene, C,,H,,, 1s 10,908.
Many chemical elements, such as carbon, sulphur, and phosphorus, exist
in modifications which are essentially different from each other in their
physical properties, but which form, when they enter into combination with
other elements, identical chemical products. Such bodies are said to have
graphite or different allotropic forms which have different thermal values.
The heat lberated when one allotropic form is changed into another, for
instance, when charcoal is converted into diamond, cannot be directly deter-
mined, but must be arrived at by indirect methods.
A given weight of carbon, whether it be charcoal or diamond, produces
exactly the same weight of carbonic acid, though the heat of combustion is
different. Thus, when a gramme each of charcoal, graphite, and diamond
are severally burnt in oxygen in the calorimetric bomb, the heats produced
are respectively 8,137, 7,900, and 7,860 thermal units ; hence 237, the differ-
ence between the two former values, represents the heat developed in the
transformation of one gramme of charcoal into graphite, and 4o, the corre-
sponding number, in the change from graphite to diamond.
The temperature of combustion, or, in the case of gases, the temperature
of the flame, is the upper limit of the temperature which can be attained by
the combustion of a body. This can be deduced from the heat of combus-
tion, and from the specific heats of the bodies produced. The theoretical
temperature of combustion of hydrogen in oxygen is calculated at 6,715° ;
this, however, is never even approximately reached, for at much lower tem-
peratures aqueous vapour is dissociated (395) into its constituents, and the
combustion cannot exceed a certain limit of temperature.
497. Animal heat.—In all the organs of the human body, as well as
those of all animals, processes of oxidation are continually goingon. Oxygen
passes through the lungs into the blood, and so into all parts of the body. In
like manner the oxidisable bodies, which are principally hydrocarbons, pass
by the process of digestion into the blood, and likewise into all parts of the
body, while the products of oxidation, carbonic acid and water, are eliminated
by the skin, the lungs, etc. Oxidation in the muscle produces motions of the
490 On Heat [497—
molecules, which are changed into contraction of the muscular fibres ; all
other oxidations produce heat directly. When the body is at rest, all its
functions, even involuntary motions, are transformed into heat. When the
body is at work, the more vigorous oxidations of the working parts are
transferred to the others. Moreover, a great part of the muscular work is
changed into heat, by friction of the muscles and of the sinews in their sheaths,
and of the bones in their sockets. Hence the heat produced by the body
when at work is greater than when at rest. The blood distributes heat
uniformly through the body, which in the normal condition has a temperature
of 37° C.=98°6° F. The blood of mammalia has the same temperature, that of
birds is somewhat higher. In feyer the temperature rises to 42° to 43°, and in
cholera, or when near death, sinks as low as 35°.
The function of producing work in the animal organism was formerly con-
sidered as separate from that of the production of heat. The latter was
held to be specially due to the oxidation of the hydrocarbons of the fat, while
the work was ascribed to the chemical activity of the nitrogenous matter.
This view has now been generally abandoned ; for it has been found that
during work there is no increase in the secretion of urea, which is the result
of the oxidation of nitrogenous matter ; moreover, the organism while at
rest produces less carbonic acid, and requires less oxygen than when it is at
work ; and the muscle itself, both in the living organism and also when
removed from it and artificially stimulated, requires more oxygen in a state
of activity than when at rest. For these reasons the production of work is
ascribed to the oxidation of the organic matter generally.
The process of vegetation in the living plant is not in general connected
with any oxidation. On the contrary, under the influence of the sun’s rays,
the green parts of plants decompose the carbonic acid of the atmosphere
into free oxygen gas and into carbon, which, uniting with the elements of
water, form cellulose, starch, sugar, and so forth. In order to effect this, an
expenditure of heat is required which is stored up in the plant, and which
reappears during the combustion of the wood, or of the coal arising from its
decomposition.
At the time of blossoming a process of oxidation goes on, which, as in
the case of the blossoming of the Victoria regia, is attended with an appre-
ciable rise of temperature.
HEATING
498. Different kinds of heating.—//eading is the art of utilising for
domestic and industrial purposes the sources of heat which nature offers to
us. Our principal source of artificial heat is the combustion of coal, coke,
turf, wood, and charcoal.
499. Fireplaces.—Fireplaces are open hearths built against a wall under
a chimney, through which the’products of combustion escape.
However much they may be improved, fireplaces will always remain the
most imperfect and costly mode of heating, for they only render available
13 per cent. of the total heat yielded by coal or coke, and 6 per cent. of that
by wood. ‘This enormous loss of heat arises from the fact that the current of
air necessary for combustion always carries with it a large quantity of the
heat produced, which is dissipated in the atmosphere. Hence Franklin said
‘fireplaces should be adopted in cases where the smallest quantity of heat
-500] Draught of Fireplaces 491
was to be obtained from a given quantity of fuel.’ Notwithstanding their
want of economy, however, they will always be preferred as the healthiest and
pleasantest mode of heating, on account of the cheerful light which they emit,
and the ventilation which they ensure.
500. Draught of fireplaces.—The draught of a fire is the upward cur-
rent in the chimney caused by the ascent of the products of combustion ;
when the current is rapid and continuous, the chimney is said to draw well.
The draught is caused by the difference between the temperature of the
inside and that on the outside of the chimney ; for, in consequence of this
difference, the gaseous bodies which fill the chimney are lighter than the
air of the room, and consequently equilibrium is impossible. The weight of
the column of gas CD, fig. 452, in the chimney being less than that of the
external column of air AB of the same height, there is a pressure from the
outside to the inside which causes the products of combustion to ascend the
more rapidly in proportion as the difference in weight of the two gaseous
masses is greater. The velocity of the draught of a chimney may be deter-
mined theoretically by the formula
y= /2ga(t’ — th,
in which g is the acceleration of gravity, a the coefficient of the expansion
of air, 2 the height of the chimney, z’ the mean temperature of the air inside
the chimney, and ¢ the temperature of the surrounding air.
The currents caused by the difference in temperature of two communi-
cating gaseous masses may be demonstrated by placing a candle near the
top and near the bottom of the partially
opened door of a warm room. At the top, A
the flame will be turned from the room to- \
wards the outside, while the contrary effect
will be produced when the candle is placed
on the ground. The two effects are caused
by the current of heated air which issues by
the top of the door, while the cold air which
replaces it enters at the bottom.
In order to have a good draught, a
chimney ought to satisfy the following con-
ditions :—
i. The section of the chimney ought not
to be larger than is necessary to allow an
exit for the products of combustion ; other- pola
wise ascending and descending currents are Dy EE ae as
produced in the chimney, which cause it to CZ. —
smoke. It is advantageous to place on the Fig. 452
top of the chimney a conical pot narrower
than the chimney, so that the smoke may escape with sufficient velocity to
resist the action of the wind.
ii. The chimney ought to be sufficiently high, for, as the draught is
caused by the excess of the external over the internal pressure, this excess is
greater in proportion as the column of heated air is longer.
iii, The external air ought to pass into the chamber with sufficient
L a
oe
ys
8
“¢ WSS aS
~ S
YY,
7,
Bi
492 On Heat [500~
rapidity to supply the wants of the fire. In an hermetically closed room
combustibles would not burn, or descending currents would be formed which
would drive the smoke into the room. Usually air enters in sufficient
quantity by the crevices of the doors and windows.
iv. Two chimneys should not communicate, for if one draws better than
the other, a descending current of air is produced in the latter, which carries
smoke with it.
For the strong fires required by steam-boilers and the like, very high
chimneys are needed ; of course the increase in height would lose its effect
if the hot column above became cooled down. Hence chimneys are often
made with hollow walls—that is, of separate concentric layers of masonry
or brickwork—the space between them containing air.
501. Stoves.—Sfoves are apparatus for heating with a detached fire,
placed in a room to be heated, so that heat radiates in all directions
round the stove. At the lower part is the draught-hole by which the air
necessary for combustion enters. The products of combustion escape by
means of iron chimney-pipes. This mode of heating is one of the most
economical, but it is by no means so healthy as that by open fireplaces, for
the ventilation is very bad, more especially where the stoves are fed from
the outside of the room. These stoves also emit a bad smell, arising in
part from the decomposition of organic substances which are always present
in the air by their contact with the heated sides of the chimney-pipes ; or
possibly, as Deville and Troost’s researches seem to show, from the diffusion
of gases through the heated sides of the stove.
The heating is very rapid with blackened metal stoves, but they also
cool very rapidly. Stoves constructed of polished earthenware, which are
common on the Continent,
tion, and this property is
used in heating baths, public
buildings, hothouses, &c.
For this purpose steam is
generated in boilers lke
those used for steam engines,
UD
YMA
\\ \\ heat more slowly, but more
Ss y :
\\ ISN pleasantly, and they retain
NN M IN the heat longer.
WS IN :
VIB x 502. Heating by steam.—
Nie Wl SS Steam, in condensing, gives.
Ni Teter aN Hl S : ‘
Ni ct tj NS up its latent heat of vaporisa-
\ SS
= ae
Ss Ss SMGGV
SSS
Tis 7 4, and is then made to circulate
a , Lk in pipes placed in the room
te :
Sy]
LW
SW
to be heated. The steam
SN
MW \ ~ SAS VC condenses, and in doing so
ee ES SS ZS 4 imparts £6: the pipes its latent
VW) WW Wi a heat, whi
which becomes free,
Fig. 453 and thus heats the surround-
ing air.
503. Heating by hot air.—Heating by hot air consists in heating the
air in the lower part of a building, whence it rises to the higher parts in
504] Fleating by Hot Water 493
virtue of its lessened density. The apparatus is arranged as represented in
fig. 453.
A series of tubes, AB, only one of which is shown in the figure, is placed
in a furnace F, in the cellar. The air passes into the tubes through the
lower end, A, where it becomes heated, and, rising in the direction of the
arrows, reaches the room M by a higher aperture, B. The various rooms
to be heated are provided with one or more of these apertures, which are
placed as low in the room as possible. The conduit O is an ordinary chim-
ney. These apparatus are more economical than open fireplaces, but they
are less healthy, unless special provision is made for ventilation.
504. Heating by hot water.—This consists of a continuous circulation
of water, which, having been heated in a boiler, rises through a series of tubes,
and then, after becoming cool, passes into the boiler again by a similar
series. Fig. 454 represents an apparatus for heating a building of several]
stories. The heating
apparatus, which is in
the basement, con-
sists of a bell-shaped
boiler, 0 0, with an in-
ternal flue, F. A long
pipe, ein stsiinythe
upper part of the
boiler, and also in the
reservoir Q, placed in
the upper part of the
building to be heated.
At the top of this re-
servoir there is a safety
valve, s, by which the
pressure of the vapour ~~“
in the interior can be
SS
ed
LELLLLLLL LLL L Lb
MQ
aes
rd
ROSS)
NANA
RQ MA AAA
S
regulated. Y WZ
The boiler, the pipe Y j 1a LI
M, andaportionof the =v Ura ELT fy
reservoir Q, being Y 1 Y ] pe. WEAN
filled with water, as it Y\ WZ | WY :
becomes heated in the GR Y sad Y
et | ZZ
mrbteed | 77 Ls ; :
A 5 7. GY NE WS Ue LEAL TELE DAE PEALE LE TBE
\ 4 \ SS SUNS SESE TEES
\
N
oP
SS ARS S
‘
= S SSS
current of hot water
rises to the reservoir
Q, while at the same time descending currents of colder and denser water
pass from the lower part of the reservoir Q into receivers 4, d, f, filled with
water. The water from these passes again through pipes into other receivers,
a, ¢, é, and ultimately reaches the lower part of the boiler.
During this circulation the hot water heats the pipes and the receivers,
which thus become true water-stoves. The number and the dimensions of
these parts are determined from the fact that a cubic foot of water in falling
through a temperature of one degree can theoretically impart the same in-
crease of temperature to 3,200 cubic feet of air (469). In the interior of the
Fig. 454
494 On Ffeat [504—
receivers, @, 4, ¢, d, e, f, there are cast-iron tubes which communicate with
the outside by pipes, P, placed underneath the flooring. The air becomes
heated in these tubes, and issues at the upper part of the receiver.
The principal advantage of this mode of heating is that of giving a
temperature which is constant for a long time, for the mass of water only cools
slowly. It is much used in hot-houses, baths, artificial incubation, drying
rooms, and generally wherever a uniform temperature is desired.
SOURCES OF COLD
505. Various sources of cold.—Besides the cold caused by the passage
of a body from a solid to the liquid state, of which we have already spoken,
cold is produced by the expansion of gases, by radiation in general, and more
especially by radiation at night.
506. Cold produced by the expansion of gases. Ice machines.—We
have seen that when a gas is compressed the temperature rises (489). The re-
verse of this is also the case : when a gas is rarefied, a reduction of temperature
ensues, because a quantity of sensible heat disappears when the gas becomes
increased to a larger volume. This may be shown by placing a delicate
Breguet’s thermometer under the receiver of an air-pump, and exhausting ;
at each stroke of the piston the needle moves in the direction of zero, and
regains its original position when air is admitted.
The production of cold when a gas is expanded has been extensively
applied in machines for artificial refrigeration on a large scale. By Wind-
hausen’s ice machine, from 15,000 to 150,000 feet of air can be cooled in an
hour, through 40 to 100 degrees in temperature, by means of a steam-engine
of from 6 to 20 horse-power. The essential parts of this machine are repre-
sented in fig. 455. The piston B in the cylinder A is worked to the right by
|
zs :
= ——— 4\
\ ————— ee
Fig. 455
a steam-engine and to the left by a steam-engine and by the compressed air.
As it moves towards the right the valve a opens, and air under the ordinary
atmospheric pressure enters the space A,. When this is full the piston moves
towards the left, the air in A is compressed to about 2 atmospheres, the
valve a is closed, the valve 4 opens, and air passes in the direction of the
—508] Cold produced by Radiation at Night 4Q5
arrows into the cooler, C. By its compression it has become strongly
heated, and the necessary cooling is effected by means of pipes through
which cold water circulates, entering at 5 and emerging at 6. The air, thus
compressed and cooled, passes out through the valve c, which is automatically
worked by the machine, into the space A,, where, in conjunction with the
steam-engine, it moves the piston to the left, and compresses the air in A, ;
for at a certain position of the piston the valve c is closed, the compressed
air in the cylinder A, expands, and thereby is cooled far below the freezing
point. As the piston moves again to the right, the valve dis opened by the
working of the machine, and the cooled air emerges through the tube 4 to
its destination. Ifit passes into an ordinary room, by condensing the moisture
it fills it with snowflakes. Machines of this kind are extensively employed
in the arts ; in breweries, oil refineries, in the artificial production of ice, and
in cooling rooms on board ship for the transport of dead meat, &c., which
has become an industry of the greatest importance.
In the Linde machine the material used is ammonia gas, which is
liquefied by compression and surface condensation. This liquid ammonia
being allowed to evaporate takes the heat for this change of state from the
surrounding bodies, which are thereby cooled. The ammonia vapour thus
formed is again liquefied, and flowing back to the refrigerator is again
evaporated, so that a small quantity of ammonia is always passing through
the same cycle of operations.
A machine of this kind worked by a steam-engine of half a horse-power
can cool in an hour 3,400 cubic yards of air from 10° to 5° C., or 1,400 cubic
yards from 6° to — 4° C.; or it will produce I cwt. of ice in the same time.
The larger machines are relatively more advantageous.
507. Cold produced by radiation at night.—During the day the ground
receives from the sun more heat than it radiates into space, and the.
temperature rises. The reverse is the case during night. The heat which
the earth loses by radiation is no longer compensated, and consequently
a fall of temperature takes place, which is greater according as the sky is.
clearer, for clouds send towards the earth rays of greater intensity than
those which come from the celestial spaces. In some winters it has been
found that rivers have not frozen, the sky having been cloudy, although the
thermometer had been for several days below — 4°; while in other less
severé winters the rivers freeze when the sky is clear. The emissive power:
exercises a great influence on the cold produced by UA oy the greater it
is, the greater is the cold.
In Bengal, the cooling by night is used in manufacturing ice. Large.
flat vessels containing water are placed on non-conducting substances, such
as straw or dry leaves. In consequence of the radiation the water freezes,
even when the temperature of the air is 10° C. The same method can be
applied in all cases with a clear sky.
The, Peruvians, in order to preserve the shoots of young plants from
freezing, light great fires in their neighbourhood, the smoke of which, pro-
ducing an artificial cloud, hinders the cooling produced by radiation.
508. Absolute zero it temperature. es a gas is increased 4, of its
volume for each degree Centigrade, it follows that at a temperature Ole aan
C. the volume of any gas measured at zero is doubled, supposing the pressure:
496 On feat [508—
to remain constant. In like manner, assuming the gaseous laws to continue
to hold, we should have at 273° below zero, PV =o (183) ; that is, either the gas
would shrink into nothing or it would be subjected to no pressure. We are
not, however, driven to either of these conclusions, since we know that all
gases are liquefied before a temperature of —273° is reached.
Nevertheless, this temperature — 273° C. is a very important one, and is
called the absolute zero of temperature. Thermodynamical considerations,
apart from the behaviour of any particular gas, point to the conclusion that
at this temperature all substances entirely lose their molecular motion, z.e.
are entirely deprived of heat. Absolute temperatures are obtained by
adding 273 to the temperature on the Centigrade scale. Thus — 35° C. is
238° on the absolute scale of temperature, and + 15° C. is 288°.
—509] Mechanical Equivalent of Heat 497
GCiAP Ditkh sock
MECHANICAL EQUIVALENT OF HEAT
509. Mechanical equivalent of heat.—If the various instances of the
production of heat by motion be examined, it will be found that in all cases
mechanical energy is expended. Thus in rubbing two bodies against each
other motion is apparently destroyed by friction ; it is not, however, lost,
but appears in the form of a motion of the particles of the body ; the motion
of the mass 1s transformed into a motion of the molecules.
Again, if a body be allowed to fall from a height, it strikes against the
ground with a certain velocity. According to older views, its motion is
destroyed, vzs viva is lost. This, however, is not the case ; the vzs viva of
the body or its £zmetic energy appears as energy of its molecules.
In the case, too, of chemical action, the most productive artificial source
of heat, it is not difficult to conceive that there is, in the act of combining,
an impact of the dissimilar molecules against each other, an effect analogous
to the production of heat by the impact of masses of matter against each
other (489).
In like manner, heat may be made to produce motion, as in the case of
the steam-engine, and the propulsion of shot from a gun.
Traces of a view that there is a connection between heat and motion are
to be met with in the older writers, Bacon for example ; and. Locke says,
‘ Heat is a very brisk agitation of the insensible parts of the object, which
produces in us that sensation from whence we denominate the object hot ;
so that what in our sensation is heat, in the object is nothing but motion.’
Rumford, in explaining his great experiment of the production of heat by
friction, was unable to assign any other cause for the heat produced than
motion ; and Davy, in the explanation of his experiment of melting ice by
friction 2% vacuo, expressed similar views. Carnot, in a work on the steam-
engine published in 1824, also indicated a connection between heat and
work.
The views, however, which had been stated by isolated writers had little
or no influence on the progress of scientific investigation, and it is in the
year 1842 that the modern theories may be said to have had their origin.
In that year Dr. Mayer, a physician in Heilbronn, formally stated that there
exists a connection of simple proportionality between heat and work ; and
he it was who first introduced into science the expression ‘ mechanical equt-
valent of heat” Mayer also gave a method by which this equivalent could be
calculated ; the particular results, however, are of no value, as the method,
though correct on principle, was founded on incorrect data.
In the same year too, Colding of Copenhagen published experiments on
KK
498 On Heat [509-
the production of heat by friction, from which he concluded that the evolu-
tion of heat was proportional to the mechanical energy expended.
About the same time as Mayer, but quite independently of him, Joule
commenced a series of experimental investigations on the relation between
heat and work. These first drew the attention of scientific men to the
subject, and were admitted as a proof that the transformation of heat into
mechanical energy, or of mechanical energy into heat, always takes place in
a definite numerical ratio.
Subsequently to Mayer and Joule, several physicists, by their theoretical
and experimental investigations, have contributed to establish the mechanical
theory of heat: namely, in this country, Lord Kelvin and Rankine; in
Germany, Von Helmholtz, Clausius, and Holtzmann; and in France,
Clapeyron and Regnault. The following are some of the most important
and satisfactory of Joule’s experiments.
A copper vessel, B (fig. 456), was provided with a brass paddle-wheel
(indicated by the dotted lines), which could be made to rotate about a
vertical axis. Two weights, E and F, were attached to cords which passed
over the pulleys C and D, and were connected with the axis A. These
weights in falling caused the wheel to rotate. The height of the fall, which
in Joule’s experiments was about 63 feet, was indicated on the scales G
and H.
The roller A was so constructed that by detaching a pin the weights
could be raised without moving the wheel. The vessel B was filled with
water and placed on a stand, and the weights allowed to sink. When they
had reached the ground, the roller was detached from the axis, and the
weights again raised, the same operations being repeated twenty times
The heat produced was measured by ordinary calorimetric methods (456).
The work expended is measured by the product of the weight into the
height through which it falls, or A, less the work lost by the friction of the
various parts of the apparatus. This is diminished as far as possible by the
use of friction wheels (78), and its amount is determined by connecting C
-509] ~ Mechanical Equivalent of Heat 499
and D without causing them to pass over A, and then determining the
weight necessary to communicate to them a uniform motion.
In this way it has been found that a thermal unit—that is, the quantity
of heat by which a pound of water is raised through 1° C.—is generated by
the expenditure of the same amount of work as would be required to raise
1,392 pounds through 1 foot, or 1 pound through 1,392 feet. This is expressed
by saying that the mechanical equivalent of the thermal unit is 1,392 foot-
pounds.
The friction of an iron paddle-wheel in mercury gave 1,397 foot-pounds,
and that of the friction of two iron plates gave 1,395 foot-pounds, as the
mechanical equivalent of one thermal unit.
In another series of experiments, the air in a receiver was compressed by
means of a force-pump, both being immersed in a known weight of water at
a known temperature. After 300 strokes of the piston the heat, C, was
measured which the water had gained. This heat was due to the compres-
‘sion of the air and to the friction of the piston. To eliminate the latter in-
fluence, the experiment was made under the same conditions, but leaving the
receiver open. The air was not compressed, and 300 strokes of the piston
developed C’ thermal units. Hence C—C’ is the heat produced by the com-
pression of the gas. Representing the foot-pounds expended in producing
this heat by W, we have for the value of the mechanical equivalent.
WwW
C-—C’
By this method Joule obtained the number 1,442.
The mean number which Joule adopted for the mechanical equivalent of
one thermal unit on the Centigrade scale is 1,390 foot-pounds ; on the
Fahrenheit scale it is 772 foot-pounds. The number is called /ozle’s egut-
valent, and is usually designated by the symbol J.
On the metrical system 424 metres are usually taken as the height through
which a kilogramme of water must fall to raise its temperature 1 degree
Centigrade. This is equal to 42,400,000 ergs or 4°24 x Io’ grammes raised
through a height of a centimetre. |
Professor Rowland of Baltimore has recently made a very careful and
complete determination of the mechanical equivalent of heat, by Joule’s
method, in which he has examined and allowed for all possible sources of
error. His results give 4:269 x 10’ grammes centimetre or 1,401 foot-pounds
as the mean value of this constant for the latitude of Baltimore ; and this
value is in close agreement with a still more recent determination by Mr.
E. H. Griffiths, who found, by an electrical method, 4°2788 x 10’ grammes cen-
timetre or 1,403°6 foot-pounds for the latitude of Greenwich (¢=981'17), and
‘by Micalescu, who found 4:267 x to’ for the latitude of Paris (= 980°96).
Hirn made the following determination of the mechanical equivalent by
means of the heat produced by the compression of lead. A large block of
sandstone, CD (fig. 457), is suspended vertically by cords ; its weight is P.
E is a piece of lead, fashioned so that its temperature may be determined by
the introduction of a thermometer. The weight of this is I, and its specific
heat c. AB is a cylinder of cast iron, whose weight is Z. If this be raised
to A’B’, a height of %, and allowed to fall again, it compresses the lead, E,
against the anvil, CD. It remains to measure on the one hand the work
-spent, and on the other the heat gained.
KK2
500 On Fleat [509—
The hammer AB being raised to a height 4, the work of its fall is Dh ;
but as, by its elasticity, it rises again to a height 4, the work is ~ (A-Z,).
The anvil CD, on the other hand, has been raised through a height H
to C’D’, and has required in so doing PH units of work. The work, W,.
definitely absorbed by the lead is # (A—Z,) —-PH. On the other hand, the
lead has been heated by 6, it has gained IIc@ thermal units, c being the
specific heat of lead, and the mechanical equivalent J is equal to the quotient
ai A series of six experiments gave 1,394 for the mechanical equivalent
as thus obtained.
QQ MQW, ©HHWd, AQ] DF.” tw
-
-_—"
——
‘GANT
ign _f ie =
au 1c | vl at ele
El
The experiments of Cantoniand Gerosa in this direction are the simplest.
They allowed mercury to fall from a funnel through a narrow tube into a
vessel below, when its temperature was measured. In this way the number
Fig. 457
1,390 was obtained.
Experiments in the opposite direction have also been made, in which the
work produced by one thermal unit was determined. This was done on a
large scale by Hirn by means of a steam-engine of one hundred horse-power.
He determined the quantity of heat contained in the steam before its action,
and then the amount contained in the water after its condensation. This was
less, for some had been expended in work ; and this work as measured by
the dynamometer was equivalent to that which had disappeared, the number
390'7 being thus obtained.
The following is the method which originally Mayer employed in calcu-
lating the mechanical equivalent of heat. It is taken, with slight modifica-
tions, from Tyndall’s work on Heat, who, while strictly following Mayer’s
reasoning, has corrected his data.
Let us suppose that a rectangular vessel with a section of a square foot
contains at o° a cubic foot of air under the ordinary atmospheric pressure ;
and let us suppose that it is inclosed by a piston without weight.
Suppose now that the cubic foot of air is heated until its volume is:
doubled ; from the coefficient of expansion of air we know that this is the
case at 273° C. The gas in doubling its volume will have raised the piston
through a foot in height ; it will have lifted the atmospheric pressure through
this distance. But the atmospheric pressure on a square foot is in round
—509] Mechanical Equivalent of Heat 501
numbers 15 x 144=2,160 pounds. Hence a cubic foot of air in doubling its
volume has lifted a weight of 2,160 pounds through a height of a foot.
Now a cubic foot of air at zero weighs 1°29 ounce, and the specific heat
of air under constant pressure—that is, when it can expand freely—as com-
pared with that of an equal weight of water, is 0:24; so that the quantity of
heat which will raise 1:29 ounce of air through 273° will only raise 0°24 x 1°29
= 0°31 oz. of water through the same temperature ; but 0°31 oz. of water raised
through 273° is equal to 5:29 pounds of water raised through 1° C.
That is, the quantity of heat which will double the volume of a cubic foot
of air, and in so doing will lift 2,160 pounds through a height of a foot, is
5'29 thermal units.
Now in the above case the gas has been heated under constant pressure,
that is, when it could expand freely. If, however, it had been heated under.
constant volume, its specific heat would have been less in the ratio 1:1°414
(469), so that the quantity of heat required under these circumstances to
raise the temperature of a cubic foot of air would be 5°29 x= 374,
Deducting this from 5:29, the difference 1°55 represents the weight of water
which would have been raised 1° C. by the excess of heat imparted to the
air when it could expand freely. But this excess has been consumed in the
work of raising 2,160 pounds through a foot. Dividing this by 1°55 we have
1,393. Hence the heat which will raise a pound of water through 1° C. will
raise a weight of 1,393 pounds through a height of a foot ; a numerical value
of the mechanical equivalent of heat agreeing as closely as can be expected
with that which Joule adopted as the most certain of his experimental
results.
Fig. 458
The law of the relation of heat to mechanical energy may be thus stated :—
Heat and mechanical energy are mutually convertible ; and heat requires for
its production, and produces by its disappearance, mechanical energy tn the
ratio of 1,390 foot-pounds for every thermal unit.
502 On Feat [509-—
A variety of experiments may in like manner be adduced to show that
whenever heat disappears work is produced. For example, suppose that the
air in a reservoir immersed in water be compressed to the extent of Io
atmospheres, and that, when the compressed air has acquired the tempera-
ture of the water, it be allowed to act upon a piston loaded by a weight, the
result is that the weight is raised. At the same time the water becomes
cooler, showing that a certain quantity of heat had disappeared in producing
the mechanical effort of raising the weight. This may also be illustrated by
the following experiment (fig. 458), due to Tyndall :-—
A strong metal box is taken, provided with a stopcock, on which can be
screwed a small condensing pump. Having compressed the air since it
becomes heated by this process, the box is allowed to stand for some time,
until it has acquired the temperature of the surrounding medium. On
opening the stopcock the air rushes out ; it is expelled by the expansive
force of the internal air: in short, the air drives itself out. Work is there-
fore done by the air against external pressure, and there should bea dis-
appearance of heat ; andif the jet be allowed to strike against the thermopile,
the galvanometer is deflected, and the direction of its deflection indicates a
cooling (fig. 456). A similar effect is observed when, on opening a bottle of
soda water, the carbonic acid gas which escapes is allowed to strike against
the thermopile.
If, on the contrary, the experiment is made with an ordinary pair of
bellows, and the current of air is allowed to strike against the pile, the
deflection of the galvanometer is in the opposite direction, indicating an
increase of temperature (fig. 459). In this case the hand of the experimenter
performs the work, which is converted into heat.
Joule placed in a calorimeter two equal copper reservoirs, which could
Fig. 459
be connected by a tube. One of these contained air at 22 atmospheres, the
other was exhausted. When they were connected, they came into equi-
librium under a pressure of I1 atmospheres; but as the gas in expanding
had done no work, there was no alteration in temperature. When, however,
-510] Dissipation of Energy 503
the second reservoir was full of water, the air in entering was obliged to
expel it and thus perform work, and the temperature sank, owing to an
absorption of heat.
For further information the student of this subject is referred to the
following works :—Tyndall on Heat as a Mode of Motion, Maxwell on feat,
Wormell’s Thermodynamics (Longmans), and Tait on Thermodynamics
(Edmondston & Douglas). A condensed, though complete and systematic,
account of the dynamical theory of heat is met with in Professor Foster’s
articles on ‘Heat’ in Watts Dictionary of Chemistry.
510. Dissipation of energy.—Rankine made the following interesting
observations on a remarkable consequence of the mutual convertibility which
has been shown to exist between heat and other forms of energy :—Lord
Kelvin has pointed out the fact that there exists, at least in the present
state of the known world, a predominating tendency to the conversion of all
other forms of physical energy into heat, and to the uniform diffusion of
heat throughout all matter. The form in which we generally find energy
originally collected is that of a store of chemical power consisting of uncom-
bined elements. The combination of these elements produces energy in the
form known by the name of electrical currents, part only of which can be
employed in electrolysing chemical compounds, and thus reconverted into a
store of chemical power; the remainder is necessarily converted into heat ; and
again, only a part of this heat can be employed in electrolysing compounds or
in reproducing electric currents. If the remainder of the heat be employed
in expanding an elastic substance, it may be converted entirely into visible
motion, or into a store of visible mechanical power (by raising weights, for
example), provided the elastic substance is enabled to expand until its
temperature falls to the point which corresponds to the absolute privation
of heat ; but unless this condition is fulfilled a certain proportion only of
the heat, depending on the range of temperature through which the elastic
body works, can be converted, the rest remaining in the state of heat. On
the other hand, all visible motion is of necessity ultimately converted into
heat by the agency of friction. There is, then, in the present state of the
known world, a tendency towards the conversion of all physical energy into
the sole form of heat.
Heat, moreover, tends to diffuse itself uniformly by conduction and radia-
tion, until all matter shall have acquired the same temperature. There is
consequently, so far as we understand the present condition of the universe,
a tendency towards a state in which all physical energy will be in the state of
heat, and that heat so diffused that all matter will be at the same temperature ;
so that there will be an end of all physical phenomena.
Vast as this speculation may seem, it appears to be soundly based on
experimental data, and to truly represent the present condition of the uni-
verse as far as we know it.
504 On Light [511—
BOO Kaa tl
ON LIGHT
CHAP thee
TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT
511. Theories of light.—ZzgA¢ is the agent which, by its action on the
retina, excites in us the sensation of vision. That part of physics which deals
with the properties of light is known as oféics.
In order to explain the origin and transmission of light, various hypo-
theses have been made, the most important of which are the evzzsszon or
corpuscular theory, and the undulatory theory.
On the emzsstzon theory it is assumed that luminous bodies emit, in all
directions, an imponderable substance, which consists of molecules of an
extreme degree of tenuity : these are propagated in right lines with an almost
infinite velocity. Penetrating into the eye they act on the retina, and deter-
mine the sensation which constitutes vision.
On the undulatory theory, all bodies, as well as the celestial spaces, are
filled by an extremely subtle elastic medium, which is called the /umindferous
ether. The luminosity of a body is due to an infinitely rapid vibratory motion
of its molecules, which, when communicated to the ether, is propagated in all
directions in the form of spherical waves, and this vibratory motion, being
thus transmitted to the retina, calls forth the sensation of vision. The
vibrations of the ether take place not in the direction in which the wave is
travelling, but in a plane at right angles to it. An idea of these may be
formed by shaking a rope at one end. The vibrations, or to and fro move-
ments, of the particles of the rope, are at right angles to the length of the
rope, but the onward motion of the wave’s form is in the directien of the
length.
On the emission theory the propagation of light is affected by a motion
or translation of particles of light thrown out from the luminous body, as a
bullet is discharged from a gun; on the undulatory theory there is no pro-
gressive motion of the particles themselves, but only of the state of disturb-
ance which was communicated by the luminous body ; and this is transmitted
by the vibratory motion of the particles of the luminiferous ether.
The luminiferous ether penetrates all bodies, but on account of its
extreme tenuity it is uninfluenced by gravitation ; it occupies space, and
although it presents no appreciable resistance to the motion of the denser
bodies, it is possible that it hinders the motion of the smaller comets. It has
—514] | Luminous Ray and Pencil 505
been found, for example, that Encke’s comet, whose period of revolution is
about 34 years, has its period diminished by about o-11 of a day at each
successive rotation, and this diminution is ascribed by some to the resistance
of the ether.
Graetz has calculated that the density of ether is 9 x 107'° that of water.
From a formula of Lord Kelvin it is calculated to be greater than Io! ;
it may accordingly be admitted to be 107!7. While the air over a square
metre weighs 10,000 kilogrammes, the ether in it, taking the height of the
atmosphere at 30 miles, would weigh only o-0022 milligramme. Kelvin
concludes that if the density of the air followed Boyle’s law, and the tem-
perature were constant, at a height equal to that of the earth’s radius it
would be only 10°**® that of water. The ether is therefore far more dense
than air so rarefied. He calculated that a volume equal to that of the earth
cannot contain less than 2,775 pounds of ether.
The fundamental principles of the undulatory theory were enunciated by
Huyghens, and subsequently by Euler. The emission theory, principally
owing to Newton’s powerful support, was for long the prevalent scientific
creed. The undulatory theory was adopted and advocated by Young, who
showed how a large number of optical phenomena, particularly those of
diffraction, were to be explained by that theory. Subsequently, too, though
independently of Young, Fresnel showed that the phenomena of diffraction,
and also those of polarisation, are explicable on the same theory, which since
his time has been generally accepted.
The undulatory theory not only explains the phenomena of light, but
reveals an intimate connection between these phenomena and those of heat
(436) ; 1t shows, also, how completely analogous the phenomena of light are
to those of sound, regard being had to the differences of the media in which
these two classes of phenomena take place.
512. Luminous, transparent, translucent, and opaque bodies.—Lwzuz-
nous bodies are those which emit light, such as the sun and ignited bodies.
Transparent or adtaphanous bodies are those which readily transmit light,
and through which objects can be distinguished ; water, gases, polished glass
are of this kind. Zvanslucent bodies transmit light, but objects cannot be
distinguished through them: ground glass, oiled paper, &c., belong to this
class. Ofague bodies do not transmit light ; for example, wood, metals, &c.
No bodies are quite opaque ; they are all more or less translucent when cut
in sufficiently thin leaves.
Foucault showed that when the object-glass of a telescope is thinly
silvered, the layer is so transparent that the sun can be viewed through it
without danger to the eyes, since the metallic surface reflects the greater
part of the heat and light.
513. Luminous ray and pencil.—A luminous ray is the direction of the
line in which light is propagated ; a /umznous pencil is a collection of rays
from the same source; it is said to be parallel when it is composed of
parallel rays, divergent when the rays separate from each other, and com-
vergent when they tend towards the same point. Every luminous body emits
divergent rectilinear rays from all its points, and in all directions.
514. Propagation of light in a homogeneous medium.—A medium is
any space or substance which light can traverse such as a vacuum, air, water,
506 On Light [514—
glass, &c. A medium is said to be homogeneous when its chemical com-
position and density are the same in all parts.
In every homogeneous medium light ts propagated in a right line. For,
if an opaque body is placed in the right line which joins the eye and the
luminous body, the light is intercepted. The light which passes into a dark
room by a small aperture is visible from the light falling on the particles of
dust suspended in the atmosphere.
Light changes its direction on meeting an object which it cannot pene-
trate, or when it passes from one medium to another. These phenomena
will be described under the heads reflection and refraction.
515. Shadow, penumbra.—When light falls upon an opaque body it
cannot penetrate into the space immediately behind it, and this space is
called the shadow.
Fig. 460
In determining the extent and the shape of a shadow projected by a body,
two cases are to be distinguished: that in which the source of light is a
single point, and that in which it is a body of any given extent.
In the first case, let S (fig. 460) be the luminous point, and M a spherical
body, which causes the shadow. If an infinitely long straight line, SG,
Fig. 46r
move round the sphere M tangentially, always passing through the point S,
this line will trace a conical surface, which, beyond the sphere, separates
that portion of space which is in shadow from that which is illuminated. In
the present case, on placing a screen, PQ, behind the opaque body the limit
—515] Shadow, Penumbra 507
of the shadow HG will be sharply defined. This is not, however, usually
the case, for luminous bodies have always a certain magnitude, and are not
merely luminous points.
Suppose that the luminous and illuminated bodies are two spheres, SL
and MN (fig. 461). If an infinite straight line, AG, moves tangentially to
both spheres, always cutting the line of centres in the point A, it will pro-
duce a conical surface with this point for a summit, and which traces behind
the sphere MN a perfectly dark space MGHN. Ifa second right line, LD,
which cuts the line of centres in B, moves tangentially to the two spheres, so
as to produce a new conical surface, BDC, it will be seen that all the space
outside this surface is illuminated, but that the part between the two conical
surfaces is neither quite dark nor quite light. So that if a screen, PO,\is
placed behind the opaque body, the portion cGdH of the screen is quite in
the shadow, while the space aé receives light from certain parts of the lumi-
nous body, and not from others. It is brighter than the true shadow, and
not so bright as the rest of the screen, and it is accordingly called the
penumobra.
Shadows such as these are geometrical shadows; physical shadows, or
those which are really seen, are by no means so Sharply defined. A certain
quantity of light passes
into the shadow, even
when the source of light
is a mere point, and con-
versely the shadow influ- £
ences the _ illuminated |
part. This phenomenon,
which will be afterwards
described, is known by
the name of adffraction
(660).
The explanation of the phenomena of eclzfses follows directly from the
theory of shadows.
When the opaque disc of the moon comes, according to the conditions,
between the sun and the earth, the shadow cast by the moon causes a more
or less complete solar eclipse on those parts of the earth which it meets.
Let S be the sun, T the earth, and L the moon placed in a position
favourable for an eclipse (fig. 462). If we can suppose the three bodies
represented with their ve/ative magnitudes and distances, we need only
repeat the graphical construction of this figure to determine the dimensions of
the cone of the shadow, and of the penumbra of the moon. The length LI
of the cone of the shadow varies between 57 and 59 terrestrial radii, accord-
ing to the relative positions of the earth and its satellite ; the distance of
the two planets varies between 55 and 62 such radii; hence, under favour-
able conditions the cone of the shadow may reach the earth, and in those
points of the earth thus touched, 7, there is a total eclipse of the sun. As
this area has relatively a small extent, an eclipse which is visible by the
inhabitants of this area is not seen by those in the neighbourhood. After the
lapse of a time which never exceeds 3 min. 13 sec. the cone will have left
the place #z and will pass to wz’, which is not necessarily on the same
oS
Sos>
PRS
Fig. 462
508 On Light [515—
parallel of latitude. It will thus sweep over the surface of the earth, in
virtue of the special motion of the two heavenly bodies, along a line which
astronomers can determine beforehand. On all points along this line (fig-
463) there will successively be a total eclipse ; for adjacent ones, which are
within the cone of the penumbra, the eclipse will be fartzal.
If the cone of the shadow does not reach the earth, there will nowhere be
a total eclipse ; but on a point m’ (fig. 464) there will be no light from the
Fig. 463
central part of the sun; this willthen appear like a black circle surrounded
by a bright ring (fig. 465), and forms what is called an axnular eclipse.
Total or partial eclipses of the moon are produced by the total or partial
immersion of the moon in the cone of the shadow cast by the earth ; for an
observer on the moon they would constitute total or partial eclipses of the sun ;
total at those parts of the moon in the shadow, fartza/ at those in the penumbra.
The ¢vanszts of Venus or of Mercury over the sun are phenomena of the
same kind as eclipses, being produced by the projection on the earth of the
Fig. 465
penumbral cones of shadow of those planets. The eclipses of the satellites
of certain planets such as Jupiter are identical with the eclipses of the moon.
The shadow of a body, a sphere for instance, in sunlight is about 110 times
as long as the body is broad. This follows from the proportion
Distance of the sun _ Diameter of the sun
Length of the shadow _ Diameter of the sphere’
516. Images produced by small apertures.—When rays of light which
pass into a dark chamber through a sa// aperture are received upon a
-516] lmages produced by Small Apertures 509
screen, they form images of external objects. These images are inverted ;
their shape is always that of the external objects, and is independent of the
shape of the aperture.
The inversion of the images arises from the fact that the luminous rays
proceeding from external objects, and penetrating into the chamber, cross
one another in passing the aperture, as shown in fig. 466. Continuing in a
straight line, the rays from the higher parts meet the screen at the lower
parts ; and conversely, those which come from the lower parts meet the
Fig. 466
higher parts of the screen. Hence the inversion of the image. In the
article Camera Obscura (613) it will be seen that the brightness and precision
of these images are increased by means of lenses.
In order to show that the shape of the image is independent of that of
the aperture, when the latter is sufficiently small and the screen at an ade-
quate distance, imagine a triangular aperture, O (fig. 467), made in the door
of a dark chamber, and let ad be a screen on which is received the image of
a flame, AB. A divergent pencil from each point of the flame passes through
the aperture, and forms on the screen a triangular image resembling the
Fig. 467
aperture. But the union of all these partial images produces a total image
of the same form as the luminous object. For if we conceive that an infinite
straight line moves round the aperture, with the condition that it is always
tangential to the luminous object AB, and that the aperture is very small,
the straight line describes two cones, the apex of which is the aperture,
while one of the bases is the luminous object and the other the luminous
object on the screen—that is, the image. Hence, if the screen is per-
pendicular to the right line joining the centre of the aperture and the centre
of the luminous body, the image is similar to the body ; but if the screen is
510 On Light [516—
oblique, the image is elongated in the direction of its obliquity. This is
what is seen in the patches of light on the ground when solar light falls upon
foliage ; the rays of the sun passing through the minute interstices between
the leaves produce images of the sun, which are either round or elliptical,
according as the ground is perpendicular or oblique to the solar rays ; arid
this is the case whatever be the shape of the aperture through which the
light passes.
517. Velocity of Light.—Light moves with such a velocity that at the
surface of the earth there is, to ordinary observation, no appreciable interval
between the occurrence of any luminous phenomenon and its perception by
the eye. And, accordingly, this velocity was first determined by means of
astronomical observations. Rdmer, a Danish astronomer, in 1675, first
deduced the velocity of light from observations of the eclipses of Jupiter’s
first satellite.
Jupiter is a planet, round which four satellites revolve, as the moon
does round the earth. This first satellite, E (fig. 468), suffers occuwltation—
that is, passes into Jupiter’s shadow—at equal intervals of time, which are
42h..28m. 36s. While the earth moves in that part of its orbit, ad, nearest
Jupiter its distance from that planet does not materially alter, and the
intervals between two successive occultations of the satellite are approximately
the same; but, in proportion as the earth moves away in its revolution
round the sun, S, the interval between two occultations increases, and when,
at the end of six
months, the earth
has passed from
the position T to
the position T’, a
total retardation of
16m. 36s.is observed
between the time
at which the phe-
nomenon is seen
and that at which
it is calculated to take place. But when the earth was in the position T, the
sun’s light reflected from the satellite E had to traverse the distance ET,
while in the second position the light had to traverse the distance ET.
This distance exceeds the first by the quantity TT’, for, from the great dis-
tance of the satellite E, the rays ET and ET’ may be considered parallel.
Consequently, light requires 16m. 36s. to travel the diameter TT’ of the
terrestrial orbit, or twice the distance of the earth from the sun, which gives
for its velocity 190,000 miles in a second.
The stars nearest the earth are separated from it by at least 206,265
times the distance of the sun. Consequently, the light which they send
requires more than 3 years to reach us. Those stars which are only visible
by means of the telescope are possibly at such a distance that thousands
of years would be required for their light to reach our planetary system.
They might have been extinguished for ages without our knowing it.
518. Foucault’s apparatus for determining the velocity of light.—Not-
withstanding the prodigious velocity of light, Foucault succeeded in deter-
Fig. 468
-518] Apparatus for determining the Velocity of Light 511
mining it experimentally by the aid of an ingenious apparatus, based on the
use of the rotating mirror, which was adopted by Wheatstone in measuring
the velocity of electricity.
In the description of this apparatus, a knowledge of the principal pro-
perties of mirrors and of lenses is presupposed. Fig. 469 represents the
chief parts of Foucault’s arrangement. The window shutter, K, of a dark
chamber is perforated by a rectangular slit, behind which the platinum
wire 9 is stretched vertically. A beam of sunlight reflected from the out-
side upon a mirror enters the dark room by the slit, meets the platinum
wire, and then traverses an achromatic lens, L, with a long focus placed
at a distance from the platinum wire less than double the principal focal
distance. The image of the platinum wire, more or less magnified, would
thus be formed on the axis of the lens; but the pencil of light, having
traversed the lens, impinges on a plane mirror, m, rotating with great
velocity ; it is reflected from this, and forms in space an image of the
Fig. 469 Fig. 470
platinum wire, which is displaced with an angular velocity double that of the
mirror (532). This image is reflected by a concave mirror, M, whose centre
of curvature coincides with the axis of rotation of the mirror 7, and with its
centre of figure. The pencil reflected from the mirror M returns upon itself,
is again reflected from the mirror m, traverses the lens a second time, and
forms an image of the platinum wire, which appears on the wire itself so
long as the mirror 7 is at rest or turns slowly.
In order to see this image without hiding the pencil of light which enters
by the aperture in K, a plane parallel mirror of unsilvered glass, V, is
placed between the lens and the wire, and is inclined so that the reflected
rays fall upon a powerful eyepiece, P.
The apparatus being arranged, if the mirror 7 is at rest, the pencil after
meeting M is reflected to 7, and thence returns along its former path, till
it meets the glass plate V in a, and being partially reflected, forms at d—
the distance ad being equal to ao—an image of the wire, which the eye is
512 On Light ~ [518-
enabled to observe by means of the eyepiece, P. If the mirror, instead of
being fixed, is moving slowly round—its axis being at right angles to the
plane of the paper—there will be no sensible change in the position of the
mirror # during the brief interval elapsing while light travels from # to M
and back again, but the image will alternately disappear and reappear. If
now the velocity of M is increased to upwards of 30 turns per second, the
interval between the disappearance and reappearance ‘is so short that the
impression on the eye is persistent, and the image appears perfectly steady.
Lastly, if the mirror turns with sufficient velocity, there is an appreciable
change in its position during the time which the light takes in making the
double journey from #z to M, and from M to mm: the return ray, after its
reflection from the mirror #, takes the direction 7d, and forms its image
at z; that is, the image has undergone a total deviation a. Speaking pre-
cisely, there is a deviation as soon as the mirror turns, even slowly ; but it is
only appreciable when it has acquired a certain magnitude, which is the case
when the velocity of rotation is sufficiently rapid, or the distance Mv suffi-
ciently great, for the deviation necessarily increases with the time which the
light takes in returning on its own path. In Foucault’s experiment the dis-
tance Mw was only 134 feet ; when the mirror rotated with a velocity of 600
to 800 turns in a second, deviations of 0°2 to 0°3 mm. were obtained.
Taking Mma=/, La=J’, oL=rs, and representing by # the number of
turns in a second, by 6 the absolute deviation dz, and by V the velocity of
light, Foucault arrived at the formula
| 8rlPar
8047)
from which the velocity of light is calculated at 185,157 miles in a second ;
this number agrees remarkably well with the value deduced from newer
determinations of the value of the solar parallax.
The mechanism by which the mirror was turned consisted of a small
steam turbine, bearing a sort of resemblance to the siren, and, like that
instrument, giving « higher sound as the rotation is more rapid: in fact, it
is by the pitch of the note that the velocity of the rotation is determined.
In this apparatus liquids can be experimented upon. For that purpose
a tube, AB, ro feet long, and filled with distilled water, is placed between the
turning mirror #, and a concave mirror M’, identical with the mirror M.
The luminous rays reflected by the rotating mirror, in the direction 72M’,
traverse the column of water AB twice before returning to V. But the return
ray then becomes reflected at c, and forms its image at #: the deviation is
consequently greater for rays which have traversed water than for those
which have passed through air alone ; hence the velocity of light is less in ,
water than in air. .
This is the most important part of these experiments. It is a necessary
consequence of the undulatory theory that the velocity of light must be less in
the more highly refracting medium (652), while the opposite is a necessary
consequence of the emission theory. Hence Foucault’s result may be
regarded as a crucial test of the validity of the undulatory theory.
519. Experiments of Fizeau.—In 1849 Fizeau measured directly the
velocity of light, by ascertaining the time it took to travel from Suresnes to
~520] Laws of the Intensity of Light 513
Montmartre and back again. Theapparatus employed was a toothed wheel,
capable of being turned more or less quickly, and with a velocity that could
be exactly ascertained. The teeth were made of precisely the same width
as the intervals between them. The apparatus being placed at Suresnes, a
pencil of rays was transmitted through an interval between two teeth to a
mirror placed at Montmartre. The pencil, directed by a properly arranged
system of lenses, returned to the wheel. As long as the apparatus was at
rest the pencil returned exactly through the same interval as that through
which it first set out. But when the wheel was turned sufficiently fast, a tooth
was made to take the place of an interval, and the ray was intercepted. As
the wheel was turned still more rapidly, the light reappeared when the in-
terval between the next two teeth had taken the place of the former tooth at
the instant of the return of the pencil.
The distance between the two stations was 28,334 feet. Froma knowledge
of this distance, the dimensions of the wheel, its velocity of rotation, &c.,
Fizeau found the velocity of light to be 196,000 miles per second—a result
agreeing with that given by astronomical observation as closely as can be
expected in a determination of this kind.
Cornu recently investigated the velocity of light by Fizeau’s method,
but with improvements so that the probable error did not exceed ;4, of the
total amount ; the two stations, which were 6:4 miles apart, were a pavilion
of the Ecole Polytechnique and a room in the barracks of Mont Valérien.
By means of electro-magnetic arrangements the rotation of the toothed disc,
and the times of obscuration and illumination, were registered on a blackened
cylinder, on the principle of the method described in art. 248. Cornu thus
obtained the number 185,420 miles—a result closely agreeing with that of
Foucault, and supported by calculations based on the results of astronomical
observations of the transit of Venus in 1874.
Newcomb improved Foucault’s method by using a slightly concave mirror
instead of a plane one, by which the image of the slit was brighter; it was
observed by a telescope through a distance of 4,000 metres. The rotations
also were reversed, by which the angle between the two positions of the
telescope was observed with greater accuracy ; he thus obtained the number
186,364 miles, while Michelson repeated a former determination and found
186,354, a difference of only about 10 miles.
520. Laws of the intensity of light.—The zzzenszty of illumination is
the quantity of light re-
ceived on the unit of sur-
face ; 1t is subject to the
following laws :—
I. The intensity of tllu-
mination on a given sur-
face ts inversely as the
sguare of tts distance from
the source of light.
Il. The intensity of Fig. 471
tllumination which ts re-
ceived obliquely ts proportional to the cosine of the angle which the luminous
rays make with the normal to the illuminated surface.
LL
S14 On Light [520-
In order to demonstrate the first law, let there be two circular screens,
CD and AB (fig. 472), one placed at a certain distance from a source
of light, L, regarded as a point, and the other at double this distance, and let
s and S be the areas of the two screens. If @ be the total quantity of light
which is emitted by the source in the direction of the cone ALB, the intensity
of the light on the screen CD—that is, the quantity which falls on the unit of
surface—is < and the intensitv on the screen AB is x
Now as the triangles ALB and CLD are similar, the diameter of AB is
double that of CD ; and as the surfaces of circles are as the squares of their
diameters, the surface S is four times s, consequently the intensity = is one-
fourth that of “.
S
Fig. 472 shows that it is owing to the divergence of the luminous rays
emitted from the same source that the intensity of light is inversely as the
square of the distance ; the illumination of a surface placed in a beam of
parallel luminous rays is the same at all distances in a vacuum. In air and
in other transparent media the intensity of light decreases, in consequence
of absorption, more rapidly than the square of the distance.
The second law of intensity corresponds to the law which we have found
to prevail for heat: it may be theoretically deduced as follows :—Let DA,
EB (fig. 472) be a pencil of parallel
rays falling obliquely on a surface,
AB, and let ov be the normal to this
surface. If S is the section of the
pencil, a the total quantity of light
which falls on the surface AB, and
I that which falls on the unit of
surface—that is, the intensity of
Fig. 472
illumination—we have I= ae But
as S is only the projection of AB on a plane perpendicular to the pencil, we
Ss ;
This
know from trigonometry that S=AB cos a, from which AB=
cos a
value substituted in the above equation gives I =% cos @; a formula which
demonstrates the law of the cosine, for as a and S are constant quantities, I
is proportional to cos a.
The law of the cosine applies also to rays emitted obliquely by a luminous
surface ; that is, the rays are less intense in proportion as they are more
inclined to the surface which emits them. In this respect they correspond
to the third law of the intensity of radiant heat.
521. Photometers.—A fhotfometer is an apparatus for measuring the
relative intensities of different sources of light.
Rumford s photometer.—This consists of a ground-glass screen, in front
of which is fixed an opaque rod (fig. 473) ; the lights to be compared—for
instance, a lamp and a candle—are placed at a certain distance in such a
manner that each projects on the screen a shadow of the rod, Theshadows
-§21] Photometers 515
thus projected are at first of unequal intensity, but by altering the position
of the lamp it may be so placed that the intensity of the two shadows is the
same. Then, since the shadow thrown by the lamp is illuminated by the
candle, and that thrown by the candle is illuminated by the lamp, the illu-
mination of the screen due to each light is the same. The intensities of the
two lights—that is, the illuminations which they would give at equal dis-
tances—are then directly proportional to the squares of their distances from
the shadows ; that is to say, if the lamp is three times the distance of the
candle, its illuminating power is nine times as great.
For if z and z’ are the intensities of the lamp and the candle at the unit
of distance, and d@ and @’ their distances from the shadows, it follows, from
the first law of the intensity of light, that the intensity of the lamp at the
distance d is, and that of the eandlea at the distance a’. On the screen
these two intensities are equal ; hence — ia =—., which was to be
z = 2
proved.
Bunsen’s photometer—When a grease-spot is made on a piece of bibu-
lous paper, the part appears translucent. If the paper be illuminated by a
light placed in front, the spot appears darker than the surrounding space ;
if, on the contrary, it be illuminated from behind, the spot appears light on
a dark ground. If the greased part and the rest appear unchanged, the
intensity of illumination on both sides is the same. Bunsen’s photometer
depends on an application of this principle. Its essential features are repre-
sented in fig. 474. A circular spot is made on a paper screen by means of a
solution of spermaceti in naphtha : on one side of this is placed a light of a
certain intensity, which serves as a standard ; in London it isa sperm candle
4 of an inch in diameter, and burning 120 grains in an hour. The light to
be tested, a petroleum lamp or a gas burner consuming a certain volume of
gas in a given time, is then moved in a right line to such a distance on the
other side of the screen that there is no difference in brightness between the
greased part and the rest of the screen. By measuring the distances of
Ela
516 On Light [521-
the lights from the screen by means of the scale, their relative illuminating
powers are respectively as the squares of their distances from the screen.
The difficulty of getting more carefully constructed candles to give a
light sufficiently uniform for standard purposes has led Harcourt to adopt
as unit the light formed by burning a mixture of 7 volumes of pentane gas and
20 volumes of air, at the rate of half a cubic foot in an hour, in a specially
constructed burner so as to produce a flame of a definite height. This has
been found to answer well in practice. By this kind of determination the
Fig. 474
degree of accuracy which can be attained is not so great as in many physical
determinations, more especially when the lights to be compared are of dif-
ferent colours ; one, for instance, being yellow, and the other of a bluish tint.
It gives, however, results which
are sufficiently accurate for practical
purposes, and is almost universally
employed for determining the il-
luminating power of coal gas and
of other artificial lights.
In” *Germany “ithe” ffve777e
Alteneck lamp is much used as
standard ; the combustible is
amylic acetate or artificial pear oil,
and a flame of constant height is produced in a burner of special con-
struction.
The absolute unit of light adopted by the International Congress of
Electricians, proposed by M. Violle, is that emitted by a square centimetre
of melted platinum at the moment of its solidification. It is equal to about
fifteen standard candles.
Wheatstone’s photomeier.—The principal part of this instrument is a
steel bead P (fig. 475), fixed on the edge of a disc, which rotates on a
pinion, 0, working in a larger toothed wheel. The wheel fits in a cylindrical
brass box which is held in one hand, while the other works a handle, A
which turns a central axis, the motion of which is transmitted by a spoke,
a, to the pinion 9. In this way the latter turns on itself, and at the same
time revolves round the circumference of the box; the bead shares the
double motion and consequently describes a curve in the form of a rose
(fig. 476).
Fig. 476
—522] Relative Intensities of various Sources of Light 517
Now, let M and N be the two lights whose intensities are to be com-
pared ; the photometer is placed between them and rapidly rotated. The
brilliant points produced by the reflection of the light on the two opposite
sides of the beads give rise to two luminous bands, arranged as represented
in fig. 476. If one of them is more brilliant than the other—that which pro-
ceeds from the light M, for instance—the instrument is brought nearer the
other light until the two bands exhibit the same brightness. The distance
of the photometer from each of the two lights being then measured, their
intensities are proportional to the squares of the distances.
522. Relative intensities of various sources of light.—The light of the
sun is 600,000 times as powerful as that of the moon ; and 16,000,000,000
times as powerful as that of a Centauri, the third in brightness of all the
stars. The moon is thus 27,000 times as bright as this star ; the sun is 5,500
million times as bright as Jupiter, and 80 billion times as bright as Neptune.
Its light is estimated to be equal to 670,000 times that of a wax candle
at a distance of 1 foot. According to Fizeau and Foucault the electric light
produced by 50 Bunsen’s cells is about 4 as strong as sunlight.
The relative luminosities of the following stars are as compared with
Vega=1: Pole Star o13, Aldebaran o°30, Saturn 047, Arcturus 0°79,
Mars 2°93, Sirius 4°291, Jupiter 8:24, Venus 38°9.
A difference in the strength of light or shadow is perceived when the
duller light is 2 of the brightness of the other, and both are near together,
especially when the shadow is moved about.
Our requirements as regards illumination are constantly on the increase ;
thus for public receptions of a state character in recent times in Paris, a
number of lamps was used corresponding to over 13 candles per square
yard, which is 6 times as much as was used on the occasion of the marriage
of the Dauphin in 1745; the former, however, is still far removed from
perfect illumination, that of daylight, which is estimated at about 180 candles
per square yard.
518 On Light [523—
CHAPTER!
REFLECTION OF LIGHT. MIRRORS
523. Laws of the reflection of light.—When a ray of light meets a
polished surface, it is reflected according to the two following laws, which,
as we have seen, also hold for heat.
I. The angle of reflection ts equal to the angle of incidence.
Il. Zhe incident and the reflected ray are both in the same plane, which
zs perpendicular to the reflecting surface.
The words are here used in the same sense as in article 424, and need
no further explanation.
first proofi—The two laws may be demonstrated by the apparatus
represented in fig. 477. It consists of a graduated circle in a vertical plane.
Two brass slides move round the cir-
cumference ; on one of them there is
a piece of ground glass, P, and on the
other an opaque screen, N, in the
centre of which is a small aperture.
Fixed to the latter slide there is also
a mirror, M, which can be more or less
inclined, but always remains in a plane
perpendicular to the plane of the gra-
duated circle. Lastly, there is a small
polished metallic mirror, 7, placed
horizontally in the centre of the circle.
In making the experiment, a pencil
of solar or any suitable artificial light,
S, is caused to fall on the mirror M,
which is so inclined that the reflected
light passes through the aperture in
N, and falls on the centre of the mirror,
=|
SSS Se m. The luminous pencil then experi-
Fig. 477 ences a second reflection in a direction
mP, which is ascertained by moving
P until an image of the aperture is found in its centre. The number of
degrees comprised in the arc AN is then read off, and likewise that in AP ;
these being equal, it follows that the angle of reflection AzzP is equal to the
angle of incidence AmM.
The second law follows from the arrangement of the apparatus, the plane
of the rays Mzz and mP being parallel to the plane of the graduated circle,
and consequently perpendicular to the mirror z.
Second proof.—The law of the reflection of light may also be demon-
—525| Reflection of Light from Plane Surfaces 519
strated by the following experiment, which is susceptible of greater accuracy
than that just described :— In the centre of a graduated circle, M (fig. 478),
placed in a vertical position, there is a small telescope movable in a plane
parallel to the limb ; ata suitable distance there is a vessel D full of mercury,
which forms a perfectly horizontal plane mirror. Some particular star of
the first or second magnitude is viewed through the telescope in the direc-
tion AE, and the telescope is then inclined so as to receive the ray AD coming
from the star after being reflected from the brilliant surface of the mercury.
Fig. 478
In this way the two angles formed by the rays EA and DA, with the hori-
zontal AH, are found to be equal, from which it may easily be shown that
the angle of incidence E’DE is equal to the angle of reflection EDA. For
if DE is the normal to the surface of the mercury, it is perpendicular to AH,
and AED, ADE are the complements of the equal angles EAH, DAH ;
therefore AED, ADE are equal ; but the two rays AE and DE’ may be
considered parallel, in consequence of the great distance of the star, and
therefore the angles EDE’ and DEA are equal, for they are alternate angles
and consequently the angle E’DE is equal to the angle EDA.
REFLECTION OF LIGHT FROM PLANE SURFACES
524. Mirrors. Images.—J/rrors are bodies with polished surfaces which
show by reflection objects presented to them. According to their shape,
mirrors are divided into plane, concave, convex, spherical, parabolic, conical, &c.
Rays of light diverging from any point of the object and falling upon a
mirror, are caused by reflection either to converge to, or to appear to diverge
from, a second point. In either case the second point is called an image of
the first point.
525. Formation of images by plane mirrors.—The determination of the
position and size of images resolves itself into investigating the images of
a series of points. And first, the case of a single point, A, placed in front of
a plane mirror, MN (fig. 479) will be considered. ey, ray, AB, incident
from this point on the mirror is reflected in the direction BO, making the
angle of reflection DBO equal to the angle of incidence DBA.
520 On Light [525—
If now a perpendicular, AN, be let fall from the point A on the mirror,
and if the ray OB be prolonged below the mirror until it meets this perpen-
dicular in the point a, two triangles are formed, ABN and BNa, which are
equal, for they have the side BN common to both, and the angles ANB,
ABN, equal to the angles aNB, aBN ; for the angles ANB and @NB are
right angles, and the angles ABN and @BN are each equal to the angle
OBM. From the equality of these triangles, it follows that aN is equal to
AN ; that is, that any ray, AB, takes such a direction after being reflected,
that its prolongation below the mirror cuts the perpendicular Aa in the point
a, which is at the same distance fromthe mirror as the point A. This
applies also to the case of any other ray from the point A ; AC, for example.
Fig. 479 Fig. 480
From this the important consequence follows, that all rays from the point
A, reflected from the mirror, follow, after reflection, the same dtrection as if
they had all proceeded from the point a. The eye is deceived, and sees a
reproduction of the point A at a, as if it were really situated at a. Hence in
plane mirrors ¢he tmage of any point ts formed behind the mirror at a distance
equal to that of the given point, and on the perpendicular let fall from this
point on the mtrror.
It is manifest that the image of any object will be obtained by construct-
ing, according to this rule, the image of each of its points, or, at least, of
those which are sufficient to determine its form. Fig. 480 shows how the
image @é of any object, AB, is formed.
It follows from this construction that in plane mirrors ¢he zmage zs of the
same size as the object ; for if the trapezium ABCD be applied to the trape-
zium DCaé, they are seen to coincide, and the object AB agrees with its
image. A further consequence is, that in plane mirrors the image is sym-
metrical in reference to the object, and not inverted.
526. Virtual and real images.—There are two cases relative to the
direction of rays reflected by mirrors according as the rays after reflection
are convergent or divergent. In the latter case the reflected rays do not
meet, but if they are supposed to be produced on the other side of the mirror,
their prolongations meet in the same point, as shown in figs. 479 and 48o.
The eye is then affected just as if the rays proceeded from this point, and
it sees an image. But the image has no rea! existence, the luminous rays do
not come from the other side of the mirror: this appearance is called the
virtual tmage. The images of real objects produced by plane mirrors are
of this kind.
528] Multiple Images from two Plane Mirrors 521
In the second case, where the reflected rays converge, as we shall
soon see in concave mirrors, the rays meet at a point in front of the mirror
and on the same side as the object. They form there an image called the
real image, for it can be received on a screen. The distinction may be ex-
pressed by saying that veal zmages are those formed by the reflected rays
themselves, and virtual tmages those formed by their prolongations.
527. Multiple images formed by glass mirrors.—Metal mirrors which
have but one reflecting surface give only one image; glass mirrors give rise
to several images, which are readily observed |
when the image of a candle is looked at obliquely
in a looking-glass. A very feeble image is first
seen, and then a very distinct one; behind this
there are several others, whose intensities gra-
dually decrease until they disappear.
This phenomenon arises from the looking-glass
having two reflecting surfaces. When the-rays
from the point A meet the surface, fig. 481, a partis
reflected and forms an image, a, of the point A, on
the prolongation of the ray dE, reflected by this
surface ; the other part passes into the glass (548), and is reflected at c from
the layer of metal which covers the hinder surface of the glass, and reaching
the eye in the direction dH, gives the image a’. This image is distant from
the first by double the thickness of the glass. It is brighter, because metal
reflects better than glass.
In regard to other images it will be remarked that whenever light is trans-
mitted from one medium to another—for instance, from glass to air—(548),
only some of the rays get through ; the remainder are reflected at the surface
which bounds the two media. Consequently when the pencil cd, reflected
from ¢c, attempts to leave the glass at @, most of the rays composing it pass
into the air, but some are reflected at d@, and continue within the glass.
These are again reflected by the metallic surface, and form a third image of
A; after this reflection they come to MN, when many emerge and render
the third image visible ; but some are again reflected within the glass, and
in a similar manner give rise to a fourth, fifth, &c., image, thereby complet-
‘ing the’ series above described. It is manifest from the above explanation
that each image must be much feebler than the one preceding it, and con-
sequently only a small number are visible—ordinarily not more than eight
or ten in all.
This multiplicity of images is objectionable in observations, and, accord-
ingly, metal mirrors are to be preferred in optical instruments.
528. Multiple images from two plane mirrors.—When an object is
placed between two plane mirrors, which form an angle with each other,
either right or acute, images of the object are formed, the number of which
increases with the inclination of the mirrors. If they are at right angles to
each other, three images are seen, arranged as represented in fig. 482. The
rays OC and OD from the point O, after a single reflection, give the one an
image O’, and the other an image O”, while the ray OA, which has under-
gone two reflections at A and B, gives the third image O’’”. When the
angle of the mirrors is 60°, five images are produced, and seven if it is 45°.
Fig. 481
522 On Light [528—
The number of images continues to increase in proportion as the angle
diminishes, and when it is zero—that is, when the murrors are parallel—the
number of images is theoretically infinite. In general, if two mirrors are
inclined to each other at an angle which is
an exact submultiple of 180° (e.g. 30°, 45°,
60°, 90°), the number of images they produce
—counting for this purpose the object as one
image—is equal to the number of times the
angle between them is contained in 360.
The alezdoscofe, invented by Sir D.
Brewster, depends on this property of
inclined mirrors. It consists of a tube, in
which are three mirrors inclined at 60° ; one
end of the tube is closed by a piece of
ground glass, and the other by a cap pro-
Rig. 484 vided with an aperture. Small irregular
pieces of coloured glass are placed at one
end between the ground glass and another glass disc, and when looked at
through the aperture, the other end being held towards the light, the objects
and their images are 'seen arranged in beautiful symmetrical forms ; by
turning the tube, an almost endless variety of these shapes is obtained.
529. Multiple images in two plane parallel mirrors.—In this case the
number of images of an object placed between them is theoretically infinite.
Physically the number is limited, for as the incident light is never totally
reflected, some of it being always absorbed, the images gradually become
fainter, and are ultimately quite extinguished.
Fig. 483 shows how the pencil La reflected once from M gives at I the:
image of the object L at a distance mI =mL; then the pencil L@ reflected
once from the mirror M, and once from N,
furnishes the image I’ at a distance zI’=~lI ;
in like manner the pencil Le, after two reflec-
tions on M, and one on N, forms the image I”
at a distance #1” =mlI’, and so on for an in-
Fig. 483
finite series. The images’ z, 2’, 2’’, are forned
in the same manner iby rays of light waich,,.
emitted by the object L, fall first on the mirror N.
530. Irregular reflection. Diffused light.—The reflection from the
surfaces of polished bodies, the laws of which have been just stated, is called
the regular or specular reflection ; but the quantity thus reflected 1s less.
-532] Intensity of Reflected Light 523
than that of the incident light. The light incident on an opaque body
separates, in fact, into three parts: one is reflected vegularly ; another
trregularly—that is, in all directions; while a third is extinguished, or
absorbed by the reflecting body. If light falls on a transparent body, a
considerable portion is transmitted with regularity.
The irregularly reflected light is called scattered light: it is that which
makes bodies visible (514). The light which is reflected regularly does not
give us the image of the reflecting surface, but that of the body from
which the light proceeds. If, for example, a beam of sunlight be incident on
a well-polished mirror in a dark room, the more perfectly the light is reflected
the less visible is the mirror in the different parts of the room. The eye
does not perceive the image of the mirror, but that of the sun. If the reflect-
ing power of the mirror be diminished by sprinkling on it a light powder, the
sun’s image becomes feebler, and the mirror is visible from all parts of the
room. Perfectly smooth, polished reflecting surfaces, if such there were,
would be invisible. The beam of light itself is only seen in the room owing
to irregular reflections from the particles of dust, and the like, which are
floating in the air. Tyndall showed that when this floating matter in the
air in an enclosed space is completely removed, the beam of sunlight or the
electric light is quite invisible. The atmosphere diffuses the light which
falls on it from the sun in all directions, so that it is light in places which
do not receive the direct rays of the sun. Thus, the upper layers of the air
diffuse the light which they receive before sunrise and after sunset, and ac-
cordingly give rise to the phenomena of fw2/ight.
531. Intensity of reflected light.—The intensity of the light reflected is
always less than that of the incident light, for some of the original vibrations
are converted into vibrations of the reflecting surfaces. The intensity
increases with the obliquity of the incident ray. For instance, if a sheet
of white paper be placed before a candle, and be looked at very obliquely,
an image of the flame is seen by reflection, which is not the case if the eye
receives less oblique rays.
The quantity of the reflected light varies with different bodies, even when
the degree of polish and the angle of incidence are the same. Thus with
perpendicular incidence, the light reflected from a metal mirror is 2 of the
incident light, $ from mercury, 34 from glass, and »4 from water. It also
varies with the nature of the medium which the ray is traversing before and
after reflection. Polished glass immersed in water loses a great part of its
reflecting power.
In the case of scattered reflection the actual lustre or brightness of a
luminous surface is only a fraction of the light which falls upon it, and
depends on the nature of the surface. If we call the incident light 100, we
have for the brightness of freshly fallen snow 78, white paper 70, white
sandstone 24, porphyry 11, and ordinary earth 8.
532. Reflection of a ray of light in a rotating mirror.—When a hori-
zontal ray of light falls on a plane mirror which can rotate about an axis, if
the mirror is turned through an angle a, the reflected ray is turned through
double the angle.
Let 2m (fig. 484) be the first position of the mirror, 77’ its position
after it has been turned through the angle a; and let OD be the fixed incident
524 On Light [532
ray. If from the centre of rotation C, with any radius we describe the cir-
cumference Ova, and from the point O, where it cuts the incident ray,
chords OO’ and OO” are drawn perpendicular respectively to mn and
m’n’ ; the pons O’ and O” are the i images of the point O in the two posi-
tions of the mirror, and if C is joined to each of
the points O, O’ and O” it will be seen that the
angles CO’D, CO”D’ are equal to each other,
since each is equal to the angle COD. Hence
the chords AO’, A’O” are equal, and therefore
the, arciAAis.equal.to the are OlO7. ihe
rotations of the reflected ray and of the mirror
are thus measured by the two arcs O’O” and
mm’ respectively.
Now, the two angles O’OO” and mCvz’ are
equal, for they have their sides perpendicular
Pig-i¢°4 each to each; but the angle O’OO”, which is
an angle at the circumference, is measured by half the arc O’O”, and the
angle #zCm/’ by the whole arc m7’ ; hence O’O” is the double of #7’, which
shows that when the mirror has turned through an angle a, the reflected ray
has turned through 2a.
533. The sextant.—This instrument is used to measure the angular
distance of any two distant objects ; its principle is as follows. Suppose A
(fig. 485) is a small mirror half silvered, so
that the eye at E, can see through the free
part. Bis a second mirror which can turn
about an axis at right angles to the plane of
the figure. When its plane is parallel to
that of A, the ray EB of a distant object,
which we will call L, is reflected from RB to
A, so that the eye sees simultaneously the
image of L reflected from the silvered part
of the mirror, and directly the object L,
through the unsilvered part in the direction
OE,, L being assumed to be so distant that
EyvB wand EB vare sparallel elie pais, non
parallel to A, but in the position repre-
sented by the shading, the ray EB is not
reflected to the eye, but the image of some
other object F in the direction BF.
Fig. 486 represents one form of sextant
which derives its name from the fact that
only one sixth of the divided circle is used.
Fig. 485 It consists of a graduated metal sector AA,
on which plays the index arm F; this is
provided with a vernier and a micrometer screw by which the index may
be accurately adjusted and also clamped ; G is a lens for more accurate
reading. The mirror B, which is called the zadex glass, is rigidly fixed to
the arm BF and moves with it. The telescope DE is fixed to one arm as
shown, and on the other arm opposite is the horizon glass C, also rigidly
-534] Measurement of Angles by Reflection from Mirrors 525
fixed, the lower half of which is silvered. The axis of the telescope just
traverses the boundary of the silvered and unsilvered part of the mirror.
K and L are dark glasses for shading off the sun’s light.
In making an ob-
servation the sextant
is held vertically by the
handle, H, so that its
plane .passes through
both the objects whose
angular distance is to
be measured. The
index arm being at the
zero of the graduation,
the two mirrors are
parallel. One of the
objects, the horizon for
instance, is viewed
through the telescope
and the unsilvered part
of the mirror C. The
index arm is then
moved until the eye
sees simultaneously Fig. 486
with this the image of
another body, the sun or a star for example, which reaches the eye after
successive reflections from the mirror B, and from the silvered part of the
mirror C. The angle which the two mirrors now form is measured by the
graduation of the sector, and is half the angular distance (532) between the
horizon and the sun.
A great advantage of this instrument is that a slight agitation does not
affect the measurement of the angle; it can accordingly be used on ship-
board, is indispensable
for use at sea, and in
travelling where the
use of a stand is ob-
jectionable.
534. Measurement
of small angles by re-
flection from a mirror.
An important applica-
tion of the laws of re-
flection in measuring
small angles of deflec-
tion in magnetic and
other observations was Fig. 487
first made by Gauss.
The principle of this method will be understood from fig. 487, in which AO:
represents a telescope, underneath which, and at right angles to its axis,
526 On Light [534-
is fixed a graduated scale ss; the centre of which, the zero, corresponds
to the axis of the telescope.
Let NS be the object whose angular deflection is to be measured, a
magnet for instance, and let sm represent a small plane mirror fixed
at right angles to the axis of the magnet. If now, at the beginning
of the observation, the telescope is adjusted so that the image of the zero
appears behind the cross wires, its axis is perpendicular to the mirror. Now
when the mirror is turned, by whatever cause, through an angle a, the eye
will see, through the telescope, the image of another division of the scale, a
for instance, the ray proceeding from which makes with the line cOA the
angle 2a.
From the distance of this division Oa from the zero of the scale and the
Oa
distance Oc from the mirror we have tan 2a = (on Thus, for instance, if Oa
C
is 12 millimetres and Oc 5,000 millimetres, then tan 2a= —, from which
: }
2a=8’ 15’. Asa practised eye can easily read +4, of a millimetre, it 1s pos-
sible by such an arrangement to read off an angular deflection of two seconds.
535. Mance’s heliograph.—The reflection of light from mirrors has been
applied by Sir H. Mance in signalling at great distances by means of the
sun’s light.
The apparatus consists essentially of a mirror about 4 inches in diameter
mounted on a tripod, and provided with suitable adjustments, so that the
sun’s light can be received upon it and reflected to a distant station. An
observer then can see through a telescope the reflection of the sun’s rays as
a spot of light. The mirror has an adjustment by which it can be made to
follow the sun in its apparent motion. There is also a lever key by which
the signaller can deflect the mirror through a very small angle either to the
right or left, and thus the observer at the distant station sees corresponding
flashes to the right or left. Under the subject of Telegraphy it will be seen
how these alternate motions can be used to form an alphabet.
The heliograph proved of essential service in the campaigns in Africa
and Afghanistan. Instead of any special form of apparatus, an ordinary
shaving mirror or handglass is frequently used ; and the proper inclination
having been given so as to send the sun’s rays to the distant station, which
is very easily effected, the signals are produced by obscuring the mirror by
sliding a piece of paper over it for varying lengths of time. In this way
longer or shorter flashes of light are produced, which, properly combined,
form the alphabet.
Of course this mode of signalling can only be used where the sun’s light
is available, but it has the advantage of being cheap, simple, and portable.
Signals have been sent at the rate of 12 words a minute, through distances,
in very fine weather, of 4o miles.
-537] Reflection from a Spherical Concave Mirror Bor,
REFLECTION OF LIGHT FROM CURVED SURFACES
536. Spherical mirrors.—It has been already stated (524) that there
are several kinds of curved mirrors ; those most frequently employed are
spherical and parabolic mirrors.
Spherical mirrors are those whose curvature is that of a sphere ; their
surface may be supposed to be formed by the revolution of an arc MN (fig.
488) about the radius CA, which unites the middle of the arc to the centre
of the circle of which it is a part. According as the reflection takes place
from its internal or from -
its external face, the
mirror is said to be coz-
cave or convex. C, the
centre of the hollowsphere
of which the mirror forms
part, is called the centre of
curvature, or geometrical
centre: the point A is the
centre of the mirror. The infinite right line AL, which passes through A and
C, is the principal axis of the mirror; any right line which simply passes
through the centre C, and not through the point A, is a secondary axis.
The angle MCN, formed by joining the centre and extremities of the
mirror, is the aperture. A principal section is the section made by a plane
through its principal axis. In speaking of mirrors those lines alone will be
considered which lie in the same principal section.
The theory of the reflection of light from curved mirrors is easily deduced
from the laws of reflection from plane mirrors, by considering the surface of
the former as made up of an infinitude of extremely small plane surfaces,
which are its e/ements. The normal to the curved surface at a given point is
the perpendicular to the corresponding element, or, what is the same thing,
to its correspondent tangent plane. It is shown in geometry that in spheres
all the normals pass through the centre of curvature, so that the normal may
readily be drawn to any point of a spherical mirror.
537. Reflection from a spherical concave mirror.—In a curved mirror the
focus of a point isa point in which the reflected rays meet or tend to meet, if
produced either backwards or forwards ; there may be either a veal focus or
a virtual focus corresponding to an incident pencil.
Real focus.—We shall first consider the case in which the rays of light
are parallel to the principal axis, which presupposes that the luminous body
is at an infinite distance. Let GD (fig. 488) be such a ray.
From the hypothesis that curved mirrors are composed of a number of
infinitely small plane elements, this ray would be reflected from the element
corresponding to the point D, according to the laws of the reflection from
plane mirrors (525); that is, that CD being the normal at the point of
incidence D, the angle of reflection CDF is equal to the angle of incidence
GDC, and is in the same plane. It follows from this, that the point F, where
the reflected ray cuts the principal axis, divides the radius of curvature AC
very nearly into two equal parts. For in the triangle DFC the angle DCF
Fig. 488
528 On Light | [537—
is equal to the angle CDG, for they are alternate angles ; likewise the angle
CDF is equal to the angle CDG, from the laws of reflection ; therefore the
angle FDC is equal to the angle FCD, and the sides FC and FD are equal
as being opposite to equal angles. Now the smaller the arc AD, the more
nearly does DF equal AF ; and when the arc is only a small number of
degrees, the right lines AF and FC may be taken as approximately equal,
and the point F may be taken as the middle of AC. So long as the aperture
of the mirror does not exceed 8 to 10 degrees, any other ray HB will, after
reflection, pass very nearly through the point F. Hence, for practical pur-
poses, we may say that when a pencil of rays parallel to the axis falls on a
concave mirror the rays intersect after reflection in the same point, which is.
at an equal distance from the centre of curvature and from the mirror. This
point is called the Arzucipfal focus of the mirror, and the distance AF is the
principal focal distance, or the focal length of the mirror.
All rays parallel to the axis meet in the point F ; and, conversely, if a
luminous point be placed at F, the rays emitted by this point will after
reflection take! the direc-
' tions} DG, BH, ‘parallel to
the principal axis; for in
this case the angles of in-
cidence and reflection have
changed places ; but these
angles always remain equal.
The case is now to be
considered in which the rays
are emitted from a luminous
point, L (fig. 489), placed on the principal axis, but at such a distance that
they are not parallel, but divergent. The angle LKC, which the incident
ray LK forms with the normal KC, is smaller than the angle SKC, which
the ray SK, parallel to the axis, forms with the same normal ; and, conse-
quently, the angle of reflection corresponding to the ray LK must be smaller
than the angle CKF, corresponding to the ray SK. And therefore the ray
LK will meet the axis after reflection in the point /, between the centre C
and the principal focus F. So long as the aperture of the mirror does not
exceed a small number of degrees, all the rays from the point L will inter-
sect after reflection in the point 7. This point is called the conjugate focus of
the point L; for there is this connection between the points L and /, that if
the luminous point were transferred to /, its conjugate focus would be at L,
ZK being the incident and KL the reflected ray.
On considering the figure 489 it will be seen that when the point L is
brought near to or removed from the centre C, its conjugate focus approaches
or recedes in a corresponding manner, for the angles of incidence and re-
flection increase or decrease together.
If the point L coincides with the centre C, the angle of incidence is
null, and as the angle of reflection must be the same, the ray is reflected on
itself and the focus coincides with the luminous point. When the luminous
point is between the centre C and the principal focus, the conjugate focus in
turn is on the other side of the centre, and is further from the centre accord-
ing as the luminous point is nearer the principal focus. If the luminous point
Fig. 489
—538] Reflectton from Convex Mirrors 529
coincides with the principal focus, the reflected rays, being parallel to the
axis, will not meet, and there is, consequently, no focus.
Virtual focus.—There is, lastly, the case in which the luminous point is
at some point, L, between the principal focus and the mirror (fig. 490). Any
ray LM, from the point L, makes with the normal CM an angle of in-
cidence LMC, greater than FMC; the angle of reflection must be greater
than CMS, and therefore the reflected ray ME diverges from the axis AK.
Fig. 490 Fig. 491
This is also the case with all rays from the point L, and hence these rays do
not intersect, and, consequently, form no conjugate focus; but if they are
conceived to be prolonged on the other side of the mirror, their prolongations
will intersect in the same point, /, on the axis, and an eye looking in the
direction KA experiences the same impression as if the rays were directly
emitted from the point 7. Hence a wzrtwal focus is formed quite analogous
to those formed by plane mirrors (525).
Hitherto the luminous point has always been supposed to be placed on
the principal axis itself, and then its focus is formed on this axis. In the
case in which the luminous point is situate on a secondary axis, LB (fig. 491),
by applying to this axis the same reasoning as in the preceding case, it will
be seen that the focus of the point L is formed at a point 7 on the secondary
axis, and that, according to the distance of the point L, the focus may be
either principal, conjugate, or virtual.
538. Reflection from convex mirrors.—In convex mirrors there are only
virtual foci. Let SI, TK .. . (fig. 492) be rays parallel to the principal axis
Of Fae T Cornvex
mirror.’ “Thesé
rays, after reflec-
tion, take the
diverging direc-
tions IM, KH,
which, . when
continued, meet
in Waliipomt ob;
which is the
principal vir- Fig. 492
tual focus of the
mirror. By means of the triangle CKF, it may be shown, in the same
manner as with concave mirrors, that the point F is approximately the
centre of the radius of curvature, CA.
If the incident luminous rays, instead of being parallel to the axis,
M M
530 On Light [538-
proceed from a point L, situated on the axis at a finite distance, it is at once
seen that a virtual focus will be formed at a point /, between the principal
focus F and the mirror.
539. Determination of the principal focus of a mirror.—In the appli-
cations of concave and convex mirrors it is often necessary to know the
radius of curvature. This is tantamount to finding the principal focus ; for
being situated at the middle of the radius, it is simply necessary to double
the focal distance. Be
To find this focus with a concave mirror, it is exposed to the sun’s rays,
so that its principal axis is parallel to them, and then with a small screen of
ground glass the point is
sought at which the image is
formed with the greatest dis-
tinctness ; this is the princi-
pal focus. The radius of the
mirror is double this distance.
If the mirror is convex,
it is covered with paper ;
but two small portions, H
Fig. 493 and I, are left exposed at
equal distances from the centre of the figure A, and on the same principal
section (fig. 493). A screen MN, in the centre of which is an opening larger
than the distance HI, is placed before the mirror. If a pencil of the sun’s
rays, SH, S’I, parallel to the axis, falls on the mirror, the light is reflected at
H and I, on the parts where the mirror is left exposed, and forms on the
screen two bright images at # and z. By moving the screen MN nearer
to or farther from the mirror, a position is found at which the distance Az is
double that of HI. The distance AD from the screen to the mirror then
equals the principal focal distance. For the arc HAI does not sensibly
differ from its chord ; and because the triangles FHI and F/AZz are similar,
a = a but HI is half of Zz, and therefore also FA is the half of FD, and
therefore AD is equal to AF. Further, FA is the principal focal distance ;
for the rays SH and S’I are parallel to the axis : consequently also twice the
distance AD equals the radius of curvature of the mirror.
540. Formation of images in concave mirrors.—It has hitherto been
supposed that the luminous or illuminated object placed in front of the
mirror was sim-
ply a point ; but
if this object has
a certain magni-
tude we can con-
ceive a second-
ary axis drawn
through each of
its points, and
thus a series of
real or virtual foci could be determined, the collection of which composes
the image of the object. By the aid of the constructions which have
Fig. 494
—340] Formation of Images in Concave Mirrors 531
served for determining the foci, we shall investigate the position and
magnitude of these images in concave and in convex mirrors.
Real tmage.—We shall first take the case in which the mirror is concave,
and the object AB (fig. 494) is on the other side of the centre. To obtain
the image or the focus of any point A, a secondary axis, AE, is drawn from
this point, and then drawing from the point A an incident ray AD, the
normal to this point, CD, is taken, and the angle of reflection CDa is made
‘equal to the angle of incidence ADC. The point a, where the reflected ray
cuts the secondary axis AE, is the conjugate focus of the point A, because
every other ray drawn from this point passes through a. Similarly if a
‘secondary axis, BI, be drawn
from the point B, the rays from
this point meet after reflection
in 6, and form the conjugate
focus of B. .And as the images
of all the points of the object
are formed between a and 4, ad
is the complete image of AB.
From what has been said about
foci (537), it follows that ths zmage zs real, inverted, smaller than the object,
and placed between the centre of curvature and the principal focus. This
image may be seen in two ways: by placing the eye in the continuation of
the reflected rays, and then it is an aérial image which is seen ; or the rays
-are collected on a screen, on which the image appears to be depicted.
If the luminous or illuminated object is placed at ad, between the prin-
‘cipal focus and the centre, its image is formed at AB. It is then a real but
inverted image; it is larger than the object, avd the larger as the object, ab,
is nearer the focus.
If the object is placed in the principal focus itself, no image is produced ;
for then the rays emitted from each point form, after reflection, as many
pencils respectively parallel to the secondary axis, which is drawn through
the point from which they are emitted (536), and hence neither foci nor
images are formed.
When all points of the object AB are above the principal axis, it is readily
seen, by repeating the preced-
ing construction (fig. 495), that
the image of.the object is
formed at ad.
Virtual tmage.—The case
remains in which the object is
placed between the principal
focus and the mirror. Let AB
be this object (fig. 496); the
incident rays from A _ after ;
reflection take the directions DI Fig. 496
and KH, and their prolonga-
tions form a virtual image, a, of the point A, on the secondary axis.
Similarly, an image of B is formed at 4; consequently an eye looking
MM 2
Fig. 495
532 On Light [540—
along the principal axis sees at ad the image of AB. TZhzs image ts virtual,
erect, and larger than the object.
From what has been stated, it is seen that, according to the distance of
the object, concave mirrors produce two kinds of images, or none at all ;
a person notices this by placing himself in front of a concave mirror. At
a certain distance he sees an image of himself inverted and smaller-—this.
is the real image; at a less distance the image becomes confused, and
disappears when he is at the focus; still nearer the image appears erect,
but larger—it is then a virtual image.
541. Formation of images in convex mirrors.—Let AB (fig. 497) be
an object placed in front of a mirror at any given distance. AC and BC are
} secondary axes, and it follows,
from what has been already
stated, that all the rays from A
are divergent after reflection,
and that their prolongations pass
through a point a, which is the.
virtual image of the point A.
Similarly the rays from B form
Fig. 497 a virtual image of it in the point
6. The eye which receives the
divergent rays, DE, KH . . - sees in ad animage of AB. Hence, whatever
the position of an object in front of a convex mirror, the zmage ts always
virtual, erect, and smaller than the object.
542. Formule for spherical mirrors.—The relation between the position
of an object and that of its image in spherical mirrors may be expressed by
a very simple formula. In the case of concave mirrors, let R be its radius
of curvature, # the distance LA of the object L (fig. 498), and #’ the distance
7A of the image from the mirror. In the triangle LM/, the perpendicular
MC divides the angle LMZ into two equal parts, and from geometry it follows
that the two segments LC, CZ are to each other as the two sides containing
the angle ; that is,
Clear AM
CTEM: therefore C/ x LM =CLx/M.
If the arc AM does not exceed 5 or 6 degrees, the lines ML and MZ are.
approximately equal to AL and AZ;,
that is, to # and f’.
Further, C/= CA—A/=R'—97,
and also CL=AL—AC=/-R.
These values substituted in the
preceding equation give
ie. (R-p)p=(P-RY2’.
From which, transposing and reducing, we have
Rp + Rp’ = 299". : : (ft)
If the terms of this equation be all divided by f/’R, we suetie
a Mog See)
— += _ : ‘ ; é (2),
i eras
which is the usual form of the equation.
—543 | Discussion of the Formule for Mirrors eae
From the equation (1) we get
R
= J R? ¢ : : : (3)
or, jee on: i
=
R’ ; : E (4)
p
which gives the distance of the image from the mirror, in terms of the
distance of the object, and of the radius of curvature.
543. Discussion of the formule for mirrors.—We shall now investigate
the different values of #’, according to the values of # in the formula (2)
or (3).
1. Let the object be placed at an infinite distance on the axis, in which
case the incident rays are parallel. Since # is infinite - is zero, and formula
(2) at once gives f’= is ; that is, the image is formed in the principal focus,
iy
=
as ought to be the case, for the incident rays are parallel to the axis.
u. If the object approaches the mirror, # decreases, and as the denomi-
nator of the formula (4) diminishes, the value of Z’ increases ; consequently
the image approaches the centre at the same time as the object, but it is
always between the principal focus and the centre, for so long as
pis > R, we have Soe and < R.
ae?
i. When the object coincides with the centre, /=R, and, consequently,
2 =k; that is, the image coincides with the object.
iv. When the luminous object is between the centre and the principal
focus, #< R, and hence from the formula (4), #’>R; that is, the image is
formed on the other side of the centre. When the object is in the focus,
p= x which gives #’ = a oo; that is, the image is at an infinite distance,
for the reflected rays are parallel to the axis.
v. Lastly, if the object is between the principal focus and the mirror, we
get p< = ; p’ is then negative, because the denominator of the formula (4)
2
is negative. Therefore, the distance /’ of the mirror from the image must
be calculated on the axis in a direction opposite to # The image is then
virtual, and is on the other side of the mirror.
If f’ be negative, the formula (2) becomes 7-7 =F ; in this form it
comprehends all cases of virtual images in concave mirrors.
In the case of convex mirrors the image is always virtual (538) ; f’ and
R are of the same sign, since the image and the centre are on the same side
of the mirror, while the object being on the opposite side, # is of the contrary
sign ; hence in the formula (2) we get
I I 2
pb ra : 5 : ; (5)
534 On Light [543-
as the formula for convex mirrors. It may also be found directly by the
same geometrical considerations as those which have led to the formula (2)
for concave mirrors.
The preceding formule are not rigorously true, inasmuch as they depend
upon the assumption that the lines LM and /M (fig. 498) are equal to LA
and A/: although this is not true, the error diminishes without limit with
the angle MCA ; and when this angle does not exceed a few degrees, the
error is so small that it may, in practice, be neglected.
544. Calculation of the magnitude of images.—By means of the above
formule the magnitude of an image may be calculated when the distance
of the object, its magnitude,
and the radius of the mirror
are given: - For .if -BD be
the object (fig. 499), dd its
image, and if the distance
AK and the radius AC be
known, Ao can be calculated
Fig. 499 by means of formula (3) of
. article 542. Ao known, oC
can be calculated. But as the triangles'BCD and dCé are similar, dd: BD!
=Co: CK, or if O and I represent respectively the linear dimensions of
object and image, = ae a = from formula (1) or (2).
Thus,
size of the image (linear) _ distance of the image from the centre of curvature
size of the object distance of the object from the centre of curvature
Or distance of the image from the mirror
distance of the object from the mirror
{|
The brightness of an image formed by a concave mirror is nearly pro-
portional to its surface, and to the coefficient of reflection ; and is inversely
as the square of the focal distance.
545. Spherical aberration. Caustics.—In the foregoing explanation
of the formation of foci and images of spherical mirrors, it has been ob-
served that the reflected rays only coincide in a single point when the aper-
ture of the mirror does not exceed 8 or Io degrees (537). With a larger
aperture the rays reflected near the edges meet the axis nearer the mirror
than those that are reflected at a small distance from the centre of the mirror.
Hence arises a want of sharpness
in these images, which is called
spherical aberration by reflection,
to distinguish it from the spherical
aberration by refraction, which
occurs in the case of lenses.
Every’ reflected ray cuts the
Fig. 500 one next to it (fig. 500), and their
points of intersection form in space
a curved surface which is called the caustic by reflection. The curve FM
represents one of the branches of a section of this surface made by the
547] Parabolic Mirrors 535
plane of the paper. When the light of a candle is reflected from the
inside of a tea cup or a glass tumbler, a section of the caustic surface
can be seen by partly filling the cup or tumbler with milk.
- 546. Applications of mirrors. Heliostat.—The applications of plane
mirrors in domestic economy are well known. Mirrors are also frequently
used in physical apparatus for sending light in a certain direction. We
have already seen an application of this in the heliograph (535). The light
of the sun can only be sent in a constant direction by making the mirror
movable. It must have a motion which compensates for the continual change
in the direction of the sun’s rays produced by the apparent diurnal motion
of the sun. This result is obtained by means of a clockwork motion, to
which the mirror is fixed, and which causes it to follow the course of the
sun. Such an apparatus is called a helzostat. The reflection of light is also
used to measure the angles of crystals by means of the instruments known
as reflecting gontometers.
Concave spherical mirrors are also often used, They are applied for
magnifying szrrors, as in the older forms of shaving mirrors. They have
been employed for burning mirrors, and are still used in telescopes. They
also serve as reflectors, for conveying light to great distances, by placing
a luminous object in their principal focus. The search light used by steamers
in passing through the Suez Canal by night and by war ships, consists of a
powerful electric light placed at the principal focus of a concave spherical
reflector. Parabolic reflectors, though theoretically preferable, are not used
for this purpose on account of the difficulty of working the parabolic surface.
The iniages of objects seen in concave or convex mirrors appear smaller
or larger, but otherwise similar geometrically, except in the case where
some parts of a body are nearer the mirror than others. The distor-
tion of features observed on looking into a spherical garden mirror is more
marked the nearer we are to the glass. Objects seen in cylindrical or
conical mirrors appear ludicrously distorted. From the laws of reflection
the shape of such a distorted figure can be geometrically constructed. In
like manner distorted pictures of objects can be constructed which, seen in
such mirrors, appear in their normal proportions. They are called axamor-
phoses.
547. Parabolic mirrors.—/Para-
bolic mirrors are concave mirrors
whose surface is generated by the
revolution of the arc of a parabola,
AM, about its axis AX (fig. 501).
It has been already stated that
in spherical mirrors the rays parallel
to the axis converge only approxi-
mately to the principal focus; and
reciprocally, when a source of light
is placed in the principal focus of
these mirrors, the reflected rays are
not exactly parallel to the axis.
Parabolic mirrors are free from this defect; they are more difficult to
construct, but are better for reflectors. It is a property of a parabola
Fig. sor
536
On Light [547-
that the right line FM, drawn from the focus F to any point M of the curve
and the line ML, parallel to the axis AF, make equal angles with the tan-
Fig.
intersections
of reflectors
directions at
passages.
gent TT’ at this point. Hence all rays parallel
to the axis after reflection meet in the focus of
the mirror F ; and conversely, whena source of
light is placed in the focus, the rays incident on
the mirror are reflected exactly parallel to the
axis. The light thus reflected tends to maintain
its intensity even at a great distance, for it has
been seen (520) that it is the divergence of the
luminous rays which principally weakens the
intensity of light.
From this property parabolic mirrors are
used in carriage lamps, and in the lamps placed
in front of and behind railway trains. These re-
flectors were formerly used for lighthouses, but
have been replaced by lenticular glasses.
When two equal parabolic mirrors are cut
by a plane perpendicular to the axis passing
ape through the focus, and are then united at their
as shown in fig. 502, so that their foci coincide, a system
is obtained with which a single lamp illuminates in two
once. This arrangement is used in lighting staircases and
-548] Phenomenon of Refraction $37,
Orn rea Reh
SINGLE REFRACTION. LENSES
548. Phenomenon of refraction.—Ae/racizon is the deflection or bending
which the rays of light experience in passing od/zguely from one medium to
another: for instance, from air into water (fig. 504). If the incident ray is
perpendicular§ to the
surface separating the
two media, it .is not
bent, but continues
its course in a right
line (fig. 503).
The zncident ray
being represented by
»O: (fig. 505), the ve-
tracted ray is the di-
rection OH which light
takes in the second
medium ; and of the
angles SOA and HOB,
which these rays form
with the normal AB, to
the surface which
separates the two
media, the first is the
angle of incidence, and
Fig. 503
Fig. £05 Fig. 504
the other the angle of refraction. According as the refracted ray approaches
or deviates from the normal, the second medium is said to be more or less
refringent or refracting than the first.
All the light which falls on the surface of a refracting substance does not
completely pass into it ; one part is reflected and scattered (530), while
another penetrates into the medium.
Mathematical analysis shows that the direction of refraction depends on
the relative velocity of light in the two media. On the undulatory theory
the more highly refracting medium is that in which the velocity of propaga-
tion is less.
In uncrystallised media, such as air, liquids, ordinary glass, the luminous
ray is singly refracted ; but in certain crystallised bodies, such as Iceland
spar, selenite, &c., the incident ray gives rise to two refracted rays. The
latter phenomenon is called double refraction, and will be discussed in another
part of the book. We shall here deal exclusively with s¢mgle refraction.
549. Laws of single refraction.—When a luminous ray is refracted in
passing from one medium into another of a different refractive power, the
following laws prevail :—
I. Whatever the obliquity of the incident ray, the ratio which the sine of
the incident angle bears to the sine of the angle of refraction ts constant for
the same two media, and the same coloured light, but varies with different
meata.
Il. The incident and the refracted rays are in the same plane, which ts
perpendicular to the surface separating the two media.
These have been known as Descartes’s laws ; they are, however, really
due to Willibrod Snell, who discovered them in 1620 ; they are demon-
strated by the same apparatus as that
S/ used for the laws of reflection (522).
ao The plane mirror in the centre of the
graduated circle is replaced by a semi-
cylindrical glass vessel, filled with water
to such a height that its level is exactly
the height of the centre (fig. 506). If
the mirror, M, be then so inclined that
a reflected ray, MO, is directed towards
the centre, it is refracted on passing
into the water, but it passes out without
refraction, because its direction is then
at right angles to the curved sides of
the vessely3In ‘order to observe “the
course of the refracted ray, itis received
on a screen, P, which is moved until the
image of the aperture in the screen N
is formed at its centre. In all positions
of the screens N and P, the sines of
the angles of incidence and refraction
are measured by means of two graduated
rules, movable so as to be always horizontal, and hence perpendicular to
the diameter AD.
On reading off the lengths which are proportional to the sines of the
angles MOA and DOP in the scales I and R, the numbers are found to vary
with the position of the screens, but their ratio is constant; that is, if the
sine of incidence becomes twice or three times as large, the sine of refraction
increases in the same ratio, which demonstrates the first law. The second
law follows from the arrangement of the apparatus, for the plane of the
/
Tipit
SS
a ATTY
s
cai
ny
Fig. 506
-551] Effects produced by Refraction 539
graduated limb is perpendicular to the surface of the liquid in the semi-
cylindrical vessel.
550. Index of refraction.—The ratio between the sines of the incident
and refracted angle is called zadex of refraction, or refractive index of the
second medium with respect to the first. Thus if z be the refractive index,
and z and rv the angles of incidence and refraction, sin¢=zsinz. The refrac-
tive index varies with the media ; for example, from air to water it is 4, and
from air to glass it is 3.
If the media are considered in an inverse order—that is, if light passes
from water to air, or from glass to air—it follows the same course, but ina
contrary direction, PO becoming the incident and OM the refracted ray.
Consequently the index of refraction is reversed ; from water to air it is then
%, and from glass to air 3.
551. Effects produced by refraction.—In consequence of refraction,
bodies immersed in a medium more highly refracting than air appear nearer
the surface of this medium, but they appear to be more
distant if immersed in a less refracting medium. Let L
(fig. 507) be an object immersed in a mass of water. In
passing thence into air, the rays LA, LB... diverge
from the normal to the point of incidence, and take the
direction AC, BD... , the prolongations of which in-
tersect approximately in the point L’, placed on the
perpendicular L’K. Supposing the points A,B... are
not far removed from the normal KL, an eye looking
vertically downwards and receiving these rays sees the
image of Lat L’. Ifthe eye looks obliquely at the object, the image rises
to the greater obliquity of the rays LA, LB. ... the higher the object appears.
For the same reason a stick placed obliquely in water appears bent, the im-
mersed part appearing raised.
An experimental illustration of the effect of refraction is the following :—
A coin is placed in an empty porcelain basin, and the position of the eye is
so adjusted that the coin is just not visible. If now, the position of the
eye remaining unaltered, water be poured into the basin, the coin becomes
visible. A consideration of fig. 508 will
suggest the explanation of this phenomenon.
Owing to an effect of refraction, stars
are visible to us even when they are below
the horizon. For as the layers of the atmo-
sphere are denser in proportion as they are
nearer the earth, and as the refractive power
of a gas increases with its density (562), it
follows that on entering the atmosphere the
luminous rays become bent, as seen in fig.
505, describing a curve before reaching the Fig. 508
eye, so that we can see the star at S’ along
the tangent of this curve instead of at S. In our climate the atmospheric
refraction does not raise the stars when on the horizon more than half a
degree.
The effect of refraction is that objects at a distance appear higher than
Fig. 507
540 On Light [551-
they are in reality ; our horizon is thereby widened. When individual layers
of air refract more strongly than usual, objects may thereby become visible
which are usually below the horizon. Thus, from Hastings, the coast of
France, which is at a distance of 56 miles, is not unfrequently seen.
552. Total reflection. Critical angle.—When a ray of light passes
from one medium into another which is less refracting, as from water into
air, it has been seen that the angle of incidence is less than the angle of
refraction. Hence, when light is propagated in a mass of water from S to
O (fig. 509), there is always a value of the angie of incidence SOB, such
that the angle of refraction AOR is a right angle, in which case the refracted
ray emerges
parallel to the
surface of the
water.
This angle,
SOB, 1s called
the. watceras
angle, since for
alla St eater
angle, POB, the
incident ray
cannot emerge,
but undergoes an internal reflection, which is called fotal reflection because
the incident light is entirely reflected. From the formula sin z= sin y we
Fig. 510
see that if 2=90° sin z=1, and if — is the corresponding value of ~ z.e. the
p
critical angle, sin ”=1. From water to air the critical angie 1S. a0 35 an
ne
from glass to air, 41° 48’.
The occurrence of this internal reflection may be observed by the follow-
ing experiment :—An object, A, is placed before a glass vessel filled with
water (fig. 510) ; the surface of the liquid is then looked at as shown in the
figure, and an image of the object A is seen at a, formed by the rays reflected
at mz, in the ordinary manner of a mirror.
In total reflection there is no loss of light from absorption or transmission,
and accordingly it produces the greatest brilliancy. If an empty test-tube
be placed in a slanting position in water, its surface, when looked at from
above, shines as brilliantly as pure mercury ; those rays which fall obliquely on
the side at an angle greater than the external angle cannot pass into the water,
and are, therefore, totally reflected upwards. Ifa little water be passed into
the tube, that portion of it loses its lustre. Bubbles, again, in water glisten
like pearls, and cracks in transparent bodies like strips of silver, for the
oblique rays are totally reflected. The lustre of transparent bodies bounded
by plane surfaces, such as the lustre of chandeliers, arises mainly from
total reflection. This lustre is the more frequent and the more brilliant
the smaller the limiting angle ; the lustre of diamond, therefore, is the most
brilliant.
553. Mirage.—The wzzrage is an optical illusion by which inverted images
of distant objects are seen asif below the ground orin the atmosphere. This
- 553] Mirage 541
phenomenon is of most frequent occurrence in hot climates, and more espe-
cially on the sandy plains of Egypt. The ground there has often the aspect of
a tranquil lake, on which are reflected trees and the surrounding villages.
Monge, who accompanied Napoleon’s expedition to Egypt, was the first to
give an explanation of the phenomenon.
It is a phenomenon of refraction, which results from the unequal density
of the different layers of the air when they are expanded by contact with the
heated soil. The least dense layers are then the lowest, and the pencil of light
from an elevated object, A (fig. 511), traverses layers which are gradually less
refracting ; for,
as will be shown
presently (562),
the refracting
power of a gas
diminishes with
lessened den-
sity. The an-.
gle of incidence
accordingly in-
creases from
one layer to the
other, and ulti-
mately reaches
the critical an-
gle, beyond
which internai
reflection succeeds to refraction (552). The pencil then rises, as seen in the
figure, and undergoes a series of successive refractions, but in the direction
contrary to the first, for it now passes through layers which are gradually
more refracting. The pencil then reaches the eye with the same direction as
if it had proceeded from a point below the ground, and hence it gives an
inverted image of the object, just as if it had been reflected at the point O,
from the surface of a tranquil lake.
The effect of the mirage may be illustrated artificially, though feebly, as
Wollaston showed, by looking along the side of a red-hot poker at a word
Of? object ter or
twelve feet distant.
At a distance less Pe
than three-eighths . . = oe
of an inch from the
line of the poker,
an inverted image was seen, and within and without that an erect image. A
better arrangement than a red-hot poker is a flat sheet-iron box, about 3.
feet in length by 5 to 7 inches in height and breadth (fig. 512) ; it is filled
with red-hot charcoal and held at a about the level of the eye. Looking
over the lid of the box in the direction pm a direct, and in the direction pm’
an inverted image of a distant point, m,is seen. The same phenomenon
is observed by looking along the sides.
Mariners sometimes see inverted images in the air of ships and distant
Fig. 511
542 On Light [553-
objects which are still below the horizon ; this is due to the same cause as
the mirage, but is in a contrary direction. The lower layers of the air being
in contact with the water are cold and dense. The rays of an object, a ship
for instance, bent in an upward direction are more and more bent away from
the vertical as they are continually passing into gradually less dense layers,
and ultimately fall so obliquely on an upper attenuated layer that they are
totally reflected downwards, and can thus reach the eye of an observer on the
sea or on the shore. Scoresby observed several such cases inthe Polar seas.
The twinkling or scintillation of the fixed stars is also to be accounted
for by alterations in the direction of their light due to refraction.
TRANSMISSION OF LIGHT THROUGH TRANSPARENT MEDIA
554. Media with parallel faces.—Any transparent medium bounded by
two parallel plane surfaces is called a A/ate. When light traverses a plate
of any substance, the emergent rays are parallel to the incident rays.
Let MN (fig. 513) bea glass plate, SA the incident and DB the emergent
ray, z and ~ the angles of incidence and of refraction at the entrance of the
ray, and, lastly, z’ and 7 the corresponding angles at its emergence. AtA
the light undergoes a first refraction, and
main? ($49).. At DD ats etractedss
sin ¢
; : sin 2’
second time, and the index is then ~——..
sin 7
But we have seen that the index of re-
fraction of glass with respect to air is the
reciprocal of the index of air with respect
to glass ; hence
sin z’_ sin¢
Fig. 513 siny sinz
But as the two normals AG and DE are parallel, the angles 7 and 2’ are
equal, as being alternate interior angles. As the numerators in the above
equation are equal, the denominators must also be equal ; the angles 7’ and
z are therefore equal, and hence DB is parallel to SA.
555. Prism.—In optics a frism is any transparent medium comprised
between two plane faces inclined to each other. The intersection of these
two faces is the edge
of the prism, and their
inclination is its re-
fracting angle. Every
section perpendicular
to the edge is called a
principal section.
The prisms used
for experiments are
Fig. 514 Fig. 515 generally right trian-
gular prisms of glass, as shown in fig. 514, and their principal section is a
triangle (fig. 515). In this section the point A is called the swmmzt of the
—556] Path of Rays in Prism. Angle of Deviation 543
‘prism, and the right line BC is called the dase: these expressions have
reference to the triangle ABC, and not to the prism.
556. Path of rays in prism. Angle of deviation.—When the laws of
refraction are known, the path of the rays in a prism is readily determined.
Let O be a luminous point (fig. 515) in the same plane as the principal sec-
tion ABC of a prism, and let OD be an incident ray. This ray 1s refracted
at D, and approaches the normal, because it passes into a more highly
refracting medium. At K it experiences a second refraction, but it then
deviates from the normal, for it passes into air, which is less refractive than
glass. The light is thus refracted twice in the same direction, so that the ray
zs deflected towards the base, and consequently the eye which receives the
emergent ray KH sees the object O at O’; that is, objects seen through a
prism appear deflected towards its summit. The angle OEO’, which the
incident and emergent rays form with each other, expresses the deviation of
light caused by the prism, and is called ¢he angle of deviation.
Besides this, objects seen through a prism appear in all the colours of
the rainbow: this phenomenon, known as dsfersion, will be afterwards
described (576).
The angle of deviation increases with the refractive index of the material
of the prism, and also with its refracting angle. It also varies with the angle
B
ne >
s
s
a ly <7
ay im iss
under which the luminous ray enters the prism. The angle of deviation
increases up to a certain limit, which is determined by calculation, knowing
the angle of incidence of the ray, and the refracting angle of the prism (548).
That the angle of deviation increases with the refractive index may be
shown by means of the folyfrism. This name is given to a prism formed
of several prisms of the same angle connected at their ends (fig. 516). These
prisms are made of unequally refracting substances, such as flint glass, rock
crystal, or crown glass. If any object—a line, for instance—be looked at
544 On Light [556-
through the polyprism, its different parts are seen at unequal heights. The
highest portion is that seen through the flint glass, the refractive index of
which is greatest ; then the rock crystal ; and so on in the order of the
decreasing refractive indices.
The prism with variable angle (fig. 517) is used for showing that the
angle of deviation increases with the refracting angle of the prism. It con-
sists of two parallel brass plates. B and C, fixed on a support. Between
these are two glass plates, moving on a hinge with some friction against the
plates, so as to close it. When water is poured into the vessel the angle
may be varied at will. If a ray of light, S, be allowed to fall upon one of
them, by inclining the other more the angle of the prism increases, and the
deviation of the ray is seen to increase.
557. Use of right-angled prisms as reflectors.— Prisms whose principal
section is an isosceles right-angled triangle afford an important application
of total reflection (552). For let ABC
(fig. 518) be the principal section of such
a prism, O a luminous point, and OH a
ray at right angles to the face BC. This
ray enters the glass without being re-
fracted, and makes with the face AB an
angle equal to B—that is, to 45 degrees
—and therefore greater than the limiting
Hig. angle of glass, which is 41° 48’ (552).
The ray OH undergoes, therefore, at H total reflection, which imparts to it
a direction HI perpendicular to the second face AC. Thus the hypotenuse
surface of this prism produces the effect of the most perfect plane mirror, and
an eye placed at I sees O’, the image of the point O. This property of right-
angled prisms is frequently used in optical instruments, such as the camera
lucida (615) and the prismatic compass (711), instead of metal reflectors,
which readily tarnish. They are also largely used in the camera. obscura in
changing the direction of images for projection purposes. The newer /gh-
house lenses are made up of such prisms.
558. Conditions of emergence in prisms.—In order that any luminous
ray refracted at the first face of a prism may emerge from the second, it
is necessary that the refractive angle
of the prism be less than twice the
critical angle of the substance of which
the prism is composed. For if LI
(fig. 519) be the ray incident on the
first face, IE the refracted ray, PI and
PE the normals, the ray IE can only
emerge from the second face when
the incident angle IEP is less than
the critical angle (552). But as the
incident angle LIN increases, the
Fig. 519 angle EIP also increases, while IEP
diminishes. Hence, according as the
direction of the ray LI tends to become parallel with the face AB, does
this ray tend to emerge at the second face.
—559] Minimum Deviation 545
Let LI be now parallel to AB, the angle ~ is then equal to the critical
angle Z of the prism, because it has its maximum value. Further, the angle
EPK, the exterior angle of the triangle IPE, is equal to ~+z’; but the
angles EPK and A are equal, because the sides which contain them are at
right angles to each other, and therefore A =7+2’; therefore also A=/+7’,
for in this case ~=/. Hence, if A=2/ or is >2/, we shall have z’=/ or >J,
and therefore the ray would not emerge at the second face, but would be
parallel to AC or would undergo internal reflection, and emerge at a third
face, BC. This would be much more the case with rays whose incident
angle is less than BIN, because we have already seen that z’ would continu-
ally increase. Thus in the case in which the refracting angle of a prism is
equal to 2/ or is greater, no luminous ray could pass through the faces of the
refracting angle.
As the critical angle of glass is 41° 48’, and twice this angle is less than
90°, objects cannot be seen through a glass prism whose refracting angle
is aright angle. As the critical angle of water is 48° 35’, light could pass
through a hollow rectangular prism formed of three glass plates and filled
with water.
If we suppose A to be greater than / and less than 2/, then of rays inci-
dent at I, some within the angle NIB will emerge from AC, others will not
emerge, nor will any emerge that are incident within the angle NIA. If we
suppose A to have any magnitude less than /, all rays incident at I within
the angle NIB will
emerge from AC,
as also will some of
those incident with-
in the angle NIA.
559. Minimum
deviation. — When
a pencil of sunlight
passes through an
aperture A, in the
side of adark cham-
ber (fig. 520), the Fig. 520
pencil is projected in a straight line, AC, on a distant screen. But if a ver-
tical prism be interposed between the aperture and the screen, the pencil is
deviated towards the base of the prism, and the image is projected at D, at
some distance from the point C. If the prism be turned so that the incident
angle decreases, the disc of light approaches the point C up to a certain
position, E, from which it reverts to its original position even when the prism
is rotated in the same direction. Hence there is a deviation, EBC, less than
any other. It may be proved mathematically that this sz¢n¢mum deviation
takes place when the angles of incidence and of emergence are equal.
The angle of minimum deviation may be calculated when the incident
angle and the refracting angle of the prism are known. For when the
deviation is a minimum, then since the angle of emergence 7” is equal to the
incident anglez (fig. 519), ~ must equal z’. But it has been shown above (558)
that A=7+z’; consequently
A=27. ; , ; ; . (1)
NN
546 On Light [559-
If the minimum angle of deviation LD/ be called d, this angle being ex-
terior to the triangle DIE, we readily obtain the equation
A=t—r+/7 —-t' = 2-27,
whence ad=21—-A : : : (2)
which gives the angle d, when z and A are known.
From the formule (1) and (2) a third may be obtained, which serves to
calculate the index of refraction of a prism when its refracting angle and the
minimum of deviation are known. The index of refraction, 7, is the ratio
sin Z
of the sines of the angles of incidence and refraction ; hence 7 = ——— ; re-
sin 7
placing z and 7 from their values in the above equations (1) and (2) we get
, (2 + “)
sin ( —
E (
eae 3)
SS BLO
sinless
2
560. Measurement of the refractive index of solids.—By means of the
preceding formula (3) the refractive index of a solid may be calculated when
the angles A and d are known.
In order to determine the angle A, the substance is cut in the form of a
triangular prism, and the angle measured by means of a goniometer (546).
The angle d is measured in the following manner :—A ray, LI, emitted
from a distant object (fig. 521), is received on the prism, which is turned
in order to obtain the
minimum deviation
EDL’. By means of
a telescope with a
graduated circle the
angle EDL’ is read
off, which the re-
fracted ray DE makes
with the ray . DL,
coming directly from
the object ; now this is the angle of minimum deviation, assuming that the
object is so distant that the two rays LI and L’D are approximately parallel.
These values then only need to be substi-
tuted in the equation (3) to give the value
of 72.
561. Measurement of the refractive index
of liquids.—Biot applied Newton’s method
to determining the refractive index of liquids.
For this purpose a cylindrical cavity, O, of
about 0°75 inch in diameter, is perforated
in a glass prism, PQ (fig. 522), from the
incident face to the face of emergence. This
cavity is closed by two plates of thin glass which are cemented on the sides
of this prism. Liquids are introduced through a small stoppered aperture,
B. The refracting angle and the minimum deviation of the liquid prism in
Fig. 521
—562] Measurement of the Refractive Index of Gases 547
the cavity O having been determined, their values are introduced into the
formula (3), which gives the index.
562. Measurement of the refractive index of gases.—A method for
this purpose, founded on that of Newton, was devised by Biot and Arago.
The apparatus which they used consists of a glass tube (fig. 523), bevelled at
its two ends, and closed by glass plates, which are at an angle of 143°.
This tube is connected with a bell-jar, H, in which there is a siphon barometer,
and with a stopcock by means of which the apparatus can be exhausted, and
different gases introduced. When the tube, AB, has been exhausted, a ray
of light, SA, is transmitted through it, which is bent away from the normal
through an angle ~—z at the first incidence, and towards the normal through
an angle z’—7’ at the second. These two deviations being added, the total
deviation, d, is y—z+z2’-7’. Inthe case of a
minimum deviation, 7=7’ and r=z’, whence
G=A— 27, since. 7+7=A (559). The index
from vacuum to air, which is evidently SIZ
sin Zz
has therefore the value
sin
B
si (ee) eee |
oft
Hence, in order to deduce the refractive
index 2 from vacuum into air, which is the
absolute index of air, it is merely necessary to
know the refracting angle, A, and the angle of
minimum deviation, @. To obtain the absolute
index of any other gas, we first produce a
vacuum, and then introduce the gas; the
angles A and d@ having been measured, the
above formula gives the index of refraction from the gas to air. Dividing
the index of refraction from vacuum to air by the index of refraction from the
gas to air, we obtain the index of refraction from vacuum to the gas; that
is, its absolute index.
It appears probable that certain relations exist between the refractive
index, 2, and the density, d, of a body. These relations are of considerable
importance in questions of theoretical chemistry regarding the constitution
of bodies. They are expressed by the formula R = pa a , which 1s
known as the constant of refraction. If this is multiplied by a, the atomic
weight, we have the atomic refraction (sar ee:
m+2 a
SM Lt
weight, 7, we have the solecular refraction Pere
The following table gives the refractive indices for the three principal
Fraunhofer’s lines (586), the red, yellow, and violet ; the last column gives
the dispersion (576), or the difference between the extreme red, 7,, and the
extreme violet, 7,, rays.
Fig. 523
or, if by the molecular
NN 2
548 | On Light [562-
A | D | H | nr - ne
| |
| Water . : : t é IEG 20) NOI 331 | 1°344 O01 4 |
Alcohol : : : ; Eten BOO da iT 364 hh is3 7s oko) |
Crown glass (light) —. SP he: 1757531) Heo Weel
a saLLCONY )enet nears ~ 1) OLO TiO12; WTO 3r o7o2I
Rock salt. A : : - | 17538 [SAS ee 5OO C031
Flint glass (light). PA eh 6OG2)} 1°000 | TOAO EPO Oasanm
ued PrChes vy) : TA 5 I-75 sry Waoo7G |
_Calcspar (ordinary) . : Ate tally e) 1659! 17683 7 1 Gorogat &
oil), (éxtradrdimary) os aba se 1°483 1°498 | O'015
_ Carbon bisulphide é , Hi eOl 2s yarOsr £5703 \ OOo] |
The following are the mean values for a few other substances, and corre-
spond nearly to the E line.
Ice : ; . ; + Et*3TO Turpentine . : ey 19303
Solution of nitre . 3 Bd Bee ds Rock crystal ; : Ape
Vitreous humour of the eye —_—1°339 Benzole ‘ ‘ . nates OO
Aqueous _,, Ps in 1355 7, Oil of cassia : : Wr eOes
Crystalline lens _,, J 1°384 Diamond . 4 ; Ry ay Ate.
Mean refractive indices of gases
Vacuum . ‘ : . _1'000000 Carbonic acid ; . 1'000449
Hydrogen . : . 1°000138 Hydrochloric acid . . 4F:000449
Oxygen . : 3 ET OCG27.2 Nitrous oxide . ‘ - 1'000503
Ainge : i 1:900204 Sulphurous acid. . 1°000665
Nitrogen. ; : . 1000300 Ethylene ‘ ; . 1:000678
Ammonia 4 ; . 1°000385 Chlorine . , ; »| ¥1°000772
LENSES, THEIR EFFECTS
563. Different kinds of lenses.—Zezses are transparent media which,
from the curvature of their surfaces, have the property of causing the luminous
rays which traverse them either to converge or to diverge. According to
their curvature they are either stherical, cylindrical, elliptical, or parabolic.
Fig. 524
Those used in optics are exclusively spherical. They are commonly made
either of crown glass, which is free from lead, or of féz7¢ glass, which con-
tains lead, and is more refractive than crown glass.
The combination of spherical surfaces, either with each other or with
plane surfaces, gives rise to six kinds of lenses, sections of which are repre-
—564] Different Kinds of Lenses 549
sented in fig. 524; four are formed by two spherical surfaces and two bya
plane and a spherical surface. .
M is a double convex, N is a pPlano-convex, O is a converging concavo-
convex, P is a double concave, Q is a plano-concave, and R is a atverging
concavo-convex. The lenses O and R are also called szenzscus lenses, from |
their resemblance to the crescent-shaped moon. :
The first three, which are thicker at the centre than at the borders, are’
converging \enses ; the others, which are thinner in the centre, are dverging.
In the first group the double convex lens only need be considered, and in the
second the double concave, as the properties of each of these lenses apply
to all those of the same group. |
In lenses whose two surfaces are spherical, the centres for these surfaces
are called centres of curvature, and the right line which passes through
these two centres is the frimcipal axis. Ina plano-concave or plano-convex
lens the principal axis is the perpendicular let fall from the centre of
curvature of the spherical face on
the plane face. {
In order to compare the path of i\
a luminous ray in a lens with that fi
in a prism, the same hypothesis is
made as for curved mirrors (536) ;
that is, the surfaces of these lenses
are supposed to be formed of an
infinity of small plane surfaces or
elements (fig. 525): the zormad at
any point is then the perpendicular
to the plane of. the corresponding
element. It is a geometrical prin-
ciple that all the normals to the
same spherical surface pass through
its centre. On the above hypothesis
we can always conceive two plane
surfaces at the points of incidence
and emergence, which are inclined
to each other, and thus produce
the effect of a prism. Pursuing
this comparison, we may compare
the three lenses, M, N, and O, to
a succession of prisms having their
summits outwards, and the lenses iT |
P, Q, and R, to a series having y
their summits inwards: from this
we see that the first ought to con- Fig. 525
dense the rays, and the latter to
disperse them, for we have already seen that when a luminous ray traverses
a prism it is deflected towards the base (556).
564. Foci in double convex lenses.—The focus of a lens is the point
where the refracted rays, or their prolongations, meet. Double convex
lenses have both real and virtual foci, like concave mirrors.
550 On Light [564-
Real foci.—We shall first consider the case in which the luminous rays
which fall on the lens are parallel to its principal axis, as shown in fig. 526.
In this case, any incident ray, LB, in approaching the normal of the point
of incidence, B, and in
diverging from it at the
point of emergence, D, is
twice refracted towards
the axis, which it cuts at
F. As all rays parallel
to the axis are refracted
in the same manner, it
can be shown by calcu-
Fig. 526 Jation that they all pass
very nearly through the
point F, so long as the arc DE does not exceed 10° to 12°. This point is
called the principal focus, and the distance FA is the principal focal dts-
tance. It is constant in the same lens, but varies with the radii of curvature
and the index of refraction. In ordinary lenses, which are of crown glass,
and in which the radii of the two surfaces are nearly equal, the principal
focus coincides very closely with the centre of curvature.
We - shall
now consider
the\ease. win
which the
point of light
is outside the
principal focus,
but! sos smear
that all inci-
dent rays form
Fig. 527 a divergent
pencil, as
shown in fig. 527. The point of light being at L, by comparing the path of
a diverging ray, LB, with that of a ray, SB, parallel to the axis, the former
is found to make with the normal an angle, LBz, greater than the angle SBz ;
consequently, after
traversing the lens,
the ray cuts the
axis at a point, J,
which is more dis-
tant than the prin-
cipal focus, F. As
all rays from the
point L intersect
big. 528 approximately in
the same point, /,
this latter is the conjugate focus of the point L; this term has the same
meaning here as in the case of mirrors, and expresses the relation existing
between the two points L and Z, which is of such a nature that, if the
luminous point is moved to /, the focus passes to L.
—566] Double Concave Lenses Soa
According as the point of light comes nearer the lens, the convergence
of the emergent rays decreases, and the focus 7 becomes more distant ;
when the point L coincides with the principal focus, the emergent rays on
the other side are parallel to the axis, and there is no focus, or, what is the
same thing, it is infinitely distant. As the refracted rays are parallel in this
case, the intensity of light only decreases slowly, and a simple lamp can
illuminate great distances. It is merely necessary to place it in the focus of
a double convex lens, as shown in fig. 528.
Virtual foct.—When a luminous point is placed between the lens and its
principal focus, the image or focus of the point is virtual, as shown in fig. 529.
In this case the incident rays make with the normal greater angles than those
made with the rays FI from the principal focus ; hence, when the former
rays emerge, they move farther from the axis than the latter, and form a
diverging pencil, HK, GM.
These rays cannot pro-
duce a real focus, but their
prolongations: intersect in
some point, 7, on the axis,
and this point is the virtual
focus of the point L (537).
565. Double concave
lenses.—In double concave
lenses there are only virtual Fig. 529
foci, whatever the distance
of the object. Let SS’ be any pencil of rays parallel to the axis (fig. 530) ;
any ray, SI, is refracted at the point of incidence, I, and approaches the
normal, CI. At the point of emergence it is also refracted, but diverges
from the normal, GC’, so that it is twice refracted in a direction which moves
it from the axis, CC’. As the same thing takes place for every other ray,
S’KMN, it follows that the rays, after traversing the lens, form a diverging
pencil, GHMN. Hence there is no real focus, but the prolongations of these
rays cut one another in a point F, which is the principal virtual focus.
Hig. 531
In the case in which the rays proceed from a point, L (fig. 531), on the
axis, it is found by the same construction that a virtual focus is formed at /,
which is between the principal focus and the lens.
566. Experimental determination of the principal focus of lenses.—
To determine the principal focus of a convex lens, it may be exposed to
the sun’s rays so that they are parallel to its axis. The emergent pencil
being received on a ground-glass screen, the point to which the rays converge
is readily seen ; it is the principal focus.
552 On Light [566—
Or an image of an object is formed on a screen, their respective
distances from which are then measured, and from these distances the focus
is calculated from the dioptric formula (573).
With a double concave lens,
the face ad (fig. 532) is covered
with an opaque substance, such as
lampblack, two small apertures @
and 6 being left in the same prin-
cipal section, and at an equal dis-
tance from the axis; a pencil of
sunlight is then received on the
other face, and the screen P, which
receives the emergent rays, is
Fig. 532 moved nearer to or farther from
the lens, until A and B, the spots
of light from the small apertures a and 4, are distant from each other by
twice ad. The distance DI is then equal to the focal distance FD, because
the triangles Fad and FAB are similar. Another method of determining the
focus of a concave lens is given in article 572.
567. Optical centre, secondary axis.—In or near every lens there is a
point called the optical centre, which is situate on the axis, and which has
the property that any luminous ray passing through it experiences no angular
deviation ; that is, that the emergent ray is parallel to the incident ray.
The existence of this point may be demonstrated in the following manner :—
Let two parallel radii of curvature, CA and C’A’ (fig. 533), be drawn to the
two surfaces of a double convex lens. Since the two plane elements of the
lens at A and A’ are parallel, as being perpendicular to two parallel right
lines, it will be granted that the refracted ray AA’ is propagated in a medium
with parallel faces. Hence a ray KA, which reaches A at such an inclination
Fig. 533 Fig. 534
that after refraction it takes the direction AA’, will emerge parallel to its first
direction (554); the point O, at which the right line cuts the axis, is there-
fore the optical centre. The position of this point may be determined for
the case in which the curvature of the two faces is the same, which is the
usual condition, by observing that the triangles COA and C’OA’ are equal,
and therefore that OC = OC’, which gives the point O. If the curvatures are
unequal, the triangles COA and COA’ are similar, and either CO or C’O may
be found, and therefore also the point O.
In double concave or concavo-convex lenses the optical centre may be
—568] ormation of Images by Double Convex Lenses 553
determined by the same construction. In lenses with a plane face this point
is at the intersection of the axis by the curved face.
Every right line PP’ (fig. 534), which passes through the optical centre
without passing through the centres of curvature, isa secondary axis. From
this property of the optical centre, every secondary axis represents a luminous
rectilinear ray passing through this point: for, since the thicknesses of the
lenses we are dealing with are supposed to be small, it may be assumed
that rays passing through the optical centre are in a right line ; that is, that
the small deviation may be neglected which rays experience in traversing a
medium with parallel faces (fig. 533).
So long as the secondary axes only make a small angle with the principal
axis, all that has hitherto been said about the principal axis is applicable to
them ; that is, that rays emitted from a point P (fig. 534) on the secondary
axis PP’ nearly converge to a certain point of the axis P’, and according as
the distance from the point P to the lens is greater or less than the principal
focal distance, the focus thus formed will be conjugate or virtual. This
principle is the basis of what follows as to the formation of images.
568. Formation of images by double convex lenses.—lIn lenses, as well
as in mirrors, the image of an object is the collection of the foci of its several
points ; hence the images furnished by lenses are real or virtual in the same
case as the foci, and their construction resolves itself into determining the
position of a series of points, as was the case with mirrors (540).
1. eal tmage.—Let AB (fig. 535) be placed beyond the principal focus.
If a secondary axis, Aa, be drawn from the outside point A, any ray AC,
from this point, will be twice refracted at C and D, and both times in the
same direction, ap-
proaching the
secondary axis,
which it cuts at a.
From. what has
just been said, the
other rays from
the point A _ will
tense ise eS
point a, which is
accordingly the
conjugate focus of the point A. If the secondary axis be drawn from
the point B, it will be seen, in like manner, that the rays from this point
intersect in the point 4; and as the points between A and B have their foci
between a and 4, a veal but inverted image of AB will be formed at ad.
To see this image, it may be received on a white screen, on which it will
be depicted, or the eye may be placed in the path of the rays emerging
from it.
Conversely, if ad were the luminous or illuminated object, its image
would be formed at AB. Two consequences important for the theory of
optical instruments follow from this :—viz., Ist, zf az object, even a very
large one, is ata sufficient distance from a double convex lens, the real and
inverted image which is obtained of it is very small—it ts near the prin-
cipal focus, but somewhat farther from the lens than this ts ; 2nd, if a very
6
a
554 | On Light [568—
small object be placed near the principal focus, but a little in front of tt, the
image which ts formed ts at a great aistance—it ts much larger, and that in
proportion as the object is near the principal focus. In all cases the object
and the image are in the same proportion as their distances from the lens.
These two principles are experimentally confirmed by receiving on a
screen the image of a lighted candle, placed successively at various distances
from a double convex lens.
i. Virtual tmage.—There is another case in which the object AB (fig. 536)
is placed between the lens and its principal focus. If a secondary axis Oa
be drawn from the point A, every ray AC, after having been twice refracted,
diverges from this axis on emerging, since the point A is at a less distance
than the principal focal distance (564). This ray, continued in an opposite
direction, will cut the axis Oa in the point a, which is the virtual focus of the
point A. Tracing the secondary axis of the point B, it will be found,
in the same manner, that the virtual focus of this point is formed at 3d.
There is, therefore, an image of AB at ad. This is a virtual image; tt ts
erect, and larger than the object.
The magnifying power is greater in proportion as the lens is more
convex, and the
object nearer
the _ principal
focus. Weshall
presently show
how the magni-
fying power may
be calculated by
means of the
formule relating
to lenses (571).
Double convex
lenses, used in this manner as magnifying glasses, are called szmple micro-
SCOPES.
569. Formation of images in double concave lenses.—Double concave
lenses, like convex mirrors, only give virtual images, whatever the distance
of the object.
Wy UF Let AB (fig. 537) be an object
LY st placed in front of sucha lens. If
WY =a the secondary axis AO be drawn
ae, falta from the point A, all rays, AC, AI,
=N from this point are twice refracted
--\ in the same direction, diverging
XY . from the axis AO; so that the eye,
| AY receiving the emergent rays DE
and GH, supposes them to proceed
from the point where their pro-
longations cut the secondary axis
AO in the point a. In like manner, drawing a secondary axis from the
point B, the rays from this point form a pencil of divergent rays, the direc-
tions of which, prolonged, intersect in 4. Hence the eye, looking along the
Fig. 536
—570| Spherical Aberration. Caustics 555
principal axis, sees at ad a virtual image of AB, which ts always erect, and
smaller than the object.
570. Spherical aberration. Caustics.—In speaking about foci, and
about the images formed by different kinds of spherical lenses, it has been
hitherto assumed that the rays emitted from a single point intersect also
after refraction in a single point. This is virtually the case with a lens whose
aperture—that is, the angle obtained by joining the edges to the principal
focus—does not exceed 10° or 12°.
Where, however, the aperture is larger, the rays which traverse the lens
near the edge are refracted toa point F (fig. 538) nearer the lens than the point
G, which is the focus of the rays which pass near the axis. The phenomenon
thus produced is named spherical aberration by refraction ; it is analogous
to the spherical aberration produced by reflection (545). The luminous sur-
faces formed by the intersection of the refracted rays are termed caustics by
refraction.
Spherical aberration is prejudicial to the sharpness and definition of an
image. If a ground-glass screen be placed exactly in the focus of a lens,
the image of an ob-
ject will be sharply
defined in’ the
centre, but indis-
tinct at the edges ;
and,’ wzce versa, if
the image is sharp
at the edges, it will
be indistinct in the
centre: "This defect
is very objection-
able, more espe-
cially in lenses used Figtese
for photography. It
is partially obviated by placing in front of the lenses diaphragms provided
with a central aperture, called s/ops, which admit the rays passing near the
centre, but cut off those which pass near the edges. The image thereby
becomes sharper and more distinct, though the illumination is less.
If a screen be held between the light and double convex lens which
quite covers the lens, but has two concentric series of holes, two images
are obtained, and may be received on a sheet of paper. By closing one
or the other series of holes by a flat paper ring, it can be easily ascertained
which image arises from the central, and which from the marginal rays.
When the paper is at a small distance the marginal rays produce the image
in a point, and the central ones in a ring; the former are converged to a
point, and the latter not. At a somewhat greater distance the marginal rays
produce a ring, and the central ones a point. It is thus shown that the
focus of the marginal rays is nearer the lens than that of the central rays.
Mathematical investigation shows that convex lenses whose radii of
curvature stand in the ratio expressed by the formula
Y 4-20? +n
Yr, 2n+n
XN
556 On Light [570—
are most free from spherical aberration, and are called lenses of best form:
in this formula ~ is the radius of curvature of the face turned to the parallel
rays, and 7, that of the other face, while is the refractive index (560). Thus,
with a glass whose refractive index is 3. vy,=6r. Spherical aberration is
2.
also destroyed by substituting for a lens of short focus two lenses of double
focal length, which are placed at a little distance apart. Greater length of
focus has the result that for the same diameter the aperture and also the
aberration are less; and as it is not necessary to stop a great part of the
lens there is a gain in luminosity, which is not purchased by indistinctness
of the images, while the combination of the two lenses has the same focus
as that of the single lens (572). Lenses which are free from spherical aber-
ration are called aplanatic.
571. Formule relating to lenses.— In all thin lenses the relations between,
the distances of the image and object, the radii of curvature, and the refrac-
tive index may
: be expressed by
rN N a formula. In
ae a | Cp the case of a
double convex
lens, let P be a
luminous point
situate on the
axis (fig. 539),
let PI be anin-
eidentiray, Lis
its direction within the lens, EP’ the emergent ray, so that P’ is the con-
jugate focus of P. Further, let C’Il and CE be the normals to the points of
incidence and emergence, and IPA be put equal to a, EP’A’=8, ECA’=
IGA=0,'NIB= 7 EC = 7eLk O =7 NH Peers,
Because the angle z is the exterior angle of the triangle PIC’, and the
angle 7’ the exterior angle of the triangle CEP’, therefore 7=a+6, and
vy’ =y+B, whence
Fig. 539
Z+7r’'=at+B+y+d. ‘ ; breeds)
But at the point I, sin 7=7 sin % and at the point E, sin 7’ =z sin z’ (550),
being the refractive index of the lens. Now if the arc AI is only a small
number of degrees, these sines may be considered as proportional to the
angles z, 7, 2’ and 7’ ; whence, in the above formula, we may replace the sines
by their angles, which gives z=mr and r’ = 72’, from which 7+ 7 =a (r+72’).
Further, because the two triangles IOE and COC’ have a common equal
angle O, therefore 7+2’=y+6, from which 7+”=a (y+6). Introducing
this value into the equation (1) we obtain
a (y+6)=a+8+y+6, from which (2-1) (y+8)=a+8 (2)
Let CA’ be denoted by R, C’A by R’, PA by g, and P’A’ by ’. Then
with centre P and radius PA describe the arc Ad, and with centre P’ and
radius P’A’ describe the arc A’z. Now when an angle at the centre of a
~572] formule relating to Lenses 554
circle subtends a_certain arc of the circumference, the quotient of the arc
divided by the radius measures the angle ; consequently
Aa Ad A’ A’/E Al
Saray we >a) ai as )Y=-p and 8=—.
Therefore by substitution in (2), (#- 1) (ee AT _Ad An
Re ae A
Now since the thickness of the lens is very small, the angles are also small
and Ad, Al, A’E, A’x differ but little from coincident straight lines, and are
therefore virtually equal. Hence the above equation becomes
(72 —1) (A+y) agthg? : ? : r (3)
This is the formula for double convex lenses ; if f be =o —that is, if the
incident rays are parallel, we have
Neer
~p’ being the principal focal distance. Calling this 4, we get
(in Boe te op : : : : (4)
from which the value of / is easily deduced. Considered in reference to
equation (4), the equation (3) assumes the form
Stara (5)
eh LEY OW fe
which is that in which it is usually employed. When the image is virtual,
_ p’ changes its sign, and formula (5) takes the form
scat) a | NN einen ae a 6)
In double concave lenses #’ and / retain the same sign, but that of p
changes ; equation (5) then becomes
Toe (7)
Lug lalt ele
Equation (7) may be obtained by the same reasonings as the other.
572. Combination of lenses.—If parallel rays fall on a convex lens A,
which has the focal distance f, and then on a similar lens B with the focal
distance 7’, at a distance @ from A, the distance from the lens B at which
the image is formed is F, then
Stak) i ea
Lenk ata
If the lenses are close together, so that d@=o0, then
558 | On Light [572-
felons?
If the lenses have the same curvature, that is f=/, hie ages ; that is to
af
say, the focal distance of the combination is half that of a single lens.
If the second lens is a diverging one of the focal distance /, then
T_ 1 _1! . and if the lenses are close together, then See
Ein feds f Fiiesaer
This formula can be used to determine the focal distance of a concave
lens, by combining it with a convex lens of shorter focus, and then deter-
mining the focal distance of the combination.
573. Relative magnitudes of image and object. Determination of
focus.-—From the similarity of the triangles AOB, aOd (fig. 536), we get
for the relative magnitudes of image and object the proportion ioe
whence Ree where AB=O is the magnitude of the object, and aé=I
that of the image ; while # and 7’ are their respective distances from the
lens. Replacing 7’ by its value from the equation 5+ = where the
yy
image is real, or from the equation ae ve => where it is virtual, we shall
obtain the different values of the ratio = for various positions of the object.
Le
In the first case we have pe ee)
Que,
Thus if pees <0
Pra i= O
Bons
In the second case when the image is virtual we shall have
ote so that in all cases 1>O.
By using the above formula we may easily deduce the focal length of a
convex lens where direct sunlight is not available. For if a luminous object
be placed on one side of the lens, and a screen on the other side, then by
altering the relative positions of the lens and the screen, a position may be
found by trial, such that an image of the object is formed on the screen of
exactly the same size as the object. Dividing now by 4 the total distance
between the object and the screen, we get the focal distance of the lens.
Another method is to place on one side of the lens, and a little beyond
its principal focus, a brightly illuminated scale, which is best of glass, on which
a strong light falls ; on the other side a screen is placed at such a distance
as to produce a greatly magnified distinct image of the scale. Then if 7 and
L are the lengths of the scale and its image respectively, and d the distance
of the screen from the lens,
]
a7 sh
Heer,
~575] Laryngoscope 559
574. Determination of the refractive index of a liquid.—By measure-
ments of focal distance the refractive index of a liquid (561) may be ascertained
in cases in which only small quantities of liquid are available.
One face of a double convex lens of known focal distance /,
and known curvature 7” 1s pressed against a drop of the liquid
in question on a plate glass (fig. 540). The liquid forms
thereby a plano-concave lens whose radius of curvature 16 7.
The focal distance F of the whole system is then determined
experimentally; this gives the focal length of the liquid lens
f from the formula
pees!
ae
while from the formula z =(#—1) I we get the value of z.
r
575. Laryngoscope.—As an application of lenses may be adduced the
laryngoscope, which is an instrument invented to facilitate the investigation
of the larynx and other cavities of the mouth. It consists of a plano-
convex lens L, and a concave reflector M, both fixed to a ring which can be
adjusted to any convenient lamp (fig. 541). The flame of a lamp is in the
principal focus of the lens, and at the same time is at the centre of curvature
of the reflector. Hence the divergent pencil proceeding from the lamp to
Cas a
the lens is changed after emerging into a parallel pencil. Moreover, the
pencil from the lamp, impinging upon the mirror, is reflected to the focus of
the lens, and traverses the lens, forming a second parallel pencil which is
superposed on the first. This being directed into the mouth of a patient,
its condition may be readily observed.
560 On Light [576—
CHAP TER ay:
DISPERSION AND ACHROMATISM
576. Decomposition of white light. Solar spectrum. Dispersive power.—
The phenomenon of refraction is by no means so simple as we have hitherto
assumed. When wz¢e light, or that which reaches us from the sun, passes
from one medium into another, z¢ zs decomposed tnto several kinds of light, a
phenomenon to which the name dzsferston is given.
In order to show that white light is decomposed by refraction, a pencil of
the sun’s rays SA (fig. 542) is allowed to pass through a small aperture in the
window shutter of a dark chamber. This pencil tends to form an oval and
colourless image of the sun at K; but if a flint-glass prism arranged hori-
zontally be interposed in its path, the beam, on emerging from the prism,
becomes refracted to-
wards its base, and
produces on a distant
screen a vertical band
rounded at the ends,
coloured in all the
tints of the rainbow,
which is called the
Solar spectrum (see
Plate: 1,).. elie thig
spectrum there is, in
reality, an infinity of
different tints, which
imperceptibly merge
into each other, but it
is Customary to distinguish seven principal colours. These are vzole¢, indigo,
blue, green, yellow, orange, red; they are arranged in this order in the
spectrum, the violet being the most refrangible, and the red the least so.
They do not all occupy an equal extent in the spectrum, violet having the
greatest extent, and orange the least.
With transparent prisms of different substances, or with hollow glass prisms
filled with various colourless liquids, spectra are obtained formed of the same
colours, and in the same order; but when the deviation produced is the
same, the length of the spectrum varies with the substance of which the
prism is made. The angle of separation of two selected rays (say in the red
and the violet) produced by a prism is called the dsferszon, and the ratio of
i]
LLL Ee
Ben
SS
SSSSSSsSSSSSSSss
SSSSSSSSSSSSSSS SESS
SSS
SSS SST
N
N ZB
Fig. 542
—578] The Colours of the Spectrum 561
this angle to the mean deviation of the two rays is called the dispersive power.
This ratio is constant for the same substance so long as the refracting angle
of the prism is small. For the deviation of the two rays is proportional to
the refracting angle; their difference and their mean vary in the same
manner, and therefore the ratio of their difference to their mean is constant.
For flint glass this is 0°043 ; for crown glass it is 00246, since the dispersive
power of flint is almost double that ‘of crown glass.
The spectra which are formed by artificial lights rarely contain all the
colours of the solar spectrum ; but their colours are found in the solar
spectrum, and in the same order. Their relative intensity is also modified.
The shade of colour which predominates in the flame’ predominates also in
the spectrum ; yellow, red, and green flames produce spectra in which the
dominant tint is yellow, red, or green.
577. Production of a pure solar spectrum.—In the above experiment the
spectrum formed is built up of a series of overlapping spectra, and the colours
are confused and indistinct. In order to obtain a pure spectrum, the slit, in
the shutter of the dark room through which light enters, should be of rect-
angular form, from 15 to 25 mm. in height and from 1 to 2 mm. in breadth.
The sun’s rays are directed upon the slit by a mirror, or still better by a
heliostat (546). An achromatic double convex lens is placed at a distance
from the slit of double its own focal length, which should be about a metre,
and a screen is placed at the same distance from the lens. An image of the
slit of exactly the same size is thus formed on the screen (573). If now there
is placed near the lens, between it and the screen, a prism with an angle of
about 60°, and with its refracting edge parallel to the slit, a very beautiful,
sharp, and pure spectrum is formed on the screen. The prism should be
placed so that it produces the minimum deviation.
578. The colours of the spectrum are simple, and unequally refrangible.—
If one of the colours of the spectrum be isolated by intercepting the others
by means of a screen E, as shown in fig. 543, and if the light thus isolated
be allowed to pass
througha second prism,
B, a refraction will be
observed, but the light
remains unchanged ;
that 1s, the image re-
ceived on the screen H
is violet if the violet
pencil has been allowed
to pass, blue if the blue
pencil, and so on. Hence the colours of the spectrum are szwzfle ; that is,
they cannot be further decomposed by the prism.
Moreover, the colours of the spectrum are unequally resrangible ; that
is, the glass of the prism possesses a different refractive index for each of
the rays of which white light is composed. The elongated shape of the
spectrum would be sufficient to prove the unequal refrangibility of the simple
colours, for it is clear that the violet, which is most deflected towards the
base of the prism, is also most refrangible ; and that red, which is least de-
flected, is least refrangible But the unequal refrangibility of simple colours.
ORO
562 On Light [578-
may be shown by numierous experiments, of which the two following may be
adduced :—
i. Two narrow strips of coloured paper, red and violet, are fastened
close to each other on a sheet of black paper. On looking at them through
a prism, they are seen to be unequally displaced, the red band to a less
extent than the violet ; hence the red rays are less refrangible than the
violet.
ii. The same conclusion may be drawn from Newton’s experiment with
crossed prisms. On a prism A (fig. 544), in a horizontal position, a pencil
of whitelight,
S, isreceived,
which, if it
had_ merely,
traversed the |
prism nae
would form
the spectrum
vv, on a dis-
tant , screen.
Buty yadiqeeaet
second prism,
B, be placed
in a vertical
Fig. 544 position be-
hind the first,
in such a manner that the refracted pencil passes through it, the spectrum
vu becomes deflected towards the base of the vertical prism ; but, instead of
being deflected in a direction parallel to itself, as would be the case if the
colours of the spectrum were equally refracted, it is obliquely refracted in
the direction 7’v’, proving that from red to violet the colours are more and
more refrangible.
These different experiments show that the refractive index differs in dif-
ferent colours ; even rays which are to perception indistinguishable may dif-
fer in refran-
gibility. In
the red band,
for instance,
the rays at
the extremity
of the spec-
trum are less
refracted than those which are nearer the orange zone. In determining
indices of refraction (550), it is usual to take, as the index of any par-
ticular substance, the refrangibility of the yellow ray in a prism formed of
that substance.
579. Recomposition of white light.—Not merely can white light be
resolved into lights of various colours, but by combining the different pencils
separated by the prism white light can be reproduced. This may be effected
in various ways..
1 es Wels ~
—=— Seer ee z 4
| AD TAD ELLE LIE LEE UEE LIED OUI TIET IOUT TTI
Fig. 545 Fig. 546
—-579] Recomposition of White Light 563
i. If the spectrum produced by one prism is allowed to fall upon a second
prism of the same material and the same refracting angle as the first, but
inverted, as shown in fig. 546, the latter reunites the different colours of
the spectrum, and it is seen that the emer-
gent pencil E, which is parallel to the pencil
S, is colourless.
i. If the spectrum falls upon a double
convex lens (fig. 545), a white image of the
sun will be formed on a white screen placed
in the focus of the lens ; a glass globe filled
with water produces the same effect as the Fig. 547
lens.
ii. If the spectrum falls upon a concave mirror, a white image is
formed on a screen of ground glass placed in its focus (fig. 547).
iv. Light may be recomposed by an experiment, which consists in receiving
the seven colours of the spectrum on seven small glass mirrors with plane
faces ; these mirrors can be so inclined in all positions that thefreflected light
may be trans-
mitted in any
given direction
(fig. 548). When
the mirrors
are suitably ar-
ranged, the
seven reflected
pencils may be
caused to fall on
the ceiling, so as
to form seven
distinct images
—red, orange,
yellow, &c.
When the mir- Fieses
rors are moved
so that the separate images become superposed, a single image is obtained,
which is white.
v. By means of Newton's disc (fig. 549) it may be shown that the seven
colours of the spectrum form white. This is a cardboard disc of about a
foot in diameter ; the centre and the edges are covered with black paper,
while in the space between there are pasted strips of paper of the colours of
the spectrum. They proceed from the centre to the circumference, and their
relative dimensions and tints are such as to represent five spectra (fig. 550).
When this disc is rapidly rotated, the effect is the same as if the retina
received simultaneously the impression of the seven colours.
vi. If by a mechanical arrangement a prism, on-which the sun’s light
falls, is made to oscillate rapidly, so that the spectrum also oscillates, the
middle of the spectrum appears white.
These latter phenomena depend on the physiological fact that sensation
always lasts a little longer than the impression from which it results (639).
002
6 LL LLL LLL LIL LANDS LLL IS PLETAL ELST TLL ELELLAL TO)
564 | On Light [579-
If a new impression is allowed to act, before the sensation arising from the
former one has ceased, a sensation is obtained consisting of two impressions.
And by choosing the time short enough, three, four, or more impressions
may be mixed with each other. With a rapid rotation the disc (fig. 549)
Fig. 549
is nearly white. It is not quite so, for the colours cannot be exactly arranged
in the same proportions as those in which they exist in the spectrum, and
moreover ~zgment colours are not pure (583).
' 580. Newton’s theory of the composition of light.—Newton was the
first to decompose white light by the prism, and to recompose it. From the
various experiments which we have described, he concluded that white light
was not homogeneous, but formed of seven lights unequally refrangible,
which he called szmple or primitive lights. Owing to the difference in
refrangibility they become separated in traversing the prism.
The designation of the various colours of the spectrum is to a very great
extent arbitrary ; for, in strict accuracy, the spectrum is made up of an in-
finite number of simple colours, which pass into one another by imperceptible
gradations of colour and refrangibility. re
581. Colour of bodies.—The natural colour of bodies results from the
fact that one portion of the coloured rays contained in white light is
absorbed at the surface of the body. If the unabsorbed portion traverses.
the body, it is coloured and transparent ; if, on the contrary, it is reflected,.
it is coloured and opaque. In both cases the colour results from the
constituents which have not been absorbed. Those which reflect or
transmit all colours in the proportion in which they exist in the spectrum
are white ; those which reflect or transmit none are black. Between these
two limits there are infinite tints according to the greater or less extent to
—582] Mixed Colours. Complementary Colours 505
which bodies reflect or transmit some colours and absorb others. Thus a
body appears yellow because it absorbs all colours with the exception of
yellow. In like manner, a solution of ammoniacal copper sulphate absorbs
preferably the red and yellow rays, transmits the blue rays almost completely,
the green and violet less so; hence the light seen through it is blue.
Accordingly bodies have no colour of their own; the colour changes
with the nature of the incident light. Thus, if a white body in a dark room
is successively illuminated by each of the colours of the spectrum, this has no
special colour, but appears red, orange, green, &c., according to the position
in which it is placed. If monochromatic light fails upon a body, it appears
brighter in the colour of this light if it does not absorb this colour; but
black if it does absorb it. Inthe light of a lamp fed by spirit in which some
common salt is dissolved, everything white and yellow seems bright, while
other colours, such as vermilion, ultramarine, and malachite, are black.
This is seen in the case of a stick of red sealing-wax viewed in such a light.
In the light of lamps and of candles, which from the want of blue rays
appear yellow, yellow and white appear the same, and blue seems like green.
In bright twilight or in moonshine the light of coal gas has a reddish tint.
582. Mixed colours. Complementary colours.—By mixed colours we
understand the impression of colour which results from the coincident action
of two or more colours on the same portion of the retina. This new im-
pression is single ; it cannot be resolved into
its components; in this respect it differs from
a complex sound, in which the ear, by practice,
can learn to distinguish the constituents. Mixed
colours may be produced by Laméert’s method,
which consists in looking in an oblique direction
through a vertical glass plate P (fig. 551) ata
coloured wafer 4, while, at the same time, a wafer 3 GF
of another colour g sends its light by reflection in ees
towards the observer’s eye ; if gis placed in a
proper position, which is easily found by trial, its image exactly coincides
with that of 8. The method of the colour disc (579) affords another means
of producing mixed colours.
A very convenient way of investigating the phenomena of mixed colours
is that of Waxwell’s colour-discs. These consist of discs of cardboard with
Wt SS
Fig. 552 Fig. 553 Fig. 554
an aperture in the centre, by which they can be fastened on the spindle of
the turning-table (fig. 552). Each disc is painted with a separate colour,
and, having a radial slit, they may be slid over each other so as to overlap to
any desired extent (figs. 553 and 554) ; and thus, when in this way two such
566 On Light [582-
discs are rotated, we get the effect due to this mixture of these two colours.
It is clear also that the effect of three colours may be investigated in the
same way.
If, in any of the methods by which the impression of mixed spectral
colours is produced, one or more colours are suppressed, the residue corre-
sponds to one of the tints of the spectrum ; and the mixture of the colours
taken away produces the impression of another spectral colour. Thus, if in
fig. 545 the red rays are cut off from the lens L, the light on the focus is no
longer white, but greenish blue. In like manner, if the violet, indigo, and
blue of the colour disc are suppressed, the rest seems yellow, while the mixture
of that which has been taken out isa bluish violet. Hence white can always.
be compounded of ¢wo tints ; and two tints which together give white are
called complementary colours. Thus of spectral tints vedand greenish yellow
are complementary ; so are orange and Prussian blue, yellow and indigo
blue, greenish yellow and violet.
The method by which Helmholtz investigated the mixture of spectral
colours is as follows :—Two very narrow slits, A and B (fig. 555), at right
angles to each other, are made in the shutter of a dark room ; at a distance
from this is placed a powerfully dispersing prism with its refracting edge
Fig. 555
vertical. When the slits are viewed through a telescope, the slit B gives the
oblique spectrum LM, while the slit A gives the spectrum ST. These two
spectra partially overlap, and when this is the case two homogeneous spectral
colours mix. Thus at 1 the red of one spectrum coincides with the green of
the other ; at 3, indigo and yellow coincide ; and so forth.
When the experiment is made with suitable precautions, the colours ob-
tained by mixing the spectral colours will be found in the table on the next
page, where the fundamental spectra to be mixed are given in the first
horizontal and vertical column, and the resultant colours where these cross.
Prismatic spectrum colours may also be investigated by the method of
von Bezold, which consists in producing two images of colours by double
refraction, and making one cover the other.
The mixture of mixed colours gives rise to no new colours. Only the
same colours are obtained as a mixture of the primitive spectral colours would
yield, except that they are less saturated, as it is called ; that is, more mixed
with white.
583. Spectral colours and pigment colours.--A distinction must be
made between sfectral colours and pigment colours. Thus a mixture of
pigment yellow and pigment blue produces green, and not white, as is the
case when the blue and yellow of the spectrum are mixed. The reason of
this is that in the mixture of pigments we have a case of subtraction of
—584] Flomogeneous Light 567
colours, and not of addition. For the pigment blue in the mixture absorbs
almost entirely the yellow and red light ; and the pigment yellow absorbs
the blue and violet light, so that only the green remains.
In the above series are two spectral colours very remote in the spectrum,
which have nearly the same complementary tints ; red, the complementary
colour to which is greenish blue ; and violet, whose complementary colour
is greenish yellow. Now when two pairs of complementary colours are
mixed together they must produce white, just as if only two complementary
colours were mixed. But a mixture of greenish blue and of greenish yellow
is green. Hence from a mixture of red, green, and violet, white must be
formed. This may easily be ascertained to be the case by means of a
colour disc on which are these three colours in suitable proportions.
Violet Green | Yellow | Red.
Red | Purple Rose | Ae Orange Red
Yellow | Roe | White vein | Yellow
ine Pale blue aoa | Green
Blue | Indigo Blue
Violet Violet
From the above facts it follows that from a mixture of red, green, and
violet all possible colours may be constructed, and hence these three spectral
colours are called the fumdamental colours. It must be remarked that the
tints resulting from the mixture of these three have never the saturation of
the individual spectral colours.
We have to discriminate three points in regard to colour. In the first
place, the ¢z7z, or colour proper, by which we mean that special property
which is due to a definite refrangibility of the rays producing it ; secondly,
the saturation, which depends on the greater or less admixture of white light
with the colours of the spectrum, these being colours which are fully satu-
rated ; and thirdly, there is the zz¢emszty, which depends on the amplitude of
vibration.
584. Homogeneous light.—The light emitted from luminous bodies is
seldom or never quite pure ; on being examined by the prism it will be found
to contain more than one colour. In optical researches it is frequently of
great importance to procure homogeneous or monochromatic light. Common
salt, or, still better, sodium bromide, in the flame of a Bunsen’s lamp gives
a yellow of great purity. For red light, ordinary light is transmitted through
568 On Light [584—
glass coloured with copper suboxide, which absorbs nearly all the rays
excepting the red. A very pure blue is obtained by transmitting ordinary
light through a glass trough containing an ammoniacal solution of copper
sulphate, and a nearly pure red by transmitting it through a solution of
iron sulphocyanide.
585. Properties of the spectrum. —Besides its luminous properties, the
spectrum is found to produce calorific and chemical effects.
Luminous properties. It appears from the experiments of Fraunhofer
and of Herschel that the hight in the yellow part of the spectrum has the
greatest intensity, and that in the violet the least.
fleating effects. It was long known that the various parts of the spectrum
differed in their calorific effects. Leslie found that a thermometer placed in
different parts of the spectrum indicated a higher temperature as it moved
from violet towards red. Herschel fixed the maximum intensity of the
heating effects just outside the red; Berard in the red itself. Seebeck
showed that these different results are affected by the nature of the prism used ;
with a prism of water the greatest calorific effect is produced in the yellow ;
with one of alcohol it is in the orange-yellow ; and with a prism of crown
glass it is in the middle of the red.
Melloni, by using prisms and lenses of rock salt, and by availing himselt
of the extreme delicacy of the thermo-electric apparatus, first made a com-
plete investigation of the calorific properties of the thermal spectrum. This
result led, as we have seen, to the confirmation and extension of Seebeck’s
observations.
Chemical properties. In numerous phenomena, light exerts a chemical
action. For instance, silver chloride blackens under the influence of light ;
transparent phosphorus becomes opaque ; vegetable colouring matters fade ;
hydrogen and chlorine gases, when mixed, combine slowly in diffused light,
and with explosive violence when exposed to direct sunlight... The chemical
action differs in different parts of the spectrum. Scheele found that when
silver chloride was placed in the violet, the action was more energetic
than in any other part. Wollaston observed that the action extended beyond
the violet, and concluded that, besides the visible rays, there are some in-
visible and more highly refrangible rays. These are sometimes called the
chemical or actinic rays.
The most remarkable chemical action which light exerts is inthe growth
of plant life. The vast masses of carbon and hydrogen accumulated in the
vegetable world. owe their origin to the carbonic acid and aqueous vapour
present in the atmosphere. The light which is absorbed by the green parts
of plants acts as a reducing agent. The reduction does not extend to the
complete isolation of carbon and hydrogen, and the individual stages of the
process are unknown to us ; but the general result is, undoubtedly, that under
the influence of the sun’s rays the chemical attraction which holds together
the carbon and oxygen is overcome ; the carbon, which is set free, assimilates
at that moment the elements of water, forming cellulose or woody fibre,
while the oxygen returns to the atmosphere in the form of gas. The
equivalent of the sunlight which has been absorbed is to be sought in the
chemical energy of the separated constituents. When we burn petroleum
—586] Dark Lines of the Spectrum 569
or coal, we reproduce, in some sense, the light which the sun has expended
in former ages in the production of a primeval vegetable growth.
The researches of Bunsen and Roscoe show that whenever chemical
action is induced by light, an absorption of light takes place, preferably of
the more refrangible parts of the spectrum. Thus, when chlorine and
hydrogen unite, under the action of light, to form hydrochloric acid, light is
absorbed, and the quantity of chemically active rays consumed is directly
proportional to the amount of chemical action.
There is a curious difference in the action of the different spectral rays.
Moser placed an engraving on an iodised silver plate and exposed it to the
light, until an action had commenced, and then placed it under a violet glass
in the sunlight. After a few minutes a picture was seen with great distinct-
ness, while when placed under a red or yellow glass it required a very long
time, and was very indistinct. When, however, the iodised silver plate was
first exposed in a camera obscura to blue light for two minutes, and was then
brought under a red or yellow glass, an image quickly appeared, but not
when placed under a green glass. It appears as if there are vibrations of a
certain velocity which could commence an action, and that there are dthers
which are devoid of the property of commencing, but can continue and
complete an action when once set up. Becquerel, who discovered these
properties in luminous rays, called the former exc7ztiéng rays and the latter
continuing or phosphorogenic rays. The phosphorogenic rays, for instance,
have the property of rendering certain objects self-luminous in the dark
after they have been exposed for some time to the hght.
586. Dark lines of the spectrum.—The colours of the solar spectrum
are not continuous. For several grades of refrangibility rays are wanting,
and, in consequence, throughout the whole extent of the spectrum there are a
great number of very narrow dark lines. To observe them, a pencil of solar
rays is admitted into a darkened room, through a narrow slit. At a distance
of three or four yards we look at this slit through a prism of flint glass,
which must be very free from flaws, taking care to hold its edge parallel to
the slit. We then observe a great number of very delicate dark lines parallel
to the edge of the prism, and at very unequal intervals.
The existence of the dark lines was first observed by Wollaston in 1802 ;
but Fraunhofer, a celebrated optician of Munich, first studied and gave a
detailed description of them. Fraunhofer mapped the lines, and indicated
the most marked of them by the letters A, a, B, C, D, E, 4, F, G, H ; they
are therefore generally known as Fraunhofer’s lines.
The dark line A (see fig. 11 of Plate I.) is at the middle, and B halfway
between this and the end of the red portion ; C, at the boundary of the red
and orange ; D is in the yellow region ; E, in the green ; F, in the blue ;
G, in the indigo ; H, in the violet. There are certain other noticeable dark
lines, such as a in the red and @ in the green. In the case of sunlight the
positions of the dark lines are fixed and definite ; on this account they are used
for obtaining an exact determination of the refractive index of a transparent
substance (550) for each colour ; only in this way is it possible accurately to
define a colour ; for example, the refractive index of the blue ray is, strictly
speaking, that of the dark line F. In the spectra of artificial lights, and of the
stars, the relative positions of -the dark lines are changed. In the electric
570 On Light [586—
light the dark lines are replaced by brilliant lines. In coloured flames—that
is to say, flames in which certain chemical substances undergo evaporation
—the dark lines are replaced by very brilliant lines of light, which differ for
different substances. _ Lastly, some of the dark lines are constant in position
and distinctness, such as Fraunhofer’s lines ; but some of the lines only
appear as the sun nears the horizon, and others are strengthened. They are
also influenced by the state of the atmosphere. The fixed lines are due to
the sun; the variable lines have been proved by Janssen and Secchi to be
due to the aqueous vapour in the air, and are called atmospheric or telluric
lines.
Fraunhofer counted in the spectrum more than 600 dark lines, more or
less distinct, distributed irregularly from the extreme red to the extreme
violet ray. Brewster counted 2,000. By causing the refracted rays to pass
successively through several analysing prisms (588), not merely has the
existence of 3,000 dark lines been ascertained, but several which had been
supposed to be single have been shown to be compound. Thollon produced a
spectrum I5 metres in length in which were 4,000 dark lines.
587. Applications of Fraunhofer’s lines.—Subsequently to Fraunhofer,
several physicists studied the dark lines of the spectrum.. In 1822 Sir J.
Herschel remarked that by volatilising substances in a flame a very delicate
means is afforded of detecting certain ingredients by the bright lines they
produce in the spectrum ; and Fox Talbot in 1834 suggested optical analysis
as probably the most delicate means of detecting minute portions of a
substance. To Kirchhoff and Bunsen, however, is really due the merit of
basing a method of analysis on the observation of the lines of the spectrum.
They ascertained that the salts of the same metal, when introduced into a
flame, always produced lines identical in colour and position, but that lines
different in colour, position, or number were produced by different metals ;
and finally, that an exceedingly small quantity of a metal suffices to disclose
its existence. Hence has arisen a new and powerful method of analysis,
known by the name of spectrum analysts.
588. Spectroscope.—The name of spectroscope has been given to the
apparatus employed by Kirchhoff and Bunsen for the study of the spectrum.
One of the forms of this apparatus is represented in fig.556. It is composed
of three telescopes mounted on a common foot, whose axes converge
towards a prism, P, of flint glass. The telescope A is the only one which
can turn round the prism. It is fixed in any required position by a clamping
screw #7. The screw-head 7 is used to focus the eyepiece. The screw-head
m serves to change the inclination of the axis.
To explain the use of the telescopes B and C we must refer to fig. 557,
which shows the passage of the light through the apparatus. The rays.
emitted by the flame G fall on the lens a, and are caused to converge to a
point 4, which is the principal focus of a second lens c. Consequently the
pencil, on leaving the telescope B, is formed of parallel rays (564). This pencil
enters the prism P. On leaving the prism the light is decomposed, and in
this state falls on the lens x By this lens x a real and reversed image of
the spectrum is formed at z. This image is seen by the observer through a
magnifying glass, which forms at ss’ a virtual image of the spectrum magni-
fied about eight times. ;
—588] Spectroscope | 57a
The telescope C serves to measure the relative distances of the lines
of the spectrum. For this purpose a micrometer is placed at 7, divided
Fige 556
into 25 equal parts. A micrometer is formed thus :—A scale of 250 milli-
metres is divided with great exactness into 25 equal parts. A photo-
Fig. 557
graphic negative on glass of this scale is taken, reduced to 15 millimetres.
The negative is taken because then the scale is light on a dark ground.
The scale is then placed at m in the principal focus of the lens e ;
572 On Light [588—
consequently, when the scale is lighted by the candle F, the rays emitted from
it leave the lens ¢ in parallel pencils ; a portion of these, being reflected from
a face of the prism, passes through a
lens x, and forms a perfectly distinct
image of the micrometer at z, thereby
furnishing the means of measuring
exactly the relative distances of the
different spectral lines.
The micrometric telescope C (fig.
556) is furnished with several adjusting
screws, Zz, 0, ~; of these, z adjusts the
focus ; 0 displaces the micrometer in
the direction of the spectrum laterally ;
vy raises or lowers the micrometer,
Fig. 558 which it does by giving different incli-
nations to the peestane
The opening whereby the light of the flame G enters the telescope B
consists of a narrow vertical slit, which can be opened more or less by
causing the movable piece a to advance or recede by means of the screw v
(fig. 558). When, for purposes of comparison, the spectra of two flames
are to be examined simultaneously, a small prism, whose refracting angle
is 60°, is placed over the upper part of the slit. Rays from one of the
flames, H, fall at right angles on one face of the prism ; they then experience
total reflection on a second face, and leave the prism by the third face, and
in a direction at right angles to that face. By this means they pass into the
telescope in a direction parallel to its axis, without in any degree mixing with
the rays which proceed from the second flame, G. Consequently the two
pencils of rays traverse the prism P (fig. 557), and form two horizontal spectra,
which are viewed simultaneously through the telescope A. In the flames G
and H are platinum wires, e, e’. These wires have been dipped beforehand
into solutions of the salts of the metals on which experiment is to be made ;
and the vaporised metals of these salts give rise to definite lines.
Each of the flames G and H is a jet of ordinary gas. The apparatus
through which the gas is supplied is known as a Bunsen’s burner. The gas
comes through the hollow stem & (fig. 556). At the lower part of this there
is a lateral orifice which admits air to support the combustion of the gas.
This orifice can be more or less closed by a small diaphragm, which acts as
a regulator. If we allow a moderate amount of air to enter, the gas burns
with a luminous flame, and the lines are obscured. But if a strong and
steady current of air enters, the carbon is rapidly oxidised, the flame loses its
brightness, and burns with a pale blue light, but with an intense heat. In
this state it no longer yields a spectrum. If, however, a metallic salt is in-
troduced either in a solid state or in a state of solution, the spectrum of the
metal makes its appearance, and in a fit state for observation.
There are three chief types of spectra; the continuous spectra, or
those furnished by incandescent solids and liquids (fig. 1, Plate I.) ; the dand
or |42ze spectrum, consisting of a number of bright lines, and produced by
incandescent gases or vapours ; and adsorption spectra, such as those fur-
nished by the sun or fixed stars. For an explanation of these see art. 591
Moy
—589] Direct Viston Spectroscope 573
Bodies at a red heat give only a short spectrum, extending at most to the
orange; as the temperature gradually rises, yellow, green, blue, and violet
successively appear, while the intensity of the lower colours increases.
Instead of the prism very pure spectra may also be obtained by means of
a grating (661). For more detailed investigations of the spectral lines a ¢vazz
of prisms is used. Fig. 559 repre-
sents one with nine prisms. The
light issuing from’ the collimeter A
passes in succession through each
of the prisms. As the successive
deviations add themselves the dis-
persion is very much increased, and }
a spectrum of great extent is ob-
tained. It is, however, feebly lumi-
nous, owing partly to its extension,
and partly to the loss of light which
is observed through the telescope B,
which it undergoes in traversing all
these refracting surfaces. In the
case of ten prisms the loss of
light has been found to amount to
ninety-nine per cent.
Christie has used with advantage
a semt-prism obtained by cutting an
isosceles prism by a plane at right
angles to the base. These semi-
prisms have the advantage that they produce as much dispersion as with
several prisms without any appreciable loss in the sharpness of the images ;
and without that absorption of light which in the case of a number of prisms
is so very considerable.
589. Direct vision spectroscope.—Prisms may be combined so as to
get rid of the dispersion without entirely destroying the refraction (596) ;
they may, conversely,
be combined so that
the light is not re-
fracted, but is decom-
posed and produces a
spectrum. | Combina-
tions ‘of prisms of this
kind are used in what are called direct vision spectroscopes. Fig. 560 repre-
sents the section of such an instrument in about 3 the natural size. A system
of two flint and three crown-glass prisms is placed in a tube which moves in
a second one; at the end of this is an aperture 9, and inside it a slit the
width of which can by a special arrangement be regulated by simply turning
aring 7 A small achromatic lens is introduced at aa, the focus of which is
just outside the slit, so that the rays pass through the train of prisms, and
the eye at e sees a virtual image of the slit opened out into a spectrum.
Such combinations have the disadvantage of absorbing much light.
On passing from one medium into another some light is always lost by
Fig. 5590
Fig. 560
574 On Light [589—
reflection. This is less the nearer are the refraction indices of the media.
Wernicke has constructed a direct vision prism in which the loss of light is
greatly reduced. It consists of two prisms of crown glass and glass plates
as shown in the figure 561, the hollow space
formed is filled with cinnamic ether, which,
while it has but a slightly larger refractive
index, has three or four times the dispersion
of crown glass. .
The reversion spectroscope contains two
Hie see equal systems of direct vision prisms ar-
ranged close to each other, but reversed, so
that two spectra are obtained with the colours in opposite order. By suitable
micrometric movement of a split lens, the two spectra may be moved apart
or nearer each other. Hence it is possible to bring any two identical
lines so that they are in the same vertical line. If now the position of
these lines in the spectrum is altered, the displacement will take place
in the opposite direction in the two spectra, and will therefore be twice as
distinct.
590. Experiments with the spectroscope.—The coloured plate at the
beginning shows certain spectra observed by means of the spectroscope.
No. I represents the continuous spectrum.
No. 2 shows the spectrum of sodium. The spectrum contains neither
red, orange, green, blue, nor violet. It is marked by a very brilliant yellow
ray in exactly the same position as Fraunhofer’s dark line D. Of all metals
sodium is that which possesses the greatest spectral sensibility. In fact, it
has been ascertained that one two-hundred-millionth of a grain of sodium
is enough to cause the appearance of the yellow line. Consequently it is very
difficult to avoid the appearance of this line. A very little dust produced in
the apartment is enough to produce it—a circumstance which shows how
abundantly sodium is distributed.
No. 3 is the spectrum of /zthzuwm. It is characterised by a well-marked
line in the red called Lia, and by the feebler orange line Lif.
Nos. 4 and 5 show the spectra of ces¢um and rubidium, metals discovered
by Bunsen and Kirchhoff by means of spectrum analysis. ‘The former is
distinguished by two blue lines, Csa and Cs@ ; the latter by two very brilliant
dark red lines, Rby and Rbé, and by two less intense violet lines, Rba and
Rb8. A third metal, thallium, has been discovered by the same method
by Sir W. Crookes in England, and independently by Lamy in France.
Thallium is characterised by a single green line. Subsequently to this
Richter and Reich discovered in association with zinc a new metal which
they call zzd@zum from a couple of characteristic lines which it forms in the
indigo ; and recently Boisbaudran has discovered a new metal which he calls
gallium associated with zinc in very minute quantities ; and in more recent
times germanium, scandium, samarium, and helium have been discovered.
The extreme delicacy of the spectrum reactions, and the ease with which
they are produced, constitute them a most valuable help in the qualitative
analysis of the alkalies and alkaline earths. It is sufficient to place a small
portion of the substance under examination on platinum wire as represented
‘in fig. 555, and compare the spectrum thus obtained either directly with that
—590] Experiments with the Spectroscope 575
of another substance or with the charts in which the positions of the lines
produced by the various metals are laid down.
With other metals the production of their spectra is more difficult,
especially in the case of some of their compounds. The heat of a Bunsen’s
burner is insufficient to vaporise the metals, and a higher tempera-
ture must be used. This is obtained by taking electric sparks between
wires consisting of the metal whose spectrum is required, and the electric
sparks are most conveniently obtained by means of Ruhmkorff’s coil.
In order to investigate solutions of salts the apparatus shown in fig. 562 is
used. A platinum wire is fixed in the bottom, and over one end a small
conical glass tube D is placed ; only so much solution is poured in that by
capillary action it just rises to the top of D. Another glass tube fused in a
platinum wire is fixed in the cork C, and its free end can be placed at any
distance from D. Thus all the metals may be brought within
the sphere of spectrum observation.
The dispersive power of the apparatus has great influence
on the nature of the spectrum; while an apparatus with one
prism only gives in a sodium flame the well-known yellow line,
an apparatus with more prisms resolves it into two or three lines.
It has been observed that the character of the spectrum
changes with the temperature ; thus chloride of lithium in the
flame of a Bunsen’s burner gives a single intense peach-coloured
line; in a hotter flame, as that of hydrogen, it gives an
additional orange line; while in the oxyhydrogen jet or the
voltaic arc a broad brilliant blue band comes out in addition.
The sodium spectrum produced by a Bunsen’s burner consists
of a single yellow line; if, by the addition of oxygen, the heat
is gradually increased, more bright lines appear; and with
the aid of the oxyhydrogen flame the spectrum is continuous.
Sometimes also, in addition to the appearance of new lines, an
increase in temperature resolves those bands which exist into a number of
fine lines, which in some cases are more and in some less refrangible than the
bands from which they are formed. It may be supposed that the glowing
vapour formed at the low temperature consists of the oxide of some difficultly
reducible metal, whereas at the enormously high temperature of the spark
these compounds are decomposed, and the true bright lines of the metal are
formed.
The delicacy of the reaction increases very considerably with the tem-
perature. With the exception of the alkalies, it is from 40 to 400 times
greater at the temperature of the electric spark than at that of Bunsen’s
burner.
The spectra of the permanent gases are best obtained by taking the
electric spark of a Ruhmkorff’s coil, or Holtz’s machine, through glass
tubes of a special construction, consisting of two wide ones connected by a
capillary tube (fig. 563), which in the wider parts are provided with electrodes
of platinum or aluminium ; they are filled with the gas in question in a state
of great attenuation, and are usually known as Ge?ssler’s tubes ; if the spark
is passed through hydrogen, the light emitted is bright red, and its spectrum
consists of one red, two blue lines, No. 7, the first two of which appear to
Fig. 562
576 On Light . [590-
coincide with Fraunhofer’s lines C and F, and the third with a line between
F and G. No. 6 represents the spectrum of oxygen. No. 8 is the spectrum
of nitrogen. The light of this gas in a Geissler’s tube is purple, and the
spectrum very complicated.
If the electric discharge takes place through a compound gas or vapour,
the spectra are those of the elementary constituents of the gas. It seems as
if, at very intense temperatures, chemical combination were impossible, and
oxygen and hydrogen, chlorine and the metals, could coexist in a separate
form, as though mechanically mixed with each other.
The nature of the spectra of the elementary gases is very materially in-
fluenced by alterations of temperature and pressure. Wiillner made a series
of very accurate observations on the gases oxygen, hydrogen, and nitrogen.
He not only used gases in closed tubes, which by various electrical means
a he raised to different temperatures ; but in one and the same
; series of experiments, in which a small induction coil was used,
i he employed pressures varying from 100 millimetres to a frac-
| tion of a millimetre ; while in another series, in which a larger
lila, @pparatus was used, he extended the pressure to 2,000 milli-
metres. At the lowest pressure of less than one millimetre, the
spectrum of hydrogen was found to be green, and consisting of
six splendid groups of lines, which at a higher pressure than
iC 1 millimetre changed to continuous bands ; at 2 to 3 millimetres
| the spectrum consisted of the often-mentioned three lines,
il which did not disappear under a higher pressure, but gradually
became less brilliant as the continuous spectrum increased in
extent and lustre. From this point the light, and therefore the
spectrum, became feebler. Using the larger apparatus, the
band spectrum appeared only under a higher pressure ; at the
highest pressure of 2,000 millimetres it gave place to the con-
tinuous spectrum, since the bright lines continually extended and
ultimately merged into each other.
591. Explanation of the dark lines of the solar spectrum.—
It has been already seen that incandescent sodium vapour
gives a bright yellow line corresponding to the dark line D of
the solar spectrum. Kirchhoff found that, when the brilliant
light produced by incandescent lime passes through a flame
coloured by sodium in the usual manner, a spectrum is pro-
duced in which is a dark line coinciding with the dark line D
of the solar spectrum ; what would have been a bright yellow
line becomes a dark line when formed on the background of the
limelight. By allowing in a similar manner the limelight to
traverse vapours of potassium, barium, strontium, &c., the bright
lines which they would have formed were found to be converted into dark
lines : such spectra are called adsorption spectra.
It appears, then, that the vapour of sodium has the power of absorbing
rays of the same refrangibility as those which it emits. And the same is true
of the vapours of potassium, barium, strontium, &c. This absorptive power
is by no means an isolated phenomenon. These substances share it, for ex-
ample, with the vapour of nitrous acid, which Brewster found to possess the
——
—591] Explanation of Dark Lines of Solar Spectrum 577
following property :—when a tube filled with this vapour is placed in the path
of the light either of the sun or of a gas flame, and the light is subsequently
decomposed by a prism, a spectrum is produced which is full of dark lines
(No. 9, Plate I.) ; and Miller showed that iodine and bromine vapour pro-
duced analogous effects.
Hence the origin of the above phenomenon is, doubtless, the absorption
by the sodium vapour of rays of the same kind—that is, having the same
refrangibility—as those which it has itself the power of emitting. Other rays
it allows to pass unchanged, but these it either totally or in great part sup-
presses. Thus the particular lines in the spectrum to which these rays
would converge are illuminated only by the feebly luminous sodium flame,
and accordingly appear dark by contrast with the other portions of the
spectrum which receive light from the powerful flame behind.
By replacing one of the flames G and H (fig. 558) by a pencil of sunlight
reflected from a heliostat, Kirchhoff ascertained by direct comparison that
the bright lines which characterise iron correspond to dark lines in the solar
spectrum. He also found the same to be the
case with sodium, magnesium, calcium, nickel,
and some other metals.
This reversal of the sodium light may be pro-
duced even without a prism by an apparatus
devised by Bunsen, and shown in fig. 564. It
consists of a Woolf’s bottle in which a small
quantity of zinc, dilute sulphuric acid, and com-
mon salt are placed so that hydrogen is slowly
liberated, charged with particles of sodium
chloride, or, better, bromide. Through the india-
rubber tube L ordinary coal gas is admitted, and
issues through the tubes Rand R’. On each
of these tubes is a metal burner. The gas
burns at the top A with a broad flat flame, C ;
the burner B is cylindrical, and over it is placed
a conical mantle closed at the top with wire
gauze. In this way a small yellow flame is
produced. On looking through this against
the wide flame, the former appears dark, as
if smoky on a light background. The light of
the posterior and far brighter flame is absorbed
by the front and cooler one, and replaced by light
of lesser intensity, which thus appears dark by
contrast.
From such observations we may draw im-
portant conclusions with respect to the consti- ,
tution of the sun. Since the solar spectrum has . ics u64
dark lines where sodium, iron, &c., give bright
ones (No. 11, Plate I.), it is probable that around the solid, or more probably
liquid, body of the sun which throws out the light, there exists a vaporous
envelope which, like the sodium flame in the experiment described above,
absorbs certain rays ; namely, those which the envelope itself emits. Hence
pat
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4
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Ke
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i
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i
i
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he
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578 On Light [591-
those parts of the spectrum which, but for this absorption, would have
been illuminated by these particular rays, appear feebly luminous in com-
parison with the other parts, since they are illuminated only by the light
emitted by the envelope, and not by the solar nucleus ; and we are at the
same time led to conclude that in this vapour there exist the metals sodium,
iron, &c.
Sir W. Huggins and Miller applied spectrum analysis to the investigation
of the heavenly bodies. The spectra of the moon and planets, whose light is
reflected from the sun, give the same lines as those of the sun. Uranus proves
an exception to this, and is probably still in a self-luminous condition. The
spectra of the fixed stars contain, however, dark lines differing from the solar
lines, and from one another. Four distinct types of spectra were distinguished
by Secchi. The first embraces the white stars, and includes the well-known
Sirius anda Lyre. Theirspectra (No. 12, Plate I.) usually contain a number
of very fine lines, and always contain four broad dark lines which coincide
with the bright lines of hydrogen. Out of 346stars 164 were found to belong
to this group. The second group embraces those having spectra intersected
by numerous fine lines like those of our sun. About 140 stars, among them
Pollux, Capella, @ Aquilz, belong to this group. The third group embraces
the red and orange stars, such as a Orionis, 8 Pegasi; the spectra of these
(Nos. 13, 14, Plate I.) are divided into eight or ten parallel columnar clusters
of dark and bright bands increasing in intensity to the red. Group four is
made up of small red stars with spectra constructed of three bright zones
increasing in intensity towards the violet. It would thus appear that
these fixed stars, while differing from one another in the matter of which
they are composed, are constructed on the same general plan as our sun.
Huggins has observed a striking difference in the spectra of the nebule ;
where they can at all be observed they are found to consist generally of
bright lines, like the spectra of the ignited gases, instead of, like the spectra
of the sun and stars, consisting of a bright ground intersected by dark lines.
It is hence probable that the nebule are masses of glowing gas, and do not
consist, like the sun and stars, of a photosphere surrounded by a gaseous
atmosphere.
We can apply the reasoning of Doppler’s principle (236) to the case of
light, and assume provisionally that the motion of light is analogous to that
of sound. When a source of light is approaching the earth, the eye receives
a greater number of waves in a given time than when there is no relative
motion, the waves are shorter ; as it moves away the opposite is the case, the
waves are longer. Hence, on the approach of yellow light, for instance, the
bright band D will.seem displaced towards the violet end of the spectrum,
and as it recedes, towards the red end. This will also be the case with the
corresponding dark line, proving that the whole medium is moved at the
same time. Accordingly, by observing the displacement of particular lines,
conclusions may be drawn as to the relative motions of what are called the
fixed stars. Thus, from careful observation of the displacement of the F line
in Sirius, Huggins has inferred that it is moving away from the earth with a
velocity of 42 miles per second.
One of the most interesting triumphs of spectrum analysis has been the
discovery of the true nature of the protuberances which appear during a
~592] Uses of the Spectroscope 579
solar eclipse as mountains or cloud-shaped luminous objects varying in size,
and surrounding the moon’s disc.
During the eclipse of 1868 it had been ascertained by Janssen that pro-
tuberances emitted certain bright lines coinciding with those of hydrogen.
They have, however, been fully understood only since Sir Norman Lockyer
and Janssen have discovered a method of investigating them at any time. The
principle of this method is as follows :—When a line of hight admitted through
a slitis decomposed by a prism, the length of the spectrum may be increased
by passing it through two or more prisms ; as the quantity of light is the same,
it is clear that the intensity of the spectrum will be diminished. This is the
case with the ordinary sources of light, such as the sun; if the light be
homogeneous, it will be merely deviated, and not reduced in intensity, by
dispersion. And if the source of light emit light of both kinds, the image
of the slit of light of a definite refrangibility, which the mixture may contain,
will stand out, by its superior intensity, on the weaker ground of the con-
tinuous spectrum. This is the case with the spectrum of the protuberances.
Viewed through an ordinary spectroscope, the light they emit is overshadowed
by that of the sun ; but by using prisms of great dispersive power the sun’s
light becomes weakened, and the spectrum of the protuberances may be
observed. Lockyer’s researches leave no doubt that they are ignited masses
of gas, principally hydrogen. By altering the position of the slit a series
of sections of the prominences is obtained, by collating which the form of
the prominence may be inferred. They are thus found to enclose the sun
usually to a depth of about 5,000 miles, but sometimes in enormous local
accumulations, which reach the height of 70,000 miles. Lockyer has not
merely examined these phenomena right on the edge of the sun, but he has
been able to observe them on the disc itself. He has shown that some of
these protuberances are the results of sudden outbursts or storms, which
move with the enormous velocity of 120 miles in a second ; and, by reasoning
as above, the direction of this motion has been determined.
For a fuller account of this branch of physics, which is incompatible with
the limits of this work, the reader is referred to special works.
592. Uses of the spectroscope.—When a liquid placed in a glass tube
or in a suitable glass cell is interposed between a source of light and the
slit of the spectroscope, the spectrum observed on looking through the
telescope will in many cases be found to be traversed by dark bands.
No. to, Plate I., represents the appearance of the spectrum when a solution
of chlorophy/, the green colouring matter of plants, is thus interposed. In
the red, the yellow, and the violet parts, dark bands are formed, and the
blue gives way to a reddish shimmer. If, instead of chlorophyll, arterial
blood greatly diluted be used, the red of the spectrum appears brighter, but
green and violet are nearly extinguished. As these bands thus differ in
different liquids as regards position, breadth, and intensity, in many cases
they afford the most suitable means of identifying bodies. Sorby and
Browning devised a combination of the microscope and spectroscope called
the mzcrospectroscope, which renders it possible to examine even very minute
traces of substances.
This application of the spectroscope has been very useful in investigating
substances which have special importance in physiology and pathology ;
PP2
580 On Light [592—
thus in examining normal and diseased blood, and in ascertaining the rate
at which certain substances pass into the various fluids of the system. The
characteristic absorption bands which certain liquids, such as wine, beer, &c.,
present in their normal state, compared with those yielded by adulterated
substances, furnish a delicate and certain means of detecting the latter.
Thus the adulteration of claret with the juice of elderberries is detected
by the appearance of faint bands near line D, which are not seen with pure
red wine. The colouring matter of malt and hops is quite distinct from
that of many other substances with which it is alleged to be adulterated.
An alkaline solution of blood to which ammonium sulphide is added, gives
two very powerful absorption bands between D and E, and between Eand0 ;
this is the most valuable test for toxicological cases. Blood charged with
carbonic oxide is unchanged on the addition of ammonium sulphide, and
thus poisoning by carbonic oxide can be detected. So, too, the appear-
ance of the characteristic bands of gall in blood, and of albumen in urine,
are indications of jaundice and of Bright’s disease respectively.
Suppose the slit of the spectroscope be divided into two halves, Ss, and s,
(fig. 565), the aperture of each of which can be varied to any measured extent
by means of micrometric screws. If then a layer
of a substance of known thickness be placed in front
of the slit s,, for instance, and the spectrum of a
_| particular portion be observed, there will be a
i! difference between the luminosities of the two parts
of the spectrum ; but by regulating the width of
the slit they may be made the same. The lumi-
nosities will then be inversely as the width of the
slit. Thatis, if the width of each were originally 1,
and the uncovered slit had to be narrowed to o°4, the intensity of the light
transmitted through the screen would only be o-4 of the incident. Vierordt
has based on this a method of quantitative spectrum analysis; thus if the
absorption produced by a definite thickness of a solution of known strength
be known, the relative concentration of any other solution of the same
substance for the same thickness may be determined.
593. Abnormal or anomalous dispersion.—A remarkable exception to the
ordinary law of dispersion was discovered by Christiansen, and subsequently
confirmed and extended by Soret and Kundt—that the solutions of certain
substances, such as indigo and potassium permanganate, give spectra in which
the order of the colours is not
I [ilfiest «fy dalek ly nach 2 ules ar Wie ae |} the same as in the prismatic
Gite FH B C D spectrum. Thus, when a hollow
' glass prism is filled with an
TL Poe a ee ee en alcoholic solution of fuchsine,
Bam Ci Ds i Ir G H the order of the colours in the
Fig. 566 spectrum which it yields is as
follows. Violet is /eas¢ refracted,
then red, and then yellow, which is vos¢ refracted. If we imagine that the
central green of an ordinary spectrum is removed, and then the position of
the rest is inverted, we get. an idea of the aunoeual spectrum of fuchsine.
This will be seen from fig. 566, in which I represents the position of Fraun-
Ie Ty
bi |
—594] Fluorescence 581
hofer’s lines in the anomalous dispersion of fuchsine, while II represents
the position in the normal spectrum. Kundt examined a great number of
substances in this direction, mostly the colours derived from aniline, and
found that the abnormal dispersion is exhibited by all substances with
surface colour. These bodies have the peculiarity that when viewed in
diffused light they exhibit a colour complementary to that which they
transmit. Thus a thin flake of fuchsine appears green in diffused, but red
in transmitted light. Metallic gold appears green in transmitted and reddish
yellow by reflected light.
The substances in solution are examined by placing them in hollow glass
prisms ; if the solutions are weak, the abnormal dispersion of the substance
is concealed by that of the solvent, while stronger solutions absorb so much
light as to be almost opaque, and prisms of very small refracting angle have
to be used. Soret gets rid of this difficulty by immersing the prism contain-
ing the solution in glass vessels with parallel sides filled with the solvent.
The dispersion due to the solvent is thereby eliminated, and only that of the
substance comes into play. Cyanine gives a well-marked abnormal spec-
trum, the order of the colours being the following: green, light blue, dark
blue, a dark space, red, and traces of orange, the green being the colour
which is least refracted. Anomalous dispersion is met with in gases which
have marked absorption bands ; thus in iodine for red light 7 = 100205, and
for violet = 1°00192.
The same explanation cannot be given of this as of the ordinary colour
of bodies (581), but the phenomenon must be ascribed to the fact that the
bodies in question totally reflect light of certain wave-lengths (651) at almost
all incidences, and that these colours are reflected on the surface. Hence
it follows that the colour of these bodies in diffused light must be almost com-
plementary to the transmitted light—a prevision which experiment confirms.
594. Fluorescence.—Stokes made the remarkable discovery that under
certain circumstances the rays of light are capable of undergoing a change
of refrangibility. The discovery originated in ey
the study of a phenomenon observed by Lb lisp,
Brewster, and by Herschel, that some varieties MtEE SE fy
of fluorspar, and also the solutions of certain LH IL
substances, when looked at by transmitted hght Rts //
appear colourless, but when viewed in reflected ALE f
light present a bluish appearance. Stokes has
found that this property, which he calls fzor-
escence from having been observed in fluorspar,
is characteristic of a large number of bodies.
If by means of a lens of long focus, prefer-
ably of quartz, a beam of the sun’s rays is
focussed on a solution of quinine sulphate con-
tained in a glass trough, a beautiful cerulean
blue cone of light (fig. 567) is formed, which
is much the brightest on the surface, and the
intensity of which rapidly diminishes as it penetrates the liquid.
It thus appears that fluorescence is due to an absorption of certain rays ;
rays of light which have passed through a sufficient thickness of a fluorescent
E
=
E
Ee
=
FE
iz
=
A=
(=
=
Zz
EEE
KQKQKKKKUXKcuss
Fig. 567
ZZ
582 On Light [594-
substance lose thereby the power of exciting fluorescence when they are
passed through a second layer of the same substance ; thus a test tube con-
taining a fluorescent liquid is brightly luminous when exposed to the sun’s
rays, but loses this lustre at once when it 1s dipped in a trough of the same
liquid, on the front of which the sun’s rays fall. This also results from a
comparison of the absorption spectrum of a fluorescent substance with the
appearance presented by this substance when the spectrum falls on it. When
the fluorescence begins there also begins the absorption, and to a maximum
of absorption corresponds a maximum of fluorescence.
The phenomenon is seen when a solution of quinine sulphate, con-
tained in a trough with parallel sides, is placed in different positions in the
solar spectrum. No change is observed in the less refrangible part of the
spectrum, but from about the middle of the lines G and H (coloured Plate) to
some distance beyond the extreme range of the violet, rays of a beautiful
sky-blue colour are seen to proceed. These invisible ultra-violet rays also
become visible when the spectrum is allowed to fall on paper impregnated
with a solution of @sculine (a substance extracted from horse-chestnut), an
alcoholic solution of stramonium, or a plate of canary glass (which is coloured
by means of uranium). If light be allowed to fall on paper impregnated with
barium platinomanganide, a beautiful green fluorescence is observed.
If a few drops of a strong solution of flworesceine in soda fall into a large
beaker of water on the front of which the sun’s rays fall, beautiful fluorescent
clouds are first produced, and on shaking the liquid the whole vessel
fluoresces with a bright green light.
This change arises from a diminution in the refrangibility of those rays
outside the violet, which are ordinarily too refrangible to affect the eye.
Glass absorbs many of these more refrangible rays, which is not the case
nearly to the same extent with quartz. When a prism and trough formed
of quartz are used, and the spectrum is received on a sheet of paper on which
a wash of solution of quinine sulphate has been made, two juxtaposed
spectra can be obtained. That which is on the part coated with quinine
sulphate extends beyond the line H to an extent equal to that of the visible
spectrum. In the spectrum, thus made visible, dark lines may be seen
analogous to those in the ordinary spectrum.
The phenomena may be observed without the use of a prism. When an
aperture in a dark room is closed by means of a piece of blue glass, and the
light is allowed to fall upon a piece of canary glass, it instantly appears self-
luminous from the emission of the altered rays. If a test tube is half filled
with a solution of quinine sulphate, and on it is poured a freshly pre-
pared solution of chlorophyl in ether, the two layers appear colourless and
green respectively in transmitted, and sky-blue and blood-red in reflected
light.
In most cases it 1s the violet and ultra-violet rays which undergo an
alteration of refrangibility, but the phenomenon is not confined to them. A
decoction of madder in alum gives yellow and violet light from about the
line D to beyond the violet ; an alcoholic solution of chlorophyl gives red
light from the line B to the limit of the spectrum. In these cases the
yellow, the green, and the blue rays experience increase of refrangibility ;
the change produces more highly refrangible rays. An exception to this rule
—596] Chromatic Aberration 583
is met with in the case of Magdala red. If on a solution of this substance
contained in a rectangular glass vessel a solar spectrum is allowed to fall,
an orange-yellow fluorescence is found even in the red part of the spectrum.
The electric light gives a very remarkable spectrum. With quartz
apparatus Sir G. Stokes obtained a spectrum six or eight times as long as the
ordinary one. Several flames of no great illuminating power emit very
peculiar light. Characters traced on paper with solution of stramonium,
which are almost invisible in daylight, appear instantaneously when illu-
minated by the flame of burning sulphur or of carbon bisulphide.
Robinson found that the light of the aurora is peculiarly rich in rays of high
refrangibility.
595. Chromatic aberration.—The various lenses hitherto described
(563) possess the inconvenience that, when at a certain distance from the
eye, they give images with coloured edges. This defect, which is most
observable in condensing lenses, is due to the unequal refrangibility of the
simple colours (576), and is called chromatic aberration.
For, since a lens may be compared to a series of prisms with infinitely
small faces, and united at their bases (563), it not only refracts light, but also
decomposes it like a prism. On account of this dispersion, therefore, lenses
have really a distinct focus for each colour. In condensing lenses, for
example, the red rays, which are the least refrangible, form their focus ata
point R on the axis of the lens,
(fig. 568) ; while the violet rays,
which are most refrangible,
coincide in the nearer point V.
The foci of the orange, yellow,
green, blue, and indigo are be-
tween these points. The chro-
matic aberration is more per-
ceptible in proportion as the Fic. 568
lenses are more convex, and as
the point at which the rays are incident is farther from the axis ; for then the
deviation, and therefore the dispersion, are increased.
If a pencil of rays which has passed through a condensing lens is
received on a screen placed at 7 within the focal distance, a bright spot is
seen with a red border ; if it is placed at ss, the bright spot has a violet
border.
The inequality in the refraction of the blue and red rays may be demon-
strated by closing’a small aperture, half with red and half with blue glass
(fig. 569) ; on each half a black arrow is painted, and
a lamp is placed behind it. By means of a lens of
60 cm. focus an image is formed on a screen at a dis-
tance of about 2 metres. If the screen is placed so
that a sharp image is obtained of the black object on the
blue ground, the outlines of the other are confused. To
get a sharp image of the arrow on the red ground the
screen must be moved farther away.
596. Achromatism.—By combining prisms which
have different refracting angles (556), and are formed of substances of
584 On Light [596—
unequal dispersive powers (576), white light may be refracted without being
dispersed. The same result is obtained by combining lenses of different
substances, the curvatures of which are suitably combined. The images of
objects viewed through such lenses do not appear coloured, and they are
accordingly called achromatic lenses ; achromatism being the term applied
to the phenomenon of the refraction of light without decomposition.
By observing the phenomenon of the dispersion of colours in prisms of
water, of oil of turpentine, and of crown glass, Newton was led to suppose
that dispersion was proportional to refraction. He concluded that there
could be no refraction without dispersion, and, therefore, that achromatism
was impossible. Almost half a century elapsed before this was found to be
incorrect. Hall, an English philosopher, in 1733, was the first to construct
achromatic lenses, but he did not publish his discovery. It is to Dollond,
an optician in London, that we owe the greatest improvement which has
been made in optical instruments. He showed in 1757 that by combining
two lenses—one a double convex crown glass lens, the other a concavo-
convex lens of flint glass (fig. 571)—a lens is obtained which is virtually
achromatic.
To explain this result, let two prisms, BFC and CDF, be joined and
turned in a contrary direction, as shown in fig. 570. Let us suppose in the
first case, that both prisms are of the same material, but that the refracting
angle of the second, CDF, is less than the
refracting angle of the first ; the two prisms
will produce the same effect as a single prism,
BAF ; that is to say, that white light which
traverses it will be not only refracted, but also
decomposed. If, on the contrary, the first prism
BCF were of crown glass, and the other CFD
of flint glass, the dispersion might be destroyed
Fig. 570 without destroying the refraction. For, as flint
glass is‘more-dispersive than crown, and as the
dispersion produced by a prism diminishes with its refracting angle (576), it
follows that by suitably lessening the refracting angle of the flint glass prism
CFD, as compared with the refracting angle of the crown glass prism BCF,
the dispersive power of these prisms may be equalised ; and as, from their
position, the dispersion takes place in a contrary direction, it is neutralised ;
that is, the emergent rays EO are parallel, and therefore give white light.
Nevertheless, the ratio of the angles BCF and CFD, which is
suitable for the parallelism of the red rays and violet rays, is not
so for the intermediate rays, and, consequently, only two of the
rays of the spectrum can be exactly combined, and the achro-
j, ==, Matism is not quite perfect. To obtain perfect achromatism,
= several prisms would be necessary, of unequally dispersive
materials, and with their angles suitably combined.
The refraction is not destroyed at the same time as the dis-
rig es persion 3 that could only happen if the refracting power of a
body varied in the same ratio as its dispersive power, which is
not the case. Consequently, the emergent ray EO is not exactly parallel to the
incident ray, and there is a refraction without appreciable decomposition.
i
Mh
|
\
ul
—596] Achromatism 585
Achromatic lenses are made of two lenses of unequally dispersive
materials : one, A, of flint glass, is a diverging concavo-convex (fig. 571) ;
the other, B, of crown glass, is double convex, and one of its faces may exactly
coincide with the concave face of the first. As with prisms, several lenses
would be necessary to obtain perfect achromatism ; but for optical instruments
two are sufficient, their curvatures being such as to combine not the extreme
red and violet, but the blue and orange rays, while at the same time regard
is had to the correction for spherical aberration. In Abbé’s afochromatic
lenses the crown glass is replaced by fluorspar, and thereby the chromatic as
well as the spherical aberration is still further reduced.
586 On Light [597.-
CHARTERS V
OPTICAL INSTRUMENTS
597. The different kinds of optical instruments.— By the term oftical
Zastrument 1s meant any combination of lenses, or of lenses and mirrors.
Optical instruments may be divided into three classes, according to the
ends they are intended to answer, viz.: 1. Microscopes, which are designed
to obtain a magnified image of any object whose real dimensions are too
small to admit of its being seen distinctly by the naked eye. 1. Zelescofes,
by which very distant objects, whether celestial or terrestrial, may be
observed. iu. Jastruments designed to project on a screen a magnified or
diminished image of any object which can thereby be either depicted or
rendered visible to a crowd of spectators; such as the camera lucida,
the camera obscura, photographic apparatus, the magic lantern, the solar
microscope, the photo-electric microscope, &c.
MICROSCOPES
598. The simple microscope.—The simple microscope, or magnifying
glass, is merely a convex lens of short focal length, by means of which we
look at objects placed between the lens and its principal focus. Let AB
(fig. 572) be the object to be observed, placed between the lens and its
principal focus, F.
Draw the second-
ary axes AO and
BO, and also from
A and B rays paral-
lel to the axis of
the lens FO. Now
these rays, on pass-
ing out of the
lens, tend to pass
through the second
principal focus F’ ;
Fig. 572 consequently they
are divergent with
reference to the secondary axes, and therefore, when produced, will cut those
axes in A’ and B’ respectively. These points are the virtual foci of A and
B respectively. The lens, therefore, produces at A’B’ an erect and magnified
virtual image of the object AB.
—599] The Simple Microscope — 587
The position and magnitude of this image depend on the distance of the
object from the focus. Thus, if AB is moved to ad, nearer the lens, the
secondary axes will contain a greater angle, and the image will be formed at
a’b’, and will be much smaller, and nearer the eye. On the other hand, if
the object is moved farther from the lens, the angle between the secondary
axes is diminished, and their intersection with the prolongation of the re-
fracted rays taking place beyond A’B’, the image is formed farther from the
lens, and is larger.
In a simple microscope both chromatic aberration and spherical aberra-
tion increase with the degree of magnification. We have already seen that
the former can be corrected
by using achromatic lenses
(596), and the latter by using
stops, which allow the pas-
sage of such rays only as are
nearly parallel to the axis,
the spherical aberration of
these rays being nearly inappreciable. Spherical aberration may be still
further corrected by using two plano-convex lenses, instead of one very con-
vergent lens. When this is done, the plane face of each lens is turned
towards the object (fig. 573). Although each lens is less convex than the
simple lens which together they replace,
yet their joint magnifying power is as
great, and with a less amount of sphert-
cal aberration, since the first lens diverts
towards the axis the rays which fall
on the secondlens. This combination of
lenses is known as Wollaston’s doublet.
There are many forms of the simple
microscope. One of the best is that re-
presented in fig. 574. On a horizontal
support E, which can be raised and
lowered by a rack K and pinion D, there
is a black eyepiece m, in the centre of
which is fitted a small convex lens. Below
this is the stage 6, which is fixed, and on :
which the object is placed between glass —
plates. In orderto illuminate the object
powerfully, diffused light is reflected from
a concave glass mirror, M, so that the reflected rays fall upon the object. In
using this microscope the eye is placed very near the lens, which is lowered or
raised until the position is found at which the object appears in its greatest
distinctness.
599. Conditions of distinctness of the images.—In order that objects
looked at through a microscope should be seen with distinctness, they must
have a strong light thrown upon them, but this is by no means enough. It
is necessary that the image be formed at a determinate distance from the
eye. In fact, there is for each person a distance of most distinct viston—a
distance, that is to say, at which an object must be placed from an observer's
», “i
NE ny Ny
le. ait
Fig. 573
588 On Light [599-
eye in order to be seen with greatest distinctness. This distance is different
for different observers, but ordinarily is between 1o and 12 inches. It is,
therefore, at this distance from the eye that the image ought to be formed.
Moreover, this is why each observer has to focus the instrument ; that is, to
adapt the microscope to his own distance of most distinct vision. This is
effected by slightly varying the distance from the lens to the object, for we
have seen above that a slight displacement of the object causes a great dis-
placement of the image. With a common magnifying glass, such as is held
in the hand, the adjustment is effected by merely moving it nearer to or
farther from the object. In the microscope the adjustment is effected by
means of a rack and pinion, which in the case of the instrument shown in
fig. 573 moves the eyepiece, but moves the object in the case of the
instrument depicted in fig. 574. What has been said about focussing the
microscope applies equally to telescopes. In the latter instrument the eye-
piece is generally adjusted with respect to the image formed in the focus of
the object-glass.
In respect of the distinctness of the image the general rules for convex
lenses apply.
In order to lessen dispersion, lenses have been constructed of diamond,
of ruby, and of other precious stones, which for a small amount of dispersion
have a great degree of refrangibility. A drop of water or of Canada balsam
in a small hole in a thin piece of wood or of metal, acts as a microscope.
600. Apparent magnitude of an object.—The apparent magnitude or
apparent diameter of a body is the angle it subtends at the eye of the
Fig. 576
observer. Thus, if AB is the object, and O the observer's eye (figs. 575, 576),
the apparent magnitude of the object is the angle AOB contained by two
visual rays drawn from the centre of the pupil to the extremities of the object.
In the case of objects seen through optical instruments, the angles
which they subtend are so small that the arcs which measure the angles do
not differ sensibly from their tangents. The ratio of two such angles is
—-601] Measure of Magnification 589
therefore the same as that of their tangents. Hence we deduce the two
following principles :—
1. When the same object ts seen at unequal distances, the apparent diameter
varies inversely as the distance from the observer's eye.
ll. [2 the case of two objects seen at the same distance, the ratio of the
apparent diameters ts the same as that of their absolute magnitudes.
These principles may be proved as follows :—i. In fig. 575, let AB be the
object in its first position, and ad the same object in its second position.
For the sake of distinctness these are represented in such positions that the
line OC passes at right angles through their middle points C and c respec-
tively. It is, however, sufficient that @ and AB should be the bases of
isosceles triangles having a common vertex at O. Now, by what has been
said above, AB is virtually an arc of a circle described with centre O and
radius OC ; likewise aé is virtually an arc of a circle whose centre is O and
radius Oc, Therefore,
A Bhi gsm sls ad
LOB GO =e TO OCGEOGd
Therefore, AOB varies inversely as OC.
ii. Let AB and A’B’ be two objects placed at the same perpendicular
distance, OC, from the eye, O, of the observer (fig. 576). Then they are
virtually arcs of a circle whose centre is O and radius OC. Therefore,
AB , AB’
-f OB? = :
ape OGemOC
=AB:A/B’,
a proportion which expresses the second principle.
601. Measure of magnification.—In the simple microscope the measure
of the magnification produced is the ratio of the apparent diameter of the
image to that of the
object, both being at
the distance of most
distinct vision. The
same rule holds good
for other microscopes.
It is, however, impor-
tant to obtain an ex-
pression for the mag-
nification depending
on data that are of
easier determination.
In fig. 577 let AB Fig, tre
be the object, and A’B’
its image formed at the distance of most distinct vision. Let @’d’ be the
projection of AB on A’B’. Then, since the eye is very near the glass, the
: 1 A’OB’ Vl eie A’B’
magnification equals OP” a ’
A’OB’ and AOB are similar, A’B’: AB=DO:CO. Now DO is the dis-
tance of most distinct vision, and CO is very nearly equal to FO, the focal
length of the lens. Therefore, the magnification equals the ratio of the
But since the triangles
590 On Light [601—
distance of most distinct vision to the focal length of the lens. Hence we
conclude that the magnification is greater, Ist, as the focal length of the lens
is smaller—in other words, as the lens is more convergent ; 2ndly, as the
observer’s distance of most distinct vision is greater.
A simpler and more general definition of the measure of magnification
may be stated thus: Let a be the angular magnitude of the object as seen
by the naked eye, 8 the angular magnitude of the image, whether real or
virtual, actually present to the eye, then the magnification is 8+a. This
rule applies to telescopes. |
By changing the lens the magnification may be increased, but only within
certain limits if we wish to obtain a distinct image. By means of a simple
microscope distinct magnification may be obtained up to 120 diameters.
The magnification we have here considered is “ear magnification.
Superficial magnification equals the square of the /zzear magnification ; for
instance, the former will be 1,600 when the latter is 4o.
602. Principle of the compound microscope.—The compound micro-
scope in its simplest form consists of two condensing lenses: one, with a
short focus, is called the odject-g/ass, or objective, because it is turned towards
the object ; the other is less condensing, and is called the fower, or eyepiece,
because it is close to the observer’s eye.
Fig. 578 represents the path of the luminous rays and the formation of
the image in the simplest form of a compound microscope. An object AB
being placed very near the principal focus F of the object-glass M, but a little
farther from the glass, a real image, ad, inverted and somewhat magnified,
is formed on the other side of the object-glass (568). Now the distance
of the two lenses M and N is regulated so that the position of the image aé is
between the eyepiece N and its focus F’’.. From this it follows that for the
eye at E, looking at the image through the eyepiece, this glass produces the
same effect as
a simple micro-
scope, and in-
stead of this
image ad, an-
other image,
20. Wiga eeSeen.
which is virtual,
and still more
magnified. This
second image,
Fig. 578 although erect
as regards the
first, is inverted in reference to the object. It may thus be said that the
compound microscope is in effect a simple microscope applied not to the
object but to its image already magnified by the first lens.
603. Compound microscope.—The principle of the compound micro-
scope has been already (602) explained; the principal accessories to the
instrument remain to be described. .
Fig. 579 represents a perspective view, and fig. 580 a section, of a com-
pound microscope. The body of the microscope consists of a series of brass
-603] Compound Mucroscope 591
tubes, DD’, H, and I; in H is fitted the eyepiece O, and in the lower part
of DD’, the object-glass 0. The tube I moves with gentle friction in the tube
DD’, which in turn can also be moved in a larger tube fixed in the ring E.
This latter is fixed to a piece BB’, which, by means of a very fine screw
worked by the milled head T, can be moved up and down an inner rod, ¢,
not represented in the figure. The whole body of the microscope is raised
and lowered with the piece BB’, so that it can be placed near or far
from the object to be examined. Moreover, the rod c¢, and all the other
pieces of the apparatus, rest on a horizontal axis A, with which they turn
under so much friction as to remain fixed in any position in which they may
be placed.
The object to be observed is placed between two glass plates, V, on a
stage, R. This is perforated in the centre, so that light can be reflected upon
the object by a concave reflecting glass mirror, M. The mirror is mounted
on a jointed support so that it can be placed in any position whatever, so
592 On Light [603—
as to reflect to the object either the diffused light of the sky, or that from a
candle or lamp. Between the reflector and the stage is a dzaphragm or stop,
K, perforated by four holes of different sizes, any one of which can be placed
over the perforation in the stage, and thus the light falling on the object may
be regulated ; the light can, moreover, be regulated by raising, by a lever z,
the diaphragm K, which is movable in a slide. Above the diaphragm is a
piece, 7, to which can be attached either a very small stop, so that only
very little light can reach the object, or a condensing lens, which illuminates .
it strongly, or an oblique prism, represented at X. The rays from the
reflector undergo two total reflections in this prism, and emerge by a lenti-
cular face that concentrates them on the object, but in an oblique direction,
which in some microscopic observations is an advantage. Objects are
generally so transparent that they can be lighted from below; but where,
owing to their opacity, this is not possible, they are lighted from above by
means of a condensing lens mounted on a jointed support, and so placed
that they receive the diffused light of the atmosphere.
Fig. 580 shows the arrangement of the lenses and the path of the rays
in the microscope. At o is the object-glass, consisting of three small con-
densing lenses, represented on a larger scale at L, on the right of the figure.
The effect of these lenses being added to each other is that they act like a
single very powerful condensing lens. The object being placed at z, a very
little beyond the principal focus of the system, the emerging rays fall upon a
fourth condensing lens, 7, the use of which will be seen presently (605).
Having become more convergent, owing to their passage through the lens
m, the rays form at @a’a real and magnified image of the object z. This
image is between a fifth condensing. lens, O, and the principal focus of this
lens. Hence, on looking through this, which acts as a magnifier (568), we
see at AA’ a virtual and highly magnified image of aa’, and therefore of the
object. The two glasses z and O constitute the eyepiece, in the same
manner as the three glasses o constitute the object-glass.
The first image, aa’, must be formed not merely between the glass O
and its principal focus, but at such a distance from this glass that the second
image, AA’, is formed at the observer’s distance of distinct vision. This
result is obtained in moving, by the hand, the body DH of the microscope
in the larger tube fixed to the ring E, until a tolerably distinct image is
obtained ; then turning the milled head T in one direction or the other,
the piece BB’, and with it the whole microscope, are moved until the image
AA’ attains its greatest distinctness, which is the case when the image aa’
is formed at the distance of distinct vision: a distance which can always be
ultimately obtained, for as the object-glass approaches or recedes from the
object, the image aa’ recedes from or approaches the eyepiece, and at the
same time the image AA’.
This operation is called focussing. In the microscope, where the distance
from the object-glass to the eyepiece is constant, it is effected by altering
their distance from the object. In telescopes, where the objects are inacces-
sible, the focussing is effected by varying the distance of the eyepiece and
the object-glass.
The microscope possesses numerous eyepieces and object-glasses, by
means of which a great variety of magnifying power is obtained. A lower
—604] Achromatism of the Microscope. Campani’s Eyeptece 593
magnifying power is also obtained by removing one or two of the lenses of
the object-glass.
The above contains the essential features of the microscope ; it is made
in a great variety of forms, which differ mainly in the construction of the
stand, the arrangement of the lenses, and in the illumination. For descrip-
tions of these the student is referred to special works on the microscope.
604. Achromatism of the microscope. Campani’s eyepiece.—When a
‘compound microscope consists of two single lenses, as in fig. 578, not only
is the spherical aberration uncorrected, but also the chromatic aberration,
the latter defect causing the images to be surrounded by fringes of the
prismatic colours, these fringes being larger as the magnification is greater.
With a view to correcting these aberrations the object-glass (see fig. 580)
is composed of three achromatic lenses, and the eyepiece of two lenses, z
and O; for the first of these, 7, would be enough to produce colour unless
the magnifying power were low.
The effect of this eyepiece in correcting the colour may be explained
as follows :—It will be borne in mind that with respect to red rays the focal
length of a lens is greater than the focal length of the same lens with refer-
ence to the violet rays.
In fact, if in the equation (4) (571) we write R’= oo, we obtain f= Bou
mu — 1
which gives the focal length of a plano-convex lens whose refractive index
is 2. Now, in flint glass, and for the red ray, 7—1 equals 0°63, and for the
violet ray 7—1 equals 0°67.
Let aé be the object, O the object-glass, which is corrected for colour.
A pencil (fig. 581) of rays falling from @ on O would converge to the focus A
without any separation of colours ; but falling on the /feld-glass C, the red
Fig. 581
rays would converge to 7, the violet rays to v, and intermediate colours to
intermediate points. In like manner the rays from 4, after passing through
the field-glass, would converge to 7’, or v’, and intermediate points. So that
on the whole there would be formed a succession of coloured images of ad ;
viz. a red image at 77’, a violet image at vv’, and between them images ot
intermediate colours. Let d be the point of the object which is situated on
the axis. The rays from d will converge to R, V, and intermediate points.
Now suppose the eye-glass O’ to be placed in such a manner that R is the
principal focus of O’ for the red rays, then V will be its principal focus for
the violet rays. Consequently, the red rays, after emerging from O, will be
parallel to the axis, and so will the violet rays coming from V, and so of any
other colour. Accordingly, the colours of @, which are separated by C, are
again combined by O’. The same is very nearly true of ~ and v, and of 7’
and v’. Hence a combination of lenses C and O’ corrects the chromatic
QQ
594 On Light | [604—
aberration that would be produced by the use of a single eye-glass. More-
over by drawing the rays towards the axis, it diminishes the spherical
aberration, and, as we shall see in the next article, enlarges the field of view.
In all eyepieces consisting of two lenses the lens to which the eye is
applied is called the eye-dens ; the one towards the object-glass is called the
jield-lens. The eyepiece above described was invented by Huyghens, who
was not, however, aware of its property of achromatism. He designed it
for use with the telescope. It was applied to the microscope by Campani.
_ The relation between the focal length of the lenses is as follows: The focal
~ length of the field-glass is three times that of the eye-lens, and the distance
between their centres is half the sum of the focal length. It easily follows
from this that the image of the point @ would, but for the interposition of
the field-lens, be formed at D, which is so situated that CD is three times.
DO’; then the mean of the coloured images would be formed midway
between C and O’.
605. Field of view.—By the tield of view of an optical instrument are
meant all those points which are visible through the eyepiece. The advan-
tage obtained by the use of an eyepiece in enlarging the field of view will be:
Fig. 582
readily understood by an inspection of the accompanying figure. As before
(fig. 582), O is the object-glass, C the field-lens, O’ the eye-lens, and E the
eye placed on the axis of the instrument. Let @ be a point of the object ; if
we suppose the field-lens removed, the pencil of rays from @ would be
brought to a focus at A, and none of them would fall on the eye-lens O’,
or pass into the eye E. Consequently, a is beyond the field of view. But.
when the field-glass C is interposed, the pencil of rays is brought to a focus.
at A’, and emerges from O’ into the eye. Consequently, a is now within
the field of view. In this manner the substitution of an eyepiece for a single.
eye-lens enlarges the field of view.
606. Magnifying power. Micrometer.—The magnifying power of any
optical instrument is the ratio of the magnitude of the image to the mag-
nitude of the object. The magnifying power in a compound microscope is
the product of the respective magnifying powers of the object-glass and of
the eyepiece ; that is, if the first of these magnifies 20 times, and the other:
10, the total magnifying power is 200. The magnifying power depends on
the greater or less convexity of the object-glass and of the eyepiece, as well
as on the distance between these two glasses, together with the distance of
the object from the object-glass. A magnifying power of 1,500 and even
upwards has been obtained ; but the image then loses in sharpness what it
gains in extent. To obtain precise and well-illuminated images, we must
limit the magnifying power to 500 to 600 diameters, which gives a superficial
enlargement 250,000 to 360,000 times that of the object.
-607] Magnifying Power. . Micrometer 595
The magnifying power is determined experimentally by means of the
glass micrometer: this is a small glass plate, on which, by means of a
diamond, a series of lines is drawn at a distance from each other of 7 or 45
of a millimetre. The micrometer is placed in front of the object-glass, and
then, instead of viewing directly the rays emerging from the eyepiece O,
they are received on a piece of glass A (fig. 583), inclined at an angle of 45°,
and the eye is placed above so as to see the image of the micrometer lines,
which is formed by reflection on a screen E, on which is a scale divided into
millimetres. By counting the number of divisions
of the scale corresponding to a certain number of
lines of the image, the magnifying power may be ~
deduced. Thus, if the image occupies a space of
45 millimetres on the scale and contains 15 lines
of the micrometer, the distances between which
shall be assumed at ;4, millimetre, the absolute
magnitude of the object will be 49, millimetre ;
and as the image occupies a space of 45 milli-
metres, the magnification will be the quotient of
45 by 743%, or 300. The eye in this experiment
ought to be at such a distance from the screen E
that the screen is distinctly visible: this distance
varies with different observers, but is usually 10 to 12 inches. The magni-
fying power of the microscope can also be determined by means of the
camera lucida ; it is increased at the expense of brightness, definition, and
field. Hence it is usual to have several eyepieces with each microscope so
as to obtain greater definition of higher magnification.
Nober?’s lines are frequently used as test objects ; these are lines ruled
on glass in series ; in the first group the lines are at a distance of z5455 to an
inch from the middle of one line to the middle of the next ; in the finest the
lines are at a distance of zsp55 Of an inch. Other test objects are the scales
of certain butterflies, and various kinds of diatoms.
When once the magnifying power is known, the absolute magnitude of
objects placed under the microscope is easily deduced. For, as the magni-
fying power is the quotient of the size of the image by the size of the object,
it follows that the size of the image divided by the magnifying power gives
the size of the object : in this manner the diameters of all microscopic objects
are determined.
Fig. 583
TELESCOPES
607. Astronomical telescope.—The astronomical telescope is used for
observing the heavenly bodies : like the microscope, it consists of a con-
densing eyepiece and object-glass. The object-glass, M (fig. 584), forms
between the eyepiece, N, and its principal focus an inverted image of the
heavenly body ; and this eyepiece, which acts as a magnifying glass, then
gives a virtual and highly magnified image, a’é’, of the image ad. The
astronomical telescope appears, therefore, analogous to the microscope ;
but the two instruments differ in this respect, that in the microscope, the
object being very near the object-glass, the image is formed much beyond
QQ2
596 On Light [607—
the principal focus, and is greatly magnified, so that both the object-glass
and the eyepiece magnify ; while in the astronomical telescope, the heavenly
body being
Bat a_ great
distance, the
incident rays
are parallel,
and the im-
age formed in
the principal
focus of the
Fig. 584 object - glass
is much smaller than the object. There is, therefore, no magnification
except by the eyepiece, and this ought, therefore, to be of very short focal
length.
Fig. 585 shows an astronomical telescope mounted on its stand. Above
ity; there sashaa.
small teiescope
which is called
the jader. Tele-
scopes with a
large magnify-
ing power are
not convenient
for finding a
star, . asi, they
have but a small
field of view:
the position of
the star is, ac-
cordingly, _ first
sought by the
finder, which has
a much larger
field of view—
SS SS that is, takes in
maki apo ei a far greater
extent ofr athe
heavens ; it is then viewed by means of the telescope.
The magnification (601) equals ae (fig. 584); that is, it equals tte
and therefore is approximately equal to sa F being the focus of the object-
OF
glass M, and being supposed very nearly to coincide with the focus of the
eyepiece N ; it may, therefore, be concluded that the magnifying power is
greater in proportion as the object-glass is less convex, and the eyepiece
more so.
When the telescope is used to make an accurate observation of the
stars—for example, the zenith distance, or their passage over the meridian—
608] 7 Terrestrial Telescope 597
a cross wire is added. This consists of two very fine metal wires or spider
threads stretched across a circular aperture in a small metal plate ‘fig. 5386).
The wires ought to be placed in the position where the inverted image is pro-
duced by the object glass, and the point where the wires cross ought to be
on the optical axis of the telescope, which thus becomes the “ve of sight or
collimation.
608. Terrestrial telescope.—The /errestrial telescope differs from the
astronomical telescope in producing images in their right positions. This is
effected by means of two condensing glasses, P and Q (fig. 587), placed
between the object-glass M and the eyepiece R. The object being sup-
posed to be at AB, at a greater distance than can be shown in the drawing,
an inverted and saben smaller image is formed at da on the other side of
the object-glass. But the second lens, P, is at such a distance that its
principal focus coincides with the image ad; from which it follows that the
luminous rays which pass through 4, for example, after traversing the lens
P,. take a direction parallel to the secondary axis 6O (567... Similarly, the
rays passing by a take a direction parallel to the axis @0. After crossing in
H, these various rays traverse a third lens Q. The pencil BH converges
towards 4’, on a secondary axis O’d’, parallel to its direction ; the pencil A@H
converging in the same manner at a’, an erect image of the object AB is pro-
duced at a’d’. This image is viewed, as in the astronomical telescope,
through a condensing eyepiece R, so placed that it acts as a magnifying glass ;
that is, its distance from the image @’0’ is less than the principal focal distance :
hence there is formed, at a4”, a virtual image of a/b’, erect and much mag-
nified. The
lenses P and
Q, which only
sérve tO! réc-
tify the posi- |
tion ("of | the
image, are
fixed ina brass
tube, at a con-
stant distance, which is equal to the sum of their principal focal distances.
The object-glass M moves in a tube, and can be moved to or from the lens
P, so that the image aé is always formed in the focus of the lens, whatever be
the distance of the object. The distance of the lens R may also be varied
so that the image ab” may be formed at the distance of distinct vision.
This instrument may also be used as an astronomical telescope by using
a different eyepiece : this must have a much greater magnifying power than
in the former case.
In the terrestrial telescope the magnifying power is the same as in the
astronomical telescope, provided always that the correcting glasses, P and
Q, have the same convexity.
In order to determine directly the magnifying power of a telescope, when
this is not great, a divided scale at a distance, or the tiles of a house may
be viewed through the telescope with one eye and directly with the other.
This with a little practice is not difficult. It is thus observed how many
unmagnified divisions correspond to a single magnified one. Thus if two
Fig. 587
508 On Light [608-
seen through the telescope appear like seven, the magnifying power is 33.
Reading ordinary printing from a distance is an excellent means of testing
and comparing telescopes.
The excellence of a telescope depends also on the
sharpness of the images. To test this, various circular
and angular figures are painted in black on a white
ground, as shown in fig. 588, in about ~ the full size.
When these are looked at through the telescope at a
distance of 80 or Ioo paces, they should appear sharply
defined, perfectly black, without distortion, and without
coloured edges. The penetration or penetrating power
of a telescope, by which stars are seen which are not visible to the naked
eye, depends mainly on the aperture of the object-glass. Even with the
strongest magnification the fixed stars appear as luminous points without
apparent diameter.
609. Galileo’s telescope.—Galileo’s ‘elescope is the simplest of all tele-
scopes, for it consists of only two lenses ; namely, an object-glass, M, and a
diverging or double con-
cave eyepiece, R (fig. 589),
and it gives at once an
evect image. Ofpera-
glasses are constructed on
this principle.
Fig; 686 If the object be repre-
sented by the right line
AB, a real but inverted and smaller image would be formed at da; but in
traversing the eyepiece R, the rays emitted from the points A and B are
refracted and diverge from the secondary axes 60’ and aO’ which corre-
spond to the points 6 and a of the image. Hence, these rays produced
backward meet their axes in a’ and 0’; the eye which receives them sees
accordingly an erect and magnified image in a’d’, which appears nearer
because it is seen under an angle, a’O’0’, greater than the angle, AOB,
under which the object is seen.
The magnifying power. is equal to the ratio of the angle @’O’d’ to the
angle AOB, and is usually from 2 to 4.
The distance of the eyepiece R from the image ad is pretty nearly equal
to the principal focal distance of this eyepiece ; it follows, therefore, that the
difference between the two lenses is the distance between their respective
focal distances ; hence Galileo’s telescope is very short and portable. It
has the advantage of showing objects in their right position ; and, further,
as it has only two lenses, it absorbs very little light : in consequence, how-
ever, of the divergence of the emergent rays, it has only a small field of view,
and in using it the eye must be placed very near the eyepiece. The eye-
piece can be moved to or from the object-glass, so that the image a’0’ is
always formed at the distance of distinct vision.
The opera-glass is usually double, so as to produce an image in each eye,
by which greater brightness is attained.
Some attribute the invention of telescopes to Roger Bacon in the
thirteenth century ; others to J. B. Porta at the end of the sixteenth ; others,
Fig. 588
—611] The Gregorian Telescope 599
again, to a Dutchman, Jacques Metius, who, in 1609, accidentally found that
by combining two glasses, one concave and the other convex, distant objects
appeared nearer and much larger. Galileo’s was the first telescope directed
towards the heavens. By its means Galileo discovered the mountains of the
moon, Jupiter’s satellites, and the spots on the sun.
610. Reflecting telescopes.—The telescopes previously described are
refracting or dioptric telescopes. It 1s, however, only in recent times that it
has been possible to construct achromatic lenses of large size ; before this a
concave metallic mirror was used instead of the object-glass. Telescopes
of this kind are called reflecting or catoptric telescopes. The principal forms
are those devised by Gregory, Newton, Herschel, and Cassegrain. )
611. The Gregorian telescope.—Fig. 590 isa representation of Gre-
gory’s telescope ; it is mounted on a stand, about which it is movable, and
can be inclined at any angle. This mode of mounting is optional ; it may
be equatorially mounted. Fig. 591
gives a longitudinal section. It
consists of a long brass tube closed
at one end by a concave metallic
mirror, M, which is perforated in
the centre by a round aperture
through which rays reach the eye.
There is a second concave metal
mirror, N, near the end of the
tube : it is somewhat larger than
the central aperture in the large
mirror, and its radius of curvature
is much smaller than that of the
large mirror. The axes of both
mirrors coincide with the axis of
the tube. As the centre of curva-
ture of the large mirror is at O,
and its focus at ad, rays such as SA
emitted from a heavenly-body are
reflected from the mirror M, and
form at aé an inverted and very
small image of the heavenly body.
The distance of the mirrors and their curvatures is so arranged that the
position of this image is between the centre, 0, and the focus, /, of the small
mirror ; hence the rays, after being reflected a second time from the mirror
N, form at a’s’ a magnified and inverted image of ad, and therefore in the
true position of the heavenly body.. This image is viewed through an eye-
piece, P, which may be either simple or compound, its object being to
magnify it again, so that it is seen at a6”.
As the objects viewed are not always at the same distance, the focus of
the large mirror, and therefore that of the small one, vary in position.
And as the distance of distinct vision is not the same with all eyes, the
image a’’b” ought to be formed at different distances. The required adjust-
ments may be obtained by bringing the small mirror nearer to or farther from
the larger one; this is effected by means of a milled head, A (fig. 590),
Fig. 590
600 On Light [611—
which turns a rod, and this by a screw moves a piece to which the mirror is
fixed.
612. The Newtonian telescope.—This instrument does not differ much
from that of Gregory ; the large mirror is not perforated, and there is a
Fig. 591
small plane mirror inclined at an angle of 45° towards an eyepiece placed
in the side of the telescope.
The difficulty of constructing metallic mirrors caused telescopes of
Gregorian and Newtonian construction to fall into disuse. Of late, how-
ever, the process of silvering glass mirrors has been carried to a high state
of perfection, and Foucault applied these mirrors to Newtonian telescopes
with great success. His first mirror was only four inches in diameter, but
he successively constructed mirrors of 8, 12, and 13 inches, and at the time
of his death had completed one of 32 inches in diameter.
Fig. 593 represents a Newtonian telescope mounted on an equatorial
stand, and fig. 592 gives a longitudinal section of it. This section shows how
the luminous rays%reflected from the parabolic mirror M meet a small rect-
angular prism, 7#z, which replaces the inclined plane mirror used in the old
form of Newtonian telescope. After undergoing a total reflection from mz,
the rays form at a’d’ a very small image of the heavenly body. This image
is viewed through an eyepiece with four lenses placed on the side of
the telescope, and magnifying from 50 to 800 times according to the size of
the silvered mirror.
In reflectors the mirror acts as object-glass, but there is, of course, no
chromatic aberration. The spherical aberration is corrected by the form
given to the reflector, which is paraboloidal, but slightly modified by trial to
suit the eyepiece fitted to the telescope.
The mirror when once polished is immersed in a silvering liquid, which
consists essentially of ammoniacal solution of silver nitrate, to which some
reducing agent is added. When a polished giass surface is immersed in
-612] The Newtonian Telescope 601
this solution, silver is deposited on the surface in the form of a brilliant
metallic layer, which adheres so firmly that it can be polished with rouge in
the usual manner. These new telescopes with glass mirrors have the
advantage over the old ones that they give purer images ; they weigh less
and are much shorter, their focal distance being only about six times the
diameter of the mirror.
These details known, the whole apparatus remains to be described. The
body of the telescope (fig. 593) consists of an octagonal wooden tube. The end
G is open ; the mirror is at the other end. At a certain distance from this
i —
lla z
NO
==
=r
"s :
on
—=
= =
end two axles are fixed, which rest on bearings supported by two wooden
uprights, A and B. These are themselves fixed to a table, PQ, which turns
on a fixed plate, RS, placed exactly parallel to the equator. On the circum-
ference of the turning-table there is a brass circle divided into 360 degrees ;
and beneath it, but also fixed to the turning-table, there is a circular toothed
wheel, in which an endless screw, V, works. By moving this in either
direction by means of the handle 7, the table PQ, and with it the telescope,
can be turned. A vernier, x, fixed to the plate RS, gives fractions of a
degree. On the axis of the motion of the telescope there is a graduated
circle, O, which serves to measure the declination of the star—that is, its
602 On Light [612-
angular distance from the equator ; while the degrees traced round the table
RS serve to measure the right ascension—that is, the angle which the
declination circle of the star makes with the declination circle passing through
the first point of Aries.
In order to fix the telescope in declination, a brass plate, E, 1s fixed
to the upright ; it is provided with a clamp, in which the limb O works, and
which can be screwed tight by means of a screw with a milled head 7»
On the side of the apparatus is the eyepiece 0, which is mounted on a
sliding copper plate, on which there is also the small prism #, represented
in section in fig. 591. To bring the image to the right place, this plate may
be moved by means of a rack and a milled head a. The handle z serves to
clamp or unclamp the screw V. The drawing is one taken from a telescope
the mirror of which is only 64 inches in diameter, and which gives a magni-
fying power of 150 to 200.
613. The Herschelian telescope.—Sir W. Herschel’s telescope, which
was for long the most celebrated instrument of modern times, was con-
structed on a method differing from those described. The mirror was so in-
clined that the image of the star was formed at aé on the side of the telescope
near the eyepiece 0; hence it is termed the /ront-view telescope. As the
rays in this telescope undergo only a single reflection, the loss of light is less
than in either of the preceding cases, and the image is therefore brighter.
The magnifying power is the quotient of the principal focal distance of the
mirror by the focal distance of the eyepiece.
Herschel’s great telescope was constructed in 1789; it was 4o feet in
length, the great mirror was 50 inches in diameter. The quantity of light
obtained by this instru-
ment was so great as
to enable its inventor to
use magnifying powers
far higher than anything
which had hitherto been
attempted.
Herschel’s telescope
has been exceeded by
one constructed by the
late Earl of Rosse. This magnificent instrument has a focal distance of 53
feet, the diameter of the speculum being six feet. It is at present used as
a Newtonian telescope, but it can also be arranged as a front-view tele-
scope.
INSTRUMENTS FOR FORMING PICTURES OF OBJECTS
614. Camera obscura.—The camera obscura (dark chamber) is, as its
name implies, a closed space impervious to light. The principle of this
apparatus is illustrated by fig. 595. The rays proceeding from an external
object AB, and entering by the aperture O on one side, form on the side
opposite an image of the object éa in its natural colours, but of reduced
dimensions, and in an inverted position. See also art. 516.
Porta, a Neapolitan physician, the inventor of this instrument, found that
—615] Camera Lucida 603
by fixing a double convex lens in the aperture, and receiving the image
on a white screen, it was much brighter and more definite.
615. Camera lucida.—-The camera lucida is a small instrument depend-
ing on internal re-
flection, and serves
for taking an out-
line of any object.
It was invented by
Wollaston in 1804.
It consists of a
small four - sided
glass prism of
which fig. 596 gives’ -
a section perpendicular to the edges. A is a right angle, and C an angle
of 135°; the other angles, B and D, are 673°. The prism rests on a
stand, on which it can be raised or lowered, and turned more or less
about an axis parallel to the prismatic edges. When the face AB is
turned towards the object, the rays from the object fall nearly perpen-
dicular on this face, pass into the prism without any appreciable refrac-
tion, and are totally refracted from BC ; for as the line ad is perpendicular to
BC, and zL to AB, the angle avL will equal the angle B ; that is, it will
contain 673°, and this being greater than the critical angle of glass (552),
the ray Lz will undergo total reflection. The rays are again totally reflected
from o, and emerge near the summit, D, in a direction almost perpendicular
to the face DA, so that the eye which receives the rays sees at L’ an image
of the object L. Ifthe outlines of the image are traced with a pencil, a very
correct design is obtained ; but unfortunately there is a great difficulty in
seeing both the image
and the point of the
pencil, for the rays
from the object give
an image which is far-
ther from the eye than
the pencil. This is
‘corrected by placing
between the eye and
prism a lens, I, which
gives to the rays from
the pencil and those
from the object the same divergence. In this case, however, it is necessary
to place the eye very near the edge of the prism, so that the aperture of the
pupil is divided into two parts, one of which sees the image and the other
the pencil.
Amici’s camera lucida, represented in fig. 597, is preferable to that of
Wollaston, inasmuch as it allows the eye to change its position to a con-
siderable extent without ceasing to see the image and the pencil at the
same time. It consists of a rectangular glass prism ABC, having one of the
faces enclosing the right angle turned towards the object to be depicted,
while the other is perpendicular to an inclined plate of glass, mw. The rays
Fig. 595
Fig. 596 Fig. 597
604 On Light [615~
LI, proceeding from the object, and entering the prism, are totally reflected
from its base at D, and emerge in the direction KH. They are then partially
reflected from the glass plate #2 at H, and form an image of the object L,
which is seen by the eye in the direction OL’. The eye at the same time
sees through the glass the point of the pencil applied to the paper, and thus
the outline of the picture may be traced with great exactness.
616. Magic lantern.—This is an apparatus by which a magnified image
of small objects may be projected on a white screen inadark room. A typical
form is the sczopticon,
fig..598) The box Cj
the side of which is
shown removed, 1s.
constructed of sheet
iron; é is the flame
of a lamp V, with
two long flat wicks,
fed by petroleum
py from the reservoir B.
i at The box is airtight,
| | ga. and the chimney F
producing a_ good
draught, the air is.
compelled to pass
through the wicks, by
which smoke and smell are avoided, and a flame of high illuminating power
is produced.
The ends of the box are closed by glass platesz7 andz. G isa hinged
door, and on its inside is a concave mirror ; 0 and 9, are two plano-convex
lenses ; # a spring clamp, in which is.
placed the transparent picture. The
sliding piece supports the lens tube, in
which are two achromatic lenses a and 0,
the fine adjustment of which is effected
by the screw S.
The rays from the flame e, reinforced
by the reflection from G, falling upon the:
lenses 0, 0,, are made parallel, or, at all
events, very slightly divergent ; these
lenses are accordingly called the con-
densing lenses. Passing through the object which is depicted on the slide
placed in #, they are concentrated to an image which is received on a
screen. The image is inverted, and hence, if objects are to be seen in their
erect position, they must be drawn inverted. But ordinary drawings are
easily adjusted by fixing an equilateral rectangular prism, P (fig. 599), in
front of the lens tube, so that the hypotenuse surface is horizontal. The
parallel rays falling on the prism are inverted in consequence of refraction
at the sides and total reflection from the hypotenuse surface, so that an
upright position is obtained instead of a reverse one. The dotted lines.
abcde and fehik give the path of two rays.
—617] Solar Microscope 605
The apparatus can be used for projecting on a screen not only horizontal
images, such as those of magnetic curves, but also simple physical experiments,
such as the expansion of a liquid in a thermometer, the divergence of the
gold leaves of an electroscope, and so forth.
Dissolving views are obtained by arranging two magic lanterns, A and B,
whichare quite alike, with different pictures, in such a manner that both pictures
are produced on exactly the same part E of a screen F G (fig. 600). The
object-glasses of both lanterns can be closed by toothed plates (fig. 601), so
that when one, A, passes slowly in front of the object-glass e, a second one, B,
exposes the other at the same time, the motion being effected by the rack
and pinion motion M. In this way one picture is gradually seen to change
into the other. In the better forms the two lanterns are arranged vertically.
Ih
— ‘j 7
Fig. 600 Fig. 601
The magnifying power of the magic lantern is obtained by dividing the
distance of the lens from the image by its distance from the object. If the
image is 100 or 1,000 times farther from the lens than the object, the image
will be 100 or 1,000 times as large. Hence a lens with a very short focus
can produce a very large image, provided the screen is sufficiently large.
617. Solar microscope.—The solar microscope is a magic lantern illumi-
nated by the sun’s rays which serves to produce highly magnified images of
very small objects. It is worked in a dark room : fig. 602 represents it fitted
in the shutter of a room, and fig. 603 gives the internal details.
The sun’s rays fall on a plane mirror, M, placed outside the room, and
are reflected towards a condensing lens, 7, and thence to a second lens, 0
(fig. 603), by which they are concentrated at its focus. The object to be
magnified is at this point ; itis placed between two glass plates, which, by
means of a spring, 7, are kept in a firm position between two metal plates,
m. The object thus strongly illuminated is very near the focus of a system
of three condensing lenses, x, which forms upona screen ata suitable distance
an inverted and greatly magnified image, ad. The distance of the lenses o
and x from the object is regulated by means of screws, C and D.
606 On Light [617-
As the direction of the sun’s light is continually varying, the position of
the mirror outside the shutter must also be changed, so that the reflection is
always in the
direction of the
AXxiIShMAOLAwtie
microscope.
The most exact
apparatus for
this purpose is
4m the heliostat
Ee WAN (546); but as
li? this instrument
is very expen-
sive, the object
is usually at-
tained by _ in-
clining the
mirror 1).. a
greater or less
extent by means
of an endless screw B, and at the same time turning the mirror io round
the lens 7 by a knob A, which moves in a fixed ste
The solar microscope labours under the objection of concentrating great
heat on the object, which soon alters it. This is partially obviated by inter-
posing a layer of a saturated solution of alum, which, being a powerfully
athermanous substance (442), cuts off a considerable portion of the heat.
Fig. 602
Fig. 603
The magnifying power of the solar microscope may be deduced experi-
mentally by substituting for the object a glass plate marked with lines at a
distance of 745 or z$,5 of a millimetre. Knowing the distance of these lines on
the image, the magnifying power may be calculated. The same method is
used with the electric light. According to the magnifying power which it is
desired to, obtain, the objective x is formed of one, two, or three lenses,
which arerall achromatic.
618. Photo-electric microscope.—This is in effect a solar microscope
which is illuminated by the electric light instead of by the sun’s rays. The
—618] Photo-electric Microscope 607
electric light, by its intensity, its steadiness, and the readiness with which
it can be produced at any time of the day, has in practice replaced the use of
sunlight. The microscope alone will be described here: the production of
the electric light will be considered under the head of Galvanism.
Fig. 604 represents the arrangement devised by Duboscq. A solar
microscope, ABD, identical with that already described, is fixed on the
outside ef a brass box. In the interior are two charcoal points which do
||
Th dl oe
fy ee ei : =
ie
Mi
‘i
KG
ce
Fig. 604
not quite touch, the space between them being exactly on the axis of the
lenses. The electricity of one pole of a powerful battery reaches the charcoal
a by means of a copper wire K ; while the electricity from the opposite pole
of the battery reaches ¢ by a second copper wire H.
During the passage of the electricity a luminous arc is formed between
the two ends of the carbons, which gives a most brilliant light, and power-
fully illuminates the microscope. This is effected by placing at D in the
inside of the tube a condensing lens, whose principal focus corresponds to
the space between the two charcoals. In this manner the luminous rays
which enter the tubes D and B are parallel to their axis, and the same
effects are produced as with the ordinary solar microscope ; a magnified image.
of the object placed between two plates of glass is produced on the screen.
608 On Light [618-
In continuing the experiment the two carbons become consumed, and to
an unequal extent, a more quickly than ¢c. Hence, their distance increasing,
the light becomes weaker, and is ultimately extinguished. In speaking
afterwards of the electric light, the working of the apparatus P, which keeps
these charcoals at a constant distance, and thus ensures a constant light,
will be explained.
The part of the apparatus MN may:be considered as a universal phofo-
genic apparatus. The microscope can be replaced by the headpieces of the
phantasmagoria, the polyorama, the megascope, by polarising apparatus, &c.,
and in this manner is admirably adapted for exhibiting optical phenomena
to a large auditory. Instead of the electric light, we may use with this
apparatus the oxyhydrogen or Drummond's light, which is obtained by heat-
ing a cylinder of lime in the flame produced by the combustion of hydrogen
or of coal gas in oxygen gas.
619. Lighthouse lenses.—Lenses of large dimensions are very difficult
of construction ; they further produce a considerable spherical aberration,
and their thickness
causes the loss of
much -. light. =In
order to avoid
these incon-
veniences, echelon
lenses have been
constructed. They
consist of a plano-
convex alens,4.-C
(figs. 605 and 606),
surrounded by a
# series of annular
and concentric
segments;, A, B,
each of which has
a plane face on
the same side as
the plane face of
the central lens,
while the face on
the other side has
such a _ curvature
that the foci of the
different segments
coincide in the
same point. These
rings form, to-
gether with the
central lens, a
single lens, a sec-
‘tion of which is represented in fig. 606. The drawing was made from a lens
of about 2 feet in diameter, the segments of which are formed of a single
—620] Photography 609
piece of glass ; but, with larger lenses, each segment is likewise formed of
several pieces.
Behind the lens there is a support fixed by three rods, on which a body
can be placed and submitted to the sun’s rays. As the centre of the support
coincides with the focus of the lens, the substances placed there are melted
and volatilised by the high temperature produced. Gold, platinum, and
quartz are melted. The experiment proves that heat is refracted in the same
way as light ; for the position of the focus for heat rays is identical with that
of the focus for the rays of light.
Formerly, parabolic mirrors were used in sending the light of ne
and lighthouses to great distances, but they have been supplanted by the use
of lenses of the above construction. In most cases oil is used in a lamp of
special construction. The light is placed in the principal focus of the lens,
so that the emergent rays form a parallel beam (fig. 528), which loses in-
tensity only by absorption in the atmosphere, and can be seen at a distance
of about 40 miles. In order that all points of the horizon may be succes-
sively illuminated, the lens is continually moved round the lamp by a clock-
work motion, the rate of which varies with different lighthouses. Hence, in
different parts the light alternately appears and disappears after equal
intervals of time. These alternations serve to distinguish lighthouses from
an accidental fire or a star. By means, too, of the number of times the light
disappears in a given time, and by the colour of the light, sailors are
enabled to distinguish the lighthouses from one another, and hence to know
their position.
Of late years the use of the electric light has to a large extent been sub-
stituted for that of oil lamps. A description of the apparatus will be given
in a subsequent chapter.
PHOTOGRAPHY
620. Photography is the art of producing permanent images of objects
by utilising the changes which certain substances undergo in the presence
of light.
Although the darkening effect of light on silver chloride was known to the
alchemists of the sixteenth century, no real advance can be said to have been
made until nearly a century later, when Scheele, the Swedish chemist, inves-
tigated the effect of sunlight on silver chloride (1770).
Thirty-two years later Thomas Wedgewood and Humphry Davy read a
paper before the Royal Institution, entitled ‘A Method of copying Paintings
on Glass, and of making Profiles by the agency of Light upon Nitrate of Silver.’
In 1810 Dr. Seebeck observed, when projecting the solar spectrum on
to paper moistened with a solution of silver chloride, that the silver was
not merely blackened, but an approximation to the natural colours was pro-
duced in their relative position in the spectrum.
In 1814 Niepce patented a process of ‘héliographie’ by coating a metal
plate with a solution of bitumen dissolved in oil of lavender, and exposing in
thecamera. After an exposure of several hours, the plate was developed by a
mixture of oil of lavender in white petroleum, which dissolved the unaffected
parts of the film away. This was the first process by which photographic
RR
610 On Light [620-
images could be preserved. This process was tedious and inefficient, and
quite useless for portraying living objects, and it was not until 1839 that a
really practical method was discovered. In that year, Daguerre in Paris
and Fox Talbot in England published their respective processes, and laid
the foundation of modern photography.
In Daguerre’s process, the Daguerreotyfe, the picture is produced on a
piece of highly burnished electro-plated copper. This is rendered sensitive
- by exposing it to the action of iodine vapour, which forms a thin layer of
silver iodide on the surface, and further sensitised by treatment with
bromine and calcium hydrate, by which a silver bromiodide is formed.
The plate is then exposed in a camera, such as is depicted in figs. 607 and
608. The brass tube A contains an achromatic condensing lens, which can
be moved by means of a
rackwork motion, by the
milled head D. At the
opposite end of the box is
a ground plate, E, which
slides in a groove, B, in
which the case containing
the plate also fits. The
camera being placed | in
position before the object,
the sliding part of the box
is adjusted until the image
is produced on the glass
with the utmost sharp-
ness ; this is the case when
the glass slide is exactl
in focus. The final adjustment is made by means of the milled head D.
The glass slide is then replaced by the case containing the sensitive
plate : the slide which protects it is raised, and the plate exposed for a given
time, which varies with the amount and nature of light reflected from the object,
the size of the aperture of the lens, and other conditions. The plate is now
Fig. 607
B | c
SISSY
ZI
< N
f
iu
is
ls
Le
&
=!
Vp ht
We
Z
LU
i
ADB
tt
LEZ
SLY
7t§
; t= SS
e namie ES il
iLL
WT
2 <
Wii Wi
TY TULIUADELUNLy
See ants!
\ |
= [———e
7
ae
Fei SA ee SR
/ 2 Bill “
iI eee Zo Nay aul
il y . fj
lis - ace @
1) la ee ‘ 7
i fo
ee
ii
ies ee
/*9|
LINES OF EQUAL MAGNETIC VARIATION, 1882.
tl i
mince i | HAA 7
bi til
requ
el | al ins
ze Ue
ERE
{| iy
Ue
ey |
Nef ieee hh)
—709] Declination Compass 691
as the reflection of a ray of light (534) and very sensitive instruments (716).
In this country the north pole moves every day from east to west from sun-
rise until one or two o’clock ; it then tends towards the east, and at about
ten o’clock regains its original position. During the night the needle is
almost stationary. Thus the westerly declination is greatest during the
warmest part of the day.
At Paris the mean amplitude of the diurnal variation from April to
September is from 13’ to 25’, and for the other months from 8’ to 10’. On
some days it amounts to 25’, and on others does not exceed 5’. The greatest
variation is not always at the same time. The amplitude of the daily varia-
tions decreases from the poles towards the equator, where it is very slight.
‘Thus in the island of Rewak it never exceeds 3’ to 4’.
708. Accidental variations and perturbations.—The declination is
accidentally disturbed in its daily variations by many causes, such as earth-
quakes, the awrora borealis, and volcanic eruptions. The effect of the aurora
is felt at great distances. Auroras, which are only visible in the most northerly
parts of Europe, act on the needle even in these latitudes, where accidental
variations of 1° or 2° have
been observed. In _ polar
regions the needle frequently
oscillates several degrees ;
its irregularity on the day
before the aurora borealis is
a presage of the occurrence
of this phenomenon.
Another remarkable phe-
nomenon is the simultaneous
occurrence of magnetic per-
turbations in very distant
countries. Thus Sabine men-
tioneda magnetic disturbance
which was felt simultaneously
at Toronto, the Cape, Prague, »
and Van Diemen’s Land. x -
Such simultaneous perturba- 2 ae
tions have received the name =
of magnetic storms (716).
709. Declination com-
pass.—The declination com-
ass isan instrument by which
the magnetic declination of : : :
any place may be determined SS ee =
when its astronomical me- Fig. 673
ridian is known. The form
represented in fig. 673 consists of a brass box, AB, in the bottom of which
is a graduated circle, M. In the centre is a pivot on which oscillates a very
light lozenge-shaped magnetic needle, a4. To the box are attached two
uprights supporting a horizontal axis, X, on which is fixed an astronomical
telescope, L, movable in a vertical plane. The box rests on a foot, P, about
v2
\LLe
692 On Magnetism [709-
which it can turn in a horizontal plane, taking with it the telescope. A fixed
circle, QR, which is called the azzmuth circle, measures the number of
degrees through which the telescope has been turned, by means of a vernier,
V, fixed to the box. The inclination of the telescope, in reference to the
horizon, may be measured by another vernier, K, which moves with the axis
of the telescope, and is read off on a fixed graduated arc, +.
The first thing in determining the declination is to adjust the compass
horizontally by means of the screws SS, and the level 7. The astronomical
meridian is then found, either by an observation of the sun at noon exactly,
or by any of the ready methods known to astronomers. The box AB is
then turned until the telescope is in the plane of the astronomical meridian.
The angle made by the magnetic needle with the diameter N, which corre-
sponds with the zero of the scale, and is exactly in the plane of the telescope,
is then read off on the graduated limb, and this is east or west, according as
the pole a of the needle stops at the east or west of the diameter N.
710. Correction of errors.—These indications of the compass are only
correct when the magnetic axis of the needle—that is, the right line passing
through the two poles—coincides with its axis of figure, or the line connect-
ing itstwoends. This
is not usually the case,
and a correction must
therefore be made;
which is done by the
method of reversion.
For this purpose the
needle is not fixed in
the cap, but merely
rests on it, so that it
can be removed and
its position reversed ;.
thus what was before
the lower is now the
upper face. The mean between the observations made in the two cases.
gives the true declination.
For, let NS be the astronomical meridian, ad the axis of figure of the
needle, and sm its magnetic axis (fig 674). ‘The true declination is not the
arc Na, bat the arc Nw, which is greater. If now the needle be turned, the
line #z2 makes the same angle with the meridian NS ; but the north end of
the needle, which was on the right of 77, is now on the left (fig. 675), so that
the declination, which was previously too small by a certain amount, is now
too large by the same amount. Hence the true declination is given by the
mean of these two observations.
_ 711. Mariner’s compass.—The magnetic action of the earth has received
its most important application in the szariner’s compass. This is a declina-
tion compass used in guiding the course of a ship. Fig. 676 represents a view
of the whole, and fig. 677 a vertical section. It consists of a cylindrical case,
BB’, which iS supported on gzmibals so as to keep the compass in a horizontal
position in spite of the rolling of the vessel. These are two concentric
rings one of which attached to the case itself, moves about the axis xd which.
Fig. 674 Fig, 675
—711] Mariner's Compass. Prismatic Compass 693
plays in the outer ring’AB, and this moves in the supports PQ, about the
axis #77, at right angles to the first.
In the bottom of the box is a pivot, on which is placed, by means of an
agate cap, a magnetic bar, ad, which is the needle of the compass. On this
is fixed a disc of mica, a little larger than the length of the needle, on which
is traced a star or vose, with thirty-two branches, making the eight points or
ae 676
rhumbs of the wind, the demi-rhumbs, and the quarters. The branch ending
in a small star, and called N, corresponds to the bar ad, which is underneath
the disc.
The compass is placed near the stern of the vessel in the dzznacle.
Knowing the direction of the compass in which the ship is to be steered, the
pilot has the rudder turned till the direction coincides with the sight-vane
passing through a line d marked on the inside of the box, and parallel with
the keel of the vessel.
The prismatic compass is greatly used for surveying, more especially
for military purposes ; it differs from the mariner’s compass mainly in its
dimensions, and in the way in which obser-
vations are made. It consists of a shallow
metal box about 2} inches in diameter (fig.
678); the needle, which is fixed below the
compass card, plays on a pivot much as in
Fig. 677
fig. 677. Ais a metal frame across which is stretched a horsehair, forming
a sight-vane. Exactly opposite this is a right-angled prism P enclosed in a
694 On Magnetism [711-—
metal case, with an eyehole and a slit as represented at the side of the
figure (fig. 678).
When an observation is to be made, the compass is held horizontally, and
so that the slit in the prism, the hair of the sight-vane, and the distant object
are seen to be in the same line; the observer, looking through the eyehole,
notes the angle which the needle makes ; a similar observation is made with
another object, and thus the angle between them, or their dearzng, is given.
The sight-vane is connected with a lever, and can be turned down, when
it presses the magnet on the pivot, thus keeping it rigid, so that the compass
can be transported 1 in any position.
As the image is seen through the convex face of the prism it 1s magnified,
and as it is seen by reflection it is reversed, so that in order to read the figures
correctly they must be reversed on the card ; the reflection being total there
is little loss of light.
712. Inclination. Magnetic equator.—It might be supposed from the
northerly direction which the magnet needle takes, that the force acting
upon it is situated in a point of the horizon. This is not the case, for if the
needle be so arranged that it can move freely in a vertical plane about a hori-
zontal axis, it will be seen that, although the centre of gravity of the needle
coincides with the centre of suspension, the north pole in our hemisphere dips
downwards. In the other hemisphere the south pole is inclined downwards.
The angle which the magnetic needle makes with the horizon, when the
vertical plane, in which it moves, coincides with the magnetic meridian, is
called the zzclination or dip of the needle. In any other plane than the
magnetic meridian the inclination zzcreases, and is 90° in a plane at right
angles to the magnetic meridian. For the magnetic inclination represents.
the direction of the total magnetic force, and may be resolved into two
forces, one acting in a horizontal and the other in a vertical plane. When
the needle is moved so that it is at right angles to the magnetic meridian,
the horizontal component can only act in the direction of the axis of suspen-
sion, and therefore cannot affect the needle, which is then solely influenced
by the vertical component, and stands vertically. The following considera-
tions will make this clearer :— .
Let NS (fig. 679) represent a magnetic needle capable of moving in a
vertical plane. Let NT represent, in direction and intensity, the entire
force of the earth’s magnetism acting
on the pole N. Then NT can be re-
solved into the forces N% and NV ;
TNA~ being the angle of inclination or
dip.
NT is termed the otal force M ; and
its components are N/, or the horizontal
force H,and NV, orthe vertical force Z.
Now it is clear that the greater the se of dip, TN4, the less becomes.*
Nf, or the horizontal force, and the greater NV, or he vertical force.
Hence, in high latitudes, the directive force of a compass, which depends on
the foetal force, 1S (ese than in low latitudes. At the magnetic poles the
horizontal force al be zzZ, and the vertical force a maximum ; here, there-
fore, the needle will be vertical. At the magnetic equator the reverse is the
Fig. 679
oo
a
UTS TET ers
"EQ8I “did OLLANOVW ‘IVNOA AO SANTI
—712] Inclination. Magnetic Equator 695
case, and the needle will be horizontal. Hence the oscillations of a compass
needle, by which, as will presently be explained, the strength of the earth’s
magnetism is measured, become fewer and fewer in a given time as the
magnetic poles are approached, although there is really an increase in the
total force of the earth.
Again, the reason why a dip needle stands vertical when placed E.
and W. is clearly that in those positions the horizontal force now acting
at right angles to the plane of motion of the needle is ineffectual to move it,
and therefore merely produces a pressure on the pivot which supports the
needle. But the vertical component of the total force remains unaffected
by the new position of the needle. Acting, therefore, entirely alone when
the dip needle is exactly E. and W., this vertical component drags the
needle into a line with itself ; that is, g0° from the horizontal plane.
The value of the dip, like that of the declination, differs in different
localities. It is greatest in the polar regions, and decreases with the latitude
to the equator, where it is approximately zero. In London at the present time
(1897) the dip-is 67° 13’... In the southern hemisphere the inclination 1s again
seen, but in a contrary direction ; that is, the south pole of a needle dips
below the horizontal line.
The magnetic poles of the earth are those places in which the dipping-
needle stands vertical ; that is, where the inclination is go°. In 1831 the
first of these, the terrestrial north pole, was found by Sir James Ross in
96° 43’ west longitude and 70° north latitude. The same observer found in
the South Sea, in 76° south latitude and 168° east longitude, that the inclin-
ation was 88° 37’. From this and other observations, it has been calculated
that the position of the magnetic south pole was at that time in about 154°
east longitude and 753° south latitude. The line of no declination passes
through these poles, and the lines of equal declination converge towards
them.
The magnetic equator, or actinic line, is the line which joins all those
places on the earth where there is no dip: that is, all those in which the
dipping-needle is quite horizontal. It is a somewhat sinuous line, not differ-
ing much from a great circle inclined to the equator at an angle of 12°, and
cutting it on two points almost exactly opposite each other—one in the
Atlantic and one in the Pacific. These points appear to be gradually moving
their position, and travelling from east to west.
Lines connecting places in which the dipping-needle makes equal angles
are called zsoclinic lines. They have a certain analogy and parallelism with
the parallels of latitude, and the term magnetzc latitude is sometimes used to
denote positions on the earth with reference to the magnetic dip. Plate IV.
is an inclination map for the year 1882, the construction of which is quite
analogous to that of the map of declination.
The inclination is subject to secular variations, like the declination, as is
readily seen from a comparison of maps of inclination for different epochs.
At Paris, in 1671, the inclination was 75° ; since then it has been continually
decreasing : in 1835 it was 67° 24’; in 1849, 67°; in 1859, 66° 16’; in 1869,
Cpeaacin 1570.06 (32 : in 1603.05 a7 Gain 1og1, G5) BF s7itt TS693..65° 6" ';
in 1895, 65°°5’; in 1896, 65°2, and in 1897, 65°'1’.
The following table gives the alterations in the inclination at London,
696 On Magnetism [712-
from which it will be seen that since 1723, in which it was at its maximum,
it has continually diminished by an average of something more than three
minutes in each year :—
Year | Inclination | Year | Inclination |
‘T3570 | jd lee. 1828 69° 47’
1600 "4 TO | 1838 OOe Fy”
1676 | 73. 26)! ARE Sie Air) 68° 31’
L723 Gl VATASE | 1859 683 2x7
ie, AZT 2° 19° 1874 07d 34
1780s DEE St 1876 eye sy
5700 44 yal geey | 1878 67. 3
1800 70. 85° 1880 C7 ea)
iozt ee Phere Rt 1881 Gi ss)
713. Inclination compass.—An z7clination compass, or dip circle, is an
instrument for measuring the magnetic inclination or dip. One form, repre-
sented in fig. 680, though not best adapted for the most accurate measure-
ments, is well suited for illustrating the principle. It consists of a graduated
iy horizontal brass circle m, sup-
(20; Pe ported on three legs, provided
TK with levelling screws. Above
iP oe this circle there is a plate A,
movable about a vertical axis,
yu
[J
dl a_@ gy ah and supporting, by means of two
aa | CTT We iii in, — aa columns, a second graduated
ies IT ee circle M, which measures the
He, L7 i j . :
| é | inclination. The needle rests
| j ‘i on a frame 7, and the diameter
i | | passing through the two zeros
i | of the circle N can be ascer-
ss = S tained to be perfectly horizontal
— 1 by means of the spirit-level 1.
Sal, Li a Ww; To observe the inclination,
Sz nt AS ‘
the magnetic meridian must
first be determined, which is
effected by turning the plate A
—— | = on the circle wz, until the needle
z 5 ae Te = is vertical, which is the case
aU : when it is in a plane at right
= angles to the magnetic meri-
Fig. 680 dian (712). The plate Ais then
turned go° on the circle mm, by
which the vertical circle M is brought into the magnetic meridian. The
angle dca, which the magnetic needle makes with the horizontal diameter, is
the angle of inclination.
There are here several sources of error, which must be allowed for. The
most important are these :—i. The magnetic axis of the needle may not
his
—715] Astatic Needle and Astatic System 697
coincide with its axis of figure; hence an error which is corrected by a
method of reversion analogous to that already described (710). ii. The
centre of gravity of the needle may not coincide with the axis of suspension,
and then the angle dca is too great or too small, according as the centre of
gravity is below or above the centre of suspension ; for in the first case the
action of gravity is in the same direction as that of magnetism, and in the
second it is in the opposite direction. To correct this error, the poles of the
needle must be reversed by remagnetising it in such a way that what was a
north 1s now made a south pole. The inclination is now re-determined,
and the mean taken of the results obtained in the two groups of opera-
tions. iil. The plane of the ring may not coincide with the true magnetic
meridian. It should be in that plane when the needle has its minimum
deviation ; an observation of this kind should therefore be taken along with
that previously described, by which the needle is moved 90° from its maxi-
mum deviation.
The dip circle may be used to determine the inclination in another
way. It is first allowed to oscillate in the magnetic meridian, and then in
a plane at right angles to it. If the number of oscillations in a given time
in the first position be z, and in the second position z,, then in the first position
the whole force of the earth’s magnetism E acts, and in the second posi-
tion only the vertical component, which is E sin x, x being the angle of dip.
Now, since the forces acting on the needle are, from the laws of the pendulum
(55), as the squares of the number of oscillations in a given time, we have
a = Za from which sin += ae
Basin 247,” sine
714. Astatic needle and astatic system.—An astatic needle is one which
is uninfluenced by the earth’s magnetism. A needle movable about an
axis in the plane of the magnetic meridian and parallel to the inclination
would be one of this kind; for the terrestrial magnetic couple, acting then
in the direction of the axis, cannot impart to the needle any determinate
direction.
An astatic system is a combination of two needles of the same moment
joined parallel to each other with the poles in contrary directions,
as shown in fig. 681. If the two needles have
exactly the same magnetic moment, the opposite
actions of the earth’s magnetism on the poles
a and 6 and on the poles a and J& counter-
balance each other ; the system is then completely
astatic.
A single magnetic needle may also be rendered
astatic by placing a large magnet near-it. By
repeated trials a certain position and distance can
be found at which the action of the magnet on the
needle just neutralises that of the earth’s mag-
netism, and the needle is free to obey any third
force ; in other words, the field (721) due to the magnet just neutralises the
earth’s field.
715. Force of the earth’s magnetism.—If a magnetic needle be moved
from its position of equilibrium, it will revert to it after a series of oscilla-
U
Fig. 681
698 . On Magnetism [715-
tions, which follow laws analogous to those of the pendulum (81). If the
magnet be removed to another place, and caused to oscillate during the
same length of time as the first, a different number of oscillations will be
observed. And the earth’s magnetic force in the two places willbe respect-
ively proportional to the squares of the number of oscillations.
If at M the number of oscillations in a minute had been 25 =~, and at
another place M’, 24 =2’, we should have—
Force of the earth’s magnetism at M__ 7” _ 625
Force of the earth’s magnetism at M’ 27? 576
= 1'085.
That is, if the force of the magnetism at the second place is taken as unity,
that of the first is 17085. If the magnetic condition of the needle had not
changed in the interval between the two observations, this method would
give the relation of the forces at the two places.
In these determinations of the force, it would be necessary to have the
oscillations of the dip-needle, which are produced by the total force of
the earth’s magnetism. These, however, are difficult to obtain with
accuracy, and therefore those of the declination needle are usually taken.
The force which makes the declination needle oscillate is only a portion
of the total magnetic force, and is smaller in proportion as the inclination
is greater. If a line ac=M (fig. 682) represent the total force, the angle z
the inclination, then the horizontal component a= H is M cosz. Hence, to
express the total force in the two places by the oscillations of the declina-
tion needle, we must substitute the values M cos z and M’ cos z’ for M and
M’ in the preceding equation, and we have—
Vi) COs Cae. Weazie GOS 2
M’cosz” 7’ M’ 2x” cosz
That is to say, having observed in two different places the
number of oscillations, 2 and 7’, that the same needle makes.
in the same time, the ratio of the magnetic forces in the two
places will be found by multiplying the ratio of the square of
the number of oscillations by the inverse ratio of the cosines of
the angle of dip.
Plate V. is a chart representing the horizontal component
of the earth’s force. Knowing the angle of dip z, the total force M, or
the vertical force Z, in any place, may be obtained from the values in the
chart by the formula M =H secz; and Z=H tanz.
The total force is least near the magnetic equator, and, increasing with
the latitude, is greatest near, but not quite at, the magnetic poles ; the places
of maximum intensity are conveniently named the magnetic foct. The chart
shows that the horizontal force diminishes as we go towards the poles: this
is not inconsistent with the above statement if we take the dip into account
(712).
The lines connecting places of equal force are called zsodynamic lines.
They are not parallel to the magnetic equator, but seem to have about the
same direction as the isothermal lines. According to Kuppfer, the force
appears to diminish as the height of the place is greater ;'a needle which
made one oscillation in 24’ vibrated more slowly by o'o1” at a height of
| pee ea
ZQOl
¢
MOUVOA IVINOZIMOH TVNOF JO SUNIT
—716] Magnetic Observatories 699
1,000 feet ; but, according to Forbes, the force is only z7455 less at a height
of 3,000 feet. There is, however, some doubt as to the accuracy of these
observations, owing to uncertainty as to the correction for temperature.
The intensity varies in the same place with the time of day: it attains its
maximum between 4 and 5 in the afternoon, and is at its minimum between
10 and 11 in the morning.
It is probable, though it has not yet been ascertained with certainty, that
the force undergoes secular variations. From measurements made at Kew
it appears that on the whole the total force experiences a very slight annual
increase (706).
716. Magnetic observatories.—During the last few years great attention
has been devoted to the observation of the magnetic elements, and observa-
tories for this purpose have been fitted up in different parts of the globe.
These observations have led to the discovery that the magnetism of the earth
is in a state of constant fluctuation, like the waves of the sea or the pressure
of the atmosphere. In studying the variations of the declination, &c., the
mean of a great number of observations must be taken, so as to eliminate
irregular disturbances and bring out the general laws.
The principle on which magnetic observations are automatically recorded
is as follows :—Suppose that in a dark room a bar magnet is suspended
horizontally, and at its centre is a small mirror ; suppose further that a lamp
sends a ray of light to this mirror, the inclination of which is such that the ray
is reflected, and is received on a horizontal drum placed underneath the lamp.
The axis of the drum is at right angles to the axis of the magnet ; it is covered
with sensitive photographic paper, and is rotated uniformly by clockwork.
If now the magnet is quite stationary, as the drum rotates, the reflected
spot of light will trace a straight line on the paper with which the revolving
drum is covered. But if, as is always the case, the position of the magnet
varies during the twenty-four hours, the effect will be to trace a sinuous line
on the paper. These lines can afterwards be fixed by ordinary photographic
methods. If we know the distance of the mirror from the drum, and the
length of the paper band which comes under the influence of the spot of light
in a given time—twenty-four hours, for instance—the angular deflection at
any given moment may be deduced by a simple calculation (534).
The observations made in the English magnetic observatories were
reduced by Sabine, and revealed some curious facts in reference to mag-
netic storms (708). He found that there is a certain periodicity in their,
appearance, and that they attain their greatest frequency about every ten
years. Independently of this, Schwabe, who for many years studied the sub-
ject, found that the spots on the sun, seen on looking at it through a
coloured glass, vary in their number, size, and frequency, but attain their
maximum about every ten or eleven years. Now Sabine established the
interesting fact that the period of their greatest frequency coincides with the
period of greatest magnetic disturbance. Other remarkable connections
between the sun and terrestrial magnetism have been observed; one,
especially, of recent occurrence has attracted considerable attention. It was
the flight of a large luminous mass across a vast sun-spot, while a simul-
taneous perturbation of the magnetic needle was observed in the observatory
at Kew ; subsequent examination of magnetic observations in various parts
700 On Magnetism [716-
of the world showed that within a few hours one of the most violent magnetic
storms ever known had prevailed.
It seems, however, that these accidental variations in the declination can-
not be due to changes in any a@vect action of a possible magnetic condition
of either the sun or the moon. For it can be shown that if the magnet-
isation of the latter were as powerful as that of the earth, the deflection
which it could produce would not amount to the 34th of a second, a quantity
which cannot be measured. In order to produce a variation of 10’, such
as is frequently met with, the magnetisation of the sun or of the moon
must be 12,000 times that of the earth ; in other words, a more powerful de-
gree of magnetisation than that of powerfully magnetised steel bars.
Magnetic storms are nearly always accompanied by the exhibition of the
aurora borealis in high latitudes ; that this is not universal may be due
to the fact that many auroras escape notice. The converse of this is true,
that no great display of the aurora takes place without a violent magnetic
storm.
The centre or focus towards which the rays of the aurora converge lies
approximately in the prolongation of the direction of the dipping-needle ; and
it may be mentioned in this connection that the appearances of the aurora
borealis have the same periods as the sun spots.
—718] The Torston Balance FO!
CHARTER ed bi
LAWS OF MAGNETIC ATTRACTION AND REPULSION
717. Law of decrease with distance.—Coulomb discovered the remark-
able law in reference to magnetism, ¢hat magnetic attractions and repulstons
are inversely as the squares of the distances of the acting poles. He proved
this by means of two methods :—(i.) that of the torsion balance, and} (ii.)
that of oscillations.
718. 1. The torsion balance.—This apparatus depends on the principle
that, when a wire is twisted through a certain angle, the angle of torsion is
proportional to the force of torsion
(90). It consists (fig. 683) of a
glass case closed by a glass top,
with an aperture 7z near the edge,
to allow the introduction of a mag-
net, A. In another aperture in the
centre of the top a glass tube fits,
provided at its upper extremity
with a micrometer. This consists
of two circular pieces : @, which is
fixed, is divided on the edge into
_ 360°, while on one e, which is mov-
able, there is a mark, c, to indicate
its rotation. D and E represent
the two pieces of the micrometer
on a larger scale. On E there
are two uprights connected by a
horizontal axis, on which is a very
fine silver wire supporting a mag-
netic needle, ad. On the side of
the case there is a graduated scale, which indicates the angle of the needle
ab, and hence the torsion of the wire.
When the mark c of the disc E is at zero of the scale D, the case is so
arranged that the wire supporting the needle and the zero of the scale in the
case are in the magnetic meridian. The needle is then removed from its
stirrup, and replaced by an exactly similar one of copper, or any unmagnetic
substance ; the tube, and with it the pieces D and E, are then turned so that
the needle stops at zero of the graduation. The magnetic needle aé, being
now replaced, is exactly in the magnetic meridian, and the wire is without
torsion.
Before introducing the magnet A, it is necessary to investigate the action
702 On Magnetism - 4718-
of the earth’s magnetism on the needle ad, when the latter is removed out of
the magnetic meridian. This will vary with the moment of the needle, with
the dimensions and nature of the particular wire used for suspension, and
with the intensity of the earth’s magnetism in the place of observation. Ac-
cordingly the piece E is turned until ad makes a certain angle with the mag-
netic meridian. Coulomb found in one of his experiments that E had to be
turned 36° in order to move the needle through 1°; that is, the earth’s
magnetism was equal to a torsion of the wire corresponding to 35°. Asthe
force of torsion is proportional to the angle of torsion when the needle is
deflected from the meridian by 2, 3 . . . degrees, the directive action of the
earth’s magnetism is equal to 2,3... times 35°.
The action of the earth’s magnetism having been determined, the magnet
A is placed in the case so that similar poles are opposite each other. In one
experiment Coulomb found that the pole a was repelled through 24°. Now
the force which tended to bring the needle into the magnetic meridian
was represented by 24° + 24 x 35 = 864, of which the part 24° was due to the
torsion of the wire, and 24 x 35° was the equivalent in torsion of the directive
force of the earth’s magnetism. As the needle was in equilibrium, it is clear
that the repulsive force which counterbalances these forces must be equal
to 864°. The disc was then turned until a6 madean angle of 12°. To effect
this, eight complete turns of the disc were necessary. The total force
which now tended to bring the needle into the magnetic meridian was com-
posed of :—1st, the 12° of torsion by which the needle was distant from its
starting point ; 2nd, of 8 x 360° = 2880, the torsion of the wire ; and 3rd, the
force of the earth’s magnetism, represented by a torsion of 12 x 35°. Hence
the forces of torsion which balance the repulsive forces exerted at a distance
of 24° and of 12° are—
24° : 864
iy 3312
Now, 3312 is very nearly four times 864 ; hence for half the distance the
repulsive force is four times as great.
719. il. Method of oscillations.—A magnetic needle oscillating under
the influence of the earth’s magnetism may be considered as a pendulum,
and the laws of pendulum motion apply to it (55). The method of oscilla-
tions consists in causing a magnetic needle to
ay oscillate first under the influence of the earth’s
magnetism alone, and then successively under the
combined influence of the earth’s magnetism and
of a magnet placed at unequal distances,
The following determination by Coulomb will
illustrate the use of the method. A magnetic needle
was used which made 15 oscillations in a minute
pe ee I under the influence of the earth’s magnetism alone.
Nike hey Sayan R being the radius.
If there is a sphere, or uniform spheroidal shell of matter, which acts on an
external point, according to the inverse square of the distance, the total action
of this sphere is the same as if the whole matter were concentrated at the
centre. This was first proved by Newton in the case of gravitation ; but it
also applies to electricity, and hence, in calculating the potential at any point
outside a sphere possessing a uniform charge, we need only consider its
distance from the centre, and for such a case we may write the value of the
potential V = 2
a
If a charge of electricity, Q, is imparted to two insulated conducting
spheres whose radii are respectively 7 and 7’, and which are connected by
a long fine wire, the capacity of which may be neglected, the electricity
will distribute itself over the two spheres, which will possess the charges
g and g’; that is, g+g’=Q (1). The whole system will be at the same
/
potential V, such that V= Yn ao (2). Combining these two equations and
ipa
reducing, we get for the quantities g and g’ on each sphere g= cla and
r+r
ge te ie Now, since the diameter of any sphere with which we can ex-
+r
periment is infinitely small compared with that of the earth, it follows that
when a sphere is connected with the earth by a fine wire the quantity of
electricity which it retains is infinitely small,
The densities on the two spheres are d=—%_ and d= 2—, from which
Anr? 4n7r
by equation (2) it 1s readily, deduced@thated :.@°=7" : 7-;, that is,. the. elec-
tric densities on two spheres in distant connection are inversely as_ the
radii. If, for instance, a fine wire is connected with a charged insulated
sphere, the distant ‘pointed end of the wire may be regarded as a sphere
740 Frictional Electricity [764—
with an infinitely small radius, and thus the density upon it would be in-
finitely great.
765. Action of points.—We have just seen that the density on a point in
connection with a conductor charged with electricity may be considered to
be infinitely great, but the greater the density the greater will be the tendency
of electricity to overcome the resistance of the air, and escape, for the electro-
static pressure is proportional to the square of the density (759). If the hand
is brought neara point on a conductor connected with an electrical machine
in action, a slight wind is felt ; and if the disengagement of electricity takes
place in the dark a luminous brush is seen. . If an electrified conductor is to
retain its electricity, all sharp points and edges must be avoided ; on the other
hand, to facilitate the outflow of electricity in apparatus and experiments
(787), frequent use is made of this action of points. A flame acts like a very
fine point in diffusing electricity.
766. Loss of electricity.—Experience shows that electrified bodies
gradually lose their electricity, even when placed on insulating supports.
This loss is mainly due to the insulating supports. The charge is gradually
dissipated in consequence of the electricity either
2 passing through the supports or creeping over the
eI surface. t All substances conduct electricity in some
degree ; those which are termed insulators are
simply very bad conductors. An electrified con-
ductor resting on supports must therefore lose a
certain quantity of electricity, either by penetra-
tion into its mass or along the surface. This loss
of electricity is a main cause of difficulty in ex-
periments on the quantitative laws of electricity ; it
3 varies with the electric density, and increases with
YYW: the hygrometric state of the air, though it does not
seem that the loss from this cause is due toa direct
conductivity by moist air. Lord Kelvin ascribes
the greater part of the loss to the conducting layer of moisture which covers the
supports; and he finds that, in comparison with this, the direct loss by even
moist air is inconsiderable.
Hence it is necessary in electric experiments to rub the supports with
warm cloths, and to surround electrified bodies by glass vessels containing
substances which absorb moisture, such as calcium chloride, or pumice
soaked with sulphuric acid.
Brown shellac and ebonite are the best insulators ; glass is a hygroscopic
substance, and must be dried with great care. It is best covered with a thin
layer of shellac varnish, as has already been stated.
Mascart’s insulator is admirably adapted for supporting bodies charged
with electricity. It consists of ‘a glass vessel of special shape (fig. 714),.
to the glass vase of which is fused the stem. This passes through the
neck and supports the plate, P ; the neck is enclosed by an ebonite stopper,
and inside the vessel is sulphuric acid, so that the stem A is always dry.
{HWY
Fig. 714
—767] Electrical Influence or Induction TAT
CHAPTER: Hi
ACTION OF ELECTRIFIED BODIES-ON BODIES IN THE NATURAL STATE.
INDUCED ELECTRICITY. ELECTRIC MACHINES
767. Electric influence or induction.—An insulated conductor, charged
with either kind of electricity, acts on bodies in a neutral state placed near
it in a manner analogous to that of the action of a magnet on soft iron; that
is, attracts the opposite and repels the like kind of electricity. The action
thus exerted is said to take place by zzflwence or induction.
The phenomena of induction may be demonstrated by means of a brass
cylinder placed on an insulating support, and with two small electric
pendulums at the ends, consisting of pith balls suspended by linen threads
(fig. 715). If this apparatus is placed near an insulated conductor m
i i ii ii i TTT TTT MTT
AIIWE Wap eaE TAUNTS = ME RSET HATRORTE TOE GRAL 0 i
4 HTM GREGG i NAA BS ie eel ES POS
inn HTN ACMI ATTEN
charged with either kind of electricity—for instance, the conductor of an
electric machine, which is charged with positive electricity—free electricity
will be developed at each end, and both pendulums will diverge. If, while
they still diverge, a stick of sealing-wax, excited by friction with flannel, is |
approached to that end of the cylinder nearest the conductor, the ccrre-
sponding pith ball will be repelled, indicating that it is charged with the same
kind of electricity as the sealing-wax—that is, with negative electricity ; while
if the excited sealing-wax is brought near the other ball it will be attracted,
showing that it is charged with positive electricity. If, further, a glass rod
748 Frictional Electricity [767-
excited by friction with silk, and therefore charged with positive electricity,
is approached to the end nearest the conductor, the pendulum will be at-
tracted; while if it is brought near the other end, the corresponding
pendulum will be repelled. If the influence of the charged conductor is
suppressed, either by removing it or placing it in communication with the
ground, the opposite electricities will recombine, and the pendulums exhibit
no divergence.
The cause of this phenomenon is obviously a decomposition of the neutral
electricity of the cylinder by the free positive electricity of the conductor ;
the opposite or negative electricity being attracted to that end of the cylinder
nearest the conductor, while the similar electricity is repelled to the other
end. Between these two extremities there is a space destitute of free
electricity. This is seen by arranging on the cylinders a series of pairs of
pith balls suspended by threads. The divergence is greatest at each
extremity, and there is a line at which there is no divergence at all, which is
called the zeutral line. The two electricities, although equal in quantity, are
not distributed over the cylinder in a symmetrical manner ; the attraction
which accumulates the negative electricity at one end is, in consequence of
the greater nearness, greater than the repulsion which drives the positive
electricity to the other end, and hence the neutral line is nearer one end than
the other. Nor is the electricity induced at the two ends of the cylinder
under the same conditions. That which is repelled to the distant extremity
is free to escape if a communication be made with the ground ; whilst, on
the other hand, the unlike electricity which is attracted is held bound or
captive by the inducing action of the electrified body. Even if contact be
made with the ground on the face of the cylinder adjacent to the inducing
body, the electricity induced on that face will not escape. The repelled
electricity, however, on the distant surface is not thus bound; it is free to
escape by any conducting channel, and hence will immediately disappear
wherever contact be made between the ground and the cylinder. Both the
pith balls will collapse, and all signs of electricity on the cylinder depart, with
the escape of the repelled or free electricity. But now, if communication with
the ground be broken, and the inducing body be discharged or removed toa
considerable distance, the attracted or bound electricity is itself set free, and
diffusing over the whole cylinder causes the pith balls again to diverge, but
now with the opposite electricity to that of the original inducing body. The
reason for the escape of the repelled electricity is as follows :—If the
cylinder be placed in connection with the ground, by metallic contact with
the posterior extremity, and the charged conductor be still placed near
the anterior extremity, the conductor will exert its inductive action as before.
But it is now no longer the cylinder alone which is influenced. It isa
conductor consisting of the cylinder itself, the wire, and the whole earth.
The neutral line will recede indefinitely, and, since the conductor has
' become infinite, the quantity of neutral fluid decomposed will be increased.
Hence, when the posterior extremity is placed in contact with the ground,
the pendulum at the anterior extremity diverges more widely. If the con-
necting-rod be now removed, neither the quantity nor the distribution will
be altered ; and if the conductor be removed or be discharged, a charge
of negative electricity will be left on the cylinder. It will, in fact, remain
—768] Faraday s Ice-Pail Experiments 7AO
charged with electricity, the opposite of that of the charged conductor. Even
if, instead of connecting the posterior extremity of the cylinder with the
ground, any other part had been so connected, the general result would
be the same. All the parts of the cylinder would be charged with negative
electricity, and, on breaking the connection with the earth, would remain
so charged.
Thus a body can be charged with electricity by induction as well as by
conduction. But, in the latter case, the charging body loses part of its
electricity, which remains unchanged in the former case. The electricity
imparted by conduction is of the same kind as that of the electrified
body, while that excited by induction is of the opposite kind. To impart
electricity by conduction, the body
must be quite insulated ; while in the
case of induction it must be in con-
nection with the earth—at all events
momentarily.
A body electrified by induction
acts in turn on bodies placed near
it, separating the two electricities in
a manner shown by the signs on the
sphere.
What has here been said has
reference to the inductive action
exerted on good conductors. Bad
conductors are not so easily acted
upon by induction, owing to the great
resistance they present to the circu-
lation of electricity ; but, when once
charged, their electric state is more
permanent.
This is analogous to what is met
with in magnetism; a magnet in-
stantaneously magnetises a piece of
soft iron, but this is only temporary, and depends on the continuance of the
action of the magnet ; a magnet magnetises steel with far greater difficulty,
but this magnetisation is permanent.
The fundamental phenomena of induction may also be conveniently in-
vestigated and demonstrated by means of the apparatus represented in fig.
716, which consists of a narrow cylindrical brass tube BA, supported by an
insulating glass handle, and held over the excited cake of an electrophorus
(775). 1
768. Faraday’s experiments.—The following experiments of Faraday,
which are often known as ‘the ice-pail.experiments,’ from the vessels with
which they were originally made, are excellent illustrations of the operation
of induction, and are of great theoretical importance :—
A carefully insulated metal cylinder, A, fig. 717, is connected by a wire
with an electroscope E, at some distance. When an insulated brass ball
C, charged with positive electricity, which is small in comparison with
the size of the cylinder, is lowered into the cylinder, the leaves of the electro-
750 Frictional Electricity [768-
scope diverge, and, as can be shown, with positive electricity, and the
divergence increases until a certain depth is attained, when there is no
further increase. The divergence now remains constant, whatever be the
position of the ball, and when the inside and outside are tested with the
proof plane they are found to be charged with negative and positive respec-
tively. Ifthe ball is withdrawn the leaves of the electroscope’ collapse, and
there is no electrification on the cylinder;
the quantities of negative and positive
electricity developed on the two surfaces
are accordingly equal to each other.
If now the ball, while still charged
with positive electricity, be brought as
before into the cylinder, and be allowed
to touch the inside, there is no altera-
tion, not even a momentary one, at the
moment of contact, in the divergence of
the leaves of the electroscope; but if
the ball be withdrawn it will now be
found to be neutral, as is also the inside
of the cylinder, while the outside is charged
with positive electricity. When the ball
touches the interior, the system forms
only a single conductor, and al! the elec-
Fig. 717 tricity passes to the outside; but since
the charge as indicated by the electro-
scope does not alter, it follows that the positive of the ball and the negative
of the inside of the cylinder are equal to each other.
If, while the ball charged with positive electricity is inside the cylinder,
the latter is momentarily put to earth, the gold leaves collapse, and the proof
plane, if applied to the outside, removes no trace of electricity ; the cylinder
‘behaves towards all external bodies as if it were neutral. The internal
surface is, however, covered with a layer of negative electricity, and this is
equivalent to the positive charge of the ball, for all trace of electricity dis-
appears if the ball is made to touch the side.
If the ball, after the cylinder has been momentarily connected to earth,
be removed without having touched the sides, the negative passes to the
outside and forms there a layer which is distributed as was the layer of
positive electricity before the cylinder was connected with the ground. The
cylinder is thus finally charged with a quantity of electricity equal and of
opposite sign to that of the inducing body.
Four such cylinders (fig. 718) are placed concentrically within each other,
_and are insulated from each other by discs of shellac, and the outer one is
-connected with the electroscope. On introducing the charged ball into the
central cavity the leaves diverge just as if the intermediate ones did not
exist. Each of these is charged with equal quantities of opposite electricities,
-all equal in value to that of the sphere. The internal charge of the cylinder
is the same as if all the intermediate cylinders were suppressed, and the
charge does not vary even when the intermediate ones are connected with
.each other or are touched by the electrified ball C.
-769] Specific Inductive Capacity 751
If, while C is in its original condition, the internal cylinder, 4, is con-
nected with the ground, the leaves collapse, and the other cylinders are in
the neutral state ; the two layers which remain, positive on C, and negative
on the adjacent cylinder, are without action on an external point. If any
other cylinder be thus treated, the external ones are reduced to the neutral
state.
With the aid of :the cylinder (fig. 717) it is easy to demonstrate that by
friction both electricities are produced at the same time, and in equal quan-
tities. For if the flannel and
sealing-wax in fig. 702 after being 479
rubbed are placed simultaneously
in the cylinder no divergence is
produced, while if each is intro-
duced separately, they produce
equal divergence but of opposite
sign. =
_ Whenever a charge of elec- = ~
tricity exists there is somewhere
an equivalent and corresponding
charge of electricity of the opposite kind. This may seem inconsistent with
the fact that an insulated sphere may have a charge of one kind of electricity.
But it is to be remembered that this is in effect the case of a Leyden
jar (792) in which the dielectric is the layer of air between the sphere and
the sides of the room which form the outer coating.
769. Specific inductive capacity.—Hitherto any possible influence of the
medium which separates the electrified from the unelectrified body in the
case of induction has been disregarded. It has been tacitly assumed that
electric actions are exerted at a distance, and the medium has been looked
upon as an inert mass through which the forces can act, but which itself is
destitute of any active properties. The researches of Faraday, however,
prove that this is not the case ; that the medium is of fundamental import-
ance, and that it is in it and not in the conductors that the electrification
must be sought. If the medium does play the essential part in the phe-
nomena of induction, it is not likely that all insulating bodies possess it in
the same degree. This seems to have been known to Cavendish. To
determine this point Faraday used the apparatus represented in fig. 710,
of which fig. 720 represents a vertical section. It consists of a brass sphere
made up of two halves, P and Q, which fit accurately into each other, like
the Magdeburg hemispheres. In the interior of this spherical envelope there
is a smaller brass sphere C, connected with a metal rod, terminating ina
ball B. The rod is insulated from the envelope PQ bya thick layer of
shellac A. The space ez receives the substance whose inductive power is
to be determined. The foot of the apparatus is provided with a screw and
stopcock, so that it can be screwed on the air-pump, and the air in #7 either
rarefied or exhausted. °
Two such apparatus perfectly identical are used, and at first they only
contain air. The envelopes PQ are connected with the ground, and the
knob B of one of them receives a charge of electricity. The sphere C thus
becomes charged like the inner coating of a Leyden jar (792). The layer
Fig. 718
752 Frictional Electricity [769—
mm represents the insulator which separates the two coatings. By touching
B with the proof plane, which is then applied to the torsion balance, the
quantity of free electricity is measured. In one experiment Faraday
observed a torsion of 250°, which represented the free electricity on B, and
was proportional to its total charge. The knob B was then placed in metallic
connection with the knob B’ of the other apparatus, and the torsion was now
found to be 125°, showing that the electricity had become equally distributed
on the two spheres, as might have been anticipated, since the pieces of
apparatus were quite equal, and each contained air in the space mz.
MMe...
Fig.720
This experiment having been made, the space wz in the second appa-
ratus was filled with the substance whose inductive power was to be deter-
mined: for example, shellac. The other apparatus, in which ez is filled
with air, having been charged and connected with the torsion balance, the
deflection C was measured. Let it be taken as 290°, the number observed
by Faraday in a special case. When the knob B of the first apparatus was
connected with the knob B’ of the second, the deflection was not found to be
145°, as would be expected. The apparatus containing air produced an
angle of 114°, and that with shellac of 113°. Hence the former had lost 176°
and had retained 114°, while the latter ought to have shown 176° instead of
113°. The second apparatus had taken more than half the charge, and
hence a larger quantity of electricity had been condensed by the shellac.
Of the total quantity of electricity, the shellac had taken 176° and the air
114°; hence the inductive power of air is to that of shellac.as 114: 1763; or
~769] Specific Inductive Capacity AGS
as 1:1°55:; that is, the inductive power of shellac is more than half as great
again as that of air.
By the following simple experiment the influence of the medium may
be shown :—At a fixed distance above a gold-leaf electroscope let an elec-
trified sphere be placed, by which a certain divergence of the leaves is
produced. If now, the charge remaining the same, a disc of sulphur or
of shellac is interposed, the divergence increases, showing that inductive
action takes place through the sulphur to a greater extent than through a
layer of air of the same thickness.
These experiments show, therefore, that insulators differ in the facility
with which they allow inductive actions to take place through them. To
express this properly, Faraday ascribed to them a varying sfecijfic inductive
capacity, and he spoke of them as dze/ectrics, as it is through them that the
electric forces are transmitted.
The following are the mean values which have been obtained by various
improved methods for the specific inductive capacities of dielectrics, or what
are called the delectric constants or dielectric coefficients. Their exact deter-
mination presents considerable difficulty :—
Air. ; 1°00 Snellacu : : ae gan!
Paraffine 2°02 Ebonite . : : Se eile
India-rubber 222 Sulphur : SIT
Gutta-percha . 4°2 Glass. : : By Seto: 0
Alcohol 25 Water” = : : ce
A condenser with a glass plate would thus have five or six times the
capacity of an air condenser of the same dimensions, or the same capacity
as an air condenser of the same surface, but five or six times as thin.
A very interesting relation exists between the dielectric constant. 4, and
the refractive index, 7, of certain substances. Thus the following numbers
have been found :—
R VR nt
Sulphur . : : god 1°96 2°04
Resin ; : : Hey: 1°59 1°54
Paraffine . 2°32 1°52 1°53
Oil of turpentine 2°23 1°49 1°47
where 7 is the refractive index (562), and ./£ the square root of the di-
electric constant. To this, which is of great theoretical importance, we shall
afterwards recur.
In crystallised bodies the dielectric constant varies with the direction
of the axes. Thus with a crystal of native sulphur Boltzmann found the
values 4°77, 3°97, and 3°81 for the direction of the longest, mean, and shortest
axes respectively.
Hopkinson found the following numbers for the dielectric constants of
certain liquids: petroleum 2:10, oil of turpentine 2°23, olive oil 3°16, and
castor oil 4°78.
Faraday was not able to detect any difference in the dielectric constants
-of various gases. Boltzmann has shown, however, that there are differences
‘among them, and that there is a very close agreement between the square
Ze
754 Frictional Electricity [769—
root of their dielectric constants and their refractive indices, as is seen from
the following table :—
R SAR n
Vacuum. : . _T'00000 I‘00000 10000
Atco tine : ; . 1°00059 T°000295 1000294
Carbonic acid. . 100095 1°00047 3 1000449
Hydrogen . : . 100026 10001 32 1000128
Ethylene . ; {, TGO0OT3I 1000656 1'000678
770. Faraday’s theory of induction.—The experiments of Faraday on the:
part which the medium plays in inductive actions, with their subsequent
mathematical expression, and development by Maxwell, have led to a profound
alteration in the mode of interpreting electrical phenomena.
Faraday regarded conductors as in a certain sense qualitatively different
from non-conductors ; these he called azelectrics, to express that they allow
electrical forces to be transmitted through them ; electric forces cannot pene-
trate into the interior of conductors, but are absorbed on the surface just as.
light is absorbed by an opaque body.
- Faraday assumed that insulators or non-conductors consisted of a number
of molecules, possibly spherical in shape, which are perfect conductors and
are disseminated in, and separated from each other by, a non-conducting
medium. When placed in an electric field, the inductive action may be taken:
to be that electrification is produced in the conducting molecules, positive on
one face and negative on the opposite one, the molecules being thus arranged
in polar chains ; those faces of the molecules which are turned towards the
inducing body having electricity of the opposite kind to that of the latter,
while those which are turned away from it have electricity of the like kind.
In the interior of the medium where successively the positive face of one mole-
cule is presented to the negative of the next, the two electricities neutralise
each other throughout, but when the non-conductor is bounded by conductors,
and the boundaries ofan electrical field are always conductors, the free electri-
fication is no longer neutralised, but constitutes the charge of electricity which
is perceived. This is analogous to the action of a magnet on iron filings, where:
they acquire a polar arrangement along the direction of the lines of force ;
the polar chains in electrification representing the lines of electrical force.
This action Faraday called delectric polarisation. \We may add that the lines
of electrical force tend to con-
tract in the direction of their
length, and they repel each other
at right angles thereto.
The following experiment
was devised by Faraday to illus-
trate the folarisation of the
Fig. 721 medium, as: he called it.” He
placed small filaments of silk
in a vessel of turpentine (fig. 721), and, having placed two conductors in the
liquid on opposite sides, he charged one by connecting it with an electrical
machine at work, and placed the other in connection with the ground. The
particles of silk immediately arranged themselves end to end, and adhered
-771] Faradays Theory of Induction 755
closely together, forming a continuous chain between the two sides. If the
chain is broken it again forms, while when the electrical action ceases the
particles disperse. An experiment by Matteucci also supports Faraday’s
theory. He placed several thin plates of mica closely together, and
provided the outside ones with metallic coatings, like a fulminating pane
(791). Having electrified the system, the coatings were removed by
insulating handles, and on examining the plates of mica successively, each
was found charged with positive electricity on one side and negative
electricity on the other.
Kleiner extended this experiment by charging a condenser the insulator
of which was mica, and determining the quantity of electricity by measuring
the discharge. He then recharged the condenser to the same extent, split
off films successively and discharged them by the same plates, and found thus,
that allowing for unavoidable losses of insulation, the charge on each film
was the same.
771. Conducting sphere in a uniform field.—In the case of a conducting
sphere placed in.a uniform electric field, it is easy to trace out the degree of
electrification at any point. If we think of each smallest part as possessing
in the neutral state equal charges of positive and negative electricity, it is
evident that, in an electric field, these charges being acted on by equal
opposite forces must undergo displacements in opposite directions, and
that there will thus be a resultant positive charge on one side of the sphere
and a negative charge on the other. From the uniformity of the field and
the geometrical symmetry of the sphere, we may infer that the electrifica-
tion will be symmetrical with respect to the diameter of the sphere parallel
to the force of the field and to the plane through the centre perpendicular
to this diameter. Further, since the sphere is a conductor, the condition of
equilibrium will be that in which the resultant electric force at any point in
or on the sphere is zero ; that is to say, it will be such that the force due to the
electrification of the sphere itself is, everywhere within the sphere, equal and
opposite to that of the field, and at the outside, such thatwhen compounded
with the force of the field the resultant is perpendicular to the surface.
In the figure let G be ‘the centre of the sphere, and let the: force
of the field act from left to mght parallel to the diameter MN. When
the sphere is unelectrified, we may think
of it as having equal quantities of positive
and negative electricity uniformly distri-
buted through it; that is, we may suppose
two uniform spheres of positive and negative
electricity respectively to be superposed,
each having the same radius and the same
centre C as the given conducting sphere.
Then the effect of the field may be described
as consisting in the displacement of the
negative sphere through the very small dis-
tance CA towards the left, and the displacement of the positive sphere through
an equal distance CB towards the right. These displacements will result in the
production of a layer of free negative electricity over the surface of the left-
hand hemisphere and of free positive electricity over that of the right-hand
sale
756 Frictional Electricity [771-
hemisphere, but there will be no free electricity elsewhere, since the two
spheres of opposite electricity overlap and neutralise each other. It is easily
shown that this electrification satisfies the conditions pointed out above. It
is evidently symmetrical relatively both to the diameter MN and to the
equatorial plane perpendicular to this diameter. To determine the direction
and intensity of the force inside the sphere resulting from this electrification,
consider a point P distant AP from the centre of the negative sphere and
BP from that of the positive sphere. Instead of estimating the force at this
point due to the free surface-charges, we will do what is evidently the same
thing, that is, calculate the resultant effect at P of the uniform spherical
negative Phares with centre A and the similar positive charge with centre B.
In each case the force due to electricity situated farther from the centre
than the point P will vanish, so that the problem is reduced to finding the
resultant force at P due to a negative sphere with centre A and radius AP,
together with a positive sphere with centre B and radius BP. Each of these
spheres acts as though the whole quantity of electricity contained in it were
concentrated at the centre. If we put p for the common density of the two
spheres of electricity, we have, for the quantity of negative electricity which
acts as though it were concentrated at A, the expression 4 7 AP® p, or Qy say.
The force due to this at the point P is Q,/AP*=¢# mp AP, and it acts in the
direction PA. Similarly, the quantity of positive electricity that we have to
regard as concentrated at B is Q,=4a BP® p, and the force due to it is
Q:/BP?=# wp BP acting in the direction BP. Consequently the sides BP
and PA Re the triangle BPA are respectively proportional to the forces which
act along them, and therefore the third side BA is proportional to the resul-
tant force at P and parallel to it. If we put / for this resultant, we have the
following proportion :
whence
J = §mpBA.
It is to be observed that this result does not depend on the position of the
point P ; it would therefore be the same whatever point of the conducting
sphere were taken for discussion. This is the same thing as saying that the
internal force due to the free surface-electrification is everywhere the same ;
further, it acts everywhere in the direction BA, that is, parallel to but opposite
to the force of the undisturbed external field. Let F stand for the force of
the field, then, anywhere inside the sphere, the total force is F—f; but, as
was pointed out above, since the sphere is a conductor and in electric
equilibrium, this must vanish, whence we get
nah ilatt
pBA= rein
The distance BA between the centres of the imaginary spheres of posi-
tive and negative electricity is evidently the same as the thickness, measured
parallel to the field, or in the figure parallel to the diameter MN, of the
supposed surface layers of free electricity. The radial thickness at any point,
—771] Conducting Sphere tn a Untform field VAY:
say L, such that the radius drawn to it makes an angle a with MN, is
BA cos a, which gives the thickness =o for points in the great circle perpen-
dicular to MN (a=90°), and gives negative values for points still farther from
N, as it should do.
As the quantity BA does not depend on the particular sphere considered,
it may be better to represent it by a more general symbol, say 6. The pro-
duct po may receive a more satisfactory physical interpretation as follows.
Suppose S to be the measure of a very small area about the point N, then
Spé will denote the quantity of electricity on this area, and we may give any
values we please to the separate factors p and 6 without altering this quan-
tity so long as the product pd remains constant. Let this constant product
be denoted by ¢,: we may then suppose 6 to diminish without limit, p
increasing at the same time, so that we always have
and the charge on the area S may be written So, and may be thought of as
a mere surface-layer without finite thickness. Dividing this charge by the
area over which it is distributed, we must interpret the quotient o, as the
surface-density of the charge at N. Similarly the surface-density at any
other point is given by the formula
go =p0d COS a=a, Cosa
if we assign the proper value to a. For instance, for the point M (a= 180°)
we get o=——07,
It remains to 5 SEN that the electric force at the surface of the sphere
has no component along the surface, in other words, that it acts along the
radius. Taking any point L on the Sree we will consider separately the
components due to the electrification of the sphere and to the field respec-
tively, which act at right angles to the radius at this point, and shall be able
to prove that they are equal and opposite to each other.
Seeing that the angle ALB is very small, it is bisected (very nearly) by
the radius CL. We will put 6 for this angle, 7 for the radius, and a for the
angle LCN. The force at L due to the sphere of positive electricity is
: . . .
mp j acting along BL ao 6), and its component perpendicular to the radius is
b 4 1 §= 46 sin a
41) = sind 6= eras 4 sin a, since, as can be easily seen, sin $ d=
p Be b
without appreciable error. Similarly, the force due to the sphere of negative
3 . .
electricity is 4 mp BY acting along LA (=a), and its component at right angles
a~
to LC is 4 mp Bs sin + 6, which may be written, without sensible error,
a
3 . .
4 ape ie 1 sina. Hence the total force perpendicular to the radius due to
i
the electrification of the sphere is
3 Vas 3
"+ =4 ao peer 2)
4 1 gj a
$ mp0. 3 sin a 3 * a ot ante
758 Frictional Electricity [771-
But, since a and /are very nearly equal and ~ is intermediate, 7*(a* + d°)/a°d°
= 2, consequently the component force in question becomes
2 Oh deel
4 no, sina=F sina,
and acts along the surface in the direction from N towards M.:
The component at right angles to the radius due to the force of the field
is at once seen to be F sin a acting in the direction from M towards N.
These two components accordingly neutralise each other, or the final resul-
tant acts along the radius.
772. Communication of electricity at a distance.—In the experiment
represented in fig. 715 the opposite electricities of the conductor and the
cylinder tend to unite, but are prevented by the resistance of the air. If the
electric density is increased, or if the distance of the bodies is diminished, the
opposed electricities at length overcome this obstacle ; they rush together
and combine, producing a spark, accompanied by a sharp sound. The
negative electricity separated on the cylinder being thus neutralised by the
positive electricity of the charged body, a charge of positive electricity
remains on the cylinder. The same phenomenon is observed when a finger
is presented to a strongly electrified conductor. The latter decomposes by
induction the neutral electricity of the body, the opposite electricities com-
bine with the production of a spark, while the electricity of the same kind as
that of the electrified conductor, which is left on the body, passes off into the
ground.
The striking distance varies with the density, the shape of the bodies,
their conducting power, and with the resistance and pressure of the inter-
posed medium.
773. Motion of electrified bodies.—The various phenomena of attrac-
tion and repulsion, which are among the most frequent manifestations of
electrical action, may all be explained by reference
to the laws of induction. If M (fig. 723) is a fixed
insulated conductor charged with positive electricity,
and N is a movable insulated body—for instance,
an electrical pendulum—there are three cases to be
considered :-—
If the pendulum is suspended by an insulating
thread, such as dry silk, M, acting inductively on N,
attracts the negative and repels the positive electricity, so that the maxima of
density are respectively at the points @ and 6. Nowa is nearer c than 6
is ; and, since attractions and repulsions are inversely as the square of the
distance, the attraction between a and c is greater than the repulsion be-
tween 6 and c; and, therefore, N will be attracted to M bya force equal
to the excess of the attractive over the repulsive force.
If the thread is not an insulation, then the electricity of the same kind as
the inducing body passes to earth through the thread and the supports, and
the attraction is stronger than in the previous case.
The uninsulated pendulum is more sensitive than the insulated one, and
should always be used when we wish to ascertain whether a body is electri-
fied or not ; but the insulated one must be used if we desire to ascertain the
kind of electricity with which a body is charged. For this purpose electri-
=
—~774] Gold-leaf Electroscope 759
‘city of known kind is imparted to the ball, and then attraction or repulsion
is observed when the charged body is approached according as its electricity
is of the opposite or the like kind to that of the body under investigation.
774. Gold-leaf electroscope.—The name e/ectroscope is given to instru-
ments for detecting the presence and determining the kind of electricity in
any body. The original pith-ball pendulum is an electroscope ; but, though
sometimes convenient, it is not sufficientiy delicate.
The gola-leaf electroscope consists of a glass cylinder B (fig. 724), stand-
ing on a metal base, which thus communicates with the ground. A metal
rod terminating at its upper extremity in a knob C, and holding at its lower
end two narrow strips of gold-leaf, 7 7, fits in the neck of the cylinder, which
is coated with an insulating varnish. The air in the interior is dried by
quicklime, or by calcium chloride, and on the insides of the glass there
are two strips of gold-leaf, a, communicating with the ground. These, being
charged by induction with the opposite electricity to that of the gold leaves,
increase the divergence, and therefore the delicacy of the apparatus. They
also prevent the leaves when diverging too suddenly from adhering to the
sides.
When the knob is touched with a body charged with either kind of
electricity, the leaves diverge ; usually, however, the apparatus is charged
by induction thus :—
If an electrified body—a stick of rubbed sealing-wax, for example—is
brought near the knob, it will separate the two electricities, attracting unlike
electricity to the knob, and retaining it there and repelling electricity of the
same kind to the gold leaves, which consequently diverge. In this way the
presence of an electrical charge is ascertained, but not its quality.
To ascertain the £z7d of electricity the following method is pursued :—It
the knob is touched by the finger while the instrument is under the influence
of the body A, which we will suppose has a negative charge, the negative
electricity produced by induction
passes off into the ground, and the
previously divergent leaves will col-
lapse; there only remains positive
electricity retained in the knob by in-
duction from A. If now first the finger
is removed, and then the electrified
body, the positive electricity previously
retained by A will spread over the sys-
tem, and cause the leaves to diverge.
If now, -while the system is charged
with positive electricity, a positively
electrified body—as, for example, an
excited glass rod—is approached, the
leaves will diverge more widely ; for
the electricity of the same kind will
be repelled to the ends. If, on the
contrary, an excited shellac rod is
presented, the leaves will tend to collapse, the electricity with which they
are charged being attracted by the opposite electricity. Hence we may
760 Frictional Electricity [774—
ascertain the kind of electricity either by imparting to the electroscope
electricity from the body under examination, and then bringing near it
a rod charged with positive or negative electricity ; or by charging the
electroscope with a known kind of electricity, and bringing the electrified
body in question near the electroscope.
The gold-leaf electroscope 1s sometimes used as an electrometer, or
measurer of electricity, the angle of divergence of the leaves being measured ;
this is done by placing behind them a graduated scale ; for small angles the
quantity of electricity is nearly proportional to the sine of half the angle of
divergence.
An electroscope in which, as in this case, the whole electrical force
depends on the electrification of the body to be investigated is called an
zatostatic one ; those in which an independent field is maintained, as is that
of Bohnenberger (839) or of Thomson (802), are called heterostatic.
ELECTRICAL MACHINES
775. Electrophorus.—It will now be convenient to describe the various
electrical machines, or apparatus for generating and collecting large quantities
of statical electricity. One of the most simple and inexpensive of these
is the electrophorus, which was invented by Volta. It consists of a cake of
resin, B (fig. 726), say about 12 inches in diameter, and an inch thick, which
is placed on a metal surface, or frequently fits into a wooden mould lined
with tinfoil, which is called the form. Besides this there is a metal disc of
a diameter somewhat less than that of the cake, and provided with an in-
sulating glass handle ; this is the cover. The mode of working isas follows :
All the parts of the apparatus having been well dried, the cake, which is
placed in the form, or rests on a metal surface, is briskly flapped with silk,
—776] Electrophorus 761
or, better, with catskin, by which it becomes charged with negative electri-
city. The cover is then placed on the cake. Owing, however, to the minute
rugosities of the surface of the resin, the cover comes in contact with only
a few points, and, from the non-conductivity of the resin, the negative
electricity of the cake does not pass off to the cover. It acts by induction
on the cover, attracting the positive electricity to the under surface, and
repelling the negative electricity to the upper. If the upper surface be now
touched with the finger, the negative electricity passes off, and the cover
remains charged with positive electricity, held, however, by the negative
electricity of the cake ; the two electricities do not unite, in consequence of
the non-conductivity of the cake (fig. 725). If now the cover be raised by
its insulating handle, the charge diffuses itself over the surface ; and if a
conductor be brought near it (fig. 726), a smart spark passes.
The metal form on which the cake rests plays an important part in
the action of the electrophorus, as it increases the quantity of electricity, and
makes it more permanent. For the negative electricity of the upper surface
of the resin, acting inductively on the neutral electricity of the lower, decom-
poses it, retaining on the under surface the positive electricity, while the
negative electricity passes off into the ground. The positive electricity thus
developed on the under surface reacts on the negative electricity of the upper
surface, binding it, and causing it to penetrate into the badly conducting
mass, on the surface of which fresh quantities of electricity can be excited
far beyond the limits possible without the action of the form. For this
reason the electrophorus, once charged, retains its state for a considerable
time, and sparks can be taken even after a long interval. If the form be
insulated, the charge obtained from it is far less than if it is on a conducting
support. For, the negative electricity developed by induction on the lower
surface being now unable to escape, the condensing action referred to cannot
take place, and only a feeble charge can be given to the resin. The retention
of electricity is greatly promoted by keeping the cake on the form, and
placing the cover upon it, by which the access of air is hindered. Instead
of a cake of resin, a disc of gutta-percha, or vulcanised cloth, or vulcanite,
may be substituted; and, of course, if glass, or any material which is
positively electrified by friction, be used, the cover acquires a negative
charge.
The electrophorus is a good instance of the conversion of work into
electropotential energy (65). When the cover is lifted from the excited cake
work must be expended in order to overcome the attraction of the electricity
in the cake for the opposite electricity developed by induction on the cover ;
and the equivalent of this work appears in the form of the electricity thus
detached. Accordingly, when a Leyden jar (792) is charged either by the
machine or by the electrophorus, the energy of the charge is a transformation
of the work of the operator.
776. Plate electrical machine.—The first electrical machine was invented
by Otto von Guericke, the inventor also of the air-pump. It consisted of a
sphere of sulphur, which was turned on an axis by means of the hand, while
the other hand, pressing against.it, served as a rubber. Resin was after-
wards substituted for the sulphur, which, in turn, Hawksbee replaced by a
glass cylinder. In ali these cases the hand served as rubber ; and Winckler,
7062 Frictional Electricity [776-
in 1740, first introduced cushions of horsehair, covered with silk, as rubbers.
At the same time Bose collected electricity, disengaged by friction, on an
insulated cylinder of tin plate. Lastly, Ramsden, in 1760, replaced the glass
cylinder by a circular glass plate, which was rubbed by cushions. The
form which the machine has now is but a modification of Ramsden’s original
machine.
Between two wooden supports (fig. 727) a circular glass plate P is sus-
pended by an axis passing through the centre, turned by means of a handle
M. The plate revolves between two sets of cushions or rubbers, F, of leather
or of silk, one set above the axis and one below, which, by means of screws,
can be pressed as tightly against the glass as may be desired. The plate
also passes between two brass rods, shaped like a horseshoe, and provided
with a series of points on the sides towards the glass ; these rods are fixed
to larger metallic cylinders C C, which are together called the prime con-
ductor. The latter are insulated by being supported on glass feet, and are
connected with each other by a smaller rod ~
The action of the machine is thus explained. By friction with the rubbers
the glass becomes positively and the rubbers negatively electrified. If now
the rubbers were insulated, they would receive a certain charge of negative
electricity which it would be impossible to exceed, for the tendency of the
opposed electricities to reunite would be equal to the power of the friction
to decompose the neutral state. But the rubbers communicate with the
ground by means of a chain; and, consequently, as fast as the negative
electricity is generated, it is continually reduced to zero by contact with
the ground. The positive electricity of the glass acts then by induction on
the conductor, attracting the negative electricity. This negative electricity
collects on the points opposite to the glass. Here its tendency to discharge
becomes so high that it passes across the intervening space of air, and
neutralises the positive electricity on the glass. The prime conductor thus
loses its negative electricity and remains charged with positive electricity.
The plate accordingly gives up nothing directly to the prime conductors ;
but its own positive charge is partly neutralised by the negative drawn from
the points.
If the hand be brought near the conductor when charged, a spark
follows, which is renewed as the machine is turned. In this case the posi-
tive electricity decomposes the neutral electricity of the body, attracting its
negative electricity, and combining with it when the two have a sufficient
tension. Thus, with each spark, the conductor reverts to the neutral state,
but becomes again electrified as the plate is turned.
777. Precautions in reference to the machine.—The glass, of which the
plate is made, must be as little hygroscopic as possible. Of late ebonite
has been frequently substituted for glass; it has the advantage of being
neither hygroscopic nor fragile, and of readily becoming electrified by friction.
It cannot, however, be relied on, as its surface in time undergoes a change,
especially if exposed to the light, whereby it becomes a conductor. The
plate is usually from 54, to 4 of an inch in thickness, and from 20 to 30 inches
in diameter, though these dimensions are not unfrequently exceeded.
The rubbers require great care, both in their construction and their pre-
servation. They are commonly made of leather, stuffed with horsehair.
—777] Plate Electrical Machine 763
Before use they are coated with powdered aurum musivum (tin sulphide),
or graphite, or amalgam. The action of these substances is not very
clearly understood. Some consider that it merely consists in promoting
friction. Others, again, believe that a chemical action is produced, and
assign in support of this view the peculiar smell noticed near the rubbers
when the machine is worked. Amalgams, perhaps, promote most power-
fully the disengagement of electricity. Avzenmayer’s amalgam is the best
of them. It is prepared as follows: One part of zinc and one part of tin
are melted together and removed from the fire, and two parts of mercury
Binminy.
FF _ ®>*” FI = =_22qmmn
I UTERAC TUTORS WA (NNN oe LOTTE
a es _ MN _ eee mn il
SS
Fig. 727
stirred in. ‘The mass is transferred to a wooden box containing some chalk,
and then well shaken. The amalgam, before it is cold, is powdered in an
iron mortar, and preserved in a stoppered glass vessel. For usea little cacao
butter or lard is spread over the cushion, some of the powdered amalgam
sprinkled over it, and the surface smoothed by a ball of flattened leather.
In order to avoid a loss of electricity, two quadrant-shaped pieces of oiled
silk are fixed to the rubbers, so as to cover the plate on both sides: one at
the upper part from a to F, and the other in the corresponding part of the
lower rubbers. ‘These flaps are not represented in the figure. Yellow oiled
764 Frictional Electricety [777—
silk is the best, and there must be perfect contact between the plate and the
cloth.
Ramsden’s machine, as represented in fig. 727, gives only positive elec-
tricity. But it may be arranged so as to give negative electricity by placing
it on a table with insulating supports. The conductor is connected with
the ground by a chain, and the machine worked as before. The positive
electricity passes off by the chain into the ground, while the negative elec-
tricity remains on the supports and on the insulated table. On bringing the
finger near the uprights, a sharper spark than the ordinary one is obtained.
Winter compared the working of an electrical machine directly with the
indications of an hygrometer, and found that the length of the spark obtain-
able is inversely as the hygrometric state.
778. Maximum of charge.—It is impossible to exceed a certain limit of
electrical charge with the machine, whatever precautions are taken, or
however rapidly the plate is turned. This limit is attained when the loss of
electricity equals its production. The loss depends on three causes : i. The
loss by the atmosphere, and the moisture it contains. 11. The loss by the sup-
ports. i. The recombination of the electricities of the rubbers and the glass.
The first two causes have been already mentioned. With reference to
the last, it must be noticed that the electrical charge increases with the
rapidity of the rotation, until it reaches a point at which it overcomes the
resistance presented by the non-conductivity of the glass. At this point, a
portion of the two electricities separated on the rubbers and on the glass
recombines, and the charge remains constant. It is, therefore, ultimately
independent of the rapidity of rotation.
779. Quadrant electrometer.—The electrical charge is roughly measured
by the guadrani or Henley’s electrometer, which is attached to the conductor.
This is a small electric pendulum, consisting of a wooden rod d, to which
is attached an ivory or cardboard scale (fig. 728). In the centre of this isa
small index of straw, movable on an axis, and termi-
nating in a pith ball. Being attached to the con-
ductor, the index diverges as the machine is charged,
ceasing to rise when the limit is attained. When the
rotation is discontinued the index falls rapidly if the
airis moist ; but in dry air it falls but slowly, showing,
therefore, that the loss of electricity in the latter case
is less than in the former.
780. Armstrong’s hydro-electric machine.—In this
machine electricity is produced by the disengagement
of aqueous vapour through narrow orifices. The dis-
covery of the machine was occasioned by an accident.
A workman having accidentally held one hand ina
jet of steam, which was issuing from an orifice in a
steam boiler at high pressure, while his other hand
grasped the safety-valve, was astonished at experiencing a smart shock.
Lord Armstrong (then Mr. Armstrong, of Newcastle), whose attention was
drawn to this phenomenon, ascertained that the steam was charged with
positive electricity, and, by repeating the experiment with an insulated
locomotive, he found that the boiler was negatively charged. Armstrong
—780] Armstrong's Hydro-electric Machine 765
believed that the electricity was due to a sudden expansion of the
steam ; Faraday, who afterwards examined the question, ascertained its
true cause, which will be best understood after describing a machine which
Armstrong devised for reproducing the phenomenon.
It consists of an insulated wrought-iron boiler (fig. 729), with a central
fire, about 5 feet long by 2 feet in diameter, and provided at the side with a
gauges. OQ.) 0 Cais pers
the stopcock, and Ti Mf
above this is the i
box B, in which
areduatherns atubes
through which the
steam is disen-
gaged. On these
are fitted jets of a pil
peculiar construc- WA
tion, shown in the Se
section of one of fe A i
them, M, _ repre- (\ nt
sented on a larger ae W777
scale. They are |
lined with hard
wood in a manner
represented by the
diagram. The box
B contains. cold
water. Thus the
steam, before es-
caping, undergoes
partial condensa-
tion, and becomes
charged with ve-
sicles of water—a
necessary condi-
tion, for Faraday found that no electricity is produced when the steam is
perfectly dry.
The development of electricity in the machine was at first attributed to
the condensation of the steam, but Faraday found that it is solely due to
the friction of the globules of water against the jet. For if the little cylinders
which line the jets are changed, the kind of electricity is changed ; and if
ivory is substituted, little or no electricity is produced. The same effect is
produced if any fatty matter is introduced into the boiler. In this case the
linings are of no use. Electricity is disengaged in case the water is
pure, and the addition of acid or saline solutions, even in minute quantity,
prevents any disengagement of electricity. If turpentine is added to the
boiler the effect is reversed—the steam becomes negatively, and the boiler
positively, electrified.
With a current of moist air Faraday obtained effects similar to those of
this apparatus, but with dry air no effect is produced.
7606 Frictional Electricity [780—
_ When liquefied carbonic acid issues from the metal cylinder in which it
is stored (385), the cylinder is found to be strongly positive, the electrification
being due to the friction of particles of solidified carbonic acid against the
sides of the jet.
781. Holtz’s electrical machine.—Before the end of last century elec-
trical machines were known in this country in which the electricity was not
developed by friction, but by the continuous inductive action of a body
already electrified, as the electrophorus ; within the last few years such
machines have been re-invented and come into use. The form represented
in fig. 730 was invented by Holtz, of Berlin.
= —— SO ENA
Fig. 730
It consists of two c.rcular plates of thin glass at a distance of 3 mm. from
each other ; the larger one, AA, which is 2 feet in diameter, is fixed by means
of 4 wooden rollers a, resting on glass axes and glass feet. The diameter of
the second plate, BB, is 2 inches less ; it turns on a horizontal glass axis,
which passes through a hole in the centre of the large fixed plate without
touching it. In the plate A, on the same diameter, are two large apertures
or windows, FF’. Along the lower edge of the window F, on the posterior
face of the plate,a band of paper, #, is glued, to which is connected a
tongue of thin cardboard, 7, joined to ~ by a thin strip of paper, and pro-
jecting into the window. At the upper edge of the window, F’, there are
corresponding parts, f’and 7’. The papers f and #’ constitute the armatures.
—781] Floltz’'s Electric Machine 707
The two plates, the armatures, and their tongues are covered with shellac
varnish, but more especially the edges of the tongues.
In front of the plate B, at the height of the armatures, are two brass
combs, OO’, supported by two conductors of the same metal, CC’. In the
front end of these conductors are two moderately large brass knobs, through
which pass two brass rods terminated by smaller knobs, 77’, and provided
with ebonite handles, KK’. These rods, besides moving with gentle friction
in the knobs, can also be turned so as to be more or less near and inclined
towards each other. The plate BB is turned by means of a winch M, anda
series of pulleys which transmit its motion to the axis; the velocity which
it thus receives is I2 to I5 turns in a second, and the rotation should take
place in the direction indicated by the arrows—that is, towards the points of
the cardboard tongues 77’.
To work the machine, the armatures #/’ must be first Avi#zed—that is,.
one of the armatures is positively and the other negatively electrified. This
is effected by means of a plate of ebonite, which is excited by striking it
with catskin ; the two knobs 77’ having been connected so that the two
conductors C, C’ form only one, as seen in fig. 731, which shows by a hori-
zontal section, through the axis of rotation, the relative arrangement of the
plates and of the conductors. The electrified ebonite is then brought near
one of them—4, for instance—and the plate B is turned. The ebonite is
charged with negative electricity, and this withdraws the positive electricity
of the armature and charges it negatively. This latter acting by induction
through the plate BB, as it turns on the conductors OCC’O’ (fig. 731), attracts
through the comb O the positive electricity which collects on the front face of
the movable plate ; while at the same time negative electricity, repelled on
the comb O’, collects, like the former, on the front face of the plate B.
Hence, the two electricities béing carried along by the rotation, at the end
of half a turn all the lower half of the plate B, from Z# to F’ (fig. 732), is posi-
tively electrified, and its upper surface from f’ to F negatively. But the two
opposite electricities above and below the window F’ concur in decomposing
the electricity of the armature f’m’ ; the part J’ 1s positively electrified, while
negative electricity is liberated by the tongue 7’, and is deposited on the
inner face of the plate B B, which from its thinness almost completely
neutralises the positive electricity on the anterior face.
The two armatures are then primed, and the same effect as at F’ is
produced at F on the armature # z—that is, that the opposite electricities.
above and below ~ 2 decomposing a new quantity of neutral electricity,
the negative charge of the part / increases, while the positive electricity which
768 Frictional Electricity [781—
is liberated by the tongue z neutralises the negative electricity which comes
from F’ towards F; and so forth, until, the machine having attained its
maximum charge,
there is equili-
brium in all its
parts. From that
point it only keeps
itself up, and in
perfectly dry air
it may work for a
long time without
its being neces-
sary to employ
the ebonite plate.
Ifthis is removed,
and the: knobs +
and 7’ are moved
apart (fig. 732) to
a distance de-
pendent on the power of the machine, [while the rotation is continued, a
torrent of sparks strikes across from one knob to the other.
With plates of equal dimensions Holtz’s machine is far more powerful
than the ordinary electrical machine (776). The power is still further increased
by suspending to the conductors C C’ two condensers (788), or small Leyden
jars, H H’ which consist of two glass tubes coated with tinfoil, inside and
out, to a fifth of their height. Each of them is closed by a cork through
which passes a rod, communicating at one end with the inner coating, and
suspended to one of the conductors by a crook at the other end. The two
external coatings are connected by a conductor, G. They are, in fact, only
two small Leyden jars (792), one of them, H, becoming charged with positive
electricity on the inside and negative on the outside; the other, H’, with
negative electricity on the inside and positive on the outside. Becoming
charged by the play of the machine, and being discharged at the same rate
by the knobs 77’, they strengthen the spark, which may attain a length of
6 or 7 inches.
The current of the machine is utilised by placing in front of the frame
two brass uprights, Q Q’, with binding screws in which are copper wires ; then,
by means of the handles K K’, the rods which support the knobs 77 are in-
clined, so that they are in contact with the uprights. The current being
then directed by the wires, a battery of six jars can be charged in a few
minutes, water can be decomposed, a galvanometer deflected, and Geissler’s
‘tubes illuminated.
Kohlrausch found that a Holtz machine with a plate 16 inches in dia-
meter, and making 5 turns in three seconds, produced a constant current
capable of decomposing water at the rate of 3} millionths of a milligramme
ina second. This is equal to the effect produced by a single Grove’s cell
in a circuit of 45,000 ohms resistance.
Rossetti, who made a series of measurements with a Holtz machine,
found that the strength of the current is nearly proportional to the velocity
Fig. 732
—782] Wimshurst’s Machine 769
of the rotation ; it increases a little more rapidly than the rotation. The ratio
of the velocity of rotation to the strength of the current is greater when the
hygrometric state increases. The current produced by a Holtz machine is
comparable with that of a voltaic couple. Its electromotive force and
resistance are constant, provided the velocity of rotation and the hygrometric
State are constant.
The electromotive force is independent of the velocity of rotation, but
diminishes as the moisture increases ; it is nearly 52,000 times as great as
that of Daniell’s cell.
The internal resistance is independent of the moisture, but diminishes
rapidly with increased velocity of rotation. Thus with a velocity of 120turns
in a minute itis represented by 2,810 million ohms (1000), and with a velocity
of 450 turns it is 646 million ohms.
Holtz’s machine is very much affected by the moisture of the air ; but
Ruhmkorff found that by spreading on the table a few drops of petroleum,
the vapours which condense on the machine protect it against the moisture
of the atmosphere.
Holtz’s machine affords a means of making a curious experiment on
reversibility. \f the two combs of a machine in the ordinary state are con-
nected with the poles of a second similar one, which is then set in action,
the combs of the first become luminous, and the plate begins to rotate, but
in the opposite direction to its ordinary course ; the electricity thus transmits
the motion of the second machine to the first ; the one expends what the
other produces. It may also be observed that the two machines are con-
nected by opposite poles, and the system constitutes a circuit which is tra-
versed in a definite direction by a continuous electrical current.
A very simple and efficient machine of this kind is made by Voss of Berlin.
One with a plate of 10 inches diameter produces a spark of 4 to 5 inches.
782. Wimshurst’s machine.—This is the simplest and most efficient of
all induction machines.
It consists (fig. 730) of two circular glass discs mounted on a fixed
horizontal spindle in such a way as to be rotated in opposite directions at a
distance of not more than a quarter of an inch apart. Both discs are well
varnished, and attached to the outer surface of each are narrow radia
sections of tinfoil arranged at equal angular distances apart.
Attached to the fixed spindle on which the discs rotate is a bent conduct-
ing rod, at the ends of which are two fine wire brushes ; twice during each
revolution two diametrically opposite conductors are put in connection with
each other by means of this conductor, as they just graze the tips of the
brushes. At the back is a similar one at right angles to that in front, and
there is a position of maximum efficiency, which is when they make an angle
of 45° with the fixed collectors. There are two forks provided with combs
directed towards each other, and towards the two discs which rotate
between them; they are supported horizontally on Leyden jars, to which
are also attached the terminal electrodes or dischargers, the distance
apart of which can be varied by turning the Leyden jar from which they
rise. .
The machine is self-exciting, and requires neither friction, nor the
spark from any outside exciter, to start it. It is one of the most remark-
3.)
770 Frictional Electrecety [782-
able features of this machine, that under ordinary conditions it attains its
full power after the second or third turn. The initial charge is probably
obtained from the electricity of the air, or from the frictional resistance
' against it.
With a machine having plates 17 inches in diameter, a powerful spark
discharge passes between the two electrodes when they are 4 to 5 inches
apart, in regular succession, at the rate of 2 or 3 for every turn of the handle.
A machine with 12 plates, 30 inches in diameter, when driven at a speed of
200 turns per minute, produces sparks between the terminals of 13} inches
in length ; and when the terminals are closed by a wire of 3,000 ohms
wl]
SE iy |
resistance (1000) a current of two-thirds of a millimpere is produced. With
these machines the increase of electricity has been found proportional to the
speed of rotation up to 5,000 turns in a minute.
It is not easy to give a satisfactory account of the theory of the machine.
Mr. Wimshurst considers that its remarkable efficiency may be partly due
to the duplex action of the apparatus, both plates being active and con-
tributing electricity to the collecting combs, the sector-shaped plates of tin-
foil acting as z#zductors when in their position of lowest efficiency as carriers,
and as carriers when in the positions at which their inductive effect is at a
minimum, and vice versd ; and as it follows from the construction of the
instrument that the inductors of the one disc are at a position of highest
—784] Work required for the Production of Electricity 771
efficiency when those of the other are at their lowest, and vzce versd, and as
this applies with equal force to the sectors when considered as carriers, it
also follows that the charging of the electrodes, and therefore the discharge
between them, is by mutual compensation maintained constant.
783. Work required for the production of electricity.—In all electrical
machines electricity is only produced by the expenditure of a definite amount
of energy, as will at once be seen by a perusal of the preceding descriptions.
The action of those machines, however, which work continuously is some-
what complex. Not only is electricity produced, but heat also ; and it has
been hitherto impossible to estimate separately the work required for the
heat from that required for the electricity. This is easily done in theory, but
not in practice: it would be, for instance, difficult to determine the tem-
perature of the cushion, or of the plate of a Ramsden machine.
By means of a Lane electrometer (799) it was found that, taking as unit
the quantity of electricity produced by one turn of a Ramsden machine with
a plate 39 inches in diameter, that produced by a Holtz machine with a
plate of 21 inches was 0°86; but as for the same work the former made I |
and the latter Io turns in a second, it follows that the quantities produced
were as 1:8°6. Comparing the quantities per unit of surface, the yield of
the Holtz machine is more than 12 times that of the Ramsden.
In lifting the plate off a charged electrophorus a certain expenditure of
energy is needed, though it be too slight to be directly estimated (775). With
a Holtz machine it may be readily shown by experiment that there is a
definite expenditure of energy in working it. If such a machine be turned
without having been charged, the work required is only that necessary to
overcome the passive resistances due to friction. If, however, a charged
ebonite plate is approached to one of the sectors, as soon as the peculiar
sound indicates that the machine is at work, it will be observed that there
must be a distinct increase in the mechanical effort necessary to work the
machine.
The work required to charge an unelectrified conductor to a given poten-
tial may be deduced from the following considerations :—To impart to a body
which is at potential V a quantity of electricity Q would require an amount
of work represented by QV (762). But if the body be unelectrified it
is at the outset at zero potential; and we may conceive the electricity
imparted to it in a series of 2 very small charges of g each, such that
azg=Q; and as the potential rises proportionally to the number of
charges, it may be assumed that the work done is equal to that required to
charge the body to an average potential of $V ; hence the work in question
W =4QV.
From the relation between the quantity of heat produced by the current
of a Holtz machine working under definite conditions, and the amount of
-work expended in producing the rotation of the plate, Rossetti made a
‘determination of the mechanical equivalent of heat, which gave the number
1,397, agreeing therefore very well with the numbers obtained by other
methods (509).
784. Thomson’s water-dropping collector.—This may be given as an
illustration of an arrangement by which a known charge may be almost
indefinitely multiplied,
Se
772 Frictional Electricity [784—
A and B, fig. 731, are insulated metal cylinders called the zaductors, and
are in metallic connection with two cylinders a and 4, also insulated, called the:
receivers, each having a funnel the nozzle ot
which isin the centre of the cylinder. Water
from the pipe e falls in drops through the
metal taps ¢ and d, the nozzles of which are:
in the centre of the cylinders A and B.
Take first the case of the cylinder A,
and suppose it to possess a small negative
charge at the outset, the drops as they fall
will be charged negatively by induction,
the corresponding positive going to earth,
through e. Falling on the funnel of the
receiver 4 they impart to it the whole of
their charge, and the water as it issues will
be neutral.
But the negative charge of B is shared
with 4, which is thus negatively electrified,.
and the drops which fall through it are
positively electrified and give up their posi-
tive charge to a, which strengthens the
positive of A. By this means even with
a very slight original charge they will
strengthen each other, until even sparks.
Fig. 734 pass. It is not even necessary to give a
charge at the outset ; the ordinary electricity
i,
“
5)
Ee,
3
of the atmosphere is sufficient.
The energy in this apparatus is derived from that of the falling body, and
would be exactly equivalent to it if there were no loss, and if the drops.
reached the.funnel without any velocity.
EXPERIMENTS WITH THE ELECTRICAL MACHINE
785. Electrical spark.—One of the most curious phenomena observed with
the electrical machine is the spark drawn from the conductor when a finger is.
presented to it. The positive electricity of the conductor, acting inductively
on the neutral electricity of the body, decomposes it, repelling the positive
and attracting the negative. When the attraction of the opposite electricities.
is sufficiently great to overcome the resistance of the air, they recombine
with a smart crack and a spark. The noise of the crack is due to the con-
densation of the air suddenly heated and expanded by the passage of
electricity and reaching the ear as sound waves.
The spark is instantaneous, and is accompanied by a sharp prickly sensa-.
tion, more especially with a powerful machine. Its shape varies. When it
strikes at a short distance it is rectilinear, as seen in fig. 735. Beyond two:
or three inches in length the spark becomes irregular, and has the form of
a sinuous curve with branches (fig. 736). If the discharge is very powerful,
the spark takes a zigzag shape (fig. 737). These latter two appearances are:
seen in the discharge of lightning.
—786] Electrical Chimes Yi
A spark may be taken from the human body by aid of the zzszzlating
stool, which is simply a low stool with stout glass legs. The person standing
on this stool touches the prime conductor, and, as the human body is a con-
ductor, the electricity is distributed over its surface as over an ordinary
insulated metallic conductor. The hair diverges in consequence of repulsion,
ae
a peculiar sensation 1s felt on the face, and if another person, standing on
the ground, presents his hand to any part of the body, a smart crack with a
pricking sensation is produced.
A person standing on an insulated stool may be negatively electrified by
being struck with a catskin. If the person holding the catskin stands on an
insulated stool, the striker becomes positively and the person struck negatively
electrified.
786. Electrical chimes.—The electrical chimes is a piece of apparatus
consisting of three bells suspended to a horizontal metal rod (fig. 738). Two
of them, A and B, are in metallic connection with the conductor ; the middle
bell hangs by a silk thread, and is thus insulated from the conductor, but is
connected with the ground by means of a chain. Between the bells are
small copper balls suspended by silk threads. When the machine is worked,
the bells A and B, being positively electrified, attract the copper balls, and
after contact repel them. Being now positively electrified, they are in turn
attracted by the middle bell, C, which is charged with negative electricity
by induction from A and B. After contact they are again repelled, an
this process is repeated as long as the machine is in action.
Fig. 739 represents an apparatus originally devised by Volta for the
purpose of illustrating what he supposed to be the motion of hail between
774 Frictional Electricity ['786—
two clouds oppositely electrified. It consists of a tubulated glass shade,
with a metal base, on which are some pith balls. The tubulure has a
metal cap, through which passes a
brass rod, provided with a metal disc
or sphere at the lower end, and at the
upper with a ring, which touches the
prime conductor.
When the machine is worked, the
sphere becoming positively electrified
en attracts the light pith balls, which are
then immediately repelled, and, having
| lost their charge of positive electricity,
4 are again attracted, again repelled,
and so on, as long as the machine
continues to:-be worked. An amusing
modification of this experiment is frequently made by placing between the
two plates small pith figures, somewhat loaded at the base. When the
machine is worked, the figures execute a regular dance.
Fig. 738
Fig. 740
787. Electric whirl or vane.—The electric whzv/ or vane consists of
5 or 6 wires, terminating in points, all bent in the same direction, and
fixed in a central cap, which rotates on a pivot (fig. 740). When the appa-
ratus is placed on the conductor, and the machine worked, the whirl begins
to revolve in a direction opposite that of the points. This motion is not
analogous to that of the hydraulic tourniquet (151).. It is not caused by a
flow of material fluid, but is owing to a repulsion between the electricity of
the points and that which they impart to the adjacent air by conduction. The
electricity, being accumulated on the points in a high state of density, passes
into the air, and, imparting thus a charge of electricity, repels this electricity,
while it is itself repelled. That this is the case is evident from the fact that »
on approaching the hand to the whirl while in motion, a slight draught is
~787] Electrical Whirl or Vane 775
felt, due to the movement of the electrified air, while in vacuo the apparatus
does not act at all. This draught or wind is known as the electrical
aura.
If the experiment is made in water, the fly remains stationary, for water
is a good conductor ; but in olive oil, which is a bad conductor, the whirl
rotates.
When the electricity thus escapes by a point, the electrified air is repelled
so strongly as not only to be perceptible to the hand, but also to engender
a current strong enough to blow out a candle. Fig. 741 shows this experi-
Fig. 741 Fig. 742
ment. The same effect is produced by placing a taper on the conductor
and bringing near it a pointed wire held in the hand (fig. 742). The current
arises in this case from the flow of air electrified with the contrary electricity
which escapes by the point under the influence of the machine. The loss
of electricity in this way by contact with easily moving bodies is analogous
to the transmission of heat by convection.
The electrical orrery and the electrical inclined plane are analogous in
their action to these pieces of apparatus.
The velocity of the electrical aura has been determined by placing a
wire gauze connected with earth at a fixed distance from the point, and an
anemometer at varying distances behind the gauze. The velocity of the
wind was found to diminish with the distance, but not in direct proportion ;
at a distance of 22 inches it was 54 feet per second, while at 60 inches its
velocity was 2 feet per second.
The production of the electrical aura is accompanied by luminous
phenomena which can be seen in the dark. If positive electricity escapes
from the point, a violet aigrette is formed ; while when the electricity is
negative a small brilliant star forms on the point.
It is pretty certain that in these experiments it is not the air itself, but
the particles in it, whether of dust or of moisture, which become electrified.
This may be illustrated by the following simple experiment. A glass globe
is filled with dense smoke of turpentine or of sal-ammoniac (fig. 743), and
the bared end of a guttapercha-covered wire is held in it while the other
end is connected with an electrical machine. On giving the machine two
or three turns the smoke is rapidly deposited, and the inside becomes
quite clear. Here the smoke consists of solid particles, which become
776 frictional Electricity [787-
polarised by induction and attract each other like the particles of silk
in fig. 721. They thereby become agglomerated, and are deposited on the
sides where they are retained if the sides are coated with glycerine.
Nahrwold proves that if air is freed from dust by filtration, it takes little
if any charge from an electrified point.
Fig. 743
This phenomenon is employed industrially in the deposition of finely
suspended powders, as in lead works. Two conductors provided with points
are connected respectively with a positive and negative source of electricity :
the powder electrified by the one point is repelled and is precipitated on the
other.
—788} Condensers or Accumulators O97
CHAPTER iw
CONDENSATION OR ACCUMULATION OF ELECTRICITY
788. Condensers or accumulators.—There are apparatus for condensing
or accumulating a large quantity of electricity on a comparatively small
surface. The phenomena may be conveniently illustrated by means of
Epenus’s condenser, fig. 744, which consists of two circular brass plates A
and B, mounted on glass legs and provided with pith ball pendulums. Be-
tween these is a support C for a glass plate or other solid insulator, and all
these can be moved along a support and fixed in any position.
a Bi
2 \
If the insulated metal plate B is connected with the prime conductor of
an electrical machine which we will suppose gives when worked a small but
constant supply of electricity, it will acquire the potential of the machine. If
now, breaking connection with the machine, the second plate A is brought
near the first, the divergence of the pith ball on B is less, showing that the
potential has fallen. If the plate A is moved away, the divergence rises to
the original amount, indicating that it has acquired the original potential.
Now the charge’ E of any conductor equals N and since, apart from
778 Frictional Electricity ['788—
losses by leakage, the quantity of electricity on the plate B is not altered in
this series of operations, while the potential is lowered, it follows necessarily
that the capacity of the plate B must have been altered by the presence of
the second one ; so that E= C’V”:
On now connecting the plate B with the prime conductor, while A is near
it the machine must be worked some time before the divergence of the pith
balls indicates that the plate has again acquired the potential of the machine.
il
rT |
Fig. 745
At this point equilibrium is established, and a limit to the charge is attained
which cannot be exceeded, for the potential of B cannot rise above that ot
the machine. The effects described are more marked if the plate A is put
to earth, and if the two are in contact with a solid dielectric such as glass or
ebonite.
It follows from this series of experiments that the presence of the second
plate has enabled the first one to take a greater charge of electricity than
when it is alone. This property is what is called the condensation or accumu-
/ation of electricity, and any arrangement in which one conductor is placed
in connection with a source of electricity separated by an insulator from a
second conductor, in conducting communication with the earth, is called a
condenser, the former plate being the collecting, and the other the condensing
plate.
For the calculation of the charge which a condenser can acquire we refer
to art. 806.
789. Slow discharge and instantaneous discharge.—While the plates
A and B are in contact with the glass (fig. 721), and the connections inter-
rupted, the condenser may be discharged either by a slow or by an instan-
taneous discharge. To do this slowly, the plate B is touched with the finger
and a spark passes. If A be now touched, a spark passes, and so on by
continuing to touch alternately the two plates. The discharge only takes
place slowly ; in very dry air it may require several hours.
An instantaneous discharge may be effected by means of the d¢scharging
rod (fig. 746). This consists of two bent brass rods, terminating in knobs
—790} Limit of the Charge of Condensers 779)
and joined by a hinge. When provided with glass handles, as in fig. 746,
it forms a glass discharging rod. In using this apparatus one of the
knobs is pressed against one plate of the condenser, and the other knob.
brought near the other. At a certain distance the
opposite electricities unite and a spark strikes from
the plate to the knob.
When the condenser is discharged by the chs.
charger no sensation is experienced, even though the
latter be held in the hand; of the two conductors
the electricity chooses the better, and hence the
discharge is effected through the metal, and not
through the body. But if, while one hand is in contact
with one plate, the other touches the second, the
discharge takes place through the breast and arms,
and a considerable shock is felt; and the larger
the surface of the condenser, and the greater the electric density, the more
violent is the shock.
790. Limit of the charge of condensers.—The quantity of electricity
which can be accumulated on each plate is, c@/er7s partbus, proportional to
the potential of the electricity on the conductor, and to the surface of the
plates ; it decreases as the insulating plate is thicker, and it differs with the
specific inductive capacity (769) of the substance. There is, however, a limit
in the case of each condenser beyond which it cannot be charged. The effect
of dielectric polarisation (770) is to put the medium into a state of strain
from which it is always trying to release itself, and which is the equivalent
of the work done in charging a condenser. This is, indeed, the seat of the
electrical energy. It is as if two surfaces were pulled together by elastic
threads which repelled each other laterally. When the strain exceeds a
certain limit, a discharge takes place through the mass of the dielectric,
generally accompanied by light and sound, and with a temporary or perma-
nent rupture of the dielectric according as it is fluid or solid. This is what
occurs when a substance—glass, for instance—is exposed to a continually
increasing weight ; a point is ultimately reached at which the glass gives
way, and the weight at that point is a measure of the resistance to fracture
of the glass. In like manner, the point at which the electrical discharge
takes place is a measure of the electrical strength of the dielectric. This
electrical strength is greater in glass than in air, and in dense than in
rarefied air.
Thus to produce a spark of o°5 cm. in air at the pressures 20, 180, and
685 mm. respectively, the potentials required were 3°23, 12°2, and a6.
We may, following Maxwell, further illustrate this point by the twisting of
a wire : a wire in which a small mechanical force produces a permanent twist
corresponds to the case of the conduction of electricity in a good conductor ;
one which having been twisted, reverts to its former shape when the twisting
couple is removed, is completely elastic, and corresponds to a perfect
insulator with respect to the charge employed. If no permanent twist can
be given to the wire by a force which does not break it, the wire is
brittle. A dielectric such as air, which does not transmit electricity except
by disruptive discharge, may be said 0 be electrically brittle.
Fig. 746
780 Frictional Electricety [791-
791. Fulminating pane. Franklin’s plate.—This is a simple form of
the condenser, and consists of a glass plate fixed ina wooden frame (fig. 747) ;
on each side of the glass, pieces of tinfoil are fastened opposite each other,
leaving a space free
between the edge
and the frame. It
is well to cover this
part of the glass
with an insulating
‘layer of shellac’
varnish. One of
the sheets of tinfoil
is connected with
the ring on the
frame by a strip ot
tinfoil, so that it can
be connected with
the ground = by
means of a chain.
To charge the pane
the insulated side
is connected with
the machine. As the other side communicates with the ground, the two
coatings play exactly the part of the condenser. On both plates there are
accumulated large quantities of contrary electricities.
The pane may be discharged by touching one knob of the discharger
against the lower surface, while the other is brought near the upper coating.
A spark ensues, due to the recombination of the two electricities ; but the
operator experiences no sensation, for the discharge takes place through the
wire. But if the connection between the two coatings be made by touching
them with the hands, a violent shock is felt in the hands and breast, for the
combination then takes place through the body.
792. Leyden jar.—The Leyden jar, so named from the town of Leyden,
where it was invented, is essentially a modified condenser, or fulminating
pane rolled up. Fig. 748
represents a Leyden jar
of the usual French shape
in the process of being
charged. It consists of
a glass jar of any conve-
nient size, the interior of
which is either coated
with tinfoil or filled with
thin leaves of copper, or
with gold-leaf. Up to a
Fig. 748% certain distance from the
neck the outside is coated
with tinfoil. The neck is provided with a cork, through which passes a
brass rod, which terminates at one end in a knob, and communicates with
Fig. 747
—792] Leyden Jar ite
the metal in the interior. The metallic coatings are called respectively the
inner and outer coatings or armatures. Like any other condenser, the jar
is charged by connecting one of the coatings with the ground, and the other
with the source of electricity. When it is held in the hand by the outer
coating, and the knob presented to the positive conductor of the machine,
positive electricity is accumulated on the inner and negative electricity on
the outer coating. The reverse is the case if the jar is held by the knob,
and the outer coating presented to the machine. The positive charge acting
inductively across the dielectric glass decomposes the electricity of the
outer coating, attracting the negative and repelling the positive, which
escapes by the hand to the ground. Thus it will be seen that the action
of the jar is the same as that of the condenser, and all that has been said
of this applies to the jar, substituting the two coatings for the two plates A
and B of fig. 742.
Like any other condenser, the Leyden jar may be discharged either
slowly or instantaneously. For the latter purpose it is held in the hand by
the outside coating (fig. 749), and the two coatings are then connected by
means of the simple discharger. Care must be taken to touch /frs¢ the
external coating with the discharger, otherwise a smart shock will be felt.
To discharge it slowly the jar is placed on an insulated plate, and first the
inner and then the outer coating touched, either with the hand or with a
metallic conductor. A slight spark is seen at each discharge.
ree in ion Ua <<
HH = =
Fig. 749 Fig. 750
Fig. 750 represents a very pretty experiment for illustrating the slow
discharge. ‘The rod terminates ina small bell, @, and the outside coating
is connected with an upright metal support, on which is a similar bell, e.
Between the two bells a light brass ball is suspended by a silk thread. The
jar is then charged in the usual manner and placed on the support m. The
internal coating contains a quantity of free electricity ; the pendulum is.
attracted and immediately repelled, striking against the second bell, to
which it imparts its free electricity. Being now neutralised, it is again
782 Frictional Electricity {792-
attracted by the first bell, and so on for some time, especially if the air be
‘dry, and the jar somewhat large. This is sometimes spoken of as the cov-
vective discharge, since the electricity is carried by moving ponderable
bodies.
793. Leyden jars with movable coatings.—This apparatus (fig. 751) is
used to demonstrate that in the Leyden jar the opposite electricities are not
accumulated on the coatings merely, but are stored up in a state of strain
into which the glass is put, and this state of strain is the mechanical equiva-
lent of the work done in charging the jar. It consists of a slightly
conical glass vessel, B, with movable coatings of zinc or tin, Cand D. ‘These
‘separate pieces placed one in the other, as shown in figure A, form a
complete Leyden jar. After the jar is charged, it is placed on an insu-
Fig. 751
lating cake ; the inner coating is first removed by the hand, or better bya
glass rod, and then the glass vessel. The coatings are found to contain
little or no electricity, and if they are placed on the table they are restored
to the neutral state. Nevertheless, when the jar is put together again, as
represented in the figure at A, a shock may be taken from it almost as strong
as if the coatings had not been removed. It is therefore concluded that the
coatings principally play the part of conductors, distributing the electricity
over the surface of the glass, which thus becomes polarised, and retains this
state even when placed on the table, owing to its imperfect conductivity.
The experiment may be conveniently made without any special form of
apparatus by forming a Leyden jar, of which the inside and outside coatings
are of mercury, charging it ; then, having mixed the two coatings, the
apparatus is put together again, upon which a discharge may be once more
taken.
794. Lichtenberg’s figures.—This experiment well illustrates the oppo-
site electrical conditions of the two coatings of a Leyden jar. Holding a
jar charged with positive electricity by the hand, a series of lines are
drawn with the knob on a cake of resin or vulcanite ; then having placed
the jar on an insulator, it is held by the knob, and another series traced
by means of the outer coating. If now a mixture of red-lead and flour of
sulphur be projected on the cake, the sulphur will attach itself to the positive
lines, and the red lead to the negative lines ; the reason being that in mixing
the powders the sulphur has become negatively electrified, and the red lead
-795] Residual Charge 753
positively. The sulphur will arrange itself in tufts with numerous diverging
branches, while the red lead will take the form of small circular spots, in-
dicating a difference in the two
electricities on the surface of
the resin (809). These figures
form, in short, a very sensitive
electroscope for investigating
the distribution of electricity on
an insulating surface (754).
Fig. 752 represents the ap-
pearance of a plate of resin,
which has been touched by
the knob of a Leyden jar
charged with positive electri-
city, and has then been dusted
with lycopodium powder.
795. Residual charge.—Noi
only do the eléctricities adhere
to the two surfaces of the in-
sulating medium which sepa-
rates them, but they penetrate
to a certain extent into the interior, as is shown by the following experi-
ment :—A condenser is formed of a plate of shellac and movable metal
plates. It is then charged, retained in that state for some time, and after-
wards completely discharged. On removing the metal coatings and ex-
amining both surfaces of the insulator, they show no signs of electricity.
After some time, however, each face exhibits the presence of some electricity
of the same kind as that of the plate with which it was in contact while the
apparatus was charged. This is explained, by some, as a kind of electrical
absorption.
A phenomenon frequently observed in Leyden jars is of the same nature.
When a jar has been completely discharged by bringing the inner and outer
coatings in metallic contact, and is then allowed to stand a short time, it
exhibits a second charge, which is called the electric restdue. ‘The jar may
be again discharged, and a second residue will be ieft, feebler than the first,
and so on, for three or four times. Indeed, with a delicate electroscope a
long succession of such residues may be demonstrated. The residue is
greater the longer the jar has remained charged. The magnitude of the
residue further depends on the amount of the charge, and also on the
degree in which the metal plates are in contact with the insulator. It
varies with the nature of the substance, but there is no residue with
either liquids or gases. Faraday found that with paraffine the residue was
greatest, then with shellac, while with glass and sulphur it was least of all.
Kohlrausch has found that the residue is nearly proportional to the thickness
of the insulator. If successive small charges, alternately positive and nega-
tive, be imparted to the jar, it is found that the residual charges come out in
the reverse order to that in which the original charges go in. This residue
is not to be confounded with that observed when a Leyden jar is discharged
at the greatest striking distance (810).
Fig. 752
784 Frictional Electricity ['795-
According to Riess about 44 of the quantity of electricity in a condenser
is discharged when the coatings are brought within striking distance d, by
means of metal conductors. If the coatings are now brought to a distance
7s @, a second discharge takes place by which +4 of the electricity remaining
is got rid of, and so on always in the same ratio until the effects are imper-
ceptible.
Maxwell proved that a dielectric composed of strata of different insulators
may exhibit the phenomena of the residual charge, even though none of the
substances composing it exhibit it when alone.
A series of superimposed liquid insulators with definite boundaries shows
a residual charge ; this is not the case if they are well mixed by shaking.
From what has been said as to the state of mechanical strain in which
the dielectric of a condenser is thrown when charged with electticity (793), it
is not difficult to account for the phenomenon of the residual charge. An
elastic body, such as a steel plate, which has been
twisted or bent, reverts to its original state when the
force which brought about the deformation ceases to
act, but not at once quite completely. A certain length
of time is required for this alteration to take place, but
the change is promoted by any gentle mechanical
action, such as tapping, which gives the molecules a
certain freedom of motion. Dr. Hopkinson made
an experiment with a Leyden jar which is quite ana-
logous to this. A glass vessel (fig. 754) contains sul-
phuric acid, and init is placed a thinner one, about half
fall of the same liquid. Platinum wires dip in the two liquids, one of which
is in connection with the prime conductor of an electrical machine, while the
other is connected with the earth. The arrangement forms, in short, a con-
denser, the coatings of which are sulphuric acid. When, after being thus
charged, the jar is discharged, a residual discharge may be taken after some
time by again connecting the wires ; if, however, the inner jar be gently
tapped with a piece of wood, the residue makes its appearance much more
rapidly. The same observer draws a parallel between the phenomena of the
residual charge and those of residual magnetism (736).
796. Electric batteries. —The charge which a Leyden jar can take
depends on the extent of the coated surface, and for small thicknesses is
inversely proportional to the thickness of the insulator. Hence, the larger
and thinner the jar the more powerful the charge. But very large jars
are expensive, and liable to break; and when too thin, the accumulated
electricities discharge themselves through the glass, especially if it is
not quite homogeneous. Leyden jars have usually from 4 to 3 square
feet of coated surface. For more powerful charges electric batteries are
used.
An electric battery consists of a series of Leyden jars, whose internal
and external coatings are respectively connected with each other (fig. 754).
They are usually placed in a wooden box lined on the bottom with tinfoil,
which is connected with two metal handles in the sides of the box. The
inner coatings are connected with each other by metal rods, and the battery
is charged by connecting them with the prime conductor, while the outer
~799] Charging by Cascade 785
coatings are connected with the ground by means of a chain fixed to the
handles. A quadrant electrometer (fig. 728) indicates the charge of the bat-
tery. Although a
large quantity of
electricity 1s accu-
mulated in the ap-
paratus, the diver-
gence is not great, —
for itis simply due | ' bc com
to the free electri- me off) 8 t é
city (onsithe (inner a!
coating. Thelarger
and more numerous
they are, the longer
is the time required
to charge the bat-
tery, but the- ef-
fects are so much
the more powerful
(806).
To discharge a
battery, the coatings are connected by means of the discharging rod, the
outside coating being touched first. Care is required, for with large batteries
serious and even fatal accidents may occur.
797. The universal discharger.—This is an almost indispensable appa-
ratus in experiments with the electric battery. On a wooden stand (fig. 755)
are two glass legs, each provided with universal joints, in which movable
brass rods are fitted. Between these legs is a small ivory table, on which is
placed the object under experiment. The two metal knobs being directed
towards the objects, one of them is connected with the outer coating of the
battery, and the moment communication is made between the outer and the
inner coating by means of the glass discharging rod, a violent shock passes
through the object on the table.
798. Charging by cascade.—A series of Leyden jars are placed each
separately on insulating supports. The knob of the first is in connection
with the prime conductor of the machine, and its outer coating joined to the
knob of the second, the outer coating of the second to the knob of the third,
and so on, the outer coating of the last communicating with the ground.
The inner coating of the first receives a charge of positive electricity from
the machine, and the corresponding positive electricity set free by induction
on its outer coating, instead of passing to the ground, gives a positive charge
to the inner coating of the second, which, acting in like manner, develops .a
charge in the third jar, and so on to the last, where the positive electricity
developed by induction on the outer coating passes to the ground. The jars
may be discharged either singly by connecting the inner and outer coatings
of each jar, or simultaneously by connecting the inner coating of the first
with the outer of the last. In this way the quantity of electricity necessary to
charge one Jar is available for charging a series of jars.
799. Measurement of the charge of a battery. Lane’s electrometer.—
3E
| “
‘i a q
Fig. 754
786 Frictional Electricity
[799-
When the outer and inner coatings of a charged Leyden jar are gradually
brought nearer each other, at a certain distance a spontaneous discharge
Opes
ensues. The dis-
tance is called the
striking or spark-
ing atstance. For
the same charge
it is inversely pro-
portional to the
pressure of the air
(790), and, with
the same jar, but
different charges,
Ay
iM
TS
—— _ SSS aaa
directly propor-
tional to the elec-
tric density of that
point of the inner
coating at which
the discharge
takes place. As
the density of any
point of the inner
coating, other
Fig. 755
is proportional to the quantity of electricity in a jar.
things remaining
the same, is pro-
portional to the
entire charge, the
striking distance
The measurement of
the charge of a battery, however, by means of the striking distance, can only
take place when the charge disappears.
By means of Lane’s electrometer, which depends on an application of
this principle, the charge of a jar or battery may be measured. This appa-
ratus, ¢ (fig. 756), consists of an ordinary Leyden jar, near which there is a
Toe UL
Tt NM at aD SR ua
Fig. 756
vertical metallic support. At
= the upper end is a brass rod,
" with a knob at one end, which
can be placed in metallic con-
nection with the outside of the
jar : the rod being movable, the
knob can be kept at a measured
distance from the knob of the
inner coating. Fig. 756 repre-
sents the operation of measuring
the charge of a jar by means
of this apparatus. The jar 4,
whose charge is to be measured, is placed on an insulated stool with
its outer coating in metallic connection with the inner coating of Lane’s jar ¢,
—801] Volta’s Condensing Electroscope 787
the outer coating of which is put to earth ; @ is the conductor of the machine.
When the machine is worked, positive electricity passes into the jar 0 ;
a proportionate quantity of positive electricity is repelled from its outer
coating and forms a charge on the inner coating of the electrometer. When
this has reached a certain limit, it discharges itself between the two
knobs, and as often as such a discharge takes place, the same quantity
of positive electricity will have passed from the machine into the battery ;
hence its charge is proportional to the number of discharges of the
electrometer.
800. Harris’s unit jar—Harris’s unit jar (fig. 757) is an application
of the same principle, and is often convenient for measuring quantities
of electricity. It consists of a small
Leyden phial, 4 inches in length and
# inch in diameter, coated to about
an inch from the end, so as to expose
about 6 inches of coated surface. It is
fixed horizontally on a long insulator,
and the charging rod connected at P
with the conductor of the machine,
while the outer coating is connected
with the jar or battery by the rod ¢ /.
When the charge of electricity in the interior has reached a certain potential
depending on the distance of the two balls m and a, a discharge ensues,
and marks a certain quantity of electricity received as a charge by the
battery, in terms of the charge of the small jar.
801. Volta’s condensing electroscope.—The condensing electroscope
invented by Volta is a modification of the ordinary gold-leaf electroscope
(774). The rod to which the gold-leaves are affixed terminates in a disc
instead of in a knob, and there is another disc of the same size provided with
an insulating glass handle. The discs are covered with a layer of insulating
shellac varnish (fig. 758).
To render very small quantities of electricity perceptible by this apparatus,
one of the plates, which thus becomes the collecting plate, is touched with
the body under examination. The other plate, the condensing plate, is con-
nected with the earth by touching it with the finger. The electricity of
the body, being diffused over the collecting plate, acts inductively through
the varnish on the other plate, attracting the opposite electricity, but
repelling that of like kind. The two electricities thus become accumulated
on the two plates just as in a condenser, but there is no divergence of the
leaves, for the opposite electricities counteract each other. The finger is
now removed, and then the source of electricity, and still there is no diver-
gence ; but if the upper plate is raised ‘fig. 759) the neutralisation ceases,
and the electricity being free to move diffuses itself over the rod and the
leaves, which then diverge widely. The delicacy of this electroscope is in-
creased by adapting to the foot of the apparatus two metal rods, terminating
in knobs ; for these knobs, being excited by induction from the gold-leaves,
react upon them. A still further degree of delicacy is attained if the rods are
replaced by two Bohnenberger’s dry piles (839), one of which presents its
positive and the other its negative pole. Instead of two gold-leaves there
our 2
ste
I=
Fig. 757
788 Frictional Electricety [801 -
is only one; the least trace of electricity causes it to oscillate either to one
side or to the other, and at the same time shows the kind of electricity.
The condensing electroscope is useful in cases where a large quantity of
electricity is available, but at a potential too low to be capable of affecting
the ordinary electroscope. Its capacity is made large by the use of the two
condensing plates, and thus it receives a relatively large charge when brought
into contact with the source. This larger charge must, when connection with
the source is broken and the upper plate is removed, raise the potential of
the electroscope in proportion to its fall in capacity, since Q = VC (762) and
Q is constant. The potential may be thus sufficiently raised to cause a
divergence of the gold-leaves.
802. Quadrant electrometer.—Lord Kelvin devised a very sensitive
form of electrometer by which accurate measurements of potential may be
made. One form of thisinstrument represented in fig. 760 consists of two
pairs of quadrants, AA’ BB’, of thin sheet metal, which together form a flat
cylindrical box, cut into four equal sectors by two diametral sections at
right angles to each other. Each of these quadrants is suspended to
the top of the case by a glass stem, and the alternate pairs are con-
nected with each other by wires. Each of the pairs is also connected with
an insulated binding screw, so that connection can be made with bodies
on the outside.
In the middle of the quadrant is hung, by a bifilar suspension, what is
cailed the zeed/e, which is essentially two quadrants of thin sheet aluminium
—803] Quadrant Electrometer 789
(fig. 761) ; for the sake of lightness, parts are cut out as shown by the dotted
lines in the figure.
If now all the quadrants are in the same electrical condition, the adjust-
ment is made so that the two fibres of the suspension are in the same plane
which is symmetrical with refer-
ence to the space between the
quadrants. If now the two pairs
of quadrants are at different po-
tentials, as when, for instance, they
are connected with the two poles
of a voltaic cell by means of the
binding screws, and if the needle is
charged to a given potential, which
is usually positive and much higher
than that of either pair of quad-
rants, one end of the needle will be
repelled by the pair of quadrants
which are electrified like itself, and
will be attracted by the other pair.
Fig. 760 Fig. 761
It will thus be subject to the action of a couple tending to set it obliquely to
the slit. In order to render the slightest motion of the needle visible, a
small silver concave mirror with a radius of about a metre is fixed above
it. The light of a petroleum lamp, not represented in the figure, strikes
against this, and is reflected as a spot on a horizontal scale. Any deflection
of the needle, either on one side or the other, is indicated by the motion of
the spot of light on the scale (534).
In order to keep the potential of the needle as constant as possible, it is
connected with the inner surface of a Leyden jar, sometimes tormed by a glass
vessel forming part of the outer case of the electrometer. In the more com-
plete forms of instrument there is a small electrical machine (called the
veplenisher) whereby the potential of the jar and needle can be brought to
any required value, and also a subsidiary electrometer (the gage) which
shows when the right value is attained.
803. Thomson’s absolute electrometer.—Another class of electrometers,
also invented by Lord Kelvin, give a direct measure of electrical constants
790 Frictional Electricety [803-
in absolute measure. Fig. 762 represents a modified form of the electro-
meter for class experiments.
Two plane metal discs A and B, about 1o cm. in diameter, are kept at a
distance from each other, which is small in proportion to their diameters,
but which can be very accurately measured. Out of the centre of the upper
one is cut a disc ¢; this is suspended by insulating threads from one end of
the arm a é of a balance, at the other end of which is a counterpoise, or a
scalepan 7. At the end of the arm is a fork, across which is stretched a
fine wire ; when the disc is exactly in the plane of the circular band or ring
which surrounds it, and which is called the guard ring, this fine wire is.
exactly across the interval between two marks in the upright, and its posi-
tion can be accurately determined by means of the lens C. The disc and the
guard ring are kept at a constant potential, being connected by a wire with
a constant source of electri-
city, while the other can be
kept at any potential or put
to earth.
Suppose now that the
whole system is at the same
potential, and that the disc
is exactly balanced so as to
be in the plane of the guard
ring. If now A is electrified
to a given potential, while
the plate B is connected with
the earth, then the body
charged with electricity of
higher potential—that is, the
disc—will be urged towards
the body of lower potential, the fixed plate ; and in order to retain it exactly
in the plane of the guard ring the force applied at the other end of the
lever must be increased. This may be done by altering the distance of the
counterpoise, or by adding weights to a scalepan, and the additional weight
thus applied is a measure of the attractive force.
This may be proved as follows.
Let A’OA (fig. 7622) be a plane con-
ducting surface of unlimited extent
electrified to surface density o, and
let P be a point in the neighbour-
hood. The charge on a small area
a,at A, is ao, and the force which
this exerts on a unit charge at P is
A’ One: A ao|AP?in the direction AP. Simi-
Fig. 7624 larly the force at P due to an equal
area at A’, situated symmetrically
with respect to P, is ac/A’P*? along A’P. Resolving these two forces into
components normal to the surface and parallel thereto, it is easy to see
that the latter components are equal and opposite and so cancel each other ;
consequently, the effective component of the force at P, due to each small
Fig. 762
—803] Thomson's Absolute Electrometer 791
part of the surface, is the component parallel to OP. For the small area
at A, this component is
ig LOM Weare
HA =i £OSTA ION
AP? AP Ap?
But @ OP/AP, or a cos APO, is the projection of the area a on a sphere
through A with centre P, and this projected area divided by the square of
the radius AP is the measure of the solid angle which the area a subtends
at P. If we put » for this solid angle we have, for the normal component,
oy OE eter
Ap2 AP
Now the resultant force at P due to the whole charged surface may be
regarded as the sum of the normal (or effective) forces due to all the small
parts of which the surface may be considered as made up ; it may therefore
be written
(@,+@,+@,+ ....)7=20.0;3
that is to say, the resultant force is obtained by multiplying the total solid
angle which the surface subtends at P by the surface-density of the charge.
For a surface extending in all directions to a distance which is great in com-
parison with OP, the total solid angle is the same as that which a hemisphere
subtends at its centre, or 27; hence we get the result that the intensity of
the force which any plane surface, uniformly electrified to density o, exerts
at a point, whose shortest distance from the surface is small in comparison
with its distance from any part of the boundary, is 270, or the force which
acts upon a charge Q in the neighbourhood of the surface is 2noQ, and is a
repulsion if « and Q are of the same sign and an attraction if they are of
opposite signs.
In the present case, o being the surface-density of the plate A and disc ¢,
the charge of the latter is So, if S is the area of the disc. Again the lower,
earth-connected plate, B, becomes electrified to density —a, and consequently
the disc is attracted towards the plate B with a force
= 2707S.
This force can be measured in dynes as explained above (p. 790), and
from the result we have to deduce the difference of potentials between the
two discs A and B. Calling the potential of the former V, that of the latter
V’, and d@ the distance between the plates, we may write,
V-We=/fd
if f stands for the force which would be exerted upon a unit of positive
electricity anywhere between the plates. In words, this equation is a state-
ment that the difference of potentials is equal to the work that must be done
against electric force to carry a unit of positive electricity from plate B to
plate A 760). The force / is made up of a repulsion 270 due to the plate
A, and an attraction 270 due to the plate B, or, altogether, f= 470. Conse-
quently
. Vie aro:
792 Frictional Electricity [803—
but, as has been already proved, 2707S =F, oro = , ane
27
Hence V-VWetgnd JE = a, /BmE.
275 5
If the disc ¢ is circular and its radius is a, we have S=7a’, and the
difference of potentials is given by the very simple formula
ViW= 2, /8r.
It is also clear that the experiment may be modified by making F constant
and the distance variable. By means of micrometric arrangements the
distance of the plates may be varied and measured with very great accuracy.
This principle is applied in a portable form of this electrometer.
804. Potential and capacity of a condenser.— These may be most con-
veniently investigated by considering the case of a spherical jar. Let us
suppose A (fig. 763) to represent an isolated metal sphere of radius R, and
let us consider it placed in conducting communication with a source of, say,
positive electricity, which is supposed to be at a constant potential V.
Then its potential V is zs its charge g= VR, and the ratio of charge to po-
tential, or the capacity of the sphere, is R.
Suppose now this sphere to be surrounded by a concentric conducting
shell or envelope B, which is in connection with the earth, then from the in-
ductive action set up, there will now be two electrical layers—one the sphere
A, and the other on the inner surface of the sphere B. These will have no
action on any external point, which is
| only possible provided the charges are equal
and contrary. If+Q is the charge on the
inner, then — Q is that on the outer sphere
(768).
' The sphere A, being still connected with
the source, has still the potential V, but its
present charge Q. is greater than the charge
g which produced the same potential when
it was isolated. In the present case, the
potential is V= _ i where the first term
Fig. 763 on the right is the potential at the centre
due to the charge Q of the sphere A taken
by itself, and the second term is the potential at the centre due to the charge
— Q of the surrounding shell. The charge Q is consequently = V ie
R’—-R
F 2
. = te es , if we write Z for R’—R the thick-
ness of the air-space between the two spherical surfaces.
If we multiply numerator and denominator of this expression by 4m, the
, ~
ie = 7 when S=47RR’
7 7
and the capacity is now
expression for the capacity takes the form C=
—805] Effects of the Electric Discharge 793
is the geometric mean of the areas of the two charged concentric surfaces.
If the radii are nearly equal, that is ¢ small, this mean area is nearly
enough equal to the area of either sphere.
If instead of air there be a solid or liquid dielectric, whose specific induc-
tive capacity is x, the formula becomes Q= NEE If the dielectric be
partly air and partly some other material, such as glass, then if the thick-
ee DOE oy are expression @ is sometimes
i ( Mal x) K
written Z’, and represents the thickness of the layer of air equivalent to it in
specific inductive capacity. It is also called the reduced thickness.
Thus, suppose a sphere of radius R=1Io cm., and this is surrounded by
an earth-connected metal shell of radius R’ = 10°2 cm., then the thickness of
the dielectric (assumed to be air) is 0°2, and the oe: of this condenser is
510 or 51 times as great as that of the ene sphere R.
The ratio of the capacities in the two cases is called the condensing force
of the given condenser.
The formula obtained above for the capacity of a spherical condenser
ness of this latter is 6, Q=
with spheres of nearly equal radius, namely, ae applies very nearly indeed
vis
to any condenser formed, like a Leyden jar, of a thin uniform layer ofa di-
electric between two parallel conducting surfaces.
If R’ is so great that the value of R in the denominator may be disre-
garded, we get C=R, which is the expression for the capacity of an isolated
sphere (762) ; such a sphere may indeed be regarded as a condenser, in
which the layer of air, between it and the sides of the room, represents the
dielectric.
When z identical Leyden jars are joined in surface, we have a condenser
whose capacity is equal to the -fold capacity of a single jar. If these jars
are joined in cascade, the capacity of the system is that of a single jar, the
dielectric of which is 7 times as thick.
THE ELECTRIC DISCHARGE
805. Effects of the electric discharge.—The recombination of the two
electricities which constitutes the electrical discharge may be either con-
tinuous or sudden: conéimuous, or of the nature of a current, as when the
two conductors of a Holtz’s machine are joined by a chain or a wire ; and
sudden or disruptive, as when the opposite electricities accumulate on the
surface of two adjacent conductors, till their mutual attraction is strong
enough to overcome the intervening resistances, whatever they may be. But
the difference between a sudden and a continuous discharge is one of degree,
and not of kind, for there is no such thing as an absolute non-conductor, and
the very best conductors, the metals, offer an appreciable resistance to the
passage of electricity. Still the difference at the two extremes of the scale
is sufficiently great to give rise to a wide range of phenomena.
Riess showed that the discharge of a battery does not consist in a
794. Frictional Electricity [805-
simple union of the positive with the negative electricity, but that it consists
of a series of successive partial discharges. The direction of the discharge
depends mainly on the length and nature of the circuit.
Feddersen examined the discharge of a Leyden jar by the arrangement
represented in fig. 764, in which the spark of the Leyden jar passes between
Fig. 764
the knobs a and 4. On the axis xx, which by means of clockwork is rotated
at a known and uniform rate, are two long focus concave mirrors, d and c ; to
the axis is also attached a brass strip, the ends of which, / and g, just touch
the bare ends of the insulated wires at the moment the spark passes between
a@ and 6; at this instant the spark is in the same vertical plane as the
principal axis of the mirror. The image of the spark is reflected on the
ground glass plate %.
Observed in this manner the spark is seen as a narrow band of light, the
length of which varied with the duration of the discharge. The duration was
found to increase with the striking distance, and with the number of jars.
When the resistance through which the circuit took place was small, it
was found that the discharge was an oscillatory one, consisting of a series of
separate discharges in alternating directions ; the image was traversed by a
number of dark lines. With a greater resistance the discharge was a single
continuous one, and its image was that of a continuous band of light. With
very great resistance the discharge was an zzfermittent one, and consisted
of sparks following each other at irregular intervals.
These oscillatory discharges may be illustrated by means of a simple
hydrostatical experiment. Suppose that in the U-tube (fig. 765) is a valve, S,
by which the two tubes are separated, and that water is
poured in one so that it is at the height +L above the
level OO, and in the other in the corresponding distance
—L’ below the level. When the valve is suddenly opened,
the water passes through, and only comes to rest in the
position OO after several oscillations about this level. Sup-
pose the valve to be suddenly closed during the oscillation,
it may easily happen that the water is higher in that limb
in which it was previously lower. This would represent
the case observed by Oettingen with the electrical residues, who found them
to be sometimes negative and sometimes positive.
-806] Work done by the Discharge of a Leyden Jar 795
Again, if the valve is only slightly opened so that great resistance is
offered, the water slowly sinks to its level, the discharge is continuous, and
there are no oscillations ; this corresponds to the case in which the elec-
trical resistance is very great.
We may further compare the dielectric in a state of strain, like the glass
of a charged Leyden jar, to a steel band, clamped at one end; if the free
end is pulled aside, the plate is in a state of strain, and when this strain is
removed the plate comes to rest after making a series of oscillations. To
prevent these oscillations the plate must be exposed to a great resistance, by
being placed, for instance, in a viscous liquid; in like manner, as we have
seen, by offering a great resistance to the electrical discharge, it becomes
continuous. The rate at which a vibrating steel plate or a stretched string
comes to rest will depend on its mass and on its inertia. In like manner
the period of oscillation of an electrical discharge depends on a certain
coefficient of self-induction (932), which represents the electro-magnetic
inertia of the medium about the circuit.
The oscillatory nature of the discharge has been confirmed by the observa-
tions of Paalzow on the luminous phenomena seen in highly rarefied gases
when it takes place in them, as well as by the manner in which a magnet
affects the phenomena. It is also proved by the simultaneous transport of
matter between two different electrodes (808). Von Helmholtz had already
inferred the necessity of such an oscillating motion from the laws of the con-
servation of energy, and Lord Kelvin and Kirchhoff deduced the conditions
under which it occurs.
806. Work done by the discharge of a Leyden jar.—The work required
2 2
to charge a Leyden jar is We" Cee a => a V’ ; that is, is pro-
portional to the surface and to the square of the potential, and is inversely
as the reduced thickness of the insulator. From the principle of the con-
servation of energy, this stored-up energy reappears when the jar is dis-
charged. It shows itself partly in the form of a spark, partly in the heating
effect of the whole system of conductors through which the discharge takes
place. When the armatures are connected by a thick short wire, the spark
is strong and the heating effect small; if, on the contrary, the jar is dis-
charged through a long fine wire, this becomes more heated, but the spark
is weaker.
If a series of identical jars are each separately charged from the same
source, they will each acquire the same potential, which will not be altered
if all the jars are connected by their inner and outer coatings respectively.
The total charge will be the same as if the battery had been charged directly
from the source, and its energy will be W=43Vzg =4VQ ; that is, the energy
of a battery of 7 equal jars is the same as that of a single jar of the same
thickness but of z times the surface.
Let us consider two similar Leyden jars having respectively the capaci-
ties c and c’; let one of them be charged to potential V, and let the other
remain uncharged. Suppose now that the inner and outer coatings of
the jars are respectively connected with each other. Then the energy of the
Ci?
charged jar alone is W=4-—< , and when it is connected with the other,
@
796 ) Frictional Electricity [806—
the original charge will spread itself over the two, so that the energy of the
2
charge in the two jars is W’= mes Hence W : W’=c+c’:c; and there-
fore, since c+c’ is always greater than c, there must be a loss of energy. In
point of fact, when a charged jar is connected with an uncharged one, a
spark passes, the connecting wire is heated, which together are the equivalent
of this loss of energy. It follows, further, that when two jars at different
potentials are united there is always a loss of energy.
If a series of # similar jars are joined in surface, and a given charge
of electricity is imparted to them, the energy is inversely as the number
of jars; but, when charged from a source of constant potential, the energy
is proportional to the number of jars. If, however, the jars are arranged
in cascade, then for a given charge the energy is z times that of a single jar,
while for a given potential it is 7 times smaller. It is sometimes con-
venient to arrange the jars in a combination of the two systems.
807. Physiological effects.—The shock from the electrical machine has
been already noticed (792). The shock taken from a charged Leyden jar
by grasping the outer coating with one hand and touching the inner with
the other is much more violent, and has a peculiar character. With a
small jar the shock is felt in the elbow ; with a jar of about a quart capacity
it is felt across the chest, and with jars of still larger dimensions in the
stomach.
A shock may be given to a large number of persons simultaneously by
means of the Leyden jar. For this purpose they must form a chain by join-
ing hands. If, then, the first touches the outside coating of a charged jar,
while the last at the same time touches the knob, all receive a simultaneous
shock, the intensity of which depends on the charge, and on the number of
persons receiving it. Those in the centre of the chain are found to receive
a less violent shock than those near the extremities.
With large Leyder jars and batteries the shock is sometimes very dan-
gerous. Priestley killed rats with batteries of 7 square feet coated surface,
and cats with a battery of about 4} square yards coating.
Experience shows that the physiological effect varies with the electrical
energy ; thus a discharge from an ordinary electrical machine which gives
a spark of nearly a foot may be taken without danger, while one of a few
millimetres from a battery of large capacity could not be borne. The
duration of the discharge has also an influence ; a battery which gives a
violent shock when discharged in ordinary conditions, gives but a feeble
one when discharged through a moist string, which only delays the rapidity
of the discharge.
808. Luminous effects. —The recombination of two electricities of high
potential (76c) is always accompanied bya disengagement of light, as is seen
when sparks are taken from a machine, or when a Leyden jar is discharged.
The better the conductors on which the electricities are accumulated, the
more brilliant is the spark ; its colour varies not only with the nature of the
bodies, but also with the nature of the surrounding medium and with the
pressure. The spark between two charcoal points is yellow, between two
balls of silvered copper it is green, between knobs of wood or ivory it is
crimson. In air at the ordinary pressure the electric spark is white
-809] Spark and Brush Discharge TOF
and brilliant; in rarefied air it is reddish; and in vacuo it is violet.
In oxygen, as in air, the spark is white; it is reddish in hydrogen, and
green in the vapour of mercury ; in carbonic acid it is also green, while
in nitrogen it is blue or purple, and accompanied by a peculiar sound.
In general, the higher the potential the greater is the lustre of the spark.
When these sparks are examined by the spectroscope (588) they show the
lines characteristic of the metals between which the spark passes, and also
of the gas in which it takes place. If the knobs are of different metals
the lines of both are seen. Part of the energy is accordingly consumed in
detaching and volatilising the metal particles on the two electrodes ; when
a powerful discharge takes place between a knob of gold and one of silver,
some of the latter metal is found on the gold knob, while some gold also is:
found on the silver knob. This is a direct proof that the discharge is an
oscillatory one (805).
809. Spark and brush discharge.—The shapes which luminous electric
phenomena assume may be classed under two heads—the sfarf and the
brush. The brush forms when the electricity leaves the conductor in a
continuous flow; the spark, when the discharge is discontinuous. The
formation of one or the other depends on the nature of the conductor and
of the conductors in its vicinity ; and small alterations in the position of the
surrounding conductors transform the one into the other.
The spark which at short distances appears straight, at longer distances.
has a zigzag shape with diverging branches. Its length depends on the
density at the part of the conductor from which it is taken ; and to obtain
the longest sparks the electricity must be of as high a density as possible, but
not so high as to discharge spontaneously. With long sparks the luminosity
is different in different parts of the spark.
The brush derives its name from’ the radiating divergent arrange-
ment of the light, and presents the appearance of a luminous cone, whose
apex touches the conductor. Its size and colour differ with the nature and
form of the conductor ; it is accompanied by a peculiar hissing noise, very
different from the sharp crack of the spark. Its luminosity is far less than
that of the spark ; for while the latter can easily be seen by daylight, the
former is only visible in a darkened room. The brush discharge may be
obtained by placing on the conductor a wire filed round at the end, or,
with a powerful machine, by placing a small bullet on the conductor. The
brush from a negative conductor is less than from a positive conductor ;
the cause of this difference has not been satisfactorily made out, but it may
originate in the fact, which Faraday has observed, that negative electricity
discharges into the air at a somewhat lower density than positive electricity ;
so that a negatively charged knob sooner attains that density at which
spontaneous discharge takes place, than does a positively charged one, and
therefore discharges the electricity at smaller intervals and in less quantities.
When electricity, in virtue of its high density and consequently high
electrostatic pressure, issues from a conductor, no other conductor being
near, the discharge takes place without noise, and at the places at which it
appears there is a pale blue luminosity called the electrical glow, or
on points a star-like centre of light. It is seen in the dark by placing
a point on the conductor of the machine. It may be regarded as a very
short brush.
798 Frictional Electricity [810—
810. Striking distance.—Sir W. Harris by means of his unit jar, and Riess
by independent researches, found that for small distances the striking distance
is directly proportional
to the quantity of
electricity, and in-
versely proportional to
the coated surface ; in
other words, it is pro-
portional to the po-
tential.” For thise/ex-
periments Riess used
the spark micrometer,
which consists of two
_metal knobs, Aand B
(fig. 9766). prowaded
with binding screws,
aand 6, and on insu-
lating supports, the
distance of which from each other could be varied by a micrometric screw.
The striking distance varies slightly with the shape of the electrodes ;
thus for the same distance the difference of potential required is slightly
greater for two spheres than for two plates.
The high temperature and short duration of the spark produces a sudden
expansion of the air through which it passes, and a compression of the
surrounding air. Hence a wave of compression starts from the path of the
spark which produces the sound.
For greater distances the difference of potential increases less rapidly
than the distance, and the greater the distance the less is the rate of increase ;
this is seen from the following tables: In the experiments the discharging
knots were 2°2 cm. in diameter.
Distance | Volts | Distance | Volts
cm. cm.
orl | 5,490 5°0 | 94,800
O'5 | 26,7 30 70 | 107,700
me | 48,600 ifexe) 119,100
2°0 | 64,800 | 12°0 | 124,200
3°0 76,800 | 15°0 | 127,800
The striking distance in air is virtually the same for the spark proper as
for the brush.
The influence of pressure on the electric discharge may be studied by
means of the electric egg. This consists of an ellipsoidal glass vessel (fig.
767) with metal caps at each end. The lower cap is provided with a stop-
cock, so that it can be screwed into an air-pump, and also into a heavy
metallic foot. The upper metal rod moves up and down ina leather stuffing-
box; the lower one is fixed to the cap. A vacuum having been made,
the stopcock is turned, and the vessel screwed into its foot ; the upper
part is then connected with a powerful electrical machine, and the lower
-812] Fleating Effects 799
one with the ground. On working the machine, the globe becomes filled
with a feeble violet light continuous from one end to the other, and resulting
from the recomposition of the positive electricity of
the upper cap with the negative of the lower. If the FF
air is gradually allowed to enter by opening the stop- |
cock, the light now appears white and brilliant, and is :
only seen as an ordinary intermittent spark.
If by means of such an apparatus the pressure of
the air is gradually increased, the striking distance is
diminished, and with a pressure of 50 atmospheres the
discharge of even a powerful machine is stopped.
Some beautiful effects of the electric discharge are
obtained by means of Geissler’s tubes (590), which
will be noticed under Dynamical Electricity.
811. Luminous tube and square.—The /umiznous
tube (fig. 768) is a glass tube about a yard long, round
which are arranged in a spiral form a series of
lozenge-shaped pieces of tinfoil, between which are
very short intervals. There is a brass cap with hooks
at each end, in which the spiral terminates. If one
end be presented to a machine in action, while the
other is held in the hand, sparks appear simultane-
ously at each interval, and produce a brilliant lumi-
nous appearance, especially in the dark.
The luminous pane is constructed on the same
principle, and consists of a square of ordinary glass, on which is fastened
a narrow Strip of tinfoil folded parallel to itself for a great number of times.
Spaces are cut out of this strip so as to represent any figure, a portico for
example. The pane being fixed between two insulating supports, the upper
extremity of the strip is connected with the electrical machine, and the
Fig. 768
lower part with the ground. When the machine is in operation, a spark
appears at each interval, and reproduces in luminous flashes the object repre-
sented on the glass.
812. Heating effects.—Besides being luminous, the electric spark is a
source of great heat. When it passes through inflammable liquids, as ether
or alcohol, it inflames them. An arrangement for effecting this is repre-
sented in fig. 769. It is a small glass cup through the bottom of which
passes a metal rod, terminating in a knob and fixed to a metal foot. A
£00 Frictional Electricity [812—
quantity of liquid sufficient to cover the knob is placed in the vessel. The
outer coating of the jar having been connected with the foot by means of a
chain, the spark which passes when the
two knobs are brought near each other
inflames the liquid. With ether the
experiment succeeds very well, but
alcohol requires to be first warmed.
Coal gas may also be ignited by
means of the electric spark. A person
standing on an insulated stool places
one hand on the conductor of amachine
which is then worked, while he presents
ibis: the other to the jet of gas issuing from
S25 = =a a metallic burner. The spark which
— — 5 passes ignites the gas. When a battery
AADIGAESESCOTASENATIOETGSAUNASAUANTSTONN PETE SOUOTSOTONUUNUAGTOET COUT UTA TNTOSOUT TPP TTTE TUTTE is discharged through an iron or steel
Fig. 769 wire, the latter becomes heated, and is
even made incandescent or melted if the discharge is very powerful.
If a jar is discharged, and the discharge does no other work, then the
whole of the energy of the charge (804) appears in the form of heat ; and if
the expression for the energy of a condenser $ = (806) be divided by Joule’s
equivalent (509), we have H =3 ey as the expression for the total heatin
5 ’ 2 jc p §
due to any charge.
The laws of this heating effect were investigated independently by Harris
and by Riess by
means of the e/ec-
tric thermometer.
In its later forms
as modified by
Riess, this consists
of a glass bulb (fig.
770), closed by a
stopper, ¢c, and at-
tached toacapillary
tube which is bent
=. twice, and termi-
= nates in an enlarge-
ment ; this contains
coloured liquid,
The whole appa-
ratus is fixed on a
hinged support, A,
which works on the base B, so that it can be inclined and fixed at any given
angle. The diameter of the tube being very small compared with that of
the enlargement, a considerable displacement of the liquid may take place
along the scale without any material alteration in pressure. Before making
the experiment the stopper c is opened so as to equalise the pressure. Be-
~813] Magnetic Effects Sol
tween the binding screws a and @a fine platinum wire is stretched. When
a Leyden jar is discharged through the wire it becomes heated, expands
the air in the bulb, and the expansion is indicated by the motion of the liquid
along the graduated stem of the thermometer. In this way it was found
that the heat in the wire is proportional to the square of the quantity of
electricity divided by the surface—a result which follows from the formula
already g riven (806). Riess also found that wzth the same charge, but with
wires of different dimensions, the rise of temperature ts inversely as the
fourth power of the diameter. Thus, compared with a given wire as unity,
the 7zse oy temperature in a wire of double or treble the diameter would
be 4; or 4, as small; but as the masses of these wires are four and nine
times as Lee the PER produced would be respectively } and 4 as a as
in a wire of unit thickness.
If a jar charged to a given potential is discharged through the evel
thermometer, the discharge will take place at a certain smalgnte distance, and
a certain Gepression will be produced which is a measure of the heating
effect int he thermometer. If now a card is interposed in the path of the
discharge, a certain proportion of its energy will be expended in the
mechanical perforation of the card, and the proportion in the thermometer
will beless. Thus Riess found that that charge which, when passed through
air, produced a depression of 15°9, when passed in addition through one
card, two cards, and a plate of mica, produced depressions of 11°7, 80, and
6°8 respectively ; showing that the heating effect was less according as
more of the energy of the discharge was used for other purposes.
When an electric discharge is sent through gunpowder placed on the
table of a Henley’s discharger, it is not ignited, but is projected in all
directions. But if a wet string is interposed in the circuit, a spark passes
which ignites the powder. This arises from the retardation which electricity
experiences in traversing a semi-conductor, such as a wet string ; for the
heating effect is proportional to the duration of the discharge.
When a charge is passed through sugar, heavy spar, fluor-spar, and other
substances, they afterwards become phosphorescent in the dark. Eggs,
fruit, &c., may be made luminous in the dark in this way.
When a battery is discharged through a gold leaf pressed between two
glass plates or between two silk ribbons, the gold is volatilised in a violet
powder which is finely divided gold. In this way what are called electric
portraits are obtained.
Siemens showed that when a jar is charged and discharged several
times in succession the glass becomes heated. Hence during the discharge
there must be movements of the molecules of the glass, as Faraday sup-
posed (770) ; we have here, probably, something analogous to the heating
produced in iron when it is rapidly magnetised and demagnetised.
813. Magnetic effects.—By the discharge of a large Leyden jar or
battery, a steel wire may be magnetised if it is laid at right angles to a con-
ducting wire through which the discharge is effected, either in contact with
the wire or at some distance. And even a steel rod or needle may be
magnetised by placing it inside a spiral of insulated copper wire, A (fig. 771),
and passing one or more discharges through it. The polarity depends on the
direction in which the electricity enters the coil and the way in which the
3F
802 Frictional Electricity [813-
wire is coiled, Thus if the jar is charged in the inside with positive elec-
tricity, and the direction in which the wire is coiled is that in which the
hands of a watch move, that end at which the
positive electricity enters will be a south pole.
It is, however, frequently observed that the
magnetism is abnormal, and that for the same
charge of the jar the north pole is first at one
end and then at the other. This is to be re-
ferred to the oscillatory character of the dis-
charge (805), the position of the poles corre-
sponding to that of the last oscillation ; uniform
results are obtained when a wet string is in-
Fig. 771 cluded in the circuit.
To effect a deflection of the magnetic needle by the electric current pro-
duced by frictional electricity is more difficult. It may be accomplished
by'making use of a galvanometer consisting of 400 or 500 turns of fine silk-
covered wire, which is further insulated by being coated with shellac varnish
and by separating the layers by means of oiled silk. When the prime con-
ductor of a machine in
action is connected with one
end of the galvanometer
wire, and the other with the
ground, a deflection of the
needle is produced.
814. Mechanical ef-
fects.—The mechanical ef-
fects are the violent lacera-
tions, fractures, and sudden
expansions which ensue
when a powerful discharge
is passed through a badly
conducting substance.
Glass is perforated, wood
and stones are fractured,
and gases and liquids are
Pn ii oT TTT = violently disturbed. The
Ah =I /
= mechanical effects of the
UTATT ANT :
ITU TA UMMA electric spark may be de-
Fig. 772 monstrated by a variety of
experiments.
Fig. 772 represents an arrangement for perforating a piece of glass or
card. It consists of two glass columns, with a horizontal cross-piece, in
which is a pointed conductor, B. The piece of glass, A, where the point
touches it, is surrounded by shellac or oil, to prevent dispersion of electricity
over the surface ; it is placed on an insulating glass support, in which is
placed a second conductor, terminating also in a point, which is connected
with the outside of the battery, while the knob of the inner coating is brought
near the knob of B. When the discharge passes between the two conductors
the glass is perforated. The experiment succeeds with a single jar only
—814] Mechanical Effects 803
when the glass is very thin ; otherwise a battery must be used. To perforate
a glass plate 1°5 cm. thick, a striking distance of 16 cm. is required.
When the discharge takes place through a piece of cardboard between
two points exactly opposite each other, the line of perforation is quite straight ;
but if not exactly opposite, a slight hole is seen near the negative point.
This phenomenon, which is known as Lullin’s experiment, is probably
connected with the fact that negative electricity discharges into air more
readily than positive (809) ; in other words, that positive electricity must
be raised to a higher potential in order to discharge, which is held to favour
the view that there is a specific difference between the two kinds of
electricity.
The perturbation and sudden expansion which the discharge produces
may be illustrated by means of what is known as K7zunersley’s thermometer.
This consists of two glass tubes (fig. 773), which fit into metallic caps and
communicate with each other. At the top of the large tube is a rod termi-
nating in a knob, and moving in a stuffing-box, and at the bottom there is
a similar rod with a knob. The apparatus contains water up to the level of
the lower knob. When the electric discharge passes between the two knobs,
the water is driven out of the larger tube and rises to a slight extent in the
small one. The level is immediately re-established, and therefore the
phenomenon cannot be due to a rise of temperature.
If the upper knob inside a Kinnersley’s thermometer be replaced by a
point, and the outside knob is connected with the prime conductor of a
machine at work, the electricity discharges itself in the form of a brush, and
a permanent displacement of the
liquid in the stem shows that this
is due to the heating effect of the
brush discharge.
For the production of mechani-
cal effects the universal discharger
(fide 773 mise OF great’ service. A
piece of wood, for instance, placed
on the table between the two con-
‘ductors, is split when the discharge
passes.
When the discharge is passed
through a thin wire this is kinked
and bent, and the effects are the
more marked as the discharges are
stronger and more frequent. At the
same time, with certain metals, a
fine dust is given off due to a purely
mechanical action.
A Leyden jar when charged
undergoes a true expansion which
isnot that due to heat. Electrical
polarisation produces characteristic deformations which are known as
electrostriction. This was most completely investigated by Quincke, one
of whose experiments*is represented in fig. 774. It consists of a glass
ZF 2
804 frictional Electricity [814—
bulb A about 2 inches in diameter at the end of a narrow capillary tube
K, on an enlargement in which a platinum wire, B,
is fused. The bulb and a portion of the stem con-
tains a conducting liquid, such as water or sulphuric
acid, and it is placed in a vessel of ice-cold water, K,
which can be connected with the earth by a conduct-
ing wire, G. If now this condenser is charged by con-
necting the wire B with an electrical machine, while:
G is in connection with the earth, there is a distinct
depression of the liquid in the tube. When the jar
is discharged the liquid resumes its original level.
Hence this cannot have been due to heat, apart from
the fact that the temperature was kept constant ; nor
is it due to a contraction of the thickness of the glass..
The same results are obtained if the outer coating is.
insulated by resting it on shellac, T, which in turn is
insulated by resting ona slab of india-rubber, the inner
coating being put to earth. Similar effects are observed
with solid condensers of other materials, and also with liquids.
815. Chemical effects.—When two gases which act on each other are
mixed in the proportions in which they combine, a single spark is often:
sufficient to determine their combination ; but when either of them is in
great excess, a succession of sparks is necessary. Priestley found that
when a series of electric sparks was passed through moist air, its volume
diminished, and blue litmus introduced into the vessel was reddened. This,
Cavendish discovered, was due to the formation of nitric acid.
Several compound gases are decomposed by the continued action of the
electric spark.
With ethylene,,
sulphuretted hy-
drogen, and
ammonia, the
decomposition is:
complete; while
carbonic acid is
partially decom-
posed into oxy-
gen and car-
bonic oxide.
The electric discharge also by suitable means can feebly decompose water,
oxides, and salts; but, though the same in kind, the chemical effects of
statical electricity are by no means so powerful and varied as those of
dynamical electricity. The chemical action of the spark is easily demon-
strated by means of a solution of potassium iodide. A small lozenge-
shaped piece of filtering paper, impregnated with this solution, is placed
on a glass plate, and one corner connected with the ground. When a few
sparks from a conductor charged with positive electricity are taken at the
other corner, brown spots are produced, due to the separation of iodine.
The electric pistol is a small apparatus which serves to demonstrate the
chemical effects of the spark. It consists of a brass vessel (fig. 775), in
-816] Chemical Effects 805
which is introduced a detonating mixture of two volumes of hydrogen and
one of oxygen, and which is then closed with a cork. In a tubulure in the
side there is a glass tube, in which fits a metal rod, terminated by the knobs
Aand B_ The vessel is held as represented in fig. 776, and brought near
the machine. The knob A becomes negatively, and B positively, electrified
by induction from the machine, and a spark passes between the conductor
and A. Another spark passes at the same time between the knob B and the
side ; this determines the combination of the gases, which is accompanied by
a great disengagement of heat, and the vapour of water formed acquires such
an expansive force that the cork is projected with a report like that of a pistol.
Among the chemical effects must be enumerated the formation of ozone,
which is recognised by its peculiar odour, and by certain chemical properties.
The odour is perceived when electricity
issues from a conductor into the air .~~-——7 a
through a series of points. It has been
established that ozone is an allotropic
modification of oxygen.
With these effects may be associated Z
a certain class of phenomena observed ~ lat
when gases are made to act as the dielec- ai(]| }
tric in a charged Leyden jar. An appa-
ratus by which this is effected is repre- ,
sented in fig. 777; it is a modification of
one invented by Siemens. It consists
of a glass cylinder, E, containing dilute
sulphuric acid ; ais a glass tube closed a1)
at the bottom, and also containing sul-
phuric acid, in an enlargement of which
at the top the inner tube ec fits. Thereis
a tube, 7, by which gas enters, and one, a’,
by which it emerges. When the acids in
E and é are respectively connected with
the two combs of a Holtz machine, or
with the two terminals of a Ruhmkorff’s
coil, a certain condition or strain (770) is
produced in the dielectric, which is known ie
as the szlent discharge or the electric Sein
efiuvium. What that condition is cannot be definitely stated ; but it gives
rise to powerful and characteristic chemical actions, often differing from
those produced by the spark.
By this apparatus large quantities of ozone may be produced. |
816. Duration of the electric spark.—Wheatstone measured the duration
of the electric spark by means of the rotating mirror which he invented
for this purpose. At some distance from this instrument, which can be made
to rotate with a measured velocity, a Leyden jar is so arranged that the spark
of its discharge is reflected from the mirror. Now, from the laws of reflec-
tion (534) the image of the luminous point describes an arc of double the
number of degrees which the mirror describes, in the time in which the
mirror passes from the position in which the image is visible to that in which
it ceases to be so. If the duration of the image were absolutely instanta-
ACOA TOT RAT
ae CA
806 Frictional Electricity {816—
neous, the arc would be reduced to a mere point. Knowing the number of
turns which the mirror makes in a second, and measuring, by means of a
divided circle, the number of degrees occupied by the image, the duration of
the spark would be determined. In one experiment Wheatstone found that
this arc was 24°. Now, in the time in which the mirror traverses 360° the
image traverses 720°; but in the experiment the mirror made 800 turns in a
second, and therefore the image traversed 576,000° in this time ; and as the
arc was 24°, the image must have lasted the time expressed by 572455, or
satéu5 Of a second. Thus the discharge is not instantaneous, but has a
certain duration, which, however, is excessively short.
To determine the duration of the electric spark, Lucas and Cazin used a
method by which it may be measured in millionths of asecond. The method
is an application of the vernier (10). A disc of mica 15 centimetres in dia-
meter is blackened on one face, and at the edge are traced 180 equal divi-
sions in very fine transparent lines. The disc is mounted on a horizontal
axis, and by means of a gas engine it may be made to turn with a velocity
of 00 to 300 turns ina second. A second disc of silvered glass of the same
radius is mounted on the same axis as the other and very close to it ; at its
upper edge six equidistant transparent lines are traced, forming a vernier
with the lines on the mica. For this, the distance between two consecutive
lines on the two discs is such that five divisions of the mica disc D C corre-
spond to six divisions of the glass disc
MoD : AB, as seen in fig. 778. Thus the vernier
\ ; gives the sixths of a division of the mica
‘ \ \ | p disc (10). In the apparatus the lines AB
pine
Auk a are not above the lines CD, but are at the
Fig. 778 same distance from the axis, so that the
latter coincide successively with the former.
The mica disc is contained in a brass box, D (fig. 779), on the hinder face
of which is fixed the vernier. In the front face isa glass window, O, through
which the coincidence of the two sets of lines can be observed by means of
a magnifying lens, L.
The source of electricity is a battery of 2 to 8 jars, each having a coated
surface of 1,243 square centimetres, and charged continuously by a Holtz
machine. The spark strikes between two metal balls aand 4, 11 millimetres
in diameter. Their distance can be varied, and at the same time measured,
by means of a micrometric screw, 7 The two opposite electricities arrive
by wires 7 and 7, and the sparks strike at the principal focus of a condensing
lens placed in the collimator C, so that the rays which fall on the vernier are
parallel.
The motion is transmitted to the toothed wheels and to the mica disc by
means of an endless band, which can be placed on any one of three pulleys.
P, so that the velocity may be varied. At the end of the axis of the pulleys
is a bent wire which moves a counter, V, that marks on three dials the
number of turns of the disc.
These details being premised, suppose the velocity of the disc is 400
turns in a second. In each second 4oo x 180, or 72,000 lines pass before the
observer’s eye in each second ; hence an interval of 73455 of a second elapses.
between two consecutive lines. But as the spark is seen only when
one of the lines of the disc coincides with one of the six lines of the ver-
—816] Duration of the Electric Spark 807
nier, and as this gives sixths of a division of the movable disc, when the
latter has turned through a sixth of a division, a second coincidence is
produced ; so that the interval between two successive coincidences is
I
72000 x 6
That being the case, let the duration of a spark be something between
23 and 46 ten-millionths of a second ; if it strikes exactly at the moment of
a coincidence, it will last until the next coincidence ; and owing to the per-
sistence of impressions on the retina (639) the observer will see two luminous
= 0'0000023 of a second.
lines. But if the spark strikes between two coincidences and has ceased
when the third is produced, only one brilliant line is seen. Thus, if with the
above velocity sometimes 1 and sometimes 2 bright lines are seen, the dura-
tion of the spark is comprised between 23 and 46 ten-millionths of a second.
By experiments of this kind, with a striking distance of 5 millimetres
between the balls a and 4, and varying the number of the jars, Lucas and
Cazin obtained the following results :—
Duration in millionths
Number of jars of a second
Ls é ; : ; : Pats
4 ; ; : ; AT
6 45
8 47
808 Frictional Electricity [816—
It will thus be seen that the duration of the spark increases with the
number of jars. It also increases with the striking distance ; but it is inde-
pendent of the diameter of the balls between which
ang the spark strikes. The spark of electrical machines
a \ has so short a duration that it could not be measured
with the chronoscope.
817. Velocity of electricity.—To determine the
. velocity of electricity, Wheatstone constructed an
ami apparatus the principle of which will be understood
from fig. 780. Six insulated metal knobs were ar-
ranged in a horizontal line on a piece of wood called
— tl p- a spark board; of these the knob I was connected
with the outer, while 6 could be connected with the inner
coating of a charged Leyden jar; the knob 1 was the
tenth of an inch distant from the knob 2 ; while between 2 and 3a quarter of a
mile of insulated wire was interposed ; 3 was likewise a tenth of an inch from
4, and there was a quarter of a mile of wire between 4 and 5 ; lastly, 5 was a
tenth of an inch from 6, from whicha wire led directly to the inner coating of
the Leyden jar. Hence, when the jar was discharged by connecting the wire
from 6 with the inner coating of the jar, sparks would pass between 1 and 2,
between 3 and 4, and between 5 and 6. Thus the discharge, supposing it to
proceed from the inner coating, has to pass in its course through a quarter
of a mile of wire between the first and second spark, and through the same
distance between the second and third.
The spark board was arranged at a distance of 10 feet from the rotating
mirror, and at the same height, both being horizontal; and the observer
looked down on the mirror. Thus the sparks were visible when the mirror
made an angle of 45° with the horizon.
Now, if the mirror were at rest, or had only a small velocity, the images
of the three spots would be seen as three dots :, but when the mirror had
a certain velocity these dots appeared as lines, which were longer as the
rotation was more rapid. The greatest length observed was 24°, which,
with 00 revolutions in a second, can be shown to correspond to a duration
of 57353 of a second. Witha sow rotation the lines present the appearance
; they are quite parallel, and the ends in the same line. But with
greater velocity, and when the rotation took place from left to right, they
presented the appearance , and when it turned from right to left
the appearance , because the image of the centre spark was formed
after the lateral ones. Wheatstone found that this displacement amounted
to half a degree before or behind Be others ; accordingly this arc corre-
sponds to a duration of about the ;;23555 of a second ; the space traversed
in this time being a quarter of a mile, gives for the velocity of electricity
in the wire used 288,000 miles ina fecoati which is greater than that of light.
For Atmospheric Electricity reference must be made to the chapter on
Meteorology.
ee 780
—818] Galvani’s Experiment and T. heory 809
BOOK xX
DYNAMICAL ELECTRICITY
CHAPTER «I
VOLTAIC PILE. ITS MODIFICATIONS
818. Galvani’s experiment and theory.—The fundamental experiment
which led to the discovery of dynamical electricity is due to Galvani, Pro-
fessor of Anatomy in Bologna. Occupied by investigations on the in-
fluence of electricity on the nervous excitability of animals, and especially of
the frog, he ob-
served that when
the lumbar nerves
of a dead frog were
connected with the
crural muscles by
a metallic circuit,
the latter became
briskly contracted.
To repeat this
celebrated experi-
ment, the legs of a
recently killed frog
are prepared, and
the lumbar nerves
on each side of the
vertebral column
are exposed in the
form of white
threads. A metal
conductor, com- Fig. 781
posed of zinc and
copper, is then taken (fig. 781), and one end introduced between the nerves
and the vertebral column, while the other touches one of the muscles of
the thighs or legs ; at each contact a:smart contraction of the muscles ensues.
Galvani had some time before observed that the electricity of machines
produced in dead frogs analogous contractions, and he attributed the pheno-
mena first described to an electricity inherent in the animal. He assumed
7, oe
y Z
iwMYG $l
Z Zip MT ¢
SELL LALLA
810 Dynamical Electricity [818—
that this electricity, which he called wztal fluid, passed from the nerves to
the muscles by the metallic arc, and was thus the cause of contraction.
This theory met with great support, especially among physiologists, but it
was not without opponents. The most considerable of these was Alexander
Volta, Professor of Physics in Pavia.
819. Volta’s fundamental experiment.—Galvani’s attention had been
exclusively devoted to the nerves and muscles of the frog; Volta’s was
directed upon the connecting metal. Resting on the observation, which
Galvani had also made, that the contraction is more energetic when the con-
necting arc is composed of two metals than when there is only one, Volta
attributed to the metals the active part in the phenomenon of contraction.
He assumed that the disengagement of electricity was due to their contact,
and that the animal parts officiated only as conductors, and at the same time
as a very sensitive electroscope.
By means of the condensing electroscope, which he had then recently
invented, Volta devised several modes of showing the disengagement of
electricity on the contact of metals, of which the following is the easiest to
perform :—
The moistened finger being placed on the upper plate of a condensing
electroscope (fig. 758), the lower plate is touched with a plate of copper, ¢,
soldered to a plate of zinc, z, which is held in the other hand. On breaking
the connection and lifting the upper plate (fig. 759), the gold leaves diverge,
and, as may be proved, with negative electricity. Hence, when soldered
together, the copper is charged with negative electricity, and the zinc with
positive electricity. The electricity could not be due either to friction or
pressure ; for if the condensing plate, which is of copper, is touched with
the zinc plate z, the copper plate to which it is soldered being held in the
hand, no trace of electricity.is observed.
A memorable controversy arose between Galvani and Volta. The latter
was led to give greater extension to his contact theory, and propounded the
principle that when ¢wo heterogeneous substances are placed in contact, one
of them always assumes the positive and the other the negative electrical
condition. In this form Volta’s theory obtained the assent of the principal
philosophers of his time. Galvani, however, made a number of highly
interesting experiments with animal tissues. In some of these he obtained
indications of contraction, even though the substances in contact were quite
homogeneous.
$20. Disengagement of electricity in chemical actions.—The contact
theory which Volta had propounded, and by which he explained the action of
the pile, soon encountered objectors. Fabroni,a countryman of Volta, having
observed that, in the pile, the discs of zinc became oxidised in contact with
the acidulated water, thought that this oxidation was the principal cause of
the disengagement of electricity. In England Wollaston soon advanced the
same opinion, and Davy supported it by many ingenious experiments.
It is true that in the fundamental experiment of the contact theory (819)
Volta obtained signs of electricity. But De la Rive showed that if the zinc
is held in a wooden clamp, all signs of electricity disappear, and that the
same is the case if the zinc is placed.in gases, such as hydrogen or nitrogen,
which exert upon it no chemical action. De la Rive accordingly concluded
-820] Desengagement of Electrictty in Chemtcal Actions 811
that in Volta’s original experiment the disengagement of electricity is due to
the chemical actions which result from the perspiration and from the oxygen
of the atmosphere.
The development of electricity in chemical actions may be demonstrated
in the following manner by means of the condensing electroscope (801) :—A
disc of moistened paper is placed on the upper plate of the condenser, and
on this a zinc capsule, in which some very dilute sulphuric acid is poured. A
platinum wire, communicating with the ground, but insulated from the sides
of the vessel, is immersed in the liquid, and at the same time the lower plate
of the condenser is also connected with the ground by touching it with the
moistened finger. On breaking contact and removing the upper plate, the
gold leaves are found to be positively electrified, proving that the upper plate
has received a charge of negative electricity.
By a number of analogous experiments it may be shown that various.
chemical actions are accompanied by a disturbance of the electrical equili-
brium ; though of all chemical actions those between metals and liquids are:
the most productive of electricity. All the various resultant effects are in
accordance with the general rule, that when a liquid acts chemically on a
metal the liquid assumes the positive, and the metal the negative, condition.
In the above experiment the sulphuric acid, by its action on zinc, becomes
positively electrified, and its electricity passes off through the platinum wire
into the ground, while the negative electricity excited on the zinc acts on the
condenser just as an excited rod of sealing-wax would do.
In many cases the electrical indications accompanying chemical actions.
are but feeble, and require the use of a very delicate electroscope to render
them apparent. Thus, one of the most energetic chemical actions, that of
sulphuric acid upon zinc, gives no more free electricity than water alone does.
with zinc.
Opinion—which, in this country at least, had, mainly by the influence of
Faraday’s experiments, tended in favour of the purely chemical origin of
the electricity produced in voltaic action—-has of late inclined more and more
towards the contact theory. The following experiments, due to Lord
Kelvin, afford perhaps the most conclusive arguments hitherto adduced
in favour of the latter view :—
A very light metal bar is suspended by fine wire, so as to be movable
about an axis perpendicular to the plane of a disc made up of two half discs,
one of zinc, Z, and the other of copper, C (fig.
782). The light bar is counterpoised so as to
be exactly over one half of the line of separa-
tion of the two discs. When the discs are
placed in contact and the bar is charged posi-
tively by being connected with a Leyden jar,
the barmoves from the zinc towards the copper ;
if the jar, and therefore the bar, is charged
negatively, its motion is in the opposite direction. The same results are ob-
tained when the discs are connected by a wire, thus showing that the contact
of the two metals causes fhem to assume different electrical conditions, the
zinc taking the positive, and the copper the negative, electricity.
When, however, the two halves, instead of being in metallic contact, are
,
Fig. 782
S12 Dynamical Electricity [820-
connected by a drop of water, no change is produced in the position of the
bar by altering its electrification, provided it hangs quite symmetrically rela-
tively to the two halvesof the ring. This result shows that, under the circum-
stances mentioned, no difference is produced in the electrical condition of
the two metals. Hence the conclusion has been drawn by Lord Kelvin
and others, that the movement of electricity in the galvanic circuit is entirely
due to the electrical difference produced at the surfaces of contact of the dis-
similar metals. These results have been confirmed by some very careful
experiments by Professor Clifton.
There are, however, other facts which are not easily harmonised with this
view ; and indeed the last-mentioned experiment can hardly be regarded as
proving that in a// cases two different metals, connected by an electrolytic
liquid (864), assume the same electrical condition. It may, however, be
regarded as possible, or even probable, that the contact between the metals
and the liquids of a cell contributes, at least in some cases, to the production
of the current.
A most complete discussion of the question as to the seat of electromotive
forces in the voltaic cell is published in a series of papers by Prof. Lodge in
the nineteenth volume of the ‘ Philosophical Magazine.’
821. Current electricity.—When a plate of zinc and a plate of copper are
partially immersed in dilute sulphuric acid, no electrical or chemical change
is apparent beyond perhaps a slight disengagement of hydrogen from the
surface of the zinc plate. If now the plates are
placed in direct contact, or, more conveniently,
are connected by a metal wire, the chemical
action sets in, a large quantity of hydrogen is
disengaged ; but this hydrogen is no longer dis-
engaged at the surface of the zinc, but at the
surface of the copper plate. Here then we have
to deal with something more than mere chemical
action, for chemical action would be unable to
explain either the increase in the quantity of
hydrogen disengaged when the metals touch, or
the fact that this hydrogen is now given off at
the surface of the copper plate. At the same
time, if the wire is examined it will be found to possess many remarkable
thermal, magnetic, and other properties which will be afterwards described.
In order tounderstand what here takes place, let us suppose that we have
two insulated metal spheres, and that one is charged with positive and the
other with negative electricity, and that they are momentarily connected by
means of a wire. Electricity will pass from a place of higher to a place of
lo wer potential—that is, from the positive along the wire to the negative—
and the potentials become equal. This is, indeed, nothing more than an
electrical discharge taking place through the wire ; and during the infinitely
short time in which this is accomplished, it can be shown that the wire
exhibits certain heating and magnetising effects, of which the increase of
temperature is perhaps the easiest to observe. If now we can imagine some
agency by which the different electrical conditions of the two spheres are
renewed as fast as they are discharged, which is what very nearly takes
—822] Voltatc Couple. Electromotive Series 813
place when the two spheres are respectively connected with the two con-
ductors K and K’ of a Holtz machine (figs. 730, 731), this equalisation of
potentials, thus taking place, is virtually continuous, and the phenomena
above mentioned are also continuous.
Now this is what takes place when the two metals are in contact in a.
liquid which acts upon them unequally. This is independent of hypothesis
as to the cause of the phenomena—whether the electrical difference is pro-
duced only at the moment of contact of the metals, or whether it is due to the
chemical action, or tendency to chemical action, between the metal and the
liquid. The rapidly succeeding series of equalisations of potential, which
takes place in the wire, being continuous, so long as the chemical action
continues, is what is ordinarily spoken of as the electrical current.
If we represent by +¢ the potential of the copper plate, and by —e the
potential of the zinc, then the electrical difference—that is, the difference of
potentials—is +e—(-e)=2e. And this is general ; the essential point of any
such combination as the above is, that it maintains, or tends to maintain, a
difference of potentials, which difference is constant. If, for instance, the
zinc plate be connected with the earth which is at zero potential, its potential
also becomes zero ; and since the electrical difference remains constant, we
have for the potential of the copper plate +2e. Similarly, if the copper be
connected with the earth, the potential of the zinc plate is negative and is -- 2e.
The conditions under which a current of electricity is formed in the above
experiment may be further illustrated by reference to the conditions which
determine the flow of water between two reservoirs containing water at dif-
ferent levels. If they are connected by a pipe, water will flow from the
one at a higher level to the one at a lower level until the water in the two.
is at the same level, when of course the flow ceases. If we imagine the
lower reservoir so large that any water added to it would not affect its level—
if it were the sea, for example—that would represent zero level, and if the:
higher reservoir could be kept at a constant level there would be a constant
flow in the pipe.
We must be careful not to dwell too much on this analogy. It is not to:
be supposed that in speaking of current of electricity we mean to assert
that anything actually flows—that there is any actual transfer of matter.
We say ‘electricity flows’ or ‘acurrent is produced,’ in much the same sense
as that in which we say ‘sound or light travels.’
822. Voltaic couple. Electromotive series.—The arrangement just
described, consisting of two metals in metallic contact, and a conducting
liquid in which they are placed, constitutes a szwple voltaic element, or couple,
or cell. So long as the metals are not in contact, the couple is said to be:
open, and when connected it is closed.
According to the chemical view, to which we shall for the present pro-
visionally adhere, it is not necessary for the production of a current that one
of the metals be unaffected by the liquid, but merely that the chemical action
upon the one be greater than upon the other. For then we may assume
that the current produced would be due to the difference between the differ-
ences of potential which each of the metals separately produces by its con-.
tact with the liquid. _ If the differences of potentials were absolutely equal—
a condition, however impossible of realisation with two distinct metals—we:
S14 | Dynamical Electricety [822~-
must assume that when the metals are joined no current would be produced.
The metal which is most attacked is called the foszt7ve or generating plate,
cand that which is least attacked the zegat¢zve or collecting plate. The posi-
tive metal determines the direction of the current, which proceeds zz the
liquid from the positive to the negative plate, and owt of the liquid through
the connecting wire from the negative to the positive plate.
In speaking of the advection of the current the direction of the positive
electricity is always understood.
In the fundamental experiment, not only the connecting wire, but also the
liquid and the plates, are traversed by the electrical current—are the scene
-of electrical actions.
The mere immersion of two different metals in a liquid is not alone suffi-
cient to produce a continuous current ; there must be chemical action. When
a platinum anda gold plate are connected with a delicate galvanometer, and
immersed in pure nitric acid, no current is produced ; but on adding a drop
of hydrochloric acid a strong current is excited, which proceeds in the liquid
from the gold to the platinum, because the gold is attacked by the nitro-
hydrochloric acid, while the platinum is less so, if at all.
As a voltaic current is produced whenever two metals are placed in
metallic contact in a liquid which acts more powerfully upon one than upon
the other, there is a great choice in the mode of producing such currents.
In reference to their electrical deportment, the metals have been arranged in
what is called an electromotive series, in which the most electroposttive are
at one end, and the most electronegative at the other. Hence when any two of
these are placed in contact in dilute acid, the current in the connecting wire
proceeds from the one lower in the list to the one higher. The principal
metals range themselves as follows :—
{?- 210 5. Iron Io. Silver
2. Cadmium 6. Nickel 11. Gold
aan 7. Bismuth 12. Platinum
4. Lead 8. Antimony 13. Graphite
9g. Copper
It will be seen that the electrical deportment of any metal depends on the
metal with which it is associated. Iron, for example, in dilute sulphuric acid
is electronegative towards zinc, but is electropositive towards copper ; copper
in turn is electronegative towards iron and zinc, but is electropositive towards
silver, platinum, or graphite.
823. Electromotive force.—The force in virtue of which continuous
electrical effects are produced throughout a circuit consisting of two metals
in metallic contact in a liquid which acts unequally upon them, is usually
called the electromotive force. The electromotive force of a cell (written
shortly E.M.F.) is equal to the difference of potentials of the terminals of
the cell, when these terminals are not connected so that no current is flow-
ing. The E.M.F. of the cell is the same whether a current is flowing or not,
depending only on the metals and liquid used, but the difference of potential
of the terminals falls as soon as a current is allowed to flow, to a greater
extent as the current is stronger. The electromotive force of a cell is
greater in proportion to the distance of the two metals from each other in
the series. That is to say, it is greater the greater the difference between
—823] Electromotive Force 815
the chemical action upon the two metalsimmersed. Thus the electromotive
force between zinc and platinum is greater than that between zinc and iron,
or between zinc and copper. The law established by experiment is, that ¢ie
electromotive force between any two metals ts equal to the sum of the electro-
motive forces between all the intervening metals. Thus the electromotive
force of a cell having zinc and platinum for its plates, is equal to the sum of
the electromotive forces of cells having zinc and iron, iron and copper, and
copper and platinum. ;
The electromotive force of acellisinfluenced by the condition of the metal for
given metals ; rolled zinc, for instance, is negative towards cast zinc. It also
depends on the degree of concentration of the liquid; in dilute nitric acid
zinc is positive towards tin, and mercury positive towards lead ; while in con-
centrated nitric acid the reverse is the case, mercury and zinc being respec-
tively electronegative towards lead and tin.
The nature of the liquid also influences the direction of the current. If
two plates, one of copper and one of iron, are immersed in dilute sulphuric
acid, a current is set up proceeding through the liquid from the iron to the
copper ; but if the plates, after being washed, are placed in solution of
potassium sulphide, a current is produced in the opposite direction—the
copper is now the positive metal. Other examples may be drawn from the
following table, which shows the electric deportment of the principal metals
with three different liquids. It is arranged like the preceding one : each
metal being electropositive towards any one lower in the list, and electro-
negative towards any one higher.
Caustic potass Hydrochloric acid ee
Zinc Zing Zinc
Tin Cadmium Copper
Cadmium Tin Cadmium
Antimony Lead Tin
Lead Iron Silver
Bismuth Copper Antimony
Iron Bismuth Lead
Copper Nickel Bismuth
Nickel Silver Nickel
Silver Antimony Iron
A voltaic current may also be produced by means of two liquids and
one metal. This may be shown by the following al
experiment :—In a beaker containing strong nitric
acid is placed a small porous pot (fig. 784), con-
taining strong solution of caustic potass. If now
two platinum wires connected with the two ends
of a galvanometer (842) are immersed respectively
in the alkali and in the acid, a voltaic current is
produced, proceeding in the wire from the nitric
acid to the potass, which thus correspond re-
spectively to the negative and positive plates in
ordinary couples.
A metal which is acted upon by a liquid can be protected from solution
by placing in contact with it a more electropositive metal, and thus forming
816 Dynamical Electricity [823-
a simple voltaic circuit. This principle is the basis of Davy’s proposal to.
protect the copper sheathings of ships, which are rapidly acted upon by sea-
water. If zinc or iron is connected with the copper, the metal so used is dis-
solved and the copper protected. Davy found that a piece of.zinc the size
of a nail was sufficient to protect a surface of forty or fifty square inches ;
unfortunately the proposal has not been of practical value, for the copper
must be attacked to a certain extent to prevent the adherence of marine
plants and shellfish.
824. Poles and electrodes.—If the wire oapeeee the two terminal
plates of a voltaic couple is cut, it is clear, from what has been said about
the nin and direction of the current, that positive
electricity will tend to accumulate at the end of the
wire attached to the copper or negative plate, and
negative electricity on the wire attached to the zinc
or positive plate. These terminals have been called
the oles of the battery. For experimental purposes,
more especially in the decomposition of salts, plates
of platinum are attached to the ends of the wires.
Instead of the term? poles, the word electrodes
(7Aextpov, and 6d0s, a way) is frequently used ; for
these are the ways through which the respective
electricities emerge. It isimportant not to confound
the positive A/aze with the positive fole or electrode.
The positive pole is that connected with the negative
plate, while the negative pole is connected with the
unm
4m
| em! positive plate.
i), ssa | 825. Voltaic pile. Voltaic battery.—When a
acne series of voltaic cells is arranged so that the
on wi zinc of one cell is connected with the copper
TTT Mu
of another, the zinc of this with the copper of
another, and so on, the arrangement is called a vol-
taic battery ; and by its means the effects produced
by a single cell are capable of being very greatly
—— Za __ increased.
Hl nn il The earliest of these arrangements was devised by
—————_—— Volta himself. It consists (fig. 785) of a series of discs
piled one over the other in the following order :—At
the bottom, on a frame of wood, is a disc of copper,
then a disc of cloth moistened by acidulated water or by brine, then a disc
of zinc ; on this a disc of copper, and another disc of moistened cloth, to
which again follow as many sets of copper-cloth-zinc, always in the same
order, as may be convenient, the highest disc being of zinc. The discs are
kept in a vertical position by glass rods.
It will be readily seen that we have here a series of simple voltaic couples,
the moisture in the cloth acting as the liquid in the cases already mentioned,
and that the terminal zinc is the negative and the terminal copper the
positive pole. From the mode of its arrangement, and from its, discoverer,
the apparatus is known as the voltaic pile, a term applied to all apparatus of
this kind for accumulating the effects of dynamical electricity.
ig
Ma
—826] Wollaston’s Battery 817
The distribution of electricity in the pile varies according as it is in con-
nection with the earth by one of its extremities, or as it is insulated by being
placed on a non-conducting cake of resin or glass.
In the former case, the end in contact with the ground is neutral, and
the rest of the apparatus contains only one kind of electricity ; this is
negative if the copper disc, and positive if the zinc disc, is in contact with the
ground.
In an insulated pile the electricity is not uniformly distributed. By
means of a proof plane and electroscope it may be demonstrated that the
middle part is in a neutral state, and that one half is charged with positive
and the other with negative electricity, the potential increasing from the
middle to the ends. The half terminated by a zinc disc is charged with nega-
tive electricity, and that by a copper with positive electricity. The pile is
thus similar to a charged Leyden jar; with this difference, however, that
when the jar has been discharged by connecting its two coatings, the elec-
trical effects cease ; while in the case of the pile, the cause which originally
brought about the distribution of electricity restores this state of charge
after the discharge ; and the continuous’ succession of charges and dis-
charges forms the current. The effects of the pile will be discussed in other
places.
826. Wollaston’s battery.—The original form of the voltaic pile has a
great many inconveniences, and possesses now only an historical interest.
It has received a great many improvements, the principal object of which
has been to facilitate manipulation, and to produce greater electromotive
force.
One of the earliest of these modifications was the crown of cups, or
couronne des tasses, invented by Volta himself. An improved form of this is
known as Wollaston’s battery (fig. 786) ; itZis arranged so that when the
current is not wanted the action of the battery can be stopped.
eile:
818 Dynamical Electricity [826-
The plates Z are of thick rolled zinc, and usually about eight inches in
length by six in breadth. The copper plates, C, are of thin sheet, and bent
so as to surround the zincs without touching them, contact being prevented
by small pieces of cork. To each copper plate a narrow strip of copper, a,
is soldered, which is bent twice at right angles and is soldered to the next
zinc plate ; and the first zinc, Z, is surrounded by the first copper C ; these
two constitute a couple, and each couple is immersed in a glass vessel, con-
taining acidulated water. The copper, C, is soldered to the second zinc
by the strip 0, and this zinc is in turn surrounded by a second copper, and
so on. 3
Fig. 786 represents a pile of sixteen couples united in two parallel series
of eight each. All these couples are fixed to across frame of wood, by which
they can be raised or lowered at pleasure. When the battery is not wanted,
the couples are lifted out of the Jiquid. The water in these vessels is usually
acidulated with 4 sulphuric and 4 nitric acid.
827. Enfeeblement of the current in batteries. Secondary currents.
The various batteries already described—Volta’s, Wollaston’s, and Hare’s,
which consist essentially of two metals and one liquid—labour under the
objection that the currents produced rapidly diminish in'strength.
This is due principally to three causes : the first is the decrease in the
chemical action owing to the neutralisation of the sulphuric acid by its com-
bination with the zinc. This is a necessary action, for upon it depends the
current ; it therefore occurs in all batteries, and is without remedy except by
replacement of acid and zinc. The second is due to what is called Jocal
action ; that is, the production of small closed circuits in the active metal,
owing to the impurities it contains. These local currents rapidly wear away
the active plate, without contributing anything to the continuance of the
general current. They are remedied by amalgamating the zinc with mercury,
by which chemical action is prevented until the circuit is closed, as will be
more fully explained (837). The third arises from the production of an
inverse electromotive force, which acting against the electromotive force of
the battery or cell tends to destroy it totally or partially. Inthe fundamental
experiment (fig. 783), when the circuit is closed, zinc sulphate is formed,
which dissolves in the liquid, and at the same time a layer of hydrogen gas
is gradually formed on the surface of the copper plate. This diminishes the
activity of the combination in more than one way. In the first place, it
interferes with the contact between the metal and the liquid ; in the second
place, in proportion as the copper becomes coated with hydrogen, we have
virtually a plate of hydrogen instead of a plate of copper opposed to the
zinc, and in addition, the hydrogen, by reacting on the zinc sulphate, which
accumulates in the liquid, gradually causes a deposition of zinc on the sur-
face of the copper ; hence, instead of having two different metals unequally
attacked, the two metals become gradually less different, and, consequently,
the total effect becomes weaker and weaker.
The folarisation of the plate (as this phenomenon is termed) may be
destroyed by breaking the circuit and exposing the copper plate to
the air; the deposited hydrogen is thus more or less completely got rid
of, and on again closing the circuit the current has nearly its original
strength. The same result is obtained when the current of another
—829] Daniell’s Battery . 819
battery is transmitted through the battery in a direction opposite to that of
the first.
When platinum electrodes are used to decompose water, a similar pheno-
menon is produced, called polarisation of the electrodes, which may be illus-
trated by an arrangement represented
in fig. 787, in which B is a constant
cell, V a voltameter (868), G a galvano-
meter (842), and H a mercury cup.
The wire L being disconnected from
H, a current is produced in the volta-
meter, the direction of which is from
° 5 ony
P to P’; if nowthe wire F be detached —.)
from sd, thd: be connected there. (lw
with, a current is produced through Pll
the galvanometer, the direction of B
which is from P’ to P; that is, the
opposite of that which the cell had produced in the voltameter. Becquerel
and Faraday have shown that this polarisation of the metals results from the
deposits caused by the passage of the current, and an important application
of this phenomenon will be found described farther on (872),
Fig. 787
CONSTANT CURRENTS
828. Constant currents.—With few exceptions, batteries composed of
elements with a single liquid have almost gone out of use, in consequence
of the rapid enfeeblement of the current due to polarisation. They have
been replaced by batteries with two liquids, which are called constant batteries,
because their action continues without material alteration for a considerable
period of time. The essential point to be at-
tended to in securing a constant current is to
prevent the polarisation of the inactive metal ;
in other words, to hinder any permanent depo-
sition of hydrogen on its surface. This is
effected by placing the inactive metal in a liquid
upon which the deposited hydrogen can act
chemically.
829. Daniell’s battery.—This was the first
form of the constant battery, and was_ in-
vented by Daniell in the year 1836. As re-
gards the constancy of its action, it is perhaps
still the best of all constant batteries. Fig. 788
represents a single element. A glass or porce-
lain vessel, V, contains a saturated solution of
copper sulphate, in which is immersed a copper
perforated cylinder, G, open at both ends. At the upper part of this cylinder
there is an annular shelf, G, perforated and below the level of the solution ;
this is intended to support crystals of copper sulphate to replace that decom-
posed as the electrical action proceeds. Inside the cylinder is athin porous
2 en.
820 Dynamical Electricity ) [829-
vessel, P, of unglazed earthenware, which contains dilute sulphuric acid, and
in itis placed the cylinder of amalgamated zinc, Z. Two thin strips of copper
p and 2, fixed by binding screws to the copper and to the zinc, serve for
connecting the elements in series.
When the circuit of a Daniell’s element is closed, the hydrogen resulting
from the action of the dilute acid on the zinc, ates of being liberated on
the surface of the copper plate, meets with tive copper sulphate, and reduces
it with the formation of sulphuric acid and metallic copper, which is deposited
on the surface of the copper plate. In this way copper sulphate in solution
is taken up ; and if it were all consumed, hydrogen would be deposited on
the copper, and the current would lose its constancy. This loss is prevented
by the crystals of copper sulphate which keep the solution saturated. The
sulphuric acid produced by the decomposition of the sulphate permeates
the porous cylinder, and tends to replace the acid used by its action on the
zinc ; and as the quantity of sulphuric acid formed in the solution of copper
sulphate is regular, and proportional to the acid used in dissolving the zinc,
the action of this acid on the zinc is regular also, and thus a constant current
is maintained.
In order to join together several of these elements to form a battery, the
zinc of one 1s counestc# by a copper wire or strip with the copper of the next,
and so on from one element to
another, as shown in fig. 792, for
another kind of battery.
Fig. 789 represents one form
of a standard Daniell. The
= vessel A contains dilute sul-
j ANT phuric acid of specific gravity
LL
mer } Ge HM | I'075, and in it is a plate, Z, of
S |__| S S|. — amalgamatedzinc. A, contains
saturated solution of copper sul-
phate, and in it is a plate of
= copper, K. The syphon tube,
= : === C C,, which connects the two
SSS SSS Ss vessels, is closed at both ends
Fig. 789 by bladder, and is filled with
dilute sulphuric acid.
The current produced bya Daniell’s cell is constant for some hours ;
its action is stronger when it is placed in hot water. Its electromotive force
is about 1°08 volt.
Taking the cost of the materials consumed in working a Daniell’s cell,
but allowing for the copper deposited, and assuming that 70 per cent. of the
electrical energy is obtained in mechanical work, it appears that the expense
per horse power per hour is at least two shillings and sixpence.
830. Grove’s battery.—In this battery the copper sulphate solution is
replaced by nitric acid, and the copper by platinum, by which greater electro-
motive force is obtained. Fig. 790 represents one of the forms of a couple
of this battery. It consists of a flat rectangular glass or porcelain vessel,
partially filled with dilute sulphuric acid (1:8); of a zinc plate bent into a U
shape, a flat porous pot contains strong nitric acid and a thin platinum foil
-831] Bunsen’s Battery 821
which can be connected with the zinc of the next cell by a suitable binding
screw. In this battery the hydrogen, which would be disengaged on the
platinum, meeting the nitric acid, decomposes
it, forming hyponitrous acid, which dissolves,
or is disengaged as nitrous fumes. Grove’s
battery is the most convenient, and one of the
most powerful of the two fluid batteries. It is,
however, expensive, owing to the high price of
platinum ; besides which the platinum is hable,
after some time, to become brittle and break
very easily. But as the platinum is not con-
sumed, it retains most of its value, and when
the plates which have been used in a battery
are heated to redness they regain their elasti-
city.
831. Bunsen’s battery. — Aumsen’s, also
known as the gzzc carbon battery, was invented
in 1843 ; it is in effect a Grove’s battery, where
the plate of platinum is replaced by a cylinder
of carbon. This is made either of the graphi- Fig. 790
toidal carbon deposited in gas retorts, or by
calcining in an iron mould an intimate mixture of coke and bituminous
coal, finely powdered and strongly compressed. Both those modifications
of carbon are good conductors. Each element consists of the following
parts: 1, a vessel, F (fig. 791), either of stoneware or of glass, containing
dilute sulphuric acid ; 2, a hollow cylinder, Z, of amalgamated zinc ; 3, a
porous vessel, V, in which ts ordinary nitric acid ; 4, a rod of carbon, C, pre-
Fig. 791
pared in the above manner. In the vessel F the zincis first placed, and init
the carbon C in the porous vessel V as seen in P. To the carbon is fixed a
binding screw, 7, to which a copper wire is attached, forming the positive
pole. The zinc is provided with a similar binding screw, 7, and wire, which
is thus a negative pole.
A single cell of the ordinary dimensions, 20 cm. in height and 9 cm. in
822 Dynamical Electricity [831—
diameter, has a resistance of about 0°14 ohm, and taking its E.M.F. at 1°82
(835), gives a current of 12 to 13 amperes when on short circuit, that is
when it is closed without measurable external resistance.
When the cells are arranged to form a battery (fig. 792) each carbon is.
connected to the zinc of the following cell by means of the clamps wm, and a
strip of copper, ¢, represented in the top of the figure. The copper is pressed
at one end between the carbon and the clamp, and at the other it is soldered
to the clamp , which is fitted on the zinc of the following cell, and so
forth. The Senay of the first carbon and that of the last zinc are alone
provided with binding screws, to which are attached the wires.
—\ me
IW
Fig. 792
The chemical action of Bunsen’s battery is the same as that of Grove’s.
Being as powerful as and less costly than Grove’s, it is very generally used on
the Continent ; but though its first cost is less, it is more expensive to work,
and is not so convenient to manipulate.
Callan’s battery is a modified form of Grove’s. Instead of zinc and plati-
num, zinc and platinised lead are used ; and instead of nitric acid Callan
used a mixture of sulphuric acid, nitric acid, and saturated solution of
nitre. The battery is said to be equal in its action to Grove’s, and is much
cheaper.
Callan also constructed a battery in which zinc in dilute sulphuric
acid forms the positive plate, and cast iron in strong nitric acid the negative.
Under these circumstances the iron becomes passive ; it is strongly elec-
tro-negative, and does not dissolve. If, however, the nitric acid becomes:
too weak, the iron dissolves with disengagement of nitrous fumes.
After being in use some time, all the batteries in which the polarisation
is prevented by nitric acid disengage nitrous fumes in large quantities, and
this is a serious objection to their use, especially in closed rooms. To
prevent this, nitric acid is frequently replaced by chromic acid, or by a
mixture of 4 parts potassium bichromate, 4 parts sulphuric acid, and 18
water. The liberated hydrogen reduces the chromic acid to the state of
chromic oxide, which combines with the sulphuric acid forming chromous
~833] Recent Batteries 823
sulphate. With the same view, sesquichloride of iron is sometimes substi-
tuted for nitric acid ; it becomes reduced to protochloride. But the action
of the elements thus modified is considerably less than when nitric acid is
used, owing to the greater resistance.
832. Smee’s battery.—In this battery the polarisation of. the negative
plate is prevented by mechanical means. Each cell consists of a sheet of
platinum placed between two vertical plates of zinc, but as there is only a
single liquid, dilute sulphuric acid, the elements have much the form of
those in Wollaston’s battery. The adherence of hydrogen to the negative
plate is prevented by covering the platinum with a deposit of finely divided
platinum. In this manner the surface is roughened, and the disengagement
of hydrogen facilitates toa remarkable extent, and consequently the resistance
of a couple diminishes. For platinum, silver covered with a deposit of finely
divided platinum is frequently substituted, as being cheaper.
833. Recent batteries.—The mercury sulphate battery (fig. 793), de-
vised by Marié Davy, is essentially a zinc-carbon element, but of smaller
dimensions than those elements usually are. In the outer vessel, V, ordi-
nary water or brine is placed, and in the porous vessel mercury sulphate.
This salt is agitated with about three times its volume of water, in which it is
difficultly soluble, and the liquid poured off fromthe pasty mass. The carbon
being placed in the porous vessel, the spaces are filled with the residue, and
then the decanted liquid poured into it.
Chemical action takes place when the cell is closed. The zinc decom-
poses the water, liberating hydrogen, which, traversing the porous vessel,
|
LLL
=a
||
LEZLLLL,
ZZ
reduces the mercury sulphate, forming metallic mercury, which collects
at the bottom of the vessel, while the sulphuric acid formed at the same
time traverses the diaphragm to act on the zinc, and thus increases the
action.
The mercury which is deposited may be used to prepare a quantity of
sulphate equal to that which has been consumed. A small quantity of the
solution of mercury sulphate may also pass through the diaphragm ; but this
is rather advantageous, as its effect is to amalgamate the zinc.
The electromotive force of this element is about a quarter greater than that
of Daniell’s element, but it has greater resistance ; it is rapidly exhausted
824 Dynamical Electricity [833—
when continuously worked, though it appears well suited for discontinuous
work, as with the telegraph, and with alarums.
Gravity batteries.—The use of porous vessels is open to many objections,
more especially in the case of Daniell’s battery, in which they gradually
become encrusted with copper, and so destroyed. A kind of battery has
been devised in which the porous vessel is entirely dispensed with, and the
separation of the liquids is effected by the difference of density. Such
batteries are called gravity batteries. Fig. 794 represents a form devised
by Callaud. V isa glass or earthenware vessel at the bottom of which is a
copper plate soldered to a wire insulated by gutta-percha. On the plate is
a layer of crystals of copper sulphate, C ; the whole is filled with water, and
the zinc cylinder, Z, is immersed in it. he lower part of the liquid becomes
saturated with copper sulphate ; the action of the battery is that of a Daniell,
and the zinc sulphate, which gradually forms, floats on the solution of copper
sulphate owing to its lower density. This battery is easily manipulated, and
when not agitated works constantly for some time, provided care be taken to
replace the water lost by evaporation ; the consumption of copper sulphate
is economical.
Metdinger’s element, which is much used in Germany for telegraph
purposes, is essentially a gravity battery of special construction, with zinc in
solution of magnesium sulphate, and copper in solution of copper sulphate.
Minotto’s battery.—This may be described as a Daniell’s element, in
which the porous vessel is replaced by a layer of sawdust or of sand. At
the bottom of an earthenware vessel (fig. 795) is placed a layer of coarsely
powdered copper sulphate a, and on this a copper plate provided with an
insulated copper wire z. On this there is a layer of sand or of sawdust dc,
and then the whole is filled with water, in which rests a zinc cylinder Z,
or the earthenware vessel may be nearly filled with moistened sawdust, and
a zinc slab placed on the top. The action is just that of a Daniell; the
sawdust prevents the mixture of the liquids, but it also offers great resist-
ance, which increases with its thickness. From its simplicity and economy,
and the facility with which it is constructed, the pale merits increased
attention.
De la Rue and Miiller’s element consists of a glass tube about 6 inches
long by 0°75 inch in diameter, closed by a vulcanised india-rubber stopper
through which passes a zinc rod 0°18 inch in diameter and 5 inches -long.
A flattened silver wire also passes through the stopper to the bottom of the
tube, in which is placed about half an ounce of silver chloride, the greater
part of the cell being filled with solution of sal-ammoniac. The hydrogen
evolved at the negative plate reduces the chloride to metallic silver, which
is thereby recovered. Since there is only one liquid, and the solid electro-
lyte is not acted upon when the circuit is open, the element is easily worked
and requires little attention. It is very compact, 1,000 elements occupying
a space of less than a cubic yard ; De la Rueand Miiller have used as many
as 14,400 such cells in investigations on the'stratification of the electric light.
A battery of 8,040 of these cells gave a spark 4 of an inch in length in air
under the ordinary atmospheric pressure ; while under a pressure of a quarter
of an atmosphere the striking distance was 14 inch (810).
The electromotive force of a silver chloride cell is 1°03 volt, and that of
-833] Recent Batteries 825
one made with silver bromide is 07908; hence a series of three of the
silver chloride cells with one of bromide gives an average electromotive
force of I volt (835).
Latimer Clark’s element is much used as a
standard of electromotive force. One form of
it, represented in fig. 796, consists of two verti-
cal glass branches, with platinum wires sealed
in the closed ends, and joining in a neck in
which is a ground glass stopper with a thermo-
meter. In one of these branches is mercury
forming the negative plate, and in the other
an amalgam of zinc and mercury forming the
positive plate. On the mercury is placed a paste
formed by triturating together mercurous sul-
phate with mercury and zinc sulphate, and on
both the amalgam and the paste is a layer of
crystals of zinc sulphate, the vessel being filled
with saturated solution of zinc sulphate. This
cell is not at all adapted for anything of the
nature of continuous work, but it furnishes a
standard of E.M.F. which when the cell is con-
structed with the proper precautions can always
be reproduced and always reliedon. Its E.M.F.
is 1°435 [1 —0°0078 (¢—15)] volts, where ¢ is the
temperature Centigrade.
A convenient form of element for many purposes is the fotasstum
bichromate, or, as it is frequently termed, the dzchromate element (fig. 797).
It consists of a zinc plate, Z, attached to a brass
rod, which slides up and down in a brass tube in an
ebonite or porcelain cover, so that it can be wholly
or partially immersed in the liquid. This is necessary,
since the zinc is attacked by the exciting liquid when
the cell is not closed. Two graphite plates, C C, are
similarly fitted in the cover, and by means of strips of
brass the carbon and the zinc plates are respectively
in connection with the binding screws, which thus form
the poles. The exciting liquid is a mixture of I part
of potassium bichromate, 2 of sulphuric acid, and Io
of water. Instead of potassium bichromate, chromic
acid, which is now prepared industrially at a cheap
rate, is often used.
The electromotive force is about 2 volts ; when the
element is closed by a wire of small resistance its
E.M.F. increases slightly at first, then remains constant
for some time, after which it rapidly sinks to half its original amount.
In MViaudet’s element a zinc cylinder dips in a solution of common salt
and surrounds a porous cell, in which is a carbon plate surrounded by
pieces of carbon and filled with chloride of lime, which does not act on the
zinc even when the circuit is closed. The electromotive force is 1°7 volt.
Fig. 796
’
826 Dynamical Electricity [833—
The element of Lalande and Chaperon consists of zinc in a 30 per cent.
solution of caustic potass and copper in contact with copper oxide which
acts as depolariser. The E.M.F. is 0°85 volt, and there is no action unless
the circuit is closed. To prevent the absorption of carbonic acid by the
potass, the solution is covered with paraffine oil.
834. Leclanché’s element.—This consists (fig. 798) of a rod of carbon,
C, placed in a porous pot, which is then very tightly packed with a mixture
of pyrolusite (manganese peroxide) and gas graphite, M, covered over
with a layer of pitch. To the top of the carbon is firmly attached a mass of
lead, L, to which is affixed a binding screw. The positive plate is a rod of
zinc, Z, in which is fixed a copper wire. The exciting liquid consists of
a strong solution of sal-ammoniac, contained in a glass vessel, G, which is
not more than one-third full. The E.M.F. of the element is 1°4 volt, or about
one-third greater than that of a Daniell’s element ; its internal resistance
varies of course with the size, from 4 to 8 ohms. The battery is not adapted
for continuous work as in heavy telegraphic circuits, or in electro-plating,
since it soon becomes polarised ; it has,
however, the valuable property of quickly
regaining its original strength when left
at rest, and is extremely well adapted for
* discontinuous work, such as that of elec-
trical bells.
A modification of this element by von
Beetz for therapeutic purposes consists
of a test tube in the bottom of which is
fused a platinum wire; this is then covered
to one-third the height with a layer of a
mixture of bruised gas cokeand pyrolusite.
In other respects the element is con-
structed like that of De la Rue and
Muller.
A rod of carbon 42 x 12x 35, inches
should have a maximum resistance of
1 ohm; but good plates made from the
carbon of gas retorts do not average
more than o'5, and in some cases o'I ohm.
If the resistance equals an ohm, the con-
ducting power of carbon is about 0°003
that of mercury.
A drawback to the use of carbon is that, from its porosity, the exciting
liquid rises, and forms local currents at the junction with the binding
screw, which injure or destroy contact. This may be remedied to a very
great extent by soaking the plates before use in hot melted paraffine, which
penetrates into the pores, expelling the air. On cooling, it solidifies and
prevents the capillary action mentioned+¢above. By carefully scraping the
paraffine from the outside, a surface is exposed which is as good a conductor
as if the pores were filled with air. Measurements have shown that the
resistance of a plate thus prepared is not altered.
In a recent modification of this cell the porous cell is dispensed with,
Oe
9 2
Fig. 798
—836] Electromotive Force of Different Elements 827
and the carbon plate C placed between two similar flat prisms, made by
compressing a mixture of 55 parts of graphite, 4o parts of pyrolusite, and 5
parts of shellac in steel moulds at a temperature of 100° under a pressure
of 300 atmospheres. The resistance of this form of element is from o-g to
1°8 ohm.
835. Electromotive force of different elements.--The following numbers
represent the electromotive force in volts of some of.the elements most fre-
quently used.
Volts
Daniell’s element . . set up with water . ‘ 1°08
% . : . pure zinc and pure water, afin aie
copper and pure ateniesie solution
of copper sulphate , el tO
Peclanchecs ; . zinc in saturated solution BE am-
monium chloride . ; : 4S
IvGlarics. 4... , ? Z : ‘ 5 : RE
Bunsen’s * carbon in nitric acid ; : Rey:
“s € carbon in chromic acid . : be 2°02
Grove’s ¥ platinum in nitric acid. ; el OG
The cell of greatest electromotive force as yet observed was examined by
Beetz, and consists of potassium amalgam in caustic potash, combined with
pyrolusite in a solution of potassium permanganate. Its E.M.F. is three
times as great as that of a Daniell’s element.
The standard of electromotive force on the C. G. S. system is the Volz.
This is equal to 100,co0,0co or 10° absolute electromagnetic units (999).
The vo/¢ is rather less than the electromotive force of a Daniell’s cell, the
mean value of which may be taken at 1°08 volt. The unit of current, which
is called an ampere, is the current due to an electromotive force of one volt
working through a resistance of one ohm.
The coulombé is the practical unit of electrical quantity ; it is that quantity
of electricity which passes in a second through the section of a conductor
traversed by a current of an ampere.
836. Comparison of the voltaic battery with a frictional electrical
machine.—Except in the case of batteries consisting of a very large number
of couples, the difference of potentials between the terminals is far weaker
than in frictional electrical machines, and is insufficient to give any visible
spark. With Dela Rue and Miller’s great battery the striking distance
between two terminals was found to increase with the potential, but for high
potentials rather more rapidly than in direct ratio. Thus while the striking
distance was o’oI2 in., with the potential due to 1,200 of their cells, it was
0'049 in. with 4,800 cells, and 0°133 in. with 11,000 cells.
In the case of a small battery or of a single cell, very delicate tests are
required to detect any signs of free electrification. But by means of a con-
densing electroscope, and by careful insulation, it can be shown that one
pole possesses a positive and the othera negative charge. Inthe experiment
for proving this one ef the plates of the electroscope is connected with one
pole, and the other with the other pole or with the ground. The electroscope
828 Dynamical Electricity [836—
thus becomes charged, and on breaking the connection and raising the plate
electroscopic indications are observed (801).
On the other hand, the strength of current which a voltaic element can
produce in a good conductor is far greater than that which can be pro-
duced by a machine. Faraday immersed two wires—one of zinc, and the
other of platinum, each ;4, of an inch in diameter—in acidulated water for ;3,
of a second. The effect thus produced on a magnetic needle in this short
time was greater than’ that produced by 23 turns of the large electrical
machine of the Royal Institution.
Nystrom ascertained by quantitative nieasurements that the potential of
the charge of the cover of an ordinary electrophorus is not less than 50,000
times as great as the potential of a Meidinger’s cell (833) ; that is, that not
less than 50,000 of those elements would be required to produce the same
potential as the electrophorus. In practice, a far greater number would be
needed, owing to the difficulty of getting good insulation.
837. Amalgamated zinc. Local currents.—Perfectly pure distilled zinc is
not attacked by dilute sulphuric acid, but becomes so when immersed in that
liquid in contact with a plate of copper or of platinum. Ordinary commercial
zinc, on the contrary, 1s rapidly dissolved by dilute acid.
This is due to what is called /ocal action (827), arising from impurities
which are always present in commercial zinc. To understand this effect, con-
sider two portions a and @ of a plate of zinc placed in dilute
acid (fig. 799), @ representing pure zinc, while 4 is supposed to
represent such an impurity as a particle of lead or iron. Here
are all the conditions for the production of an electrical cur-
rent, two different metals in metallic connection, and in contact
with a liquid, which acts upon them unequally ; the effect is
that a current is produced from a to 4 through the liquid, and
the zinc is eaten away.
All ordinary zinc contains metallic impurities, such as lead
and iron, which realise the above conditions, forming innu-
merable local electrical currents, which rapidly wear away the
active plate without contributing anything to the general
current.
Zinc, when amalgamated, acquires the properties of perfectly pure zinc,
and is unaltered by dilute acid, so long as it is not in contact with a copper
or some other metal plate immersed in the same liquid. To amalgamate
a zinc plate, first immerse the plate in dilute sulphuric or hydrochloric
acid so as to obtain a clean surface, and then place a drop of mercury on
the plate and spread it over with a brush. The amalgamation takes place
immediately, and the plate has the brilliant aspect of mercury. Zinc and
other metals are readily amalgamated by dipping them in an amalgam
of one part sodium and 200 parts of mercury. Zinc may also be amalga-
mated in the mass by melting it in a closed vessel with 4 per cent. of
mercury, and running it into moulds.
The amalgamation of the zinc removes from its surface all the impurities,
especially the iron. The mercury effects a solution of pure zinc, which covers
the surface of the plate as with a liquid layer. The process was first applied
to electrical batteries by Kemp. Amalgamated zinc is not attacked so long
—839] Bohnenberger’s Electroscope 829
as the circuit is not closed—that is, when there is no current ; when closed
the current is more regular, and at the same time stronger, for the same
quantity of metal dissolved.
838. Dry piles—In dry piles the liquid is replaced by a solid hygro-
metric substance, such as paper. They are of various kinds ; in Zambonvs,
which is most extensively used, the materials are tin or silver and man-
ganese peroxide. To construct one of these piles a piece of paper
silvered or tinned on one side is taken ; the other side of the paper is coated
with finely powdered manganese peroxide by slightly moistening it, and
rubbing the powder on with a cork. Having placed together seven or eight
of these sheets, they are cut by means of a punch into discs an inch in
diameter. These discs are then arranged in the same order, so that the tin
or silver of each disc is in contact with the manganese of the next. Having
piled up 1,200 or 1,800 couples, they are placed in a glass tube, provided
with a brass cap at each end. Ineach cap there isa rod and knob, by which
the leaves can be pressed together, so as to produce better contact. The knob
in contact with the manganese corresponds to the positive pole, while that
at the other end, which is in contact with the silver or tin, is the negative
pole.
Dry piles are remarkable for the duration of their action, which may
last for several years. Their action depends greatly on the temperature
and on the hygrometric state of the air. It is stronger in summer than in
winter, and the action of a strong heat revives it when it appears extinct. A
Zambonr’s pile of 2,000 couples gives neither shock nor spark, but can be
used to charge a Leyden jar and other condensers.
What are known as @ry bat/eries are often convenient, especially for trans-
port. The positive and negative plates are imbedded in some porous material
such as sawdust, cocoanut fibre, gypsum, infusorial earth, or the like, which
has been soaked or boiled with a suitable liquid. They are covered with a
layer of pitch in which is an aperture for the disengagement of gas. They
are best suited for discontinuous work.
839. Bohnenberger’s electroscope.— Bohnenberger constructed a dry-
pile electroscope of great delicacy. It is a condensing electroscope (fig. 758),
from the rod of which is suspended a single gold leaf. This is at an equal
distance from the opposite poles of two dry pi'es placed vertically, inside
the bell jar, on the plate of the apparatus. When the gold leaf has
any free electricity it is attracted by one of the poles and repelled by the
other, and its electricity is obviously contrary to that of the pole towards
which it moves.
830 Dynamical Electricity [840-
CHARTER):
DETECTION AND MEASUREMENT OF VOLTAIC CURRENTS
840. Detection and measurement of voltaic currents.—The remark-
able phenomena of the voltaic battery may be classed under the heads phy-
siological, chemical, mechanical, and physical effects ; and these latter may
be again subdivided into the thermal, luminous, and magnetic effect. For
ascertaining the existence and measuring the strength of voltaic currents,
the magnetic effects are more suitable than any of the others, and, accord-
ingly, the fundamental magnetic phenomena will be described here, and
the description of the rest postponed to a special chapter on Electro-
magnetism.
841. Oersted’s experiment.—Oersted published in 1838 a discovery
which connected magnetism and electricity in a most intimate manner, and
became, in the hands of Ampere and of Faraday, the source of a new branch
of physics. The fact discovered by Oersted is the directive action which a
fixed current exerts at a distance on a magnetic needle.
To make this experiment a copper wire is suspended horizontally in the
direction of the magnetic meridian over a movable magnetic needle, as repre-
sented in fig. 800. So long as the wire
is not traversed by a current, the needle
remains parallel to it ; but as soon as
the ends of the wire are respectively
connected with the poles of a battery
or of a single cell, the needle is de-
flected, and tends to take a position
which ts the more nearly at right angles
to the magnetic meridian as the current
7s Stronger.
In reference to the direction in
which the poles are deflected, there are
several cases which may, however, be
referred to a single principle. Remembering our assumption as to the
direction of the current in the connecting wire (824), the preceding experi-
ment presents the following four cases :—
i. If the current passes above the needle, and goes from south to north,
the north pole of the magnet is deflected towards the west ; this arrangement
is represented in the above figure.
i. If the current passes below the needle, also from south to north, the
north pole is deflected towards the east.
—842] Galvanometer or Multiplier 831
11. When the current passes above the needle, but from north to south,
the north pole is deflected towards the east.
iv. Lastly, the deflection is towards the west when the current goes from
north to south below the needle.
Ampére has given the following memoria technica by which all the various
directions of the needle under the influence of a current may be remembered,
If we imagine an observer placed in the connecting wire in such a manner
that the current entering by his feet issues by his head, and that his face is
always turned towards the needle, we shall see that in the above four posi-
tions the north pole is always deflected towards the left of the observer. By
thus personifying the current, the different cases may be comprised in this
general principle : /z the directive action of currents on magnets, the north
pole ts always deflected towards the left of the current.
842. Galvanometer or multiplier.—The name galvanometer, or some-
times multiplier or rheometer, is given to a very delicate apparatus by which
the existence, direction, and intensity of currents may be determined, It
was invented by Schweigger a short time after Oersted’s discovery.
2
In order to understand its principle, let us suppose a magnetic needle
suspended by a filament of silk (fig. 801), and surrounded in the plane of the
magnetic meridian by a copper wire, #vofg, forming a complete circuit
round the needle in the direction of its length. When this wire is traversed
by a current, it follows, from what has been said in the previous paragraph,
that in every part of the circuit an observer lying in the wire in the direction
of the arrows, and looking at the needle ad, would have his left always turned
towards the same point of the horizon, and consequently, that the action of
the current in every part would tend to turn the north pole in the same
direction ; that is to say, that the actions of the four branches of the circuit
concur to give the north pole the same direction. By coiling the copper
wire in the direction of the needle, as represented in the figure, the action
of the current has been multiplied. If, instead of a single one, there are
several circuits, provided they are insulated, the action becomes still more
multiplied, and the deflection of the needle increases. Nevertheless, the
action of the current cannot be multiplied indefinitely by increasing the
number of windings, for, as we shall presently see, the strength of a current
diminishes as the length of the circuit is increased.
As the directive action of the earth continually tends to keep the needle
832 Dynamical Electricity [842-
in the magnetic meridian, while the action of the current tends to turn it at
right angles to the meridian, the effect of the current is increased by the use
of an astatic system of two needles (714), as shown in fig. 802. The action
of the needle is then very feeble, since it depends on the difference of their
moments, and this difference may be made as small as we please. The action
of the current on the two needles becomes increased. In fact, the action of
the circuit, from the direction of the current indicated by the arrows, tends to
deflect the north pole of the lower needle towards the west. The upper needle,
a’b’, is subjected to the action of two contrary currents, 770 and gf, but as the
first is nearer, its action preponderates. Now this current, passing below the
needle, evidently tends to turn the pole a’ towards the east, and, consequently,
the pole J’ towards the west ; that is to say, in the same direction as the pole
a of the other needle.
From these principles it will be easy to understand the action of the
multiplier. The apparatus represented in fig. 803 consists of a thick copper
. plate, D, resting on levelling
screws ; on this is a rotating
plate, P, of the same metal,
to which is fixed a copper
frame, the breadth of which
is almost equal to the length
of the needles. On this is
coiled a great number of
turns of wire covered with
silk. The two ends terminate
in binding screws, z and o.
Above the frame is a gradu-
ated circle, C, with a central
slit parallel to the direction
in which the wire is coiled.
The zero corresponds to
the position of this slit, and
the graduations extend on
each side of this zero up to
go°. By means of a very fine
filament of silk, an astatic
system is suspended ; it con-
sists of two needles ad and
a’b’, one above the scale,
and the other within the cir-
cuit itself. These needlés,
which are joined together
by copper wire, like those
in fig. 681 and fig. 802, and cannot move separately, must not have
exactly the same magnetic moment ; for if they are exactly equal, every
current, strong or weak, would always put them at right angles to the
coil.
When an experiment is to be made with this instrument, the diameter,
to which corresponds the zero of the graduation, is brought into the magnetic
Sa = Ge
= \. ;
SULT Tn EET TTP bt lat
ff i AY
\
eC!
| —S=- ME
|
“
See cm
rer.
—843] Dead-beat Galvanometer — 833
meridian by turning the plate P until the end of the needle a4 corresponds
to zero. The instrument is fixed in this position by means of the screw
clamp T.
The length and diameter of the wire vary with the purpose for which the
galvanometer is intended. For one which is to be used in observing the
currents due to chemical actions, a wire about } millimetre in diameter, and
making about 800 turns, is well adapted. Those for thermo-electric currents,
where the E.M.F. is low, require a thicker and shorter wire ; for example,
thirty turns of a wire 3 millimetre in diameter. For very delicate experi-
ments, as in physiological investigations, galvanometers with as many as
30,000 turns have been used.
By means of a delicate galvanometer consisting of 2,000 or 3,000 turns
of fine wire, the coils of which are carefully insulated by means of silk and
shellac, currents, such as those due to the electrical machine (813), may be
shown. One end of the galvanometer is connected with the prime con-
ductor, or one electrode (fig. 730) and the other with the ground or with the
other electrode, and when the machine is worked the needle is deflected,
affording thus an illustration of ‘the identity of statical with dynamical
electricity.
The deflection of the needle increases with the strength of the current ;
the relation between the two is, however, so complex, for the type of
galvanometer described above, that it cannot well be deduced from theoretical
considerations, but requires to be determined experimentally for each
instrument. And in the majority of cases the instrument is used as a
galvanoscope—that is, to ascertain the presence and direction of currents
—rather than as a galvanometer in the strict sense; that is, as a measure
of their intensity.. The term ga/vanometer is, however, commonly used.
In the aferential galvanometer the frame is provided with two coils of wire
of the same kind and dimensions, carefully insulated from each other, and pro-
vided with suitable binding screws, so that separate currents can be passed
through each of them. If the currents are of the same strength but in
different directions, no deflection is produced ; where the needle is deflected
one of the currents differs from the other. Hence the apparatus is used to
ascertain a difference in strength of two currents, and to this it owes its
name. |
843. Dead-beat galvanometer.—When a current is passed through a
galvanometer, the needle does not usually at once attain its final position
of equilibrium, but oscillates about this position, which in observations
causes much loss of time. If such a needle is surrounded by a mass of a
good conductor such as copper, currents are induced in the mass which, as
will afterwards be explained (926), impede, or damp, the motion of the
magnetic needle and tend to bring it to rest. Such an arrangement is
called a damper, and in practice is frequently used ; the copper frame on
which the wires of the galvanometer are coiled, and the wires themselves,
act in this way. The natural logarithm of the ratio of the amplitudes of two
successive oscillations of the needle is called the Jogarithmic decrement.
The logarithmic decrement A is proportional to the product of the damping
power ¢ and the time of a single oscillation ¢; that is, \=e¢, By diminish-
ing the directive powerof the earth on the magnet by making it astatic, the
3H
834 Dynamical Electricity [843—-
logarithmic decrement becomes infinite, and the needle attains its position
of equilibrium without oscillations. Galvanometers in which the needle
acquires at once this final deflection are known as aperiodic, or dead-beat
galvanometers.
To this class belong that of Deprez and D’Arsonval represented in
fig. 804, which is a development of Lord Kelvin’s syphon recorder (913).
Between the branches of a strong horseshoe magnet is a light iron cylinder,
which is supported independently and becomes magnetised by induction.
Between this and the magnet is a light rectangular wire coil, supported by
wires conveying the current which are in connection with binding screws.
When the current passes, the coilis deflected at right angles to the field, and
equilibrium is established when the electro-magnetic action is equalled by
the torsion of the wire. The motion of the coil can be read off by a spot
of light reflected from a mirror
(844) attached to it, and _ for
small angles the current is
proportional tothe tangent of the
angle of deflection (845). In-
duction currents due to the
motion of the coil in the field
are produced, and as this is very
powerful, the galvanometer is
virtually dead-beat when closed
by a small resistance.
When a current of very small
duration is passed through a
galvanometer, a momentary de-
flection or swung or throw of the
needle will be produced. It can
be shown that the product of a
—— = ;
SS ——— — constant into the sine of half
‘gl oP ah ee WL the angle of the first swing is
Fig. 804 then a measure of the strength
of. the... current, +.so ; that jem
momentary currents of different strengths are passed through one and the
same galvanometer, they will be measured by the sines of the corresponding
angles of deflection, or by the angles themselves where these are small.
The condition is that the duration of the current must be small in comparison
with the time of oscillation of the needle of the galvanometer. This is
known as the ballistic method (82) of measuring currents, and the galvano-
meters adapted for the purpose are known as éadlistic galvanometers.
844. Thomson’s marine galvanometer.—During the laying of submarine
cables the want was felt of a galvanometer which should be sufficiently
sensitive to test insulation, and at the same time be unaffected by the pitch-
ing and rolling of the ship. To supply this want, Lord Kelvin invented his
marine galvanometer. B (fig. 805) represents a coil of many thousand turns
' of very fine copper wire, carefully insulated throughout, terminating in the
binding screws, EE. In the centre of this coil is a slide, which carries the
magnet, the arrangement of which is represented on a larger scale in D.
—844] Thomson's Marine Galvanometer 835
The magnet itself is made of a piece of fine watch-spring about a centimetre
in length, and does not weigh more than a grain ; it is attached to a small
and very slightly concave mirror of very thin silvered glass. A single fibre
of silk is stretched across the slide, and the mirror and magnet are attached
to it in such a manner that the fibre passes exactly through the centre of
gravity in every position. As the mirror and magnet weigh only a few
grains, they retain their position relatively to the instrument, however the
ship may pitch and roll. The slide fits ina groove in the coil, and the whole
is enclosed within a wrought-iron case with an aperture in front and a
wrought-iron lid on the top. The effect of this is to act as a magnetic screen
and thereby counteract the influence of terrestrial magnetism when the ship
changes its course.
Underneath the coil is a large bent steel magnet N, which compensates
the earth’s directive action upon the magnet D (714); and in the side of the
case, and on a level with D, a pair of magnets, C, are placed with opposite
rr
|
h
LTT
yeti) my)
poles together. Bya screw, suitably adjusted, the poles of the magnets may
be brought together ; in which case they quite neutralise each other, and thus
exert no action on the suspended magnet, or they may be slid apart from
each other in such a manner that the action of either pole on D prepon-
derates to any desired extent. This small magnet is thus capable of very
delicate adjustment. The large magnet, N, and the pair of magnets, C, are
analogous to the coarse and fine adjustment of a microscope.
At a distance of about a metre, there is a scale with the zero in the
centre and the graduation extending on each side. Underneath this zero
point is a narrow slit, through which passes the light of a paraffine lamp, and
which, traversing the window, is reflected from the bent mirror against the
graduated scale. By means of the adjusting magnets the image of the slit
is made to fall on the centre of the graduation.
This being the case, if any arrangement for producing a current, however
weak, be connected with the terminal, the spot of light is deflected either to
ZH2
836 Dynamical Electricity [844~
one side or the other, according to the direction of the current ; the stronger
the current the greater the deflection of the spot ; and if the current remains
of constant strength for any length of time, the spot is stationary in a cor-
responding position, and without appreciable error the strength of the
current may be taken to be represented by the number of divisions
read off.
In the later and more improved form of this instrument a current of the
one thousand-millionth of an ampere will produce a deflection of one division
of the scale.
The movement, on a screen, of a spot of light reflected from a body, is the
most delicate and convenient means of observing motions which of them-
selves are too small for direct measurement or observation. Hence this
principle is frequently applied in experimental investigations and in lecture
illustrations (534). It is used in observing the motion of oscillating bodies,
in measuring the variations of magnetism, in determining the expansion of
solids, &c.
845. Tangent compass, or tangent galvanometer.—When a magnetic
needle is suspended in the centre of a voltaic circuit in the plane of the
magnetic meridian, it can be proved that the strength of a current is directly
proportional to the tangent of the angle of deflection, provided the needle
is sufficiently small compared with the diameter of the circuit. An
instrument based on this principle
is called the fangent galvanometer
or fangent compass. It consists
of a copper ring, 12 inches in
diameter (fig. 806) and about
an inch in breadth, mounted
vertically on a stand; the lower
half of the ring is generally fitted
in a semicircular frame of wood to
keep it steady. In the centre of
the ring is suspended a delicate
magnetic needle, whose length must
not exceed -/; or 34, of the diameter
of the circle. Underneath the
—_ @ needle there is a graduated circle.
Fane =m The ends of the ring are prolonged
in copper wires, fitted with mercury
cups, ad, by which the ring can be
connected with a battery orelement.
The ring is placed in the plane of the magnetic meridian, and the deflection
of the needle is directly read off on the circle, and its tangent obtained from
a table of tangents.
For the more accurate measurement of the deflection a light index is
sometimes placed at right angles to the needle.
On account of its small resistance, the tangent galvanometer is well
adapted for measuring currents of low potential, in which a considerable
quantity of electricity is set in motion—that is, for measuring strong currents.
To prove that the strengths of currents are proportional to the tangents
Fig. 806
—845] Tangent Compass, or Tangent Galvanometer 837
of the corresponding angles of deflection, let NS (fig. 807) represent the
ring of the galvanometer and ws the needle, and let @ be the angle of
deflection produced when a current C is passed. Two forces now act upon
each pole of the needle—the force of the earth’s magnetism, which we will
denote by H, which tends to place the needle in the magnetic meridian, and
the force due to the strength of the current C, which strives to place it at
right angles to the magnetic meridian. Let the magnitudes of these forces
be represented by the corresponding lines az and 67. Resolving these
forces parallel and perpendicular to the needle, we have mg and #f as the
components acting in opposite directions on the needle; and since the
needle is at rest these forces must be equal. The components parallel to the
needle are without effect.
The angle zag is equal to the angle ¢, and therefore 7g=an sin $ ; and
in like manner the angle 47f is equal to @ and zf=6z cos ¢ ; and therefore
: sin
since 2f=ng, 61 cos @=an sin q, or b4=an she pager p; but 4” Is
cos
proportional to the current = KC, where K is a constant and az =H, there-
fore KC =H tan ¢.
If any other current is passed through the galvanometer, we shall have
similarly C’=H tan ¢’; and since the earth’s magnetism does not appre-
ciably alter in one and the same place, C: C’=tan ¢: tan ¢’.
In this reasoning it has been assumed that the action of the current on
the needle is the same whatever be the angle by which the needle is
deflected. This only holds when the dimensions of
the needle are small compared with the diameter of the
ring : it should not be more than 4 or #4 the diameter,
so that the field in which it moves is sensibly constant.
This is especially the case with the reflecting galvano-
meter, in which the current strength may without ap-
preciable error be considered proportional to the number
of divisions read off by the telescope.
Wiedemann’s tangent galvanometer consists of a short
thick copper tube, in which is suspended, instead of a
needle, a thin piece of soft iron, silvered on one side so as
to act as a mirror, the position of which can be observed
by a telescope and scale (534). On each side of the
copper tube, and sliding in grooves, are coils of wire which
can be pushed over the tube. By this lateral arrange- ier fa?
ment of the current in reference to the magnetic needle,
the error of the tangent galvanometer is diminished ; for when the needle
is deflected, though one end moves away from the current, the other
approaches it.
In the tangent galvanometer of Helmholtz and of Gaugain the wires are
coiled on the surface of a cone the angle of which is 120°, and the point on
which the needle works is placed in the position of the corresponding apex
of the cone: the law of the tangent holds then even with longer needles, and
especially if the wire is divided between two such cones, placed on opposite
sides of the needle. .
If the ring of the tangent galvanometer is so constructed that it can
turn about its horizontal diameter, which is in the magnetic meridian, the
838 Dynamical Electricity [845—
action of the current on the needle is inversely proportional to the cosine
of the angle 6, through which the ring is turned. Hence by increasing 6
we may make the action of any current on the needle as small as we
please, and thus very powerful currents may be measured by this
instrument.
846. Sine galvanometer.—This is another form of galvanometer for
measuring powerful currents. Round the circular frame M (fig. 809},
several turns of stout insulated copper wire are coiled, which terminate
on the binding screws at E. Ona table in the centre of the ring there is a
magnetic needle, #z ; a second light needle, 7, of glass or aluminium, fixed
to the first, serves as pointer along the graduated circle N. Two copper
wires, a, 6, from the source of electricity to be measured, are connected
with E. The circles M and N are supported on a foot O, which can
move about a vertical axis passing through the centre of a fixed horizontal
ercle ik
The circle M being then placed in the magnetic meridian, and therefore
in the same plane as the needle, the current is allowed to pass. The needle
being deflected, the circuit M is turned until it coincides with the vertical
plane passing through the magnetic needle 7. The directive action of the
current is now exerted perpendicularly to the direction of the magnetic
needle, and it may be shown that the strength of the current is propor-
tional to the sine of the angle
through which the galvanometer
has been turned: this angle is
measured on the circle H by
means of a vernier on the piece
C. The latter, fixed to the foot
O, turns it by means of a knob
A. This angle being known,
and hence its sine, the strength
of the current may be thus de-
————
————_
pn UNIT
vii ee
Pe till
al Ui}
Fig. 80% Fig. 809
duced : let 772’ be the direction of the magnetic meridiarf, C the strength
of the current, and H the directive action of the earth. If the direction
and intensity of this latter force are represented by a@&, it may be replaced
847] Ohn’s Law 839
by two components, af and ac (fig. 808). Now, as the first has no directive
action on the needle, the component ac must alone counterpoise the force
due to the current C; call this force 2C where & is a constant. Then
&kC=ac. But in the triangle ack, ac=ak cos cak, from which ac=H sin d,
for the angle caz is the complement of the angle d, and aé is equal to H ;
hence, lastly, #C =H sin d, which was to be proved. In like manner for any
other current C’, which produces a deflection a’, we shall have £C’=H sin
@., whence (> C=sined ssid .
847. Ohm’s law.—For a knowledge of the conditions which regulate
the action of the voltaic current, science is indebted to the late G. S. Ohm.
His results were at first deduced from theoretical considerations ; but by
his own researches as well as by those of Fechner, Pouillet, Daniell, De la
Rive, Wheatstone, and others, they received the fullest confirmation, and
their great theoretical and practical importance has been fully established.
1. The force or cause by which electricity is set in motion in the voltaic
circuit is called the electromotive force. The quantity of electricity which in
any unit of time flows through a section of the circuit is called the zzfenszty,
or, perhaps better, che strength of the current. Ohm found that this strength
is the same in all parts of one and the same circuit, however heterogeneous
they were; one and the same magnetic needle is deflected to the same
extent over whatever part of the circuit it is suspended; and the same
voltameter, wherever interposed in the circuit, indicates the same disengage-
ment of gas ; he also found that the strength is proportional to the electro-
motive force.
It has further been found that when the current from the same element
is passed respectively through a short and through a long wire of the same
material, its action on the magnetic needle is less in the latter case than in
the former. Ohm accordingly supposed that in the latter case there was a
greater veststance to the passage of the current than in the former; and he
proved that ‘for a constant electromotive force ¢he strength of the current ts
inversely proportional to the resistance,
On these principles Ohm founded the celebrated law which bears his
name, that ¢he strength of the current ts equal to the electromotive force
divided by the reststance.
This is expressed by the simple formula
guides
R
where C is the strength of the current, E the electromotive force of the cell
or battery, and R the resistance of the circuit.
i. As applied to a portion of the circuit Ohm’s law may be stated thus :
let y be the resistance of a conductor forming part of a closed circuit, through
which a current C flows, and let e be the difference of potential between the
ends of 7, the C= ..
iii. The resistance of a conductorjdepends on three elements : its comdzc-
tivity, which is a constant special property, determined for each conductor ;
its sectzon ; and its /emgth. ‘The resistance is obviously inversely proportional
to the conductivity ; that.1s, the less the conducting power, the greater the
840 Dynamical Electricety [847—
resistance. It has been proved that ¢he reststance ts inversely as the section
and directly as the length of a conductor. If then x is the conductivity, the
section, and A the length of a conductor, we have
Ree
K@
iv. Ina circuit containing a voltaic battery composed of different elements,
the strength of the current is equal to the sum of the electromotive forces of
all the elements divided by the sum of the resistances. - Usually, however, a
battery is composed of elements of the same kind, each having the same
electromotive force and the same resistance.
In any simple circuit there are essentially two resistances to be con-
sidered : 1. That offered by the liquid conductor between the two plates,
which is called the zz¢ernal resistance ; and 2. That offered by the interpolar
conductor which connects the two plates outside the liquid ; this conductor
may either consist wholly of metal, or be partly of metal and partly of
liquids to be decomposed ; it is the external resistance. Calling the former
R and the latter 7, Ohm’s formula becomes
E
eheyy 6
v. If any number, 7, of similar elements are joined together, there is
m times the electromotive force, but at the same time z times the internal
resistance, and the formula becomes - ee :
C=2R+r7
interpolar, 7, is very small—which is the case, for instance, when it is a short,
thick copper wire—it may be neglected in comparison with the internal
resistance, and then we have
If the resistance in the
ae:
Cs22a
mR R’
that is, a battery consisting of several elements produces in this case no
greater effect than a single element.
vi. If, however, the external resistance is very great, as when the current
has to work a long telegraphic circuit, advantage is gained by using a large
number of elements, for then we have the formula
if is very great as compared with zR, so that the latter may be neglected,
the expression becomes
that is, the strength, within certain limits, is pr portional to the number of
elements.
In the case of a thermo-electric pile (972), which consists of very short
metallic conductors, the internal resistance R is so small that it may be
-847] Ohm's Law 841
neglected, and the strength is inversely as the length of the connecting
wire.
vil. If the plates of an element be made zz times as large, there is no
increase in the electromotive force, for this depends solely on the nature
of the metals and of the liquid (822); but the resistance is 7 times as small,
for the section is 7 times as large: the expression becomes then
Py 8 772i8
R R+wmr
Wmr7r
Hence, an increase in the size of the plate—or, what is the same thing, a
decrease in the internal resistance—does not increase the strength to an
indefinite extent ; for ultimately the resistance of the element R vanishes in
comparison with the resistance 7, and the strength continually approximates
to the value C = E
r
vill. Ohm’s law enables us to arrange a battery so as to obtain the greatest
effect in any given case. For instance, with a battery of six elements there
are the following four ways of arranging them :—1. In a single series (fig.
810), in which the zinc Z of one element 1s united with the copper C of the
842 Dynamical Flectrecity [847-
second, the zinc of this with the copper of the third,and so on. 2. Arranged
in a system of three double elements, each element being formed by joining
two of the former (fig. 811). 3. In a system of two elements, each of which
consists of three of the original elements joined, so as to form one of
triple the surface (fig. 812). Lastly, of one large element, all the zincs and
all the coppers being joined, so as to form a pair of six times the surface
(fig. 813).
With a series of twelve elements there may be six different combinations,
and so on for a larger number.
Now let us suppose that in the particular case of a paneer of six elements
the internal resistance R of each element is 3, and the external resistance
y=12. Then in the first case where there are six elements arranged in
series we have the value |
CE SE eee ee a
6R+r 6x3+12 30
If they were united so as to form three elements, each of double the
surface as in the second case (fig. 811), the electromotive force would then
be three times the electromotive force in each element : there would also bea
resistance R in each element, but this would be only half as great, for the
area of the plate is now double ; hence the strength in this case would be
; 2k; 2b. 6E
CORR Gian ea aPiae coe Te f (2)
I a+r EE agree
2)
accordingly this change would lessen the strength.
If, with the same elements, the resistance in the connecting wire were
only ~= 2, we should have the values in the two cases respectively—
The result in the latter case is, therefore, more favourable. If the re-
sistance ~ were 9, the strength would be the same in both cases. Hence,
then, by altering the size of the plates or ‘their arrangement, favourable
or unfavourable results are obtained according to the relation between R
and 7
848. Arrangement of multiple battery for maximum current.—-It can be
shown that z7 amy given combination the maximum effect ts obtained when
the total resistance of the battery ts egual to the external resistance. For
let N be the total number of cells available for a given combination, and
let 2 be the number of cells arranged fandem, or in series—that is, when
the zinc of one is connected with the copper of the next, and so on; then
there will be N elements arranged abreast or in parallel. If e be the elec-
nt
- 848] Arrangement of Multiple Battery 843
tromotive force and ~ the resistance of one cell, while 7 is the external
resistance, then the strength of the current will be
Came ne etere,
ur nr Ah EL
CO MRIS a
N N Ne
nN
oe 45 {ir : ME EeTA Ass f ur
Therefore C is a maximum when N He iS. a@ minimum, » Sut — x u
Ip y un
ri . , MANY oi ia mr
= is a constant, therefore the sum —_ +“ is a minimum when “ = f .
N N 2 N n
9
, ads : :
that is, when N =/, or when the total internal resistance is equal to the
external resistance.
>
For if « and ~~ are any two quantities whose product is A’, then
25
_ A? 2474+ A?-2Ar+2Ar_(x-A)
Cae eer ive See als ao Na eee
oe ac 8
This is greater than 2A unless x—A =o, in which case it is equal to 2A, and
is a minimum. In that case x=A, and therefore
It follows thus from the above formula that the best effect is obtained
N/
“it
If in a given case we have 8 elements, each offering a resistance 15
and an interpolar with the resistance 4o, we get z=4°6. But this is an
impossible arrangement, for it is not a whole number, and the nearest
whole number must be taken. This is 4; and it will be found, on making
a calculation analogous to that above, that when the battery is arranged
so as to form 4 elements, each of double surface, the greatest current is
obtained.
when 2=
The formula for the strength of current from several elements, C eae
may also be applied to the currents produced by a magneto-electrical
machine (940). In that case z stands for the number of coils which in a
given. time cut the lines of force of a magnetic field.
The principle that the best effect is obtained when the total internal is
equal to the total external resistance, holds also for the currents produced by
these machines.
~
844 Dynamical Electricity [849-
CHAP TreRe ii)
EFFECTS OF THE CURRENT
849. Physiological actions.—Under this name are included the effects
produced by a battery current on living organisms or tissues.
When the electrodes of a battery of many cells are held in the two hands a
violent shock is felt, especially if the hands are moistened with acidulated
water, which increases the conductivity. The violence of the shock increases
with the number of elements used, and with a large number—as 200 Bunsen’s
cells—is even dangerous.
The power of contracting upon the application of a voltaic current seems
to be a very general property of fvotopflasm—the physical basis of both
animal and vegetable life ; if, for example, a current of moderate strength is
passed through such a simple form of protoplasm as an amceba, it imme-
diately withdraws its processes, ceases its changes of form, and contracts into
a rounded ball—soon, however, resuming its activity upon the cessation of
the current. Essentially similar effects of the current have been observed in
the protoplasm of young vegetable cells.
If a frog’s fresh muscle (which will retain its vitality for a considerable
time after removal from the body of the animal) is introduced into a galvanic
circuit, no apparent effect will be observed during the steady passage of the
current, but every opening or closure of the circuit will cause a muscular
contraction, as will also any sudden and considerable alteration in the
strength of the current. By very rapidly interrupting the current, the
muscle can be thrown into a state of uninterrupted contraction, or physiolo-
gical ¢e¢anis, each new contraction occurring before the previous one has
passed off. Other things being equal, the amount of shortening exhibited
by the muscles increases, up to a certain limit, with the intensity of the
current. These phenomena entirely disappear with the life of the muscle ;
hence the experiments are somewhat more difficult with warm-blooded
animals, the vitality of whose muscles, after exposure or removal from the
body, is maintained with more difficulty ; but the results of careful experi-
ment are exactly the same here as in the case of the frog.
The influence of an electric current upon living nerves is very remark-
able ; as a general rule, it may be stated that its effect is to throw the nerve
into a state of activity, whatever its special function may be: thus, if the
nerve be one going to a muscle, the latter will be caused to contract ; if it
be one of common sensation, pain will be produced ; if one of special sense,
the sensation of a flash of light, or of a taste, &c., will be produced, accord-
ing to the nerve irritated. These effects do not manifest themselves during
the even passage of the current, but only when the circuit is either opened or
—850] Electrotonus 845
closed, or both. Of course the continuity of the nerve with the organ where
its activity manifests itself must be maintained intact. The changes set up
by the current in the different nerve-trunks are probably similar, the various
sensations, &c., produced depending on the different terminal organs with
which the nerves are connected.
Professor Burdon Sanderson has ascertained that the movement which
causes the Dionea muscipula (Venus’s fly-trap), one of those which are
called carnivorous plants, to close its hairy leaves and thereby entrap in-
sects which alight upon it, is accompanied by an electrical current in a manner
analogous to that manifested in muscular contraction. The manner in which
the irritation is caused seems immaterial.
850. Electrotonus.—In a living nerve, as will be stated more fully in
Chapter X., certain parts of the surface are electropositive to certain other
parts, so that if a pair of electrodes connected with a galvanometer be applied
to these two points, a current will be indicated ; if now another part of the
nerve be interposed in a galvanic circuit, it will be found that, if this extra-
neous current be passing in the same direction as the proper nerve-current,
the latter is increased, and vice versé ; and this although it has previously
been demonstrated experimentally that none of the battery current escapes
down the nerve, so as to exert any influence of its own on the galvanometer.
This alteration of its natural electromotive condition, produced through the
whole of a nerve by the passage of a constant current through part of it, is
known as the e/lectrotonic state ; it is most intense near the extraneous, or, as
it is called, the exczting current. It continues as long as the latter is pass-
ing, and is attended with important changes in the erczfadbz/zty of the nerve,
or, in other words, the readiness with which the nerve is thrown into a state
of functional activity by any stimulus applied to it. Pfluger, who has inves-
tigated these changes, has named the part of the nerve through which the
exciting current is passing the zw¢rapolar region ; the condition of the nerve
close to the positive pole is called amelectrotonus ; that near the negative
pole, kathelectrotonus. The excitability of the nerve is diminished in the
anelectrotonic region, so that with a motor nerve, for example, a stronger
stimulus than before would need to be applied at this part in order to obtain
a muscular contraction ; in the kathelectrotonic region, on the contrary, the
excitability of the nerve is heightened. Moreover, with an exciting current
of moderate strength, the power of the nerve to conduct a stimulus is lowered
in the anelectrotonic region, and increased in the kathelectrotonic ; with
strong currents it is said to be diminished in both.
These facts have to be taken into account in the scientific application of
galvanism to medical purposes. If, for instance, it is wished to diminish the
excitability of the sensory nerves of any part of the body, the current should
be passed in such a direction as to throw the nerves of that part into a state
of an electrotonus —and similarly in other cases.
If a powerful electric current be passed through the body of a recently
killed animal, violent movements are produced, as the muscles ordinarily
retain their vitality for a considerable time after general systematic death :
by this means, also, life has been re-established in animals which were appa-
rently dead—a properly applied current stimulating the respiratory muscles
to contract. *
846 Dynamical Electricity [851-
851. Heating effects.—When a voltaic current is passed through a metal
wire the same effects are produced as by the discharge of an electric battery
(812) ; the wire becomes heated, and even incandescent if it is very short
and thin. With a powerful battery all metals are melted, even iridium and
platinum, the least fusible of metals. Carbon is the only element which has
not hitherto been fused by it. Despretz, however, with a battery composed
of 600 Bunsen’s elements joined in six series (831), raised rods of very pure
carbon to such a temperature that they were softened and could be welded
together, yielding an incipient fusion.
A battery of 30 to 40 Bunsen’s elements is sufficient to melt and volatilise
fine wires of lead, tin, zinc, copper, gold, silver, iron, and even platinum, with
differently coloured sparks, Iron and platinum burn with a brilliant white
light ; lead with a purple light ; the hght of tin and of gold is bluish-white ;
the hght of zinc
is a mixture of
white and gold ;
finally, copper
and silver give
a green light.
The thermal
t effects of the
voltaic current
aréwi usediwnfar
firing mines for
~ military — pur-
poses and _ for
blasting opera-
tions. The fol-
lowing arrange-
ment (fig. 814)
serves to illus-
trate the prin-
ciple :—Two moderately stout copper wires, 20’, insulated by being covered
with gutta-percha, are deprived of this coating at the ends, which are then
passed through and through the box in the manner represented in the
figure. The distance between them is 2 of an inch, and a very fine
platinum wire is soldered across. The object of arranging the wires in
this manner is that they shall not be in contact, and that the strain which
they exert may be spent on the box, and not on the platinum wire joining
them, which, being extremely thin, would be broken by even a very slight
pull. The box is then filled with fine grained powder, and the lid tied
down. The wires of the fuse are then carefully joined to the long con-
ducting wires which lead to the battery: these should be of copper, and
as thick as is convenient, so as to offer very little resistance. The fuse
is then introduced into the charge to be fired: if it is for a submarine
explosion, the powder is contained in a canister, the neck of which, after
the introduction of the fuse, is carefully fastened by means of cement:
When contact is made with the battery, the current traversing the platinum
wire renders it incandescent, which fires the fuse ; and thus the ignition is
communicated to the charge in which it is placed.
Fig. 814
-852] Laws of Heating Effects. Galvanothermometer. 847
When any circuit is closed, a definite amount of heat, H, is produced
throughout the entire circuit ; and the amount of heat, 2, produced in any
particular part of the circuit bears to the total heat, H, the same ratio which
the resistance, ~ of this part bears to R, that of the entire circuit. That is
h:H=r:R. Hence, in firing mines, the wire to be heated should be of as
small section and of as small conductivity as practicable. These conditions
are well satisfied by platinum, which has over iron the advantage of being
less brittle and of not being lable to rust. Platinum too has a low specific
heat, and is thus raised to a higher temperature, by the same amount of
heat, than a wire of greater specific heat. On the other hand, the con-
ducting wires or /eads should present as small a resistance as possible,
a condition satisfied by a stout copper wire; and again, as the heating
effect of any circuit is proportional to the square of the electromotive
force, and inversely as the resistance, a battery with a high electromotive
force and small resistance, such as Grove’s or Bunsen’s, should be selected.
Another application of the heating effect is to what are called safety
catches or automatic cut-outs. These are lengths of lead wire or strips
interposed in the circuit of the powerful currents used for electrical lighting
and the like. Their dimensions are calculated so that when the current
attains a certain strength, the heat generated is sufficient to melt them and
thus break the continuity of the circuit. As this can be arranged with great
accuracy, it is possible so to regulate the circuit that it shall not exceed a
certain limit.
By means of a heated platinum wire, parts of the body may be safely
cauterised which could not be got at by a red-hot iron; the removal of
tumours and the like may be effected by drawing a loop of cold platinum
wire round their base, making the wire hot by a current, and gradually
pulling its ends together. It has been observed that when the temperature
of the wire is about 600° C., the combustion of the tissues 1s so complete that
there is no haemorrhage ; while at 1,500° the action of the wire is like that of
a sharp knife. For other purposes of this
galvanic cautertsation, platinum wire coiled
-in grooves cut in a porcelain rod is used.
852. Laws of heating effects. Galvano-
thermometer.—Although the thermal effects
are most obvious in the case of thin wires,
they are by no means limited to them. The
laws of the heating effect were investigated by
Lenz, by means of an apparatus called the
Galvanothermometer (fig. 815). A wide-
mouthed stoppered bottle was fixed upside
down, with its stopper, 4, in a wooden box ; 7 y N “
the stopper was perforated so as to give pas- 7 ddd si Y
sage to two thick platinum wires, connected 2 'Yff jj
at one end with binding screws, ss, while their {/ VM
free ends were provided with platinum cones
by which the wires under investigation could
be readily affixed ; the vessel contained alcohol, the temperature of which
was indicated by a thermometer fitted in a cork inserted in a hole made in
8.48 Dynamical Electricity [852—
the bottom of the vessel. The current is passed through the platinum
wires, and its strength measured by means of a tangent compass inter-
posed in the circuit. By observing the increase of temperature in the
thermometer in a given time, and knowing the weight of the alcohol, the
mass of the wire, the specific heat, and the calorimetric values (462) of
the vessel, and of the thermometer, compared with alcohol, the heating
effect which is produced by the current in a given time can be calculated.
By apparatus of this kind the truth of the following law may be esta-
blished.
The heat disengaged in a given time, ¢, ts directly proportional to the
square of the strength of the current, and to the resistance.
This is known as /ow/e’s daw, and is expressed in the formula JH =
2
C7RL= Bed =EC/, where J is the mechanical equivalent of heat. If we
divide the values E,C, Rexpressed in ergs, by the mechanical equivalent
of a water-gramme degree, that is, by 4°16 10’, we get the value H in
water-cramme degrees.
In the above formula the symbols H, C, R, E refer to the whole circuit.
If H denote the heat developed in a wire of resistance 7, in a time # due to
the passage of a current C, the potential difference at the ends of ~
29
e°
being 2, the corresponding formule are JH =C?77— Cez—_7
je
If the current passes through a chain of alternate links of platinum and
silver wire of equal sizes, the platinum becomes more heated than the silver
from its greater resistance ; and with a suitable current the platinum may
become incandescent while the silver remains dark. This experiment was
devised by Children.
If a long thin platinum wire is raised to dull redness by passing a voltaic
current through it, and if part of it is cooled down by being dipped in hot
water, the resistance of the cooled part is diminished, the strength of the
current increases, and the rest of the wire becomes brighter than before.
If, on the contrary, a part of the feebly incandescent wire is heated by a
spirit-lamp, the resistance of the heated part increases ; the effect is the
same as that of introducing additional resistance, the strength of the
current diminishes, and the wire ceases to be incandescent in the non-
heated part.
Radiation and convection of heat lower the temperature to which a wire
is raised by the passage of a given current through it. A round wire is more
heated by the same current than the same wire which has been beaten out
flat: for the latter with the same section offers a greater surface to the
cooling medium than the other. For the same reason, when a wire is
stretched in a glass tube on which two brass caps are fitted air-tight, and the
wire is raised to dull incandescence by the passage of a current, the incan-
descence is more vivid when the air has been pumped out of the tube, because
it now simply loses heat by radiation, and not by communication to the
surrecunding medium.
Similarly, a current which will melt a wire in air will raise it only to dull
redness in ether, and in oil or in water will not heat it to redness at all, for
the liquids conduct heat awav more readily than air does.
-854] Relation of Heating Effect to Work of a Battery 849
From the above laws it follows that the heating effect is the same in a wire
whatever be its length, provided the current is constant ; but it must be remem-
bered that by increasing the length of the wire we increase the resistance,
and consequently, to maintain the current constant, we must apply a larger
E.M.F. ; further, in a long wire there is a greater surface, and hence more
heat is lost by radiation and by conduction.
It must be added that Joule’s law only holds provided the current does
no external work, such as inductive actions on adjacent conductors, or mag-
nets—that, in short, the thermal is the only action of the current.
853. Graphical representation of the heating effects in a circuit.
The law representing the production of heat in a circuit in the unit of time
is very well seen by the following geometrical construction, due to Professor
Foster.
The heat H produced in a circuit in the unit of tinie is proportional to
the square of the strength of the current C, and to the resistance R (851),
2
thatiseri aC Riesput since.© == (847), we have H = a
Draw a straight line DAB (fig. 816), and from any point A init drawa
line AC, at right angles to DAB, and of a length proportional to the electro-
motive force of
$e) ice.) shay.
off a length AB
proportional to
the resistance n
of the circuit.
Join CB, and at
GAdraw a; line
at right angles
to +BG band, let Le) : RB
D be the point % sie B
where this line ng
cuts the line DAB. Then the length AD is proportional to the eat produced
in the whole circuit in unittime. For the triangles ADC and ACB are similar,
anditherefore"AD:AC = AC:AB; that is, AD ee that is) HAE
The above construction holds good if R and E, instead of being the
resistance of the whole circuit and the E.M.F. of the battery, are respectively
the resistance of any part of the circuit and the potential difference at the
ends of this part.
854. Relation of heating effect to work of a battery.—In every
closed circuit chemical action is continuously going on ; in ordinary cir-
cuits, the most common action is the solution of zinc in sulphuric acid, which
may be regarded as an oxidation of the zinc to form zinc oxide, and
a combination of this zinc oxide with sulphuric acid to form water and
zinc sulphate. It is a true combustion of zinc, and this combustion serves
to maintain all the actions which the circuit can produce, just as all the
work which a steam-engine can effect has its origin in the combustion of
fuel (493). :
By independent experiments it has been found that, when a given weight
a1
850 Dynamical Electricity [854—
of zinc is dissolved in sulphuric acid, a certain definite measurable guantity
of heat is produced, which, as in all cases of chemical action, is the same,
whatever be the rapidity with which this solution is effected. If this solution
takes place while the zinc is associated with another metal so as to form a
voltaic couple, the rapidity of the solution will be altered and the whole cir-
cuit will become heated—the liquid, the plates, the containing vessel as well
as the connecting wire. But although the distribution of the heat is thus
altered, its quantity is not. If the values of all the several heating effects in
the various parts of the circuit be determined, it will still be found that
however the resistance of the connecting wire be varied, the sum of these
values is exactly equivalent to the heat produced by the solution of a certain
weight of zinc.
If the couple is made to do external mechanical work, the case is dif-
ferent. Joule made the following remarkable experiment :—A small zinc
and copper couple was arranged in a calorimeter, and the amount of heat
determined while the couple was closed for a certain length of time by a
short thick wire. The couple still contained in the calorimeter was next
connected with a minute electromagnetic engine (920), by which a weight was
raised, It was then found that the heat produced in the calorimeter in a
given time—while, therefore, a certain amount of zinc was dissolved—was
less while the couple was doing work than when it was not; and the
amount of this diminution was the exact thermal equivalent of the work
performed in raising the weight (509).
That the whole of the chemical work and disengagement of heat in the
circuit of an ordinary cell has its origin in the solution of zinc in acid is
confirmed by the following experiment, due to Favre :—
' In the muffle of his calorimeter (473), five small-zinc platinum elements
were introduced ; the other muffle contained a voltameter. Now when the
element was closed until one equivalent of zinc was dissolved in the whole of
the cells, 4 of an equivalent of water should be decomposed in the voltameter
(868), which was found to be the case. In one case the current of the
battery was closed without inserting the voltameter, and the heat disengaged
during the solution of one equivalent of zinc was found to be 18,796 thermal
units ; when, however, the voltameter was introduced, the quantity disengaged
was only 11,769 thermal units. Now the difference, 7,027, is represented by
the chemical work of decomposing 4 of an equivalent of water : this agrees
34,462
5
very well with the number, 6,892 = , which represents the heat disen-
gaged during the formation of 4 of an equivalent of water.
However complicated may be the chemical processes involved in a voltaic
combination, the total heat produced in it is the sum of the quantities of heat
which are produced and absorbed in these various chemical processes.
We may illustrate this important principle by reference to the element
of De la Rue and Miller (833), the chemical actions in which are perhaps
the simplest of all constant elements. The normal action is that, when the
element is closed, zinc decomposes ammonium chloride with the formation
of zinc chloride, while the liberated ammonium unites with the chlorine of
the silver chloride, re-forming ammonium chloride and depositing silver.
The heat of decomposition and of re-formation of the ammonium chloride
—855] Luminous Effects 851
compensate one another, and the net result is the formation of zinc chloride,
and the decomposition of silver chloride. Now the heat produced in the
formation of a molecule of zinc chloride (ZnCl,) is 112,840 gramme units,
and that of the equivalent silver chloride (2Ag Cl) is 58,760. The difference
is 54,080, which is less than 58,360, the heat required to decompose a mole-
cule of water. Hence it is that one such element will not effect a continuous
decomposition of water, but at least two are required for the purpose. In
like manner the heat available by the substitution of zinc for copper in one
Daniell’s cell is represented by 47,300, and accordingly at least two of these
elements are also required.
In some cases, however, the current of a single cell does produce a feeble
but continuous decomposition of water. This arises from the fact that the
water of the voltameter contains air in solution, and the hydrogen as it is
liberated unites with the dissolved oxygen. This process is known as
electrolytic convection.
This principle is, however, not of universal validity. Fora great number
of cells the electrical energy is less than corresponds to the thermal tonation,
and part of their energy is transformed into heat ; while for a small number
the electrical energy is greater ; such cells when closed absorb heat from the
surrounding medium.
855. Luminous effects.—Luminous effects are obtained when the battery
is sufficiently powerful, by bringing the two electrodes very nearly in contact ;
a succession of bright
sparks springs sometimes
across the interval, which
follow each other with ,
such rapidity as to produce i
continuous light. Although ian ni
the quantity of electricity f
put in motion by the
voltaic current iS very +f |
great, the distance across
which the spark passes is
very small. Jacobi found
that with a battery of 12
Grove’s elements the elec-
trodes could be approached
within o70013 mm. before
the spark passed.
When one terminal of
a battery of a few elements
is connected’ with a file,
and an iron wire connected
with the other is moved |
over the file, a stream of brilliant luminous sparks is obtained, which obviously
arises from a combustion.
The most beautiful effect of the electric light is obtained when two pencils
of charcoal are connected with the terminals of the battery in the manner
represented in fig. 817. The charcoal 6 is fixed, while the charcoal @ can
zi 2
852 Dynamical Electricety | [855-
be raised and lowered by means of a rack and pinion motion, ¢. The two
charcoals being placed in contact, the current passes, and their ends soon
become incandescent. If they are then removed to a distance of about the
tenth of an inch, according to the strength of the current, a luminous arc
extends between the two points, which has an exceedingly brilliant lustre,
and is called the voltaic arc.
The length of this arc varies with the strength of the current. In air it
may exceed 2 inches, with a battery of 600 elements, arranged in six series
of 100 each, provided the positive pole is uppermost, as represented in the
figure ; if it is undermost, the arc is about one-third shorter. In a partial
vacuum the distance of the charcoals may be greater than in air ; in fact,
as the electricity meets with no resistance, it springs between the two
charcoals, even before they are in contact. The voltaic arc can also be
produced in liquids, but it 1s then much shorter, and its brilliancy is greatly
diminished.
The voltaic arc has the property that it is attracted when a magnet is pre-
sented to it—a case of the action of magnets on currents (889).
The voltaic arc may be considered as formed of a very rapid succession
of bright sparks. Its colour and shape depend on the nature of the conduc-
tors between which it is formed, and it is probably due to the incandescent
particles of the conductor, which are volatilised and transported in the direc-
tion of the current; that is, from the positive to the negative pole. The
more easily the electrodes are disintegrated by the current, the greater
is the distance at which the electrodes can be placed. Charcoal, which is a
very friable substance, is one of the bodies which give the largest luminous
Ar:
Davy first made the experiment of the electric light in 1801, by means of
a battery of 3,000 plates, each four inches square. He used charcoal points
made of light wood charcoal which had been heated to redness, and im-
mersed in a mercury bath ; the mercury penetrating into the pores of the
charcoal increased its ponductiany When any substance was introduced
into the voltaic arc produced by this battery, it became incandescent ; pla-
tinum melted like wax in the flame of a candle ; sapphire, magnesia, lime,
and most refractory substances were fused. Fragments of diamond, of
charcoal, and of graphite rapidly disappeared without undergoing any
previous fusion.
As charcoal rapidly burns in air, it was necessary to operate in vacuo,
and hence the experiment was for a long time made by fitting the two points
in an electric egg, like that represented in fig. 767. At present the electrodes
are made of gas graphite, a modification of charcoal deposited in gas retorts ;
this is hard and compact, and only burns slowly in air ; hence it is unneces-
sary to operate in vacuo. When the experiment is made in vacuo, there is
no combustion, but the charcoal wears away at the positive pole, while it is
somewhat increased on the negative pole, indicating that there is a transport
of solid matter from the positive to the negative pole.
It appears from the researches of Edlund that the disintegration of the
electrodes which takes place when the voltaic arc is formed gives rise to a
counter-electromotive force which is analogous to the polarisation which
takes place in the decomposition of water (863), and the existence of which
—857] Regulator of the Electric Light 853
can be demonstrated by similar experiments. The magnitude of this force
varies with the nature of the electrodes ; it is greatest with carbon, amount-
ing to 35 volts ; with iron it is 25 ; copper, 24; zinc, 19; and cadmium
10 volts.
The resistance of the arc itself, due to the medium, increases like
other resistances with the distance of the terminals; it diminishes as the
strength of the current increases, for then the temperature increases.
With carbon electrodes, it was found to amount to 1°3 ohm for each mm. of
distance.
This counter-electromotive force explains how it is that a continuous
arc can only be obtained by the application of considerable electromotive
force.
856. Foucault’s experiment.—This consists in projecting on a screen
the image of the charcoal points produced in the camera obscura at the
moment at which the electric light is formed (fig. 818). By means of this
i nt irk
( ul It :
Fig. 818
experiment, which is made by the photo-electric microscope already de-
scribed (fig. 604), the two charcoals can be readily distinguished, and the
positive charcoal is seen to become somewhat hollow and diminished, whiie
the other increases. The globules represented on the two charcoals arise
from the fusion of a small quantity of silica contained in the charcoal. When
the current begins te pass, the negative charcoal first becomes luminous,
but the light of the positive charcoal is the brightest ; as it also wears away
about twice as rapidly as the negative electrode, it ought to be rather the
larger.
857. Regulator of the electric light.—When the electric light is to be
used for illumination, it must be as continuous as other modes of lighting.
For this purpose, not only must the current be constant, but the distance of
the charcoals must not alter, which necessitates the use of some arrange-
ment for automatically bringing them nearer together in proportion as they
854 Dynamical Electricity [857—
wear away. One of the best modes of effecting this is by an apparatus in-
vented by Duboscq.
In this regulator the two charcoals are movable, but with unequal veloci-
ties, which are virtually proportional to their waste. The motion is trans-
mitted by a drum placed on the axis xy (fig. 819). This turns, in the direc-
tion of the arrows, two wheels, aand 4, the diameters of hich AYE "AS "ites
and which respectively trans-
mit their motion to two
rackworks, CGC and ti.) @
lowers the positive charcoal,
~p, by means of a rod sliding
in the tube H, while the
other C’ raises the negative
charcoal, 2, half as rapidly.
By means of the milled
head y the drum can be
wound up, and at the same
time the positive charcoal
moved by the hand; the
milled head 2 moves the
negative charcoal also by
the hand, and independently
of the first. For this pur-
pose the axis, xy, consists of
two parts pressing against
each other with some force,
so that, while the milled
head x is held between the
fingers, the other, y, may be
moved, and by holding the
latter we may move the
former. But the friction is
sufficient when the drum
works to move the two
wheels a and 4 and the two
rackworks.
The two charcoals being
placed in contact, the cur-
rent of a powerful battery
of 40 to 50 elements reaches
the apparatus by means of
the wires E and E’. The current rising in H descends by the positive
charcoal, then by the negative charcoal, and reaches the apparatus, but
without passing into the rackwork C, or into the part on the right of the
plate N ; these pieces being insulated by ivory discs placed at their lower
part. Thecurrent ultimately reaches the bobbin B, which forms the foot of
the regulator, and passes into the wire E’. Inside the bobbin is a bar of
soft iron, which is magnetised as long as the current passes in the bobbin,
and demagnetised when it does not pass, and this temporary magnet is
—858] Browning's Regulator 855
the regulator. It acts attractively on an armature of soft iron, A, open in
the centre so as to allow the rackwork C’ to pass, and fixed at the end of a
lever, which works on two points, 77, and transmits a slight oscillation to
a rod, ad, which, by means of a catch, z, seizes the wheel z,as is seen ona
larger scale in fig. 820. By an endless screw, and a series of toothed wheels,
the stop is transmitted to the drum, and the rackwork being fixed, the same
is the case with the carbons. This is what takes place so long as the
‘magnetisation in the bobbin is strong enough to keep down the armature
A; but in proportion as the carbons wear away, the current becomes
feebler, though the voltaic arc continues, so that ultimately the attraction
of the magnet no longer counterbalances a spring 7, which continually tends
to raise the armature. It then ascends, the piece @d disengages the stop 2,
the drum works, and the carbons come nearer; they do not, however,
touch, because the strength of the current gains the upper hand, the
armature A is attracted, and the carbons remain fixed. As their distance
only varies within very narrow limits, a regular and continuous light is
obtained with this apparatus until the carbons are quite used.
By means of a regulator, Duboscq illuminates the photogenic apparatus
represented in fig. 604, by which all optical experiments may be performed for
which sunlight was formerly essential.
858. Browning’s regulator. —A
much simpler apparatus, represented
in fig. 821, has been devised by Brown-
ing, which is less costly than the other
lamps, and also requires a smaller
number of elements to work it. The
current enters the lamp by a wire at-
tached to a binding screw on the base
of the instrument, passing up the pillar
by the small electro-magnet to the
centre pillar along the top of the hori-
zontal bar, down the left-hand bar
through the two carbons, and away by
a wire attached to a binding screw on
the left hand. A tube holding the
upper carbon slides freely up and down
a tube at the end of the cross-piece,
and would by its own weight rest on
the lower carbon, but the electro-mag-
net is provided with a keeper, to which
is attached a rest that encircles the
carbon tube and grasps it. When the =
electro-magnet works and attracts the SSS
keeper, the rest tightens, and thereby i .
prevents the descent of the carbon.
When the keeper is not attracted the rest loosens, and the carbon-holder
descends.
When the two carbons are in contact, and the battery circuit is com-
pleted, the current traverses both carbons and no light is produced.: But if
Fig. 821
856 Dynamical Electricity [858-
the upper carbon is raised ever so little, a brilliant light is emitted. When
the lamp is thus once set to work, the rod attached to the upper carbon
may be let go, and the magnet will afterwards keep the lamp at work For
when some of the carbon is consumed, and the interval between the two 1s
increased, the current is enfeebled and the magnet loses some of its
power, the keeper loosens its hold on the carbon, which descends by its
own weight As the carbons approach, the current strength increases ; the
magnet again draws on the keeper, and the keeper again checks the
descent of the carbon, and so forth. Thus the points are retained at the
right distances apart, and the light is continuous and brilliant.
Stohrer has devised a regulator for the electrical light which is very
simple in principle, and which also only requires a few elements. Its essen-
tial features are represented in fig. 822, in which @ is a cylinder containing
vaseline and surrounded by the wire of the circuit f In this is a hollow
cylindrical floater a, nearly as wide as the vessel ; at its top is a copper
tube ¢, in which the carbon point @ can be fixed. A stout copper wire fixed
to the bottom of the float dips in an iron tube filled with mercury, with
which is connected one pole of the battery ; the other pole is
connected with the carbon a’, which is supported in a suitable
manner. The size of the float is such that it moves slowly
upwards, so that the carbon d presses with but very slight force
against @. The pressure can be regulated by small weights
on the collar ¢c. An insulated wire forming part of the cir-
cuit is coiled in a spiral & round the cylinder, and aids the
regulation.
859. Properties and intensity of the electric light.—The
electric light has similar chemical properties to sunlight; it
effects the combination of chlorine and hydrogen, acts chemi-
cally on silver chloride, and can be applied in photography.
Passed through a prism, the electric light, like that of the
sun, is decomposed and gives a spectrum. Wollaston, and
more especially Fraunhofer, found that the spectrum of the
electric light differs from that of other lights, and of sunlight,
by the presence of several very bright lines, as has been
already stated (586). Wheatstone was the first to observe
that, with electrodes of different metals, the spectrum and the
lines are modified.
Masson, who experimented upon the light of the electric machine, that of
the voltaic arc, and that of Ruhmkorff’s coil, found the same colours in the
electric spectrum as in the solar spectrum, but traversed by very brilliant
luminous bands of the same shades as that of the colour in which they occur.
The number and position of these bands do not depend on the intensity of
the light, but, as we have seen (855), upon the substances between which
the voltaic arc is formed.
With carbon the lines are remarkable for their number and brilliancy ;
with zinc the spectrum is characterised by a very marked apple-green tint ;
silver produces a very intense green; with lead a violet tint predominates,
and so on with other metals.
Bunsen, in experimenting with 48 couples, and removing the charcoals to
-860] Electric Lighting 857
a distance of a quarter of an inch, found that the intensity of the electric
light is equal to that of 572 candles.
Fizeau and Foucault compared the chemical effects of the sun and the
electric lights by investigating their action on iodised silver plates. Re-
presenting the intensity of the sun’s light at midday at 1,000, these physicists
found that the light from a battery of 46 Bunsen’s elements was 235, while
that from one of 80 elements was only 238. It follows that the intensity does
not increase to any material extent with the number of the couples ; but ex-
periment shows that it increases considerably with their surface. For with
a battery of 46 elements, each consisting of three elements, with their zinc
and copper respectively united so as to form one element of triple surface
(847), the intensity was 385, the battery working for an hour ; that is to say,
more than a third of the intensity of the solar light.
Too great precautions cannot be taken against the effects of the electric
light when they attain a certain intensity. The light of 109 couples may
produce very painful affections of the eyes. With 600, a single moment’s
exposure to the light is sufficient to produce very violent headaches and
pains in the eye, and the whole frame is affected as by a powerful sunstroke.
860. Electric lighting.—Great progress has been made in the applica-
tion of the electric light to purposes of ordinary illumination. This
progress has been mainly due to the improvements which have been
made in the means
of generating elec-
tricity, for which
some form of mag-
neto- or dynamo-
electrical machine
(934, 939), driven
by steam or water
power or by gas
engines (486), is
used. So long as
the electricity from
the voltaic battery
was alone avail-
able for the pro-
duction of the elec-
tric light, no great
extension was pos-
sible, for the cost
and inconvenience a
were far too great at
pa
.to permit it to be |
B _ ia
used for anything = ~eee'
more than lecture Seca
purposes and oc-
casional scenic il-
lumination.
Very considerablé improvements have also been made in the lamps
Fig. 824
858 Dynamical Electricity [860-
which are ordinarily divided into avc lamps, in which the hght is produced
between carbon points automatically kept at a constant distance by the
action of the current itself, and zzcandescent lamps, in which the light is
produced by the incandescence of a thin continuous solid conductor. To
this may be added the electrical candles, of which the best known is the
Jablochkofgf candle. It consists (fig. 823) of two rods of gas carbon, a and
6, from 2 to 4 mm. in diameter, separated by a layer of kaolin or Chinese
clay about 2 mm. thick, fixed respectively in the supports, to which the
positive and negative electrodes A B are respectively attached. The rods
are insulated from each other by the whole being bound by some insulating
material.
The current is started by a small piece of carbon, 2, placed across the
top. As the arc passes, the kaolin melts away, and the arrangement
may therefore fitly be called a candle. The positive electrode wears
away twice as fast as the negative, which would soon destroy the arc, but
by using alternating currents the unequal waste of the carbons is pre-
vented.
Fig. 818, which represents one of the forms of an arc lamp, may be
taken as an example of the manner in which the regulation of the arc is
effected.
Reynier s electric lamp, fig. 824, consists of a rectangular copper rod, B,
moving in a copper tube A, guided by four pulleys, 7, of which only two are
shown ; to B is fixed a cross-piece holding a thin carbon pencil, a, the lower
part of which passes through a silver guide, and its end presses, but not
quite over the centre, against a carbon disc, #z, which moves about a hori-
zontal axis. The piece supporting this is insulated from A, but is connected
with the negative pole by a wire, 4. The positive current, entering by A,
passes by C to a small block of carbon, 0, which presses against the pencil.
Thus the current passes through only a very small portion of this pencil,
and it is this small portion which becomes incandescent and forms the are.
The rod, as it burns away and sinks by its own weight, rotates the disc 7
slowly, and prevents its being irregularly worn away.
When either of the carbon electrodes which produce the electric light is
increased in size, its increase of temperature is lessened, while that of the
other is greater. When the negative electrode is large the light of the
positive electrode is very bright. This is seen in Werdermann’s electric
lamp, which consists essentially of a carbon disc about 2 inches in diameter
and an inch in thickness, which is connected with the negative pole of the
battery ; the positive pole is a rod of carbon about 3 mm. in diameter, of any
suitable length ; it slides vertically in a copper tube, which serves both as a
guide and as a contact for it; this is pressed upwards against the centre by
a weight passing over a pulley. The current can be passed adveast through
as many as ten of such lamps, though it seems that the total illuminating’
power of this arrangement is not so great as when only two parallel lights
are employed.
The electrical arc has had a very useful application to the welding or
autogenous soldering of metals, that is to say, joining them without the use
of a solider; a method which is of great service, particularly in the case of
iron. The two plates to be joined are placed in contact, and having been
—860] Electric Lighting 859
connected with the negative pole, the positive carbon fixed in a suitable
holder is held at such distance that the arc passes, which then melts one
plate on the other. In other cases the two pieces of metal are pressed
against each other, and the current passed through the line of contact.
For these operations accumulators (872) are used charged by dynamos,
which yield very powerful currents ; by means of a commutator the electro-
motive force and the strength of the current can be varied within very wide
limits at the will of the operator.
Von Hefner’s differential lamp is represented in fig. 825; the current
arriving by A divides at z (868); one portion passing through a fine wire
coil, R, offering a large resistance, and the other through a short thick coil
vy, whence it passes to a lever which turns about @; to this is connected
at one end, 7, a soft iron core which plays in the two coils, and at the other
end is the positive carbon C,.
When the carbons are apart a great resistance is presented, and the
current passes through R, so that the core is drawn within R, and the lever,
and with it the carbon C, falls ; the fastening in the holder a@ is such that at
a certain angle the carbon C, slips in the holder and touches the lower one,
and the current passes by x d C, C, B; the iron core is then drawn down,
but the holder a moves up, grips the carbon, which it moves with it, and the
arc is reproduced ; when its normal
length is attained its resistance in-
creases to an amount such that the
currents passing through the two
coils now balance themselves, and
their attraction on the iron being
equal the core is stationary. Several
such lamps may be arranged in a
circuit, and the extinction of one of
them does not affect the others.
Schwendler devised a new unit
of luminous intensity, which he
calls the platinum light standard,
specially for use with the electric Fig. 825
light. It is the incandescence pro-
duced by a current of known strength passing through a (J-shaped strip of
platinum foil 36:28 mm. in length, 2 mm. in breadth, and o-o17 mm. in thick-
ness. The circuit contains a rheostat and a aananomeree by which the
constancy of the current can be observed and ensured. When the strength
of the current is constant the intensity of the light, radiated by the platinum,
is constant also, and fulfils all the conditions of a standard measure of light,
as it can always be reproduced in exactly the same form from pure platinum.
The standard of light adopted by the International Congress of Electri-
cians in 1884 is the light emitted by a square centimetre of melted platinum
when on the point of solidifying.
According to Rossetti the Bee Rae AA: of the positive carbon in the electric
arc is between 2400° and 3900° C. ; it is higher the smaller is the radiating
surface. The temperature of the negative electrode lies between 2138° and
2530°. It appears that the temperature of the positive carbon does not rise
860 Dynamical Electricity | [860—
above a certain limit. Violle considers this to be the temperature of evapo-
ration of carbon, and has indirectly determined it at 3500°.
The resistance of the heated air in the arc is from I to 12 ohms (1000).
Incandescent lamps, though not so economical! as arc lights, lend them-
selves best to the distribution of the electric light. We have seen that when
a strong current of electricity is passed through a wire of small conductivity
(851), its temperature is raised to incandescence ; if the strength of the
current is increased, the brightness of the light increases, but in a greater
ratio than the strength of the current. At such high temperatures, however,
wires even of the most difficultly fusible metals fuse or are disintegrated ;
and the only material which does not fuse at the highest temperature is
carbon. ‘The first lamps in which this material was applied were constructed
independently by Edison in America and Swan in this country. Fig. 826 is
a representation of Swan’s lamp. Inside the neck of a globular glass vessel,
and fused to it, is a glass rod, through which pass two platinum wires, bent
outside in loops. These loops can be easily fitted in the two bent wires in
the holder (fig. 827), which are in contact with the binding screws, and thus
allow a current to be transmitted. The spring-wire exerts an upward pres-
sure, so as to always ensure good contact. To the other ends of the platinum
is fixed the characteristic part, the carbon filament ; this is about 0°25 mm.
in diameter, and is bent in the form of a double loop. It is prepared by im-
mersing crochet cotton in sulphuric acid of a certain strength, by which it
is converted into what is known
as vegetable parchment, and
then carbonising it by heating
it to a high temperature in a
closed vessel. The bulb, before
being sealed, is exhausted of air
by means of a Sprengel pump,
and the vacuum is made so
perfect that electricity does not
pass init. The carbon of such
a lamp, which is a thread about
12°7 cm. in length and o’013 cm.
in diameter, has a resistance of
143 ohms in its normal incan-
descence. .
In Edison’s lamp the carbon
filament is made of a special:
kind of bamboo carbonised at
high temperatures in closed nickel moulds. In the Maxim lamp, and in
that of Lane Fox, the carbon filaments, after being carbonised and mounted,
are heated by the current itself in an atmosphere of coal gas or the vapour
of a hydrocarbon ; in this way carbon is deposited on the thinner and there-
fore hotter parts of the filament, which is thus rendered more uniform and
durable.
If we surround an electric light in one case by an opaque calorimeter,
which therefore absorbs the entire radiation, and then by a transparent one,
which allows the light to pass, it will be found that the luminous radiation
—861] Mechanical Lffects of the Battery 861
is about Io per cent. of the total in the case of arc lamps and 5 in that of
incandescent lamps.
The relation between lighting power and strength of current varies in
different lamps according to the strengths of the currents. Edison’s lamp,
giving 16-candle power, requires a current of o°6 ampere; taking its resist-
ance when hot at 170 ohms, the potential difference at the connections
would be from Ohm’s law (847) 0°6 x 170 = 102 volts. For the same standard
of light, Swan’s lamp requires a current of 1°28 amperes, its resistance is 40,
and hence the potential difference is 52 volts.
The power absorbed bya lamp or other conductor through which a
current flows is equal to C E, where C is the current and E the difference
of potential at the terminals. The unit of power is the watt. Thus 1 watt
=I ampere x I volt. A horse-power is equal to 746 watts. A kilowatt =
1,000 watts = 1°34 h.p. An incandescent lamp may be taken to absorb about
4 watts per candle. Lamps are usually classed according to the number of
volts they require. Asa rule, the greater this number the more brilliant is
the light. Whatever care may be exerted in their manufacture, the carbons
at last give way ; their life, however, ought to be from 1,000 to 2,000 hours.
The temperature of the carbon in a Ioo volt lamp is 1290°, and at 1330° it
begins to volatilise.
861. Mechanical effects of the battery.—Under this head may be in-
cluded the motion of solids and liquids effected by the current. An example
of the former is found in the voltaic arc, in which there is a passage of the
molecules of carbon from the positive to the negative pole (855).
The mechanical action of the current may be shown by means of the
following experiment (fig. 828). A glass tube, AB, bent at the two ends, about
50 cm. in length and I cm. in diameter, is almost filled with dilute sulphuric
acid, and a globule of mercury, 7z, is introduced. The whole is fixed in a
support, and the level of the tube can be adjusted by the screw z, the drop
of mercury itself serving as index.
When the two poles of a battery of 4 or 5 cells are introduced into the two
ends, the globule of mercury elongates and moves towards the negative pole
with a velocity which in-
creases with the number of
elements. With 24, a long
column of mercury can be
moved through a tube a
metre in length; with 50,
the velocity is greater and
the mercury divides into
globules, all moving in the
same direction. If the direc-
tion of the current is reversed,
the mercury first remains ‘5
stationary, and then moves — =
in the opposite direction.
If the tube is gently in-
clined towards the positive pole, the mercury is still moved with the current ;
and a moment is at length reached at which there is equilibrium between
=
tL <= My.
862 Dynamical Electricity [861-
the force due to the current and the weight of the mercury. The component
of this weight parallel to the plane may then be taken as representing the
mechanical action of the current which traverses the globule of mercury.
A similar phenomenon, known as électrical endosmose, is observed in the
following experiment, due to Porret. Having divided a glass vessel into two
compartments by a porous diaphragm, he poured water into the two com-
partments to the same height, and immersed two platinum electrodes in
connection with a battery of 80elements. As the water became decomposed,
part of the liquid was carried in the direction of the current through the
diaphragm, from the positive to the negative compartment, where the level
rose above that in the other compartment. A solution of copper sulphate is
best for these experiments, because then the disturbing influence of the dis-
engagement of gas at the negative electrode is avoided.
A porous vessel is necessary, for otherwise the transport by the liquid
would be at once hydrostatically equalised.
The converse of these phenomena, that is, the production of electrical
currents, when a liquid is forced through a diaphragm by mechanical means,
has also been observed. Such currents, which were discovered by Quincke,
are called diaphragm currents. A porous diaphragm, 7, is fixed ina glass
tube (fig. 829), in which are also fused two platinum wires terminating in
platinum electrodes, a and 6; on forcing a liquid through the diaphragm the
existence of a current is evidenced by a galvanometer with which the wires
are connected, the direction of the current being that of the flow of the
liquid. The difference of potential due to this flow is proportional to the
pressure.
According to Zollner, all circulatory motions in liquids, especially when
they take place in partial contact with solids, are accompanied by electrical
currents, which have gene-
rally the same direction as
that in which the _ liquid
flows. And he regards earth
currents as analogous to dia-
phragm currents ; there are
currents in the liquid mass in the interior of the earth, and these currents
coming in contact with the solidified masses produce electrical currents.
Wertheim found that the elasticity of metal wires is diminished by the
current, and not by the heat alone, but by the electricity ; he has also found
that the cohesion is diminished by the passage of a current.
To the mechanical effects of the current may be assigned the sounds
produced in soft iron when submitted to the magnetising action of a discon-
tinuous current—a phenomenon which will be subsequently described.
862. Electrocapillary phenomena.—If a drop of mercury be placed in
dilute sulphuric acid containing a trace of chromic acid, and the end of a
bright iron wire be so fixed that it dips in the acid and just touches the edge
of the mercury, the latter begins a series of regular vibrations which may
last for hours. The explanation of this phenomenon, which was first ob-
served by Kiihne, is as follows :—When the iron first touches the mercury,
an iron-mercury couple is formed, in consequence of which the surface of the
mercury is polarised by the deposition of an invisible layer of hydrogen ;
—862] Electrocapillary Phenomena 863
this polarisation (827) increases the surface-tension of the mercury (139), it
becomes rounder, and contact with the iron is broken ; the chromic acid
present depolarises the mercury, its original shape is restored, the couple is
again formed, and the process repeats itself continuously.
Lippmann was led by the observation of this phenomenon to a series
of interesting experimental results, which have demonstrated a relation
between capillary and electrical phenomena. Of these results the most
important is the construction of a capillary electrometer.
A glass tube, A (fig. 830), is drawn out to a fine point, and is filled with
mercury: its lower end dips in a glass vessel, B, containing mercury at the
bottom and dilute sulphuric acid at thetop. Platinum wires are fused in the
tubes A and B, and terminate in the binding screws a and 6 respectively.
At the beginning of the experiment, the position of the mercury in
the drawn-out tube is such that the pressure due to the surface-tension at
the surface of separation of the mercury in the tube and the liquid is: suff-
cient to counterbalance the pressure of the column of mercury, A. This
position is observed by means of a microscope, the focus of which is at the
fiducial mark on the glass at which the mercury stops. If now a difference
of potential be established between a and 4, 6 being at the higher potential,
the surface-tension is increased, the mercury ascends in the capillary tube,
and in order that the meniscus may be brought to its former position the
pressure on A must be increased. ‘This increase is most simply effected by
means of a thick caout-
chouc tube, T, connected
with the top of A, and with
a manometer, H, and
capable of more or less
compression by means of a
screw, E. The difference
in level of the two legs of
the manometer is thus
a measure of the increase
of the surface-tension,
and therewith of the
difference of potential.
Lippmann found by
special experiments, that
this increase is almost
directly proportional to
the electromotive force,
up to about o9 of a
Daniell’s element. Each
electrometer requires a
special table of gradua- JZ #5
tion, but when once this ww wommTmmT mn 0w°iw0 AO WiN00000 ii Ai
is constructed it can be Fig. 830
directly used for deter-
mining electromotive forces. It should not be used for greater electro-
motive forces than 06 of a Daniell ; but it can estimate the one-thousandth
=> nisl — —
864 Dynamical Electricity [862-
part of this quantity, and, as its electrical capacity is very small, it shows
rapid changes of potential, which ordinary electrometers cannot do. For
very small electromotive forces, the pressure is kept constant, and the dis-
placement of the meniscus is measured by the microscope. Its use is
especially convenient with zero methods.
863. Chemical effects.—The first decomposition effected by electricity
was that of water, in 1800, by Carlisle and Nicholson, by means of a voltaic
pile. Water is rapidly decomposed by 4.or 5 Bunsen’s cells ; the apparatus
(fig..831) is convenient for the purpose. It consists of a glass vessel fixed on
a wooden base. In the bottom of the vessel two platinum electrodes, # and
m, are fitted, communicating by means of copper wires with the binding
screws. The activity of these electrodes is increased by covering them by
electrolysis with a deposit of pulverulent platinum. The vessel is filled with
water to which some sulphuric acid has been added to increase its conduc-
tivity, for pure water is a very imperfect conductor (867) ; two glass tubes
filled with water are inverted over the electrodes, and on interposing the
apparatus in the circuit of a battery, decomposition is rapidly set up, and gas
bubbles rise from the surface of each pole. The volume of gas liberated at
the negative electrode is about double that at the positive, and on examina-
tion the former gas is found to be
hydrogen and the latter gas oxygen.
This experiment accordingly gives
at once the qualitative and quanti-
tative analysis of water. The oxy-
gen thus obtained has the peculiar
and penetrating odour observed
when an electrical machine is
worked (815), which is due to
ozone. The water contains at the
same time peroxide of hydrogen,
in producing which some oxygen
Fig. 831 is consumed. Moreover, oxygen
is somewhat more soluble in water
than hydrogen. Owing to these causes the volume of oxygen is less than
that required by the composition of water, which is two volumes of hydrogen
to one of oxygen. Hence voltametric measurements are most exact when
the hydrogen alone is determined, and when this is liberated at the surface
of a small electrode (827).
864. Electrolysis.—The term electrolyte was applied to those substances
which, like water, are resolved into their elements by the voltaic current, by
Bacay, to whom the principal discoveries in this subject and the nomen-
clature are due. /ectrolysts is the decomposition by the voltaic battery ;
the positive electrode, or that by which positive electricity enters, Faraday
called the azode, and the negative electrode the Zathode. The products
of . decomposition are zoms; kation, that which appears at the kathode ; ;
and anion, that which aipeare at he anode.
By means of the battery, the compound nature of several substances
which had previously been considered as elements has been determined. By
means of a battery of 250 couples, Davy, shortly after the discovery of the
—864] Electrolysis 865
decomposition of water, succeeded in decomposing the alkalies potass and
soda, and proved that they were the oxides of the hitherto unknown metals
potasstum and sodium. The decomposition of potass may be demonstrated,
with the aid of a battery of 4 to 6 elements, in the following manner: a
small cavity is made in a piece of solid caustic potass, which is moistened,
and a drop of mercury placed in it (fig. 832). The potass is placed on a
piece of platinum connected with the positive pole of the battery. The
mercury is then touched with the negative pole. When the current passes,
the potass is decomposed, oxygen is liberated at the positive electrode, while
the potassium liberated at the negative pole amalgamates with the mercury.
On distilling this amalgam out of contact with air, the mercury passes off,
leaving the potassium.
A very convenient arrangement for the preparation of metallic magnesium
and some of the rarer metals consists of an ordinary clay tobacco pipe (fig. 833),
in the stem of which an iron wire is inserted just extending tothe bowl, which
is nearly filled with a mixture of the chlorides of potassium and magnesium.
This is melted by a Bunsen’s burner, and a piece of graphite connected by a
wire with the positive electrode of a battery is dipped in it, the wire in the
stem forming the negative electrode. When the current passes, chlorine gas
is liberated at the positive electrode, while metallic magnesium collects about
the end of the iron wire in the bowl.
The decomposition of binary compounds—that is, bodies containing two
elements—is quite analogous to that of water and of potass; one of the
elements goes to the positive and the other to the negative electrode. The
bodies separated at the positive electrode are called electronegative ele-
ments, because at the moment of separation they are considered to be
charged with negative electricity, while those separated at the negative
electrode are called electrofositive elements. One and the same body may
be electronegative or electropositive, according to the body with which it is
associated. For instance, sulphur is electronegative towards hydrogen, but
is electropositive towards oxygen. The various elements may be arranged
in such a series that any one in combination is electronegative to any
following, but electropositive towards all preceding ones. This is called
the electrochemical series, and begins with oxygen as the most electro-
negative element, terminating with potassium as the most electropositive.
The decomposition of solution of hydrochloric acid into its constituents,
3K
866 Dynamical Electricity [864-
chlorine and hydrogen, may be shown by means of the apparatus represented
in fig. 834. Carbon electrodes must, however, be substituted for those of
platinum, this metal being attacked by the liberated chlorine: a quantity of
common salt also must be added to the hydrochloric acid, in order to
; diminish the solubility of the liberated chicane. he
decomposition of potassium iodide may be demon-
strated by means of a single element. For this
purpose a piece of bibulous paper is soaked with a
solution of starch, to which potassium iodide has
been added. On touching this paper with the elec-
trodes, a blue spot is produced at the positive pole,
due to the action of the liberated iodine on the starch.
One of the best methods of determining whether
a liquid is, or is not, an electrolyte, is to immerse in
it the two platinum electrodes connected with a
battery, and then, disengaging the electrodes from
the battery, connect them with a detaching galvano-
meter, and observe whether a reverse current, due
to polarisation of the electrodes (827), passes through
the galvanometer. Such a current, being due to the accumulation of
different substances on the two electrodes, is a proof that the substance has
been electrolytically decomposed by the original current from the battery.
This method can often be applied when it is difficult, by direct chemical
methods, to establish the presence of products of decomposition at the
electrodes.
865. Decomposition of salts.—Ternary salts in solution are decomposed
by the battery, and then present effects varying with the chemical affinities
and the intensity of the current. In all cases the acid, or the body which is
chemically equivalent to it, is electronegative in its action towards the other
constituent. The decomposition of salts may be readily shown by means of
the bent tube represented in fig. 834. This is nearly filled with a saturated
solution of a salt, say sodium sulphate, coloured with syrup of violets.
Platinum electrodes connected with a battery of four Bunsen’s elements are
then placed in the two legs of the tube. After a few minutes the liquid in
the positive leg, A, becomes of a red, and that in the negative leg, B, of a
green colour, showing that the salt has been resolved into acid which has
passed to the positive, and into a base which has gone to the negative pole,
for these colours are the effects whicha free acid and a free base respectively
produce on syrup of violets.
In a solution of copper sulphate free acid and oxygen gas appear at the
positive electrode, and metallic copper is deposited at the negative electrode.
In like manner, with silver nitrate, metallic silver is deposited on the nega-
tive, while free acid and oxygen appear at the positive electrode.
This decomposition of salts was formerly explained by saying that che
acid was liberated at the positive electrode and the base at the negative. Thus
potassium sulphate, K,OSO,, was considered to be resolved into sulphuric
acid, SO,, and potash, K,O. This view regarded salts composed of three
elements as different in their constitution from binary or haloid salts. Their
electrolytic deportment has led to a mode of regarding the constitution of
—————— Eee
—867] Transmissions effected by the Current 867
salts which brings all classes of them under one category. In potassium
sulphate, for instance, the electropositive element is potassium, while the
electronegative element is a complex of sulphur and oxygen, which is regarded
as a single group, SO,,and to which the name oxy-su/phion may be assigned.
The formula of potassium sulphate would thus be K,SO,, and its decom-
position would be quite analogous to that of potassium chloride, KCl,
lead chloride, PbCl,, potassium iodide, KI. The electronegative group:
SO, corresponds to a molecule or two atoms of chlorine or iodine. In the
decomposition of potassium sulphate, the potassium liberated at the negative
pole decomposes water, forming potash and liberating hydrogen. In like
manner the electronegative constituent SO,, which cannot exist in the free
state, decomposes into oxygen gas, which is liberated, and into anhydrous
sulphuric acid, SO,, which immediately combines with water to form ordi-
nary sulphuric acid, H,SO,. In fact, where the action of the battery is
strong, oxygen and hydrogen are liberated at the corresponding electrodes ;
in other cases they combine in the liquid itself, reproducing water. The
constitution of copper sulphate, CuSO,, and of silver nitrate, AgNO,, and
their decomposition, will be readily understood from these examples.
866. Transmissions effected by the current.—In chemical decompositions
effected by the battery there is not merely a separation of the elements, but
a passage of the one to the positive and of the other to the negative electrode.
This phenomenon was demonstrated by Davy by means of several experi-
ments, of which the following two are examples :—
i. He placed solution of sodium sulphate in two capsules connected by a
thread of asbestos moistened with the same solution, and immersed the
positive electrode in one of the capsules, and the negative electrode in the
other. The salt was decomposed, and at the expiration of some time all
the sulphuric acid was found in
the first capsule, and the soda in
the second.
ii. Having taken three glasses,
A, B, and C (fig. 835), he poured
into the first solution of sodium
sulphate, into the second dilute
syrup of violets, and into the
third pure water, and connected rise
them by moistened threads of
asbestos. The current was then passed in the direction from C to A. The
sulphate in the vessel A was decomposed, and in the course of time there
was nothing but soda in this glass, which formed the negative end, while
all the acid had been transported to the glass C, which was positive, B con-
taining only pure water. If, on the contrary, the current passed from A to
C, the soda was found in C, while all the acid remained in A; but in both
cases the remarkable phenomenon was seen that the syrup of violets in B
became neither red nor green by the passage of the acid or base through
its mass, a phenomenon the explanation of which is based on the hypothesis
enunciated in the following paragraph.
867. Grothiiss’s hypothesis.—Grothiiss gave the following explanation
of the chemical decompositions effected by the battery. Adopting the
SK
868 Dynamical Electricity [867—
hypothesis that in every binary compound, or body which acts as such, one
of the elements is electropositive, and the other electronegative, he assumes
that, under the influence of the contrary electricities of the electrodes, there
is effected, in the liquid in which they are immersed, a series of successive
decompositions and recompositions from one pole to the other. Hence it is
only the elements of the terminal molecules which do not recombine, but,
remaining free, appear at the electrodes. Water, for instance, is formed of
one atom of oxygen and two atoms of hydrogen ; the first gas being electro-
negative, the second electropositive. Hence when the liquid is traversed by
a sufficiently powerful current, the molecule a in contact with the positive
pole arranges itself as shown in fig 836—that is, the oxygen is attracted and
the hydrogen repelled. The oxygen of this molecule is then given off at the
positive electrode, the liberated hydrogen immediately unites with the oxygen
of the molecule 4, the hydrogen of this with the oxygen of the molecule c,
and so on, to the negative electrode, where the last atoms of hydrogen
become free and appear on the poles. The same theory applies to the
metallic oxides, to the acids and salts, and explains why in the experiment
mentioned in the preceding paragraph the syrup of violets in the vessel B
becomes neither red nor green. The reason why, in the fundamental ex-
periment, the hydrogen is given off at the negative pole when the circuit is
closed will be readily understood from a consideration of this hypothesis.
Clausius objected that, according to this theory, a very great force must
be required for overcoming the affinity for each other of the oppositely
electrolysed particles of the com-
if = : | pound ; and that below a certain
minimum strength of current no
decomposition could occur. Now
- Buff showed that the action of
even the feeblest currents, sy455
of an ampere, for instance, con-
tinued fora long time can produce decomposition. Again, when the necessary
potential is obtained, it should be sudden and complete ; whereas we know
that it is proportional to the strength of the current.
To overcome this difficulty Clausius applied the theory now generally
admitted of the constitution, of liquids (296), which was originally pro-
pounded by Williamson on the basis of purely chemical considerations.
On this theory the particles of a compound liquid have not the rigid un-
alterable condition of a solid body ; they are in a perpetual state of separa-
tion and reunion, so that we must suppose compound bodies and their
elementary constituents to coexist with each other in a liquid. Water, for
instance, contains particles of water, together with particles of oxygen and
of hydrogen ; the former are being continually decomposed and the latter
continually reunited.
The theory of Van’t Hoff on the nature of solutions (141), and the
experimental researches to which it has led, support the present explanation
of electrolytic phenomena, which is due to Arrhenius. In the case of a
solution of potassium chloride, KCl, in water, a certain proportion, probably
considerable, of the molecules of the salt is in a state of dissociation. (395),
which proportion increases with the dilution of the solution ; so that along
\
SSS
Fig. 836
—868] Laws of Electrolysis 8€9
with molecules of the undecomposed salt there are present the free ions potas-
sium and chlorine. These latter are exclusively the carriers of the positive and
negative electricity respectively. They may in this respect be regarded as
performing a function analogous to that of the pith ball in the convective
discharge (792). When the voltaic current passes, it acts on the motion of
the ions in such a manner that the negatively electrical ions of chlorine pass
to the positive electrode, and the positively electrical ions of potassium to
the negative electrode, and there give up their charges and are liberated in
the free state. Hence the current does not bring about the decomposition,
but utilises it, to give definite direction to the particles which are already
separated.
These considerations explain why the conductivity of a liquid increases
with the temperature (990) ; for this increases the velocity of the molecules
(298) and also the dissociation, that is, the number of partial molecules.
It also shows that the conductivity should increase with the concentra-
tion of the liquid, seeing that an increase in the number of decomposable
molecules must be favourable to the movement of electricity. On the other
hand, an increase in the number must give rise to an increased number of
collisions ; hence it is that, though for very dilute solutions the conductivity
increases with the concentration, it does so more slowly than in direct ratio,
and it is not difficult to understand that for some liquids there is a concentra-
tion which corresponds to a maximum conductivity, and this in a great many
cases is below the point of saturation of the solution.
This also explains why chemical compounds, such as water and pure
acids, which within the ordinary range of temperatures are not subject
to dissociation (395), are not electrolysed and therefore not decomposed,
while mixtures of acids and water, and solutions of salts, which may be re-
garded as chemical compounds in a state of dissociation, are easily electro-
lysed and conduct well.
In dealing with molecular magnitudes, theoretical investigations make it
probable that the electrolytic resistance, which the ions experience in
being moved by the current, is of the same order of magnitude as the
capillary resistance which results from their friction in the liquid (149).
Nothing is opposed to the idea that electrolysis is a purely mechanical
process. Decomposition occurs in the first place by dissociation ; the
difference of potential is the force in virtue of which the previously united
ions are urged in contrary directions. The moving ions are the carriers of
the motion of electricity and produce the current ; the resistance which they
thereby experience is the electrical resistance of the liquid. This, therefore,
is the cause of the development of heat in the liquid.
868. Laws of electrolysis.—The laws of electrolysis were discovered
by Faraday ; the most important of them are as follows :—
I. Electrolysis cannot take place unless the electrolyte ts a conductor.
Hence ice is not decomposed by the battery, because it is a bad conductor.
Other bodies, such as lead oxide, silver chloride, &c., are only electrolysed in
a fused state—that is, when they can conduct the current. The converse of
this is true ; if a liquid transmits a current it must be an electrolyte. From
the fact that he was able to obtain a current in liquids which deflected a
galvanometer without producing any visible decomposition, Faraday inferred
870 Dynamical Electricity [868—-
that liquids had a slight conductivity like that of metals independently of
their electrolytic conductivity. This apparent conductivity is, however, to
be assigned to electrolytic convection (854).
Il. The energy of the electrolytic action of the current is the same in all
its parts.
For if a number of voltameters, V, V’, V” (vzde inf.), are arranged in
series so that they are all traversed by the same current (fig. 837), itis found
that the weight of hydro-
v’ vie gen in each of them in
the same time is the same,
whatever may be the
nature and distance apart
of the electrodes, the pro-
portion and nature of the
acid.
ul If the current from the
vy: battery divides at A into
two branches (fig. 838),
in which are two equal
/ voltameters V, and V.,,
Fig. 838 then the quantities of gas
liberated in V and V” will
still be equal to each other ; and the quantities in V, and V, will be equal
to each other, but each will be only half that quantity which passes in
either of the voltameters V and V”.
Ill. Zhe same quantity of electrictty—that ts, the same electric current—
decomposes chemically equivalent quantities of all the bodies which tt tra-
verses ; from which it follows, that the weights of elements separated in these
electrolytes are to each other as their chemical equivalents.
In a circuit containing a voltameter, V, Faraday introduced a tube, AB,
containing tin chloride kept in a state of fusion by the heat of a spirit lamp
V2
(fig. 839).. In the bottom of the tube a platinum wire was fused, which
served as the negative electrode, while the positive electrode consisted of a
rod of a graphite; when the current passed chlorine was liberated at the
—868] as Of Electrolysis 871
positive, while tin collected at the negative pole ; lead oxide contained in a
similar tube was also electrolysed and yielded lead at the negative and oxygen
at the positive pole. Comparing the quantities of substances liberated, they
are found to be in a certain definite relation. Thus for every 18 parts of water
decomposed in the voltameter there will be liberated two parts of hydrogen,
207 parts of lead, and 117 of tin at the respective negative electrodes, and 16
parts of oxygen and 71 (or 2 x 35°5) parts of chlorine at the corresponding
positive electrodes. Now these numbers are exactly as the equivalents (not
as the atomic weights) of the bodies.
It will further be found that in each of the cells of the battery 65 parts
by weight of zinc have been dissolved for every two parts by weight of
hydrogen liberated ; that is, that for every equivalent of a substance decom-
posed in the circuit one equivalent of zinc is dissolved. This is the case
whatever be the number of cells. An increase in the number only has the
effect of overcoming the great resistance which many electrolytes offer, and
of accelerating the decomposition. It does not increase the relative quantity
of electrolyte decomposed. If in any of the cells more than 65 parts of zinc
are dissolved for every two parts of hydrogen liberated, the excess arises from
a disadvantageous local action (837) ; and the more perfect the battery, the
more nearly is the ratio 65:2 satisfied.
Chemistry takes account of the valency of an element, and divides elements
into monads, dyads, triads, and tetrads—a classification based on their equiva-
lence to and their power of replacing other elements ; thus one atom of the
monad hydrogen (H = 1), the basis of this classification, or one atom of monad
silver (Ag = 108), would combine with one atom of chlorine (Cl = 35°5) or one
atom of iodine (I=127). One atom of oxygen (O = 16) unites with two atoms
of hydrogen to form water, or with two atoms of silver to form silver oxide,
Ag,O; one atom of the dyad zinc (Zn=65) unites with one atom of the
dyad oxygen to form ZnO, or with the dyad sulphur (S = 32) to form ZnS.
Again, gold is a triad, and one atom (Au=196) can combine with three
atoms of chlorine to form AuCl,, and, accordingly, one monad is equivalent
to one-third of the atom of the triad. Now electrolysis proceeds according
to the eguzvalence ; that is, the same quantity of electricity which liberates
one atom of a monad liberates half an atom of a dyad, and a third of an atom
of a triad. This remark applies also to the compound groups, such as NO.,
which acts as a monad, and SO,, which acts as a dyad.
Thus the same current which decomposes 200 grammes Hg in HgNO.,
decomposes I1oo grammes Hg(CN),.
IV. It follows from the above law, that the guantity of a body decomposed
in a given time ts proportional to the strength of the current. On this is
founded the use of Faraday’s voltame¢er, in which the strength of a current
is ascertained from the quantity of water which it decomposes in a given
time.
A convenient form of this instrument is that represented in fig. 840. The
vessel a is that in which the water is decomposed, and contains two platinum
plates, and is in connection with the flask 4, which contains water. In this
is a lateral delivery tube, c, which is inclined until the level of the liquid in it
is the same as inthe funnel tube 7. The air is then under the same pressure
as the atmosphere. When the battery is connected with the decomposing
872 Dynamical Electricity [868-
cell a, the gases disengaged expel a corresponding volume of water through
the delivery tube ¢ ; at the conclusion of the experiment, this tube is inclined
until the liquid is at the same level as in the tube z and in the flask. The
weight of the liquid expelled is then a direct measure of the volume of the
disengaged gases.
The use of this voltameter appears simple and convenient ; Jacobi pro-
posed as unit of the strength of current, that current which in one minute
yields a cubic centimetre of mixed gas reduced to the temperature 0° and the
pressure 760 mm. This is equal to 009567 ampere, that is, an ampere
liberates 10°44 ccm. mixed gas in a minute. Yet, for reasons mentioned before
(863), the measurements should be based on the volume of hydrogen
liberated.
niki Si
DTN
Au | My
=| .
3
= ‘
i} y
Poggendorff’s silver voltameter (fig. 841) is an instrument for measuring
the strength of the current. A solution of silver nitrate of known strength
is placed in a platinum dish which rests on a brass plate that can be con-
nected with the negative pole of the battery by means of the binding screw *
6. In this solution dips the positive pole, which consists of a rod of silver
wrapped round with muslin, and suspended to an adjustable support. When
the current passes, silver separates at the negative pole, and is washed, dried,
and weighed ; and the weight thus produced in a given time is a very
accurate measure of the strength of the current. Some silver particles
which are apt to become detached from the positive pole are retained in the
muslin. Edison has used a zznc voltameter for measuring the powerful
currents employed for technical purposes.
It has been found by experiment that, when water is decomposed, a
current of 1 ampere liberates 0:000010386 granime of hydrogen in a second ;
this, then, is the electrochemical equivalent of hydrogen, and from this we can
—869] Migration of the Ions 873
deduce the weight of any element liberated in the same time by unit current,
if we multiply it by the equivalent weight of the element referred to hydrogen.
The equivalent of silver is usually taken at 108 ; hence, if any of its salts are
decomposed, the weight of silver liberated by an ampere in a second is
O‘OOII217 gramme; this is the electrochemical equivalent of silver, and
similarly that of copper is 0'0003271 and that of zinc 0'0003375.
According to the best direct determinations the electrochemical equiva-
lent of silver is:o‘oo11181. The electrochemical equivalent of hydrogen
deduced from this is 0°000010353.
The quantity of electricity which passes through a conductor with a current
of one ampere is called a coulomb (1000), and thus we may say that a coulomb
of electricity in traversing an electrolyte carries with it a weight of a
metal which is represented by its electrochemical equivalent. The quantity
of electricity which is thus associated with each valency represents a
minimum quantity of electricity—the electrical atom or e/ectron as it has
been called by Johnstone Stoney. By various theoretical considerations it
has been attempted to estimate its amount; Richarz obtained the number
1:29, Ebert 1:4, and Stoney 3 x 10!° CGS. units:; numbers which thus arrived
at independently agree very well as to the order of their magnitude. It was
calculated by Weber that if the quantity of positive electricity required to
decompose a grain of water were accumulated on a cloud at a distance of
3,000 feet from the earth’s surface, it would exert an attractive force upon
the earth of upwards of 1,500 tons. Helmholtz estimated that if the+E
attached to the atoms of 1 milligramme of water could be transferred without
loss to a sphere, and the—E similarly to another sphere at a distance of a
kilometre, the two spheres would attract each other with a force equal to
the weight of 26,800 kilogrammes.
869. Migration of the Ions.—From what has been said, it would seem
that when a solution of copper sulphate is electrolysed between copper elec-
trodes, for every equivalent of copper deposited at the negative electrode
an equivalent weight should be dissolved at the positive, and, the transfer
taking place as described, the concentration of the solution should remain
unchanged. This, however, is not the case; when the operation takes
place without any agitation of the solution, the liquid about the negative
pole becomes lighter in colour, indicating that the solution there is weaker.
This phenomenon, which was investigated by Hittorf, is ascribed by him
to the fact that in electrolysis both electricities, associated with their zoms or
products of electrolytical decomposition, travel in the liquid towards their
respective electrodes, but with unequal velocities, and this transference is
called the mzgration of the tons. Each ion has a special velocity in the liquid
independently of the compound of which it forms part; thus in CuSO,
solution SO, travels twice as fast as Cu.
The number which expresses this rate of travel is called 7, and has this
meaning : let us conceive a vertical layer in the liquid the concentration of
which remains unchanged by what takes place on each side ; then, if after
electrolysis we determine the quantity of the constituents on each side, there
is an increase of the positive on one side and of the negative on the other.
These increases correspond to the quantities of the two constituents which
have been driven through.
874 Dynamical Electricity [869-
The number 7 expresses the ratio of the number of molecules of the
anion which passes through the imaginary layer in a given time to that of
the electrolyte decomposed.
If £ is the velocity of the kation, and a that of the anion, then
a R I-”_k
vii Bee ee pi Fer Wyk Bode
Hittorf has shown that z is a constant independent of the strength of the
current, but varying with the concentration of the liquid.
870. Comparison between the tangent galvanometer and the voltameter.
There are several objections to the use of the voltameter. In the first
place, it does not indicate the current strength at any given moment, for in
order to obtain measurable quantities of gas the current must be continued
for some time. Again, the voltameter gives no indications of the changes
in the current strength which may take place in this time, but only the mean
strength. It offers also great resistance, and can thus only be used in the
case of strong currents ; for weak currents either do not decompose water,
or only yield quantities too small for accurate measurement. In addition to
this, the indications of the voltameter depend not only on the strength of the
current, but on the acidity of the water, and on the distance and size of the
electrodes. But although it does not measure the strength of the current
at any one time, it does, apart from accidental influences, give a measure
of the total quantity of electricity that has passed within the period of
observation.
Magnetic measurements are preferable to chemical ones. Not only
are they more delicate, but they give the current strength at any moment.
On the other hand, indications furnished by the tangent galvanometer hold
only for one special instrument. They vary with the diameter of the ring
and the number of turns ; moreover, one and the same instrument will give
different indications on different places, seeing that the force of the earth’s
magnetism varies from one place to another (712).
The indications of the two instruments may, however, be readily com-
pared with one another. For this purpose the voltameter and the tangent
galvanometer are szwzul/faneously inserted in the circuit of a battery, and the
deflection of the needle and the amount of gas liberated in a given time are
noted. In one set of experiments the following results were obtained :—
Number of elements Deflection | Gas liberated in three minutes
| 12 2055 4 | 125 CC
8 24°8 106
6 22H 93 |
9 - 1
3 PS he | 56
2 6'9 | a
| |
If we divide the tangents of the angles into the corresponding volumes of
gas liberated in ove minute, we should obtain a constant magnitude which
represents how much gas is developed in a minute by a current which could
—871] Polarisation 875
produce on the tangent ygalvanometer the deflection 45°, for tang. 45°=1.
Making this calculation with the above observations, we obtain a set of
closely agreeing numbers the mean of which is 76:5. The gas was measured
under a pressure of 737 mm. and at a temperature of 15°, and therefore
under normal conditions (339) its volume would be 70 cubic centimetres.
That is to say, this is the volume of gas which corresponds to a deflection
of 45°. Hence in chemical measure the strength C of a current which pro-
duces in Z/zs particular tangent galvanometer a deflection of $° is
C= 70 tang. @.
For instance, supposing a current produced in this tangent galvano-
meter a deflection of 54°, this current, if it passes through a voltameter,
would liberate in a minute 70x tang. 54°= 70x 1°376=96°32 cubic centi-
metres of gas.
If once the reduction factor for a tangent galvanometer has been deter-
mined, the strength of any current may be readily calculated in chemical
measure by a simple reading of the angle of deflection. This reduction
factor of course only holds for one special instrument, and for experiments
in the same place, seeing that the force of the earth’s magnetism varies in
different places.
The indications of the sine-compass may be compared with those of the
galvanometer in a similar manner.
871. Polarisation.—When the platinum electrodes, which have been used
in decomposing water, are disconnected from the battery, and connected
with a galvanometer, the existence of a current is indicated which has the
opposite direction to that which had previously passed. This phenomenon
is explained by the fact that oxygen has been condensed on the surface of the
positive plate, and hydrogen on the surface of the negative plate, analogous
to what has been already seen in the case of the non-constant batteries (828).
The effect of these is to set up an electromotive force e opposed to that of
the battery (827) and called ¢he electromotive force of polarisation. The
polarisation is not instantaneous, but may increase continuously from
zero to a certain maximum limit which may be considerable ; it increases
with the strength of the current, attaining the force of about 1°5 volts with
platinum plates in dilute sulphuric acid. It constitutes a negative electro-
motive force, and must be allowed for in Ohm’s formula (847), which then
becomes
_E-e
eae
The quantity of electricity required to produce a given state of polarisa-
tion depends on the condition and dimensions of the plate, and is often
called the capacity of polarisation relative to the given system. When the
electrodes consist of plates of the same metal as that of the salt decomposed,
there is practically no polarisation. Thus the polarisation is negligible when
a copper salt is electrolysed between copper electrodes or a silver salt
between silver electrodes.
If a test tube containing mercury is placed in a vessel of mercury, and
the electrodes of a voltaic battery are connected with the two masses of
876 Dynamical Electricity [871-
mercury separated by the glass, no current passes at the or dinary tempera-
ture. But if the arrangement is gradually heated a current is set up which
increases with the temperature, while the physical condition of the glass
appears quite unchanged. If the battery is removed and the electrodes
connected with a galvanometer, a polarised current in the opposite direction
to the primary one is observed. The surfaces of the glass are thus polarised,
and the electricity must have been transmitted by the hot glass.
872. Secondary batteries. Accumulators.---Ritter was the first to show
that on this principle batteries might be constructed of pieces of metal of
the same kind—for instance, platinum-- which otherwise give no current.
A piece of moistened cloth is interposed between a pair of metal plates,
and the ends of this system are connected with the poles of a battery.
After some time the apparatus has received a charge, and if separated from
the battery can itself produce all the effects of a voltaic battery. Such
batteries are called secondary batteries or, also, accumulators. Their
action depends on an alteration of the surface of the metal produced by the
electric current, the constituents of the liquid with which the cloth is
moistened having become accumulated on the opposite plates of the
secondary circuit.
Planté first showed the practical importance of these batteries. His ele-
ment (fig. 842) is constructed as follows : A broad strip of sheet lead with a
tongue is laid upon a second
similar sheet, contact being
prevented by narrow strips
of felt; and two similar
strips having been laid on
the upper piece, the sheets
are rolled together so as to
form a compact cylinder.
This is placed in a vessel
containing dilute sulphuric
Fig. 842 acid, and, being connected
by wires attached to the
tongues with a battery of two Grove’s cells, a current (the primary current)
is passed through it. The effect of this is that water is decomposed, oxygen
being liberated at the anode, or plate, which serves as positive pole, and
there unites with the lead, forming peroxide of lead, while hydrogen is
accumulated at the other plate. If now the plates are detached from the
charging battery and are connected with each other, a powerful polarisation
current is produced in the opposite direction to the primary; the oxygen of
the peroxide at the anode decomposes the dilute acid, combining with its
hydrogen, and so travels through to the other plate, where it combines with
the lead. When these operations are repeated several times the activity of
the element increases, owing in great measure to the alteration in the —
surfaces which is thereby produced. The element does, in fact, require a
considerable expenditure of energy and time to form it, which is a source of
expense, even when the energy of the discharge is expended in forming new
plates.
Faure made a great improvement in this direction. It consists in coating
the lead plates with a thick paste of red lead, Pb,O,, soas to have about one
872] Secondary Batteries. Accumulators O77
gramme to the square centimetre. This is kept in its place by a sheet of
parchment paper and slips of felt, and is then coiled up as in Planté’s (fig.
843). When the current is passed, the ultimate effect is that the red lead
at the one electrode is oxidised to Pb,O,, while the other is reduced to
granular porous grey metallic lead, both which coatings present a large sur-
face. Such coatings, however, are liable to become detached, and a con-
siderable advance was made in the introduction of gvzds, or gratings of lead
in which square or round holes are filled with com-
pressed lead oxide; the object being to store firmly
as much of the porous material as possible, consis-
tently with strength, lightness, and compactness.
There are many plans by which this may be
effected. Fig. 844 represents one of the batteries of
the Electric Power Storage Company ; it will be seen
that the whole of one set of six plates, forming the
negative electrode, are fixed together, and a corre-
sponding set of five plates, also joined together, can be
placed between the other set, being kept from touching
each other by staples or studs of some insulating
material. Each set of plates forms in effect a single
large plate, which is thus placed with its coated face
opposite the coated faces of the other plate. The
object of bringing the plates near each other is to
diminish the internal resistance.
The inverse electromotive force of such a cell while it is being charged
rises to about 23 times that of a Daniell’s cell, so that three Daniell’s
or two Grove’s cells are required to
charge it. In charging, a considerable
number of elements are joined together
by their similar poles, and connected
with the respective electrodes of the
charging battery or of the dynamo ; the
effect is the same as that of using a
single element of a surface equal to the
sum of the surfaces of all the elements.
By means of a specially contrived com-
mutator a given number of such batteries
may be combined so as to produce at will
the effects either of high potential or of
quantity.
So long as such batteries could be
charged only from a voltaic battery they
could never be economical; but the fact
that after having been once charged they
retain the charge for a considerable time,
has led to their use in what is called
‘storing electricity’ produced by mechani-
cal power through the agency of powerful dynamo and magneto-electrical
machines. What they do is to store the products of chemical decomposition,
and that in a form in which they are immediately available for electrical effects.
Fig. 844
878 Dynamical Electricity [872-
They are usually charged by shunt wound dynamos (944), whereby
about 75 per cent. of the. energy is available. An accumulator of a given
size can only consume in each interval of time a definite quantity of gas for
its formation by oxidation and reduction. If more gas is developed it escapes
uselessly. The charging current must be neither too strong nor too weak,
For each accumulator there is a special rate of charge, which is most advan-
tageous.
An accumulator of great capacity is obtained by placing a zinc plate ina
solution of sodium or potassium zincate, and a porous plate of copper obtained
by compression. During the charge the zinc in the solution is precipitated
on the zinc plate, and the copper absorbs an equivalent quantity of oxygen.
During the discharge the copper is reduced and the zinc redissolves. This
accumulator, however, does not retain its charge, and is only suitable for
cases in which the discharge rapidly succeeds the charge. So far accumu-
lators with lead plates have alone proved to be of practical utility.
Figure 845 represents the course of charging an accumulator from an
actual experiment in which a steady current of 22 ampere-hours (vzd. zu/f.)
was used. In the first hour or so the E.M.F. rose rapidly until it was about
2,00 ENouas
2
Fig. 845
2:08 volts, when it was almost stationary for about 1o hours when 220 ampere-
hours had been put in, and the E.M.F. was 2°13 volts ; from this point there
was a rapid rise until 2°53 volts were reached. The maximum usually
obtained is 2°5 volts, at which the liquid becomes milky owing to a disengage-
ment of gas in the body of the liquid itself, which indicates that the charge
is complete.
A charged accumulator gradually loses its charge by leakage, and the
efficiency of an accumulator depends on the power of retaining its charge.
In this respect great improvement has been made by attention to a number
of minute points ; the durability now extends to years, whereas it was
formerly measured by months or weeks.
The efficiency further depends on the cafaczty, which is the quantity of
electrical energy which can be stored for unit weight of the accumulator, and
which must not be confounded with the electrostatic capacity. It is usually
represented by the number of amzfere-hours ; that is, a current of an ampere
maintained for an hour, or 3,600 coulombs of electricity, for each kilogramme
of plates.
—872] Secondary Batteries. Accumulators 879)
Of perhaps greater importance in judging of an accumulator is the
éffictency, by which is meant the ratio of the electrical work which is accu-
mulated in order to charge it to that which it gives out in sinking to its
initial condition.
The energy stored up in an accumulator is measured by the potential at
the terminals during the charging, multiplied by the strength of the current
and by the time. The product gives the energy in volt-amperes-seconds. In
like manner the energy given out in the discharge is the potential into the
current strength into the time of discharge. The whole charge which can
be imparted to an accumulator cannot be advantageously utilised, for the
accumulator is injured if this is done, and in practice the charge is only
allowed to run down until the potential is 10 per cent. less than at starting.
Thus a given accumulator was charged for 10°16 hours with a current of
5 amperes, the average potential being 2°15 volts; hence the energy stored
is 10°I6x 2°15 x 5=109 watt-hours. In the discharge, which lasted 7°35
hours, the average potential was 1°88, and the current 6°5 amperes, repre-
senting therefore 90 watt-hours ; the ratio of the two is o'826—that is, the
efficiency of the accumulator is 82:6 per cent. ; a number which is now
required for a good accumulator.
It cannot be said that the reactions which take place during the charge
and discharge of an accumulator are thoroughly understood ; they are
undoubtedly more complicated than has been represented above, in which
no account has been taken of the sulphuric acid. During the charge, the
strength of the dilute sulphuric acid, and therewith its conductivity, gradually
diminish, while during the discharge both increase. Hence a determination
of the specific gravity of the solution at any time is a convenient practical
method of measuring the state of the charge. This is effected by flat densi-
meters (131) which float between the plates. The density may vary between
I'I2 and 1°22, representing respectively about 16 and 30 per cent. of sul-
phuric acid, SH,O,.
As an example, one cell of the Electric Power Storage Company had
an internal resistance of o‘oo12 ohm at the beginning, and 0'0028 at the
end, and weighed 50 kilos. In such a cell 880 watt-hours could be accumu-
lated, and 680 watt-hours, or about 79 per cent., obtained in the discharge.
Thus each kilo represents 13°6 watt-hours of available energy, or »; of a’
horse-power ; that is, it could yield »; H.P. for an hour, or 1 H.P for 1°1
minute. As a horse power is equal to 270,000 kilogrammetres per second
(482), this gives 5,000 kilogrammetres for each kilo, sufficient, therefore, to
raise the battery itself through a height of 5,000 metres.
In accumulators which are to be used to work motors, as in tram-
cars, electrical boats, &c., the cafaczty is of first importance, while with
stationary accumulators, as in electric lighting, the efficiency is the chief
point.
Many instructive comparisons may be made between a secondary bat-
tery and a charged Leyden jar. Thus, for instance, when the poles of a
secondary battery have been connected until no current passes, and are
then disconnected for a while, a current in the same direction as the first is
obtained on again cgnnecting them ; this is the ves¢dual discharge. The
capacity of asecondary battery depends on the area of the electrodes, on their
880° Dynamical Electricity [872-
nature, and on that of the interposed liquid, but not on the distance between
them. The energy of the Leyden jar is stored in that state of mechanical
strain which is called polarisation of the dielectric ; in the secondary battery
the energy consists in the products which are stored up on the surface of
the electrodes in a state ranging from chemical combination to mechanical
adherence or simple juxtaposition.
A dry pile which has become inactive may be used ¢7; a secondary battery.
When a current is passed through it, in a direction contrary to that which the
active battery would itself yield, it regains its activity.
873. Grove’s gas battery.—On the property, which metals have, of con-
densing gases on their surfaces, Sir W. Grove constructed his gas battery (fig
846). A single cell consists of two glass tubes, B and A, in each of which is
fused a platinum electrode, provided on the outside with binding screws.
These electrodes are made more efficient by being covered with finely divided
platinum. One of the tubes is partially filled with hydrogen, and the other
partially with oxygen, and they are inverted over dilute sulphuric acid, so
that half the platinum is in the liquid and half in gas. On connecting the
electrodes with a galvanometer, the existence of a current is indicated whose
direction in the connecting wire is from the platinum in oxygen to that in
hydrogen ; so that the latter is negative towards the former. As the current
passes through water this is decomposed : oxygen is separated at the positive
plate and hydrogen at the other. These gases unite with the gases con-
densed on their surface, so that the volume of gas in the tubes gradually
diminishes, but in the ratio of one volume of oxygen to two volumes of
hydrogen. These elements can be formed into a battery (fig. 792) by joining
the dissimilar plates with one another just as they are joined in an ordinary
battery. One
© element of such
aa
si Se —~ a battery is suf-
Cn ficient to decom-
a —
iz pose potassium
iodide, and four
will decompose
water.
Mond and
Langer have
constructed a
battery on this
principle. On
each side of a
plate of plaster
is a lead grid,
the holes of
which are filled
with platinum black. Air and hydrogen are forced through these holes and
combine, forming water, and alsoan electric current, the electromotive force
of which is one volt.
874. Passive state of iron.—With polarisation is probably connected
a very remarkable chemical phenomenon, which many metals exhibit, but
876] Arbor Saturni.. Arbor Diane 881
more especially iron. When this is immersed in concentrated nitric acid it is
unattacked. This condition of iron is called the fasszve state, and upon it
depends the possibility of the zinc-iron battery (831). It is probable that in
this experiment a thin superficial layer of iron protosesquioxide is formed ;
on the one hand this protects the iron from further attack, and on the other
itacts as an electromotor, like the layer of lead peroxide in Planté’s element
(872).. The position of passive iron in the electromotive series is near that
of platinum.
875. Nobili’s rings.—When a drop of copper acetate is placed on a
silver plate, and the silver is touched in the middle of a drop with a piece
of zinc, there are formed around the point of contact a series of copper rings
alternately dark and light. These are /Vodzli’s coloured rings. They may
be obtained in beautiful iridescent colours by the following process : A solu-
tion of lead oxide in potash is obtained by boiling finely powdered litharge
in a solution of potash. In this solution is immersed a polished plate of
silver or of German silver, which is connected with the positive electrode of
a battery of eight Bunsen’s elements. With the negative pole is connected
a fine platinum wire fused in glass, so that only its point projects ; and this
is placed in the liquid at a small distance from the plate. Around this point
lead peroxide is separated on the plate in very thin concentric layers, the
thickness of which decreases from the middle. They show the same series
of colours as Newton’s coloured rings in transmitted light (664). The lead
peroxide owes its origin to a secondary decomposition ; by the passage
of the current some lead oxide is decomposed into metallic lead, which is
deposited at the negative pole, and oxygen which is liberated at the positive ;
and this oxygen combines with some lead oxide to form peroxide, which
is deposited on the positive pole as the decomposition proceeds. This
process is used for the metallic coloration of objects of domestic use and
ornamentation.
The effects are also well seen if a solution of copper sulphate is placed
on a silver plate, which is touched with a zinc rod, the point of which is
in the solution ; for then a current is formed by these metals and the
liquid.
876. Arbor Saturni, or lead tree. Arbor Dianz.—When in a solu-
tion of a salt is immersed a metal which is more oxidisable than the metal
of the salt, the latter is precipitated by the former, while the immersed metal
is substituted, equivalent for equivalent, for the metal of the salt. This pre-
cipitation of one metal by another is attributable partly to the difference
in their affinities, and partly to the action of a current which is set up as
soon as a portion of the less oxidisable metal has been deposited. The
action is promoted by the presence of a slight excess of acid in the solu-
tion.
A remarkable instance of the precipitation of one metal by another is
the Arbor Saturnt. This name is given to a series of brilliant ramified
crystallisations obtained by zinc in solutions of lead acetate. A glass flask
is filled with a clear solution of this salt, and the vessel closed with a cork,
to which is fixed a piece of zinc in contact with some copper wire. The
flask, being closed, is left to itself. The copper wire at once begins to be
covered with a moss-like growth of metallic lead, out of which brilliant
att
882 Dynamical Electricity [876-
crystallised laminze of the same metal continue to form ; the whole pheno-
menon has great resemblance to the growth of vegetation, from which indeed
the old alchemical name is derived. For the same reason the name A7vbor
Diane has been given to the metallic deposit produced in a similar manner
by mercury in a solution of silver nitrate. |
If a rod of zinc is dipped in an acid solution of stannous chloride,
crystallised tin is formed upon it ; the experiment is rendered more beautiful
by dipping the platinum electrodes of a battery in the solution ; if the poles
are reversed, the crystallised laminz disappear at one pole to reappear at
the other.
ELECTROMETALLURGY
877. Electrometallurgy.—The decomposition of salts by the battery
has received a most important application in e/ectrometallurgy, or galvano-
plastics, or the art of precipitating certain metals from their solutions by the
action of a voltaic current. The processes are twofold ;in the one, e/ectro-
typing or galvanoplasiics proper, a mould is used, on which a metal, usually
copper, is more or less thickly deposited ; the deposit can afterwards be de-
tached, and gives a copy of the original object ; in the other, which is known
as electroplating, a thin coherent coating of metal—gold or silver, for instance
—is deposited on objects and remains adherent to them. The art was dis-
covered independently by Spencer in England and by Jacobi in St. Petersburg.
In order to obtain a galvanoplastic reproduction of a metal or any other
object, a mould must first be made, on which the layer of metal is deposited
by the electric current.
For this purpose several substances are in use, and one or another is
preferred according to circumstances. For medals and similar objects
which can be submitted to pressure, gutta-percha may be used with advan-
tage. The gutta-percha is softened in hot water, pressed against the object
to be copied and allowed to cool, when it can be detached without difficulty.
For the reproduction of engraved wood blocks or type, wax moulds are now
commonly used. They are prepared by pouring into a narrow flat pan a
suitable mixture of wax, tallow, and Venice turpentine, which is allowed to
set, and is then carefully brushed over with very finely powdered graphite.
While this composition is still somewhat soft, the wood block or type is
pressed upon it either by a screw press or, still better, by hydraulic pressure.
If plaster-of-Paris moulds are to be made use of, it is essential that they be
first thoroughly saturated with wax or tallow, so as to become impervious to
water. 6
In all cases, whether the moulds be of gutta-percha or wax, or any non-
conducting substance, it is of the highest importance that the surface be
brushed over very carefully with graphite, and so made a good conductor.
The conducting surface thus prepared must also be in metallic contact with
a wire or a strip of copper by which it is connected with the negative elec-
trode. Sometimes the moulds are made of a fusible alloy (344), which may
consist of 5 parts of lead, 8 of bismuth, and 3 of tin. Some of the melted
alloy is poured into a shallow box, and just as it begins to solidify, the medal
is placed horizontally on it in a fixed position. When the alloy has become
cool, a slight shock is sufficient to detach the medal. A copper wire is then
-877] Electrometallurgy 883
bound round the edge of the mould, by which it can be connected with the
negative pole of the battery, and then the edge and the back are covered
with a thin non-conducting layer of wax, so that the deposit is formed only
on the mould itself.
The most suitable arrangement for producing an electro-deposit of copper
consists of a trough of glass, slate, or wood, lined with india-rubber or
coated with marine glue (fig. 847). This contains an acid solution of copper
sulphate, and across it are stretched copper rods, B and D, connected
respectively with the negative and positive poles ofa battery. By their copper
conductors the moulds, #z, are suspended in the liquid from the negative
rod B, whilst a sheet of copper, C, presenting a surface about equal to that
of the moulds to be covered, is suspended from the positive rod D, at the
distance of about two inches, directly opposite to them.
The copper plate suspended from the positive pole not only acts as an
electrode, but keeps the solution in a state of concentration, for the acid
liberated at the positive pole dissolves the copper, and reproduces a quantity
of copper sulphate equal to that decomposed by the current.
The battery employed for the electric deposition of metals ought to be
one of great constancy, and—on the small scale—-Daniell’s and Smee’s are
mostly in use. These batteries have in large establishments been supplanted
by accumulators or by dynamo machines (939), which furnish the electricity
at one quarter the expense, and which are specially constructed so as to
furnish currents which have small E.M.F. and small internal resistance.
The density of a current is its strength divided by the surface of the
electrodes, or the number of amperes per square decimetre, and a statement
of this density in conjunction with a knowledge of the composition and
strength of the bath is a succinct way of defining the conditions of electric
deposition. The density at the electrodes has a great influence on the form
in which the ions are separated out ; thus with a moderate density silver
separates in a crystallised form, and at a greater one in the form of a black
powder.
Another, and very simple, process for producing the electric deposit of
copper consists in making use of what is in effect a Daniell’s cell. A porous
pot or a glass
cylinder,covered
at the bottom
with bladder or
with vegetable
parchment, is
immersed in a
vessel of larger
éapacity, con. 7) mm a i
taining a con S==2S ate — a
centrated solu- Be
tion of copper
sulphate. The
porous vessel
contains acidu- .
lated water, and in it is suspended a piece of amalgamated zinc of suitable
cassee
884 Dynamical Electricety [877—
form, and having a surface about equal to that of the mould. The latter is:
attached to an insulated wire connected with the zinc, and is immersed in
the solution of copper sulphate in such a position that it is directly opposite
to the diaphragm. The action commences by the mould becoming covered
with copper, commencing at the point of contact with the conductor, and
gradually increasing in thickness in proportion to the action of the Daniell’s.
element thus formed. It is, of course, essential in the process to keep the:
solution of copper sulphate at a uniform strength, which is done by agi-
tating.the liquid and suspending in it bags filled with crystals of this salt.
How great is the delicacy which such electric deposits can attain appears.
from the fact that galvanoplastic copies can be made of daguerreotypes,.
which are of the greatest accuracy.
An important industrial application is made of electrolysis in the refinzng
of copper. The metal is extracted by the ordinary metallurgical processes.
so as to obtain plates containing 95 per cent. of pure copper. These plates
are then used as positive electrodes in a bath of copper sulphate, and the metal
is deposited in a state of perfect purity on thin sheets of pure copper, which
form the negative electrode, while the impurities fall to the bottom. As the
electrodes are practically identical, there is no polarisation (827), and the
work of the current is solely employed in overcoming the resistance of the
baths. The application of electrolysis to the extraction of metals was of
limited use until the powerful currents of dynamos became available. In
mountainous countries, where water-power can be had, it may in many cases
be practicable to deal zz sztuz with the extraction of metals from their ores.
878. Electrogilding.—The old method of gilding was by means of
mercury. It was effected by an amalgam of gold and mercury, which was
applied on the metal to be gilded. The objects thus covered were heated ina
furnace, the mercury volatilised, and the gold remained in a very thin layer
on the objects. The same process was used for silvering ; but they were
expensive and unhealthy methods, and have now been entirely replaced by
electrogilding and electrosilvering. Electrogilding only differs from the
process described in the previous paragraph in that the layer is thinner and
adheres more firmly. Brugnatelli, a pupil of Volta, appears to have been
the first, in 1803, to observe that a body could be gilded by means of the
battery and an alkaline solution of gold ; but De la Rive was the first who
really used the battery in gilding. The methods both of gilding and silver-
ing owe their present high state of perfection principally to the improve-
ments of Elkington, Ruolz, and others.
The pieces to be gilded have to undergo three processes before gilding.
The first consists in heating them so as to remove the fatty matter which.
has adhered to them in previous processes.
As the objects to be gilded are usually of what is called g7/ding metal or
red brass, which is a special kind of brass rich in copper, and their surface
during the operation of heating becomes covered witha layer of cupric or
cuprous oxide, this is removed by the second operation. For this purpose
the objects, while still hot, are immersed in very dilute nitric acid, where
they remain until the oxide is removed. They are then rubbed with a hard
brush, washed in distilled water, and dried in gently heated sawdust.
To remove all spots they must undergo the third process, which consists:
~880] Llectric Deposition of Iron, Nickel, Cobalt, ete. 885
in rapidly immersing them in ordinary nitric acid, and then in a mixture of
nitric acid, bay salt, and soot.
When thus prepared, the objects aré attached to the negative pole of a
battery consisting of three or four Bunsen’s or Daniell’s elements. They are
then immersed in a bath of gold as previously described. They remain in
the bath for a time, which depends on the thickness of the desired deposit.
There is a great difference in the composition of the baths. The most in
use consists of I part of gold chloride and Io parts of potassium cyanide,
dissolved in 200 parts of water. In order to keep the bath in a state of con-
centration, a piece of gold is suspended from the positive electrode, which
dissolves in proportion as the gold dissolved in the bath is deposited on the
objects attached to the negative pole. The density of the current should not
exceed o°8 ampere for each square decimetre of the surface of the kathode.
The method which has just been described can also be used for silver,
bronze, German silver, &c. But other metals, such as iron, steel, zinc, tin,
and lead, are very difficult to gild well. To obtain a good coating, they must
first be covered with a layer of copper, by means of the battery and a bath
of copper sulphate ; the copper with which they are coated is then gilded
as in the previous case.
The tint of the deposit is modified by adding solutions of copper or of
silver to the gold bath ; the former gives a reddish and the latter a greenish
tint.
879. Electrosilvering.—What has been said about gilding applies exactly
to the process of electrosilvering. The difference is in the composition of
the bath, which consists of 2 parts of silver cyanide and 2 parts of potas-
sium cyanide, dissolved in 250 parts of water. To the positive electrode is
suspended a plate of silver, which prevents the bath from becoming poorer ;
its surface should be equal to the total. surface of the objects to be silvered ;
the pieces to be silvered, which must be well cleaned, are attached to the
negative pole. It may here be observed that these processes succeed best
with hot solutions, and when the baths are old. The density of the current
should be one-third of an ampere per square decimetre.
Knowing the weight of any given metal which is transported by unit of
electricity (868), it is easy to calculate the weight deposited in a given time
by a current of known strength. Thus the current just specified would
deposit 1°46 gramme of silver in an hour. A deposit of one ounce of silver
on a square foot of surface gives a good coating ; its thickness, ;4; inch or
0°03 mm., is about half that of thin writing paper.
880. Electric deposition of iron, nickel, cobalt, and platinum.—One
of the most valuable applications of the electric deposition of metals is to
what is called the steeling (acterage) of engraved copper plates. The bath
required for this purpose is obtained by suspending a large sheet of iron,
connected with the positive pole of a battery, in a trough filled with a satu-
rated solution of sal-ammoniac ; whilst a thin strip of iron, also immersed, 1s
connected with the negative polé. By this means iron from the large plate
is dissolved in the sal-ammoniac, while hydrogen is given off on the surface
of the small one. When the bath has thus taken up a sufficient quantity
of iron, an engravedscopper plate is substituted for the small negative strip.
A bright deposit of iron begins to form on it at once, and the plate assumes
886 Dynamical Electricity [880-
the colour of a polished steel plate. The deposit thus obtained in the course
of half an hour is exceedingly thin, and an impression of the plate thus
covered does not seem different from one obtained from the original copper
plate ; it possesses, however, an extraordinary degree of hardness, so that a
very large number of impressions can be taken from such a plate before the
thin coating of iron is worn off. When, however, this is the case, the film
of iron is dissolved off by dilute nitric acid, and the plate is again covered
with the deposit of iron.
An indefinite number of perfect impressions may, by this means, be
obtained from one copper plate, without altering the original sharp condition
of the engraving.
The covering of metals by a deposit of zckel has of late come into use.
The process is essentially the same as that just described. The bath used
for the purpose can, however, be made more directly by mixing, in suitable
proportions, salts of nickel with those of ammonia. The positive pole con-
sists of a plate of pure nickel. A special difficulty is met with in the electric
deposition of nickel, owing to the tendency of this metal to deposit in an un-
even manner, and then to become detached. This difficulty is overcome by
frequently removing the articles from the bath and submitting them toa
polishing process. /
Objects coated with nickel show a highly polished surface of the charac-
teristic bright colour of this metal ; the surface layer is moreover very hard
and durable, and is not affected either by the atmosphere or even by sulphu-
retted hydrogen. A deposit of 2 grammes of nickel on the square decimetre
represents a coating 0’023 mm. in thickness. |
The deposit of cobalt has a brighter tint than that of nickel. Professor
Silvanus Thompson uses a bath of cobalt sulphate or chloride, to which
magnesium sulphate is added.
To obtain a deposit of Alatznum, the hydrate of this metal is dissolved
in syrupy phosphoric acid, and this solution diluted with water so that it
contains I°2 to 1°5 per cent. of the hydrate. An anode of platinum or of
carbon is used, and the strength of the bath is kept constant by the addition
of the hydrate. Objects made of iron, nickel, and zinc must previously be
coated with copper.
—881] Electrodynamics 887
CHAPTER Lv.
ELECTRODYNAMICS. ATTRACTION AND REPULSION OF CURRENTS
BY CURRENTS
881. Electrodynamics.—By the term electrodynamics are understood the
laws of electricity in a state of motion, or the action of electric currents upon
each other and upon magnets, while e/ectrostatics deals with the laws of elec-
tricity in a state of rest.
The action of one electrical current upon another was first investigated
by Ampére, shortly after the discovery of Oersted’s celebrated fundamental
warmed ||)
©)
Fig. 848
experiment (841). All the phenomena, even the most complicated, follow
from two simple laws, which are—
I. Zwo currents which are parallel, and in the same direction, attract one
another.
Il. Zwo currents parallel, but in contrary directions, repel one another.
In order to demonstrate these laws, the circuit which the current traverses
must consist of two parts, one fixed and the other movable. This is effected
$38 Dynamical Electricity [881—
by the apparatus (fig. 848), which is a modified and improved form of one
originally devised by Ampére.
It consists of two brass columns, A and D, between which is a shorter
one. The column D is provided with a multiplier (842) of 20 turns, MN (fig.
850), the sensitiveness of the instrument increasing with the number of turns.
This frame can be adjusted at any height, and in any position, by means of
a universal screw clamp (see figs. 850-85 3).
The short column is hollow, and in its interior slides a brass tube termi-
nating in a mercury cup, ¢, which can be raised or lowered. On the colunin
A is another mercury cup represented in section at
fig. 849 in its natural size. In the bottom is a
capillary aperture through which passes the point
of a-sewing-needle fixed to a small copper .ball.
This point extends as faras the mercury, and. turns
freely in the hole. The movable part of the circuit
consists of a copper wire proceeding from a small
ball, and turning in the direction of the arrows
from the cup a to the cup c. The two lower branches are fixed to a thin
strip of wood, and the whole system is balanced by two copper balls, sus-
pended to the ends.
These details being known, the current of a Bunsen’s battery of 4 or 5 cells
ascending by the column
A (fig: 850) tolthe ‘cup re,
traverses the circuit BC,
reaches the cup c, descends
the central column, and
thence passes by a wire,
P, to the multiplier MN,
whence it returns to the bat-
tery bythe wire Q. Now, if,
before the current passes,
the movable = circuit has
been.arranged in the plane
of the multiplier, with the
sides B and M_ opposite
each other, ‘when the cur-
Figsgee rent passes, the side B is re-
pelled, which demonstrates
the second law; for in the branches B and M the currents, as indicated
by the arrows, are proceeding in opposite directions.
To demonstrate the first law the experiment is arranged as in fig. 850—
that is, the multiplier is reversed ; the current is then in the same direc-
tion both in the multiplier and in the movable part ; and when the latter is
removed out of the plane of the multiplier, so long as the current passes
it tends to return to it, proving that there is attraction between the two
parts.
882. Roget’s vibrating spiral.—The attraction of parallel currents may
also be shown by an experiment known as that of Roget’s vibrating spiral,
fig. 851. A copper wire about 0:7 mm. in diameter is coiled in a spiral of
~$83] Laws of Angular Currents 889
about 30 coils of 25 mm. in diameter. At one end it is hung vertically from
a binding screw, while the other just dips in a mercury cup. On passing the
current of .a batter) of 3 to 5 ;
Grove’s cells through the spiral by
means of the mercury cup and the
binding screw, its coils are tra-
versed by parallel currents; they
therefore attract one another, and
rise, and thus the contact with the
mercury is broken. The current
having thus ceased, the coils no
longer attract each other, they fall
by their own weight, contact with
the mercury is re-established, and
the series of phenomena is inde-
finitely reproduced. The experi-
ment is still more striking if a
magnetised rod the thickness of
a pencil is introduced into the
interior. This will be intelligible
if we consider the action between
the parallel Amperian currents
(890) of the magnet and of the
helix. Fig. 851
883. Laws of angular currents.
I. Two rectilinear currents, the directions of which form an angle with
each other, attract one another when both approach or recede from the apex
of the angle.
Il. They repel one another tf one approaches and the other recedes from
the apex of the angle.
These two laws may be demonstrated by means of the apparatus above de-
scribed, replacing
the movable circuit
by the circuit BC
(fig. 852). If then
the multiplier is
placed horizontally,
so that its current
is in the same direc-
tion as in the moy-
able current, on re-
moving the latter it
quickly approaches
the multiplier,
which verifies the
first law.
To prove the
second law, the multiplier is turned so that the currents are in opposite direce _
tions, and then repulsion ensues (fig. 852).
890 Dynamical Electricity [883-
Both laws are included in the statement that the two circuits tend to
become parallel to each other with their currents in the same direction.
In a rectilinear current each element of the current repels the succeeding
one, and ts ttself repelled.
This is an important consequence of Ampére’s law, and may be experi-
mentally demonstrated by the following arrangement, which was devised
by Faraday. A U-shaped piece of copper wire, the ends of which dip
in two separate deep mercury cups, is suspended from one end of a delicate
balance and suitably equipoised. When the mercury cups are connected
with the two poles of a battery, the wire rises very appreciably, and sinks
again to its original position when the current ceases to pass. The current
passes into the mercury and into the wire ; but from the construction of the
apparatus the former is fixed, while the latter is movable, and is accord-
ingly repelled.
884. Laws of sinuous currents.—Zhe action of a sinuous current ts
equal to that of a rectilinear current of the same length in projection.
This principle is demon-
strated by arranging the
multiplier vertically and
placing near it a movable
circuit of insulated wire
half sinuous and_ half
rectilinear (fig. 853). It
will be seen that there
is neither attraction nor
repulsion, showing that
the action of the sinuous
portion m2 is equalled
by that of the rectilinear
portion.
An application of this
principle will presently be
g. 853 “met with in the appara-
tus called solenoids (896),
which are formed of the combination of a sinuous with a rectilinear current.
885. Action of an infinite current on a current perpendicular to its
direction.—From the action exerted between two angular currents (883) the
action of a fixed and infinite rectilinear current, PQ (fig. 854), on a movable
current, KH, perpendicular to its direction can be determined. Let OK be
the perpendicular common to KH and PQ, which is null if the two lines PQ
and KH meet. The current PQ flowing from Q to P in the direction of the
arrows, let us first consider the case in which the current KH approaches the
current QP. From the first law of angular currents (883) the portion OQ of
the current PQ attracts the current KH, because they both flow towards the
summit of the angle formed by their directions. The portion PO, on the con-
trary, will repel the current KH, for here the two currents are in opposite
directions at the summit of the angle. If then sg and mp stand for the two
forces, one attractive and the other repulsive, which act on the current KH,
and which are necessarily of the same intensity, since they are symmetrically
a
i
Q
—885] Action of an Infinite Current 89OL
arranged in reference to the two sides of the point O, these two forces may
be resolved into a single force, #7, which tends to move the current KH
parallel to the current QP, but in a contrary direction.
A little consideration will show that when the current KH is below the
current PQ, its action will be the opposite of what it is when above.
On considering the case in which the current KH moves away from PQ
(fig. 855), it will be readily seen from similar considerations that it moves
parallel to this current, but in the same direction.
H H
Acad wn
Be ee
Ae ee zane a,
} a aS & vb f
K IK
P Pout e : .
a ) <— <— 0 <—
Fig. 854 Fig. 855
Hence follows this general principle. A /finzte movable current which
approaches a fixed infinite current ts acted on so as to move tn a atrection
parallel and opposite to that of the fixed current; of the movable current
tends from the fixed current, tt ts acted on so as to move parallel to the
current and in the same direction.
It follows from this, that if a vertical current is movable about an axis,
XY, parallel to its direction (figs. 856 and 857), any horizontal current PQ
will have the effect of turning the movable current about its axis, wafzl the
x acd | ae:
: :
so la
Vatiwey diva td“ Bo Mle i ae 'y
P Q P :) Q
oa <— +— a gna ee
Fig. 856 Fig. 857
plane of the axis and of the current have become parallel to PQ ; the vertical
current stopping, in reference to its axis, o7 the stde from which the current
PQ comes (fig. 856), or on the side towards which it ts directed (fig. 857),
according as the vertical current descends or ascends—that is, according as it
approaches or moves from the horizontal axis. :
It also follows from this principle that-a system of two vertical currents
rotating about a vertical axis (figs. 858 and 859) is directed by a horizontal
current, PQ, in a plane parallel to this current when one of the vertical
892 Dynamical Electricity [885—
currents is ascending and the other descending (fig. 858); but that if they are
both ascending or both descending (fig. 859), they are not directed.
sapere. Jatt | Ki
baa, ne oy ima
faa fiat | choles
Pp my! Bh Pp Yio a
Fig. 858 Fig. 859
886. Action of an infinite rectilinear current on a rectangular or
circular current.—It is easy to see that a horizontal infinite current exer-
cises the same directive action on a rectangular current movable about a
vertical axis (fig. 860) as that which has been above stated. For from the direc-
tion of the currents indicated by the arrows, the part QY acts by attraction
not only on the horizontal portion YD (/aw of angular currents), but also on
the vertical portion AD (daw of perpendicular currents). The same action
evidently takes place between the part PY and the parts CY and BC.
Hence, the fixed current PQ tends to direct the movable rectangular current
ABCD into a position parallel to PQ, and such
that in the wires CD and PQ the direction of
the two currents ts the samte.
This principle is readily demonstrated by
placing the circuit ABCD on the apparatus with
two supports (fig. 860), so that at first it makes
an angle with the plane of the supports. On
passing a somewhat powerful current below the
circuit in the same plane as the supports, the
movable part passes into that plane. It is best
to use the circuit in fig. 850, which is astatic,
Fig. 860 _ while that of fig. 860 is not.
What has been said about the rectangular
current in fig. 860 applies also to circular currents, and is demonstrated by
the same experiments.
887. Rotation of a finite horizontal current by an infinite horizontal
rectilinear current.—The attractions and repulsions which rectangular
currents exert on one another
ae am
a a R may readily be transformed
i wley ‘ va into a continuous circular mo-
1 yA \ tion. Let ni es roa ie
ae Sei fm current movable about the
Ax we fr point O in a horizontal plane,
pc ied ont ai and let PQ be a fixed infinite
Se eee 7 current also horizontal. As
these two currents flow in the
is : direction of the arrows, it fol-
lows that in the position OA_the movable current is attracted by the current
Fig. 861 Fig. 862
-888] Rotation of a Vertical Current 893
PQ, for they are in the same direction. Having reached the position OA’,
the movable current is attracted by the part NQ of the fixed current, and
repelled by the part PN. Similarly in the position OA”, it is attracted by
MQ and repelled by PM, and so on; from which follows a continuous rota-
tory motion in the direction AA’A”A”’. If the movable current, instead of
being directed from O towards A, were directed from A towards O, it is
easy to see that the rotation would take place in the contrary direction.
Hence, by the action of a fixed infinite current, PQ, the movable current
OA tends to a continuous motion 27 a direction opposite to that of the fixed
current.
If, both currents being horizontal, the fixed current were circular instead
of being rectilinear, its effect would still be to produce a continuous circular
motion. For, let ABC (fig. 852) be a fixed circular current, and mz a rec-
tilinear current movable about the axis #, both currents being horizontal.
These currents, flowing in the direction of the arrows, would attract one
another in the angle 7AC, for they both flow towards the summit (883). In
the angle 7AB, on the contrary, they repel one another, for one goes towards
the summit and the other moves from it. Both effects coincide in moving
the wire 7772 in the same direction ACB.
888. Rotation of a vertical current by a horizontal circular current.—
A horizontal circular current, acting on a rectilinear vertical, also imparts
to it a continuous rotatory motion. In order to show this, the apparatus
represented in fig. 863 is used.
_ It consists of a brass vessel, round which are rolled several coils of in-
sulated copper wire, through which a current passes. In the centre of the
vessel is a brass support, a, terminated by a small cup containing mercury.
In this dips a pivot supporting a copper wire, 44, bent at its ends in two ver-
tical branches, which are soldered to a very light copper ring immersed in
acidulated water contained in the vessel. A current entering through the
wire 2, reaches the wire A, and, having made several circuits, terminates
at B, which is connected by a wire underneath with the lower part of
the column a. Ascending in this column, it passes by the wires 46 into
the copperring,
into the acidu-
lated water, and
into the sides
of the vessel,
whence it re-
turns to the
battery by the
strip Jae ue
circuit being
thus closed, the
wire 066 and
the ring tend to turn ina direction contrary to that of the fixed current, a
motion due to the action of the circular current on the current in the vertical
branches 64; for, as follows from the two laws of angular currents, the
branch 6 on the right is attracted by the portion A of he fixed current, and
the branch 4 on the left is attracted in the contrary direction by the opposite
Fig. 863
894 Dynamical Electricity [888—
part, and these two motions coincide in giving the ring a continuous rotatory
motion in the same direction. The action of the circular current on the
horizontal part of the circuit 64 would tend to turn it in the same direction ;
but from its distance the effect due to it may evidently be neglected.
889. Rotation of magnets by currents.—Faraday proved that currents
impart the same rotatory motions to magnets that they do to currents. This
may be shown by means of the apparatus represented in fig. 864. It consists
of a large glass vessel, almost filled with mercury. In the centre of this is
immersed a magnet, A, about eight inches in length, which projects a little
above the surface of the mercury, and is loaded at the bottom with a
platinum cylinder. At the top of the magnet is a small cavity containing
mercury ; the current ascending the column 7 passes into this cavity
by the rod C. From the magnet it passes by the mercury to a copper
ring, G, when it emerges by the column #7. When the current flows the
magnet begins to rotate round its own axis with a velocity depending on its
magnetic power and on the intensity of the current.
Instead of making the magnet rotate on its axis, it may be caused to
rotate round a line parallel to its axis by arranging the experiment as shown
(fig. 861). ;
This rotatory motion is readily intelligible on Ampére’s theory of mag-
netism (gor), according to which, magnets are traversed on their surface
by an infinity of circular currents in the same direction, in planes perpen-
dicular to the axes of the magnet. At the moment at which the current
passes from the
magnet into the
mercury, it di-
vides on the
surface of the
mercury into an
infinity of rec-
| tilinear currents
proceeding from
the axis of the
magnet to the
circumference of
the glass. Figs.
- 866 “and? $67,
which corre-
= = spond respec-
Fig. 854 Fig. 865 tively to figs.
864 and 865,
give on a larger scale, and on a horizontal plane passing through the surface
of the mercury, the direction of the currents to which thé rotation is due. In
fig. 864, the north pole being at the top, the Amperian currents pass round
‘the magnet in the reverse direction to that of the hands of a watch, as indi-
‘cated by the arrow? (fig. 865), while the currents which radiate from the rod C
towards the metal ring GG’, have the direction CD, CE. Thus (883) any
‘given element ¢ of the magnetic current of the bar A is attracted by the
-890] Directive Action of Magnets on Currents 895
current CE and repelled by the current CD; hence results a rotation of
the bar about its axis in the same direction as the hands of a watch.
In fig. 867 the
currents CD, CF,
being in the oppo-
site direction to
those of the bar,
would repel the
latter, which would
be attracted by the
eurrents. CE; GH:
Pence. pithee bar
rotates in a circular
direction, shown by
the arrow s, about the vertical axis which passes through the rod C. |
If the north pole is below, or if the direction of the current is altered, the
rotation of the magnet is in the opposite direction.
Fig. 866 Fig. 867
ACTION OF THE EARTH AND OF MAGNETS ON CURRENTS
890. Directive actions of magnets on currents.—Not only do currents
act upon magnets, but magnets also act upon currents. In Oersted’s funda-
mental experiment (fig. 848), the magnet being movable while the current is
fixed, the former is directed and tends to set at right angles to the current.
If, on the contrary, the magnet is fixed and the current movable, the latter is
directed and sets across the direction of the magnet. This may be illus-
trated by the apparatus represented in fig. 868. This is the original form
uy IT TTT TATU cc |
fi ii Ce m7 il) ie
of Ampére’s stand, and is frequently used in experimental demonstration.
It needs no explanation. The circuit which the current traverses is movable,
896 : — Dynamical Electricity [890—
and below its lower branch a powerful bar magnet is placed ; the circuit
immediately begins to turn, and stops after some oscillations in a plane
perpendicular to the axis of the magnet.
For demonstrating the action of magnets upon currents, De la Rive’s
floating battery (fig. 869) is well adapted. It consists of plates of zinc and
copper which are immersed in dilute sulphuric acid contained in a glass
bulb slightly loaded with mercury to keep it upright, and which can float
freely on water. With the plates can be connected either circular or rect-
angular wires, coils, or solenoids ; they are then traversed by a current, and
can be subjected to the action either of magnets or of currents.
891. Rotation of currents by magnets.—Not merely can currents
be directed by magnets, but they may also be made to rotate, as is seen
from the following experiment, devised by Faraday (fig. 870). On a base
with levelling screws, and resting on an ivory support, is a copper rod, BD.
It is surrounded in part of its length by a bundle of magnetised wires, AB,
and at the top of it isa mercury cup. A copper circuit, EF, balanced on a
steel point, rests in the cup, and the other ends of the circuit, which terminate
in steel points, dip in an annular trough full of mercury.
The apparatus being thus arranged, the
current from 4 or 5 Bunsen’s elements enters
at the binding screw 4; it thence rises in the
rod D, descends by the two branches, reaches
the mercury by the steel points, whence it
passes by the framework, which is of copper,
to the battery by the binding screw a. If
now the magnetised bundle is raised, the
circuit EF rotates, either in one direction or
the other, according to the pole by which
it is influenced. This rotation is due to
currents assumed to circulate round mag-
nets ; currents which act on the vertical
branches EF in the same way as the circular
current on the branches 44 in fig. 863.
In this experiment the magnetised bundle |
may be replaced by a solenoid (898) or by
an electromagnet, in which case the two
binding screws in the base of the apparatus
on the left give entrance to the current
which is to traverse the solenoid or electro-
magnet.
892. Electrodynamic and electromagnetic
rotation of liquids.—The condition of a linear
current assumed in the previous experiments
is not necessary. This may be illustrated by
a simple form of experiment devised by Clerk
Maxwell.. At the bottom of a small beaker, a copper disc is placed with
an insulated tongue bent at right angles, and connected with a similar
zinc disc supported about an inch above the copper. Dilute acid is placed
so as to cover both discs, and, some fine sawdust having been added to
Fig. 870
893] Directive Action of the Earth on Vertical Currents 897
the liquid, the whole is placed on the pole of an electromagnet. The
rotation of the liquid is then shown by that of the sawdust.
893. Directive action of the earth on vertical currents.—The earth,
which exercises a directive action on magnets (703), acts also upon currents,
giving them in some cases a fixed direction, in others a continuous rotatory
motion.
The first of these two actions may be thus enunciated: Avery vertical
current movable about an axis parallel to ttself, places ttself under the direc-
tive action of the earth in a plane through this axis perpendicular to the
magnetic meridian, and stops after some oscillations, on the east of tts axts
of rotation when it 7s descending, and on the west when tt ts ascending.
This may be demonstrated by means of the apparatus represented in fig.
872, which consists of two brass vessels of somewhat different diameters.
’ The larger, a, about 13 inches in diameter, has an aperture in the centre,
through which passes a brass support, 4, insulated from the vessel a, but
communicating with the vessel K. This column terminates in a small cup,
Fig. 872
in which a light wooden rod rests on a pivot. At one end of. this rod a fine
wire is coiled, each end of which dips in acidulated water, with which the
two vessels are respectively filled.
The current arriving by the wire 7z passes to a strip of copper, which is
connected underneath the base of the apparatus with the bottom of the
column 6. Ascending in this column, the current reaches the vessel K
and the acidulated water which it contains ; it ascends from thence in the
wire ¢, redescends by the wire e, and, traversing the acidulated water, it
reaches the sides of the vessel a, and so back to the battery through the
wire 7.
The circuit being thus closed, the wire e moves round the column 4, and
stops to the east of it, when it descends, as is the case in the figure ; but if
it ascends, which is effected by transmitting the current by the wire z, the
wire e stops to the west of the column 4, in a position directly opposite to
that which it assumes when it is descending.
If the rod with a single wire, in fig. 872, is replaced by one with two
3M
898 Dynamical Electricity — -[893-
wires as in fig. 872, the rod will not move, for as each wire tends to place
itself on the east of the column a, two equal and contrary effects are produced
which counterbalance one another.
894. Action of the earth on horizontal currents movable about a
vertical axis.—The action of the earth on horizontal currents is not direc-
tive, but ezves them a continuous rotatory motion.
This may be illustrated by means of the apparatus represented in fig. 873
which only differs from that of fig. 872 in having but one vessel. The
current, ascending by the column a, traverses the two wires cc, and descends
by the wires 04, from which it regains the battery ; the circuit ccd then begins
a continuous rotation
anti-clockwise or clock-
wise, according as in
the wires cc the current
goes from the centre, as
is the case in the figure,
or goes towards it, which
is the case when the
current enters by the wire
m instead of by z But
we have seen (893) that
the action of the earth on the vertical wires 46 is destroyed ; hence the
rotation is that produced by the action on the horizontal branches cc. This
rotatory action of the earth on horizontal currents is an instance of the
rotation of a finite horizontal by an infinite horizontal current (885).
The motion of a movable current in a magnetic field is also illustrated
by Barlow's wheel, represented in fig. 874. It consists of a light toothed metal
wheel which can rotate about a horizontal axis, and is so arranged that one
or more teeth dip in a mercury trough. The two branches of a horseshoe
Fig. 875
magnet are on opposite sides of the trough, and when the poles of a battery
are connected with the axis and mercury respectively, the wheel at once
rotates. If the current flows from the centre to the circumference of the
wheel, and the north pole is in front, the wheel rotates in a UifeCHon opposite
that bf the hands of a watch.
~896]| Structure of a Solenoid 899
Faraday’s disc (fig. 875) is similar ; the current arrives and departs by two
springs, one B which presses against the axis, and the other A against the cir-
cumference of the wheel. H represents the direction of the lines of force of
the field.
895. Directive action of the earth on closed currents movable about
a vertical axis.—If the current on which the earth acts is closed, whether
it be rectangular or circular, the result is not a continuous rotation, but a
directive action, as in the case of vertical currents (893), in virtue of which
the current places ttself in a plane perpendicular to the magnetic meridian,
so that tt ts descending on the east of tts axts of rotation, and ascending on
the west.
This property, which can be shown by
the apparatus represented in fig, 876, is
a consequence of what has been said about
horizontal and vertical currents. For in
the closed circuit BA, the current in the
upper and lower parts tends to turn in oppo-
site directions, from the law of horizontal
currents (894), and hence is in equilibrium ;
while in the lateral parts the current on the
one side tends towards the east, and on the
other side to the west, from the law of vertical
currents.
From the directive action which the earth Fig. 876
exerts on currents, it is necessary, in many
experiments, to neutralise this action. This is effected by arranging the
movable circuit symmetrically about its axis of rotation, so that the directive
action of the earth tends to turn the two branches in opposite directions.
This condition is fulfilled in the circuit in fig. 876. Such circuits are hence
called astatic circutts.
896. Structure of a solenoid.—A solenoid or electromagnetic cylinder is a
system of equal and parallel circular currents formed of the same piece of
covered copper wire and coiled in the form of a helix or spiral, as represented
in fig. 877. A solenoid or electromagnetic cylinder, however, is only complete
when part of the wire BC passes in the direction of the axis in the interior of
the helix. With this arrangement, when the circuit is traversed bya current
it follows from what has been said
about sinuous currents (884) that the
action of a solenoid in a longitudinal
direction, AB, is counterbalanced by that
of the rectilinear-current BC. This action
is accordingly null in the direction of the length, and the action of a solenoid
in a direction perpendicular to its axts is equivalent to that of a series of equal
parallel currents.
A solenoid as defined by Ampére is only a mathematical conception, being
an arrangement of zzfinztely small closed equal currents all perpendicular to
the same line called the avectrix, which passes through their centres This
cannot be realised any more than can the simple pendulum, and we must.
3M2
Fig. 877
goo Dynamical Electricity [896-
regard the above apparatus as bearing much the same relation to the ideal
solenoid, as the compound does to the simple pendulum.
897. Action of currents on solenoids.—What has been said of the
action of fixed rectilinear currents on finite rectangular or circular currents
(885) applies evidently to each of the circuits of a solenoid, and hence a
rectilinear current must tend to direct these circuits parallel to itself. To
demonstrate this fact experi-
mentally, a solenoid is con-
structed as shown in fig. 878,
so that it can be suspended
by two pivots in the cups @
and ¢ of the apparatus repre-
sented in fig. 876. The sole-
noid is then movable about
a vertical axis, and if a recti-
linear current QP be passed
beneath it, which at the same
time traverses the wires of
the solenoid, the latter is seen
Fig. 878 to turn and tends to set at
. right angles to the lower cur-
rent—that is, in such a position that its circuits are parallel to the fixed
current ; and, further, the current in the lower part’of each of the circuits
is in the same direction as in the rectilinear wire.
If, instead of passing a rectilinear current below the solenoid, it is passed
vertically on the side, an attraction or repulsion will take place, according
as the two currents in the vertical wire, and in the nearest part of the
solenoid, are in the same or in contrary directions. .
898. Directive action of the earth on solenoids.—If a solenoid is
suspended in the two cups (fig. 879), not in the direction of the magnetic
Fig. 879
meridian, and a current is passed through the solenoid, the latter will
begin to move, and will finally set in such a position that its axis is in the
direction of the magnetic meridian. If the solenoid is deflected from its
—901] Ampéere’s Theory of Magnetism gol
position of equilibrium, it will, after a few oscillations, return, so that its axis
is in the magnetic meridian. Further, it will be found that in the lower
half of the coils of which the solenoid consists the direction of the current
is from east to west ; in other words, the current is descending on that side
of the coil turned towards the east and ascending on the west. The directive
action of the earth on solenoids is accordingly a consequence of that which
it exerts on circular currents. In this experiment the solenoid is directed like
a magnetic needle, and the zorth pole, as in magnets, is that end which
points towards the north, and the south fole that which points towards the
south. This experiment may be made by means of a solenoid fitted on a
De la Rive’s floating battery (890).
899. Mutual action of magnets and solenoids.—The same phenomena
of attraction and repulsion exist between solenoids and magnets as between
magnets themselves. For if one of the poles of a magnet is presented
to a movable solenoid, traversed by a current, attraction or repulsion will
take place, according as the poles of the magnet and of the solenoid are
of contrary or.of the same name. The same phenomenon takes place
when a solenoid traversed by a current and held in the hand is presented to
a movable magnetic needle. If one pole of a long bar magnet is presented
to the centre of the floating coil (fig. 869), then if the direction of the current
in the coilis the same as that of the Ampérian current (901) in that pole of the
magnet, the coil will be attracted to the magnet, and, encircling it, will move
towards the middle, where it is stationary ; if the currents are opposite, then
the coil will first of all be repelled, it will then turn round, and proceed as
before.
900. Mutual action of solenoids.—When two solenoids traversed by a
powerful current are allowed to act on each other, one of them being held
in the hand and the other being movable about a vertical axis, as shown
in fig. 879, attraction and repulsion will take place just as in the case of
two magnets. These phenomena are easily explained by reference to
what has been said about the mutual action of the currents, bearing in
mind the direction of the currents in the extremities presented to each
other.
gor. Ampére’s theory of magnetism.— Ampére propounded a theory based
on the analogy between solenoids and magnets, by which all magnetic phe-
nomena may be referred to electrodynamical principles.
Instead of attributing magnetic phenomena to the existence of two fluids
Ampére assumed that each individual molecule of a magnetic substance is
traversed by an electric current, and further that these molecular cur-
rents are free to move about their centres. The coercive force, however, which
is little or nothing in soft iron, but considerable in steel, opposes this motion,
and tends to keep the molecular currents in any position in which they happen
to be. When the magnetic substance is not magnetised, these currents,
under the influence of their mutual attractions, occupy such positions that
their total action on any external substance is null. Magnetisation consists
in giving to these molecular currents a parallel direction, and the stronger
the magnetising force the more perfect the parallelism. The /mzt of mag-
netisation 1s attained when the currents are completely parallel.
902 Dynamical Electricity [901—
The resultant of the actions of all the molecular currents is equivalent to
that of a single current which traverses the outside of a magnet. For by
inspection of fig. 880, in which
the molecular currents are re-
presented by a series of small
internal circles in the two ends
of a cylindrical bar, it will be
seen that the adjacent parts of
the currents oppose one another
and cannot exercise any external
electrodynamic action. ' This is
not the case with the surface ;
there the molecular currents at
ab are not neutralised by other
currents, and as the points adc
are infinitely near, they form a series of elements in the sare direction
situated in planes perpendicular to the axis of the magnet, thus constituting
a true solenoid.
The direction of these currents in magnets can be ascertained by con-
sidering the suspended solenoid (fig. 878). If we suppose it traversed by a
current, and in equilibrium in the magnetic meridian, it will set in such a
position that in the lower half of each coil the current flows from eas¢ zo
west. We have then the following rule :— When the north pole of a magnet
zs looked at, the direction of the Amperian currents ts opposite to that of the
hands of a watch; and when the south pole ts looked at, the direction ts the
same as that of the hands.
go2. Terrestrial current.—In order to explain terrestrial magnetic effects
on this supposition, the existence of electrical currents is assumed, which
continually circulate round our globe from east to west perpendicular to the
magnetic meridian. The resultant of their action is a single current travers-
ing the magnetic equator from east to west. They are supposed by some to
be thermo-electric currents due to the variations of temperature caused by
the successive influence of the sun on the different parts of the globe from
east to west. |
These currents direct magnetic needles; for a suspended magnetic
needle comes to rest when the molecular currents on its under-surface are
parallel and in the same direction as the terrestrial currents. As the
molecular currents are at right angles to the direction of its length, the
needle places its greatest length at right angles to east and west, or north
and south. Natural magnetisation is probably imparted in the same way
to iron minerals.
903. Hall’s experiment.-—In the action of magnets on currents which
has been described in the foregoing sections, we have been concerned with
the action of the magnet on the body which conveys the current.
Professor Hall of Baltimore has made the following experiment to
determine whether the path of a current itself in the body of a conductor is
or is not deflected when it is exposed to the direct action of a magnetic field.
A strip of gold leaf A B, 9 centimetres in length by 2 centimetres broad (fig.
$81), is fastened on a glass plate, placed between the poles of an electro-
Fig. 880
—$03] Hall's Experiment 903
magnet in such a manner that the plane of the strip is at right angles to the
lines of force of the magnetic field. The ends of this strip A and B are in
connection with the poles of a Bunsen’s cell. Two wires leading to a
galvanometer @ and 6 are connected with two equipotential points at the
opposite edges of the strip ; that is to say, at two points, found by trial,
in which there is no deflection in the galvanometer (760). Fig. 882 shows
the general direction of the lines of flow of the current when the electro-
Fig. 882 Fig. 882
magnet is not excited, the dotted lines being equipotential lines. When the
electromagnet is excited by passing a current through it, a distinct deflection
is produced in the galvanometer, showing that the position of the equipoten-
tial lines is varied (fig. 883), and that the paths of the current in the conducting
strip have been deflected. This deflection is permanent, and cannot there-
fore be due to induction, and its direction is reversed when the current in
the electromagnet is reversed (fig. 884).
Fig. 883 Fig. 884
The magnetic field acts thus upon the current in the gold leaf in sucha
manner as to displace it towards one edge or the other, and to cause a
small portion to pass through the circuit of the galvanometer.
The electricity is displaced in the direction of the electromagnetic force,
due to the magnet, from a to 4 through the galvanometer in the case of iron,
zinc, and cobalt, but from 4 to a through the galvanometer, with nickel,
gold, and bismuth. Of all metals, bismuth shows the phenomenon in far the
highest degree.
904 Dynamical Electricity [904—
CHAPTER V
MAGNETISATION BY CURRENTS. ELECTROMAGNETS.
ELECTRIC TELEGRAPHS
904. Magnetisation by currents.—A wire conveying a current creates
about it a magnetic field. The existence of this field may be conveniently
shown by a vertical wire forming part of a voltaic circuit which passes at right
angles through a piece of cardboard. When iron filings are sprinkled on
the cardboard they are seen to
arrange themselves in circles con-
centric with the wire as represented
in fig. 885. If the direction of the
current in the wire xy is that
shown by the arrow, the direction
of the lines of force is from right to
left for an observer placed in the
current. The direction of the par-
ticles of iron is that which an in-
Fig. 885 finitely small magnet would have if
placed there. When a wire tra-
versed by a current is immersed in iron filings, they adhere to it in large
quantities (fig. 886), each particle setting perpendicularly to the wire ; they
become detached as soon as the current ceases, and there is no action on
any non-magnetic metal.
In like manner an iron or steel bar is magnetised when placed at right
angles, and near to a current ; the effect is increased by coiling an insulated
copper wire round a glass tube, in which there is an unmagnetised steel rod.
If a current is passed through the wire, even for a short time, the bar be-
comes strongly magnetised.
If, as we have already seen (813), the discharge of a Leyden jar be trans-
mitted through the wire, by connecting one end with the outer coating, and
the other with the inner coating, the bar is also magnetised. This is a
convenient way of illustrating the identity between the effects of frictional
and voltaic electricity.
If in this experiment the wire is coiled on the tube in such a manner
-905] Magnetisation by Currents 905
that when it is held vertically the downward direction of the coils is from
right to left on the side next the observer, this constitutes a 7ight-handed
or dextrorsal sptral or helix (fig. 887), of which the ordinary screw is an
example. In a /e/¢t-handed or sinistrorsal helix the coiling is in the opposite
direction—that is, from left to right (fig. 888).
In a right-handed spiral the north pole is at the end at which the current
emerges, and the south pole at the end at which it enters ; the reverse is the
case in a left-handed spiral. But whatever the direction of the coiling, the
polarity is easily found by the following rule: lf a person swimming in the
current looks at the axts of the spiral, the north pole is always on his left.
If the wire is not coiled regularly, but if its direction is reversed, at each
change of direction a consequent pole (696) is formed in the magnet. The
simplest method of remembering the
polarity produced is as follows : What-
ever be the nature of the helix, whether
right or left handed, if the end facing
the observer has the current flowing
in the direction of the hands of a watch
it is a south pole, and vice versd. The
same polarity is produced whether or
not there is an iron core within the
helix.
In order to magnetise a steel bar
by means of electricity, it need not be
placed in a tube, as shown in figs. 887
and 888. It is sufficient to coil round
it a copper wire, covered with silk,
cotton, or gutta-percha, in order to in-
sulate the circuits from one another.
go5. Electromagnets.—The ar-
rangement which has been described
above of a long length of insulated
wire coiled on a bar or core of soft
iron, and traversed by a current, forms
what is called an electromagnet. In
the case of soft iron the magnetisation
is only temporary ; when the current
ceases the magnetisation of the bar
ceases also, and the iron reverts almost wholly to its ordinary magnetic but
unmagnetised condition.
Fig. 889
906 Dynamical Electricity [905-
From its property of producing a powerful magnetic field, the coil in
this experiment constitutes a magnetising coil or spiral; and the mag-
netisation of the iron by its means is an application of the principle of
magnetic induction. From the fact that electromagnets are far more
powerful than permanent magnets, and, still more, that their magnetisation
can be instantaneously evoked and destroyed, they have met with a host of
applications of the very greatest importance ; and the form, dimensions,
and strength of such electromagnets vary greatly with the purpose for ree
they are intended.
Fig. 890 Fig. 891
There are, however, two principal types ; dar magnets, as in fig. 894,
or horseshoe magnets, either in one piece, as shown in fig. 889, or else
formed of two straight electromagnets, each joined to a cross-piece of soft
iron or yoke, T, as shown in fig. 891. It is better to have theiron in one piece,
but the bending of large masses is difficult, and is apt to increase the
coercive force, so that the other plan is generally adopted, great care being
taken that the surfaces in contact be very accurately fitted to each other.
In order that the poles at the two ends may be of opposite kinds, the
wire must go round each branch in the same direction as it would do if the
core had been bent after the winding had been finished. The windings
ought to appear in opposite directions on the
SO Soe & . two legs to an observer who is looking at the
\ _ two ends (fig. 890), the current going like the
\ WZ? hands of a watch round the south pole, and in
== the opposite direction round the north pole.
aN} Fig. 892 represents a compact form of
electromagnet devised by Joule, the core
and armature of which may be constructed
Hig? foe by sawing a piece of wrought iron tubing
| lengthwise. There must be space enough to
contain the wire necessary. The volume of the wire is determined by the
condition of not exceeding a certain temperature.
The magnetisation in the core depends on the strength of the field
due to the magnetising coil, and on the nature ee dimensions of
the core ; it is represented by the formula I = «H, I being the magnetisation,
H-the magnetic force producing it and « the coefficient of susceptibility ; for
a long bar placed inside a long coil, the actual magnetic force H is nearly
4niit
the same as that due to the coil alone, namely - where # is the number
of turns per unit length, and z the current in amperes. Similarly the mag-
~905] Electromagnets 907
netic induction (number of lines of force per sq. cm.) B, in the core depends
Ampere
mia)
If a soft iron ring or Zore be coiled round with insulated wire through
which a current is passed, it is the seat of a very powerful magnetic in-
duction, though it has no poles, and therefore no external action. Such a
system forms a closed magnetic circuit; the arrangement represented in
fig. 889, where the two poles of an electromagnet are connected by an arma-
ture, also forms such a circuit, and an interesting analogy may be made
between it and a closed electrical circutt.
upon the magnetising force, and we have the equation B = »H =
: ‘ ; Z ;
If for z in the above expression we write — , where z is the total number
n
of turns of the wire, and / the length of the bar, and consider the total in-
duction through the cross section s, the formula may be put
ieee Annet
is
ps
in which it is quite analogous to Ohm’s formula for an electric current (847)
4nnz being the magnetic equivalent of the electromotive force, and may
accordingly be called the szagnetomotive force ; while is the analogue of
pS
electric resistance. It is called the magnetic resistance or reluctance.
Its value, it will be seen, is directly as the length of the bar, and inversely as
the cross section, and the permeability » being the equivalent in magnetism
of conductivity in electricity (726); it represents conductivity for lines of
magnetic force. This analogy also holds if we consider the magnetic circuit
as made up of bodies of different permeabilities, and also in the case of
divided magnetic circuits.
The analogy fails, however, in one important respect ; electrical resist-
ance is quite independent of electromotive force, while permeability differs
in value with the value of the magnetising force. Hence the analogy is
rather formal than real ; it is, however, useful in dealing with calculations
about electromagnets.
The expression 4772 shows that we get the same magnetic effect whether
we have a small number of turns of wire with a strong current, or a great
number of turns with a weak current. Thus, with a given bar the same
effect is produced by one turn conveying a current of one ampere as by ten
turns with a current of one-tenth of an ampere. In the case of electro-
magnets the magnetising force is usually defined by the number of ampere
turns used.
With a given battery the greatest magnetising force is obtained when
the resistance in the magnetising spiral is equal to the other resistances in
the circuit, those of the battery included, and the length and diameter of the
wire must be so arranged as to satisfy these conditions.
Taking the permeability of air as unity, that of iron is many hundred
times as great ; hence the introduction of a layer of air in a magnetic circuit
is analogous to the introduction of a bad conductor in an electric circuit.
Iron being the most permeable of all substances, a magnetic circuit should
908 Dynamical Electrectty (905-
have as much iron as possible. The junctions also should be made close
and true, since each joint increases the magnetic reluctance.
If we take a given magnetising spiral, at right angles to the magnetic
meridian, and place at some distance from it, and in the line of its axis, a
small magnetic needle, on passing a current through the spiral the needle
is deflected, and this deflection (or, more strictly, its tangent) is a measure of
the magnetic moment acquired by the spiral; if the current be gradually
increased the deflection will also be increased, and in proportion to the
strength of the current. .
If, however, the spiral contains a bar of soft iron, the case is not so simple.
If we plot the curve which represents the ratio of the magnetising force to
the magnetisation, as measured by the deflection jof the needle, it will be
found that at first the magnetisation is proportional to the magnetising force,
then a stage is reached when the magnetisation increases more rapidly than
in direct proportion to the magnetising force, but the rate of increase gradu-
ally becomes less, and the magnetisation ultimately approaches a limit which
is not materiaily exceeded, even by a considerable increase in the magnetising
force. This represents a state of saturation (737), and it corresponds to the
case in which the axes of the molecular magnets (gor) are all strictly parallel
to the axis of the spiral.
The intensity of the magnetisation which can be imparted toa bar is
about 1,700 C.G.S. units in the case of wrought iron, 1,240 with cast iron, and
515 in the case of nickel. Steel can acquire pretty much the same intensity
of magnetisation as wrought iron, and retains about one half in the form of
permanent or residual magnetism. Soft iron almost wholly loses its mag-
netisation when the current ceases, and the more so the purer the iron, and
the more carefully it is annealed. In many applications it is of great
importance that the cessation of the magnetisation with the current should
be as complete as possible. Perxmanent and residual magnetism are in fact
the same, but the former expression is used when it is desired to retain the
magnetism, and the latter when its presence is objectionable.
Residual magnetism is greater in long magnets, that is to say, those
in which the diameter is small in comparison with the length. Hence for
rapid demagnetisation the cores should. be short and thick. A bundle of
soft iron wires is more rapidly demagnetised than a massive bar of the same
size. Residual magnetism is greater when the magnetising current is
not stopped suddenly, as is usually the case, but is gradually brought back
to zero by successively introducing increasing resistances. By suddenly
stopping the current it has sometimes been found with thick rods of very
soft iron, that a reversed magnetisation is met with which is called abnormal
magnetisation. ‘This is easily understood from the tendency of molecular
magnets to revert to their primitive condition (744\. In doing this they
experience a certain friction or resistance, and when the magnetisation
gradually diminishes, this hinders any reversal of the molecules ; but when
the cessation is sudden, the molecules, from the greater vis véva of their
reversal, will sooner come back to their original position, or even pass it, and
come to rest on the opposite side.
The effects of residual magnetism are lessened by preventing the
—905] Electromagnets 909
armature from coming in direct contact with the magnet, either by inter-
posing a thin sheet of paper or by providing the cores with brass studs.
With uniform magnetisation the portative force of a magnet may be
readily calculated. It is expressed by the formula ¢P =27B?S, where P is
the mass in grammes, ¢=981, Bis the induction (726) and S the available
surface. If 800 is the value of B in C.G.S. units, we get for the portative
force about 4 kilos. per square centimetre, which is what is looked for in
good specimens of permanent magnets. With soft iron in a strong field
values of Io to 12 kilos. are obtained.
When an armature is not in contact with the poles the attraction di-
minishes very rapidly with the distance ; for in the first place the attraction
is inversely proportional to the distance, and then the effect of this distance is
to introduce a layer of air which from its very great reluctance greatly lessens
the induction in the magnetic circuit.
According to the researches of Bidwell, it appears that for low degrees of
magnetisation the portative force increased less rapidly than the current
strength up to a certain point, at which the field was about 240 units and the
load supported 14,000 grammes per square centimetre. From this point
the magnetising current and the load increased in the same ratio. When
the field had an intensity of 585 units, the greatest weight supported was
15,900 grammes per sq. cm., or 226 pounds per square inch.
Joule found that under a magnetising force which he considered sufficient
to saturate the iron, but which appears to have been less than Ioo units, the
length of an iron bar was increased by g7j4g5- When the bar with its coil
was placed in a sort of water thermometer consisting of a glass flask provided
with a capillary tube, Joule found, using the same magnetising force as
before, that allowing for the expansion of water
due to the heat of the current, there was no
motion in the capillary tube ; from this he con-
cluded that the volume of the iron was un-
altered by magnetisation, and also that.since
its length was increased, its diameter must
have diminished.
In Shelford Bidwell’s investigation of these
phenomena, a far higher magnetising force
was employed (up to nearly 1,500 units), and
the results showed that Joule’s conclusions
required modification. It was found that if
the magnetising force is increased beyond the
point at which the magnetic elongation of the A
rod is greatest a further change takes place ;
the length of the rod, instead of remaining un- aie
altered, steadily diminishes. Fora certain value of the magnetising force,
the rod resumes its original length, and on further increase of the magnetising
force becomes shorter. The diameter of the rod is also changed ; with small
forces it is diminished, and with large forces increased, but the longitudinal
and transverse changes of dimensions are not often related in such a manner
as to leave the volume of the bar unaltered. A magnetising force of 80 or
go units has indeed generally no effect upon the volume ; with a smaller
ee oe
~QIo Dynamical Electricity [905-
force, however, the volume is diminished, while with a larger one it is
increased. He also found that as regards magnetic changes of length, the
behaviour of a cobalt rod is the reverse of that of an iron one, contracting
under small and lengthening under great magnetic forces. A nickel rod is
always shortened whether the magnetising force is great or small.
In fig. 893 the abscissz represent magnetising forces,and the ordinates
the corresponding magnetisations in a soft iron bar. The curve O A repre-
sents the magnetisations starting from the magnetising force O and rising
to F. The curve ACA’ represents decreasing values of the force from F
to —F’, that is, an equal current in the opposite direction ; and, lastly, the
curve A’BA represents increasing values from —F to + F.
It will thus be seen that the magnetisation of a bar for a given force
depends not only on its existing condition, but also on its previous state.
The magnetisation is greater in the descending than in the ascending period
for the same value of the magnetising force. This is due to residual mag-
netisation ; there is a retardation or lag of the magnetisation in respect of
the magnetising force to which Prof. Ewing has applied the term Aysteresis.
The hysteresis is greater the wider the difference in the two curves. Hys-
teresis 1s diminished if the body is submitted to vibrations during the pro-
cess of magnetisation. If the circuit be broken while a horseshoe electro-
magnet Is supporting even a heavy weight attached to the keeper, it frequently
happens that the keeper does not at once become detached ; if now the
magnet is gently tapped so as to set the molecules in vibration, the keeper
immediately drops, and is no longer attracted when again placed in contact.
To destroy residual magnetism, as, for instance, in a watch spring which
has accidentally become magnetised by having been under the influence of
a strong magnetic field, near a powerful dynamo for example, it should be
submitted to a series of magnetising forces in alternate directions gradually
decreasing to zero. A bar may also be rendered neutral by being heated to
redness and cooled in a horizontal position at right angles to the magnetic
meridian.
When a soft iron bar is submitted to magnetisations and demagnetisations
in rapid succession, its temperature rises. This represents the work of mag-
netisation converted into heat. If in the above curve the magnetising force
and the magnetisation are expressed in C.G.S. units, the area AB A’C repre-
sents the value in ergs of the work so transformed per unit of volume of the
iron. The loss may attain 15,000 ergs per cubic centimetre of soft iron for’
each complete cycle. One erg represents 4°17 x 10“ calories (456), and since
the density of iron is 7°8, and its specific heat o:11 (467), the calorific capacity
of a cubic centimetre is 0'°858. So that, taking the above number, we have
0°0004° as the rise in temperature for each complete cycle.
If a bar magnet is suspended by a spring so that its axis is in the prolon-
gation of that of the spiral, and the current is now passed, it will be seen
that the magnet will be attracted or repelled according as the direction of the
current is the same as that of the current in the spiral or not. In the case
of attraction, ana if the magnet be not too long and be sufficiently free
to move, it will be drawn within the spiral. The force with which the magnet
is drawn in is nearly proportional to the strength of the current and to the
number of turns of the wire.
-907] Vibratory Motion and Sounds produced by Currents git
Magnetism is not uniformly distributed in the section of electromagnets ;
the external layer exhibits a stronger magnetisation than the inner ones,
and with feeble forces there is only a magnetic excitation in the outer layer.
The magnetism in solid and in hollow cylinders of the same diameters is
the same, provided in the latter case there is sufficient thickness of iron for
the development of the magnetisation. With currents below a certain
strength, wide tubes of sheet-iron are far more powerfully magnetised than
solid rods of the same length and weight ; but with more powerful currents
the magnetism of the latter preponderates.
906. Vibratory motion and sounds produced by currents.—When a
rod of soft iron is magnetised by a strong electric current, it gives a very
distinct sound, which, however, is only produced at the moment of closing
or opening the circuit. This phenomenon is due to a vibratory motion
of the molecules of iron in consequence of a rapid succession of magneti-
sations and demagnetisations.
When the circuit is broken and closed at very eNore intervals, De la Rive
observed that, whatever be the shape or magnitude of the iron bars, two
sounds may always be distinguished ; one, which is musical, corresponds to
that which the rod would give by vibrating transversely ; the other, which
consists of a series of harsh sounds, corresponding to the interruptions of
the current, was compared by De la Rive to the noise of rain falling on a
metal roof. The most marked sound is that obtained by stretching, on a
sounding-board, pieces of soft iron wire, well annealed, from I to 2 mm. in
diameter and Ito 2 yardslong. These wires, being placed in the axis of one
or more bobbins traversed by powerful currents, send forth a number of
sounds, which produce a surprising effect, and much resemble that of a
number of church bells heard at a distance. Rods of zinc, copper, or brass
give no note even with strong currents.
Wertheim also obtained the same sounds by passing a discontinuous.
>
w
Fig. 894
current through the wires themselves. The musical sound is then stronger
and more sonorous in general than in the previous experiment. The hy-
pothesis of a molecular movement in the iron wires at the moment of their
magnetisation and demagnetisation is confirmed by the researches of
Wertheim, who found that their elasticity is then diminished.
907. Reis’s telephone.—The essential features of this instrument (fig.
gI2 Dynamical Electricity [907
894) are a sort of box, B, one side of which is closed by a membrane C,
while there is a mouthpiece, A, in another side. On the membrane is a piece
of thin metal-foil C, which is connected with a wire leading to one pole of the
battery G, the other pole of which is put to earth. Just above the foil, and
almost touching it, is a metal point D, which is connected by the line wire
(908) with one end of a coil of insulated wire surrounding an iron rod, the
other end of the wire being put to earth.
When the mouthpiece is spoken or sung into, the sounds set the mem-
brane in vibration ; this coming into contact with the point D causes a rapid
succession of currents to pass into the line and through the electromagnet
in which the corresponding sounds are produced.
ELECTRIC TELEGRAPH
908. Electric telegraphs.—These are apparatus by which signals can be
transmitted to considerable distances by means of voltaic currents propa-
gated in metallic wires. Towards the end of the last century, and at the
beginning of the present, many philosophers proposed to correspond at a
distance by means of the effects produced by electrical machines when pro-
pagated in insulated conducting wires. In 1811, Semmering invented a
telegraph, in which he used the decomposition of water for giving signals.
In 1820, at a time when the electromagnet was unknown, Ampére proposed
to correspond by means of magnetic needles, above which a current was sent,
as many wires and needles being used as letters were required. In 1834,
Gauss and Weber constructed an electromagnetic telegraph, in which a voltaic
current transmitted by a wire acted on a magnetised bar, the oscillations of
which under its influence were observed by a telescope. They succeeded in
thus sending signals from the Observatory to the Physical Cabinet in Got-
tingen, a distance of a mile and a quarter,
and to en belongs the honour of having
first demonstrated experimentally the
possibility of electrical communication
at a considerable distance. In 1837,
Steinheil in Munich, and Wheatstone in
London, constructed telegraphs in which
several wires each acted on a single
needle; the current, in) the first (case
being produced by an: electromagnetic
machine, and in the second by a constant
battery.
Every electric telegraph consists
essentially of three parts: I, a cévcuit consisting of a metallic connection
between two places, and an electromotor for producing the current; 2, a
transmitter for sending the signals from the one station ; and, 3, an z#-
dicator for receiving them at the other station. The manner in which these
objects, more especially the last two, are effected can be greatly varied, and
we shall limit ourselves to a description of the three principal methods.
On the larger circuits dynamos or accumulators or combinations of the
two are used ; on smaller ones where there is constant work some form of
a :
DD
~909] Electric Telegraph 913
Daniell’s battery is used, and for other circuits Leclanché’s cell is coming
into more extended use. In France, Daniell’s battery i used for telegraphic
purposes.
The connection between two stations is made by means of galvanised i iron
wire suspended by porcelain supports (fig. 895), which insulate and protect
them against the rain, either on posts or against the sides of buildings. In
England and other moist climates special attention is required to be aid to
the perfection of the insulation. In towns, wires covered with gutta-percha
are placed in tubes laid in the ground. Submarine cables, where great
strength is required combined with lightness and high conducting power,
are formed on the general type of one of the Atlantic cables, a longitudinal
view of which is given in fig. 896, while fig. 897 represents a cross section.
Fig. 896
In the centre is the core, which is the conductor ; it consists of seven copper
wires, each I mm. in diameter, twisted in a spiral strand and covered with
' several layers of gutta-percha, separated from each other by a coating of Chat-
terton’s compound—a mixture of tar, resin, and gutta-percha. This forms
the zzsw/ator proper, and it should have great resistance to the passage of
electricity, combined with low specific inductive capacity (769). Round the
insulator is a coating of hemp, and on the outside is wound spirally a pro-
tecting sheath of steel wire, spun round with hemp.
At the station which sends the despatch, the line is connected with the
positive pole of a battery, the current passes by the line to the other station,
and if there were a second return line, it would traverse it in the opposite
direction to return to the negative pole. In 1837, Steinheil made the very
important discovery that the earth might be used for the return conductor,
thereby saving the expense of the second line. For this purpose the end of
the conductor at the one station, and the negative pole of the battery at the
other, are connected with large copper plates, which are sunk to some depth
in the ground. The action is then the same as if the earth acted as a
return wire. The earth is, indeed, far superior to a return wire; for the
added resistance of such a wire would be considerable, whereas the resist-
ance of the earth beyond a short distance is absolutely zz7. The earth really
dissipates the electricity, and does not actually return the same current to
the battery.
909. Wheatstone and Cooke’s single-needle telegraph. —Phis' . con-
sists essentially of a vertical multipher (842) with an astatic needle, the
arrangement of which is seen in fig. 899, while fig. 898 gives a front view
of the case in which the apparatus is placed. A (fig. 899) is the bobbin,
consisting of about 4oo feet of fine copper wire, wound in a frame in two
3.N
914 Dynamical Electricity [909—
connected coils. Instead of an astatic needle, Mr. Walter has found it ad-
vantageous to use a single needle formed of several pieces of very thin steel
strongly magnetised ; it works with the bobbin, and a light index joined to:
it by a horizontal axis indicates the motion of the needle on the dial.
—
SSS ——
SS
SaS5ssse
SSE
The signs are made by transmitting the current in different directions
through the multiplier, by which the needle is deflected either to the nght
or left, according to the will of the operator. The instrument by which this
is effected is a commutator or key, G, fig. goo ; its action is shown in fig. 9o1,
which also shows on a large scale how two stations are connected. It con-
sists of a cylinder of boxwood with a handle, which projects in front of
the case (fig. 898). On its circumference parallel to the axis are seven brass
strips (fig. 900), the spaces between which are insulated by ivory; these
strips are connected at the end by metallic wires, also insulated from each
other, in the following manner: @ with 6 and ¢, fwith d,andewithg. Four
springs press against the cylinder ; 2 and y are connected with the poles of
the battery, #z, with the earth plate, and z with one end of the multiplier, N.
When not at work the cylinder and the handle are in a vertical position,
as seen on the left of the diagram. The circuit is thus ofem, for the pole
springs, x and y, are not connected with the metal of the commutator. But
-910] Wheatstone and Cooke's Single-Needle Telegraph 915
if, as in the figure on the right, the key is turned to the right, the battery
is brought into the circuit, and the current passes in the following direc-
SN
tion: + pole, 2’a0’7’M’g’N’, line gf/MuacmE#, earth p’E’m’e’g’y’, — pole.
The coils N and N’ are so arranged that by the action of the current the
motion of the needle corresponds to the motion of the handle. By turn-
ing the handle to the left the current would have the following direction :
+ pole «’dfm’E’p’, earth PEmcabnMg, p~’9’M’n’'b’a’y’, —pole, and thus the
needle would be deflected in the opposite direction.
The signs are given by differently combined deflections of the needle
as represented in the alphabet on the dial (fig. 898). \. denotes a deflection
of the upper end of the needle to the left, and “ a deflection to the right ; I,
for instance, is indicated by two deflections to the left, and M by two to the
right. D is expressed by right-left-left, and C by right-left-right-left, &c.
These signs are somewhat complicated, and require great practice :
usually not more than 12 to 20 words can be sent ina minute. The single-
needle telegraph was formerly sometimes replaced by the double-needle one,
which is constructed on the same principle, but there are-two needles and
two wires instead of one,
gio. Morse’s telegraph.—The telegraph just described leaves no trace
of the despatches sent, and if any errors have been made in copying the
signals there is no means of remedying them. These objections are met in
the case of the writing telegraphs, in which the signs themselves are printed
on a strip of paper at the time at which they are transmitted.
Of the numerous printing and writing telegraphs which have been devised,
that of Morse, first brought into use in North America, is best known. It
3N 2
Q1Goen yee a Dynamical Electricity “) «[ones
has been almost universally adopted on the Continent. In this instrument
there are three distinct parts: the vecezver, the sender, and the relay ; figs.
QO1, 902, 903, and 904 represent these apparatus.
Recetver.—We will first describe the receiver (figs. 901 and go2), leaving
out of sight for the moment the accessory pieces, G and T, placed on the
right of the figure. The current which enters the indicator by the wire, C,
passés into an electromagnet, E, which when the circuit is closed attracts an
armature of soft iron, A, fixed at the end of a horizontal lever movable about
Fig. gor
an axis, x; when the circuit is open the lever is raised by a spring. By
means of two screws, # and 7, the amplitude of the oscillations is regulated.
At the other end of the lever there is a pencil which writes the signals.
For this purpose a long band of strong paper, 4/, rolled round a drum, R,
passes between two copper rollers with rough surfaces, w and ¢, and turning
in contrary directions. Drawn in the direction of the arrow, the band of
paper becomes rolled on a second drum, Q, which is turned by hand. A
clockwork motion placed in the box, BD, works the rollers, between which
the band of paper passes.
The paper being thus set in motion, whenever the electromagnet works,
the point strikes the paper, and, without perforating it, produces an inden-
tation the shape of which depends on the time during which the point is in
contact with the paper. If it only strikes it instantaneously, it makes a dof
(-).or short stroke ; but if the contact has any duration, a dash (—) of corre-
sponding length is produced. Hence, by varying the length of contact of
the transmitting key at one station, the operator produces a combination of
dots and dashes at another station, and it is only necessary to give a definite
meaning to these combinations.
~-910] Morse’s Telegraph QI7
In order to make an indentation a considerable pressure is required, which
necessitates the employment of a strong current, and the newer instruments _
(fig. go2) are
based on the
use of z7k-
writers. The
paper band
passes close to,
but not touch-
ing, a metal
disc with a fine
edge, c, which
turns against
a small z7zg-
voller, a, all pee
being rotated by He same mechanism. When the end A is attracted, the
bent plate at the other end presses the paper against the disc, which is
inked by contact with the ink-roller, and thus produces a mark on the
SINGLE
NEEDLE.
SINGLE |
eat Oe ee
NEEDLE. |
PRINTING.
PRINTING.
paper, which is either short or long according to the duration of the con-
tact. The signs are thus more legible, and are produced by far weaker
currents.
The same telegraphic alphabet is now universally used wherever tele-
graphic communication exists ; and the signals for the single-needle instru-
ment (fig. 898) as well as those used for printing have been Fovarliaed so that
they now correspond to each other. Thus a Beat of the top of the needle to
g18 | Dynamical Electricety [910-
the left \_ is equivalent to a dot: and a beat to the right / toa dash. The
figure on the preceding page gives the alphabet.
The flag signals used in military operations are similarly used. A swing
of the flag from its upright vertical position to the right or left has the same
bcos as the corresponding motion of the top end of the needle. So, too,
long or short obscurations of the limelight used in signalling by night, or
of the heliograph (535), correspond to dashes and dots.
Sender or key. This consists of a small mahogany base, which acts as
support for a metal lever aé (fig. 903), movable about a horizontal axis which
passes through its middle. The end @ of this lever is always pressed
upwards by a spring beneath, so that it is only by pressing with the finger
on the key B that the lever strikes the button x Round the base are
three binding screws, one connected with the wire P, which comes from the
positive pole of the battery; the second connected with L, the line wire ;
and the third with the wire
A, which passes to the
indicator ; for of course
two places in communica-
tion are each provided
with an indicator and
communicator.
These details known,
there are two cases to be
considered. 1. The key
arranged so as to receive
a message from a distant
station ; the end @ is then down, as represented in the figure, so that the
current which arrives by the line wire L, and ascends in the metal piece
m, descends in the wire a, which leads it to the indicator of the station at
which the apparatus is placed. 2. A message is to be transmitted ; in this
case the key B is pressed so that the lever comes in contact with the button x.
The current of the local battery which comes by the wire P, ascending then
in the lever, descends by # and joins the wire L, which conducts it to the
station to which the despatch is addressed. According to the length of time
during which B is pressed, a dot or dash 1s produced in the receiver to which
the current proceeds. '
Relay. In describing the receiver we have assumed that the current of
the line coming by the wire C (fig. 902) entered directly into the electro-
magnet, and worked the armature A, producing a despatch ; but when the
circuit consists of many miles of wire, the current may be too weak to act
upon the electromagnet with sufficient force to print a despatch. Hence it
is necessary to have recourse to a ve/ay—that is, to an auxiliary electromagnet
which is still traversed by the current of the line, but which serves to intro-
duce into the communicator the current of a Jocal battery of four or five
elements placed at the station, and which is only used to print the signals
transmitted by the wire.
For this purpose the current entering the relay by the binding screw, L
(fig. 905), passes into an electromagnet, E, whence it passes into the earth
by the binding screw T. Now, each time that the current of the line
$10] Working of Morse’s Telegraph 919
passes into the relay, the electromagnet attracts an armature, A, fixed at
the bottom of a vertical lever, 4, which oscillates about a horizontal axis.
At each oscillation the top of the lever # strikes against a button 2,
and at this moment the current of the local battery, which enters by the
binding screw ¢, ascends the column wv, passes into the lever ~, descends
by the rod 0, which transmits it to the screw Z: thence it enters the
electromagnet of the indicator, and returns to the local battery from which
it started. Then, when the circuit of the line is open, the electromagnet of
the relay does not act, and the lever Z, drawn by a spring 7, leaves the button
A”, as shown in the drawing, and the local current no longer passes. Thus
Fig. 904
the relay transmits to the indicator exactly the same phases of passage and
intermittence as those effected by the manipulator in the station which sends
the despatch.
With a general battery of 25 Daniell’s elements the current is usually
strong enough at upwards of 90 miles from its starting-point to work a relay.
For a longer distance a new current must be taken, as will be seen in the
paragraph on the change of current (vzde zz/fra).
Working of the three apparatus. The three principal pieces of Morse’s
apparatus being thus known, the following is the actual path of the current.
The current of the line coming by the wire L (fig. 902) passes at first to
the piece T intended to serve as lightning-conductor, when, from the in-
fluence of atmospheric electricity in time of storm, the conducting wires
become so highly charged with electricity as to give dangerous sparks.
This apparatus consists of two copper discs, d@ and f, provided with teeth on
the sides opposite each other, but not touching. The disc d is connected
with the earth by a metal plate at the back of the stand which supports this
lightning-conductor, while the disc fis in the circuit. The current coming
by the line L enters the hghtning-conductor by the binding screw fixed at
the lower part of the stand on the left ; then rises to a commutator, 7, which
conducts it to a button, c, whence it reaches the disc f by a metal plate at
the back of the stand ; in case a lightning discharge should pass along the
wire, it would now act inductively on the disc d, and emerge by the points
without danger to those about the apparatus. Moreover, from the disc f, the
920 Dynamical Electricity [910-
current passes into a very fine wire insulated ona tube, ¢. As the wire is
melted when the discharge is too strong, it acts as a safety catch (851) ; the
electricity does not pass into the apparatus, which still further removes
any: danger.
Lastly, the current proceeds from the foot of the support to a screw on
the right, which conducts it to a small galvanometer, G, serving to indicate
by the deflection of the-needle whether the current passes. From this
galvanometer the current passes to a key (fig. 903), which it enters at L,
emerging at A to go to the relay (fig. 904). Entering this at L, it works
the electromagnet, and establishes the communication necessary for the
passage of the current of the local battery, as has been said in speaking of
the relay.
Change of current. To complete this description of Morse’s apparatus, it
must be observed that in general the current which arrives at L, after having
traversed several miles, has not sufficient force to register the despatch, or
to proceed to a new distant point. Hence in each telegraphic station a
new current must be taken, that of the Jostal battery, which consists of 20 to
30 Daniell’s elements, and is not identical with the local battery.
This new current enters at P (fig. 901), reaches a binding screw which
conducts it to the column H, and thence only proceeds further when the
armature A sinks. A small contact placed under the lever then touches the
button z ; the current proceeds from the column H to the metallic mass
BD, whence by a binding screw and a wire, not represented in the figure, it
reaches, lastly, the wire of the line, which sends it to the following station,
and so on from one point to another.
911. Cowper’s writing telegraph.—This remarkable invention is a true
telegraph, in that it faithfully reproduces at a distance an exact facsimile of
a person’s handwriting. The following gives a general idea of the principle
of the instrument.
Two line wires are required, which are severally connected at the re-
ceiving station with two galvanometers, whose coils are at right angles to
each other. At the sending station is a vertical pencil with two light rods,
jointed to it at right angles to each other. One of these contact rods guides
a contact piece which is connected by a wire with one pole of a battery, the
other pole of which is to earth. This contact piece slides over the edges of
a series of contact plates insulated from each other, between each of which
and the next a special resistance is interposed, and the last of the contact
plates is connected with one line wire. The other contact piece slides over
a second series of such plates connected with the other line wire.
Let us consider one contact piece alone ; as it moves over the contact
‘plates in one direction or the other, it brings less or more resistance into the
circuit, and thereby alters the strength of the current. The effect of this is
that the needle of the corresponding galvanometer is less or more deflected.
Now the end of this needle is connected by a light thread with a receiving
pen, which is a capillary tube full of ink. An oscillation of the needle would
produce an up and down motion of the pen, and if simultaneously a band of
paper passed under the pen, being moved regularly by clockwork, there
would be produced on it a series of up and down strokes. A corresponding
effect would be produced by the action of the needle of the other galvano-
~912]} Induction in Telegraph Cables 921
meter, except that its strokes would be backwards and forwards instead of
up and down.
Now the action of the writing pen is that it varies simultaneously the
strengths of the two currents, and they produce a motion of the receiving
pen which is compounded of the two movements described above, and
which is an exact reproduction, on a smaller scale, of the original motion.
The following line is a facsimile.
___ Rowil—socety—Prurkinyton owe —
x Fig. 905
Both the paper written in pencil at the sending station and that written
in ink at the receiving station move along as the writing proceeds, and the
messages have only to be cut off from time to time.
Experiments made with this instrument show that it will write through
resistances equal to 36 miles of telegraph wire.
912. Induction in telegraph cables—In the earliest experiments on the
use of insulated subterranean wires for telegraphic communication it was
found that difficulties occurred in their use which were not experienced with
overhead wires. This did not arise from defective insulation, for the:better
the insulation the greater the difficulty. It was suspected by Siemens and
others that the retardation was due to statical induction, taking place be-
tween the inner wire through the insulator and the external moisture ; and
Faraday proved that this was the case by the following experiments among
others. A length of about 100 miles of gutta-percha-covered copper wire
was immersed in water, the ends being led into the observing-room.
When the pole of a battery containing a large number of cells was momen-
tarily connected with one end of the wire, the other end being insulated, and
a person simultaneously touched the wire and the earth contact, he obtained
a violent shock.
When the wire, after being in momentary contact with the battery, was
placed in connection with a galvanometer, a considerable deflection was
observed ; there was a feebler one 3 or 4 minutes after, and even as long as
20 or 30 minutes afterwards.
When the insulated galvanometer was permanently connected with one
end of the wire, and then the free end of the galvanometer wire joined to the
pole of the battery, a rush of electricity through the galvanometer into the
wire was perceived. The deflection speedily diminished and the needle
ultimately came to rest at zero. When the galvanometer was detached
from the battery and put to earth, the electricity flowed as rapidly out of the
wire, and the needle was momentarily deflected in the opposite direction.
These phenomena are not difficult to explain. The wire with its thin
insulating coating of gutta-percha becomes statically charged with electricity
from the battery like a Leyden jar. The coating of gutta-percha through
which the inductive action takes place is only 4, of an inch in thickness, and
the extent of the coatings (copper wire on the one side, and water on the
other side of the dielectric gutta-percha) is very great. The surface of the
copper wire amountsso 8,300 square feet and that of the outside coating is
four times as much. The potential can only be as great as that of the
922 Dynamical Electricity — [912-
battery, but from the enormous surface the capacity, and therefore the
quantity (804), is very great. Thus the wires, after being detached from the
battery, showed all the actions of a powerful electric battery.. These effects
take place, but to a less extent, with wires in air; the external coating is
here the earth, which is so distant that induction and charge are very small,
more especially i in the long lines.
Hence the difficulty in submarine telegraphy. The electricity which
enters the insulating wire must first be used in charging the large Leyden
jar which it constitutes, and only after this has happened can the current
reach the distant end of the circuit.
The current begins later at the distant
end, and ceases later. The electricity
is not projected like the bullet from
a gun, but rather hke a quantity of
water flowing from a large reservoir
into a canal in connection with large
“basins which it has to fill as well as it-
self. If the electrical currents follow
too rapidly, an uninterrupted current
will appear at the other end, which in-
dicates small differences in strength,
but not with sufficient clearness differ-
ences in duration or direction. Hence
in submarine wires the signals must be
slower than in air wires to obtain clear
indications. Ther retardation €eia
directly as the length and the self-
Fig. 906 induction (930) of the line. Bythe use
of alternating currents sent bya special
form of key—that is, of currents which are alternately positive and negative
(933)—these disturbing influences may be materially lessened, and communi-
cation be accelerated and made more certain, but they can never be entirely
obviated.
In the Atlantic Cable, instruments on the principle of Thomson’s reflect-
ing galvanometer (844) are used for the reception of signals ; the motions of
the spot of light to the right and left forming the basis of the alphabet.
913. Syphon recorder.—Lord Kelvin invented an extremely ingenious
instrument called the syAhon recorder, by which the very feeble signals
transmitted through long lengths of submarine cable are observed and also
recorded.
A light rectangular coil of iron s (fig. 906), connected with the line wire
by the screws # and g, hangs by a bifilar suspension between the two poles
of a powerful electromagnet AB, so that its plane is parallel to the lines of
force between the poles. The space inside the coil is occupied by a mass of
soft iron f, by which the strength of the fluid is greatly increased. Whena
current is passed this coil tends to place itself perpendicular to the lines of
force, and is deflected either to the right or the left according to the direction
of the current ; its movements are almost dead-beat (843), as the damping is
considerable.
—914] Duplex Telegraphy 923
A very light capillary tube ¢ dips with its short end in a reservoir of
ink, while the other end is in front of a paper ribbon which is moved along
at a uniform rate like the ribbon in a Morse’s recorder. In order to get
rid of friction against the paper, this ink is electrified, and spurts out in a
continuous series of fine drops against the paper, marking on it a straight line
so long as no current passes in the coil. The syphon is, however, connected
by a system of silk threads with the coil, and according as this is deflected
to the right or the left the end of the syphon is deflected too, and traces a
wavy line (fig. 907) on the paper, which represents deflections right or left
of the central line, that are, in short, the Morse signals (910).
Ney fee io aa YU yp
a b Cc a € | MWe h z 7 k Z Mm
Sk eae hem oct all Foow? oat PY cen 8 Vega co Phe
0 2p g x Ss t ut uv zu ie y z
Fig. 907
The electrification of the ink is effected bya small electrostatic induction
machine ; this is worked by clockwork, which at the same time pays out the
paper ribbon.
914. Duplex telegraphy.—By this is meant a system of telegraphy by
which messages may be simultaneously sent in opposite directions on one
and the same wire, whereby the working capacity of a line is practically
doubled.
Several plans have been devised for accomplishing this very important
improvement ; no more can here be attempted than to give a general account
of the principle of the method in one or two cases.
Let m (fig. 908) represent the electromagnet of a Morse’s instrument
which is wound round with two equal coils in opposite directions ; these coils
are represented by the full and dotted lines, and one of them, which may be
called the “ve cozl, is joined to the line LL’, which connects the two stations.
The other coil, that represented by the dotted line, which may be called the
equating cotl, is in connection with the earth at E by means of an adjustable
resistance, or artificial line, R. By this means the resistance of the branch
aRE may be made equal to that of the branch aLL’a’. The battery 6 has
one pole to earth at E, and the other pole, by means of a Morse key, c, can
be connected at a, where the two oppositely wound coils bifurcate. The
back contact of the key is also connected with earth.
The station at B is arranged in a similar manner, as is represented by
corresponding dashed letters.
Now when B depresses his key and sends a current into the line, inasmuch
as the electromagnet of his instrument is wound with equal coils in opposite
directions, the armature is not attracted, for the core is not magnetised be-
cause the currents in the two coils counteract one another. Thus, although
a current passes from ‘B, there is no indication of it in his own instrument—
a condition essential in all systems of duplex telegraphy.
924 Dynamical Electricety [914-
But with regard to the effect on A, there are two cases, according as he
is or is not sending a message at the same time. If A’s key 1s not down, .
then the current
will circulate
round the core
of the electro-
magnet and will
reach the earth
by the ‘path
LacE ; the core
will therefore
become magnet-
ised, the arma-
ture attracted,
and asignal pro-
duced in the or-
dinary way.
Ea If, however, —
at the moment
at which B has his key down, A also depresses his, then it will be seen that,
as the batteries 3’ are exactly alike, their electromotive forces neutralise
one another, and no current passes in the line aLL’a’: it is, as it were,
blocked. But though no current passes in the line coil, a current does pass
at each station to earth, through the equating coil, which, being no longer
counterbalanced by any opposite current in the line coil, magnetises the
core of the electromagnet, which thus attracts the armature and produces a
signal.
We have here supposed that A and B both send, for instance, the same
currents to line: the final effect is not different if they send opposite currents
at the same time. For then, as they neutralise each other in the line LL’,
the effect is the same:as if the resistance of the line were diminished. More
electricity flows to line from each station through the line coil being no longer
balanced by the equating coil ; the current of the line coil preponderates and
then works the electromagnet.
Hence, in both these cases, each station, so to speak, produces the signal
which the other one wishes to send.
Another method is based on the principle of Wheatstone’s bridge (986).
At each station is a battery P (fig. 909), one pole of which is to earth while
the other is connected with the key M. The wire from M bifurcates at A
into the two branches AB and AC, between B and C is connected the galvano-
meter or the receiving instrument. The branch AB goes to line and AC
to earth. There are exactly corresponding parts at the other station. Now,
from the principle of the bridge, the resistances AB and AC may be adjusted
in such a manner that the potentials at the points B and C are equal when
the key is depressed and the current sent ; accordingly, no current passes
in the bridge, and the galvanometer is at rest ; but the current from A passing
to line bifurcates at B’, traversing the galvanometer and going to earth;
hence a signal is received at that station.
~
Sa ee er,
-— sw eis
~
aot
RERNSS WS an Ais SS SSS Ko. ee
Fig. 908
~917] Bain’s Electrochemical Telegraph 925
Other methods of duplex telegraphy are based on the principle of leakage ;
but for these as well as for quadruplex telegraphy, special manuals must be
consulted. B Re
eae eee
915. Earth currents.—In long tele-
graph circuits more or less powerful cur-
rents are produced, even when the battery
is not at work. This arises from a differ-
ence of potential being established in the
earth at the two places between which the
communication is established. These cur-
rents are sometimes in one direction and
sometimes in another, and are at times
SO powesmlanturrepuianvas: qiite to in- | ee
terfere with the working of the lines. “8ser* Senay
Lines running NE and SW are most ee
frequently affected ; lines running NW and SE are less so, and the currents
are far weaker. Their strength often amounts to as much as 4o millamperes
(1000), which isa stronger current than is required for working ordinary tele-
graph instruments.
These currents do not seem to be due to atmospheric electricity, for they
cease if a wire is disconnected at one of its ends, and they appear in under-
ground wires.
According to Wild, they are the prime cause of magnetic storms, but not
of the periodical variations in the magnetic elements.
916. Bain’s electrochemical telegraph.—If a strip of paper is soaked
in a solution of potassium ferrocyanide and is placed on a metal surface
connected with the negative pole of a battery, on touching the paper with a
steel pointer-connected with the positive pole, a blue mark due to the forma-
tion of some Prussian blue will be formed about the iron, so long as the current
passes. The first telegraph based on this principle was invented by Bain.
The alphabet is the same as: Morse’s, but the despatch is first composed at
the departure station on a long strip of ordinary paper. The paper is per-
forated successively by small round and elongated holes, which correspond
respectively to the dots and marks. The strip so prepared is interposed
between a small metal wheel and a metal spring, both forming part of the
circuit. The wheel, in turning, carries with it the paper strip, all parts of
which pass successively between the wheel and the plate. If the strip were
not perforated, it would, not being a conductor, constantly offer a resistance
to the passage of acurrent ; but, in consequence of the holes, every time one
of them passes, there is contact between the wheel and the plate. Thus the
current works the relay of the station to which it is sent, and traces in blue,
on a paper disc, impregnated with potassium ferrocyanide, the same series
of points and marks as those on the perforated paper.
917. The sounder.—The sound produced when the armature of the electro-
magnet in a Morse’s instrument is attracted by the passage of the current
is so distinct and clear that many telegraph operators have been in the
habit of reading the messages by the sounds thus produced, and at most of
checking their reading. by comparison with the signs produced on the
paper.
926 Dynamical Electricity [917—
Based on this fact a form of instrument invented in America has come
into use for the purpose of reading by sound. The sounder, as it is called,
is essentially a small electromagnet on an ebonite base, resembling the relay
in fig. 905. The armature is attached to one end of a lever, and is kept at
a certain distance from the electromagnet by a spring. When the current
passes, the armature is attracted against the electromagnet with a sharp
click, and when the current ceases it is withdrawn by the spring. Hence the
interval between the sounds is of longer or shorter duration according to the
will of the sender, and thus in effect a series of short or long intervals which
represent short and long sounds can be produced which correspond to the
dots and dashes of the Morse alphabet. Such instruments are simple, easily
adjusted, and portable, not occupying more space than an ordinary field-glass.
They are coming into extended use, especially for military telegraph work.
918. Electric alarum.—One form of these instruments is represented in
fig. gio. On a wooden board arranged vertically is fixed an electromagnet,
E ; the line wire is connected with the bind-
ing screw, #z, with which is also connected
one end of the wire of the electromagnet ;
the other end is connected with a spring, ¢, to
- which is attached the armature, @; this again
is pressed against by a spring, C, which in
turn is connected with the binding screw 2,
from which the wire leads to earth.
Whenever the current passes, which is
effected by a small contact-maker called a
push, the armature a is attracted, carrying
with it a hammer, P, which strikes against
the bell Tand makes it sound. The moment
this takes place, contact is broken between
the armature @ and the spring C, and the
current being stopped the electromagnet
does not act ; the spring c, however, in virtue
of its elasticity, brings the armature in con-
tact with the spring C, the current again
passes, and so on as long as the current con-
tinues to pass.
g19. Electrical clocks.—Electrical clocks are clockwork machines, in
which an electromagnet is both the motor and the regulator, by means of
an electric current regularly interrupted, in a manner resembling that de-
scribed in the preceding paragraph. Fig. 911 represents the face of such a
clock, and fig. 912 the mechanism which works the needles.
An electromagnet, B, attracts an armature of soft iron, P, movable on a
pivot, a. The armature P transmits its oscillating motion to a lever, s, which
by means of a ratchet, 7, turns the wheel A. This, by the pinion, D, turns
the wheel C, which by a series of wheels and pinions moves the hands. The
small one marks the hours, the large one the minutes ; but as the latter does
not move regularly, but by sudden starts from second to second, it follows.
that it may also be used to indicate the seconds.
Fig. g1o
—920}] | Electromagnetic Motors » O27
It is obvious that the regularity of the motion of the hands depends on
the regularity of the oscillations of the piece P. For this purpose, the oscil-
lations of the current, before passing into the electromagnet B, are regulated
by a standard clock, which itself has been previously regulated by a seconds.
iy | ih iH | !
ieee
i |
iy . i s 1)
4y5 of a degree
between the two resistances. It has been used by the inventor to measure
the distribution of heat in the solar spectrum. By its means he has been
able to map the dark heat of the spectrum, and to extend it far beyond the
limits which were previously known. It has also been used in the investiga-
tion of electrical vibrations (1002).
996. Divided or branch circuits.—In fig. 1021 the current from a Bunsen’s
cell passes from the point g to the point , by two paths, the resistances of
which are # and x. By applying Ohm’s law we see at once that the currents
in these two branches (¢ in gf and c’ in gx) are inversely proportional to
the resistances and x. For, the difference of potential between g and x
must be independent of the path by which the electricity travels from the one
to the other. Hence if the PD =e, by Ohm’s law ¢ =c x p=c' x x, and
therefore:C|c= 9:
Fig. 1025 Fig. 1026
—998] Use of Shunts 1035
Let C be the strength of the current in the undivided part of the circuit,
there Cacre Eyl ad LE, Epre _ vp prr
zat ce
AisoeG=c+<¢ Tei 2 = é (3 +=): If # and x are removed and replaced
by a single wire of resistance R, such that the value of C, and therefore of e,
SSeS
qu
Fig. 1027
. I
is not altered, we must have C= : , therefore ne bed slind generally if two
R ee 2 et
points are connected by a number of conductors whose resistances are ~, 7,
r., &c., the resistances R of all of them taken together, that is the resistance
which might replace them, are such that DL ODM SURRY ase
Ta hs
997. Use of shunts.—The principle of divided or branch circuits has
an important application in shumd¢s, by which any given proportion of even a
powerful current may be transmitted through delicate
galvanometers, and thus their range is greatly extended.-
They consist of a set of resistances usually 4, s4, and
géz, of that of the galvanometer, arranged as represented
in fig. 1028. G and G’ are in connection with the ter-
minals of the galvanometer, and P, P’ with those of the
battery. The gaps, O, A, B, C, can be closed by plugs,
and thus the corresponding resistances introduced. When
they are all open, the entire current would pass through the
galvanometer. By plugging O the currentis short-circuited,
and none of it passes through the galvanometer.
If 2 is the resistance of the galvanometer, s that of
the shunt, C the total current, and ¢ that which passes p
through the galvanometer and produces the deflection, 4
we may deduce from the laws of branch circuits
a+ S
ge=s (C—c) or C et oe Ge Fig. 1028
The expression & oe =m is Called the multiplying power of the shunt ;
it is the value by which the observed current must be multiplied to obtain
the principal current. In the above cases the muitiplying powers are 10,
100, and 1,000 respectively.
998. Blectrieai measuring instruments.—The numerous and important
technical applications of electricity have given rise to the invention of
1036 Dynamical Electricity [998—
a number of instruments for the direct measurement of electrical currents.
‘The amperemeter, or briefly ammeder, for instance, gives at once the strength
of a current in amperes.
As a type of these instruments we may take a recent form of that invented
by Professors Ayrton and Perry; it depends on the principle that when a
portion of an iron core is partly within and partly without a magnetising
coil, it is drawn inwards when a current is passed through the coil. The
essential feature of the apparatus is a coil of insulated wire, in the axis of
which is a spiral attached at one end to an index moving over a graduated
scale. At the other end of the spiral is a brass cap to which is attached a
thin cylinder of sheet iron, which is in fact the core; it encircles the
spiral and projects outside the coil. The spiral itself is formed of a ribbon
of thin phosphorus bronze coiled so as to form a very
narrow cylinder. This construction gives it the property
that unlike ordinary spirals, when its length increases
the free end rotates through a considerable distance.
Accordingly, when the current passes through the coil,
the iron tube is drawn within the spiral to an extent vary-
ing with the strength of the current ; this thereby elongates
the spiral to which it is attached, and the index attached
to the latter moves over the scale, finally taking up a
position which depends on the strength of the current.
Such instruments are graduated empirically and within
any desired range by observing the deflection caused by
passing through them currents of known strength.
The voltmeter, which is not to be confounded with
the voltameter (868), measures the difference of potential
between any two points of a circuit. It consists essen-
tially of a coil such as the above, but with a great length
of long fine wire, offering, therefore, between two points in
a circuit a great resistance. This can be inserted as a
shunt without appreciably altering the resistance of the
circuit. It is empirically graduated like the ammeter.
Cardew’s voltmeter depends on the heating effect pro-
duced when a current traverses a wire, and consists essen-
tially of a long fine platinum wire, stretched by a spring or a weight to which
is attached a multiplying motion and an index. This wire, being introduced
between the points of the circuit to be measured, becomes heated to an extent
proportional to the square of the difference of potentials, and the motion of
the index is a measure of this heating.
The principle of the electrodynamometer is that of measuring attraction
and the repulsion between parallel currents, one of them being fixed and the
other movable. Fig. 1029 represents the main features of a form devised by
Siemens for measuring the strength of the powerful currents used in electric
lighting ; w is a coil of stout copper wire, and w’ a single wire ; m# are
mercury cups, and £% binding screws, by which connection is made with the
main circuit LL.
The wire w’ is surmounted by a stout spiral spring, which is connected
at one end with this wire, and at the other with a screw, s; the latter is pro-
Fig. 1029
~999] Absolute Electrical Units 1037
vided with an index, z, which moves over a graduated scale, S. An index,
22’, is also fixed to the wire w’. At the outset both indexes point to zero ;
when the current passes it will be seen from the direction of the arrows that
it traverses the fixed and movable coils in opposite directions, and the point
z’ is displaced along the scale. By turning the screw s it is brought back to
zero, in doing which the index ¢ is moved through an angle which is a
measure of the torsion of the spiral spring f, and this angle is proportional
to the square of the strength of the current by which the movable coil is
deflected.
This electrodynamometer has by no means the sensitiveness which can
be readily obtained with ordinary galvanometers ; but it has the advantage
that its indications are independent of the external magnetic field, and when
the two coils are traversed by the same current they are also independent of
the direction of the current, and can accordingly be used with advantage in
measuring alternating currents.
An electrodynamometer devised by Giltay on a principle first introduced
by Bellati is remarkable for its great sensitiveness. A bundle of fine iron
wires hangs by a bifilar suspension inside the coil of a multiplier, the plane
of which is at an angle of 45° with the magnetic meridian. The bundle
itself is at an angle of 45° with the plane of the coils, and is thus at right
angles to the magnetic meridian. When alternating currents are passed
through the coil they magnetise the wires with alternate poles, so that
the bundle is always deflected in the same direction. The deflections are
read off by a mirror and scale, and when small are directly proportional
to the square of the current. The apparatus is so sensitive that deflec-
tions of 18 cm. on the scale are produced by the currents of an ordinary
telephone.
999. Absolute electrical units——The great importance of having a
uniform system of measurements of physical magnitudes which should be
universally adopted is at once obvious, and has been more especially felt
in the applications of electricity. The first step in this direction was taken
by the British Association, which adopted the system of absolute units
known as the C.G.S. system, of which mention has already been made
(62, 729), and which this account is intended to supplement.
The essence of an absolute system of physical measurements is that
the various units may be directly expressed in terms of the fundamental
units (62) of length, time, and mass. A system of absolute electrical units
may be based on either the electrostatic the electromagnetic, or again on
the electrodynamic actions. There is no theoretical reason why one should
be preferred to another of these, but in practice only the former two are
used. Of these the electrostatic system is perhaps the simpler, but that
based on electromagnetism is most convenient, and best lends itself to the
practical determination of the most important standards, such as those of
electromotive force and resistance.
Electrostatic Units
We shall distinguish these units by small letters placed in brackets.
Quantity of Electricity. g. Coulomb’s law gives for the repulsive force
Loss Dynamical Electricety [999-
9
~
between two equal quantities g, of electricity at the distance 7, f= a (756),
from which g=/,/f Hence we have for the dimensions of unit quantity of
electricity [g]=Z*#= L2M!T-.
Potential. v. The potential at a point distant / from g,a quantity ‘of
electricity, is the quotient of the quantity by the distance. Hence [v] =7 os
L?M?T}.
Capacity. c. The capacity of a conductor is the quotient of the quantity
of electricity with which it is charged, by the potential which this quantity
produces in it; [<]=% from which [¢]=L. Accordingly the capacity of a
conductor is expressed by a length. Unit capacity is thus that of a body
which is raised by unit quantity to unit potential. An insulated conducting
sphere which has a radius of one centimetre has unit capacity.
Current. t. The strength of a current is the quantity of electricity which
passes in a given time; [‘]=2 =L3M?T*. Therefore unit current is that
which conveys unit quantity of electricity in a second.
Resistance. ry From Ohm’s law (847), the resistance of a conductor is
the quotient of difference of potentials at the two ends of a wire by the
strength of a current. Hence [7] =” —L-'T, which shows that the dimen-
2
sions of resistance are the inverse of a velocity.
Electromagnetic Units
2
‘
“
Quantity of magnetism. From Coulomb’s law /= - , where M equals'a
quantity of magnetism at a point, or strength of magnetic pole, from which
[M]=L? ®M!T-+—that is, the same as that of quantity of electricity on the
electrostatic system. Unit magnetic pole is that which repels an equal pole
at a distance of a centimetre with a force of a dyne.
Magnetic Field. H. Unit magnetic fluid is that field in which unit
quantity magnetism is acted on by unit force. Hence F = HM, from which
he) =e
Current. 1. The unit of electrical current in the electromagnetic system
is that which, traversing unit length of an arc of a circle of unit radius, exerts
unit force on unit pole, or unit magnetism at its centre. Its dimensions are
Pie Mr,
Quantity of electricity. Q. The quantity of electricity conveyed by a con-
ductor is the product of the current by the time that it lasts. Hence unit
quantity is that which passes in a second in a conductor in which unit current
is flowing, [Q]=IT = L3Mé.
Resistance. ®. The resistance of a conductor may be defined by Joule’s
law, W=l?RT. Hence [R]=<—that is, the resistance of a conductor is
expressed by a velocity.
Electromotive force. Difference of potentials [E]. From Ohm’s law,
E=IR=L3MiT~.
1000] Practical Untts 1039
1000. Practical units.—The values of the absolute units in the C.G.S.
system are not convenient for measuring the magnitudes which ordinarily
occur. Thus the absolute unit of resistance is that represented by the
twenty-thousandth part of a millimetre of pure copper wire a millimetre in
diameter. It has therefore been necessary to choose units better suited for
practical uses, and at the International Congress of Elec-
tricians at Paris in 1881 an International Commission was
formed for the purpose 9f deciding on such units and deter-
mining their value. In 1892 a Committee of the Board of
Trade agreed to recommend the following, which are in the
main those originally introduced by the British Association.
The practical unit of resistance is equal to 10° absolute
electromagnetic C.G.S. units of resistance, and 1s called the
Ohm. It has been decided to represent it by a column of
pure mercury of uniform section 106°3 cm. in length at 0° C.,
and with a mass of 14°521 grammes. Copies of this standard
may be made either in mercury (fig. 1030) or in wire (fig. 1029),
and each copy-has the value marked upon it, which is correct for a certain
temperature. A wire of pure copper, a millimetre in diameterand 46°25 metres
in length, has a resistance of one ohm. Siemens’s unit (983) has a resistance
of 0°94339 ohm. The copper conducting wire of an ordinary submarine cable
has a resistance of about 11 ohms per mile.
In order to express multiples and submultiples the prefixes mega and
micro are used, which are respectively a million times as great or as small.
Thus a megohm is 10° ohms—that is, 10 absolute units of resistance. In
like manner a microhm is 10° ohm—that is, 10? = 1,000 such units.
The Volt is the practical unit of electromotive force or of difference of
potentials, and is equal to 10° absolute units. From the difficulty of getting
an element which is perfectly constant, more especially when it is closed, the
standard of E.M.F. is best derived from measurements of resistance and of
strength of current, which are both convenient and very accurate. Com-
pared with the electrostatic unit of potential the volt is very small, being
only 34,5 of such a unit. The Board of Trade Committee takes the Clark
cellstandard of electromotive force as equal to 1°434 volt ; so that
ies electromotive force of Clark cell at 15° C.
1°434
The Amfere is the unit of current, and is the current produced by the
electromotive force of a volt in a circuit having a resistance of an ohm. It
is therefore equal to 10! C.G.S. units. It is equal to the current that can
deposit o‘001118 gramme of silver per second from a neutral solution of silver
nitrate. A mzllampere is the thousandth of an ampere.
The resistance of a Daniell’s element with an external cylinder of zinc,
8 inches high and 34 in diameter, surrounding the porous pot, is about 1°3
ohm, and taking its E.M.F. at 1°08 volt, its current when on short circuit is
about o°8 ampere. In like manner a medium-sized Bunsen has a resistance
of about o'r ohm, and as its E.M.F-. is 1°8 volt, the current on short circuit is
18 amperes. A Brush machine the current of which ignited 16 arc lamps
in series had an E.M.F. of 839 volts ; its internal resistance was 10°55, and
1040 Dynamical Electricety {1000-
the external, including the lamps, was 73 ohms. Accordingly the current
was 10°64 amperes. A Holtz machine has in electromagnetic measurement
an E.M.F. of 90,000 volts ; its internal resistance, when it makes two turns —
in a second, is calculated at 27 x 10° ohms ; thus its current is sg4y55 of an
ampere, or ;'5 of a millampere. Sucha current is too weak for telegraph
work ; the currents used with the ordinary Morse receivers have a strength
of 14 to 16 millamperes.
The Coulomé is the unit of quantity of electricity, and is that quantity
which traverses the section of a conductor in a second, when a current of an
ampere is passing through it. A coulomb of electricity in traversing an
electrolyte decomposes a weight of the body expressed by 000001038 of
its chemical equivalent.
The electric energy expended when a coulomb of electricity falls in
potential by one volt is a called a Joule. _ Its value in C.G.S. units is 107 x
10° = 10/.ergs.
The Farad is the unit of capacity, and is such that in a condenser of that
capacity the quantity of a coulomb produces a difference of potential of a
a volt. It is 10% C.G.S. units. The farad is far too
large a unit for practical use ; thus the capacity of the
globe is only 0:000636 of a farad, that of the Sun does
not amount to a farad. Accordingly the technical
unit of capacity is the millionth part of the farad, and
p is called the mzcrofarad. This is to” absolute units.
A Leyden jar with a total coated surface of a square
metre, the glass of which is 1 mm. thick, has a
capacity of »+; of a microfarad. The capacity of an
ordinary submarine cable may be taken at about 4 of
a microfarad per £vzof or nautical mile of 1852 metres.
A sphere nine kilometres in radius has a capacity of a
microfarad.
The practical standards consist of circular or square sheets of tinfoil with
projecting tongues, a and a’ (fig. 1031), fastened on thin sheets of mica. Be-
tween each such coated sheet is placed an uncoated one of mica, the two
sets of tongues being severally connected with each other, and thus the
coatings represent the coated surfaces of a condenser. The whole is en-
closed in a box ; a condenser having a capacity of a microfarad will repre-
sent a coated surface of over 6 square yards.
Wati.—The energy, W, of an electrical current in unit time may be
2
variously expressed ; thus W =C?R= = =CE. This latter expression is the
al
a
th
ua
Fig. 1031
most convenient for practical purposes ; if the factors which express the watt
are given in practical units, it represents the work done per second by unit
current (ampere) when impelled by an E.M.F. of a volt. It is thus a wolt-
ampere, and on the proposal of the late Sir W. Siemens has been called a watz.
If the factors are given in absolute units, V A is equal to 107 ergs per second.
It may also be defined as the work done by the quantity of electricity of a
coulomb falling through a difference of potentials equal to a volt, and in this
form the definition is closely analogous to that of a kilogramme metre.
The watt is -4, of an English horse-power, or one horse-power = 746 watts.
-1001] Relation of Electrostatic to Electromagnetic Unit 1041
The French cheval-vapeur of 75 kilogramme-metres or 542°4 foot-pounds per
second is equal to 736 watts.
In addition to the above, a practical unit of inductance has been adopted,
and is called the hezry. The self-inductance of a circuit is one henry, if an
opposing electromotive force of one volt results from a variation of the
strength of current in the circuit at the rate of one ampere per second. The
mutual inductance of two circuits is one henry if an electromotive force of
one volt in one of them results from a variation of the strength of current in
the other at the rate of one ampere per second. The value of the henry in
C.G.S. measure is consequently 10°.
1001. Relation of the electrostatic to the electromagnetic unit.—If we
compare the dimensions of the units of quantity and of the other electrical
magnitudes in the electrostatic with those of the corresponding dimensions
as expressed in the electromagnetic system, we find that the ratios are
independent of the unit of mass, and that = that is, the expression of a
velocity, always enters into the ratio between them. Now the ratio of the
two sets of units may be determined experimentally. Suppose’ that a con-
denser is charged with electricity. Its dimensions being known, the quantity,
g, of the charge may be determined in electrostatic measure, by measuring,
for instance, the repulsion which a given proportion of the total charge
produces in a torsion balance of known dimensions. The same con-
denser, being charged to the same extent, may be discharged through a
galvanometer, and by measuring the deflection produced, and knowing the
constants of the instrument, we may obtain the quantity in electromagnetic
units, and thus the ratio of the quantity expressed in the two sets of units
may be deduced. Or, again, the E.M.F. of a Daniell’s cell may be measured
first by the aid of an absolute electrometer (803), which will give in electro-
static units of potential about 070036. On the other hand, the potential
determined in electromagnetic measure has the value 1°088 x 10°, Hence
it would thus be found that in round numbers the electromagnetic unit
of quantity is equal to 3 x 10° electrostatic units of quantity. This can be
understood if we consider that the latter is the quantity of electricity which
attracts or repels another equal quantity at a distance of I cm. with a force
of a dyne, while the former is the quantity which traverses the wire in a
second when the current has unit intensity. Similarly, by making deter-
minations of the ratio in all cases in which the same magnitude may be
determined in electrostatic as well as in electromagnetic measure, it is found
that the agreement in the numbers found is very close, and that the mean of
the best results is 2.9857 x 10'°. As the ratio between the units is always of
the dimensions of a velocity, and holds under the condition that the centi-
metre is the unit of length, and the second is the unit of time, this velocity
is 298,570 kilometres, or 185, 530 milesinasecond. Nowthis ee agrees
very closely with that which has been experimentally found for the velocity
of light—185,420 miles (519).
We may illustrate the relation between the two units as follows. Suppose
a ring with a uniform charge of one electrostatic unit on each unit of length,
the centimetre ; if this is rotated about its own axis, it carries with it a certain
‘ 3x
1042 Dynamical Electricity [1001—
charge of electricity in the same way as a current in a ring at rest would do ;
this has been shown by Rowland by direct experiment.
The number wv expresses the velocity with which the unit of length of
ring must be rotated so as to produce the electromagnetic unit of quantity.
This, as we have seen, is practically equal to that of light, namely 300,000
kilometres per second. It expresses the number of electrostatic units which
the electromagnetic unit carries through each section of the conductor in
unit time. Hence the quantity of electricity represented by the electro-
magnetic unit is exceedingly great in comparison with the electrostatic unit,
and thus the current of a Holtz machine, for instance, produces very slight
action on the galvanometer.
1002. Electromagnetic theory of light.—Faraday, discarding the idea of
action at a distance, considered that electrical forces are transmitted
through an elastic medium, and that this was the luminiferous ether (651)
Maxwell, starting from these ideas, was led to the development of his
electromagnetic theory of light ; this theory requires that an electromagnetic
wave motion must be transmitted with a velocity represented by the ratio of
the electrostatic to the electromagnetic unit of quantity of electricity ; this,
as we have seen, is equal to the velocity of light. Now, if luminous and
electromagnetic waves are transmitted in one and the same medium and
with the same velocity, it is natural to suppose that they are identical in
kind. The theory also requires the relation between the refractive index of
a body and the dielectric constant which we have already found to exist
(769).
These theoretical previsions of what is known as the ‘ Faraday-Maxwell’
theory received a striking confirmation in a most remarkable and beautiful
series of experiments by the late Professor Hertz, of which we can only give
an outline of some of the principal results. .
In order to demonstrate that light is essentially an electromagnetic
phenomenon, it would be necessary to produce, with a vibratory motion of
a purely electromagnetic origin, the same class of phenomena as can be
produced with ordinary light, such, more especially, as interference and re-
fraction. The difficulty is the great length of the waves with which we have
to deal; for from the laws of wave motion (256), if the frequency of the
electrical oscillations were even as great as ten thousand in a second, that
would represent a wave-length of 30 kilometres, and for a wave-length of
3 metres the duration should not be greater than the hundred-millionth of a
second. Now in the discharge of a Leyden jar, or the still more rapid one
which takes place between the ends of the secondary wire of a Ruhmkorff’s
coil, the duration of the oscillation is comprised within the ten-thousandth
and the hundred-thousandth of a second.
Hertz devised an apparatus which he calls a wzébrator or discharger for
obtaining by continuous but very rapid electrical oscillations, true vays of
electrical energy. "Two spheres or plates of metal, AA’ (fig 1032), are pro-
vided with straight metal rods with small knobs at the end, the distance,
C, of which can be adjusted. The rods are in connection with the poles
of a small Ruhmkorff’s coil B, which charges the two spheres to different
potentials, and a spark passes at C. This spark, by heating the air, forms,
as it were, a path for the subsequent oscillations, and the vibrator now
-1002] Electromagnetic Theory of Light 1043
discharges itself independently, as if it were detached from the coil, forming
between the discharges of the Ruhmkorff a series of oscillations of ex-
treme rapidity. Theory shows that if the
resistance of the circuit is so small as to
be neglected, the period, Zz, of such an
oscillation is proportional to the square
root of the capacity, and the coefficient
of self-induction, ¢= 27./ LC ; and accord-
ingly by suitably choosing the dimen-
sions of the apparatus it has been pos-
sible to obtain electrical oscillations with
a frequency of 5 x Io! in a second, re-
presenting a wave-length of 6cm. This
is still 12,000 times that of light.
If a wire frame is connected with
one of the spheres, as shown on the
right of the figure, the potentials are
equal at a and 8, and no spark passes
between them. But if the connection is
made asymmetrically, as shown in the left
—that is to say, is nearer one knob than the other—there is a difference of
potential, and very minute sparks pass continuously.
If we have a vibrating tuning-fork producing sound waves therefore,
and we approach to it a body tuned in unison with the fork, the body in
question begins to vibrate also; such bodies, as we have seen, are called
resonators (259). In order to investigate the distribution of electrical waves
inthe region about a vibrator, Hertz used what he calls an electrical resonator.
This consists (fig. 1033) of a wire ring, one end terminating in a point and
the other in a knob, which by a micrometric arrangement, not shown in the
figure, may be kept at any desired distance. The dimensions of the frame
are adjusted—czuned as it were—so that its oscillations synchronise with
those of the vibrator. If now the resonator is placed with its axis parallel
to the axis of the vibrator—that is, to the line joining a and 8—positions are
found in which a flow of minute sparks passes between the ends of the
resonator; their quantity and strength diminish as
the distance from the vibrator increases, but are per-
ceptible at even 50 or 60 feet. These waves are
transverse to the direction of propagation, as appears
from the fact that when in a given position the
resonator is giving sparks, it ceases to do so when
turned at right angles. When the vibrator works well
the whole room is pervaded by electrical waves, and
by varying the position and distance of the resonator
in reference to the vibrator, it is possible to plot
out the exact form of the wave motion in the field. Sparks can be taken
between any two pieces of metal ; by presenting a penknife to a gaspipe
and the like.
These electrical waves pass through ordinary conductors, such as a door
or a wall, but are reflected from a conducting surface. If the vibrator is °
eye swe
pAL
B0G a
Fig. 1033
1044 Dynamical Electricity [1002--
placed at a suitable distance in front of a large sheet of metal, the waves
are reflected from the wall, and interfering with incident rays give rise to
stationary waves made up of nodes and loops at regular intervals, quite
analogous to the corresponding acoustical phenomenon. This may be
demonstrated by means of the resonator, which gives
no spark if placed at a node, but does so if in a loop.
If the metal is a perfect conductor, there is formed
a node at the reflecting surface and others at equal
distances. This is analogous to the case of a stopped
pipe. |
If the vibrator is placed in front of a tall cylindrical
metal reflector with a parabolic section (fig. 1034), the
effects produced are more pronounced, and can be per-
ceived at a greater distance than before. A mass of
= = electrical rays parallel to the focal line is formed, and
—- the experiment of the conjugate mirrors (427) may be
repeated. An insulating screen placed between the two
mirrors does not stop the action, but a conducting screen does. It forms
an électrical shadow.
The electrical rays undergo a refraction on passing from one medium to
another. This Hertz demonstrated by means of a huge prism of pitch,
weighing about half a ton, 5 feet in height, with a refracting angle of 30°,
and with a face of over a square yard. When the rays, rendered parallel by
the mirror, fell on this, they were deflected towards the base, and by means
of the resonator the position of minimum deviation could be obtained, and
thus the refractive index was found to be 1°69 ; the optical refractive index
is between 1°5 and 1°6.
_ By allowing electrical rays to fall on a plane reflecting surface, part are
absorbed and part reflected, and it is readily shown that the angle of reflec-
tion, as with light and heat, is equal to the angle of incidence (523).
If the electrical rays concentrated by a mirror fall on a grating formed
of parallel copper wires, it is found that when the grating is in the direction
of the rays—that is, when the wires are parallel to the focal line of the mirror
—they are transmitted, but are stopped when the wires are turned at right
angles to the direction. This is a phenomenon of polarisation ; the grating
acts in regard to the rays like a tourmaline in respect of plane polarised
light (680). In another experiment Hertz reproduced the phenomena of
diffraction (660). He also showed that electrical waves can exert a mechani-
cal action by causing them to strike against a small tube of gold paper very
delicately suspended. A straight insulated wire fixed perpendicularly to the
centre of a metal plate placed close to one of the knobs of the discharger is
traversed by waves which, reflected from the end of the wire, also give rise
to stationary vibrations. The distance from one node to another is constant,
whatever be the nature of the wire, and this value is the same as for air. It
follows from this that the propagation takes place through the air, and not
through the wire.
We might infer from the extreme rapidity of the oscillations that the
phenomenon does not penetrate beyond the surface of the wire. Hertz
demonstrated this directly by the following arrangement (fig. 1035). The
Fig. 1034
-1002] Electromagnetic Theory of Light 1045
wire is cut at A, and the gap is enclosed in a kind of cage made of metal
wires stretched between two discs, a and. The disc a is in contact with
the wire ; the disc 8 is supported by a tube yé, which surrounds the wire, but
does not touch it. As the waves arrive in the direction of the arrow, there
is no spark at A if the tube is connected at 6 with the wire ; the electrical
action stops at the outer surface. The sparks reappear, however, if the tube
is insulated at 6; the oscillations travel through the dielectric between the
wire and the inner surface of the tube.
Hertz’s experiments have been reproduced by many observers, and with
other resonators.and modifications in the way of experimenting. Dragoumis
found that Geissler’s tubes were well fitted for this purpose. Lecher’s method
of investigation is convenient. The vibrator is formed of two metal plates,
rf &
g E
|
!
iS yr"
Ae
Fig. 1036
ab (fig. 1036), connected with the terminals of a Ruhmkorff’s coil as in
fig. 1032, opposite which are two similar ones, a’d’; from these pass long
wires, s¢ s’/’, parallel from s to 4, which are tightly stretched by means of
strings.
If a Geissler’s tube g with or without electrodes is placed across the
wires, it becomes luminous. If now a metal wire, xx’, is placed across, the
luminosity ceases, but by moving the cross wires backwards or forwards,
positions are found in which it again appears. These positions represent
the nodes. According to Lecher, this is a phenomenon of electrical resonance ;
a principal vibration is formed from a@ sxx’s’b’, which by induction produces
secondary vibrations in the rest of the wire.
If a portion of each of the wires is cut off, the resonance is disturbed,
the tube is dark, and to restore the luminosity the bridge xv’ must be moved
nearer to F’; the amount of displacement’ is half the length of the pieces
thus cut off. “i
1046 Dynamical Electricity [1002-
If a sheet of tinfoil is attached to each end, this increases the capacity ;
the period of the vibration is increased, the wave-length greater, and to keep
the tubes luminous the cross wires must be moved nearer the ends ¢#’.. This
leads to a method of determining capacities and dielectric constants by
means of very rapid vibrations. The apparatus furnishes also a ready
means of determining the electrical wave-length. In certain experiments
with a period of vibration of the hundred-thousandth of a second, the distance
of two consecutive nodes, or half a wave-length, was found to be 1°4 m., so
that from the formula (256) this gives for the velocity of electricity 280,000
kilometres—that is, virtually the same as that of light (519).
The velocity is the same whatever be the nature of the wires used, from
which it follows that the transmission is effected by the surrounding medium
and not by the wire itself.
All these experiments show that the analogy is complete between the
waves of light and of electricity, and we are led to the conclusion that elec-
trical, thermal, and luminous phenomena have one and the same origin,
which is a vibratory motion of the ether, and that they only differ in the
length of the waves. The wave-length of the longest visible rays is about
o’00005 cm., that of the longest dark thermal ray hitherto observed is
0°003 cm., while the shortest electrical wave is 50cm., or a million times that
of light.
These experiments lead to a fundamental change in our views as to the
way in which the electrical current is transmitted. It has hitherto been
considered that when the circuit is closed the wire itself is the agency by
which the current is transmitted. We must for the future consider that the
surrounding medium, the ether, transmits the electrical energy, and that this
energy enters the wire from the outside; it is there destroyed as electro-
magnetic energy, but is converted into heat, which heat travels by radiation
from layer to layer like changes of temperature in a conductor. The less
rapidly electrical forces change their direction in the medium the more com-
pletely does heat penetrate the wire ; when the change takes: place many
million times in a second the interior of the wire is not affected by the current.
This is analogous to the case of a body which is subject to excessively rapid
alternations of heat and cold.
1003. Telegraphing without wires.—In connection with these researches
some account may be given of recent experiments on establishing telegraphic
communication between two places without employing connecting wires.
These experiments depend on using Hertz waves to produce signals accord-
ing to a conventional code, and the practical arrangements consist simply of
convenient means of producing waves at one station, and of detecting their
arrival at the other. The ¢vansmitter or sender (910) is an ordinary Morse
signalling key interposed in the circuit with a battery and the primary of an
induction coil, the secondary terminals of which are connected with two
carefully insulated metal balls at a small distance from each other. By
depressing the signalling key for a longer or shorter period, series of sparks
of corresponding duration pass between the balls, these longer or shorter
intervals representing the ordinary signals of the Morse telegraph (910).
The vecezver is an application of an experiment made by Branley. He
formed a circuit of a Daniell’s cell, a glass tube containing iron filings with
-1003] Telegraphing without Weres 1047
suitable connections, and a galvanometer: on closing the circuit no current
passed. When, however, the spark of an electrical machine or of a Leyden
jar was produced in the neighbourhood of the tube, the needle of the galvano-
meter was powerfully deflected, indicating the passage of a current. When
the tube containing the iron filings is gently tapped the current ceased to
pass, but did so when a spark was again produced, and so on.
What is the action of the spark cannot perhaps be exactly stated ;
the effect is as though it enormously diminishes the resistance of the tube:
the particles of iron in the original condition being separated by a non-
conductor, air, the resistance is very great, but if the minute film of air
between the neighbouring particles is broken down by the passage of an
infinitesimal spark a permanent current can pass. Lodge supposes that
the effect of the spark is to bring the particles in actual electrical contact,
and to make them cohere, and the term coherer by which he designates this
apparatus is that by which it is now known.
In signalling, the coherer is placed in the focal line of such a mirror as
that represented in fig. 1034, and is connected up with a battery and a
Morse or other receiving instrument. When the key is depressed and sparks
produced between the balls, the electromagnetic waves, falling on the coherer,
affect it so that the current passes and a signal is produced. In order to
interrupt this current and to restore the coherer to its original condition so
that it may be ready to receive another signal, the tube must each time be
gently tapped ; this is done by the tongue of an electromagnetic arrangement
worked automatically by the current itself.
In this way distinct signals have been sent through such great distances
as nine miles.
1048 Dynamical Electricity [1004—
Cot Ad lx.
ANIMAL ELECTRICITY
1004. Muscular currents.—The existence of electrical currents in living
muscle was first indicated by Galvani, but his researches fell into oblivion
after the discovery of the voltaic pile, which was supposed to explain all the
phenomena. Since then, Nobili, Matteucci, Du Bois Reymond, and others,
have shown that electric currents do exist in living muscles and nerves.
For investigating these currents it is necessary to have a delicate gal-
vanometer, and also electrodes which will not become polarised or give a
current of their own, and which will not in any way alter the muscle when
placed in contact with it ; the electrodes which satisfy these conditions best
are those of Du Bois Reymond, as modified by Donders. Each consists of
a glass tube, one end of which is narrowed and stopped by a plug of paste
made by moistening china-clay with a solution of common salt ; the tube is
then partially filled with a saturated solution of zinc sulphate; and into
this dips the end of a piece of thoroughly amalgamated zinc wire, the other
end of which is connected by a copper wire with the galvanometer; the
moistened china-clay is a conducting medium which is perfectly neutral to
the muscle, and amalgamated zinc in solution of zinc sulphate does not
become polarised. 7
1005. Currents of muscle at rest.—In describing these experiments the
surface of the muscle is called the zatural longitudinal section ; the tendon
the watural transverse section; and the sections obtained by cutting the
muscle longitudinally or transversely are respectively the artificial longitu-
dinal and artificial transverse sections.
If a living irritable muscle is removed from a recently killed frog, and
the clay of one electrode is placed in contact with its surface, and of the
other with its tendon, the galvanometer will indicate a current from the
former to the latter ; showing, therefore, that the surface of the muscle is
positive with respect to the tendon. By varying the position of the elec-
trodes, and making various artificial sections, it is found—
1. That any longitudinal section is positive to any transverse section.
2. That any point of a longitudinal section nearer the middle of the
muscle is positive to any other point of the same section farther from the
centre:
3. In any artificial transverse section any point nearer the periphery is
positive to one nearer the centre.
4. The current obtained between two points in a longitudinal or in a
transverse section is always much more feeble than that obtained between
two different sections.
1005] Currents of Muscles at Rest 1049
5. No current is obtained if two points of the same section equidistant
from its centre are taken.
6. To obtain these currents it is not necessary to employ a whole muscle,
or a considerable part of one, but the smallest fragment that can be experi-
mented with is sufficient.
7. If a muscle is cut straight across, the most powerful current is that
from the centre of the natural longitudinal section to the centre of the arti-
ficial transverse ; but if the muscle is
cut across obliquely, as in fig. 1037, the
most positive point is moved from c
towards J,and the most negative from
d towards a (‘currents of inclination’).
To explain the existence and rela-
tions of these muscular currents, it may be supposed that each muscle is
made up of regularly disposed electromotor elements, which may be re-
garded as cylinders whose axes are parallel to that of the muscle, and
whose sides are charged with positive and their ends with negative electri-
city ; and, further, that all are suspended and enveloped in a conducting
medium. In such a case (fig. 1037) it is clear that throughout most of the
muscle the positive electricities of the opposed surfaces would neutralise one
another, as would also the negative charges of the ends of the cylinders ; so
that, so long as the muscle was intact, only the charges at its sides and ends
would be left to manifest themselves by the production of electromotive
phenomena; the whole muscle being enveloped in a conducting stratum, a
current would constantly be passing from the longitudinal to the transverse
section, and, a part of this being led off by the wire circuit, would manifest
itself in the galvanometer.
This theory also explains the currents between two different points on the
same section ; the positive charge at 4, for instance (fig. 1038), would have more
resistance to overcome in get-
ting to the transverse section
than that at d@, therefore it has a
higher potential ; andif éandd
are connected by the electrodes,
6 will be found positive to d,
and a current will pass from
the former to the latter. What
are called currents of tnclina-
tion are also explicable on the
above hypothesis, for the
oblique section can be repre-
sented as a number of elements arranged as in fig. 1039, so that both the
longitudinal surfaces and the ends of the cylinders are laid bare, and it can
thus be regarded as a sort of oblique pile whose positive pole is towards 6
and its negative at a, and whose current adds itself algebraically to the
ordinary current and displaces its poles as above mentioned.
A perfectly fresh muscle, very carefully removed, with the least possible
contact with foreign matters, sometimes gives almost no current between its
different natural sections, and the current always becomes more marked after
Fig. 1038
IO50 Dynamical Electricity [1005-
the muscle has been exposed a short time; nevertheless, the phenomena
are vital, for the currents disappear completely with the life of the muscle,
sometimes becoming first irregular or even reversed in direction.
1006. Rheoscopic frog. Contraction without metals.—The existence of
the Sereculat currents can be manifested without a galvanometer, by using
another muscle as a galvanoscope.
Thus, if the nerve of one living
muscle of a frog is dropped sud-
denly on another living muscle, so
as to come in contact with its longi-
tudinal and transverse sections, a
contraction of the first muscle will
occur, due to the stimulation of its
nerve by the passage through it of the electric current derived from the
surface of the second.
1007. Currents in active muscle.—When a muscle is made to contract
there occurs a sudden diminution of its natural electric current, as indicated
by the galvanometer. This is so instantaneous that, in the case of a single
muscular contraction, it does not overcome the inertia of the needle of the
galvanometer ; but if the contractions are made to succeed one another very
rapidly—that is, if the muscle is ¢e¢anzsed (849)—then the needle swings
steadily back towards zero from the position in which the current of the
resting muscle had kept it, often gaining such momentum in the swing as to
pass beyond the zero point, but soon reverting to some point between zero
and its original position.
The negative variation in the case of a simple muscular contraction can,
however, be made manifest by using another muscle as a rheoscope ; if the
nerve of this second muscle is laid over the first muscle in such a position
that the muscular current passes through it, and the first muscle is then made
to contract, the sudden alteration in its strength of the current stimulates
the nerve laid on it (849), and so causes a contraction of the muscle to which
the latter belongs.
The same phenomenon can be demonstrated in the muscles of warm-
blooded animals ; but with less ease, on account of the difficulty of keeping
them alive after they are laid bare or removed from the body. Experiments
made by placing electrodes outside the skin, or passing them through it, are
inexact and unsatisfactory.
1008. Electric currents in nerve.—The same electrical indications can
be obtained from nerves as from muscles—at least, as far as their smaller
size will permit ; the currents are more feeble than the muscular ones, but
can be demonstrated by the galvanometer inasimilar way. Negative varia-
tion has been proved to occur in active nerve as in active muscle. The
effect of a constant current passed through one part of a nerve on the amount
of the normal nerve-current, measured at another part, has already been
described (849).
1009. Electrical fish.—Electrical fish are those fish which have the re-
markable property of giving, when touched, shocks like those of the Leyden
jar. Of these fish there are several species, the best known of which are the
torpedo, the gymnotus, and the silurus. The torpedo, which is very common
Fig. 1039
-1009] Electrical Fish 1051
in the Mediterranean, was carefully studied by Becquerel and Breschet in
France, and by Matteucci in Italy. The gymnotus was investigated by
Humboldt and Bonpland in South America, and in England by Faraday,
who had the opportunity of examining live specimens.
The shock which they give serves as a means both of offence and of
defence. It is purely voluntary, and becomes gradually weaker as it is
repeated and as these animals lose their vitality, for the electrical action
soon exhausts them materially. According to Faraday, the shock which the.
gymnotus gives is equal to that of a battery of I5 jars exposing a coating of
25 square feet, which explains how it is that horses frequently give way under
the repeated attacks of the gymnotus.
Numerous experiments show that these shocks are due to ordinary
electricity. For if, touching with one hand the back of the animal, the
belly is touched with the other, or with a metal rod, a violent shock is felt
in the wrists and arms ; while no shock is felt if the animal is touched with
an insulating body. Further, when the back is connected with one end of a
galvanometer wire and the belly with the other, at each discharge the needle
is deflected, but immediately returns to zero, which shows that there is an
instantaneous current ; and, moreover, the direction of the needle shows that
the current goes from the back to the belly of the fish. Lastly, if the cur-
rent of a torpedo be passed through a helix in the centre of which is a small
steel bar, the latter is magnetised by the passage of a discharge.
By means of the galvanometer, Matteucci established the following
facts :—
1. When a torpedo is lively, it can give a shock in any part of its body,
but as its vitality diminishes, the parts at which it can give a shock are
nearer the organ which is the seat of the development of electricity. 2. Any
point of the back is always positive as compared with the correspond-
ing point of the belly. 3. Of any two points at different distances from
the electrical organ, the nearest always plays the part of a positive pole,
and the farthest that of a nefative pole. With the belly the reverse is the
case.
The organ where the electricity is produced in the torpedo is double, and
formed of two parts symmetrically situated on two sides of the head and
attached to the skull-bone by the internal face. Each part consists of nearly
parallel lamellze of connective tissue enclosing small chambers, in which lie
the so-called electrical plates, each of which has a final nerve ramification
distributed on one of its faces. The face, on which the nerve ends, is
turned the same way in all the plates, and when the discharge takes place
is always negative to the other.
Matteucci investigated the influence of the brain on the discharge. For
this purpose he laid bare the brain of a living torpedo, and found that the
first three lobes could be irritated without the discharge being produced, and
that when they were removed the animal still possessed the faculty of giving
a shock. The fourth lobe, on the contrary, could not be irritated without
an immediate production of the discharge ; but if it was removed, all dis-
engagement of electricity disappeared, even if the other lobes remained
untouched. Hence it would appear that the primary source of the electricity
elaborated is the fourth lobe, whence it is transmitted by means of the nerves
1052 Dynamical Electricity [1009-
to the two organs described above, which act as multipliers. In the silurus
the head appears also to be the seat of the electricity ; but in the gymnotus
it is found in the tail.
1o1o. Application of electricity to medicine.—The first applications of
electricity to medicine date from the discovery of the Leyden jar. Nollet
and Boze appear to have been the first who thought of the application, and
soon the spark and electrical friction became a universal panacea ; but it
must be admitted that the results of subsequent trials did not come up to the
hopes of the early experimentalists.
After the discovery of dynamic electricity Galvani proposed its applica-
tion to medicine ; since which time many physicists and physiologists have
been engaged upon this subject, and yet there is still much uncertainty as
to the real effects of electricity, the cases in which it is to be applied, and
the best mode of applying it. Practical men prefer the use of currents to
that of statical electricity, and, except in a few cases, discontinuous to
continuous currents. There is, finally, a choice between the currents of the
battery and induction currents; further, the effects of the latter differ,
according as induction currents of the first or second order are used. In
fact, since induction currents, although very intense, have a very feeble
chemical action, it follows that when they traverse the organs they do not
produce the chemical effects of the current of the battery, and hence do not
tend to produce the same disorganisation. Further, in electrifying the
muscles of the face, induction currents are to be preferred, for these currents
only act feebly on the retina, while the currents of the battery act energeti-
cally on this organ, and may affect it dangerously. There is a difference in
the action of induced currents of different orders ; for while the primary
induced current causes lively muscular actions, but has little action on the
cutaneous sensibility, the secondary induced current, on the contrary, in- |
creases the cutaneous sensibility to such a point that its use ought not to be
prescribed to persons whose skin is very irritable.
Hence electrical currents should not be applied in therapeutics without
a thorough knowledge of their various properties. They ought to be used
with great prudence, for their continued action may produce serious acci-
dents. Matteucci says: ‘In commencing, a feeble current must always be
used. This precaution now seems to me the more important as I did not
think it so before seeing a paralytic person seized with almost tetanic con-
vulsions under the action of a current formed of a single element. Take
care not to continue the application too long, especially if the current is
energetic. Rather apply a frequently interrupted current than a continuous
one, especially if it be strong ; but after twenty or thirty shocks, at most, let
the patient take a few moments’ rest.’
Of late years, however, feeble continuous currents have come more into
use. They are frequently of great service when applied skilfully, so as to
throw the nerves of the diseased part into a state of katelectrotonus or
anelectrotonus (850), according to the object which is wished for in any
given case.
~1012] | Meteorograph 1053
ELEMENTARY FOU 1 LINES
OF
MBG BOROLOGY WAND SCIIMATOROGY
METEOROLOGY
1011. Meteorology.—The phenomena which are produced in the atmo-
sphere are called meteors ; and meteorology is that part of physics which is
concerned with the study of these phenomena.
A distinction is made between aerza/ meteors, such as winds, hurricanes,
and whirlwinds ; agweous meteors, comprising fogs, clouds, rain, dew, snow,
and hail ; and /wmdznous meteors, as lightning, the rainbow, and the aurora
borealis.
1012. Meteorograph.—The importance of being able to make continuous
observations of various meteorological phenomena has led to the construc-
tion of various forms of automatic arrangements for this purpose, of which
that of Osler in England may be mentioned. One of the most compre-
hensive and complete is Secchi’s mmeteorograph, which consists of a base
of masonry about 2 feet high (fig. 1040) ; on this are fixed four columns
about 24 yards high, which support a table on which is a clockwork
regulating the whole of the movements. The phenomena are registered
on two sheets which move downwards on two opposite sides, their motion
being regulated by the clockwork. One of them occupies ten days in
so doing, and on it are registered the direction and velocity of the wind,
the temperature of the air, the height of the barometer, and the occurrence
of rain; on the second, which only takes two days, the barometric height
and the occurrence of rain are repeated, but on a much larger scale ; this
gives moreover the moisture of the air.
Direction of the wind.—The four principal directions of the wind are re-
gistered by means of four pencils fixed at the top of thin brass rods, a, 4, ¢, d
(fig. 1040), which are provided at the bottom ends with soft iron keepers
attracted by two electromagnets, E E’, for west and north, and by two
other electromagnets lower down for south and east. These four electro-
magnets, as well as all the others on the apparatus, are worked by a single
battery of twenty-four elements. The passage of the current in one or
1054 Meteorology [1012-
the other of these electromagnets is regulated by means of a vane (fig. 1041)
consisting of two plates at an angle of thirty degrees with each other, by
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which greater steadiness is obtained than with a single plate. In the rod of
the vane is a small brass plate, 0; this part is in the centre of four metal
=
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—1012] Velocity of the Wind 1055
sectors, insulated from each other, and each provided with a-binding-screw,
by which connection is established with the binding-screw K, and the elec-
tromagnets EE’. The battery current
reaches the rod of the vane by the wire a,
and thence the sliding contact 0, which
leads it to the electro-magnet for the
north, for instance.
If the current passed constantly in this
electromagnet, the pencil on the rod d
would be stationary ; but from the electro-
magnet E’ the current passes into a second
electromagnet, 7, over the clockwork, and
is thereby alternately opened and closed,
as will be seen when we speak of the
velocity of the wind. Hence the armature
of the rod @, alternately free and attracted,
oscillates ; and its pencil, which is always
pressed against the paper AD by the
elasticity of the rod, traces on it a series
of parallel dashes as the paper descends,
and so long as the wind is in the north.
If the wind changes then to west, for in-
stance, the rod a@ oscillates, and its pencil
ie
E
HH re
——————
HECLARO
Fig. 1041
traces a different series of marks. The rate of displacement of the paper
being known, we get the direction of the prevalent wind at a given moment.
Velocity of the wind.—This is indi-
cated by a Robinson’s anemometer, and
is registered in two ways : by two counters
which mark in decametres and kilometres
the distance travelled by the wind ; and
by a pencil which traces on a table a curve,
the ordinates of which are proportional to
the velocity of the wind.
Robinson, who originally devised this
form of anemometer (fig. 1042), proved
that its velocity is proportional to that of
the wind; in this apparatus the length
of the arms is so calculated that each re-
volution corresponds to a velocity of ten
metres. The anemometer is placed at a
considerable distance from the meteoro-
graph, and is connected with it by a
copper wire, @, which passes to the electro-
magnet, 2, of the counter. On its rod there
is, moreover, an excentric, which at each
turn touches a metal contact in connec-
tion with the wire @. The battery current
Fig. 1042
reaches the anemometer by a wire a, the circuit is closed once at each
rotation, and the current passes to the electromagnet 7, which moves the
1056 Meteorology [1012--
needle of the dial through one division. There are fifty such divisions, which
represent as many turns of the vane, and therefore so many multiples of ten
metres. The lower dial marks the kilometres.
The curve of velocities is traced on the sheet by a pencil, z, fixed to a
horizontal rod. This is joined at its two ends to two guide-rods, o and y,
which keep it horizontal. The pencil and the rod are moved laterally by a
chain which passes over two pulleys, 7’ and 7, and is then coiled over a pulley
placed on the shaft of the counter, but connected with it merely by a ratchet-
wheel ; and moved thus by the counter and the chain, the pencil traces
every hour on the sheet a line the length of which is proportioned to the
velocity of the wind. From hour to hour an excentric moved by clockwork
detaches, from the shaft of the counter, the pulley on which is coiled the
chain, and this pulley becoming out of gear, a weight, 2, connected with the
pencil z, restores this to its starting point. All the lines, V, traced succes-
sively by the pencil, start as ordinates from the same straight line, and their
ends give the curve of velocities.
The counters on the right and left are worked by electromagnets, 7 2’,
and are intended to denote the velocity of special winds ; for instance, those
of the north and south, by connecting their electromagnets with the north
and south sectors of the vane (fig. 1041).
Temperature of the atr.—This is indicated by the expansion and con-
traction of a copper wire of 16 metres in length stretched backwards and
forwards on a fir post 8 metres in length. The whole being placed on the
outside—on the 1oof, for instance—the expansion and contraction are trans-
mitted by a system of levers to a wire, v, which passes to the meteorograph,
where it is jointed to a bent lever, 7 This is jointed to a horizontal rod, s,
which supports a pencil, and at the other end is jointed to a guide-rod, x.
Thus the pencil, sharing the oscillations of the whole system, traces the curve
of the temperatures.
Pressure of the atmosphere.—This is registered by the oscillations of a
barometer, B, suspended at one end of a bent scale-beam, I F, playing ona
knife-edge (fig. 1045). The arm F supports a counterpoise ; to the arm I is
suspended the barometer B, which is wider at the top than at the bottom.
A wooden flange or floater, Q, fixed to the lower part of the tube, plunges in
a bath of mercury, so that the buoyancy of the liquid counterbalances part of
the weight of the barometer. Owing to the large diameter of the barometric
chamber, a very slight variation of level in this chamber makes the tube
oscillate, and with it the scale-beam 1 F. To the axis of this is a triangle,
. ghk, jointed to a horizontal rod, which in turn is connected with a guide-rod,
g. In the middle of this rod is a pencil which, sharing in the oscillations of
the triangle g/£, traces the curve H of pressure. A bent lever at the bottom
of the barometer tube keeps this in a vertical position.
Rainfall.—This is registered between the direction of the winds and the
curve H by a pencil at the end of a rod, wz, which is worked by an electro-
magnet, e¢. On the roof is a funnel which collects the rain, and a long tube
leads the water to a small water-balance, with the cups placed near the
meteorograph (fig. 1044). To the axis of the scale-beam one pole of the
battery is connected ; the left cup being full, tips up, and a contact, a,
closes the current, which passes then to one of the binding-screws, C, and
‘
—1012] Measurement of the Rainfall 1057
hence to the electromagnet, ¢. Then the right cup, being in turn full, tips
in the opposite direction, and the contact 4 now transmits the current to the
electromagnet. Thus, at each oscillation this latter attracts its armature,
and with it the rod a, which makes a mark by means of a pencil at the end.
If the rain is abundant, the oscillations of the beam are rapid, and the marks,
being very close together, give a deep shade ; if, on the contrary, the oscilla-
tions are slow, the marks are at a greater distance, and give a light shade.
When the rain ceases the oscillations cease also, and
the pencil makes no mark.
To complete this description of the art face of
the meteorograph: S is the alarum-bell of the clock-
work ; OO a cord supporting a weight which moves
the works of the hour-hand ; LZ is a second cord that
supports the weight which works the alarum; the
wheel U, placed below the clockwork, winds up the
sheet AD when it is at the bottom of its course.
The second sheet (fig. 1044) gives the barometric
height and the rainfall like the first, but on a larger
scale, since the motion of the sheet is five times as
rapid. Its principal function is that of registering the
moisture of the air. This is effected by means of the
psychrometer (fig. 1043). T and T’ are two thermo-
meters fixed on two plates. The muslin which covers
the second is kept continually moist by water dropping on it. In each of
the bulbs is fused a platinum wire; the stems of the thermometers are
open at the top, and in them are two platinum wires, 7 and 7, suspended
to a metal frame movable on four pulleys supported by a fixed piece, B.
The frame A, in contact with the current of the battery, is suspended to a
steel wire, L, which passes over a pulley to the meteorograph (fig. 1043)
Here is a long triangular lever, W, which supports a small wheel, to which
is, fixed the wire L. The lever W, which turns about an axis, f, is moved
by a rod, a, by means of an excentric, which the clock works every
quarter of an hour. At each oscillation the lever W transmits its motion
to a small chariot, on which is an electromagnet, x, and at the same time to
the steel wire L, which supports the frame A (fig. 1045). The chariot, moved
towards the left by the rotation of the excentric, lets the frame sink. The
moment the first platinum wire reaches the mercurial column of the dry-
bulb thermometer, which is the highest, the circuit is closed, and the current
passes into the electromagnet of the chariot. An armature at once causesa
pencil to mark a point on the sheet which is the beginning of a line repre-
senting the path of the dry-bulb thermometer. As the frame continues to
descend, the second platinum wire touches the mercury of the wet bulb, and
causes a current to flow in a relay, M, which opens the circuit of the electro-
magnet, x The pencil is then detached ; then, returning upon itself, the
chariot reproduces the closing and opening of the circuit in the opposite
direction, the pencil making another mark, which is the end of the line.
There are thus formed two series of dots arranged in two curves, one of which
represents the path of the dry, and the other the path of the wet, bulb. The
horizontal distance of the two points of these curves is proportional to the
3¥
Fig. re
1058 Meteorology [1012-
difference 7—7, of the temperatures indicated at the same moment by the
thermometers (fig. 1045).
Bl |
Lic cA
ff ili}
MUG ne
Fig. 1044
Quantity of ratn.—The quantity of rain which falls in a given time
is registered on a disc of paper on a pulley, R. On the groove of this is
coiled a chain to which is suspended a brass tube, P. This is fixed at the
1013] Direction and Velocity of Winds 1059
bottom to a float, which plunges in a reservoir placed in the base of the
meteorograph. On passing out of the water-balance (fig. 1041) the water
passes into this reservoir, and as its section is one-fourth that of the funnel,
the height of water which falls is quadrupled ; it is measured on a scale, G,
divided into millimetres.
As the float rises, a weight, Z, moves the pulley in the contrary direction,
and its rotation is proportional to the height of water which. has fallen. A
pencil moves at the same time from the centre to
the circumference of the paper disc with a velocity
of 5 mm. in 24 hours: hence the quantity of rain
which falls every day is noted on a different place
on the paper disc.
1013. Direction and velocity of winds.— Wznds
are currents moving in the atmosphere with vari-
‘able directions and velocities. There are eight
principal directions in which they blow—vorth,
north-east, east, south-east, south, south-west, west,
and zorth-west. Mariners further divide each of
the distances between those eight directions into
four others, making in all 32 directions, which are
called points or rhumbs. A figure of 32 rhumbs
on a circle, in the form of a star, is known as the
mariners cara.
Velocity is determined by means of the
anemometer (fig. 1042), a small vane with _ fans,
which the wind turns ; the velocity is deducted from
the number of turns made in a given time. In our
climate the mean velocity is from 18 to 20 feet ina
second. With a velocity of less than 18 inches in
a second no movement is perceptible, and smoke
ascends straight ; with a velocity between 13 and
2 feet per second the wind is perceptible and
moves a pennant ; from 13 to 22 feet it is moderate,
it stretches a flag and moves the leaves of trees ; with from 23 to 36 feet
velocity it is fresh, and moves the branches of trees ; with 36 to 56 feet it is
strong, and moves the larger branches and the smaller stems ; with a velocity
of 56 to 9o feet it is a storm, and entire trees are moved; and from 90 to
120 it is a hurricane.
To measure the pressure of the wind a plate is used, which by means of
a vane is always kept in a direction opposite that of the wind. Behind the
plate are one or more springs, which are the more pressed the greater is the
pressure of the wind against the plate. Knowing the distance through which
the plate is pressed, we can calculate the pressure which the wind exerts on
the plate in question.
With some degree of approximation, and for low velocities, the pressure
may be taken as proportional to the square of the velocity. Thus, if the
pressure on the square foot is 0005 pound with a velocity of 1°5 foot in
a second, it is 0.02 pound with a velocity of 3 feet, and 0°123 with a velocity
bfo7-33 feet, .
Fig. 1046
ge:
1060 Meteorology [1014-
1014. Causes of winds.—Winds are produced by a disturbance of the
equilibrium in some part of the atmosphere ; a disturbance always resulting
from a difference in temperature between adjacent countries. Thus, if the
temperature of a certain extent of ground becomes higher, the air in contact
with it becomes heated, expands and rises towards the higher regions of
the atmosphere ; whence it flows, producing winds which blow from hot to
cold countries. But at the same time the equilibrium is destroyed at the
surface of the earth, for the barometric pressure on the colder adjacent parts
is greater than on that which has been heated, and hence a current will be
produced with a velocity dependent on the difference between these pressures ;
thus two distinct winds will be produced—an upper one setting outwards
from the heated region, and a lower one setting zzzwards towards it.
Ioi5. Regular, periodical, and variable winds.—According to the more
or less constant directions in which winds blow, they may be classed as
regular, periodical, and variable winds.
i. Regular winds are those which blow all the year through in a virtually
constant direction. These winds, which are also known as the frade winds,
are uninterruptedly observed far from the land in equatorial regions, blowing
from the north-east to the south-west in the Northern Hemisphere, and from
the south-east to the north-west in the Southern Hemisphere. They prevail
on the two sides of the equator as far as 30° of latitude, and they blow in
the same direction as the apparent motion of the sun—that is, from east to
west.
The air above the equator being gradually heated, rises as the sun passes
round from east to west, and its place is supplied by the colder air from the
north or south. The direction of the wind, however, is modified by this fact,
that the velocity which this colder air has derived from the rotation of the
earth—namely, the velocity of the surface of the earth at the point from
which it started—is less than the velocity of the surface of the earth at the
point at which it has now arrived: hence the currents acquire, in reference
to the equator, the constant direction which characterises the trade winds.
i. Periodical winds are those which blow regularly in the same direction
at the same seasons and at the same hours of the day: the monsoon,
simoom, and the land and sea breeze are examples of this class. The name
monsoon is given to winds which blow for six months in, one direction and
for six months in another. They are principally observed in the Red Sea
and in the Arabian Gulf, in the Bay of Bengal and in the Chinese Sea.
These winds blow towards the continents in summer, and in a contrary
direction in winter. The sz700m 1s a hot wind which blows over the deserts
of Asia and Africa, and which is characterised by its high temperature and
by the sands which it raises in the atmosphere and carries with it. During
the prevalence of this wind the air is darkened, the skin feels dry, the
respiration is accelerated, and a burning thirst is experienced.
This wind is known under the name of szvocco in Italy and Algiers, where
it blows from the great desert of Sahara. In Egypt, where it prevails from
the end of April to June, it is called amsin. The natives of Africa, in order
to protect themselves from the effects of the too rapid perspiration occasioned
by this wind, cover themselves with fatty substances.
A wind characteristic of Switzerland and known as the Fv/m, originates as
-1017] Law of the Rotation of Winds 1061
follows: a mass of air coming from the south-east being impelled over a
mountain ridge becomes rarefied as it ascends ; the temperature falls, and it
deposits its moisture on the other side as rain or snow. Being driven still
forward into the valleys, the superincumbent pressure being greater, the air
is condensed and its temperature rises, and having parted with its moisture
it appears as a wind which is at once hot and dry. One observation gave
the temperature at 31°4° C., while it only contained 20 per cent. of moisture.
The Zand and sea breeze is a wind which blows on the sea-coast, during
the day from the sea towards the land, and during the night from the land
to the sea. For during the day the land becomes more heated than the sea,
in .consequence of its lower specific heat and greater conductivity, and
hence, as the superincumbent air becomes more heated than that upon the
sea, it ascends and is replaced by a current of colder and denser air flowing
from the sea towards the land. During the night the land cools more
rapidly than the sea, and hence the same phenomenon is produced, but in a
contrary direction. The sea breeze commences after sunrise, increases up
to three o’clock in the afternoon, decreases towards evening, and is changed
into a land breeze ‘after sunset. These winds are only perceived at a slight
distance from the shores. They are regular in the tropics, but less so in our
climates ; traces of them are seen as far as the coasts of Greenland. The
proximity of mountains, and also of forests, likewise gives rise to periodical
daily breezes.
1. Variable winds are those which blow sometimes in one direction and
sometimes in another, alternately, without being subject toanylaw. In mean
latitudes the direction of the winds is very variable ; towards the poles this
irregularity increases, and under the arctic zone the winds frequently blow
from several points of the horizon at once. On the other hand, in approach-
ing the torrid zone they become more regular. The south-west wind prevails
in England, in the north of France, and in Germany ; in the south of France
the direction inclines towards the north, and in Spain and Italy the north
wind predominates.
1016. Law of the rotation of winds.—Notwithstanding the great irregu-
larity which characterises the direction of the winds in our latitude, it has
been ascertained that the wind has a preponderating tendency to veer round
according to the sun’s motion—that is, to pass from north, through north-east-
south-east to south, and so on round in the same direction from west to
north ; that it often makes a complete circuit in that direction, or more
than one in succession, occupying many days in doing so, but that it rarely
veers, and very rarely or never makes a complete circuit in the opposite
direction. This course of the winds is most regularly observed in winter.
According to Leverrier, the displacement of the north-east by the south-
west wind arises from the occurrence of a whirlwind formed upon the Gulf
Stream. For a station in south latitude a contrary law of rotation prevails.
This law, though more or less suspected for a long time, was first formally
enunciated and explained by Dove, and is known as Dove's law of rotation
of winds.
1017, Weather charts.—A considerable advance has been made in
weather forecasts by the frequent and systematic publication of weather
charts ; that is to say,smaps in which the barometric pressure, the tempe-
1062 M eleorology [1017-
rature, the force of the wind, &c., are expressed for considerable areas in an
exact and comprehensive manner. A careful study of such maps renders
possible a forecast of the weather for a day or more in advance. We can
here do no more than explain the meaning of the principal terms in use.
If lines are drawn through those places on the earth’s surface where the
corrected barometric height at a given time is the same, such lines are
called zsobarometric lines, or, more briefly, zsobaric lines, or zsobars. Between
any two points on the same isobar there is no difference of pressure.
Isobars are usually drawn for a difference of 2°5 mm. or of 34, of an inch.
If we take a horizontal line between two isobars, and at that point at
which the pressure is greatest draw a perpendicular line on any suitable
scale, which shall represent the dzference in pressure between the two places,
the line drawn from the top of this perpendicular to the lower isobar will
form an angle with the horizontal, and the steepness of this angle is a
measure of the fall in pressure between the two stations, and is called the
barometric gradient. Gradients are usually expressed in England and
America in hundredths of an inch of mercury for one degree of sixty nautical
miles, and on the Continent in millimetres for the same distance. The
closer are the isobars the steeper is the gradient, and the more powerful
the wind ; and though no exact numerical relationship can be proved to exist
between the steepness of the gradient and the force of the wind, it may
be taken that a gradient of about 6 represents a strong breeze; and a
gradient of 10, or a difference in pressure of ;4, of an inch for 60 miles,
is a stiff gale.
The direction of the wind is from the place of higher pressure to that of
lower, and in this respect the law of Buys Ballot may be mentioned, which
has been found to hold in all cases of the Northern Hemisphere, where
local configuration does not come into play. //f we stand with our back to
the wind, the line of lower pressure is on the left hand. ¥or places in the
Southern Hemisphere exactly the opposite law holds.
If within any area the pressure is lower, the wind blows round that area,
the place of lowest pressure being on the left. The direction of the wind is,
in short, contrary to that of the hands of a watch. Such acirculation is called
cyclonic ; it 1s that which is characteristic of the West Indian hurricanes,
which are known as cyclones. Conversely, the wind blows round an area of
higher pressure in the same direction as the hands of a watch ; and this cir-
culation is called azte-cyclonic.
Cyclonic systems are by far the most frequent, and are characterised by
steep gradients ; the air in them tends to move in towards the centre, and
thence to the upper regions of the atmosphere. They bring with them over
the greater part of the region which they cover much moisture, an abundance
of cloud, and heavy rain. An anti-cyclonic system has the opposite charac-
teristics : the gradients are slight, the wind is light, and moves with the hands
of a watch. The air is dry, so that there is but little cloud, and no rain.
Cyclonic systems, from the dampness of the air, produce warm weather in
winter, and cold wet weather in summer. Anti-cyclonic systems bring our
hardest frosts in winter and greatest heat in summer, as there is but little
moisture in the air to temper the extremes of climate. Both systems travel
over the earth’s surface—the cyclones rapidly, but the anti-cyclones more
slowly.
~1019] fogs and Mists 1063
1018. Fogs and Mists.—When aqueous vapour rising from a vessel of
boiling water diffuses in the colder air, it is condensed ; a sort of cloud is
formed, consisting of a number of small vesicles of water, which remain
suspended in the air. These are usually spoken of as vapour, yet they are
not so—at any rate, not in the physical sense of the word, for in reality they
are condensed vapour.
When this condensation of aqueous vapour is not occasioned by contact
with cold solid bodies, but takes place throughout large spaces of the atmo-
sphere, it constitutes fogs or mzs¢s, which, in fact, are essentially the same,
the appearance seen over a vessel of hot water.
A chief cause of fogs consists in the moist soil being at a higher tem-
perature than the air. The vapours which then ascend condense and become
visible. In all cases, however, the air must have reached its point of satura-
tion before condensation takes place. Fogs may also be produced when a
current of hot and moist air passes over a river at a lower temperature than
its own ; for then, the air being cooled as soon as it is saturated, the excess
of vapour present is condensed. The distinction between mists and fogs is
one of degree rather than of kind. A fog is a very thick mist.
By observations based on diffraction phenomena (660), the diameter of
fog vesicles has been found to vary from o’0154 to o’0521 mm.; the longer
the continuance of fine weather, the smaller are the vesicles ; before rains
they increase rapidly.
Dines, by direct microscopic measurement, found that the diameter of
fog particles varied with the same fog from o'o15 to 0127 mm. ; the larger
occur in dense fogs, in lighter fogs they sink to 070033. Kamtz found from
ool 4 to 0°035 mm.
When water is coated with a layer of coal-tar, it is prevented from
evaporating. Sir Edward Frankland ascribes the dry fog met with in
London to the large quantities of coal-tar and paraffine vapour which are
sent into the atmosphere, and which, condensing on the vesicles of fog, pre-
vent their evaporation.
Aitkin has shown that aqueous vapour never condenses unless some
liquid or solid is present on which it is deposited. Particles of dust in the
air are the nuclei for clouds and fogs. This he showed by passing steam
into filtered air; it remained quite clear, while a turbidity was produced
under the same circumstances in unfiltered air. The density of the cloud
was found to depend on the number of particles of dust in the air. A most
abundant source of dust is the combustion of coal. ‘The sulphur in the coal
in burning also forms sulphurous acid, which, though a gas, is found to act
as a nucleus.
1019. Clouds.—C/ouds are masses of vapour condensed into little drops
or vesicles of extreme minuteness, like fogs. There is no difference of kind
between fogs and clouds. Fogs are clouds resting on the ground. Toa
person enveloped in it, a cloud on a mountain appears like a fog. They
always result from the condensation of vapour which rises from the earth.
The horizontal base of a cloud denotes the layer of air in which the ascending
current of air has attained the dew-point. According to their appearance,
clouds were divided by Howard into four principal kinds : the zzdéus, the
stratus, the cumulus, and the cirrus.’ These four kinds are represented in
1064 Meteorology [1019—
fig. 1047, and are designated respectively by one, two, three, and four birds
on the wing.
The cirrus consists of small whitish clouds, which have a fibrous or
wispy appearance, and occupy the highest regions of the atmosphere. The
name of mares’ tails, by which they are generally known, well describes.
their appearance. From the low temperature of the spaces which they
occupy, it is certain that cirrus clouds consist of frozen particles ; and
hence it is that halos, coronz, and other optical appearances, produced by
refraction and reflection from ice-crystals, appear almost always in these
clouds and their derivatives. Their appearance often precedes a change of
weather.
The czzziZus are rounded spherical forms which look like mountains of
cotton wool piled one on the other. They are more frequent in summer
Fig. 1047
than in winter, and after being formed in the morning, they generally dis-
appear towards evening. If, on the contrary, they become more numerous,
and especially if surmounted by cirrus clouds, rain or storms may be expected.
Any such cumulus is nothing more than an ascending current of air which
makes its path visible by condensed aqueous vapour.
Stratus clouds consist of very large and continuous horizontal sheets,
which form chiefly at sunset and disappear at sunrise. They are frequent
in autumn and unusual in spring-time, and are lower than the preceding.
The wzmbus, or rain clouds, which are sometimes classed as one of the
fundamental varieties, are properly a combination of the three preceding
kinds. They affect no particular form, and are solely distinguished by a
uniform grey tint and by fringed edges. They are indicated on the right of
the figure by the presence of one bird.
-1020] formation of Clouds 1065
The fundamental forms pass into one another in the most varied manner.
Howard classed these transitional forms as c7rro-cumulus, ctrro-stratus,
and cumulo-stratus, and it is often very difficult to tell, from the appearance
of a cloud, which type it most resembles. The cirro-cumulus is most cha-
racteristically known as a ‘mackerel sky ;’ it consists of small roundish
masses, disposed with more or less irregularity. It is frequent in summer,
and attendant on warm and dry weather. Czrro-stratus appears to result
from the subsidence of the fibres of cirrus to a horizontal position, which
at the same time approach laterally. The form and relative position when
seen in the distance frequently give the idea of shoals of fish. The tendency
of cumutlo-stratus is to spread, settle down into the zzméus, and finally fall
as rain.
The height of clouds varies greatly ; in the mean it is from 1,300 to I,500
yards in winter, and from 3,300 to 4,300 yards in summer. But they often
exist at greater heights ; Gay-Lussac, in his balloon ascent, at a height of
7,030 yards, observed cirrus clouds above him, which appeared to be at a
considerable height. In Ethiopia, D’Abbadie observed storm-clouds whose
height was only 230 yards above the ground.
In order to explain the suspension of clouds in the atmosphere, Halley
first proposed the hypothesis of vesicular vapours. He supposed that clouds
are formed of an infinity of extremely minute vesicles, hollow, like soap-
bubbles filled with air, which are hotter than the surrounding air, so that
these vesicles float in the air like so many small balloons. Others assume
that clouds and fogs consist of extremely minute droplets of water, which are
retained in the atmosphere by the ascensional force of currents of hot air,
just as light powders are raised by the wind. Ordinarily, clouds do not
appear to descend, but this absence of downward motion is only apparent.
In fact, clouds do usually fall slowly, but then the lower part is continually
dissipated on coming in contact with the lower and more heated layers ; at
the same time the upper part is always increasing from the condensation of
new vapours, so that from these two actions clouds appear to retain the
same height.
1020. Formation of clouds.—Many causes may concur in the formation
of clouds.. The usual cause of the formation of a cloud is the ascent, into
higher regions of the atmosphere, of air laden with aqueous vapcur ; it
thereby expands, being under diminished pressure; and in consequence
of this expansion it is cooled, and this cooling produces a condensation of
vapour. Hence it is that high mountains, stopping the currents of air and
forcing them to rise, are an abundant source of rain. If the air is quite dry,
its temperature would be one degree lower for every 300 metres. The case
is different with moist air ; for when the air has ascended so high that its
temperature has fallen to the dew-point, aqueous vapour is condensed, and
in consequence of this heat is liberated ; when the dew-point is thus attained,
and the air is saturated, the cooling due to the ascent and expansion of air
is counteracted by this liberation of latent heat, so that the diminution of
temperature with the height 1s considerably slower in the case of moist than
of dry air. About one-half of the entire quantity of moisture in the air is
contained in the first six or seven thousand feet upon the ground.
The following calculation will give us the quantity of water separated
1066 Meteorology [1020—
in a given case: Suppose air at a temperature of 20° to be saturated with
aqueous vapour at that temperature ; the pressure of the vapour will be 17:4
mm., and the weight contained in one cubic metre of air 17°1 grammes.
If the air has risen to a height of 3,500 metres, it has come under a
pressure which is only % of what it was: its temperature is 4°, and its
volume about r$ times what it originally was. As it remains saturated the
pressure will be 6:1 mm., and the quantity of vapour will be 6:4 grammes
in a cubic metre—that is to say, 6°4 x 15 =9°6 grammes in the whole mass of
what was originally a cubic metre. The pressure of aqueous vapour has
sunk during the ascent from 17°4 mm. to 6°I mm., and its weight from 17°!
grammes to 9°6 grammes; that is, a weight of 7°5 grammes has been deposited
from the mass of air which at the sea-level occupied a space of one cubic
metre. These 7°5 grammes are in the form of the small droplets which
constitute fogs or clouds.
If the mass of air has risen to a height of 8,500 metres, where the pres-
sure is only one-third that on the sea-level, the temperature is — 28°, and
the space it occupies three times. as great as at first. The prescure of
aqueous vapour is 0’°5 mm., and its weight o°6 gramme ina cubic metre.
Hence there is now only 1°8 gramme left of the entire quantity of aque-
ous vapour originally present, and the remaining 15°3 grammes would be
separated as water orice. A similar calculation will show that at a height
of 4,200 metres, where the temperature is zero and the pressure 2, the quan-
tity of water present in the original cubic metre is only 0°82 gramme, the
rest being deposited.
Thus, a mass of air which, at the sea-level, occupies a space of a cubic
metre, and is saturated with aqueous vapour at 20°, and then contains 17°1
grammes, will contain only 9°6 grammes at a height of 3°500 metres, 8°2
grammes at 4,200 metres, and 1°8 gramme at 8,500 metres. Hence, while
a mass of air rises from the sea-level to a height of 4,200 feet, 8-9 grammes
of aqueous vapour are separated as cloud-vesicles ; at 8,500 metres, or about
double the height, 6:4 grammes are separated in the form of ice.
A hot moist current of.air mixing with a colder current undergoes a
cooling, which brings about a condensation of the vapour. Thus, the hot
and moist winds of the south and south-west, mixing with the colder air of
our latitudes, give rain. The winds of the north and north-east tend also,
in mixing with our atmosphere, to condense the vapours ; but as these winds,
owing to their low temperature, are very dry, the mixture rarely attains
saturation, and generally gives no rain.
The formation of clouds in this way is thus explained by Hutton. The
pressure of aqueous vapour, and therewith the quantity present in a given
space when saturated, diminishes according to a geometrical progression,
while the temperature falls in arithmetical progression, and therefore the
elasticity of the vapour present at any time is reduced by a fall of tempera-
ture more rapidly than in direct proportion to the fall. Hence, if a current
of warm air, saturated with aqueous vapour, meets a current of cold air also
saturated, the air acquires the mean temperature of the two, but can retain
only a portion of the vapour in the invisible condition, and a cloud or mist
is formed. Thus, suppose a cubic metre of air at 10° C. mixes with a cubic
metre of air at 20° C., and that they are respectively saturated with aqueous
-1021} Rain 1067
vapour. By formula (408) it is easily calculated that the weight of water
contained in the cubic metre of air at 10° C. is 9,397 grammes, and in that
at 20° C. is 17°153 grammes, or 26°559 grammes in all. When mixed they
produce two cubic metres of air at 15° C.; but as the weight of water
required to saturate this is only 2 x 12°8=25°6 grammes, the excess, 0°95
gramme, will be deposited in the form of mist or clouds.
1021. Rain.—When the individual vapour-vesicles become larger and
heavier by the condensation of aqueous vapour, and when, finally, individual
vesicles unite, they form regular drops, which fall as raz.
The quantity of rain which falls annually in any given place, or the annual
rainfall, is measured by means of a vatu-gauge, or pluviometer. Ordinarily
it consists of a cylindrical vessel,
M (figs. 1048 and 1049), closed
at the top by a funnel-shaped
lid, in which there is a very
small hole, through which the
rain falls. At the bottom of the
vessel is a glass tube, A, in
which the water rises to the
same height as inside the rain-
gauge, and is measured by a
scale on the side, as shown in
the figures.
The apparatus being placed
in an exposed situation, if at the
end of a month the height of water in the tube is two inches, for example,
it shows that the water has attained this height in the vessel, and, conse-
quently, that a layer of two inches in depth expresses the quantity of rain
which this extent of surface has received.
It has been noticed that the quantity of rain indicated by the rain-gauge is
greater the nearer this instrument is to the ground. This has been ascribed
to the fact that the raindrops, which are generally colder than the layers of
air which they traverse, condense the vapour in these layers, and therefore
constantly increase in volume. Hence more rain falls on the surface of the
ground than at a certain height. But it has been objected that the excess
of the quantity of rain which falls, over that at a certain height, is six or
seven times that which could arise from condensation, even during the whole
course of the raindrops from the clouds to the earth. The difference must
therefore be ascribed to purely local causes, and it is now assumed that the
difference arises from eddies produced in the air about the rain-gauge, which
are more perceptible the higher it is above the ground : as these eddies dis-
perse the drops which would otherwise fall into the instrument, they diminish
the quantity of water which it receives.
In any case it is clear that, if raindrops traverse moist air, they will, from
their lower temperature, condense aqueous vapour and increase in volume.
If, on the contrary, they traverse dry air, the drops tend to vaporise, and less
rain falls than at a certain height; it might even happen that the rain did
not reach the earth.
From measurements of the coronze (1019), Delezenne determined the
EZ ee
YL ty Yj
Fig. 1049
1068 Meteorology f1021-
diameter of the globules in the case of rain-clouds just about to fall, and in
the case of the cloud from a low-pressure steam-engine (481). The former
was found to vary from 0°0565 to 070226 mm., and the latter from 0'0051 to
0'0042 mm. With the former, 5,500 droplets would be needed to make a
drop of water a millimetre in diameter, and with the latter 50,000.
According to the same author, there would be about 15 mgr. of globules in
a cubic metre of a cloud which produced a rainfall of to mm. of water in an
hour. With this number the mean distances of the vesicles with the above
magnitudes are respectively 1°845, 0°706, 0°167, and o'148 mm.
Many local circumstances may affect the quantity of rain which falls in
different countries ; but, other things being equal, most rain falls in hot cli-
mates, for there the vaporisation is most abundant. The rainfall decreases,
in fact, from the equator to the poles. At London it is 23°5 inches; at
Bordeaux it is 25°8; at Madeira it is 27°7; at Havannah it is 91°2; and at
St. Domingo it is 107°6. The quantity varies with the season : in Paris, in
winter, it is 4°2 inches ; 1n spring, 6°9 ; in summer, 6°3 ; and in autumn, 4°8
inches. The heaviest annual rainfall at any place on the globe is on the
Khasi Hills, in Bengal, where it is 600 inches ; of which 500 inches fall in
seven months. On July 1, 1851, a rainfall of 254 inches on one day was
observed at Cherrapoonjee. At Kurrachee, in the north-west of India, the
rainfall is only 7 inches.
The rainfall diminishes with the height of a station above the sea-level at
the rate of 3 or 4 per cent. for each 100 feet of altitude above the sea.
The driest recorded place in England is Lincoln, where the mean rainfall
is 20 inches ; and the wettest is Stye, at the head of Borrowdale, in Cumber-
land, where it amounts to165 inches. The greatest average amount of rain-
fall in any one day, taking the means of all stations, is 14 inch; though
individual stations far exceed this amount, sometimes reaching 4 inches.
An inch of rain on a square yard of surface expresses a fall of 46°74
pounds, or 4°67 gallons. On an acre it corresponds to 22,622 gallons, or
100°9935 tons. 100 dons fer inch per acre isa ready way of remembering
this.
1022. Waterspouts.—On hot summer days, and when the weather is
otherwise calm, we often notice sand and dust carried forward in a column
with a whirling motion. As storms come on, larger whirlwinds of this kind
are formed, which carry with them leaves, straw, and even small branches.
When they are of larger dimensions they form real whirlwinds. They are
probably due to the contact of two winds blowing in the upper regions of the
atmosphere. When they pass over land they form large conical-shaped
masses of dust, which make them visible at a distance; when they pass
over rivers or the sea they present a curious phenomenon: the water is
disturbed, and rises in the form of a cone, while the clouds are depressed
in the form of an inverted cone; the two cones then unite and form a
continuous column from the sea to the clouds (fig. 1050). Even, however,
on the high seas the water of these waterspouts is never salt, proving
that they are formed of condensed vapour, and not of sea-water raised by
aspiration.
1023. Influence of aqueous vapour on climate.—Tyndall applied the
property possessed by aqueous vapour of powerfully absorbing and radiating
-1023]. lnfluence of Aqueous Vapour on Climate 1069
heat to the explanation of some obscure points in meteorology. He esta-
blished the fact that in a tube 4 feet long the atmospheric vapour on a day of
average dryness absorbs Io per cent. of obscure heat. With the earth warmed
by the sun as a source, at the very least Io per cent. of its heat is intercepted
within 10 feet of the surface. The absorption and radiation of aqueous
vapour is more than 16,000 times that possessed by dry air.
The radiative power of aqueous vapour may be the main cause of the
torrent-like rains that occur in the tropics, and also of the formation of
cumulus clouds in our own latitudes. The same property probably causes
the descent of very fine rain, called sévezz, which has more the characteristics
of falling dew, as it appears a short time after sunset, when the sky is clear ;
its production has therefore been attributed to the cold resulting from the
Fig. 1050
radiation of the air. It is not the air, however, but the aqueous vapour in
the air, which by its own radiation chills itself, so that it condenses into
SCrein.
The absorbent power of aqueous vapour is of even greater importance.
Whenever the air is dry, terrestrial radiation at night is so rapid as to cause
intense cold. Thus, in the central parts of Asia, Africa, and Australia, the
daily range of the thermometer is enormous; in the interior of the last-
named continent a difference in temperature of no less than 40° C, has been
recorded within 24 hours. In India, and even in the Sahara, ice has been
formed at night, owing to the copious radiation. But the heat which aqueous
vapour absorbs most largely is of the kind emitted from sources of low
temperature ; it is to a large extent transparent to the heat emitted from the
sun, whilst it is almost opaque to the heat radiated from the earth. Con-
1070 Meteorology [1023-
sequently, the solar rays penetrate our atmosphere with a loss, as estimated
by Pouillet, of only 25 per cent., when directed vertically downwards, but
after warming the earth they cannot retraverse the atmosphere. Through
thus preventing the escape of terrestrial heat, the aqueous vapour in the air
moderates the extreme chilling which is due to the unchecked radiation from
the earth, and raises the temperature of that region over which it is spread.
In Tyndall’s words, ‘aqueous vapour is a blanket more necessary to the
vegetable life of England than clothing is to man. Remove for a single
summer night the aqueous vapour from the air which overspreads this
country, and every plant capable of being destroyed by a freezing tempera-
ture would perish. The warmth of our fields and gardens would pour itself
unrequited into space, and the sun would rise upon an island held fast in the
iron grip of frost.’
1024. Tyndall’s researches.—Tyndall found that the action of the sun or of
the electric light decomposed certain highly rarefied vapours. He used a glass
tube, which could be exhausted and then filled with air charged with the va-
pours of volatile liquids, by allowing the air to bubble through small Wolff
bottles containing them. By mixing the air charged with vapour with differ-
ent proportions of pure air, and by varying the degrees of exhaustion, it was
possible to have a vapour under any degree of attenuation. The tube could
also be filled with the vapour ofa liquid alone. The tube having been filled with
air charged with vapour of amyl nitrite,a somewhat convergent beam from
the electric lamp was passed intothe tube. Fora moment the tube appeared
optically empty, but suddenly a shower of liquid spherules was precipitated
on the path of the beam, forming a luminous white cloud. The nature of
the substance thus precipitated was not specially investigated. This effect
was not due to any chemical action between the vapour and the air, for
when either dry oxygen or dry hydrogen was used instead of air, or when
the vapour was admitted alone, the effect was substantially the same. Nor
was it due to any heating effect, for the beam had been previously sifted by
passing through a solution of alum, and through the thick glass of the lens.
The unsifted beam produced the same effect ; the obscure calorific rays did
not seem to affect the result. The sun’s light also effects the decomposition
of amyl nitrite vapour ; and this decomposition was found to be mainly due
to the more refrangible rays. When the electric light, before entering the
experimental tube, was made to pass through a layer of liquid amy] nitrite
an eighth of an inch in thickness, the luminous effect was not appreciably
diminished, but the chemical action was almost entirely stopped. Thus,
that special constituent of the luminous radiation which effects the decom-
position of the vapour is absorbed by the liquid. The decomposition of
liquid amyl nitrite by light, if it take place at all, is far less rapid and
distinct than that of the vapour. The absorption is the same, whether the
nitrite is in the liquid or in the vaporous state, showing that it is not the act
of the molecule as a whole, but that it is atomic ; that is, that it is to the atoms
that the peculiar rate of vibration is transferred which brings about the
decomposition of the body.
It was also found that a vapour which when alone resists the action of
light may, by being associated with another gas or vapour, exhibit a vigorous
action.. Thus, when the tube was filled with atmospheric air, mixed with
—1024] Tyndall’s Researches 1071
butyl nitrite vapour, the electric light produced very little effect ; but with
half an atmosphere of this mixture, and half an atmosphere of air which had
passed through hydrochloric acid, the action of the light was almost instan-
taneous. In another case, mixed air and butyl nitrite vapour were passed
into the tube so that the mixture was under a pressure of 2°5 mm. Air passed
through aqueous hydrochloric acid was introduced until the pressure was
3 inches. The condensed beam passed through at first without change, but
afterwards a superb blue cloud was formed.
In cases where the vapours are under a sufficient degree of attenuation,
whatever otherwise be their nature, the visible action commences with the
formation of a blue cloud. The term ‘cloud,’ however, must not be understood
in its ordinary sense ; the blue cloud is invisible in ordinary daylight, and
to be seen must be surrounded by darkness, z¢ a/ome being illuminated by a
powerful beam of light. The blue cloud differs in many important particulars
from the finest ordinary clouds, and may be considered to occupy an inter-
mediate position between these clouds and true cloudless vapour.
By graduating the quantity of vapour, the precipitation may be obtained
of any required degree of fineness ; forming either particles distinguishable
by the naked eye, or particles beyond the reach of the highest microscopic
power. ‘The case is similar to that of carbonic acid gas, which, diffused in
the atmosphere, resists the decomposing action of solar light, but is decom-
posed when in contact with the chlorophyll in the leaves of plants.
When the blue cloud produced in these experiments was examined by
any polarising arrangement, the light emitted laterally from the beam—that .
is, in the direction at right angles to its axis—was found to be perfectly polar-
ised. This phenomenon was observed in its greatest perfection the more
perfect the blue of the cloud. It is produced by any particles, provided they
are sufficiently fine. This is quite analogous to the light of the blue sky.
When this is examined by a Nicol’s prism, or any other analyser, it is found
that the light emitted at mght angles to the path of the sun’s rays is
polarised.
The phenomena of the firmamental blue, and the polarisation of the
sky-light, thus find definite explanations in these experiments. We need only
assume the existence, in the higher regions of the atmosphere, of excessively
fine particles of water; for particles of any kind produce this effect. It
is easy to conceive the existence of such particles in the higher regions,
even on a hot summer’s day. For the vapour must there be in a state of
extreme attenuation ; and inasmuch as the oxygen and nitrogen of the atmo-
sphere behave like a vacuum to radiant heat, the extremely attenuated
particles of aqueous vapour are practically in contact with the absolute cold
of space.
‘ Suppose the atmosphere surrounded by an envelope impervious to light
but with an aperture on the sunward side, through which a parallel beam, of
solar light could enter and traverse the atmosphere. Surrounded on all
sides by air not directly illuminated, the track of such a beam would resemble
that of the parallel beam of the electric light through an incipient cloud.
The sunbeam would be blue, and it would discharge light laterally in the
same condition as that discharged by the incipient cloud. The azure revealed
by such a beam would be to all intents and purposes a blue cloud,’
1072 Meteorology [1025-
1025. Dew. Hoarfrost.—Dew is aqueous vapour which has condensed
on bodies during the night in the form of minute globules. It is occasioned
by the chilling which bodies near the surface of the earth experience’ in
consequence of nocturnal radiation. Their temperature having then sunk
several degrees below that of the air, it frequently happens, especially in hot
seasons, that this temperature is below that at which the atmosphere is
saturated. The layer of air which is immediately in contact with the chilled
bodies, and which has virtually the same temperature, then deposits a por-
' tion of the vapour which it contains (401) ; just as when a bottle of cold water
is brought into a warm room it becomes covered with moisture, owing to
the condensation of aqueous vapour upon it.
According to this theory, which was first propounded by Dr. Wells, all
causes which promote the cooling of bodies increase the quantity of dew.
These causes are the emissive power of bodies, the state of the sky, and the
agitation of the air. Bodies which have a great radiating power more readily
become cool, and therefore ought to condense more vapour. In fact there
is generally no deposit of dew on metals, whose radiating power is very
small, especially when they are polished ; while the ground, sand, glass, and
plants, which have a great radiating power, become abundantly covered
with dew.
The state of the sky also exercises a great influence on the formation of
dew. If the sky is cloudless, the planetary spaces send to the earth an in-
appreciable quantity of heat, while the earth radiates very considerably, and
therefore, becoming very much chilled, there is an abundant deposit of dew.
But if there are clouds, as their temperature is far higher than that of the
planetary spaces, they radiate in turn towards the earth, and as bodies on the
surface of the earth experience only a feeble chilling, no deposit of dew takes
place.
Wind also influences the quantity of vapour deposited. If it is feeble, it
increases it, inasmuch as it renews the air; if it is strong, it diminishes it,
as it heats the body by contact, and thus does not allow the air time to
become cooled, Finally, the deposit of dew is more abundant according as
the air is moister, for then it is nearer its point of saturation.
Hoarfrost and rime are dew which has been deposited on bodies cooled
below zero, and has become frozen. The flocculent form which the small
crystals present of which rime is formed, shows that the vapour solidifies
directly without passing through the liquid state. Hoarfrost, like dew, is
formed on bodies which radiate most, such as the stalks and leaves of vege-
tables, and is chiefly deposited on the parts turned towards the sky.
We must distinguish between the dew formed in consequence of lowering
of temperature by radiation, and the deposit formed by warm moist air
passing over a cold wall ; in mild weather this deposit forms a liquid, and in
severe weather a snow or icy coating. Unlike dew, a deposit of this kind is
most abundantly found on good conductors, for they are the coldest.
1026, Snow. Sleet.—Svzow is water solidified in stellate crystals, vari-
ously modified, and floating in the atmosphere. These crystals arise from
the congelation of the minute vesicles which constitute the clouds, when the
temperature of the latter is below zero. They are more regular when formed
inacalm atmosphere. Their form may be investigated when they are collected
—1028] Hail 1073
on a black surface and viewed through a strong lens. The regularity, and
at the same time variety, of their forms are truly beautiful. Fig. 1051
shows some of these forms as seen through a microscope. Very roughly, a
fall of one foot of snow may be taken as equal to an inch of rain.
It snows most in countries near the poles, or lying high above the
sea-level. By the limit of perpetual snow—or, briefly szow-/¢me—is meant that
‘height above the sea-level at which the snow does not melt, even in the
hottest summers. It is lower nearer the poles than the equator : it does not
depend solely on the latitude, but is influenced by many local circumstances.
Steet is also solidified water, and consists of small icy needles pressed
together in a confused manner. Its formation is ascribed to the sudden
congelation of the minute globules of the clouds in an agitated atmosphere.
Fig. 1051
When the ground is cooled below zero after severe frost and a thaw sets
in, the moist air passing over the ground deposits its moisture, which is
converted into a continuous sheet of ice ; this is known as glazed frost (the
French verg/as) ; it may also occur when raindrops which have been cooled
below zero in the higher regions of the air, and are accordingly in a state of
superfusion (349), fall on the ground, which may even be above the freezing-
point.
1027. Hail.—/az/ is a mass of compact globules of ice of different sizes
which fall in the atmosphere. In our climate hail falls principally during
spring and summer, and at the hottest times of the day; it rarely falls at
night. The fall of hail is always preceded by a peculiar noise.
Hail is generally the precursor of storms ; it rarely accompanies them,
and follows them still more rarely. Hail falls from the size of a small pea to
that of an egg or an orange, with a core of compressed snow which is sur-
rounded by concentric layers of ice. While snowstorms may last for days,
hailstorms do not last for more than a quarter of an hour. The formation
of hailstones has never been altogether satisfactorily accounted for; nor,
more especially, their great size.
1028. Ice. Regelation.—Ice is an aggregation of snow-crystals, such as
are shown in fig. 105% The transparency of ice is due to the close contact
32
1074 Meteorology [1028—
of these crystals, which causes the individual particles to blend into an un-
broken mass, and renders the substance of¢ically, as well as mechanically,
continuous. When large masses of ice slowly melt away, a crystalline form
is sometimes seen by the gradual disintegration into rude hexagonal prisms ;
a similar structure is frequently met with, but in greater perfection, in the
ice-caves or glaciers of cold regions.
An experiment of Tyndall shows the beautiful structure of ice. When a
piece of ice is cut parallel to its planes of freezing, and the radiation from
any source of light 1s permitted to pass through it, the disintegration of the
substance proceeds in a remarkable way. By observing the plate of ice
through a lens, numerous small crystals will be seen studding the interior of
the block ; as the heat continues these crystals expand, and finally assume
the shape of six-rayed stars of exquisite beauty.
This is a kind of negative crystallisation, the crystals produced being
composed of water; they owe their formation to the molecular disturbance
caused by the absorption of heat from the source. Nothing is easier than to
reproduce this phenomenon, if care be taken in cutting the ice. The planes
of freezing can be found by noting the direction of the bubbles in ice, which
are either sparsely arranged in striz at right angles to the surface, or thickly
collected in beds parallel to the surface of the water. A warm and smooth
metal plate should be used to level and reduce the ice to a slab not exceed-
ing half an inch in thickness.
A still more important property of ice remains to be noticed. Faraday
discovered that when two pieces of melting ice are pressed together they
freeze into one at their points of contact. This curious phenomenon is now
known under the name of Regelatzon. The cause of it has been the subject
of much controversy, but the simplest explanation seems to be that given by
its discoverer. The particles on the exterior of a block of ice are held by
cohesion on one side only: when the temperature is at o° C., these exterior
particles, being partly free, are the first to pass into the liquid state, anda film
of water covers the solid. But the particles in the interior of the block are
bounded on all sides by the solid ice, the force of cohesion is here a maximum,
and hence the interior ice has no tendency to pass into a liquid, even when
the whole mass is at 0°. If the block is now split in halves, a liquid film
instantly covers the fractured surfaces, for the force of cohesion on the
fractured surfaces has been lessened by the act. By placing the halves
together, so that their original position shall be regained, the liquid films on
the two fractured surfaces again become bounded by ice on both sides.
The film being excessively thin, the force of cohesion is able to act across
it ; the consequence of this is, the liquid particles pass back into the solid:
state, and the block is reunited by vegelation. Not only do ice and ice thus
freeze together, but regelation also takes place between moist ice and any
non-conducting solid body, as flannel or sawdust ; a similar explanation to
that just given has been applied here, substituting another solid for the ice
on one side. It must be remarked, however, that many eminent philosophers
dissent from the explanation here given.
Whatever may be the true cause of regelation, there can be no doubt that
this interesting observation of Faraday’s explains many natural phenomena.
For example, the formation of a snowball depends on the regelation of the
-1030] Glaciers 1075
snow-granules composing it; and as regelation cannot take place at tem-
peratures below o° C., for then both snow and ice are dry, it is only possible
to make a coherent snowball when the snow is melting.
The snow-bridges, also, which span wide chasms in the Alps and else-
where, and over which men can walk in safety, owe their existence to the
regelation of gradually accumulating particles of snow.
We see an example of this formation of ice from pressure in the glazed
appearance of the tracks in snow on roads over which heavy carts have
passed.
Bottomley has made a very instructive experiment which illustrates rege-
lation. A block of ice is suspended on two supports, and a fine piano wire
with heavy weights at each end 1s laid across it. After some time the wire
has slowly cut its way through, but the cut surfaces have reunited, and, except-
ing a few bubbles, show no trace of the operation ; the wire is below zero, as
is proved by placing it in cold water, upon which some ice forms round it.
1029. Glaciers.—Tyndall applied this regelating property of ice to an
explanation of the formation and motion of glaciers, of which the following
is a brief description: In elevated regions, the szow-lime (1026) marks the
boundary of eternal snow, for above this the heat of summer is unable to
melt the winter’s snow. By the heat of the sun and the consequent percola-
tion of water melted from the surface, the lower portions of the snow-field
are raised to o°C. ; at the same time this part is closely pressed together. by
the weight of the snow above ; regelation therefore sets in, converting the
loose snow into a coherent mass.
By increasing pressure the intermingled air which renders snow opaque
becomes ejected and the snow becomes transparent ; ice is then formed.
Its own weight and the pressure from behind urge downwards the glacier
which has thus been formed. In its descent the glacier behaves like a river,
passing through narrow gorges with a certain velocity, and then spreading
out and moving more slowly as its bed widens. Further, just as the central
portions of a river move faster than the sides, so Forbes ascertained that the
centre of a glacier moves more quickly than its margin, and from the same
reason (the difference in the friction encountered) the surface moves more
rapidly than the bottom. To explain these facts Forbes assumed ice to be a
viscous body capable of flexure, and flowing like lava ; but asice has not the
properties of a viscous substance, the now generally accepted explanation of
glacier motion is that supplied by the theory of regelation. According to
this theory, the brittle ice of the glacier is crushed and broken in its passage
through narrow channels, such as that of Trélaporte on Mont Blanc; and
then, as it emerges from the gorge which confined it, becomes reunited by
virtue of regelation ; in this instance forming the well-known Mer de Glace.
By numerous experiments Tyndall established that regelation is adequate
to furnish this explanation, and artificially imitated, on a small scale, the
moulding of glaciers by the crushing and subsequent regelation of ice.
1030. Atmospheric electricity. | Franklin’s experiment.—The most
frequent luminous phenomena, and the most remarkable for their effects,
are those produced by the free electricity in the atmosphere. The first
physicists who observed the electric spark compared it to the gleam of
lightning, and its crackling to the sound of thunder. But Franklin, by the
Ese:
1076 Meteorology | [1030-
aid of powertul Leyden batteries, first established a complete parallelism
between lightning and electricity; and indicated, in a memoir published
in 1749, the experiments necessary to attract electricity from the clouds by
means of pointed rods. The experiment was tried by
Dalibard in France ; and Franklin, pending the erec-
tion of a pointed rod on a spire in Philadelphia, had the
happy idea of flying a kite, provided with a metal
point, which could reach the higher regions of the
atmosphere. In June, 1752, during stormy weather,
he flew the kite in a field near Philadelphia. The
kite was flown with ordinary packthread, at the end
of which Franklin attached a key, and to the key a
silk cord, in order to insulate the apparatus ; he then
fixed the silk cord to a tree, and having presented
his hand to the key, at first he obtained no spark.
He was beginning to despair of success, when, rain
having fallen, the cord became a good conductor, and
a spark passed. Franklin, in his letters, describes his |
emotion on witnessing the success of the experiment as
being so great that he could not refrain from tears.
Franklin imagined that the kite drew from the
cloud its electricity ; it is, in fact, a simple case of
induction, and depends on the inductive action which
the thunder-cloud exerts upon the kite and the cord.
1031. Apparatus to investigate the electricity of
the atmosphere.—To observe the electricity in fine
weather, when the quantity is generally small, an ap-
paratus may be used as devised by Saussure for this
kind of investigation. It is an electroscope similar to
that already described (774), but the rod to which the
gold leaves are fixed is surmounted by a conductor
2 feet in length, and terminates in either a knob or
a point (fig. 1052). To protect the apparatus against
rain, it is covered with a metal shield 4 inches in
diameter. The glass case is square instead of being round, and a divided
scale on its inside face indicates the divergence of the gold leaves. This
electrometer gives signs of atmospheric electricity only as long as it is
raised in the atmosphere so that its pointed end is in layers of air of different
electrical potential from its own.
To ascertain the electricity of the atmosphere Saussure also used a
covver ball, which he projected vertically with his hand. This ball was
fixed to one end of a metal wire, the other end of which was attached to
a ring, which could glide along the conductor of the electrometer. From
the divergence of the gold leaves, the electrical condition of the air at
the height which the ball attained could be determined. Becquerel, in ex-
periments made on the St. Bernard, improved Saussure’s apparatus: by
substituting for the knob an arrow, which was projected into the atmosphere
by means of a bow. A gilt silk thread, 88 yards long, was fixed with one end
to the arrow, while the other end was attached to the stem of an electro-
-1031] Apparatus to investigate Atmospheric Electricity 1077
scope. Peltier used a gold-leaf electroscope, at the top of which was a
somewhat large copper globe. Provided with this instrument, the observer
places himself in a prominent position ; it is then quite sufficient to raise the
electroscope even a foot or so to obtain signs of electricity.
To observe the electricity of clouds, where the potential is very con-
siderable, use is made of a long bar terminating in a point. This bar,
which is insulated with care, is fixed to the summit of a building, and its
lower end is connected with an electrometer, or even with electric chimes
(fig. 738), which announce the presence of thunder-clouds. As, however, the
bar can then give dangerous shocks, a metal ball must be placed near it,
which is well connected with the ground, and which is nearer the bar than
Fig. 1053
the observer himself; so that if a discharge should ensue, it will strike
the ball, and not the observer. Richmann, of St. Petersburg, was killed in an
experiment of this kind, by a discharge which struck him on the forehead.
Sometimes also captive balloons or kites have been used, provided with
a point, and connected by means of a gilt cord with an electrometer.
A good collector of atmospheric electricity consists of a fishing-rod with
an insulated handle which projects from an upper window. At the top is
a bit of lighted tinder held in a metallic forceps, the smoke of which, being
an excellent conductor, conveys the electricity of the air downa wire attached
to the rod. A sponge moistened with alcohol, and set on fire, is also an
excellent conductor.
A convenient instrument for investigating atmospheric electricity was
introduced by Lord Kelvin, one form of which, used in the Meteorological
Observatory of Montseuris, is represented in fig. 1053. It consists of a
large metal vessel, A, resting on three insulating glass legs fixed to the top
1078 Meteorology [1031-
of a tall column of cast iron. A sheet-metal mantle, B, protects the supports
from the rain. The apparatus is arranged in the open, and can be filled
with water from a pipe, C. The water issues through a long lateral jet
in A, in a stream so fine that the volume of the water is not appreciably
altered. An insulated wire, z, passing through the column, connects the vessel
A with an electrometer placed indoors. This plan of collecting the atmo-
spheric electricity is adopted in balloons, where a flame, for instance, is out of
the question.
The manner in which the electricity of the atmosphere is registered is seen
from fig. 1054, which represents the form in use at the above observatory.
In a light-tight box is a band of sensitised photographic paper, stretched on
the surface of a cylinder and moved by clockwork.
AES ATT
awa)
Fig. 1054
In one side of the box is a long cylindrical glass lens, in front of which
at E are two quadrant electrometers (802). Both of these are connected with
the same collector of electricity, placed outside, and their sectors are charged
by the same source of electricity, but one of them is ten times as sensitive
as the other. Near one side of the box is a gas-burner with an opaque
chimney, A, in two opposite sides of which are longitudinal slits, through
which the light passes to two total-reflection prisms (557), # Z’, which are
arranged so as to send two pencils of light on the mirrors, 7 mz’, of the
electrometer. This is shown on a larger scale on the left of the figure: the
two pencils fall upon the lens, L, which concentrates in a point the slices of
light issuing from the chimney and reflected from the mirror. These follow
1032] Ordinary Electricity of the Atmosphere 1079
the motion of the mirror, and thus impress on the sensitive paper the curves
of electrical potential of the air. There is also an arrangement by which an
electromagnet puts the electrometers to earth for a few minutes at every
hour, and thus discharges them. The mirrors revert then to their original
position and commence a new trace.
If we replace the electrometer with its mirror attached by a magneto-
meter, we can easily see how the variations in the magnetic declination may
be recorded (716).
1032. Ordinary electricity of the atmosphere.—-By means of the dif-
ferent apparatus which have been described, it has been found that the
presence of electricity in the atmosphere is not confined to stormy weather,
but that the atmosphere always contains free electricity, in the vast majority
of cases positive, but occasionally negative. When the sky is unclouded
the potential is always positive, and it increases with the height above the
ground. Its value is greatest in the highest and most isolated places.
No trace of positive electricity is found in houses, streets, and under trees ;
in towns, positive electricity is most perceptible in large open spaces, on
quays, or on bridges. Lord Kelvin found in the Isle of Arran, at a height of
9 feet above the ground, a difference of potential equal to 200 to 400 Daniell’s
elements, or from 216 to 432 volts. This represents a rise of potential of
from 24 to 48 volts for each foot of ascent. This is subject to great varia-
tion ; with winds from the north and north-east the potential was often six to
ten times as much as the higher of these amounts. The change of potential
is most rapid in cold dry weather, when the quantity of moisture in the air
is at its lowest. Thus, at a temperature of —8° to —12° C., Exner found a
change of 600 Daniells per metre in the direction of the vertical. Witha
vapour-pressure of 2°3 mm. the change was 325, with 6°8 it was 116, and
with 12°5 it was 68.
Between 5 and 7°30 A.M. the positive electricity in the air is at a mini-
mum ; it increases from 7 to 9.30 A.M., according to the season, and then
attains its first maximum. It then decreases rapidly until from 2.30 to
4.39 P.M., and again increases till it reaches its second maximum, from 6.30
to 9.30 P.M. ; the remainder of the night the electricity decreases until sun-
rise. Thus the greatest amount of electricity is observed when the baro-
metric pressure is highest. These increasing and decreasing periods, which
are observed all the year, are more perceptible when the sky is clearer
and the weather more settled. The positive electricity of fine weather is
much stronger in winter than in summer. It may, in short, be said that
electricity of the air follows the opposite course to that of temperature and
moisture.
When the sky is clouded, the electricity is sometimes positive and some-
times negative. According to Palmieri, the occurrence of negative electricity
is a certain indication that within a distance of 4o miles it either rains,
or snows, or hails. It often happens that the electricity changes its sign
several times in the course of the day, owing to the passage of an electrified
cloud. During storms, and when it rains or snows, the atmosphere may be
positively electrified oneday, and negatively the next, and the numbers of the
two sets of days are virtually equal.
1080 Meteorology [1032 -
During a thunderstorm the changes in potential and sign of electricity
are so rapid that the photographic method of registration fails.
From a long series of observations on the electricity of the atmosphere
made in the early morning, Dellman found that the electricity increased
with the density of the fog, but in a far more rapid ratio.
The electricity of the ground was found by Peltier to be always negative,
and this seems to be the cardinal fact in reference to atmospheric electricity ;
it is so, however, to different extents, according to the hygrometric state
and temperature of the air. The density is, moreover, exceedingly small,
being calculated at 0°00036 unit per square centimetre, from which it
follows: that the electrical pressure (759) is o'o0000082 dyne per square
centimetre, or less than the millionth of a milligramme in weight. Even if
the pressure were ten times as great, it would be insufficient to raise even
the lightest bodies.
1033. Causes of atmospheric electricity.—Although many hypotheses
have been propounded to explain the origin of atmospheric electricity, it
must be confessed that our knowledge is in an unsatisfactory state.
Volta first showed that the evaporation of water produced electricity.
Pouillet subsequently showed that no electricity is produced by the evapo-
ration of distilled water ; but that if an alkali or a salt is dissolved, even
in small quantity, the vapour is positively and the solution is negatively
electrified. The reverse is the case if the water contains acid. Hence it
has been assumed, that as the waters which exist on the surface of the earth
and on the sea always contain salt dissolved, the vapours disengaged ought
to be positively and the earth negatively electrified. The devolopment of
electricity by evaporation may be observed by heating strongly a platinum
dish, adding to it a small quantity of liquid, and placing it on the upper
plate of the condensing electroscope (fig. 758), taking care to connect the
lower plate with the ground. When the water of the capsule is evaporated,
the connection with the ground is broken, and the upper plate raised. The
gold leaves then diverge if the water contains salts, but remain quiescent
if the water is pure.
Reasoning from such experiments, Pouillet ascribed the development
of electricity by evaporation to the separation of particles of water from
the substances dissolved ; but Reich and Riess showed that the electricity
disengaged during evaporation could be attributed to the friction which
the particles of water carried away in the current of vapour exert against
the sides of the vessel, just as in Armstrong’s electrical machine (780). By
a series of experiments, Gaugain arrived at the same result.
Sohncke recalls an experiment of Faraday which he has repeated, showing
that the friction of minute vesicles of water against dry ice is an abundant
source of electricity ; he ascribes atmospheric electricity to this origin,
suggesting that in the upper regions particles of both water and ice may
coexist. ‘The ice particles become positively electrified, while those of water
are negative. When these fall in rain, they carry with them their negative
electricity. A similar theory has been propounded by Luvini.
1034. Electricity of clouds.—Clouds are in general electrified usually
positively, but sometimes negatively, and differ only in their higher or
lower potential. The formation of positive clouds is by some ascribed to
—1035] Lightning 1081
the vapour disengaged from the ground and condensed in the higher
regions. Negative clouds are supposed to result from fogs, which, by their
contact with the ground, become charged with negative electricity, which
they retain on rising into the atmosphere ; or to have been separated from
the ground by layers of moist air, and negatively electrified by induction
from the positive clouds, which have repelled into the ground positive
electricity. Thunder-clouds are sometimes as low as 700 to 1,000 feet ;
but their usual height appears to be 3,000 to 6,000 feet.
Whatever be the origin of atmospheric electricity, there can be no
doubt that the invisible aqueous vapour is the carrier of it, and it is
easy to explain the high potential of clouds from the condensation of this
vapour. For suppose 1,000 vapour-particles, each possessing the same
charge of electricity, coalesce to form a single droplet, the diameter of such
a droplet will be ten times that of the individual particles—that is, its
capacity is ten times as great, since the capacity is equal to the radius
(762) ; but the quantity of electricity will be I,ooo times as great as on
the small one, and therefore the potential will be 100 times as great.
Now the number of vapour-particles which go to form a single droplet is
rather to be counted by billions ; hence, however small be the finite value
which we assign to the potential of the electricity of the vapour-particles,
that of the drops will be enormously pico and sufficient to account
for the high potential of clouds.
1035. Lightning.—This, as is well known, is the dazzling light emitted by
the electric spark when it shoots from blonds charged with electricity. In
the lower regions of the atmosphere the light is white, but in the higher
regions, where the air is more rarefied, it takes a somewhat reddish tint ; as
does the spark of the electrical machine in a rarefied medium (808).
The flashes of lightning are often more than a mile, and sometimes
extend to four or five miles, in:length ; they generally pass through the
atmosphere in a zigzag direction—a phenomenon ascribed to the resistance
offered by the air condensed by the passage of a strong discharge. The
spark then diverges from a right line, and takes the direction of least resist-
ance. In avacuum, electricity passes in a straight line.
De la Rue and Miiller have calculated that the potential required
to produce a flash a mile in length would be that of 3,516,480 of their
cells (833).
We cannot, however, regard the length of a lightning flash as the direct
striking distance between two conductors. Owing to the number of droplets
met on its path, the discharge is rather to be compared with that of the
luminous tubes and panes (811). ‘The experiments of Mascart on the rela-
tion between the striking distance (810) and the potential required to pro-
duce it, show that the striking distance increases far more rapidly than the
potential. Thus, while the potential required for a striking distance of 1 cm.
is represented by 8°3, for 4 cm. it iS 15:9, for 8 cm. 20°5, and for 15 cm.
233. From this it is possible that a lightning discharge is produced by a
difference of potentials between two clouds which is not greatly out of
proportion with those obtained by our electrical machines.
Several kinds of lightning flashes may be distinguished—1, the zigzag
flashes, which move with extreme velocity in the form of a line of fire with
1082 Meteorology ay [1035-
sharp outlines, closely resembling the spark of an electrical machine. The
recent investigation of the shape of lightning discharges by means of extra
rapid photographic dry plates (622) has shown that the path of a dis-
charge is not so sharply zigzag as is usually represented, but has more the
shape of the course of a river as shown on a map, and with frequent branch-
ings; 2, the see¢ flashes, which, instead of being linear, like the preceding,
fill the entire horizon without having any distinct shape. This kind, which
is most frequent, appears to be produced in the cloud itself, and to illuminate
the mass. According to Kundt, the number of sheet discharges is to the
zigzag discharges as 11:6; and from spectrum observations it would appear
that the former are brush discharges between clouds, while the latter are
true electrical discharges between the clouds and the earth. Another kind,
called heat lightning, is ascribed to distant lightning flashes which are below
the horizon, but illuminate the higher strata of clouds, so that their bright-
ness is visible at great distances ; they produce no sound, probably in con-
sequence of the fact of their being so far off that the rolling of thunder
cannot reach the ear of the observer. There is, further, the very unusual
phenomenon of glode lightning, or the flashes which appear in the form of
globes of fire 18 inches in diameter. These, which are sometimes visible for
as much as ten seconds, descend from the clouds to the earth with such
slowness that the eye can follow them. They often rebound on reaching
the ground ; at other times they burst and explode with a noise like that
of the report of many cannon. No adequate explanation has been given
of these, though Planté with a large battery of his cells has imitated the
phenomena.
The duration of the light of the first three kinds does not amount to the
millionth of a second, as was determined by Wheatstone by means of his
rotating wheel, which was turned so rapidly that the spokes were invisible :
on illuminating it by the lightning flash, its duration was so short that
whatever the velocity of rotation of the wheel, it appeared quite stationary ;
that is, its displacement is not perceptible during the time the lightning exists.
The hight produced by a lightning flash must be comparable to the sun
in brightness, though it does not appear to us brighter than ordinary moon-
light. But considering its excessively brief duration, and that the full effect
of any light on the eye is only produced when its duration is at least the
tenth of a second, it follows that a landscape continuously illuminated by the
lightning flash would appear 100,000 times as bright as it actually appears
to us during the flash.
Here also may be mentioned the phenomenon known as St. Elmo's fire,
which occurs in a highly electrical state of the atmosphere when the clouds
are low. It isa sort of brush discharge (809), appearing like small flames
issuing from prominent point-objects such as masts, tops of trees, lightning-
conductors ; it has also been observed on the points of helmets and lances,
alpenstocks ; it is of course most easily seen in the dark, and is accompanied
by a slight rustling noise. On the sea during thunder-storms it is not un-
common on mastheads and yardarms.
1036. Thunder.— 7hunder is the violent report which succeeds lightning
in stormy weather. The occurrence of lightning and thunder is practically
simultaneous, but an interval of several seconds is generally observed
-1037] Thunder 1083
between the perception of these two phenomena, which arises from the fact
that sound travels at the rate of only about 1,100 feet in a second (235),
while the passage of light is almost instantaneous. Hence an observer will
hear the noise of thunder only five or six seconds, for instance, after the
lightning, according as the distance of the thunder-cloud is five or six times
1,100 feet. The noise of thunder arises in some such manner as the crack
of a whip or the report of a gun. The lightning discharge, whether by
heating the air or by a purely mechanical action, such as is illustrated with
Kinnersley’s thermometer (fig. 773), is expanded with explosive violence,
which is only possible by a compression of the surrounding air. This com-
pressed air rushes in to fill the partial vacuum, forming itself, in turn, a partial
vacuum, and thus, giving rise to alternate condensation and rarefaction,
constitutes the wave-motion producing the sound. The depth of the note
represents a great wave-length, and shows that the disturbance must have
a great length. Near the place where the lightning strikes the sound is
sharp and of short duration. Ata greater distance a series of reports are
heard in rapid succession. At a still greater distance the noise, feeble at
first, changes into a prolonged rolling sound of varying intensity. If the
lightning is at a greater distance than 14 or 15 miles, it is no longer heard,
for sound is more imperfectly propagated through air than through solid
bodies : hence there are lightning discharges without thunder ; these occur
at times when the sky is cloudless.
The rolling of thunder, the alternate rise and fall of the sound, occurs
ordinarily with sheet lightning, less so with forked lightning, when the sound
is short and crackling.
Various causes contribute to produce the rolling ; one cause is the reflec-
tion from the ground, from clouds, and even from layers of air of unequal
density. Lightning, too, is not a single discharge, but a series of discharges,
each of which gives rise to a particular sound, and which are variously reflected
by objects which they meet on their path. If two waves reach the ear
simultaneously they strengthen each other if they are in the same phase, but
if in different ones they interfere partially or wholly and the sound sinks.
Thus it may happen that the sound after sinking may rise again. This is
the well-known phenomenon of beats (266). The phenomenon has finally
been ascribed to the zigzags of lightning themselves, assuming that the
air at each salient angle is at its greatest compression, which would
produce the unequal intensity of the sound. The distance of the nearest
point of a lightning flash is obtained in kilometres if we divide the time in
seconds which elapses between the lightning flash and the beginning of the
thunder by 3.
This is evident since s = v¢ (233) and v the velocity found is 330 metres or
4 kilometre per second.
1037. Effects of lightning.—The lightning discharge is the electric
discharge which strikes between a thunder-cloud and the ground. The latter,
by the induction of the electricity from the cloud, becomes charged with
contrary electricity ; and when the tendency of the two electricities to com-
bine exceeds the resistance of the air, the spark passes, which is often ex-
pressed by saying that ‘a thunderbolt has fallen. Lightning in general
strikes from above, but ascending lightning is also sometimes observed ;
1084 Meteorology [1037—
probably this is the case when the clouds being negatively the earth is
positively electrified ; for experiments show that at the ordinary pressure
positive electricity passes through the atmosphere more easily than negative
electricity.
The discharge usually falls first on the nearest and best conducting
objects, and, in fact, trees, elevated buildings, metals, are particularly struck
by the discharge. Hence it is imprudent to stand under trees during a
thunderstorm.
According to Hellman, the frequency with which trees are struck is: fir
5, beech 7, oak 18; in like manner of soils the ratio is : chalk 1, clay 7, sand
9g, and loam 22.
The effects of lightning are very varied, and of the same kind as those
of Leyden batteries (805), but of far greater power. The lightning discharge
kills men and animals, ignites combustibles, melts metals, breaks bad con-
ductors in pieces. When it penetrates the ground it melts the silicious
substances on its path, and thus produces in the direction of the discharge
those remarkable vitrified tubes called /ulgurztes, some of which are as much
as 12 yards in length ; in most cases there are found to be accumulations of
water below such fulgurites. When it strikes bars of iron it magnetises
them, and often inverts the poles of compass needles.
The action of lightning on trees is very singular. When struck by it
they are sometimes stripped of their bark, either wholly or partially, or the
wood is often split into thin laths, or intoa mass of fibres. Franklin ascribed
this to the sudden evaporation of the water.
After the passage of lightning a highly peculiar odour is frequently
produced, like that perceived in a room in which an electrical machine
is being worked. This is due to the formation of ozone, a peculiar allotro-
pic modification of oxygen (815). An electrified cloud forms with the earth
below a condenser, the intervening mass of air being the dielectric. This
mass of air is therefore in a state of strain, like the dielectric in a charged
Leyden jar, and it is to this state of strain which precedes the actual
discharge, rather than to the discharge itself, that is due the production of
ozone.
Heated air conducts better than cold air, probably only owing to its
lesser density. Hence it is that large numbers of animals are often killed
by a single discharge, as they crowd together in a storm, and a column of
warm air rises from the group.
1638. Return shock.—This is a violent and sometimes fatal shock which
men and animals experience, even when at a great distance from the place
where the lightning discharge passes. It is caused by the inductive action
which the thunder-cloud exerts on bodies placed within the sphere of its
activity. ‘These bodies are then, like the ground, charged with the opposite
electricity to that of the cloud ; but when the latter is discharged by the
recombination of its electricity with that of the ground, the induction ceases,
and the bodies reverting rapidly from the electrical state to the neutral state,
the concussion in question is produced—the return or back shock. A gradual
decomposition and reunion of the electricity produces no visible effects ; yet it
is alleged that such disturbances of the electrical equilibrium are perceived
by nervous persons.
1039] Lightning-Conductor 1085
The return shock is always less violent than the direct one ; there is no
instance of its having produced any inflammation, yet plenty of cases in
which it has killed both men and animals ; in such cases no broken limbs,
wounds, or burns are observed. |
The return shock may be imitated by placing a gold-leaf electroscope
connected by a wire with the ground near an electrical machine ; when the
machine is worked, at each spark taken from the prime conductor the gold
leaves of the electroscope suddenly diverge.
It is stated that persons struck by lightning often lose their lives only
by a temporary injury to the nerves which control the act of respiration ; so
that under favourable circumstances such persons might probably be saved
by producing artificial respiration.
1039. Lightning-conductor.—This was invented by Franklin in 1755.
There are two principal parts in a lightning-conductor, the rod and the
conductor. The vod (fig. 1055) is a pointed bar of iron, preferably galvanised,
P, fixed vertically to a tube or rod of iron, which, by means
of a collar aa, and tube g, is fitted on the roof of the edifice
to be protected ; it is from 6 to Io feet in height, and its
basal section is about 2 or 3 inches in diameter. The cov-
ductor is best formed of a wire rope, C, attached to the rod
by a metal collar, 4. The section of the metallic conductor
ought to be about half a square inch, and the individual wires
0°04 to o'06 inch in diameter: they ought to be twisted in
strands, like an ordinary cord. The conductor is usually led
into a well, a pond, or other continuous mass of water, and
to connect it better with the ground it should terminate in a
plate called an earth plate, or if a strand of wires the separate
wires should be spread out. This plate should be of the
same metal as the conductor, so as to avoid the possibility
of local galvanic action (837), by which one or the other
metal would be eaten away and the continuity destroyed.
If there is no well near, a hole is dug in the soil to the depth
of 6 or 7 yards, or to where the earth is permanently damp ;
where the ground is naturally dry it is advantageous to direct
the rainfall from the roof towards where the plate is placed,
and the ends of the conductor having been introduced, the
hole is filled with powdered coke, which conducts very well.
A good earth contact is obtained when it is possible to
connect the wire conductors with large iron gas or water
pipes.
The action of a lightning-conductor is regarded as an illustration of the
action of induction and of the property of points (758) ; when a storm cloud
positively electrified, for instance, forms in the atmosphere, it acts inductively
on the earth, repels the positive and attracts the negative electricity, which
accumulates on bodies placed on the surface of the soil, the more abundantly
as these bodies are at a greater height. The density is then greatest on the
highest bodies, which are therefore most exposed to the electric discharge ;
but if these bodies are provided with metal points, like the rods of conductors,
the negative electricity, withdrawn from the soil by the influence of the cloud,
1086 | Meteorology [1039-
flows into the atmosphere, and neutralises the positive electricity of the cloud.
Hence the action of the lightning-conductor is twofold ; not only does it tend
to prevent the accumulation of electricity on the surface of the earth, but it
also tends to restore the clouds to their natural state, both which concur in
preventing lightning discharges. This mode of action of lightning-conductors
is often overlooked ; it is stated in reference to Pietermaritzburg that until
lightning-conductors became common in that town it was constantly visited
by thunderstorms at certain seasons. They come as frequently as ever, but
cease to give flashes on reaching the town ; they do so, however, when they
have passed over it. The quantity of electricity is, however, sometimes so
abundant that the lightning-conductor is inadequate to discharge the elec-
tricity accumulated, and the lightning strikes ; but the conductor receives
the discharge, in consequence of the greater conductivity, and the edifice
is preserved.
A conductor, to be efficient, ought to satisfy the following conditions :—
(i.) The rod ought to be so large as not to be melted if the discharge passes.
(ii.) It ought to terminate in a point, or in several points, to give readier issue
to the electricity disengaged by induction from the ground. (ii1.) Copper
was formerly preferred to iron owing to its greater conductivity. But the
lightning discharge is strictly analogous to the discharge of a Leyden jar,
which according to circumstances may form either a continuous discharge
like a steady current, or a series of oscillations (805). In the latter case the
discharge is restricted to the surface owing to the effect of impedance (933),
which may have a greater influence than the ohmic resistance, so that the
advantage of the greater conducting power of copper disappears. The con-
ductor must be continuous from the point to the ground, and the connection
between the rod and the ground must be as intimate as possible; this is the
most important of all, and the one point most frequently neglected in the
older arrangements. A lightning-conductor with bad earth contact is not only
useless but dangerous. In regard to this, it may be said that the best earth for
contact is water. The continuity of the conductor may be tested by means
of a voltaic cell and a portable form of galvanometer. (iv.) If the building
which is provided with a lightning-conductor contains metallic surfaces of
any extent, such as zinc roofs, metal gutters, or ironwork, these ought to
be connected with the conductor, or, still better, have each a separate earth
connection. If the last two conditions are not fulfilled, there is a great
danger of lateral discharges—that is to say, that the discharge takes place
between the conductor and the edifice, and then it increases the danger.
Colladon concludes, from the observation of a series of lightning dis-
charges, that a tall tree, such as a poplar, whose roots are in moist ground,
may act as a good lightning-conductor, if on the other side of the house
there does not happen to be a well or pool, towards which the electricity can
spring through the house.
The requirements above laid down are based on the older view of the
protection of buildings. Another mode of protection is based on the screen-
ing action of a closed conducting surface either continuous or formed of wire
gauze. Suchan enveloping conductor, as we have seen (757), protects a body
inside it from external electrical action, and probably does so also in the
case of violent and sudden electrical discharges. If a building could be
-1040] Rainbow 1087
surrounded by a wire cage which itself had good earth contact, this would
be an efficient protection. Accordingly, an alternative plan aims at provid-
ing all the ridges, eaves and corners, and chimneys of a building with abun-
dance of galvanised iron wire, preferably barbed, and with wire netting, all
in metallic connection with each other and with the earth.
Copper conductors with a surface of 50 sq..mm. have been known to be
raised to nearly a red heat by a lightning discharge, and such as have a
section of 5 sq. mm. have frequently been melted. An estimate based on
this fact gives for the quantity of electricity passing in such a discharge
values of not less than 50 nor more than 290 coulombs.
1040. Rainbow.—The vazzdow is a luminous phenomenon which appears
in the clouds opposite the sun when they are resolved into rain. It consists
of seven concentric arcs, presenting successively the colours of the solar
spectrum. Sometimes only a single bow is perceived, but there are usually
two ; a lower one, the colours of which are very bright ; and an external or
secondary one, which is paler, and in which the order of the colours is re-
versed. In the interior rainbow the red is the highest colour ; in the other
rainbow the violet is. It is seldom that three bows are seen ; theoretically
a greater number may exist, but their colours become so faint that they can-
not be perceived.
The phenomenon of the rainbow is produced by decomposition of the
white light of the sun when it passes into the drops, and by its reflection
from their inside face. In fact, the same phenomenon is witnessed in dew-
drops and in jets of water—in short, wherever sunlight passes into drops of
water under a certain angle.
The appearance and the extent of the rainbow depend on the position of
the observer, and on the height of the sun above the horizon ; hence only
some of the rays refracted by the raindrops, and reflected in their concavity
to the eye of the spectator, are adapted to produce the phenomenon. Those
which do so are called effective rays.
To explain this let us suppose z (fig. 1056) to be a drop of water, into
which a solar ray S a penetrates. At a point of incidence, a, part of the
light is reflected from the surface of the liquid ; another, entering it, is de-
composed and traverses the drop in the direction a 6. Arrived at 4, part of
the light emerges from the raindrop, the other part is reflected from the
concave surface, and tends to emerge at g. At this point the light is again
partially reflected ; the remainder emerges in a direction gO, which forms
with the incident ray, S a, an angle called the angle of deviation. It is
such rays as gO, proceeding from the side next the observer, which produce
on the retina the sensation of colours, provided the light is sufficiently
intense.
It can be shown mathematically that in the case of a series of rays which
impinge on the same drop, and only undergo one reflection in the interior,
the angle of deviation increases from the ray S’’7, for which it is zero, up toa
certain limit, beyond which it decreases, and that near this limit rays passing
parallel into a drop of rain also emerge parallel. From this parallelism a
beam of light is produced sufficiently intense to impress the retina ; these
are the rays which emerge parallel and are efficient.
As the different colours which compose white light are unequally refran-
1088 Meteorology [1040-.
gible, the maximum angle of deviation is not the same for all. For red rays
the angle of deviation corresponding to the active rays is 42° 2’, and for
violet rays itis 40° 17’. Hence, for all drops placed so that rays proceeding
from the sun to the drop make, with those proceeding from the drop to the
eye, an angle of 42° 2’, this organ will receive the sensation of red light ;
this will be the case with all drops situated on the circumference of the
base of a cone, the summit of which is the spectator’s eye; the axis of
this cone is parallel to the sun’s rays, and the angle formed by the two
opposed generating lines is 84° 4’. This explains the formation of the red
band in the rainbow ; the angle of the cone in the case of the violet band
is 80° 34’.
The cones corresponding to each band have a common axis called the
visual axts. As this right line is parallel to the rays of the sun, it follows
that when this axis is on the horizon, the visual axis is itself horizontal, and
the rainbow appears as a semicircle. If the sun rises, the visual axis sinks,
and with it the rainbow. Lastly, when the sun is at a height of 42° 2’, the
Fig. 1056
arc disappears entirely below the horizon. Hence the rainbow is never seen
except in the morning and evening.
What has been said refers to the interior arc. The secondary bow is
formed by rays which have undergone two reflections, as shown by the ray
S’id feO, inthe drop g. The angle S’IO formed by the emergent and
incident rays is called the angle of deviation. The angle is no longer suscep-
tible of a maximum, but of a minimum deviation, which varies for each kind of
rays, and to which also efficient rays correspond. It is calculated that the
minimum angle from violet rays is 54°7’, and for red rays only 50° 57’ ; hence
it is that the red bow is here on the inside, and the violet arc on the outside.
There is a loss of light for every internal reflection in the drop of rain, and
therefore the colours of the secondary bow are always feebler than those of
the internal one. The secondary bow ceases to be visible when the sun is
54° above the horizon.
The moon sometimes produces rainbows like the sun, but they are very
pale.
1o41. Aurora borealis.—The aurora borealis, or northern light, or more
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—1041] Aurora Borealis 1089
properly folar aurora, is a remarkable luminous phenomenon which is fre-
quently seen in the atmosphere in high latitudes. Fig. 1057 represents an
aurora borealis observed at Bossekop, in Lapland, lat. 70°, in the winter of
1838-39.
Plate III. represents a very beautiful aurora observed by Lemstrém on
the north coast of Norway. The radial divergence of the aurora and the
convergence towards a corona is due to an effect of perspective. The work
of this author (Z’Auwrore Boréale, Gauthier Villars, Paris) is a storehouse of
information on this subject.
A French scientific commission to the North observed 350 aurore
boreales in 200 days ; it appears that at the poles, nights without an aurora
borealis are quite exceptional, so that it may be assumed that they take
place every night, though with varying intensity: They are visible at a
considerable distance from the poles, and over an immense area. Some-
Fig. 1057
times the same aurora borealis has been seen at the same time at places
so widely apart as Moscow, Warsaw, Rome, and Cadiz. The height of
the aurora above the surface of the ground is probably lower than has
generally been stated. Lemstrém holds that from 22 to 44 miles is a close
approximation to the truth ; and it may be regarded as certain that even in
more southern latitudes the aurora is often seen much lower—at a height of
two or three miles, for instance. In polar countries certain forms of aurora,
more especially those of weak flames, are seen to proceed from the ground
on the tops of certain mountains. They are most frequent at the equinoxes,
and least so at the solstices. The number differs in different years, attain-
ing a maximum every II years at the same time as the sun-spots, and
like these a minimum which is about five or six years from the maximum.
The years 1844, 1855, 1866, and 1877 were poor in the appearance of the
aurora.
AA
1090 Meteorology [1041-
There is, moreover, a period of about 60 years ; for the years 1728, 1780,
and 1842 have been remarkable for the prevalence of the aurora. The last
two periods are also remarkable for the occurrence of disturbances in the
earth’s magnetism.
Numerous hypotheses have been devised to account for the aurore
boreales. As they share the rotation of the earth, they must have an atmo-
spheric origin. Their direction is not due north and south, but is always
parallel to that of the dipping-needle, pointing to the magnetic pole ; this,
together with their action on the magnetic needle (708), seems to prove that
they ought to be attributed to electric currents in the higher regions of the
atmosphere. In high latitudes the aurora borealis acts powerfully on the
wires of the electric telegraph; the alarums are for a long time violently
rung, and telegraphic messages frequently interrupted, by the spontaneous
abnormal working of the apparatus (915). In the lower discharges a crack-
ling sound has been heard, and during balloon ascents a strong smell of
ozone has been perceived when the balloon was among the luminous rays.
The spectrum of the aurora borealis has been found to consist of several
lines in the green, and of an indistinct line in the blue ; to which must be
added a red line due to the red protuberances ; these lines are the same as
those of nitrogen, greatly rarefied and at a low temperature ; one special
line between the green and the yellow, and called the yellow line, is so
characteristic of the aurora that it is visible even when the eye can discern
no other trace of this light ; this line has not been produced in laboratory
experiments.
De la Rive held that aurore boreales were due to electric discharges
which take place in polar regions between the positive electricity of the
atmosphere and the negative electricity of the earth. The positively elec-
trified aqueous vapours are supposed to be carried by the equatorial current
in the higher regions of the atmosphere to the poles, where the neutralisa-
tion takes place. These discharges produce luminous appearances of the
same kind as are observed in Geissler’s tubes ; and De la Rive showed by
means of an apparatus specially devised for the purpose (fig. 980) that the
forms of the luminous phenomena are in accordance with this theory.
By direct experiments Lemstrém has been able to imitate and reproduce
a peculiar form of aurora observed in winter as a flame-like appearance on
the tops of two mountains 800 and 1,100 metres in height, and to show
that it is of electrical origin. He erected on the summit of a hill a system
of pointed rods extending over a surface of nearly 4,000 square feet ; each
rod was carefully insulated from the earth by means of a Mascart’s insulator
(fig. 714), but was connected with the rest, and an insulated wire led down
from this system into the valley, where it was connected with one ter-
minal of a galvanometer, the other being put to earth. The existence of
a positive current from the air to the earth was observed, and at the same
time yellowish-white columns of light, reaching to a height of 120 metres,
were observed to issue from the points. Observed with the spectroscope it
gave the characteristic lines between D and E.
Making similar experiments on even a larger scale in Lapland on a
detached peak, he observed that the characteristic luminous phenomena
were produced there, while the neighbouring peaks remained dark.
-—1043] Mean Temperature 1OQI
The investigations of Exner relative to the fall ot atmospheric electrical
potential lend a further support to the view that the aurora is due to elec-
tricity. In the polar regions the rate of fall of potential is 13 times greater
in summer, and 18 times greater in winter than at the equator. Hence an
electrical phenomenon, which depends on the magnitude of this fall of
potential, must be more intense in winter and in high latitudes than in
summer and in the torrid zones.
The occurrence of irregular currents of electricity which manifest them-
selves by abnormal disturbances of telegraphic communications is not in-
frequent : such currents have received the name of earth currents. Sabine
held that irregular magnetic disturbances are due to a peculiar action of the
sun, and are probably independent of its radiant heat and light. It has
also been ascertained that the aurora borealis as well as earth currents in-
variably accompanies these magnetic disturbances. According to the late
. Balfour Stewart, aurorz and earth currents are to be regarded as secondary
phenomena due to small but rapid changes in the earth’s magnetism : he
likened the body of the earth to the magnetic core of a Ruhmkorft’s coil (949) :
the lower strata of the atmosphere forming the insulator, while the upper
and rarer, and therefore electrically conducting, strata may be considered
as the peony coil.
On this analogy the sun may perhaps be likened to the primary current
which performs the part of producing changes in the magnetic state of the
core. Now in Ruhmkorff’s coil the energy of the secondary current is
derived from that of the primary current. Thus, if the analogy be correct,
the energy of the aurora borealis may in like manne: come from the sun ;
but until we know more of the connection between the sun and terrestrial
magnetism, these ideas are to be accepted with some reserve.
CLIMATOLOGY
1042. Mean temperature.—The mean daily temperature is that obtained
by adding together 24 hourly observations, and dividing by 24. A very
close approximation to the mean temperature is obtained by taking the
mean of the highest and lowest temperatures of the day and of the night,
which are determined by means of the maximum and minimum ther-
mometers. These ought to be protected from the sun’s rays, to be raised
above the ground, and far from all objects which might influence them by
their radiation.
The temperature of a month is the mean of the temperature of 30 days,
and the temperature of the year is the mean of those of 12 months. Finally,
the temperature of a place is the mean of its annual temperatures for a great
number of years. The mean temperature of London is 8:28° C., or 46°9° F.
The temperatures in all cases are those of the air, and not those of the
ground.
1043. Causes which modify the temperature of the air.—The principal
causes which modify the temperature of the air are the latitude of a place,
its height, the direction of the winds, and proximity of seas.
Influence of the latitude——The influence of the latitude arises from the
4A2
1092 Meteorology [1048 -
greater or less obliquity of the solar rays, for as the quantity of heat absorbed
is greater the more perpendicular are the rays (421), the heat absorbed de-
creases from the equator to the poles, for the rays become more oblique.
This loss is, however, in summer, in the temperate and arctic zones, partially
compensated by the length of the days. Under the equator, where the
length of the days is constant, the temperature is almost invariable ; in the
latitude of London, and in more northerly countries, where the days are
very unequal, the temperature varies greatly ; but in summer it sometimes
rises almost as high as under the equator. The lowering of the temperature
produced by the latitude is small; thus, in a latitude 115 miles north of
Paris, the temperature is only 1° C. lower.
Influence of hetght.—The height of a place above the sea level has a
much more considerable influence on the temperature than its latitude.
The cooling on ascending in the atmosphere has been observed in
balloon ascents, and a proof of it is seen in the perpetual snows which cover .
the highest mountains. Itis due in part tothe greater rarefaction of the air,
which necessarily diminishes its absorbing power ; besides which the air is
at a greater distance from the ground, which heats it by contact ; and finally,
dry air is very diathermanous.
The law of the diminution of temperature corresponding to greater
heights in the atmosphere has not been made out, in consequence of the
numerous disturbing causes which modify it, such as the prevalent winds,
the hygrometric state, the time of day, the season of the year, &c. The
difference between the temperatures of two places at unequal heights is not
proportional to the difference of level, but for moderate heights an approxi-
mation to the law may be made. As the mean of a series of very careful
observations made during balloon ascents, a diminution of 1° C. corresponded
to an increase in height of 232 yards.
It will thus be seen that at a certain height above the ground there must
be a surface or layer where the temperature is uniformly zero. The height
of this isothermal surface (1045) will vary materially with the time of the year,
being lower in the cold months: it varies also with the time of day, rising
rapidly about midday. In summer this height may be taken at from 3,400
to 3,700 metres above the sea-level.
Direction of winds.—As winds share the temperature of the countries
which they have traversed, their direction exercises great influence on the
air in any place. In Paris, the hottest winds are the south ; then come the
south-east, the south-west, the west, the east, the north-west, north, and
lastly, the north-east, which is the coldest. The character of the wind
changes with the seasons ; the east wind, which is cold in winter, is warm in
summer.
Proximity of the sea.—The neighbourhood of the sea tends to raise the
temperature of the air, and to render it uniform. The average temperature
of the sea in equatorial and polar countries is always higher than that of the
atmosphere. With reference to the uniformity of the temperature, it has
been found that in temperate regions—that is, from 25° to 50° of latitude—
the difference between the highest and lowest temperature of a day does not
exceed, on the sea, 2° to 3° ; while upon the continent this amounts to from
12° to 15°. Inislands the uniformity of temperature is very perceptible, even
No. 5.
ISOTHERMS- FOR JULY:
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Niso. 170 160 150 140 130 120° 110 100 90 80 70
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-1046] Climase 1093
during the greatest heats. In continents, on the contrary, the winters for
the same latitudes become colder, and the difference between the tempera-
ture of summer and winter becomes greater.
1044. Gulf Stream.—A similar influence to that of the winds is exerted
by currents of warm water. To one of these, the Gulf Stream,,the mildness
of the climate in the north-west of Europe is mainly due. This great body
of water, taking its origin in equatorial regions, flows through the Gulf of
Mexico, whence it derives its name; passing by the southern shores of
North America, it makes its way in a north-westerly direction across the
Atlantic, and finally washes the coast of Ireland and the north-west of Europe
generally. .Its temperature in the Gulf is about 28° C. ; and it is usually a
little more than 5° C. higher than the rest of the ocean on which it floats,
owing to its lower specific gravity. Toits influence is due the milder climate
of West Europe as compared with that of the opposite coast of America ; thus
the river Hudson, in the latitude of Rome, is frozen over three months in the
year. It also causes the polar regions to be separated from the coasts ot
Europe by a girdle of open sea; and thus the harbour of Hammerfest is
open the year round. Besides this influence in thus moderating climate, the
Gulf Stream is an important help to navigators.
1045. Isothermal lines.— When on a map all the points whose tempera- '
ture is known to be the same are joined, curves are obtained which Hum-
boldt first noticed, and which he called zsothermal lines. If the temperature
of a place only varied with the obliquity of the sun’s rays—that is, with the
latitude—isothermal lines would all be parallel to the equator ; but as the
temperature is influenced by many local causes, especially by the height, the
isothermal lines are always more or less curved. On the sea, however, they
are almost parallel. Maps 4, 5, and 6 represent these lines for the Year,
for January, and for July.
A distinction is made between zsothermal lines, tsotheral lines, and iso-
chimenal lines, where the mean general, the mean summer, and the mean
winter temperatures are respectively constant. An zsothermal zone is the
space comprised between two isothermal lines. Kupffer also distinguishes
Zsogeothermic lines where the mean temperature of the soil is constant.
1046. Climate.—By the climate of a place are understood the whole of the
meteorological conditions to which the place is subjected ; its mean annual
temperature, summer and winter temperatures, and the extremes within
which these are comprised. Some writers distinguish seven classes of
climates, according to their mean annual temperature: a hot climate from
30° to 25° C. ; a warm climate from 25° to 20° C.; a mild climate from 20°
to 15° C.; a ¢emperate climate from 15° to 10° C. ; a cold climate from 10°
to 5° C.;a very cold climate from 5° to zero C. ; and an arctic climate where
the temperature is below zero.
Those climates, again, are classed as constant climates where the dif-
ference between the mean and summer and winter temperatures does not
exceed 6° to 8°; variable climates, where the difference amounts to from
16° to 20° ; and extreme climates, where the difference is greater than 30°.
The climates of Paris and London are variable ; those of Pekin and New
York are extreme. Island climates are generally little variable, as the
temperature of the sea is nearly constant ; and hence thedistinction between
1094 Meteorology [1046—
land and sea climates. Marine climates are characterised by the fact that
the difference between the temperature of summer and winter is always
less than in the case of continental climates. But the temperature is by
no means the only character which influences climate ; there are, in addi-
tion, the moisture of the air, the quantity and frequency of the rains, the
number of storms, the direction and intensity of the winds, and the nature
of the soil.
1047. Distribution of temperature on the surface of the globe.—The
temperature of the air on the surface of the globe decreases from the equator
to the poles ; but it is subject to perturbing causes so numerous and so
purely local, that its decrease cannot be expressed by any law. It has
hitherto not been possible to do more than obtain by numerous observations
the mean temperature of each place, or the maximum and minimum tempera-
tures. The following table gives a general idea of the distribution of heat in
the Northern Hemisphere.
Mean temperature at different latitudes
Abyssinia. : eo Om ebitesels., oh Oreagtee
Calcutta : : aZo.s Strasburg : ; a OG
Jamaica. : : Ame ORE Geneva . E27,
Senegal. / : Beer ie) Boston . BP Sekt)
Cairo ¢ : end London . : : Regs)
Constantine . : ei yao Stockholm Me Be
Naples . : ; SOME Ke Bee Moscow . , ; fe Beo
Mexico . ; feel OO St. Petersburg A PR
Marseilles. : Dn eb St; Gothard .o; : . -1°0
Constantinople. ai e7 Greenland ; ' Rene 6 |
Pekin . . : SM Oty Melville Island ; .- 187
Paris. 44; : Fi LOus
These are mean yearly temperatures. The highest temperature which
has been observed on the surface of the globe is 47°4° at Esne, in Egypt,
and the lowest is —75° in the Arctic Expedition of 1876 ; which gives a
difference of 122° between the extreme temperatures observed on the surface
ot the globe.
The highest temperature observed at Paris was 38:4° on July 8, 1793,
and the lowest — 23°5° on December 26,1798. The highest observed -at
Greenwich was 35° C. in 1808, and the lowest —20° C. in 1838.
No arctic voyagers have succeeded in reaching the poles, in consequence
of the seas round them being completely frozen, and hence the temperature
there is not known. In our hemisphere the existence of a single glacial pole
—that is, a place where there was the maximum cold—has been long assumed.
But the bendings which the isothermal lines present in the Northern
Hemisphere have shown that in this hemisphere there are two cold poles—
one in Asia, to the north of Gulf Tamour ; and the other in America, north
of Barrow’s Straits, about 15° from the earth’s north pole. The mean
temperature of the first of these poles has been estimated at —17°, and that
of the second at —19°. With respect to the southern hemispheres, the
ISOTHERMS FOR. JANUARY:
Ss \4 {| i f TR i
Ay
mY,
=i oN
| Wi} |
Hi \\
: esr |
ill i y
Wii} | 3
ae
i I \ ,
|
thf
\
Pg
VE:
AW,
xt | Wh
"| I TTT
i tI
§ fhe, mm sy
K ? Re
yyy
bs iT} ties aN
{
I Het ety oof HOH di
tbe, is °
i D &
ue
1049] Temperatures of Lakes, Seas, and Springs 1095
observations are not sufficiently numerous to decide whether there are one
or two poles of greatest cold, or to determine their position.
1048. Temperatures of lakes, seas, and springs.—In the tropics the
temperature of the sea is generally the same as that of the air; in polar
regions the sea is always warmer than the atmosphere.
The temperature of the sea in the torrid zone is always about 26° to
27° at the surface : it diminishes as the depth increases, and in temperate
as well as in tropical regions the temperature of the sea at great depths is
between 2°5° and 3°5°. The low temperature of the lower layers is caused by
submarine currents which carry the cold water of the polar seas towards the
equator.
The variations in the temperature of lakes are more considerable ; their
surface, which becomes frozen in winter, may become heated to 20° or 25° in
summer. The temperature of the bottom, on the contrary, is virtually 4°,
which is that of the maximum density of pure water.
Springs, which arise from rain water which has penetrated into the crust
of the globe to a greater or less depth, necessarily tend to assume the tempera-
ture of the terrestrial layers which they traverse. Hence, when they reach
the surface their temperature depends on the depth which they have attained.
If this depth is that of the layer of invariable temperature, the springs have
a temperature of 10° or 11° in this country, for this is the temperature of this
layer, or about the mean annual temperature. If the springs are not very
copious, their temperature is raised in summer and cooled in winter by that
of the layers which they traverse in passing from the invariable layer to the
surface. But if they come from below the layer of invariable temperature
their temperature may considerably exceed the mean temperature of the
place, and they are then called thermal springs. The following list gives
the temperatures of some of them :—
Wildbad . ; ; : ; ‘ , : Unsyice Ae
Vichy : ; : : ; : ; : : edo
Bath , : ; ; : ; : ; ; AS
Ems ; , : : ; : 3 : , oe 40
Baden-Baden . ‘ : 4 : , : : 075
Chaudes-Aigues ; : : : : : : oe) fete
Trincheras , : ‘ : : : ' : hey:
Great Geyser, in Iceland, at a depth of 66 feet : . 124
From their high temperature they have the property of dissolving many
mineral ‘substances which they traverse in their passage, and hence form
mineral waters. The temperature of mineral waters is not modified in
general by the abundance of rain or of dryness; but it is by earthquakes,
after which they have sometimes been found to rise and at other times to sink.
1049. Distribution of land and water.—The distribution of water on
the surface of the earth exercises great influence on climate. The area
covered by water is considerably greater than that of the dry land ; and the
distribution is unequal in the two hemispheres. The entire surface of the
globe occupies about 200 millions of square miles, nearly three-fourths of
which are covered by water ; that is, the extent of the water is nearly three
1096 Meteorology [1049
times as great as that of the land. The surface of the sea in the Southern
Hemisphere is to that in the Northern in about the ratio of 13 to 9.
The depth of the open sea is very variable; the lead generally reaches
the bottom at about 300 to 450 yards; in the ocean it is often 1,300 yards,
and instances are known in which a bottom has not been reached at a depth
of 4,500. it has been computed that the total mass of the water does not
exceed that of a liquid layer surrounding the earth with a depth of about
I,100 yards,
PROBLEMS AND EXAMPLES
IN PHYSICS
I. EQUILIBRIUM
1. A body being placed successively in the two pans of a balance, requires 180
grammes to hold it in equilibrium in one pan, and 181 grammes in the other; poguitad
the weight of the body to a milligramme.
From the es v= yas we have
= »/180 x 181 = 1808", 499.
2. What resistance does a nut offer when placed in a pair of nutcrackers at a
distance of 3 of an inch from the joint, if a pressure of 5 pounds applied at a distance
of 4 inches foe the joint is just sufficient to crack it? Ans, 262 pounds.
3. What force is required to raise a cask weighing 6 cwt. into a cart o°8 metre
high along a ladder 2°75 metres in length ? Ans. 1954 pounds.
4. If a horse can move 30 cwt. along a level road, what can it move along a road
the inclination of which is 1 in 80, the coefficient of friction on each road being | ?
Ans, 26% ay
' 5, The piston of a force-pump has a diameter of 8 centimetres, and the arms of
the lever by which it is worked are respectively 12:and 96 centimetres in length; what
force must be exerted at the longer arm if a pressure of 12°36 pounds on a square cen-
timetre is to be applied? Ans. 77°69 pounds.
IL) (GRAVITATION
6. Astone is thrown from a balloon with a velocity of 50 metres in a second. How
soon will the velocity amount to 99 metres ina second, and through what distance
will the stone have fallen ?
To find the time requisite for the Seely: to have acquired the velocity of 99 metres in
a second, we have
v= V+ gt;
in which V is the initial velocity, g the acceleration of gravity, which, with sufficient
approximation, is equal to 9'8 metres in a second, and #/ the time. Substituting these
values, we have
t= 99 — 5° = 49 = ¢ seconds.
9°8 9°8
For the space traversed we have
S= Vit ket = 50 x5 + 46% 25 =972'5 metres,
7. A projectile was thrown vertically upwards to a height of 510™‘22, Disregard-
ing the resistance of the air, what was the initial velocity of the body ?
The velocity is the same as that which the body would have acquired on falling
from a height of 510°22 metres.
From the formula v = /2 5 we get
= /2 x 98 x 510°22 = »/10000 = 100 metres
8. A stone is thrown vertically upwards with an initial velocity of Ioo metres.
After what time would it return to its original position?
1098 Problems and Examples in Physics
The time of rising and falling is the same, but the time of falling is _ (from the
s
formula v=g?) or ~~ =10'2, which is half the time required ; therefore ¢=20°4 sec.
9°
9. A stone is thrown vertically upwards with an initial velocity of 100 metres ; after
x seconds a second stone is thrown with the same velocity. The second stone is rising
8°7 seconds before it meets the first. What interval separated the throws?
The rising stone will have the velocity v = V — gt, whence v = 100 — 9‘8 x 8°7.
On the other hand, the falling stone, at the moment the stones meet, will have the velocity
given by the equation v = gt’, in which @’ is the time during which the stone falls
before it meets the second one. This time is equal to 8°7 seconds + x — — Hence
9°
its velocity is
Equating the two values of v and reducing, we obtain x = 3 seconds.
10. A body moving with a uniformly accelerated motion traverses a space of 1000
metres in ro seconds. What would be the space traversed during the eighteenth
second if the motion continued in the same manner ?
The formula s = 4 gt? gives for the accelerating force g = 20 metres per second.
The space traversed during the eighteenth second will be equal to the difference of
the space traversed in 18 seconds and that traversed at the end of the seventeenth.
ZORA 1G we cO nn 572
Bie 2
x= = 350 metres.
11. A cannon-ball has been shot vertically upwards with a velocity of 250 metres in
asecond. After what interval of time would its velocity have been reduced to 54 metres
under the retarding influence of gravity, and what space would have been traversed by
the ball at the end of this time ?
If ¢ be the time, then at the end of each second the initial velocity would be dimi-
nished by 9™°8. Hence we shall have
54 = 250 — # x g'8, whence ¢ = 20 seconds;
and for the space traversed
9°8 x 207
= 250 X 20 —
2
= 3040 metres.
12. Required the time in which a body would fall through a height of 2000 metres,
neglecting the resistance of the air.
From s = 3 g¢? and substituting the values, we have
8
2000 = 2° 72, whence ¢ = 20°2 seconds.
2
13. A body falls in air from a height of 4000 metres. Required the time of its fall
and its velocity when it strikes the ground.
From the formula s = 4 g¢? we have for the time ¢ = -—~; and, on the other
hand, from the formula for velocity v = gt we have ¢ = — i OLA:
Hence 2 = vA ae from whichv = »/ 2 5g, and substituting the values for s and
e
g, v = 280 metres.
14. A stone is thrown into a pit 150 metres deep and reaches the bottom in
4 seconds. With what velocity was it thrown, and what velocity had it acquired on
reaching the ground? Azs. The stone was thrown with a velocity of 17°9, and on
reaching the ground had acquired the velocity 57°r.
15. A stone is thrown downwards from a height of 150 metres with a velocity of
10 metres per second. How long will it require to fall ?
The distance through which the stone falls is equal to the sum of the distances
Gravitation 1099
through which it would fall in virtue of its initial impulse and of that which it would
28
traverse under the influence of gravity alone; that is, 150 = 107 +
2
Taking the positive value only we get ¢ = 4°61 seconds.
16. How far will a heayy body fallin vacuo during the time in which its velocity
increases from 40°25 feet per second to 88°55 feet per second?
Ans. Taking the value of g at 32°2 feet, the body falls through 96°6 feet.
17. Required the time of oscillation of a single pendulum whose length is 0°9938,
and in a place where the intensity of gravity is 9°81.
From the general formula ¢ = 7 a, 2 in which ¢ expresses the time of one
&
oscillation, 7 the length of the pendulum, and g the intensity of gravity, we have
i= 3°1416 eee = I second.
9°81
18. What is the intensity of gravity in a place in which the length of the seconds
pendulum is o™*ggi ?
la
U ,
In) this|case Za: ree and also z = 7 7 and therefore 2 = i from
& Si & g
which g’ = Bs Substituting in this latter equation the values of 2’, 7, and 7, we
have g/ = 9™'782.
19, In a place at which the length of the seconds pendulum is 0’99384, it is required
to know the length of a pendulum which makes one oscillation in 5 seconds.
In the present case, as g remains the same in the general formula, and ¢ varies, the
length 7 must vary also. We shall have, then,
Ose eas Jak say
& &
from which, reducing and introducing the values, we have
fem a5" X. 000304 = 24'S46,
20. A pendulum, the length of which is 1™’95, makes 61,682 oscillations in a day.
Required the length of the seconds pendulum. Ans. 0°99385 metre.
21. A pendulum clock loses 5 seconds in a day. By how much must it be
shortened to keep correct time ?
Let s = the number of seconds in one day, and s’ the number indicated by the
clock, then s:’=2:2'=t:t=r/1': /7 .*. 86400 : 86395=1: A/xx."..x = '9998843.
Hence 1—x=0'0001157 Avs.
22, What is the normal acceleration of a body which traverses a circle of 42
metres diameter with a rectangular velocity of 3 metres? Ans. 4°286 metres,
23. An iron ball falls from a height of 68 cm. on a horizontal iron plate, and
rebounds to a height of 27 cm. Required the coefficient of elasticity of the iron.
If an imperfectly elastic ball with the velocity wv strikes against a plate, it rebounds
with the velocity v, = — #v, from which, disregarding the sign, 4 = “4. Now we
v
have the velocity v, = “2 gh, and v = /2 gh, from which & Vt, Substitut-
fh
ing the corresponding values, we get & = 0°63.
24. Two inelastic bodies, weighing respectively 100 and 200 pounds, strike against
each other with velocities of 50 and 20 feet ; what is their common velocity, after the
impact? Ams. 30, or 3°3, according as they move in the same or in opposite directions
before impact.
I100 Problems and Examples in Physics
III. ON LIQUIDS AND GASES
25. The force with which a hydraulic press is worked is 20 pounds ; the arm of the
lever on which this force acts is 5 times as long as that of the resistance; lastly, the
area of the large piston is 70 times that of the smaller one. Required the pressure
transmitted to the large piston.
If F be the power, and # the pressure transmitted to the smaller piston, we have
from the principle of the lever x 1 = / x 5. Moreover, from the principle of the
equality of pressure :
FxiI= p~p* 7O = 5 X 20 X 70 = 7000 pounds.
26. The force with which a hydraulic press is worked being 30 kilos. and the arm
of the lever by which this force is applied being ro times as long as that of the resist-
ance, and the diameter of the small piston being two centimetres; find the diameter of
the large piston, in order that a pressure of 2000 kilos may. be produced.
Ans. 5°164 centimetres.
27. One of the limbs of a U-shaped glass tube contains mercury, to a height of
o™*575 ; the other contains a different liquid to a height of o™42; the two columns
being in equilibrium, required the density of the second liquid with reference to mer-
cury and to water.
If dis the density of the liquid as compared with mercury, and d, the density com-
pared with water, then 1 x o'175 = 0°42 x d; and 136 x .0°'175 = 0°42 x @,;
whence d@d = o'416andd, = 5°66.
28. What force would be necessary to support a cubic decimetre of platinum in
mercury at zero? Density of mercury 13°6 and that of platinum 21°5.
From the formula P = VD the weight of a cubic decimetre of platinum is
I x er’s = 21*s and that. of a cubic decimetre of mercury 15 © x 13°65=13".0.
From the principle of Archimedes, the immersed platinum loses part of its weight
equal to that of the mercury which it displaces. Its weight in the liquid is therefore
21'5 — 13°6 = 7°9, and this represents the force required.
29. Given a body 4 which weighs 7°55 grammes in air, 5°17 gr. in water, and
6°35 gr. in another liquid, B ; required from these data the density of the body 4 and
that of the liquid B.
The weight of the body 4 loses in water 7°55 — 5°17 = 2°38 grammes; this repre-
sents the weight of the displaced water. In the liquid B it loses 7°55 — 6°35 = 1'2 gr.;
this is the weight of the same volume of the body B, as that of 4 and of the displaced’
water. The specific gravity of 4 is therefore
; TRV ene ey T2000 en
scp 3°172, and that of B See 0°504.
30. A cube of lead, the side of which is 4 cm., is to be supported in water by
being suspended to a sphere of cork. What must be the diameter of the latter, the
specific gravity of cork being 0°24, and that of lead 11°35?
The volume of the lead is 64 cubic centimetres; its weight in air is therefore
64 x 11°35, and its weight in water 64 x 11°35 — 64 = 662°4 gr.
If ~ be the radius of the sphere in centimetres, its volume in cubic centimetres will
3 5 ;
bets.) , and its weight in grammes is sas Tey Now, as the weight of, the
3
displaced water is obviously 47 in grammes, there will be an upward buoyancy
3 my
represented by
AMI 4.07 % O24 _ 477 x 0°76
3
5 3
477 x 0°76
which must be equal to the
weight of the lead ; that is, = 662'5, from which x = 5°™‘o25 and the
diameter = 11°85.
On Liguids and Gases 1101
31. A cylindrical steel magnet 15 cm. in length and 1‘2 mm. in diameter is loaded
at one end with a cylinder of platinum of the same diameter and of such a length that
when the solid thus formed is in mercury, the free end of the steel projects 10 mm.
above the surface. Required the length of this platinum, specific gravity of steel
being 7°8 and of platinum 2r’s.
The weight of the steel in grammes will be 15 7 7? x 7°8 and of the platinum
“er? X% 21'S.
These are together equal to the weight of the displaced mercury, which is
a 72 (14 + x) 13°6, from which = 9‘29 cm.
32. A cylindrical silver wire o™‘oors in diameter weighs 3°2875 grammes; it is to
be covered with a layer of gold o™‘ooo2 in thickness. Required the weight of the gold,
the specific gravity of silver being 10°47 and that of gold 19°26.
If vis the radius of the silver wire and & its radius when covered with gold, then
yr = ofo75 and R = o%'095. The volume of the silver wire will be ™7?Z and its
weight 7 7? 7 10°47, from which 7 = 17°768.
The volume of the layer of gold is
mw (R2 — rv?) 17°768,
and its weight
m (0'0952 — 0°075”) x 17°768 xX 19°26 = 3°656 nearly.
33. A kilogramme of copper is to be drawn into wire having a diameter of 0°16
centimetre. What length will it yield? Specific gravity of copper 8°88.
The wire produced represents a cylinder 7 cm. in length, the weight of which is
nw v2 7 8°88, and this is equal to 1000 grammes. Henced = 56™'0085.
34. The specific gravity of cast copper being 8°79, and that of copper wire being
8°88, what change of volume does a kilogramme of cast copper undergo in being
100
* 86617"
35. Determine the volumes of two liquids, the densities of which are respectively
1°3 and 0’7, and which produce a mixture of three volumes having the density og.
If x and y be the volumes, then from 7? = VD,13% + o'7 y = 3 x 0o’9 and
x +y = 3, from which = rand y = 2.
drawn into wire? Ans
36. The specific gravity of zinc being 7 and that of copper 9, what weight of each
metal must be taken to form 50 grammes of an alloy having the specific gravity 8s, it
being assumed that the volume of the alloy is exactly the sum of the alloyed metals ?
Let x = the weight of the zinc, and y that of the copper, then x + y = 50, and
from the formula P = VD, which gives V = < the volumes of the two metals and of
the alloy are respectively * 4+ i = a From these two equations we get x = 17°07
7 :
and y = 32°93.
37. A platinum sphere 3 cm. in diameter is suspended to the beam of a very ac-
curate balance, and is completely immersed in mercury. It is exactly counterbalanced
by a copper cylinder of the same diameter completely immersed in water. Required
the height of the cylinder. Specific gravity of mercury 13°6, of copper 8°8, and of
platinum 21's. Ans. 2°'025 centimetres.
38. To balance an ingot of platinum 27 grammes of brass are placed in the other
pan of the balance. What weight would have been necessary if the weighing had been
effected in vacuo? The density of platinum is 21°5, that of brass 8°3, and air under
a pressure of 760 mm. and at the temperature o° has 22 the density of water.
772
The weight of brass in air is not 27 grammes, but this weight minus the weight of
a volume of air equal to its own.
Since P = VD.", V = - and the weight of the air is —— = =f,
x 770 83x 770
By similar considerations, if x is the weight of platinum in vacuo, its weight in air
1102 Problems and Examples in Phystcs
will be x minus the weight of air displaced, that is x — ae ee Rene ae weight
orc x 970
is equal to that of the true weight of the brass ; and we have
Pe pains BED ARS 27___: from which x = 26'9c6.
21°5 X 770 ul Sc Sux e770
39. A body loses in carbonic acid 1°15 gr. of its weight. What would be its loss
of weight in air and in hydrogen respectively ?
Since a litre of air at o? and 760 mm. weighs 1'293 gramme, the same volume of
carbonic acid weighs 1°293 X 1°524 = I’‘97gramme. We shall, therefore, obtain the
volume of carbonic acid corresponding to 1°15 gr. by dividing this number by 1°97,
which gives 0°5837 litre. This being then the volume of the body, it displaces that
volume of air, and therefore its loss of weight in air is 0°5837 x 1'293 = 0°7547 gramme,
and in hydrogen 0°5837 x 1°293 x 0°069 = 0°052076.
40. Calculate the ascensional force of a spherical balloon of oiled silk which, when
empty, weighs 62°5 kilos, and which is filled with impure hydrogen, the density of
which is * that of air. The oiled silk weighs 0'250 kilo. the square metre.
13
The surface of the balloon is 62°5 = 250square metres, This surface being that of
0°25
a sphere, is equal to 4 7 &?, whence 4 RX? = 250 and & = 4°459; therefore V = qa kK’
me)
= 371°52 cubic metres.
The weight of air displaced is 371°52 x 1°293 kilo. = 480°375 kilos. ; the weight
of the hydrogen is 36°88 kilos., and therefore the ascensional force is
480°375 — (36°88 + 62°5) = 380°995.
41. A balloon 4 metres in diameter is made of the same material and filled with
the same hydrogen as above. How much hydrogen is required to fill it, and what
weight can it support?
The volume is * 7 R35 = 33°51 cubic metres, and the surface 4 R? = 50°265 square
metres. The weight of the air displaced is 33°51 x 1'293 = 43°328 kilos, and that of
the hydrogen is from the above data 3°333 kilos, while the weight of the material is 12°566
kilos. Hence the weight which the balloon can support is
43°328 — (12°566 + 3°333) = 27°429 kilos.
42. Under the receiver of an air-pump is placed a balance, to which are suspended
two cubes; one of these is 3 centimetres in the side,and weighs 26°324 gr. ; and the other
is 5 centimetres in the side, and weighs 262597 grammes. When a partial vacuum is
made these cubes just balance each other. What is the pressure ? Ans\'O™37a%
43. A soap-bubble 8 centimetres in diameter was filled with a mixture of one
volume of hydrogen gas and 15 volumes of air. The bubble just floated in the air;
required the thickness of the film.
The weight of the volume of air displaced is 4 73 x 0001293 gramme, and that
of the mixture of gases 4 on 73 x 0°00I293 X 320093 ; and the difference of
I
these will equal the weight of the soap-bubble.
This weight is that of a spherical shell, which, since its thickness ¢ is very
small, is with sufficient accuracy 4 7 7* 7s in grammes, where s is the specific gravity
=‘1.. tilence
37 7 (001293 — ‘001293 xX Ie) = 4ig2et tz,
Dividing each side by 4 + 72, and putting y = 4, we get
4 X ‘001293 (: as ios) =3°3¢;
On Liquids and Gases 1103
or
"001293 X ESE os 3°37:
4
whence ¢ = ‘00009116629 cm.
44. In a vessel whose capacity is 3 litres, there are introduced 2 litres of hydrogen
under the pressure of 5 atmospheres ; 3 litres of nitrogen under the pressure of half an
atmosphere, and 4 litres of carbonic acid under the pressure of 4 atmospheres. What
is the final pressure of the gas, the temperature being supposed constant during the
experiment ?
The pressure of the hydrogen, from Dalton’s law, will be te 5, that of the nitro-
gen will remain unchanged, and that of the carbonic acid will be 4 * 4. Hence the
total pressure will be
Lome Tyax6
= + —~ + — = go atmospheres.
3 2 3
45. A vessel containing ro litres of water is first exposed in contact with oxygen
under a pressure of 78 cm. until the water is completely saturated. It is then placed
in a confined space containing roo litres of carbonic acid under a pressure of 72 cm.
Required the volumes of the two gases when equilibrium is established. The coeffi-
cient of absorption of oxygen is o’042, and that of carbonic acid unity.
The volume of oxygen dissolved is 0°42. Being placed in carbonic acid it will
act as if it alone occupied the space of the carbonic acid, and its pressure will be
Toux PGE 0°326 cm.
100°42 :
Similarly the 1o litres of water will dissolve ro litres of carbonic acid gas, the total
volume of which will be 110, of which 100 are in the gaseous state and ro are dissolved.
Its pressure is therefore 72 x TOO = 65°454 cm.
IIo
Hence the total pressure when equilibrium is established is
0°326 + 65°454 = 65°78 cm. ;
and the volume of the oxygen dissolved reduced to the pressure 65'78 is
Naas olit‘o9208, and that of the carbonic acid 10 x oe Apeeee 9°95.
65°78 65°78
46. In a barometer which is immersed in a deep bath the mercury stands 743
mm. above the level of the bath. The tube is lowered until the barometric space,
which contains air, is reduced to one-third, and the mercury is then at a height of 7o1
mm. Required the atmospheric pressure at the time of observation. Azs. = 764mm,
47. What is the pressure on the piston of a steam boiler of 8’ decimetres diameter
if the pressure in the boiler is 3 atmospheres ? Ans. 10385'85 kilos.
48. What is the pressure of the atmosphere at that height at which an ascent of 21
metres corresponds to a diminution of 1™™ in the barometric height ? Azs. 378°9™™,
olit-42 x
49. What would be the height of the atmosphere if its density were everywhere
uniform ? Ans. 7954'1 metres, or nearly 5 miles.
50. How high must we ascend at the sea-level to produce a depression of 1 mm.
in the height of the barometer ?
Ans. Taking mercury as 10,500 times as heavy as air, the height will be 10°5 metres.
51. Mercury is poured into a barometer tube so that it contains 15 cc. of air under
the ordinary atmospheric pressure. The tube is then inverted in a mercury bath and
the air then occupies a space of 25 cc. ; the mercury occupying a height of 302 mm.
What is the pressure of the atmosphere ?
Let x be the amount of this pressure, the air in the upper part of the tube will have
a pressure represented by en and this, together with the height of the mercurial
2
column 302, will be the pressure exerted in the interior of the tube on the level of the
1104 Problems and Examples in Physics
mercury in the bath, which is equalto the atmospheric pressure ; that is TS¥ + 302
25
= x, from which x = 755 mm.
52. What effort is necessary to support a cylindrical bell-jar full of mercury
immersed in mercury ; its internal diameter being 6 centimetres, its height 02 above
the surface of the mercury (fig. 1) 18 centimetres, and the pressure of the atmosphere
0°77 centimetre?
The bell-jar supports on the outside a pressure equal to that of a column of mercury
the section of whose base is cd, and the height that of the barometer. This pressure is
equal to
Whee (aw CO pienek 3-0,
The pressure on the inside is that of the atmosphere less the weight of a column
of mercury whose base is cd and height 0d. Thisis equal tom R? x (0°77 —0°18) x 13°6
and the effort necessary is the difference of these two
pressures. Making: # = 3, cm.,. this. is found \to ‘he
69'216 kilos.
53. A barometer is placed within a tube which is after-
wards hermetically closed. At the moment of closing, the
temperature is 15° and the pressure 750 mm. The ex-
ternal space is then heated to 30°. What will be the height
of the barometer ?
The effect of the increase of temperature would be to
raise the mercury in the tube in the ratio r + pies to 1 +
fe)
™5_ and the height Z would therefore be
S5Se
este
= 75(2 * 550
Tobit T5S_ Fig. I.
555°
and since in the closed space the elastic force of the air increases in the ratio
I + 30a :12 + 15a, we Shall have finally 2 = 301°74 mm.
54, The heights of two barometers 4 and B have been observed at — 109? and
+ 15°, respectively, tobe A = 737 and B = 763. Required their corrected heights
BtiO-. Ans. A = 738°33. B = 760'94.
55. A voltaic current gives in an hour 840 cubic centimetres of detonating gas
under a pressure of 760 and at the temperature 12°'5 ; a second voltaic current gives
in the same time 960 cubic centimetres under a pressure of 755 and at the temperature
15°°5. Compare the quantities of gas given by the two currents, Ams. 1 : 1°129.
56. The volume of air in the pressure gauge of an
apparatus for compressing gases is equal to 152 parts. jim
By the working of the machine this is reduced to
7 parts, and the mercury is raised through 0°43
metre. What is the pressure of the gas?
Here AB = 152, AC = 37 parts, and BC =o0™-48. |e
The pressure of air therefore in AC is, from Boyle's
law, both
rs 4atm-ro8 = 3™°122, a
37 -—
ee
The pressure in the receiver is therefore
3°122 + 0°48 = °3™'602,
which is equal to 4°74 atmospheres.
57. An airtight bladder holding two litres of |
air at the standard pressure and temperature is |
immersed in sea-water to a depth of too metres, |
where the temperature is 49. Required the volume ~
of the gas.
E
E|
ATT TEM NTT
asi :
Air Pump L105
The specific gravity of sea-water being 1‘026, the depth of 100 metres will repre-
sent a column of pure water 102°6 metres in height. As the pressure of an atmo-
sphere is equal to a pressure of 10°33 metres of pure water, the pressure of this column
J) *r02°68
10°33
Hence, adding the atmospheric pressure, the bladder is now under a pressure of 10°94
= 9°94 atm.
atmospheres, and its volume being inversely as the pressure will be aie De 0'183 litre,
10°94
if the temperature be unaltered. But the temperature is increased by 4°, and therefore
the volume is increased in the ratio 277 to 273, and becomes
o°183 x 277 = 0'18568 litre.
273
58. To what height will water be raised in the tube of a pump by the first stroke of the
piston, thelength of stroke of which is o’5m., the height of the tube 6 metres, and its section
zy that of the piston? At starting the air in the tube is under a pressure of ro metres.
If we take the section of the tube as unity, that of the body of the pump is 10; and
the volumes of the tube and of the body of the pump are in the ratio of 6 to s. Then
if x is the height to which the water is raised in the pipe, the volumes of air in the
pump before and after the working of the pumpare 6 at the pressure 10, and 5 + 6 — x
at the pressure Io — x.
Forming an equation from these terms, and solving, we have two values, x’ = 18™ 26
and x” = 2°74. ‘The first of these must be rejected as being physically impossible ;
and the true height is x = 2°75 metres.
59, A receiver with a capacity of to litres contains air under the pressure 76 cm.
It is closed by a valve, the section of which is 32 square centimetres, and is weighted
with 25 kilogrammes. The temperature of the air is 30°; its density at o° and 76 cm,
pressure is 1 that of water. The coefficient of the expansion of gases is 0°00366.
Required hassel of air which must be admitted to raise the valve.
The air already present need not be taken into account, as it is under the pressure
of the atmosphere. Let x be the pressure in centimetres of mercury of that which is
x 1.1316
nee
admitted, will represent in kilogrammes its pressure on a square centi-
metre; and therefore the internal pressure on the valve, which is equal to the ex-
2X 13 OK, Ge
1000
ternal pressure of 25 kilogrammes, is = 25k. Fromwhich x = 57°44.
For the weight we shall have
be ERC eadice piel ie 88055 grammes,
I + 0'00366 x 30 =. 7600
60. A bell-jar contains 3°17 litres of air; a pressure gauge connected with it marks
zero when in contact with the air (fig. 3). The jar is
closed and the machine worked; the mercury rises
to 65 cm. A second barometer stands at 76 cm,
during the experiment. Required the weight of air
withdrawn from the bell-jar and the weight of that
which remains.
Ato® and 76cm. the weight of air in the bell-jar is
1'293 X 3°17 = 4°'09881.
At 0° and under the pressure 76 — 65 the weight
of the residual air is
4°09881r x II
7a)
and therefore the weight of that which is withdrawnis
4°0988 — 0°5932 = 3°5056 gr.
61. The capacity of the receiver of an air-pump
= 0°5932,
1106 Problems and Exaniples in Physics
is 7°53; it is full of air under the ordinary atmospheric pressure and at 0°. Re-
quired the weight of air when the pressure is reduced to o'21; the weight with-
drawn by the piston; and the weight which would be left at 15°.
The weight of 7°53 litres of air under the ordinary conditions is 9'736 grammes.
Under a pressure of o’2r it will be 2°69 grammes, and at the temperature 15° it will
be pete 00 Bh ee 0255 gramme.
Fret 'O'00300 xX 15
62. In a theoretically perfect air-pump, how great is the rarefaction after ro strokes,
if the volumes of the barrel and the receiver are respectively 2 and 3?
Ans, = 4°59™™; or about - & of an atmosphere.
aa
63. What must be the capacity of the barrel of an air-pump if the air in a re-
ceiver of q litres is to be reduced to 4 the density in two strokes? AUS. Zit:
64. The reservoir of an air-gun, the capacity of which is 4o cubic inches, contains
air whose density is 8 times that of the mean atmospheric pressure. A shot is fired
when the atmospheric pressure is 741 mm. and the gas which escapes occupies a volume of
80 cubic inches. What is the elastic force of the residual air? Azs, 6'05 atmospheres.
65. Suppose that at the limit of the atmosphere the pressure of the attenuated
air is the —*— of a millimetre of mercury and the temperature — 135°, and that ina
1000
place at the sea-level, in latitude 45°, the pressure of the atmosphere is 760™™ and its
temperature 159 C. Determine from these data the height of the atmosphere.
From the formula 18400 { 1 + o'002{7 + ¢} | log oy we get for the height in metres
82237, which is equal to 51°1 miles. .
66. If water is continually flowing through an aperture of 3 square inches with a
velocity of 10 feet, how many cubic feet will flow out in an hour? -Azs. 750 cubic feet.
67. With what velocity does water issue from an aperture of 3 square inches, if
37°5 cubic feet flow out every minute? Ans. 36 feet:
68. What is the ratio of the pressure in the above two cases ? LASTS TO:
69. What is the theoretical velocity of water from an aperture which is 9 feet
below the surface of water ? Ans. 24 feet.
70. Ina cylinder, water stands 2 feet above the aperture and is loaded by a piston
which presses with a force of 6 pounds on the square inch. Required the velocity of
the effluent water. Ans, 32 feet.
71. How deep must the aperture of the longer leg of a syphon, which has a sec-
tion of 4 square centimetres, be below the surface of the water in order that 25 litres
may flow out in a minute? Ans. 5°535 cm,
72. Through a circular aperture having an area of o’196 square cm. in the bottom
of a reservoir of water which was kept at a constant level, 55 cm. above the bottom,
it was found that 98°5 grammes of water flowed in 22 seconds. Required the coeffi-
cient of efflux. .
Since the velocity of efflux through an aperture in the bottom of a vessel is given by
the formula v =»/2 gh, it will readily be seen that the weight in grammes of water
which flows ina given time, ¢, will be given by the formula w = aq tr/ 22h, where a is
the area in square centimetres, a the coefficient of efflux, ¢ the time in seconds, and &
the height in centimetres. Hence in this case a= 0699.
73. Similarly through a sgware aperture, the area of which was almost exactly the
same as the above, and at the same depth, 104°4 grammes flowed out in 21°6 seconds,
In this case 2 = 0'73.
Sound 1107
IV, ON SOUND
74. A stone is dropped into a well, and 4 seconds afterwards the report of its
striking the water is heard. Required the depth, knowing that the temperature of the
air in the pit was 109°74.
From the formula v = 333 4/1 + a¢ we get for the velocity of sound at the tem-
perature in question 339°05 metres.
Let ¢ be the time which the stone occupies in falling; then 4.72 = x will represent
the depth of the well; on the other hand, the time occupied by the report will be 4 — 4,
and the distance will be (4 — ¢) v = ~ (i); thus (4 — ¢) v = 3g? (ii), from which,
substituting the values,
(4 — 2) 3395 = 49 2
¢ = 3°793 seconds, and substituting this value in either of the equations (i) or (ii),
we have the depth = 72°6 metres nearly,
75. A bullet is fired from a rifle with a velocity of 414 metres, and is heard to strike
a target 4 seconds afterwards. Required the distance of the target from the marks-
man, the temperature being assumed to be zero.
age Mee As Gan 730 e
76. At what distance is an observer from an echo which repeats a sound after
3 seconds, the temperature of the air being 109?
In these 3 seconds the sound traverses a distance of 3 x 339 = 1017 metres ; this
distance is twice that between the observer and the reflecting surface ; hence the dis-
tance is
IOI7
= 508'5 metres.
77. Between a flash of lightning and the moment at which the corresponding
thunder is first heard, the interval is the same as that betweea two beats of the pulse.
Knowing that the pulse makes 80 beats in a minute, and assuming the temperature
of the air to be 15° C., what is the distance of the discharge? Ams.’ 454°I metres.
78. A stone is thrown into a well with a velocity of 12 metres, and is heard to
strike the water 4 seconds afterwards. Required the depth of the well.
Ans, About 110 metres.
79. What is the velocity of sound in coal gas at 0°, the density being 0°5?
Ans. 470°9 metres.
80. What must be the temperature of air in order that sound may travel in it with
the same velocity as in hydrogen at 0° ? Ans, About 3680° C.
81. What must be the temperature of air in order that the velocity of sound may
be the same as in carbonic acid at 0°? Ans. — 10595 C.
82. Kendall, in a North Pole Expedition, found the velocity of sound at — 40°
was 314 m. How closely does this agree with that calculated from the value we have
assumed for 0° ? Ans, 6°64 metres too much.
83. The report of a cannon is heard 15 seconds after the flash is seen, Required
the distance of the cannon, the temperature of the air being 22°,
From the formula for the velocity of sound we have
I5 X 333 »/1 + 0°003665 x 22 = 5190 metres.
84. If a bell is struck immediately at the level of the sea, and its sound, reflected
from the bottom, is heard 3 seconds after, what is the depth of the sea ?
Ans. 7140 feet.
4B2
1108 Problems and Examples in Physics
85. A person stands 150 feet on one side of the line of fire of a rifle range 450 feet
in length and at right angles to a point 150 feet in front of the target. What is the
velocity of the bullet if the person hears it strike the target * of a second later than
the report of the gun? The temperature is assumed to be 16°°5. Azs. 2038 feet.
86. An echo repeats five syllables, each of which requires a quarter of a second to
pronounce, and half a second elapses between the time the last syllable is heard and
the first syllable is repeated. What is the distance of the echo, the temperature of
the air being 10° C. ? Ans, 297'47 metres.
87. The note given by a silver wire a millimetre in diameter and a metre in
length being the middle C, what is the tension of the wire? Density of silver 10°47.
Ans, 22°67 kilogrammes.
88. The density of iron being 7°8 and that of copper 8°8, what must be the
thickness of wires of these materials, of the same length and equally stretched, so that
they may give the same note ?
From the formula for the transverse vibration of strings we have for the number of
vibrations 2 = — yas ey As in the present case, the tensions, the length of the
strings, and the se if vibrations a are the same, we have
at hich Spe Ly.
i / a? ri aa eae drags
é
whence bee eh AN 8. hence os wf 3 oer obs.
ad 4 7°38
89. A wire stretched by a weight of 13 kilos: sounds a certain note. What must
be the stretching weight to produce the major third ?
The major third having 5 the number of vibrations of the fundamental note, and as,
all other things being the same, the numbers of vibrations are directly as the square
roots of the stretching weight, we shall have x = 20°312 kilos.
90. The diameters of two wires of the same length and material are o’oo15 and
00038 m. ; and their stretching weights 400 and 1600 grammes respectively. Required
the ratio of the numbers of their vibrations. Ans) 75 t =E 26608
91. A brass wire r metre in length stretched by a weight of 2 kilogrammes, and a
silver wire of the same diameter, but 3°165 metres in length, give the same number of
vibrations. What is the stretching weight in the latter case ?
Since the number of vibrations is equal, we shall have
I adi TP a ica
rl na Ke Sz d, :
from which, replacing the numbers, we get x = 25 kilos.
92. A brass and a silver wire of the same diameter are stretched by the weights of 2
and 25 kilogrammes respectively, and produce the same note. What are their lengths,
knowing that the density of brass is 8°39, and of silver 10°47?
Ans. The length of the silver wire is 3°16 times that of the brass,
93. A copper wire 1°25 mm. in diameter and a platinum one of 0°75 mm. are
stretched by equal weights. What is the ratio of their lengths, if, when the copper
wire gives the note C, the platinum gives F on the diatonic scale?
Ans. The length of the copper is to the length of the platinum = 1°264 : I
94. An organ pipe gives the note C at a temperature 0°; at what temperature
will it yield the major third of this note? Anspirsavc.
95. A brass wire a metre in length, and stretched by a weight of a kilogramme,
yields the same note asa silver wire of the same diameter but 2'5 metres in length and
stretched by a weight of 7°5 kilogrammes, Required the specific gravity of the silver.
Ans. 10°068.
96. How many beats are produced in a second by two notes, whose rates of vibra-
tion are respectively 340 and 354? Ans. 14.
Fleat 1109
VoSON Hea Tt
97. Two mercurial thermometers are constructed of the same glass ; the internal
diameter of one of the bulbs is 7™™:5 and of its tube 2's; the bulb of the other is
6°2 in diameter and its tube 1°5. What is the ratio of the length of a degree of the
first thermometer to a degree of the second?
Let 4: and B be the two thermometers, D and D the diameters of the bulbs, and
d and a’ the diameters of the tubes. Let us imagine a third thermometer C with the
same bulb as B and the same tube as 4, and let Z /’, and 7” denote the length of a
degree in each of the thermometers respectively. Since the stems of 4 and C
have the equal diameters, the lengths Z and 7” are directly as the volumes of the
tubes, or what is the same, as the cubes of their diameters; and as Band C have
the same bulk, the lengths 2’ and 2” are inversely proportionate to the sections of
the stems, or what amounts to the same, to the squares of their diameters. We
have then
Z D5 d OT hae
ee sy n Fie se hea
Z D's Z a’
introducing the values and solving, we have
l
— = 0°638.
7 a
98. At what temperature is the number on the
Centigrade and Fahrenheit thermometers the same ?
Ans, — 40°.
99. The same question for the Fahrenheit and
Réaumur scales. Ans, — 25'6.
100. A capillary tube is divided into 180 parts
of equal capacity, 25 of which weigh 1’2 gramme.
What must be the radius of a spherical bulb to be
blown to it so that 180 divisions correspond to 150
degrzes Centigrade?
Since 25 divisions of the tube contain 1'2
gramme, 180 divisions contain ED ouige) = 304, Fig. 4.
ce
And since these 180 divisions are to represent 150 degrees, the weight of mercury
corresponding to a single degree is aoa But as the expansion corresponding to
150
8°64 a
one degree is only the apparent expansion of mercury in glass, the weight - eaten
150 480
of the mercury in the reservoir, which is 4 7R3, From this R = 1°8755 centimetre.
3
101. By how much is the circumference of an iron wheel, whose diameter is 6 feet,
increased when its temperature is raised 400 degrees? Coefficient of expansion of
iron = 00000122, Ans. By 0'0g2 foot.
102. What must be the length of a wire of this metal which for a temperature of
1° expands by one foot? ins, 81967 feet.
103. A pendulum consists of a platinum rod, on a flattening at the end of which
rests a spherical zinc bob. The length of the platinum is Z at 0°. What must be the
diameter of the bob, so that its centre is always at the same distance from the point of
suspension whatever be the temperature? Coefficient of expansion of platinum
0'0000088 and of zinc 0’0000294.
Ans. The diameter of the bob must be 3 of the length of the platinum.
104. Two walls, which when perpendicular are 30 feet apart, have bulged out-
wards to the extent of 2°4 inches. ‘They are to be made perpendicular by the contrac-
IITIO Problems and Examples in Physics
tion of an iron bar. By how much must its temperature be raised above that of the air,
which is taken at 0°? Ans. 546°4.
105. An iron wire 4 sq. mm. in cross section is stretched ae its length by a
weight of 1 kilogramme. What weet must be applied toa ae 9g sq. mm. in cross
section, when it is heated from 0° to 20°, in order to prevent it from expanding ?
Ans. 44°5 kilos.
106. At the temperature zero a solid is immersed 0'975 of its total volume in
alcohol. At the temperature 25° the solid is wholly immersed. ‘The coefficient of
_expansion of the solid being 0’000026, required the coefficient of expansion of the
alcohol, Ans. O°OOI052.
107. Into a glass globe, the capacity of which at 0° is 250 cc., are introduced
25 cc. of air measured at 0° and 76cm. ‘The flask being closed and heated to 100°,
required the internal pressure. Coefficient of cubical expansion of glass aay
38700
o
At 100° the capacity of the flask is 250 (: + 02) ; again at 100? the volume of
38700
the free air under the pressure 76 is 25 (I + 100 X 0'00366). But.its real volume is
250 x a under a pressure x. Hence
3°7
WO 2 *% =. 250,x aS :25 x 1°366, from which x = 10°3548 cm.
3°97
108. The specific gravity of mercury at 0° being 13°6, required the volume of
3 kilogrammesat 85°. Coefficient of expansion ae :
fo)
The volume at 0° will be —*— and at 85° 3 x (: +e ey) = 0°22309 litre.
13°6 136 5550
109. A hollow copper sphere 20 cm. in diameter is filled with air at o° under a
pressure of 14 atmosphere ; what is the total pressure on the interior surface when the
enclosed air is heated to a temperature of 600° ? Ans, 6226'°5 kilogrammes.
110. Between the limits of pressure 700 to 780mm. the boiling-point of water varies.
0°'0375 C. for each mm. of pressure. Between what limits of temperature does the
boiling point vary, when the height of the barometer is between 735 and 755 mm. ?
Ans. Between 99°'0625 and 99°°8125.
111. Liquid phosphorus cooled down to 30°, is made to solidify at this tempera-
ture. Required to know if the solidification will be complete, and if not, what weight
will remain melted? The melting point of phos pneriad is 44°2; its latent heat of fusion
5°4, and its specific heat o°2.
Let x be the weight of phosphorus which solidifies; in so doing it will give out a
quantity of heat = 5°4 4%; this is expended in raising the whole weight of the phos-
phorus from 30 to 44"2. Hence we have 5°4* = I x (44°2 — 30) o'2, from which
x= 7 oe 0'526, so that 0°474 of phosphorus will remain liquid.
54
112. A pound of ice at oon is placed in two pounds of water at o°; required the
weight of steam at 1009 which will melt the ice and raise the temperature of the mix-
ture to 30°. The latent heat of the liquefaction of ice is 79’2, and that of the vaporisa-
tion of water 536. Ans. °279 pound.
113. 65°5 grammes of ice at — 20° having been placed in x grammes of oil of
turpentine at 13°3°, the final temperature is found to be 3°19. The specific heat of
turpentine is 0°4, and it is contained in a vessel weighing 25 grammes, whose specific
heat iso‘z. The specific heat of ice iso'5. Required the value of x.
Ans, x = 1475 grammes.
114. In what proportion must water at a temperature of 30° and linseed oil
(sp. heat = o'5) at a temperature of 50° be mixed so that there are 20 kilogrammes of
the mixture at 40°? Ans. Water = 6°66 kilos. and linseed oil = 13°34.
Fleat ox III1
115, By how much will mercury at 0° be raised by an equal volume of water at
100° ? wns) 68°19 Ga
116. The specific heat of gold being 0'03244, what weight of it at 45° will raise a
kilogramme of water from 12°9°3 to 15°'7?
Let x be the weight sought ; then x kilogrammes of gold in sinking from 45° to
15°°7 will give out a quantity of heat represented by x (459 — 15°°7) 00324, and this is
equal to the heat gained by the water, that is to 1 (15°7 — 12°3) = 3°4, thatis x = 3°58.
117. The specific heat of copper sulphide is o‘r2r12, and that of silver sulphide
0'0746. 5 kilos. of a mixture of these two bodies at 40°, when immersed in 6kilos. of
water at 7°669°, raises its temperature to 10°. How much of each sulphide did the
mixture contain ?
The weight of the copper sulphide = 2, and that of the silver sulphide 3.
118. Into a mass of water at 0°, 100 grammes of ice at — 12° are introduced; a
weight of 7°2 grammes of water at 0° freezes about the lump immersed, while its
temperature rises to zero. Required the specific heat of ice. Latent heat of water
79°2. Ans. 0°4752.
119, Four pounds of copper filings at 130° are placed in 20 pounds of water at 20°,
the temperature of which is thereby raised 2 degrees. What is the specific heat, ¢, of
copper ? AN S.s6i == 40" 0020s
120. Two pieces of metal weighing 300 and 350 grammes, heated toa temperature
x, have been immersed, the former in 3351°6 grammes of water at 10°, and the latter in
1935'4 grammes at the same temperature. ‘The temperature in the first case rises to
2o~, and in thesecond to 30°. Required the original temperature and the specific heat
of the metal. 475.2 the temperature = 10009 }/¢ the specific. heat =" orm.
121. In what proportions must a kilogramme of water at 50° be divided in order that
the heat which one portion gives out in cooling to ice at zero may be sufficient to change
the other into steam at 100° ? ARS AL =f O°0209-
122. Three mixtures are formed by mixing two and two together, equal quantities
of ice, salt, and water at 0°. Which of these mixtures will have the highest and which
the lowest temperature ? Ams. The mixture of ice and salt will produce the lowest
temperature, while that of ice and water will produce no lowering of temperature.
123. In 25°45 kilogrammes of water at 12°°5 are placed 6'17 kilos. of a body at a
temperature of 80° ; the mixture acquires the temperature 14°°r. Required the specific
heat of the body.
If ¢c isthe specific heat required, then mc (# — 9) represents the heat lost by the body
in cooling from 80° to 149°1; and that absorbed by the water in rising from 12°'5 to
14°°r is m’ (9 — ¢), ‘These two values are equal. Substituting the numbers, we have
¢ = O'IOOT4. |
124. Equal lengths of the same thin wire traversed by the same electrical current are
placed respectively in 1 kilogramme of water and in 3 kilogrammes of mercury. The
water is raised 10° in temperature; by how much will the mercury be raised ?
Ans. 100°'04.
125. How many cubic feet of air under constant pressure are heated through 1° C.
by one thermal unit ? Ans. 55°3 cubic feet.
126. Given two pieces of metal, one x weighing 2kilos. heated to 80°, and the other
y weighing 3 kilos., and at the temperature 50°. To determine their specific heats
they are immersed in a kilogramme of water at 10°, which is thereby raised to 269°3.
The experiment is repeated, the two metals being at the temperature roo? and 40°
respectively, and, as before, they are placed in a kilogramme of water at 10°, which
this time is raised to 289’4. Required the specific heats of the two metals.
ASK =) O7LIS j Y= OLO535.
127. For high temperatures the specific heat of iron is o'1053 + 0’000017 #. What
is the temperature of a red-hot iron ball weighing a kilogramme, which, plunged in 26
Lire Problems and Examples in Physics
kilogrammes of water, raises its temperature from 12° to 249? What was the tempe-
rature of the iron?
(0'1053 + o'000017 Z) (¢ — 24) = 16 (24 — 12),
or ‘oooo17 2% + ‘1048892 ¢ — 2°5272 = 192;
transposing and dividing by the coefficient of 77, we get
f@-+ 6176 t = |AT442770,
#2 + 6170 ¢ + (3085)? = 20960001
hence ¢+ 3085 = 4578°3 nearly; .°. ¢ = 1493°3.
128. A kilogramme of the vapour of alcohol at 80° passes through a copper worm
placed in 10°8 kilogrammes of water at 12°, the temperature of which is thereby raised
to 36°. The copper worm and copper vessel in which the water is contained weigh
together 3 kilogrammes. Required the latent heat of alcohol vapour. 10.
A Siemens unit is equal to the resistance of a column of pure mercury a metre in
length and a square mm. in cross section. It is equal to 0’9536 of an ohm or BA
unit; ora BA unit equals 10485 Siemens unit, or equals a column of mercury 1°0485
metre in length and a square mm. in cross section.
194, A single thermo-electric couple deflects a galvanometer of roo ohms resist-
ance 0° 30’; how much will a series of 30 such couples deflect it, the connections being
made by short thick wires ? Ans, TA°*40":
195. Suppose a sine galvanometer had been used in the last question, and the
first reading had been 09°30’, what would the second be? Ansei5 16h
196. The internal resistance of a cell is halfan ohm; when a tangent galvano-
meter of 1 ohm resistance is connected with it by short thick wires it is deflected 15° ;
by how much will it be deflected if for one of the thick wires a thin wire of 14 ohm
resistance is substituted ? ANS]? t3Gh
197, What will be the deflection if each of the wires is replaced by a thin wire of
14 ohm resistance ? AAG SOs
198. A cell of one-third of an ohm resistance deflects a tangent galvanometer of
unknown resistance 45°, the connection being made by two short thick wires. If a wire
of 3 ohms resistance be substituted for one of the short wires the deflection is 30°. What
is the resistance of the galvanometer? AMS, 3°75 ohms.
199. What would be the deflection if for the cell in the last question three exactly
similar cells in series were substituted (2) when the galvanometer alone is in circuit ;
(4) when both the galvanometer and the thin wire are in circuit ?
Ans, & 68°48, 0 = B79*4r",
200. A galvanometer offering no sensible resistance is deflected 50° by a cell
connected with it by short thick wires. Ifa resistance of 3 ohms be put in the circuit,
the deflection is 20°. Find the internal resistance of the cell. Ans, 1°32;
201. Suppose the results in the last question were produced by two exactly similar
cells in series, find the internal resistance of each. Ans, 0°659.
202. Suppose they were produced by two exactly similar cells placed side by side,
find the internal resistance of each. Ans. 2°639.
203. If the resistance of 130 yards of a particular copper wire of an inch in
I
diameter is an ohm, express in that unit the resistance of 8242 yards of copper wire fee
12
of an inch in diameter. ; Ans. 35°66.
203. One form of fuse for firing mines by voltaic electricity consists of a platinum
wire 2 of an inch long, of which a yard weighs 2 grains. Required its resistance in
terms of a Siemens unit. Specific gravity of platinum 22, and its conducting power
11°25 that of mercury. Ans, 0°131.
205. Express in ohms the resistance of one mile of copper wire } of an inch in
diameter of the same quality as that referred to in 203. Ans, 0'8461,
1118 Problems and Examples in Physics
206. The whole resistance of a copper wire going round the earth (24800 miles) is
221650 ohms. Find its diameter in inches. Ans. 0'0738.
207. What length of platinum wire 0’o5 of an incn in-diameter must be taken to
get a resistance equal to 1 ohm, the specific resistance of platinum being taken at 5°55
that of copper ? Ans. 14'9 metres,
208. 660 yards of iron wire 0'0625 of an inch in diameter have the same electrical
resistance as a mile of copper wire o’0416 of an inch in diameter. Find the specific
resistance of iron, that of copper being unity. Ans, 6°02.
209. Ten exactly similar cells in series produce a deflection of 45° in a tangent
galvanometer, the external resistance of the circuit being ro ohms. If arranged so
that there is a series of 5 cells, of two abreast, a deflection of 33°42!’ is produced ;
find the internal resistance of the cell. Ans. 4 ohm.
210. On the bobbins of the new Post Office pattern of a single needle instrument
are coiled 225 yards of No. 35 copper wire 0°0087 inch in diameter, the resistance of
which is about 92 ohms. Required the conducting power of the wire in terms of
mercury. Ansiess 6.
211. Ten exactly similar cells each of § of an ohm resistance give, when arranged
in 2 series of five each, a deflection of 239°57’; but when arranged in 5 series of 2 each
a deflection of 33°°42’. Required the external resistance of the circuit including that
of the galvanometer. Ans, 35.
212. A cell ina certain circuit deflects a tangent galvanometer 18° 26’; two such
cells abreast in the same circuit deflect it 23° 57’; two such cells in series in the same
circuit diminished by 1 ohm deflect it 29°°2’.. Find the internal resistance of one cell
and that of the circuit. Ans. Ros 4 st 66,
213. What is the best arrangement of 6 cells, each of % of an ohm resistance,
against an external resistance of 2 ohms?
Ans. Indifferent whether in 6 cells of 1 each or in 3 cells of 2 each.
214. What is the best arrangement of 20 cells, each of 0’8 ohm resistance, against
an external resistance of 4 ohms? Ans. to cells of 2 each.
215. Ina circuit containing a galvanometer and a voltameter, the current which
deflects the galvanometer 45° produces 10°32 cubic centimetres of mixed gas in a
minute. ‘The electrodes are put farther apart, and the deflection is now 20° ; find
how much gas is now produced per minute. Ans. 3°757 cc.
216. 100 inches of copper wire weighing 100 grains has a resistance of 0'1516 ohm,
Required the resistance of 50 inches weighing 200 grains. Ans. 0°0379.
217. A knot of nearly pure copper wire weighing one pound has a resistance of
1200 ohms at 15°’5 C.; what is the resistance at the same temperature of a knot of the
same quality of wire weighing 125 pounds? Ans. 96 ohms,
218. Find the length in yards of a wire of the same diameter and quality as the
knot pound in 217, having a resistance of 2 ohms. Ans. 3°38 yards.
219. Find the length in yards of a wire of the same quality and total resistance as
the knot pound in 217, but of three times the diameter. Ans, 18261 yards.
220. The specific gravity of platinum is 2} times that of copper; its resistance 5%
as great. What length of platinum wire weighing roo grains has the same resistance
as roo inches of copper wire also weighing Ioo grains? Ans. 27,
221. Acell with a resistance of an ohm is connected by very short thick wires with the
binding screws of a tangent galvanometer, the resistance of which is half an ohm, and
the deflection is 45° ; if the screws of the galvanometer be also connected at the same
time by a wire of 1 ohm resistance, find the deflection. Ans. 36° 52’.
222. The resistance of a galvanometer is half an ohm, and the deflection when
Voltaic E lectricity : L119
the current of a cell is passed through it is 30°. When a wire of 2 ohms resistance is
introduced into the circuit the deflection is 15°; find the internal resistance of the cell.
ASS Toa
223. When the current of a cell, the resistance of which is $ of an ohm, is passed
through a galvanometer connected with it by very short thick wires, the deflection is
45°; when the binding screws are also connected by a shunt having a resistance of 1
the deflection is 33°°42’. Find the resistance of the galvanometer. aoe 2
224. A cell whose internal resistance is 2 ohms has its copper pole connected with
he binding screw A of a galvanometer formed of a thick band of copper. From
the other screw Ba wire of 20 ohms resistance passes to the zinc pole, and the deflection
read off is 79°8’. Find the deflection when B is at the same time connected with the
zine pole by a second wire of 30 ohms resistance. ANS ei ie G
225. What would be the deflection in 224 if the second wire instead of passing
from B to the zinc pole passed directly from the zinc pole to the copper pole?
Ans, 6°°47'.
226. A Leclanché cell deflects a galvanometer 30° when 200 ohms resistance are
introduced into the circuit, 15° when 570 ohms are introduced; a standard Daniell
cell deflects it 30° when 100 ohms are in circuit, and 15° when 250 additional ohms are
introduced. Required the electromotive force of the Leclanché in terms of that of the
Daniell. Ans, 1°48.
227. A Bunsen and a Daniell cell are placed in the same circuit in the first case
so that the carbon of the first is united to the zinc of the Daniell; and in the second
case so that their currents oppose each other.. The currents are respectively 30°°2’,
and in the second 10°°6’. Required the electromotive force of the Bunsen in terms of
the Daniell. Ans. 1°89.
228. A telegraph line constructed of copper wire, a kilometre of which weighs 30°5
kilogrammes, is to be replaced by iron wire a kilometre of which weighs 135°6 kilo-
grammes. In what ratio does the resistance alter? Avs. The resistance of the iron
wire will be 1°18 times that of the copper wire for which it is substituted.
229. A telegraph line which has previously consisted of copper wire weighing 30°5
kilogrammes to the kilometre is to be replaced by an iron wire of the same length
which shall offer the same resistance. What must be the section of the latter, and
what its weight per kilometre ?
Ans. The section of the copper wire is 3°4357 sq. mm., that of the iron by which
it is replaced is 20°6 sq. mm., and its weight per kilometre is 160°4 kilogrammes.
230. When the poles of a voltaic cell are connected by a conductor of resist-
ance 1, acurrent of strength 1°32 is produced ; and when they are connected by a
conductor of resistance 5 the strength of the current is 0°33. Find from these data
the internal resistance and the electromotive force of the cell. Ans. R=} H=1'76.
231. A silver wire is joined end to end to an iron wire of the same length, but of
double the diameter, and six times the specific resistance; the other ends are joined
to the battery, the current of which is transmitted for five minutes, during which time
a total quantity of 45 units of heat is generated in the two wires. How is it shared
between them ? Ans, Ag: Fe=18 : 27.
232. A window casement of iron faces the south, and the hinges which support it
are on the east. What electrical phenomena are observed (a) when the window is
opened, and (4) when it is closed ?
233. Two points 135° apart in a uniform circular conducting ring are connected
with the opposite poles of a voltaic battery. Compare the strength of the current in
the two portions of the ring.
234. A mile of cable with a resistance of 3°59 ohms was put in water, with the
end B insulated ; its core having been pricked with a needle the resistance tested from
the end 4 was found to be 2°81 ohms. 4 being insulated, a test from B showed the
resistance to be 2°76. Required the distance from & to the injured spot.
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INDEX
(THE NUMBERS REFER TO THE ARTICLES)
ABE
BERRATION,
spherical, 545
Abnormal dispersion, 593
Absolute electrical units, 999
Absolute expansion of mercury, 326
Absolute measure of electrical resistance,
985; temperature, 508
Absorbent power of aqueous vapour, 1023
Absorbing power, 431
Absorption, electrical, 795; of gases by
chromatic,
5953
solids, 196; of gases by liquids, 192; |
of heat by liquids, 442; by vapours,
443; heat produced by, 492
Acceleration of a force, 27, 62, 78
Accidental haloes, 641; images, 640;
magnetic variations, 706
Accommodation (of the eye), 634
Accumulator, hydraulic, 154
Accumulators, 788
Achromatism, 596 ; of the microscope, 604 |
Achromatopsy, 646
Acidometer, 128
Acierage, 880
Aclinic lines, 712
Acoustic foci, 240 ; attraction and repul-
sion, 294
Acoustics, 223-295
Actinic balance, 995 ; rays, 441, 585
Action and reaction, 39
Ader’s telephone, 960
Adhesion, 87
Aerial meteors, 10II ; perspective, 631
Aerolites, 490
#ésculine, 594
Affinity, 86
After action, elastic, 89
Agents, 6
Agonic line, 706
Air, aspirating action of currents of, 210;
causes which modify temperature of,
1012, 1043 ; heating by, 503; thermo-
meter, 338 ;resistance of, 48; trap, 170;
velocity of, 25; gap, 951
ANI
Air-balloons, 199 ; chamber, 220
Air-brake, 212; pump, 203, 477; Bian-
chi’s, 206 ; condensing, 212; Deleuil’s,
207; gauges, 2Cc4; rarefaction in,
203 5 “receiver of, (203.50 Sprengel s;
208 ; uses of, 213
Ajutage, 148
Alarum, electric, 918
Alcarrazas, 377
Alcohol thermometer, 310
Alcoholic value of wines, 382
Alcoholometer, 129 ; Gay-Lussac’s, 129;
centesimal, 129
| Allotropic states, 466
Alloys, 344
Alternate currents, 936
Amagat’s experiments, 98, 184
Amalgam, electrical, 777
Amalgamated zinc, 837
Amber, 745
Amici’s camera lucida, 615
Ammeter, 998
Ampere, 835
Ampere’s memoria technica, 841; stand,
890 ; theory of magnetism, 901
Amplitude of vibration, 55
Analogous pole, 754
Analyser, 670
Analysis, spectral, 587; of solar light,
437
Anamorphoses, 546
Anelectrics, 746
Anelectrotonus, 850
Anemometer, IO12
Aneroid barometer, 167, 190
Angle of deviation, 556; critical. 552;
optic, 630; of polarisation, 668; of
reflection and incidence, 523, 5483
of refraction, 548 ; visual, 630
Angular currents, laws of, 883 ; velocity,
53
Animal heat, 497
Anion, 864
La 22
ANN
Annealing, 91, 95
Annual variations of magnetism, 707
Anode, 864
Anticyclone, 1017
Antilogous pole, 754
Anvil of an induction coil, 949
Aperiodic galvanometer, 843
Aperture of a lens, 570
Aplanatic lenses, 570
Aqueous humour of the eye, 625
Aqueous vapour, its influence on climate,
1023; tension of, 359-365
Arago’s experiment, 184
Arbor Dianz, 876; Saturni, 876
Arc lamps, 860
Arc of vibration, 55 ; voltaic, 855
Archimedes’ principle, 14; applied to
gases, 198 ,
Area, unit of, 22
Argon, 160
Armatures, 739; drum, 941; Siemens’,
03%
Arms of levers, 40
Armstrong’s hydro-electric machine, 780
Artesian wells, 112
Artificial magnets, 695
Ascension, angle of right, 612
Ascent of liquids in capillary tubes, 133 ;
between surfaces, 134
Aspirating action of air currents, 210
Astatic needle and system, 714; circuits,
895
Astronomical telescope, 607
Athermancy, 442
Atmolysis, 193
tmosphere, its composition, 160; crush-
ing force of, 162 ; amount of, determi-
nation of, 166; electricity in the,
10323 moisture of, 407
Atmospheric electricity, causes of, 1033,
1034 $ pressure, 161, 166, 1012
Atomic heat, 468 ; weight deduced from
specific heat, 468
Atoms, 3
Attraction, capillary, 132; and repulsion
produced by capillarity, 138; mole-
cular, 84 ; universal, 67
Attraction, magnetic, laws
electrical, laws of, 756
Atwood’s machine, 78
Audiometer, 962
Audiphone, 243
Aura, electrical, 787
Aurora borealis, 708, 1041
Aurum musivum, 777
Austral pole, 703
Avoirdupois, 23
O17 ET:
Index
BER
Axis of crystal, 654 ;- electric; 7545
lenses, 567; optic, 654 ; of a magnet,
696 ; of oscillation, 80
Azimuth circle, 709
AD conductors, 411
Bain’s telegraph, 916
Balance, 72 ; actinic, 995; beam of, 73;
compensating, 324; delicacy of, 74;
hydrostatic, 114, 121; induction, 962 ;
knife-edge of, 72 ; physical and chemi-
cal, 75; spring, 89 ; torsion, 90, 717,
756
Ballistic galyanometer, 843; pendulum,
82
Balloons, 199-202; Montgolfier, 199;
weight raised by, 202
Bands of spectrum, 586
Barker’s mill, 151
Barlow’s wheel, 894
Barometers, 167 ; aneroid, 167, 1005
Bunten’s, 170; cistern, 168 ; corrections
in, 172 ; determination of heights by,
181; differential, 189; fixed, 178;
Fortin’s, 169; Gay-Lussac’s, 170;
glycerine, 179; Huyghen’s, 180; pre-
cautions with, 171; wheel; 177;
variations of height of, 174
Barometric formula, Laplace’s, 181 ;
gradients, 1017; height, corrected
for heat, 331; manometer, 189; va-
riations, 175
Baroscope, 198
Bassoon, 276
Battery, Bunsen’s, 831; Callan’s, 831;
chemical effects of, 863; Daniell’s,
829; electric, 796; floating, 38090;
gas, 873; gravity, 833; Grove's, $304
Leclanché’s, 834; Leyden, 796; con-
stant, 828 ; luminous effects, 855 ; mag-
netic, mechanical effects of, 861 ; Mi-
notto’s, 833; Marié Davy’s, 833;
secondary, 872; Smee’s, 832 ; mercury
sulphate, 833; thermo-electric, 972 ;
voltaic, 825, 826; Wollaston’s, 826
Beam of a balance, 73; of a steam-
engine, 477
Beats, 266
Beaume’s hydrometer, 128
Becquerel’s pyrometer, 979;
electric battery, 974
Bell of a trumpet, 242
Bell’s telephone, 960 ; photophone, 966
Bellows, 246; hydrostatic, 102; water, 210
Bells, 286
Berthelot’s calorimetrical bomb, 495
thermo-
Index
BER
Berthollet’s experiment, 191
Bianchi’s air-pump, 206
Biaxial crystals, double refraction in,
658; rings in, 681
Bidwell’s experiments, 905
Binnacle, 711
Binocular vision, 635
Biot’s apparatus, 691
Biquartz, 692
Black’s experiments
479
Bladder, swimming, 118
Blagden’s law, 347
Block and tackle, 41
Blood-globules, 12
Blue cloud, 1024
Bodies, properties of, 7, 88
Bohnenberger’s electroscope, 839
Boiler, 476
Boiling, 367; by cooling, 371
Boiling-point, influence of dissolved sub-
stances on, 369; of nature of vessel,
370 ; of pressure on, 371 ; in a. ther-
mometer, 306; measurement of heights
by, 373
Bolometer, 995
Bomb, calorimetrical, 495
Borda’s method, 76
Boreal pole, 703
Bottomley’s experiment, 1028
Boutigny’s experiments, 391
Boxes, resistance, 984
Boyle’s law, 183-185
Boys’s radiomicrometer, 976; threads,
go
Brake, friction, 483; air, 212
Bramah’s hydraulic press, 109
Branch currents, 996
Breaking weight, 92
Breezes, land and sea, 1015
Breguet’s thermometer, 313
Bridge, Wheatstone’s, 986
British imperial yard, 22; and French
system of weights and measures, 126
Brittle bodies, 94
Browning’s regulator, 858
Brush discharge, 809; dynamo-electrical
machine, 942
Brushes, displacement of, 943
Bulbs, specific gravity. 124
Bunsen’s Sprengel-pump, 209 ; battery,
831;. burner, 58%; ice calorimeter,
460 ; photometer, 521
Bunsen and Kirchhoff’s researches, 588
Bunten’s barometer, 170
Buoyancy of liquids, ror
Burning mirfors, 427
on latent heat,
CHE
ABLE telegraph, 912
Ceesium, 590
Cagniard-Latour’s sirene, 2453 experi-
ments on formation of vapour, 374
Cailletet’s and Pictet’s researches, 386
Calibration, 302
Callan’s battery, 831
Calorescence, 441
Calorie, 456
Calorific effects of electrical discharge,
Si2; of currents electricity S01 of
Ruhmkorff’s coil, 949, 9513; of the
spectrum, 585
Calorimeter, 459; Bunsen’s ice, 460;
Black’s, 459; Favre and Silbermann’s,
4/73; Lavoisier and Laplace’s, 459
Calorimetry, 456
Camera lucida, 615; Amici’s,
Wollaston’s, 615 ; obscura, 614
Campani’s eyepiece, 604
Capacity, error of barometric, 168; elec-
trical, 762; specific inductive, 769
Capillarity, 132; attraction and repulsion
produced by, 1383; correction for, 172
Capillary phenomena, 132-140; electro-
meter, 862 ; tubes, 133
Capsule, of the eye, 625
Carbon, 831
Cardan’s suspension, 169
Cardew’s voltmeter, 998
Carré’s mode of freezing, 378
Carriage lamps, 547
Cartesian diver, 117
Cascade, charging by, 798
Cataracts of a steam engine, 477
Cathetometer, 89
Catoptric telescopes, 610
Caustics, 545
Cauterisation, galvanic, 851
Celsius’ scale, 307
Centesimal alcoholometer, 129
Centigrade scale, 307
Centimetre, 126
Centre, optical, 567; of gravity, 69; of
parallel forces, 38; of pressure, 103
Centrifugal force, 53
Centripetal force, 53
Charge of a Leyden jar, penetration of,
7953; measurement of, 799; residual,
125
Charging by cascade, 798
Charles’s law, 335
Chatterton’s compound, 908
Chemical affinity, 86; combination, 493:
decomposition, 863 ; effects of electrical
discharge, 815; of voltaic currents,
863; of Ruhmkorff’s coil, 951 ; har-
AN GEZ
615 5
I124
CHE
monicon 282; hygrometer, 400 ; pro-
perties of the spectrum, 585
Chemistry, I
Cheval-vapeur, 1000
Children’s experiment, 852
Chimes, electrical, 786
Chimney, 500
Chladni’s experiments, 286
Chlorophane, 649
Chlorophyl, 592
Chords, major and minor, 250; physical
constitution of, 268 ; tones dominant
and subdominant, 251; vocal, 263
Choroid, 625
Chromatic scale, 253; aberration, 595
Chromium, magnetic limit of 741
Ciliary processes, 625
Circle, azimuthal, 709
Circular polarisation, 683
Cirrocumulus, 101g
Cirrostratus, 1019
Cirrus, 1019
Cistern barometer, 168
Clamond’s thermo-electric battery, 975
Clarinet, 276
Clarke’s magneto-electrical machine, 934
Cleavage, electricity produced by, 753
Clef, 255
Clément-Désorme’s experiment, 210
Climate, 1046; constant, 1046 ; influence
of aqueous vapour on, 1023
Climatology, 1042-1049
Clocks, «823° ‘erutelyof, 9525 velectrical,
919
Clouds, 1019 ; electricity of, 1034 ; forma-
tion of, 1020
Coatings, 769 ; Leyden jar with movable,
793
Cobalt, 741
Coercive force, 701
Coefficients of linear expansion, 317-320;
conductivity, 412 ; Poisson’s, 89
Cohesion, 85
Coil, primary, 921; Ruhmkorff’s, 949 ;
effects produced by, 951; resistance,
984; secondary, 921
Cold, apparent reflection of, 429 ; pro-
duced by evaporation, 377 ; expansion
of gases, 506; by nocturnal radiation,
507 ; sources of, 505
Colladon and Sturm’s experiments, 237
Collecting plate, 801i
Collimation, 607
Collision of bodies, 58
Colloids, 142
Coloration produced by rotatory polari-
sation, 689
Index
CON
Colour. 7 ; of bodies, 581; of heat, 444 ;
of thin plates, 664
Colour discs, 579
Colour disease, 646
Colours, contrast of, 641; mixed, 582;
simple, 578; complementary, 582 ;
produced by polarised light, 676-
682
Combustion, 493 ; heat disengaged dur-
Ing, 494
Comma, musical, 251!
Common reservoir, 748
Commutator, 929, 950
Compass, correction of errors, 736; de-
clination, 709; mariner’s, 711 ; incli-
nation, 713; sine, 846; tangent, 845
Compensation, method of magnets, 730 ;
pendulum, 324; balance, 324; grid-
iron, 324; strips, 324
Complementary colours, 582
Component forces. 32
Composition of velocities, 52
Compound microscope, 602 ;
dynamo, 944
Compressed glass, colours produced by,
682
Compressibility, 7, 16; of gases, 157,
183 ; of liquids, 08
Concave mirrors, 426, 537
Concert pitch, 254
Concordant tones, 250
Condensation of vapours, 379
Condensed gas, 196, 212; wave, 228
Condenser, ’ electrical; 755 >>" “ot wim
engine, 477 ; limits to charge of, 790;
of Ruhmkorff’s coil, 950; Liebig’s,
381
Condensing engine, 481 ; air-pump, 212 ;
electroscope, 801 ; plate, 819 ; hygro-
meters 401
Conduction of heat, 411; of electricity,
747; lightning, 1039
Conductivity of bodies for heat, 411 ; co-
efficient of, 412; of gases, 416; of
liquids, 414 ; for electricity, 989
Conductors, 747; equivalent, 987 ; good
and bad, 411; lightning, 1039; resist-
ance of, 983
Congelation, 347
Conjugate mirrors, 427; focus, 537
Conservation of energy, 6
Constant currents, 828
Contact theory of electricity, 819
Contractile force, 323
Contraction, coefficient of, 89
Convection, 415 ; currents, 453 ; electro-
lytic, 854
wound
Lundex
CON
Convective discharge, 792
Convex meniscus, 132 ; mirrors, 536, 538
Cooling, method of, 464 ; Newton’s jaw
of, 423
Corliss engine, 481
Cornea, 625
Cornet-a-piston, 284
Cornish engine, 477
Corona, 1041
Corpuscular theory of light, 511
Corti’s fibres, 264
Cosine, law of the, 421, 520
Coulomb, 835, 1000
Coulomb’s law, 756
Couple, 37; terrestrial magnetic, 704;
voltaic, 822; thermo-electric, 972
Couronne des tasses, 826
Cowper’s writing telegraph, 911
Coxwell’s balloon, 199
Crab winch, 42
Crane, 42
Critical angle, 552; current, 945; tem-
perature, 374
Crookes’s radiometer, 453; vacuum, 208,
4543 experiments, 956
Cross-wire of a telescope, 607
Crutch of a clock, 82
Cryohydrate, 352
Cryophorus, 377
Crystal, hemihedral, 754
Crystalline, 625
Crystallisation, 348
Crystalloids, 142
Crystals, 348; expansion of, 320; doubly
refracting, 653, 673; uniaxial, 654;
positive and negative, 657
Cumulostratus, 1019
Cumulus, 1019
Current electricity, 821
Currents, action on currents, 881 ; action
of magnets, 890 ; action of earth on,
895; action on solenoids, 897 ; con-
stant, 828 ; divided, 986 ; diaphragm,
861; direct and inverse, 921; effects
of enfeeblement of, 827; extra, 930 ;
intensity of, 847 ; induction by, 921 ;
laws of angular, 883 ; laws of sinuous,
884; local, 827; magnetisation by,
904 ; motion and sounds produced by,
906 ; muscular, 1004; rotation of mag-
nets by, 889; secondary, 827; terres-
trial,),9G2.¢ thermal effects’ of,” $51;
transmissions by, 866
Curves, magnetic, 720
Cut-out, 851
Cyclones, 1017
Cymbal, 286
DIE
Oye eee 620
Daltonism, 646
| Dalton’s laws on gases and vapours, 389;
method of determining the tension of
aqueous vapour, 360
Damper, 283, 843, 929
Daniell’s battery, 829 ; hygrometer, 402 ;
pyrometer, 315
Dark lines of the spectrum, 586; of
solar spectrum, 591
Day, apparent, 21
Dead-beat galvanometer, 843; -point, 480
Decimetre, 126
Declination compass, 709; errors of,
7iO; magnetic, 705; ‘of needle, 705%
variations in, 706; of a star, 612
Decomposition, chemical, 863 ; of white
light, 576
Decrement, logarithmic, 843
Degrees of a thermometer, 307
De la Rive’s floating battery, 890; ex-
periments, 957
De la Rue and Miiller’s experiments,
Deleuil’s air-pump, 207
Delezenne’s circle, 929
Delicacy of balance, 743; of thermo-
meter, 311
Densimeter, 131
Density, 24; of an electrical current,
877; of the earth, 68 ; electric, 755;
gravimetrical, 188; of gases, 339-
341; maximum of water, 334; of
vapours, Gay-Lussac’s method, 392 ;
Dumas’s, 394 ; Deville and Troost’s,
394 ; Hofmann’s, 393
Depression of liquids in capillary tube,
132; between surfaces, 134; coefh-
cient of, 347
Derived currents, 996
Descartes’ laws of refraction, 549
Developer, 620
Deviation, angle of, 556
Deville and Troost’s method, 394
Dew, 1025; point, 401
Dewar’s experiments, 388
Diabetic urine, analysis of, 693
Diagram indicator, 483
Dialyser, 142
Dialysis, 142
Diamagnetism, 968
Diapason, 254
Diaphanous bodies, 512
Diaphragm, 603; currents, 861
Diathermancy, 442
Diatonic scale, 251
Dielectric polarisation, 770
1126
DIE
Dielectrics, 769
Differential barometer, 189; galvano-
meter, 842 ; lamp, 860; thermometer,
S127 note, 207
Diffraction, 515; spectra, 662; fringes,
660
Diffusion of gases, 193; of heat, 445 ; of
liquids, 142
Digester, Papin’s, 375
Dimensions of units, 62
Dioncea muscipula, 849
Dioptric telescopes, 610
Diosmose, I4I
Dip, magnetic, 712
Diplopia, 645
Dipping needle, 712
Direct vision spectroscope, 5&9
Directrix of a selenoid, 896
Disc, Newton’s, 579; Maxwell’s colour,
582
Discharge, convective, 792; electrical,
effects of the, 805; lateral, 1039;
silent, 815; slow and instantaneous,
789
Discharging rod, 789
Dispersion, 556; abnormal, 593
Dispersive power, 576
Displacement, 46
Disruptive discharge, 805
Dissipation of energy, 510
Dissociation, 395, 496, 867
Dissolving views, 617
Distance, estimation of, 631; adaptation
of eye to, 634
Distillation, 380
Distribution of free electricity, 757 ; of
magnetism, 742; of temperature,
1047 ; of land and water, 1049
Diurnal variations of magnetism, 707
Diver, Cartesian, 117
Divided currents, 996
Dividing machine, II
Divisibility, 7, 12
Dobereiner’s lamp, 492
Dolbear’s experiments, 960
Dominant chords, 251
Doppler’s principle, 236
Double refraction, 653, 666
Double-weighing, 76
Doublet, Wollaston, 598
Dove’s law of storms, 1016
Draught of fire-places, 500
Drawplate, 93
Dredging machines, 152
Driving wheels, 480
Drum, 287
Drum armature, 941
Index
ELE
Drummond’s light, 618
Dry batteries, piles, 838 ; plates, 622
eae microscope, 618; regulator,
Ds
Ductility, 7, 93
Duhamel’s graphic method, 248
Dulong and Arago’s experiments on
Boyle’s law, 184; method of deter-
mining the tension of aqueous vapour,
361
Dulong and Petit’s determination of ab-
solute expansion of mercury, 326;
method of cooling, 464 ; law, 467
Dumas’s method for vapour density, 394
Duplex telegraphy, 914
Duration of electric spark, 816
Dutroche’s endosmometer, 141
Dynamic radiation and absorption, 450
Dynamical theory of heat, 436
Dynamo-electrical machine, 939, 941,942.
Dynamo-magnetic machine, 939
Dynamometer, 91, 433
Dyne, 62
AR, the, 264
Ear trumpet, 242
Earth, density of, 68; its action on
currents, 895 ; action on solenoids, 898;
current, 915, 1041; flattening of, by
rotation, 83; magnetic poles of the,
703 ; magnetisation by, 735
Earth’s magnetism, 705
Ebullition, 354 ; laws of, 367
Eccentric, 479
Echelon lenses, 619
Echoes, monosyllabic, trisyllabic, mul-
tiple, 240
Eclipses, 515
Eddy currents, 959
Edelmann’s hygrometer, 401
Edison’s phonograph, 295 ;
963; telephone, 964
Efficiency ot an accumulator, 872; of a
machine, 152, 483, 945; of. heat
engines, 484
Effluvium, electrical, 815
Efflux, velocity of, 144; quantity of,
147; influence of tubes on, 148
Effusion of gases, 194
Elastic bodies, 58; after action, 89
Elastic force of gases, 155; of vapours,
tasimeter,
ci)
Elasticity, 7, 17 ; limit of, 17, S05q08
traction, 89 ; modulus of, 89 ; of tor-
sion, 90; of flexure, QI.
Electric alarum, 918; batteries, 796 ;
charge, 799; chimes, 786; clocks,
Index
ELE
919; density, 758; discharge, 805 ;
egg, 810; fish, 1009 ; lamp, 860 ; light,
856-860 ; pendulum, 746; poles, 754;
residue, 794 ; shock, 805 ; spark, 785;
telegraphs, 908-920; tension, 759;
whirl, 737
Electric endosmose, 861; field, 761;
potential, 760; capacity, 762, mea-
surement of, 763; machines, 775-
7843 precautions In, 7773 resistance,
unit of, 984; conductivity, 747, 989;
quantity, 762; units, 999
Electricity, 6, 745; application of, to
medicine, 1012; atmospheric, 1030-
1039; contact theory, 819; current,
821; communication of, 772; de-
velopment of, by friction, 746; by
pressure and cleavage, 753; distribu-
tion of, 7573; disengagement of, in
chemical’ actions, 820; loss of, 766;
mechanical effects, 814; power cf
points, 765; velocity of, 817; theories
of, 750; work required for production
of, 783
Electrocapillary phenomena, 862
Electrochemical equivalent, 868 ; series,
864
Electrodes, 824; polarisation of, $27
Electrodynamics, 881
Electrodynamometer, 998
Electrogilding, 878
Electrolysis, 864 ; laws of, 868
Electrolyte, 864
Electrolytic convection, $54
Electromagnetic motors, 920 ;
999 ; theory of light, 1002
Electromagnets, 905
Electrometallurgy, 877
Electrometer, 774; Lane’s, 799; quad-
rant, 779; Thomson’s, 803
Electromotive series, 822; force, 823 ;
determination of, 993; force of ele-
ments, 835
Electron, 868
Electrophorus, 775 ; work of an, 783
‘Electropyrometer, 979
Electroscope, 746 ; Bohnenberger’s, 839 ;
Volta’s condensing, 801 ; gold leaf, 774
Electrosilvering, 879
Electrostatic units, 999
Electrostriction, 814
Electrotonus, 850
Elliptical polarisation, 683, 686
Emission theory, 511
Emissive power, 432
Emmetropic eye, 643
Emulsions, 142; gelatine, 622
units,
1127
EYE
Endosmometer, 141
Endosmose, 141; electrical, 861; of
gases, 193
Endosmotic equivalent, 141
Endothermic reactions, 496
Energy, 63; conservation of, 66; dissi-
pation of, 510; transformations of, 65 ;
varieties of, 64
Engines, gas, 486; steam, 475; low
and high pressure, 481 ; single action,
479; locomotive, 480; fre, 222 ;
Cornish, 477; horizontal, 478 ; work
of, 482 ; hot air, 485
Equator, 696; magnetic, 712
Equilibrium of forces, 35; of floating
bodies, 1163; of heavy bodies, 70; of
liquids, 105; mobile of temperature,
422 5 euiiaet7 basta ple.. 7 kta ins
stable, 71
Equivalent, electrochemical, 868; en-
dosmotic, 141 ; conductors, 987
Erg, 62
Escapement, 82; wheel, 82
Ether, 436; luminiferous, 511
Eustachian tube, 264
Evaporation, 354; causes which accele-
rate it, 366; cold due to, 377 ; latent
heat of, 376
Evaporation and ebullition, 368
Ewing’s experiments, 744
Exchanges, theory of, 422
Exhaustion, produced by air-pump, 204 ;
by Sprengel’s pump, 208
Exosmose, 141
Exothermic reactions, 496
Expanded wave, 228
Expansibility of gases 156
Expansion, 300 ; apparent and real, 325 ;
absolute, of mercury, 326; apparent,
of mercury, 327; of liquids, 330;
of gases, 335-337 ; linear and cubical,
coefficients of, 317; measurement of
linear, 318; of crystals, 320; applica-
tions of, 323 ; force of, 323
Expansion of gases, cold produced by,
506 ; problems on, 336
Expansive force of ice, 350
Experiment, Berthollet’s, 191; Frank-
lin’s;,. 3723. Florentine, 98); Pascal’s,
165; Torricellian, 164
Extension, 7, 9
Extra current, 930
Eye, 625 ; accommodation of, 634; not
achromatic, 642; refractive indices of
media of, 626; path of rays in, 628
dimensions of various parts of, 627
Eye lens, 604 ; Campani’s, 604
Ties
FAH
AHRENHEIT’S hydrometer, 124 ;
scale, 307
Falling bodies, laws of, 77
Falsetto notes, 263
Farad, 1000
Faraday’s experiments, 768 ; disc, 894;
theory of induction, 770; voltameter,
868 ; wheel, 639
Fatigue, elastic, 89
Favre and Silbermann’s calorimeter,
473 ; determination of heat of com-
bustion, 494
Fibres, Corti’s, 264
Field, electric, 761 ; magnetic, 721 ; of a
microscope, 604; of view, 605
Field lens and glass, 605
Field magnets, 938
Figures, Lichtenberg’s, 794
Filament, solenoidal, 724
Filter-pump, 209
Filters, 15
Finder, 607
Fire-ball, 1035; -engine, 222; -places,
499 ; -works, 151
Firmamental blue, 1024
Fish, electrical, 1009
Fishes, swimming bladder of, 118
Fizeau’s experiments, 320, 519
Flag signals, 910
Flame, 493 ; sensitive, 282
Flask, specific gravity, 122
Flattening of the earth, 83
Fleming’s rule, 928
Flexure, elasticity of, 91
Floating bodies, 116
Florentine experiment, 13, 98
Fluid, 4; imponderable, 6 ; elastic, 155 ;
magnetic, 699
Fluidity, 7
Fluorescence, 594
Flute, 284
Flux of magnetic force, 723
Fluxes, 344
Focal distance, 426
Foci, acoustic, 240; of convex mirrors,
538 ; in double convex lenses, 564
Focus, 426, 537; of a parabola, 145; con-
jugate, 537; determination of the prin-
ciple, 539 ; of aspherical concave mirror,
537 3 in double convex lens, 564
Focussing the microscope, 599, 603
Fog-signal, 245
Fogs, 1018
Fon, I015
Foot, 22
Foot-pound, 61, 482
Force, 26; acceleration of, 78; centri-
Lndex
GAL
fugal, 53; condensing, of electricity,
804; conservation of, 66; coer-
Cive, 701; direction of, 305 elastic,
of gases, 155; lines of magnetic, 722 ;
of expansion and contraction, 323;
electromotive, 823, 835 ; representation
of, 30 ; parallelogram of, 33 ; of liquids,
3333 portative, 740
Forces, 6; along the same line, che
equilibrium of, 35; impulsive, 57 ;
magnetic, 722; molecular, 84 ; mo-
ments of, 36; polygon of, 34 ; triangle
of, 35
Formulz for expansion, 322; barome-
tric, 181; for sound, 234; for spheri-
cal mirrors, 542 ; for lenses, 571
Fortin’s barometer, 169
Foucault’s currents, 959 ; determination
of velocity of light, 518; experiment,
856,959
Fountain in vacuo, 213; at Giggleswick,
217 ; intermittent, 215 ; Hero’s, 214
Fovea centralis, 625
Franklin’s experiment, 372, 1030; plate,
791; theory of electricity, 750
Fraunhofer’s lines, 586
Freezing, apparatus for, 378
Freezing mixtures, 351; point in a ther-
mometer, 306
French weights and measures, 126
Fresnel’s experimentum crucis,
rhomb, 685
Friction, 43, 47; heat of, 488; hy-
draulic, 149; internal, of liquids, 48,
149 ; of gases, 454; development of elec-
tricity by, 746
Friction wheels, 78
Frigorific rays, 429
Fringes, 660
Frog, rheoscopic, 1006
Frost, 1025
Frozen mercury, 377, 385, 391
Fulcrum, 40
Fulgurites, 1037
Fulminating pane, 791
Furnace, electrical, 946
Fuse, Schaw’s, 851
Fusing point, 342
Fusion, laws of, 342; vitreous, 342;
latent heat of, 470; of ice, 459
659;
ALILEO’S telescope, 609
Galleries, whispering, 240
Gallium, 590
Gallon, 126
Galvani’s experiment, 818
Index
GAL
Galvanometer, 842, 979; differential,
842 ; sine, 846; Thomson’s, 844
Galvanoscope, 842
Galvano-thermometer, 852
Gas battery, 873 ; engines, 486
Gaseous state, 4
Gases, absorption of, by liquids, 192;
by solids, 196; by vapours, 443;
application of Archimedes’ principle
to, 198 ; cold produced by expansion
of, 506; compressibility of, 157, 183;
condensed, 196, 212; conductivity of,
416; diamagnetism of, 968; density
of, 339; dynamical theory of, 297;
expansion of, 156, 3353; endosmose
of, 193; effusion, 194; transpiration
of, 195 ; index of refraction of, 562 ;
laws of mixture.of, 191 ; permanent,
384; liquefaction of, 384; physical
properties of, 155; pressure exerted
by, 159; radiation of, 4493; specific
heat of, 469; velocity of sound in,
234; viscosity of, 454; weight of, 158
Gauge, air-pump, 204 ; rain, 1021
Gay-Lussac’s alcoholometer, 129 ; baro-
meter, 170; determination of the ex-
pansion of gases, 335; of vapour-.
density, 392 ; stopcock, 389
Geissler’s tubes, 208, 590, 954
Geographical meridian, 705
Geometrical shadows, 515
Germanium, 590
Giffard’s injector, 210
Gilding metal, 878
Gimbals, 711
Glacial pole, 1047
Glaciers, 1029
Glashier’s balloon ascents, 199 ; factors,
VU
Ge compressed, 682 ; expansion of,
329; magnifying, 598; object, 602;
opera, 609 ; unannealed, 682
Glasses, weather, 177
Globe lightning, 1035
Glow, electrical, 809 ; worm, 649
Glycerine barometer, 179
Gold-leaf electroscope, 774
Goldschmid’s aneroid, 190
Gong, 286
Goniometers, 546
Good conductors, 411
Governor of a steam engine, 478
Gradient, barometric, 1017
Gramme, 24, 126
Gramme’s magneto-electrical machine, 940
Graphic method, Duhamel’s, 248 ; Fos-
ter’s, 853
HEF
Graphite, 831
Graphophone, 295
Gratings, 661
Grave harmonic, 267
Gravesand’s ring, 300
Gravimetrical density, 188
Gravitation, 6, 83; terrestrial, 68, 83 ;
accelerative effect of, 27
Gravity, battery, 833
Gravity, centre of, 69; Jolly’s determina-
tion of constant of, 76
Gregorian telescope, 611
Gridiron pendulum, 324
Grimaldi’s experiment, 659
Grotthiiss’ hypothesis, 867
Grove’s battery, 830; gas, 873
Guard ring, 803
Guericke’s air-pump, 203
Guide-blades of a turbine, 152
Guitar, 283
Gulf Stream, 1044
Guthrie’s researches, 352
Gymnotus, 1009
AlL,F1027
Hair hygrometer, 406
Haldat’s apparatus, 102
Hall’s experiment, 903
Hallstrom’s experiments, 334
Haloes, 641, 660, 1019
Hammer, oscillating, 949 ; ofa piano, 283
Harceurt’s pentane lamp, 521
Hardening, 91
Hardness, 7; scale of, 94
Harmonie triad, 251; grave, 267
Harmonicon, chemical, 282
Harmonics, 257, 277
Harp, 283 ; Marloye’s, 285
Harris’s unit jar, S00
Heat, 296; animal, 497; absorption of,
by vapour, &c., 443, 448; atomic,
468 ; conduction of, 4113; diffusion of,
445; developed by induction, 959 ;
dynamical theory of, 436; hypothesis
on, 296; latent, 345 ; mechanical equi-
valent of, 509; polarisation of, 694 ;
produced by absorption and imbibi-
tion, 492; radiated, 410; radiant,
ANS, AZ Ined SSyerenection of; (424 ;
scattered, 4313; sources of, 487-497 ;
specific, 457-469; transmission of,
410 ; terrestrial, 491
Heaters, 476
Heating, 498; by steam, 502; by hot
air, 503; by hot water, 504
Hefner Alteneck lamp, 521
1130
HEI
Height of barometer, 168; variations |
in, 174
Heights of places, determination of, by
barometer, 181 ; by boiling point, 373
Heliograph, 535
Heliostat, 546
Helium, 590
Helix, 45, 896, 904
Helmholtz’s analysis of sound, 259 ; re-
searches, 262
Hemihedral crystal, 754
Hemispheres, Magdeburg, 163
Henley’s electrometer, 779
Henry, 1000
Herapath’s salt, 672
Hero’s fountain, 214
Heroult’s electrical furnace, 946
Herschelian rays, 437; telescope, 613
Her'z’s experiments, 1002
Hirn’s experiments, 509
Hoar-frost, 1025
Hofmann’s density of vapours, 393
Holtz’s electrical machine, 781
Homogeneous light, 584 ; medium, 514
Hope’s experiments, 334
Horizontal line, 68 ; plane, 68
Horn, 284
Horse-power, 61, 482
Hot-air, engines, 485; heating by, 503
Hotness, 301
Hot-water, heating by, 504
Houre2t
Howard’s nomenclature of clouds, 1019
Hughes’s microphone, 961; induction
balance, 962
Humour, aqueous, of the eye, 625
Huyghens’ barometer, 180; eyepiece,
604
Hyaloid membrane, 625
Hydraulic press, 109 ; engine, 154 ; fric-
tion, 149 ; lift, 109 ; power, application
of, 109; ram, 153; tourniquet, 151
Hydraulics, 96
Hydrodynamics, 142
Hydro-electric machine, 780; currents,
969
Hydrometers, 120; Nicholson’s, 121 ;
Fahrenheit’s, 124 ; with variable im-
mersion, 127 ; Beaumé’s, 128 ; of con-
stant immersion, 127; specific gravi-
ties, 120; uses of tables of, 126
Hydrostatic bellows, 102; paradox, 104 ;
balance, 114, I2I
Hydrostatics, 96
Hygrometers, 399, 406 ; chemical, 400;
condensing;* gor 5’ ‘Daniell’s;» 402 ;
wet-bulb, 4o ; Regnault’s, 403
Index
INS
Hygrometric state, 398 ; substances, 397
Hygrometry, 397 ; problem on, 408
Hygroscope, 406
Hypermetropia, 643
Hypothesis, 5
Hypsometer, 373
Hysterisis, 905
CE, 1028; method of fusion of, 459
Ice calorimeter, 460; Bunsen’s,
460; expansive force of, 350; ma-
chine, 506
Iceland spar, 673
Ideal gas, 296; solution, 141
Idioelectrics, 746 -
Image and object, magnitudes of, 573
Images, accidental, 640; condition of
distinctness of, 599; formation of, in
concave mirrors, 540; in convex mir-
rors, 541; in plane mirrors, 525; of
multiple, 528; magnitude of, 544;
produced by small apertures, 516;
virtual and real, 526; inversion of, 629
Imbibition, 196 ; heat produced by, 492
Impedance, 933
Impenetrability, 7, 8
Imperial British yard, 22
Imponderable matter, 6
Impulsive forces, 57
Incandescent lamps, 860
Inch, 526
Incident ray, 424, 548
Inclination, 712 ; compass, 713
Inclined plane, 43 ; motion on, 50
Index of refraction, 550; measurement
of, in solids, 560; in liquids, 561; in
gases, 562
Indicator, 908 ; diagram, 483
Indices, refractive, table of, 562
Indium, 590
Induced currents, 921-932
Induction, © balance,’ 96253 “by the?
earth, 929.3. of ‘a’ current om itsely
930; electrical, 767; in telegraph
cables, 912 ; Faraday’s theory of, 770 ;
heat developed by, 959; by magnets,
925; magnetic, 700
Inductive capacity, specific, 769
Inductorium, 949
Inelastic bodies, 58
Inertia, 7, 19 ; applications of, 20
Influence, magnetic, 700; electrical, 777
Ingenhaus’s experiment, 411
Injector, Giffard’s, 210
Insects, sounds produced by, 245
Insolation, 650
Index
INS
Instruments, optical, 597; polarising,
O70 en OOUuL, 2758 reed 27.0
stringed, 283 ; wind, 274
Insulating bodies, 748; stool, 785
Insulators, 747
Intensity of the current, 847; of the
electric light, 859; of reflected light,
5215 OL asamusical @ note,’ 249.3" of
radiant heat, 421; of sound, causes
which influence, 229; of terrestrial
magnetism, 715; of terrestrial gravity,
3
Interference of light, 659; of sound, 265
Intermittent fountain, 215; springs, 217 ;
syphon, 217 -
Intervals, musical, 250
Intrapolar region, 850
Inversion, of images, 629; thermo-
electric, 970
Ions, 864
Iris, 625
Iron, passive state of, 874; electrical
deposition of, 880
Iron ships, rhagnetism of, 736
Irradiation, 641
Irregular reflection, 530
Isobars, 1017
Isochimenal line, 1045
Isoclinic lines, 712
Isodynamic lines, 715
Isogeothermic lines, 1045
Isogonic lines, 706
Isotheral lines, 1045
Isothermal lines, 413, 1045 ; zone, 1045
ABLOCHKOFF candle, 860
Jar, Harris’s unit, 800
Jar, Leyden, 792-800
Jet, lateral, 145; height of, 146; form
of, 150
Jew’s harp, 276
Jolly’s spring balance, 89; air thermo-
meter, 338; determinaticn of gravity, 76
Jordan’s glycerine barometer, 179
Joule’s experiment on heat and work,
509 ; equivalent, 509 ; law, 852 ; elec-
tromagnet, 905
Jupiter, 517
Jurin’s laws of capillarity, 133
ALEIDOPHONE, 639
Kaleidoscope, 528
Kamsin, I015
Kater’s pendulum, 80
Kathelectrotonus, 850
hist
LEN
Kathode, 864
Kation, 864
Keepers, 739
Kelvin, Lord (see Thomson)
Kerr’s electro-optical experiments, 967
Keynote, 252
Kienmayer’s amalgam, 777
Kilogramme, 126
Kilogrammetre, 61, 482
Kilowatt, 945
Kinemetograph, 640
Kinetic energy, 63, 509
Kinnersley’s thermometer, 814
Knife-edge, 72
Knot, 1000
Konig’s apparatus,
flames, 292
Kundt’s velocity of sound, 281
260; manometric
ABYRINTH of the ear, 264
Lactometer, 130
Lag, magnetic, 905
Lalande and Chapercn’s element, 833
Lambert’s method, 582
Lamps, incandescent, 860; Dobereiner,
402; differential, 860
Land and water, distribution of, 1049
Lane’s electrometer, 799
Langley’s observations on the spectrum,
439
Lantern, magic, 616
Laplace’s barometric formula, 181
Laryngoscope, 575
Larynx, 263
Latent heat, 345; of fusion, 470; of
vapours, 376, 471
Lateral jet, 145
Latitude, magnetic, 712: influence of,
on the temperature of the air, 1047 ;
parallel of, 83
Lavoisier and Laplace’s calorimeter, 459 ;
method of determining linear expan-
sion, 318
Law, 5
Laws of mixture of gases and liquids, 389
Lead, angle of, 943
Lead tree, 876
Leads of a voltaic battery, 851
Lechatellier, the:mopile, 979
Leclanche’s elements, 834
Ledger lines, 255
Leidenfrost’s phenomenon, 391
Lemniscate, 681
| Lenard’s experiments, 958
p
Length, unit of, 22 ; of undulation, 228
Lens, axis of, 563
E32
LEN
Lenses, 56325 72'; achromatic, 500%
aplanatic, 570; centres of curvature,
563; combination of, 572; echelon,
619; foci in double convex, 564; in
double concave, 565; formation of
images in double convex, 568; in
double concave, 569; formule relat-
ing to, 5713; lighthouse, 619 ; optical
centre, secondary axis of, 567
Lenz’s law, 923
Leslie's cube, 430;
thermometer, 312
Level, water, 1103 spirit, 111
Level surface, 68
Levelling staff, 110
Lever, 40
Leyden discharge, inductive action of, 924
Leyden jars, 792-799; charged by
Ruhmkorff’s coil, 951; potential of,
804 ; work by, 806
Lichtenberg’s figures, 794
Liebig’s condenser, 381
Lift, hydraulic, 10g
Ligament, suspensory, 625
Light, 511; diffraction of, 660; homo-
peneous, 5645; imvensity, of, . 5203
interference of, 659; laws of reflec-
tion of, 523 ; oxyhydrogen, 618 ; polar-
isation of, 666; relative intensities of,
522; sources of, 648 ; theory of polar-
ised light, 675; undulatory theory
of, 511, 651; velocity of, 517-520
Lighthouse lenses, 557, 619
Lighting, electric, 855
Lightning, 1035; effects of, 1037; 3 con-
ductor, 1039
Limit of elasticity, 17; magnetic, 741;
of perceptible sounds, 247
Linde’s ice-machine, 506 ; apparatus, 388
Line, aclinic, 712; of collimation, 607 ;
isoclinic, 712 ; agonic, 706; isogonic,
700 ; isodynamic, ibe tol sight, 607
Linear expansion, coefficients of, 317
Lines of magnetic force, 722; of elec-
trical force, 761
Lippmann’s capillary electrometer, 862
Liquefaction of gases, 384; of vapours,
379
Liquids, 97; buoyancy of, 101; com-
pressibility of, 98; conductivity of,
414; calculation of density of, 108;
diffusion of, 142; diamagnetism of,
968 ; expansion of, 330; equilibrium
of, 105; manner in which they are
heated, 4153; pressure on sides of
vessel, 103; refraction of, 561; rota-
tory power of, 691 ; spheroidal form
experiment,
Bil 3
Index.
MAG
of, 85; spheroidal state off 3913
specific heat of, 465; volatile and
fixed, 353; tensions of vapours of,
363 ; of mixed liquids, 364
Lissajous’s experiments, 288-290
Litre, 24, 126
Local action, 837 ; attraction, 736; bat-
tery, 910
Locatelli’s lamp, 435
Locomotives, 480
Lodestar, 695
Lodestone, 695
Long sight, 643
“Loop circuit, 960
Loops and nodes, 273
Loss of electricity, 766 ; of weight in air,
correction for, 409
Loudness of a musical tone, 249
Lullin’s experiment, 814
Luminiferous ether, 511
Luminous bodies, 512; effects of the
electric discharge, 808, 855 ; of Ruhm-
korff’s coil, 949 ; heat, 442 ; meteors,
IOIIL; paint, 650; pane, 789; pencil,
513; radiation, 440; ray, 513; tube,
SII; square, 811
ACHINE, Atwood’s, 78;
trical, 775-782
Mackerel-sky, 1019
Macleod’s gauge, 208
Magazine magnetic, 738
Magdeburg hemispheres, 163
Magic lantern, 616
Magnetic attraction and repulsion, 717 ;
battery, 738; couple, 704; curves,
720; declination, . 7053 dip. 71 am
effects of the electrical discharge, 813 ;
equator, 712; field, 721 ; fluids, 699 ;
induction, 700 ; influence, 700 ; limit,
740.5 \meridian, 705 7a neediew.7oam
observatories, 716; poles, 7123; satu-
ration, 737; storms, 706, 708
Magnetisation, 731; by the action of the
earth, 735; by currents, 904; single
touch, 732
Magnetism, 6, 695; determination of,
in absolute measure, 729 ; earth’s, 703 ;
of iron ships, 736; Ampere’s theory
elec-
of, QOI ; remanent, 905; theory of,
699; terrestrial, 703; distribution of
free, 742
Magneto and dynamo-electrical machines,
934-945 ve
Magneto-electrical apparatus, 934
Magnetomotive force, 905
Index
MAG
Magnets, artificial and natural, 695 ;
broken, 698 ; action of earth on, 703 ;
floating, 743 ; heat developed by, 959 ;
north and south poles of, 696 ; normal,
741; portative force of, 740 ; saturation
of, 737 ; influence of heat, 741 ; induc-
tion by, 925 ; inductive action on moy-
ing bodies, 926; action on currents,
890; on solenoids, 899; rotation of
induced currents by, 957; optical
effects of, 965; total action of two,
727
Magnification, linear and _— superficial
measure of, 601, 606 ; of a telescope,
607
Magnifying power, 606
Magnitude, 9; apparent, of an object,
600 ; of images in mirrors, 544
Major chord, 250; triads, 251
Malleability, 7, 93
Mance’s heliograph, 535 ; method, 988
Manganese, magnetic limit of, 741
Manhole, 476
Manometer, 98, 186; with compressed
air, 187; Regnault’s barometric, 189
Manometric flames, 292
Mares’ tails, 1019
Marie-Davy battery, 833
Marine barometer, 168; engines, 476;
galvanometer, 844
Mariner’s card, 1013 ; compass, 711
Mariotte and Boyle’s law, 183
Mariotte’s tube, 183
Marloye’s harp, 285
Mascart’s insulator, 766
Maskelyne’s experiment, 68
Mason’s hygrometer, 405
Mass, measure of, 23 ; unit of, 23
Matter, 2
Matteucci’s experiment, 924
Matthiessen’s thermometer, 312 ; electri-
cal conductivity, 989
Maxim’s lamp, 860
Maximum and minimum thermometers,
314
Maximum current, conditions of, 848
Maxwell’s electromagnetic theory of light,
770, 1002; colour discs, 582
Mayer’s floating magnets, 743
Mean temperature, 1042
Measure of force, 29 ; of work, 60
Measure of magnification, 601, 606 ; of
mass, 225. ol/space,) 22 5 ofitime; 21;
of velocity, 25
Measurement of small angles by reflec-
tion, 534
Mechanical equivalent of heat, 509;
ELB4
MIS
effects of electrical discharge, 814;
battery, 861
Melloni’s researches, 435; thermomul-
tiplier, 419, 976
Melting point, influence of pressure on,
343
Membranes, semipermeable, 141; sensi-
tive, 232; vibrations of, 287
Memoria technica, Ampere’s, 841
Meniscus, 132; convex, 1323 in baro-
meter, 172; Sagitta of, 172
Mensbrugghe’s experiment, 135
Mercury, frozen, 377, 385,391; pendulum,
324; coefficient of apparent expan-
sion, 327 ; expansion of, 326; pump,
2113 purification of, 171
Meridian, 21; geographical and mag-
netic, 705
Metacentre, 116
Metal, lRose’s
344
Metals, conductivity of, 989
Meteoric stones, 490
Meteorograph, 1012
Meteorology, 101i
Meteors, aerial, IOII
Metre, 22, 126
Metronome, 82
Mica, 678
Microfarad, 1000
Micrometer, 606 ; screw, II
Microphone, 961
Microscope, 12; achromatism of, 604 ;
Duboscq’s, 618 ; compound, 602 ; field
of, 604; focussing, 599; magnifying
- powers of, 601 ; photo-electric, 618 ;
simple, 598; solar, 617
Microspectroscope, 592
Microvolt, 1000
Migration of the ions, 869
Mill, Barker’s, 151
Milliampere, 1000
Millimetre, 126
Mineral waters, 1048
Mines, firing, by electricity, 851
Minimum thermometer, 314 ; deviation,
and Wood’s fusible,
559
Minor chord, 250
Minotto’s battery, 833
Minute, 21
Mirage, 553
Mirrors, 524; applications of, 546; burn-
ing, 427 ;concave, 426, 537, 540 ; con-
jugate, 427; convex, 538; glass, 527;
parabolic, 547; rotating, 532, 816;
spherical, 536
Mists, 1018
1134
MIX
Mixture of gases, 191; of gases and
liquids, 192 ; laws of, 389
Mixtures, freezing, 351 ; method of, 461
Mobile equilibrium, 422
Mobility, 7, 18
Modulus of elasticity, 88
Moisture of the atmosphere, 407
Molecular forces, 3; attraction, 84 ; sieve,
1413; state of bodies, 43 state, relation
of absorption to, 451; velocity, 295
Molecules, 3
Moments of forces, 36
Momentum, 28
“Monochord, 270
Monochromatic light, 584
Monosyllabic echo, 240
Monsoon, 1015
Montgolfier’s balloon, 199; ram, 153
Moon, 522
Morin’s apparatus, 79
Morren’s mercury pump, 211
Morse’s telegraph, 910
Moser’s images, 196
Motion, 18; on an inclined plane, 50;
curvilinear.) 25 ; inva cinele,,/5 3,545
rectilinear, 25; resistance to, in a
fluid, 48; uniformly accelerated rec-
tilinear, 49; quantity of, 28; of a
pendulum, 55; of projectile, 51
Mouth instrument, 275
Multiple battery, 848
Multiple echoes, 240; images formed by
mirrors, 527
Multiplication, method of, 929
Multiplier, 842
Muscular currents, 1004-1008
Music, 223; physical theory of, 249-268
Musical boxes, 285; comma, 251 ;
intervals, 250; scale, 251; tempera-
ment, 253; note, properties of, 249;
intensity, 249; notation, 255 ; pitchand
timbre, 249; sound, 224; range, 255
Myopia, 643
ASCENT state, 86
Natterer’s apparatus, 385
Natural magnets, 695
Needle, declination of, 705; dipping,
Vis s\"astatic, Vids magnelic,.2705);
thermoelectric, 981
Negative plate, 822
Negatives on glass, 621.
Neumann’s law, 468
Nerve-currents, 1008
Neutral line, 767; equilibrium,
point, 767 ; temperature, 970
71;
Index
OSC
| Newton’s disc, 579 ; law of cooling, 423 ;
rings, 664, 665; theory of light, 580
Newtonian telescope, 612 '
Niaudet’s element, $33
Nicholson’s hydrometer, 121
Nickel, electrical deposition of, 880;.
magnetic limit of, 741
Nicol’s prism, 674
Nimbus, 1019 _ .
Nobert’s lines, 606
Nobili’s battery, 973; rings, 875; ther-
momultipliers, 976; thermo-electric
pile, 973.
Nocturnal radiation, 507
Nodal points, 273, 278, 659
Nodes and loops, 273 ; of an organ pipe,
278 ; explanation of, 280
Noises, 223
Nonconductors, 747
Normal magnets, 741
Norremberg’s apparatus, 671
Northern hight, 1041
Norwegian stove, 417
Notation, musical, 255
Notes in music, 249 ; musical, of women
and boys, 263 ; wave-length of, 256
Nut of a screw, 45
BJECT-GLASS, 602
Objective, 602
Oboe, 276
Obscure radiation, 440;
transmutation of, 441
Observatories, magnetic, 716
Occlusion of gases, 197
Occultation, 517
Octave, 250
Oersted’s experiment, 841
Ohm, 1000
Ohm’s law, 847
Opaque bodies, 512
Opera-glasses, 609
Ophthalmoscope, 647
Optic axis, 630; axis of biaxial crystals,
658; angle, 630; nerve, 625
Optical centre, 567; effects of magnets,
965; instruments, 597
Optics, 511
Optometer, 632
Orbit of the eye, 625
Organ, 284 ; pipes, 278; nodes and loops
of, 278
Orrery, electrical, 787
Orthochromatic plates, 622
Oscillating discharges, 805
Oscillations, 553; axis of, 80; method of,
719
rays, 441
Index
OSM
Osmotic pressure, 141
Otto von Guericke’s air-pump, 203
Otto’s gas engine, 486
Outcrop, 112
Overshot wheels, 152
Oxyhydrogen light, 618
Ozone, 815, 863, 1037
ACINOTTITS ring, 940
Paddles of steam vessels, 152
Paint, luminous, 650
Pallet, 82
Pandzean pipe, 284
Pane, fulminating, 791
Papin’s digester, 375
Parabola, 51, 145
Parabolic mirrors, 547 5
Parachute, 201
Paradox, hydrostatic, 104
Parallel of latitude, 83; forces, 37;
centre of, 37
Parallel rays, 513
Parallelogram of forces, 33
Paramagnetic bodies, 968
Partial current, 996
Pascal’s law of equality of pressures, 99 ;
experiments, 165
Passage tint, 692
Passive state of iron, 874
Path, mean, of molecules, 298
Pedal, 283
Peltier’s cross, 980 ; effect, 980
Pendulum, 55; application to clocks,
82 ; ballistic, 82 ; compensation, 324 ;
electrical, 746; gridiron, 324; mer-
curial, 324; length of compound, 80;
reversible, 80; verification of laws of,
81
Penetration of a telescope, 608
Pentane lamp, 521
Penumbra, 515
Percussion, heat due to, 489
Permanent gases, 384 ; magnetism, 905
Permeability, magnetic, 725, 905
Persistence of impression on the retina,
639
Perspective, aerial, 631
Perturbations, magnetic, 708
Phantasmagoria, 618
Phenakistoscope, 639
Phenomenon, 5
Phial of four elements, 107
Phonautograph, 291
Phonograph, Edison’s, 295
Phosphorescence, 649
Phosphorogenic rays, 585
curve:. 70/01
1135
POL
Phosphoroscope, 650
Photo-electric microscope, 618
Photo-electricity, 754
Photogenic apparatus, 618
Photography, 620-624
Photometers, 521
Photophone, 966
Physical phenomena, 5; agents, 6;
properties of gases, 155; shadows,
515
Physics, object of, 1
Physiological effects of the electric dis-
charge, 807, of the current, 849 ; of
Ruhmkorff’s coil, 951
Piano, 283
Piezo-electricity, 754
Piezometer, 98
Pigment colours, 583
Pile, voltaic, 825-838
Pincette, tourmaline, 680
Pipes, organ, 278
Pisa, tower of, 70
Pistol, electric, 815
Piston of air-pump, 203; rod, 477
Pitchiiconcerie 2s 4 wolva notes "240 5
a screw, 45
Planejs 43 smielectrical
mirrors, 524
Planté’s secondary battery, $72
Plate electrical machine, 776
Plates, colours of thin, 664 ; vibrations
of, 286 ; Chladni’s, 286 ; photographic
dry, 622
Plumb line, 68
Pluviometer, 1021
Pneumatic syringe, 157, 489
Point, boiling, 367
Points, action of, 765; nodal, 273
Poisseuille’s apparatus, 149
Poisson’s coefficient, 89
Polar aurora, 1041
Polarisation, 871; angle of, 668; cur-
reniyo7 13) of -electrodesa" S27" by
double refraction, 666; by reflection,
667 ; by single refraction, 669; ellip-
tical and circular, 683 ; of heat, 694 ;
galvanic, 827, 871; light, 666; of the
electric medium, 770 ; rotatory, 687
Polarised light, theory of, 675 ; colours
produced by the interference of, 676-
682
Polariser, 670
Polarising instruments, 670
Polarity, boreal, austral, 703
Pole, glacial, 1047
Poles, 824; electric,” 754 3-of' the earth,
703 ; magnetic, 712; of a magnet, 696 ;
inclined,
7073
1136
POL
mutual action of, 697; austral and
boreal, 703
Polygon of forces, 34
Polyorama, 618
Polyprism, 556
Ponderable matter, 6
Pores; 13
Porosity, 7, 13; application of, 15
Portative force, 740
Positive plate, 824
Postal battery, g10
Potential energy, 63; of electricity, 760 ;
of a Leyden jar, 804; of a sphere, -764
Pound, 126; avoirdupois, 23, 29; foot, 61
Poundal, 27
Power ofa lever, 40; of a microscope, 606
Presbyopia, 643
Press, hydraulic, 109
Pressure, centre of, 103; on a body ina
liquid, 113; atmospheric, 161 ; amount
of, on human body, 166; experiment
illustrating, 213; influence on melting
point, 343; heat produced by, 489 ;
electricity produced by, 753
Pressures, equality of, 99 ; vertical down-
ward, 100; vertical upward, IOI ; in-
dependent of form of vessel, 102 ; on
the sides of vessels, 103 ; rate of trans-
mission of, 100
Prévost’s theory of exchanges, 422
Primary coil, 921
Principle of Archimedes, 114
Prismatic compass, 711
Prisms, 555; double refracting, 673;
Nicol’s, 674; with variable angle, 556
Problems on expansion of gases, 336;
on mixtures of gasesand vapours, 389 ;
on hygrometry, 408
Projectile, motion of, 51
Prony’s brake, 483
Proof plane, 757
Propagation of light, 514
Protoplasm, 849
Protuberances, 591
Ps¥chrometer, 405, 1012
Pulley, 41
Pump, air, 203 ; condensing, 212 ; filter,
209
Pumping engine, 477
Pumps, different kinds of, 218; suction,
219 ; suction and force, 220
Punctum czecum, 625
Pupil of the eye, 625
Pyknometer, 122
Pyroelectricity, 754
Pyroheliometer, 490
Pyrometers, 315 ; electric, 979
Index
REF
UADRANT electrometer, 779, 802
Quadrantal deviation, 736 —
Quartz threads, 90
ADIANT heat, 418 ; detection and
measurement of, 419; causes
which modify the intensity of, 421 ;
Melloni’s researches on, 435; relation
of gases and vapours to, 446; relation
to sound, 455
Radiating power, 432; identity of ab-
sorbing and radiating, 433; causes
which modify, &c., 434; of gases,
449
Radiation, cold produced by, 507 ; from
powders, 451; of gases, 449; luminous,
and obscure, 440 ; laws of, 420; solar,
490.
Radiative power of vapours, 1023
Radiometer, 453
Radiomicrometer, 976
Railway, electrical, 948; friction on
centrifugal, 47, 53, 480
Rain, 1021 ; clouds, 1021; bow, 1040;
fall, 1012, 1021, 1022); gauge, 1021 ;
drop, velocity of, 48
Ram, hydraulic, 153; powder, 489
Ramsden’s electrical machine, 776
Raoult’s researches, 347
Rarefaction in air-pump, 203; by Spren-
gel’s pump, 208
Ray, incident, 548; luminous.
ordinary and extraordinary, 666
Rays, actinic, or Ritteric, 441; diver-
gent and convergent, 513; frigorific,
429; of heat, 418, 436 ; Herschelian,
4373; invisible, 436; obscure, 440 ;
path of, in eye, 628; phosphorogenic,
585 ; polarised, 666; transmission of
thermal, 442
Reaction and action, 39
Real volume, 14 ; foci, 564 ; focus, 537 ;
image, 526, 540
Réaumur scale, 307
Receiver of air-pump, 203
Recomposition of white light, 579
Reed instruments, 276
Reeds, free and beating, 276
Refining of copper, electrical, 877
Reflected light, intensity of, 531
Reflecting power, 430; goniometer,
546 ; sextant, 533; stereoscope, 637 ;
telescope, 610
Reflection, apparent, of cold, 429; of
heat, 425 ; from concave mirrors, 426 ;
irregular, 530; laws of, 424; in a
5133
lndex
REF
vacuum, 428 ; of light, 523 ; of sound,
239
Refracting stereoscope, 638; telescope,
610
Refraction, 548-562 ; double, 653; po-
larisation by, 666, 669; explanation
of single, 652 ; of sound, 241
Refractive index, 550; determination of,
5743 of gases, 562; of liquids, 561;
of solids, 560; indices of media of
eye, 626
Refractory substances, 342
Refrangibility of light, alteration of, 594
Regelation, 1028
Regnault’s experiments, 232; determi-
nation of density of gases, 340 ; mano-
meter, 189; methods of determining
the expansion of gases, 337 ; of specific
heat, 463; of tension of aqueous va-
pour, 360; hygrometer, 403
Regulator of the electric light, 857
Regulus, 344
Reis’s telephone, 907
Relay, 910
Reluctance, magnetic, 905
Remanent magnetism, 905
Replenisher, $02
Repulsion, magnetic,
laws of, 756
Reservoir, common, 748
Residual charge, 795 ; magnetism, 905
Residue, electric, 795
Resinous electricity, 750
Resistance, limiting angle of, 43; of a
conductor, 847, 983; boxes, 984; of
an element, 988
Resonance, 240, 258; box, 254; globe,
259 :
Rest, 18
Resultant of forces, 32-34
Retardation, magnetic, 905, 933 ;
Retina, 625; persistence of impression
on, 625 ;
Return shock, 1038
Reversible pendulum, 80, _-
Reversibility of Holtz’s machine, 781
Reversion, method of, 710; spectroscope,
8
ee electric lamp, $60
Rheometer, 842
' Rheoscopic frog, 1006
Rheostat, 982
Rhomb, Fresnel’s, 685
Rhumbs, 711
Richness, hygrometric, 398
Riess’s thermometer, 812
Right ascension, 612
electrical
TPs
1137
SCH
Rime, 1025
Ring inductor, 940
Rings, coloured, 680; Gravesand’s, 300;
in biaxial crystals, 681 ; Newton’s, 664, -
665 ; Nobili’s, 875
Ritchie’s experiment, 433
Ritteric rays, 441
Robinson’s anemometer, 1012
Rock salt, heat transmitted through, 44
Rods, vibrations of, 285
Roget’s vibrating spiral, 882
Rolling mill,. 93
Rontgen rays, 958
Rose’s fusible metal, 344
Rotary engine, 481
Rotating mirror, 532, 816
Rotation, electrodynamic and _ electro-
magnetic, of liquids, 892 ; winds, 1016
Rotation of the earth, 83; of magnets
by currents, 889 ; of currents by mag-
nets, 891; of induced currents by
magnets, 957
Rotatory power of liquids, 691 ; polarisa-
tion, 687; coloration produced by, 689
Rousseau’s densimeter, 131
Roy and Ramsden’s measurement of
linear expansion, 319
Rubbers of an electrical machine, 776
Rubidium, 590
Ruhlmann’s barometric and thermome-
tric observations, 182
Ruhmkorff’s coil, 949 ; effects produced
by, 951
Rumford’s photometer, 521
Rutherford’s thermometers, 314
ACCHARIMETER, 692
Saccharometer, 128
Safety-catch, 851; tube, 383; valve, 100,
375
Sagitta of meniscus, 172
Salimeters, 130
Salts, decomposition of, 865
Samarium, 590
Saturation, degree of, 397; magnetic,
7373 of colours, 583
Saussure’s hygrometer, 406
Savart’s toothed wheel, 244
Scale of hardness, 94
Scales in music, 251; chromatic, 253 ;
of a thermometer, 307
Scandium, 590
Scattered heat, 431; light, .530
Schehallien experiment, 68
Scheiner’s experiment, 632
Schwendler’s platinum light standard, 860
4D
11338 Index
Sel SPE
Scintillation of stars, 553 Size, estimation of, 631
Sciopticon, 616 Sky, 1024
Sclerotica, 625
Scott’s phonautograph, 291
Scraping sound, 285
Scratching sound, 285
Screen, magnetic, 725
pcrew, 11545
Search light, 546
Secchi’s meteorograph, 1012
pecond Of tiinmew2T 25 !
Secondary axis of a lens, 567 ; batteries,
87.2 3 currents; 627¢0col soe lm
Seconds pendulum, 80
Secular magnetic variations, 706
Segments, ventral.and nodal, 273, 278
Segner’s water-wheel, 151
Selenite, 678
Selenium, 966, 992
Self-induction, 930
Semicircular deviation, 736
Semi-conductors, 747
Semipermeable membranes, 141
Semiprism, 589
Semitones, 252
Senarmont’s experiment, 413
Sensitive membrane, 232
Serein; 1023
Series, thermo-electric, 970 ; -wound ma-
chine, 944
Serum, 12
Sextant, 533
Shadows, 515
Sharpness of sight, 633
Shock, electric, 805 ; return, 1038
Shooting stars, 490
Short circuit, 831 ; sight, 643
Shunt, 997 ; -wound machine, 944
Siemens’ armature, 937; dynamo-elec-
trical machine, 941; unit, 983, 1000;
electrical thermometer, 995
Sieve, molecular, 141
Sight, line of, 607
Silurus, 1009
Silent discharge, 815
‘Silver voltameter, 868
Simoom, I015
Sine compass, 846
Sines, curve of, 56
Singing of liquids, 367
Sinuous currents, 884
Sinusoidal currents, 933
Siphon, 216 ; barometer, 170; recorder,
913
Sirene, 245
Sirocco, 1015
Sixe’s thermometer, 314
Sleet, 1026
Slide valve, 479
Sling, 53
Smee’s battery, 832
Snow, 1026 ; line, 1026
Soap-bubble, colours of, 664
Solar constant, 490 ; microscope, 617 ;
light, thermal analysis of, 437 ; radia-
tion, 4903; spectrum, 576; properties
of the, 585 ; dark lines of, 586; time,
21; day, 21
Soldering, 87; autogenous, 860
Soleil’s saccharimeter, 692
Solenoidal filament, 724
Solenoids, 896
Solidification, 347; change of volume
on, 350; retardation of, 349
Solidity, 4, 7
Solids, conductivity of, 411; index of
refraction in, 550; diamagnetism of,
968 ; linear and cubical expansion of,
317.3 surface tension of, 92
Solids, formule of expansion, 322
Solution, 346; ideal, 141
Sondhauss’s experiments, 241
Sonometer, 270, 962
Sonorous body, 225
Sound, 224; cause of, 225; not propa-
gated in vacuo, 226; propagated in all
elastic bodies, 227 ; propagation of, in
air, 228; causes which influence inten-
sity of, 229 ; apparatus to strengthen,
230; interference of, 265 ; velocity of, in
air, 2333 in gases) -23acprineliqume
237; (solids, 238 3 ‘reflection off 230.
refraction of, 241 ; relation of radiant
heat to, 455; transmission “of, 12371.
waves, 232
Sound, Helmholtz’s analysis of, 259
Sound, Konig’s apparatus, 260; Kundt’s,
Sole
Sounder, 917
Sounds, intensity of, 293; limit of percep-
tible, 247; synthesis of, 261; percep-
tions of, 264; produced by currents, 906
Space, measure of, 22
Spar, Iceland, 673
Spark and brush discharge, 8cqg ; electri-
cal, 785; duration and velocity of, 816
Speaking trumpet, 242; tubes, 231
Specific gravity, 24, 120, 125; bottle. 122;
hydrometer, 121.3 of solids, 121 ¢aan
gases, 339; of liquids, 124; tables of, |
125, 126
Specific heat, 457-469
lndex
SPE
Specific inductive capacity, 769
Spectacles, 644
Spectra, 662
Spectral analysis, 587; colours and pig-
ment, 583
Spectroscope, 588 ; direct vision, 589;
experiments with, 590 ; uses of the, 592 |
Spectrum, 437; colours of, 578; pure,
577 ; solar, 576
Spectrum, calorific, 585 ; chemical, 585
Spectrum, dark lines of, 586
Spectrum, diffraction, 662
Spectrum, luminous properties of, 585
Spectrum of aurora borealis, 1041
Specular reflection, 530
Spherical, aberration, 545 ; mirrors, 536 ; |
focus of, 537; formulze for, 542
Spheroidal form of liquids, 85; state, 391
Spherometer, 11
Spiral, 904; Roget’s vibrating, 882
Spirit-level, 111
Sprains, 17
Spray producer, 210
Sprengel’s air-pump, 208
Spring balance, 89
Springs, 1048; intermittent, 217
Stable equilibrium, 71
Standard cell, Daniell’s, 829 ; L. Clark’s,
833
Stars, declination of, 612 ; spectral analysis
of, 591
Staubbach, 77
Stave, 255 |
Steam, heating by, 502
Steam-engines, 475; boiler, 476; horn,
245; pipe, 210; various kinds of, 481; |
work of, 483
Steeling, 880
Stereometer, 188
Stereoscopes, 636-638
Stethoscope, 243
Stills, 380
Stool, insulating, 785
Stopcock, doubly exhausting, 205 ; Gay-
Lussac’s, 389
Storage batteries, 872
Storms, magnetic, 708, 716
Stoves, 501 ; Norwegian, 417
Stratification of electric light, 953
Stratus, 1019
Strength, electrical, 790
Stringed instruments, 283
Strings, 269; transverse vibration of, 269
Subdominant chords, 251
Substance, 2
Suction pump, 219; and force pump, |
220; load which piston supports, 221
|
BL359
TEN
Sun, 522; thermal analysis of light of,
437, 591
Sun-spots, 716
Superfusion, 349
Surface level, 68 ; tension, 92, 135, 139
Susceptibility, magnetic, 726
Suspension, axis of, 71 ; Cardan’s, 169
Suspensory ligament, 625
Swan lamps, 860
Swimming, 119;
118
Swing of a needle, 843
Switch, 962 |
Symmer’s theory of electricity, 750
Synthesis of sounds, 261
Syphon, 216; barometer, 170; inter-
mittent, 217 ; recorder, 913
Syringe, pneumatic, 157, 489
-bladder of fishes,
ieee eee metal, 95
Tangent compass, or galvanometer,
845, 870
Tasimeter, 963
Tears of wine, 136
Telegraph, cables, Cowper’s writing,
QI13 induction in, 912 ; electric, 9g08~
Qt ; electrochemical, 916
Telegraphy, duplex, 914; without. wires,
1003
Telephone, 907, 960; Edison’s, 964 ;
Reis’s, 907 ; toy, 239
Telescopes, 607; astronomical, 607 ;
Galileo’s, 609; Gregorian, 611 ; Her-
schelian, 613; Newtonian, 612; re-
Hlecting, Rosse’s, 613
Telluric lines, 586
Telpherage, 948
Temperament, musical, 253
Temperature, 301, correction for, in
barometer, 1733 critical, 374; deter-
mined by specific heat, 466
Temperature, absolute zero of, 508 ; in-
fluence of, on specific gravity, 125 ;
mean, 1042; how modified, 1043;
distribution of, 1047; of lakes, seas,
and springs, 1048
Temperatures, different remarkable, 316 ;
influence on expansion, 321
Tempering, 91, 95
i Tenacity, 7, 92
|
|
Tension, 922; electric, 759; maximum
of, electrical machine, 778; maxi-
mum of, vapours, 357 ; of aqueous vapour
at various temperatures, 360 ; of mixed
liquids in two communicating vessels,
365 ; free surface, 135
I140
TER
Terrestrial currents, 902, 915; heat, 491;
magnetic couple, 704 ; magnetism, 703-
715; telescope, 608
Terrestrial gravitation, 68, 83
Terrestrial magnetic couple, 704
Test objects, 606
Tetanus, 849
Thallium, 590
Thaumatrope, 639
Theodolite, 10
Theory, 5; of induction, 770
Thermal analysis of sunlight, 437; unit,
456, 494; springs, 1048
Thermal effects of the current, 852
Thermal rays, transmission of, 442 ;
unit, 456
Thermobarometer, 373
Thermochrose, 444
Thermo-dynamic efficiency, 484
Thermo-electric battery, 419, 972;
couples, 972 ; currents, 971, 973, 977;
pile, 419, 438, 973; series, 970
Thermo-electricity, 969
Thermo-element, 970
Thermometer, electric, 995
Thermometers, 302; Becquerel’s elec-
trical, 979 ; correction of readings, 332 ;
differential, 312; division of tubes of,
303; filling, 304; graduation of, 305 ;
determination of fixed points of, 306 ;
scale of, 307; displacement of zero,
308 ; limits to use of, 309; alcohol,
310 ; conditions of delicacy of, 311 ;.
Kinnersley’s,- "6143 \Tesheé’s, "3712 ;
Matthiessen’s, 312; Breguet’s, 313;
maximum and minimum, 314; Sie-
mens’ electrical, 995; weight, 328 ; air,
338
Thermometry, 301-304
Thermo-multiplier, Melloni’s, 419, 976
Thermoscope, 312
Thomson effect, 981
Thomson’s electrometers, 803; galvano-
meter, 844; apparatus for atmospheric
electricity, 1031
Thread of a screw, 45
Threads, fine, 90
Throw of a needle, 843
Thunder, 1036
Timbre, 249
Time, measure of, 21 ; mean solar, 21
Tint, 583 ; transition, 692
Tonation, thermal, 854
Tones, combinational,
"367
Tonic, 251
Toothed wheel, 244
267; differential,
Index
URI
Tore, 905
Torpedo, 1009
Torricelli’s experiment,
144 5 vacuum, [71
Torsion, angle of, 90;
756; force of, go
Total reflection, 552
Tourmaline, 672, 7543; pincette, 680
Tourniquet, hydraulic, 151
Tower of Pisa, 70
Toy telephone, 238
Trachea, 263
Traction, elasticity of, 89
Trajectory, 25
‘Transformation of energy, 65
Transformers, 952
Transit, 21
Transition tint, 692
Translucent bodies, 512
Transmission of heat, 410; of light, 511,
554; by the current, 866
Transmission of sound, 231
Transmitter of photophone, 966
‘Vransparency, 7, 512
Transparent media, 554.
Transpiration of gases, 195
Triad, harmonic, 251
Triangle, 285
Triangle of forces, 35
Trumpet, speaking, ear, 242
Tubes, Geissler’s, 208, 954; luminous,
S11; safety, 383 ; speaking, 231
Tuning-fork, 254, 285, 294
Turbines, 152
Twaddle’s hydrometer, 128
Twilight, 530
Twinkling of stars, 553
Tympanum, 264
Tyndall’s researches,
1029
164; theorem,
balance, 90, 717,
438, 455, 1024,
LTRAGASEOUS state, 956
Unannealed glass, colours pro-
duced by, 682
Undershot wheels, 152
Undulation, length of, 228, 651
Undulatory theory, 511, 651
Uniaxial crystals, 654 ; double refrac-
tion in, 658 ; positive and negative, 657
Unit jar, Harris's, 800 ; Siemens’, 9383 ;
thermal, 456
Unit of length, area and volume, 22;
heat, 456 ; of work, 61
Units, fundamental, 62
Unstable equilibrium, 71
Urinometer, 130
Index
VAC
ACUUM, application of air-pump
to formation of, 203; extent of,
produced by air-pump, 204 ; Crookes’s,
454; fall of bodies in a, 77; forma-
tion of vapour in, 356 ; heat radiated in,
420 ; reflection ina, 428 ; Torricellian,
171
Valency, of an element, 868 ; change of,
467
Valve, safety, 109, 375; face, 479
Van der Waals’ formula, 185
Vane, electrical, 787
Van ’t Hoff’s theory, 141, 867
Vaporisation, 354; latent heat of, 376,
472
Vapour, aqueous, tension of, at various
temperatures, 359; formation of, in
closed tube, 374; latent heat of,
376
Vapours, 353; absorption of heat by.
443; absorptive powers of, 448 ;
density of, Gay-Lussac’s method, 392 ;
Hofmann’s, 393; densities of, 395;
determination of latent heat of, 376,
471; Dumas’s method, 394; elastic
force of, 355; formation of, in vacuo,
356; saturated, 3573 unsaturated,
358; tension of different liquids, 363 ;
of mixed liquids, 364 ; in communicat-
ing vessels, 365
Variations, magnetic, annual, 707; ac-
cidental, 708 ; barometric, 174 ; causes
of, 175; diurnal, 707 ; relation of, to
weather, 176
Velocity, 25, 62; direction of, 56; of
efflux, 144; of electricity, 817; of
light, 517; graphic representation of
changes of, 56; Kundt’s method, 280;
molecular, 298; of sound in air, 233;
gases, 234, 235; formula for calcula-
ting, 235; of winds, 1012
Velocities, composition of, 52; examples
of, 25
Vena contracta, 147
Ventral and nodal segment, 273, 278
Verdet’s. constant, 965
Vernier, 10
Vertical line, 68
Vestibule of the ear, 264
Vibrating spiral, Roget’s, 882
Vibration, 225; arc of, 55; produced
by currents, 906; of tuning-forks,
294
Vibrations, 269; formule, 279; of
membranes, 287; measurement of
number of, 244; number of, produc-
ing each note, 254 ; of musical pipe,
Hoy Bai
WEL
279; of rods, 285; of plates, 286;
of strings, 269
Vierordt’s quantitative spectrum analysis,
592
View, field of, 605
Vinometer, 382
Violin, 283
Virtual and real images, 526, 540 ; focus,
5373 velocity, 46
Viscosity, 97, 149; of gases, 454
Vision, distance of distinct, 633; bino-
cular, 635
Visual angle, 630
Vis viva, 84, 457, 509
Vital fluid, 818
Vitreous body, 625; electricity, 750;
fusion, 342 ; humour, 625
Vocal chords, 263
Volatile liquids, 353
Volt, 835, 1000
Voltas condensing electroscope, 801 ;
electrophorus, 775; fundamental ex-
periment, 819
Voltaic arc, 855; couple, 822; in-
duction, 921 ; pile and battery, 825
Voltameter, silver, 868; Faraday’s, 868
- Voltmeter, 998
Volume, 22; unit of, 22, 24; determi-
nation of, 115; change of, on solidi-
fication, 350; of a liquid and that of
its vapour, relation between, 396
Volumometer, 188
Voss’s electrical machine, 781
ATER barometer, 179; bellows,
210; decomposition of, 863 ;
- hammer, 77; hot, heating by, 504;
level, 110; maximum density of, 334;
spouts, 1022 ; wheels, 152
Wave, condensed, 228; expanded, 228 ;
lengths, 651; plane, 652; of a note,
256
Weather, its influence on barometric va-
riations, 176; glasses, 1773; charts,
1017; forecasts, 1017
Wedge, 44
Wedgwood’s pyrometer, 315
Weighing, method of double, 76
Weight, 23, 83; relative, 43; of bodies
weighed in air, correction for loss
of, 409 ; of gases, 158; thermometer,
328
Weights and measures, 126
Welding, electrical, 860
Wells’s theory of dew, 1025
Wells, artesian, 112
1142
WER
Werdermann’s electric lamp, 860
Wet-bulb hygrometer, 405
Wheatstone’s bridge, 986 ; photometer,
521; rheostat, 982; rotating mirror, |
816 ; and Cooke’s telegraph, 909
Wheel and axle, 42
Wheel barometer, 177
Wheels, friction, 78; escapement, 82 ;
water, 152
Whirl, electrical, 787
Whispering galleries, 240
White light, decomposition of, 576; re-
composition of, 579
Wiedemann and Franz’s tables of con- |
ductivity, 411
Wild’s magneto-electrical machine, 938
Wimshurst’s machine, 782
Winch, 42 |
Winckler’s cushions, 776
Wind chest, 276; instruments, 274, 284
Wind pipe, 263
Windhausen’s ice machine, 506
Winds, causes of, 1014; direction and |
velocity of, 1012, 1013; law of rota-
tion of, 1016; periodical, regular, and
variable, 1615
Wine, alcoholic value of, 382 ; tears of,
136
Wire, telegraph, 908
Index
ZON
| Wollaston’s battery, 826; camera lucida,
615; cryophorus, 377 ; doublet, 598
Wood, conductivity of, 411
Wood’s fusible metal, 344
Work, 46, 59; measure of, 60; of an
engine, 482; rate of, 483; unit of, 61;
internal and external, of bodies, 299 ;
of a voltaic battery, 854; required for
the production of electricity, 783
Writing telegraphs, 911
ARD, British, 22, 126
Yellow spot, 625
Yoke, 905
Young and Fresnel’s experiment, 659
Young’s modulus, 89
AMBONTDS pile, 338
Zero, absolute, 508; tension of
aqueous vapour below, 359 ; displace-
ment of, 308
Zigzag lightning, 1035
Zinc, amalgamated, 837 ; carbon battery,
831
Zither, 283
Zoetrope, 639
Zone, isotherma], 1045
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Physiology. By W. R. McNas,
M.D. With 42 Diagrams. Fep.
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THERMODYNAMICS. By RICHARD.
WoORMELL, M.A., D.Sc. With 4r1.
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PRACTICAL ELEMENTARY SCIENCE SERIES.
ELEMENTARY PRACTICAL PHY-
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JOHN ‘THORNTON, M.A., Head
Master of the Central Higher Grade
School, Bolton. With 215 Lllustra-
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PRACTICAL DOMESTIC HYGIENE.
By J. LANE NoTTER, M.A., M.D.,
Professor of Hygiene in the Army
Medical School, Netley, etc.; and
Re EIR Te, Sep RAGS. arAssistane
Professor of Hygiene in the Army
Medical School, Netley, etc. With
83 Illustrations. Crown 8vo., 2s. 6d.
PRAGLIGAL... INTRODUCTION
TO THE STUDY OF BOTANY:
Flowering Plants. By J. BRETLAND
FARMER, M.A., Professor of Botany
in the Royal College of Science,
London; formerly Fellow of Mag-
dalen College, Oxford. With 121
Illustrations. Crown 8vo, 2s. 6d.
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108 Illustrations and 254 Experiments.
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ELEMENTARY PRACTICAL PHY--.
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Assistant Professor in Physics in the
Royal College of Science, London,
etc. With r2o Illustrations and 193.
Exercises. Crown 8vo., 2s. 6d.
ELEMENTARY PRACTICAL ZOO-
LOGY. By FRANK E. BEDDARD,
M.A. Oxon., F.R.S., Prosector to.
the Zoological Society of London;
Lecturer on Biology at Guy’s Hospi-
tal. With g3 Illustrations. Crown.
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