= Y.
These equations give U 2 = X' 2 + Y 2 , which determines the magnitude of the
resultant, and then, since both sin $ and cos < are known, is determined
without ambiguity.
Thus let P, Q, and R be forces of 100, 150, and 120 units, respectively,
Fig.
-35] Conditions of Equilibrium of Forces. 19
and suppose XAP, XAQ, and XAR to be angles of 45, 120, and 210 re-
spectively. Then their components along Ax are 70*7, - 75, 103*9, an< i
their components along AY are 707,+ 129-9, 60. The sums of these two
sets being respectively 108-2 and 140-6, we have U cos <= io8'2 and
U sin 0= 140-6;
therefore IP - (io8'2) 2 + (140-6)-
or U = 177-4
hence 177-4 cos = - 108*2, and 177-4 sin 0- 104-6.
If we made use of the former of these equations only, we should obtain and
towards the same part as O P, draw
AB parallel to, and towards the
same part as OQ, and take AB
such that P : Q : : D A : A B.
Through B draw B C parallel to
and towards the %ame part as O R,
taking BC such tha.t Q : R::AB : B C ; join C D ; through O draw O S
parallel to and towards the same part as C D, then the required force acts
along O S, and is in magnitude proportional to C D.
It is to be observed that this construction can be extended to any number
of forces, and will apply to the case in which these directions are not in
one plane, only in this case the broken line ABCD would not lie wholly in
one plane. The above construction is frequently called the Polygon of
Forces.
The case of three forces acting on a point is, of course, included in the
above ; but its importance is such that we may give a separate statement of
2o On Matter, Force, and Motion. [35-
it. Let P, Q, R (fig. 12) be three forces in equilibrium on the point O. From
any point B draw B C parallel to and towards the same part O P, from C
draw C A parallel to and towards the same part as O Q, and take C A such
that P : Q : : B C : C A ; then, on joining A B, the third force R must act along
O R parallel to and towards the same part as A B, and must be proportional
in magnitude to AB. This construction is frequently called the Triangle of
Forces. It is evident that while the sides of the triangle are severally pro-
portional to P, Q, R, the angles A, B, C are supplementary to Q O R, R O P,
POO respectively ; consequently, every trigonometrical relation existing
between the sides and angles of A B C will equally exist between the forces
P, Q, R, and the supplements of the angles between their directions. Thus
in the triangle A B C it is known that the sides are proportional to the sines
of the opposite angles ; now, since the sines of the angles are equal to the
sines of their supplements, we at once conclude that when three forces are in
equilibrium, each is proportional to the sine of the angle between the directions
of the other two.
We can easily obtain from the equations which determine the resultant
of any number offerees (34) equations which express the conditions of equi-
librium of any number offerees acting in one plane on a point ; in fact, if U
= o we must have X = o and Y = o ; that is to say, the required conditions of
equilibrium are these :
o = P cos a + Q cos /3 + R cos y -f . . .
and o = P sin a + O sin /3 + R sin y + . . .
The first of these equations shows that no part of the motion of the point can
take place along Ax, the second that no part can take place along Ay. In
other words, the point cannot move at all.
36. Composition and resolution of parallel forces. The case of the
equilibrium of three parallel forces is merely a particular case of the equili-
brium of three forces acting on a point. In fact, let P
and Q be two forces whose directions pass through the
points A and B, and intersect in O ; let them be balanced
by a third force R whose direction produced intersects
the line AB in C. Now suppose the point O to move
along A O, gradually receding from A, the magnitude and
direction of R will continually change, and also the point
C will continually change its position, but will always lie
between A and B. In the limit P and Q become parallel
forces, acting towards the same part balanced by a parallel
force R acting towards the contrary part through a point
. X between A and B. The question is : First, on this
limiting case what is the value of R ; secondly, what is the
position of X ? Now with regard to the first point it is plain that if a tri-
angle abc were drawn as in art. 35, the angles a and b in the limit will vanish,
and c will become 180, consequently ab ultimately equals ac + cb ;
or R = p + Q.
With regard to the second point it is plain that
OC sin POR = OC sin AOC = AC sin CAO
and OC sin ROQ = OC sin BOC = CB
-37] Centre of Parallel Forces. 2 1
therefore AC sin CAO : CB sin CBO::sin FOR : sin ROQ
::Q:P(3S)-
Now in the limit, when OA and OB become parallel, OAB and OB A
become supplementary ; that is, their sines become equal ; also AC and C B
become respectively AX and XB ; consequently
AX : XB::Q: P,
a proportion which determines the position of X. This theorem at once
leads to the rules for the composition of any two parallel forces, viz.
I. When two parallel forces P and Q act towards the same part, at rigidly
connected points A and B, their resultant is a parallel force acting towards
the same part, equal to their sum, and its direction divides the line A B into
two parts A C and C B inversely proportional to the forces P and Q.
II. When two parallel forces P and O act towards contrary parts at
rigidly connected points A and B, of which P is the greater, their resultant
is a parallel force acting towards the same part as P, equal to the excess of
P over Q, and its direction divides B A produced in a point C such that C A
and C B are inversely proportional to P and O.
In each of the above cases if we were to apply R at the point C, in opposite
directions to those shown in the figure, it would plainly (by the above theorem)
Fi S- J 4- Fig. 15.
balance P and Q, and therefore when it acts as shown in figs. 14 and 15 it is
the resultant of P and Q in those cases respectively. It will, of course, follow
that the force R acting at C can be resolved into P and O acting at A and B
respectively.
If the second of the above theorems be examined, it will be found that no
force R exists equivalent to P and Q when these forces are equal. Two
such forces constitute a couple, which may be defined to be two equal
parallel forces acting towards contrary parts ; they possess the remarkable
property that they are incapable of being balanced by any single force what-
soever. .
In the case of more than two parallel forces the resultant of any two can
e found, then of that and a third, and so on to any number ; it can be shown
t however great the number of forces they will either be in equilibrium or
will reduce to a single resultant or to a couple.
7. Centre of parallel forces. On referring to figs. 14 and 15, it will be
remarked that if we conceive the points A and B to be fixed in the directions
22 On Matter, Force, and Motion. [37-
AP and BQ of the forces P and O, and if we suppose those directions to be
turned round A and B, so as to continue parallel and to make any given
angles with their original directions, then the direction of their resultant will
continue to pass through C ; that point is therefore called the centre of the
parallel forces P and Q.
It appears from investigation, that whenever a system of parallel forces
reduces to a single resultant, those forces will have a centre ; that is to say,
if we conceive each of the forces to act at a fixed point, there will be a point
through which the direction of their resultant will pass when the directions
of the forces are turned through any equal angles round their points of
application in such a manner as to retain the parallelism of their directions.
The most familiar example of a centre of parallel forces is the case in
which the forces are the weights of the parts of a body ; in this case the
forces all acting towards the same part will have a resultant, viz. their sum ;
and their centre is called the centre of gravity of the body.
38. Moments of forces.- Let P (fig. 16) denote any force acting from B
to P, take A any point, let fall AN a perpendicular from A on BP. The
product of the number of Units of force in P, and the number of units of
length in AN, is called the moment of P with respect to A. Since the force
P can be represented by a straight line, the moment of P can be represented
by an area. In fact, if BC is the line representing P, the moment is properly
represented by twice the 'area of the triangle ABC. The perpendicular AN
is sometimes called the arm of the pressure. Now if a watch were placed
with its face upwards on the paper, the force P would cause the arm AN to
turn found A in the contrary direction to the hands of the
Watch. Under these circumstances, it is usual to con-
sider the moment of P with respect to the point A to be
positive. If P acted from C to B, it would turn NA in
the same direction as the hands of the watch, and now its
moment is reckoned negative.
The following remarkable relation exists between any
forces acting in one plane on a body and their resultant.
Take the moments of the forces and of their resultant with respect to any
one point in the plane. Then the moment of the resultant equals the sum
of the moments of the several forces, regard being had to the signs of the
moments.
If the point about which the moments are measured be taken in the
direction of the resultant, its moment With respect to that point will be zero ;
and consequently the sum of the moments with respect to such point will be
zero.
39. Equality of action and reaction.- We will proceed to exemplify
some of the principles ho\v laid doWn by investigating the conditions of
equilibrium of bodies in a few simple cases ; but before doing so we must '
notice a law which holds good whenever a mutual action is called into play
between two bodies. Reaction is always equal and contrary to actio?i; that
is to say, the mutual actions of two bodies on each other are always forces
equal in amount and opposite in direction. This law is perfectly general,
and is equally true when the bodies are in motion as well as when they are
at rest. A very instructive example of this law has already been given (33),
-41]
Pulleys.
in which the action on the spring CD (fig. 7) is the weight W transmitted
by the spring to C, and balanced by the reaction of the ground transmitted
from B to D. Under these circumstances the spring is said to be stretched
by a force \V. If the spring were removed, and the thread were continuous
from A to B, it is clear that any part of it is stretched by two equal forces,
viz. an action and reaction, each equal to W, and the thread is said to sustain
a tension W. When a- body is urged along a smooth surface, the mutual
action can only take place along the common perpendicular at the point of
contact. If, however, the bodies are rough, this restriction is partially re-
moved, and now the mutual action can take place in any direction not
making an angle greater than some determinate angle with the common per-
pendicular. This determinate angle has different values for different sub-
stances, and is sometimes called the limiting angle of resistance, sometimes
the angle of repose.
40. Tfce lever is a name given to any bar straight of curved, AB (fig. 17)
resting on a fixed point of edge c called the fulcrum. The forces acting on
the lever are the weight or fesistance Q, the
power P, and the feaction of the fulcrum.
Since these are in equilibrium, the fesultant
of P and Q must act through c, fof othef-
wise they could not be balanced by the fe-
action. Draw cb at fight angles to QB and
ca to PA produced ; then obsefving that
P x ca, and Q * cb are the moments of P and
Q with respect to <:, and that they have con-
trary signs, we have by (38),
P x ca = Q x cb ;
an equation commonly expressed by the
rule, that in the lever the power is to the Fig. 17.
weight in the inverse ratio of their arms.
Levers are divided into three kinds, according to the position of the
fulcrum with respect to the points of application of the power and the weight.
In a letter of the first kind \hz fulcrum is between the power and resistance,
as in fig. 17, and as in a pokef and in the common steelyard ; a pair of
scissors and a carpenter's pincers are double levers of this kind. In a lever
of the second kind the resistance is between the power and the fulcrum, as in
a wheelbarrow, or a pair of nutcrackers, or a door ; in a lever of the third
kind the power is between the fulcrum and the resistance, as in a pair of
tongs or the treadle of a lathe.
41. Pulleys. The pulley is a hard circular disc of wood or of metal, in
the edge of which is a groove, and which can turn freely on an axis in the
centre. Pulleys are either fixed, as in fig. 18, where the stirrup or fork is
rigidly connected with some immovable body, and where the axis rotates in
the stirrup ; or it may be movable, as in fig. 19, where the axis is fixed to
the fork, and it passes through a hole in the centre of the disc. The rope
which passes round the pulley in fig. 18, supports a weight at one end ; while
at the other a pull is applied to hold this weight in equilibrium.
On Matter, Force, and Motion.
[41-
We may look upon the power and the resistance as acting at the circum-
ference of the circle ; hence as the radii are equal, if we consider the pulley
as a lever, the two arms are
equal, and equilibrium will
prevail when the power and
the resistance are equal.
The fixed pulley affords thus
no mechanical advantage,
but is simply convenient in
changing the direction of the
application of a force.
In the case of the mov-
able pulley the one end of
the rope is suspended to a
fixed point in a beam, and
the weight is attached to the
hook on which the pulley
acts. The tension of the
rope is everywhere the same ;
one portion of the weight is
Fig. 18.
Fig. 19.
supported by the fixed part
and the other by the power, and these are equal to each other, and are
together equal to the weight, including the pulley itself; hence in this case
P = *Q-
If several pulleys are joined together on a common axis in a special
sheath, which is fixed, and a rope passes round all those and also round a
similar but movable combination of pulleys, such an arrangement, which is
represented in fig. 20, is called a block and tackle.
If we consider the condition of the rope it will be found to have every-
where the same tension ; the weight Q which is attached to the hook
common to the whole system is supported by the six portions of the rope ;
hence each of these portions will sustain one sixth of the weight ; the force
which is applied at the free end of the rope which passes over the upper
pulley, and which determines the tension, will have the same value ; that is
to say, it will support one sixth of the weight.
The relation between power and resistance in a block and tackle is
expressed by the equation P = -* in which P is the power, Q the weight,
n
and n the number of cords by which the weight is supported.
42. The wheel and axle. The older form of this machine, fig. 21, is
that of an axle, to which is rigidly fixed, concentric with it, a wheel of larger
diameter. The power is applied tangentially on the wheel, and the resistance
tangentially to the axle, as for instance in the treadmill and water-wheel.
Sometimes, as in the case of the capstan, the power is applied to spokes
fixed in the axle, which represent semi-diameters of the wheel ; in other
cases, as in the windlass, the handle is rigidly fixed to the axis.
In all its modifications we may regard the wheel and axle as an applica-
tion of the lever, the arms of which are the radii of the wheel and axle
respectively, and in all cases equilibrium exists where the power is to the
-42]
Wheel and Axle.
25
Thus in
resistance as the radius of the axle is to the radius of the wheel,
fig. 21, P : Q = ab : ac, or P x ac = Q x ab.
Frequent applications of wheels of different diameters are met with in
which the motion of one
wheel is transmitted to an-
other, either by means of
teeth fitting in each other on
the circumference of the
wheels, as in fig. 22, or by
means of bands passing over
the two wheels, as in the
illustration of Ladd's Mag-
neto-Electrical Machine (see
Book viii.).
In fig. 22, which repre-
sents the essential parts of a
crab winch, in order to raise
the weight O a power/ must ^ jg 4 Fig 2I
be applied at the circumfe-
rence of the wheel such that
Q ^p in which
R
r and R
are the radii of the axle b
and of the toothed wheel a
respectively.
The rotation of the wheel
a is effected by means of the
smaller wheel c or crab, the
teeth of which fit in those of
a. But if this wheel c is to
exert at its circumference a
power/, the power P which
is applied at the end of
the handle must be P = /, in which r' is the radius of c, R'the length of
R
a lever at the end of which P acts, and consequently
Fig. 22.
Q.'
'~
The radius of the wheel c is to that of the wheel a as their respective cir-
cumferences ; and, as the teeth of each are of the same size, the circum-
ferences will be as the number of teeth.
Trains of wheelwork are used, not only in raising great weights by the
exertion of a small power ; as in screw jacks, cranes, crab winches, &c., but
also in clock and watch works, and in cases in which changes in velocity or
in power or even in direction are required. Numerous examples will be met
with in the various apparatus described in this work.
C
26
On Matter, Force, and Motion.
[43-
43. Inclined Plane. The properties and laws of the inclined plane may
be conveniently demonstrated by means of the apparatus represented in
fig. 23. RS represents the section of a smooth piece of hard wood hinged at
R ; by means of a screw it can be clamped at any angle x against the arc-
shaped support, by which at the
same time the angle can be mea-
sured ; a 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 by
direct experiments what weights
R 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 incli-
nation.
The line RS represents the
Fig. 23.
lengfh, ST the height, and RT the base 01 inclined plane.
In ascertaining the theoretical conditions of equilibrium we have a useful
application of the parallelogram ot forces. Let the line ab, 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 or
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 opposite directions.
It can be readily shown that the triangle abc is similar to the triangle
SRT, and that. the sides ac and ab are in the same proportion as the sides
ST and SR. But the line ac represents the power, and the line ab the
weight ; hence
ST : SR = P : W;
that is, on an inclined plane, equilibrium obtains when the power is to the
weight as the height of the inclined plane to its length.
S T
Since the ratio -_ is the sine of the angle x, we may also state the
S R
principle thus :
P=Wsinx
The component da or be, which represents the actual pressure against the
plane, is equal to W cos x ; 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 maybe applied so as to act horizontally. It will then
be seen from fig. 24 that the weight W may be decomposed into two forces,
one of which, ab, 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 acb and STR, ac \bc=ST \ TR
= h\b\ but be is equal to W, and ac is equal to P, hence the power which
_44J The Wedge. 27
must be applied at b 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 inclina-
tion x ; that is, P = W tan x. The pressure upon the plane in this case may
be easily shown to be ab = , that
cos x
is = . This is sometimes called
cos x
the relative weight on the plane.
If the force P which is to counter-
balance 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.
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, the laws of equili-
brium and of motion on an inclined plane undergo modification. The/r/t--
tion, for instance, which comes into play amounts on ordinary roads to from
^ to i, and on railways to from ^ to of the relative weight. This 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 tl\e plane. Hence the use of the inclined plane in unloading heavy
casks into cellars, c.
A body on an inclined plane which cannot rotate does not move provided
the inclination is below a certain amount (39). The determination of this
limiting angle of resistance, at which a body on an inclined plane just begins
to move, may serve as a rough illustration of a mode of ascertaining the
4 coefficient of friction.'
For in the case in which the power is applied parallel to the plane, the
component of the weight which presses against the plane or the actual load,
L, is W cos x ; and the component which tends to move the body down the
plane is equal to W sin x. If the friction, R, is just sufficient to hold this in
equilibrium, the coefficient of friction will be = tan x.
L W cos x
Thus if we place on the plane a block of the same 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 is the limiting angle of
resistance, and its tangent is the coefficient of friction for that material.
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, etc. Fig. 25 represents in section
the application of the wedge to this purpose. The side ad is the back, the
vertex of the angle acb which the two faces ac and be make with each other
represents the edge, and the faces ac and be the sides of the wedge. The
power P is usually applied at right angles to the back ; and we may look
c 2
28
On Matter, Force, and Motion.
[44-
upon the cohesion between the fibres of the wood as representing the resist-
ance 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 he 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 equili-
brium must therefore be equal to eh. Now efh is
similar to the triangle acb, therefore ab : ac = eh . ef;
but these lines represent the pressure applied at the
back of the wedge, and the pressure on the face ac,
hence if P represent the former and O the latter,
there is equilibrium when P : O = ab : be, 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 resistance 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 also applied when very heavy weights are to be raised through a short
distance, as in launching ships, and in bracing columns and walls to the
perpendicular.
45. The Screw. Let us suppose a piece of paper in the shape of a
right-angled triangle aee' be applied with its vertical side ac'e' against a
cylinder, and parallel to the axis, and be wrapped round the cylinder ; the
hypotenuse will describe on the surface of the cylinder a screw line or
helix (fig. 26) ; the points abode will occupy the positions respectively a b'
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 abc be-
comes an inclined plane traced on the surface of the cylinder ; the distance
ac' being the height of the plane.
Fig. 25.
Fig. 28.
Fig 26.
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 square or sharp screws accordingly.
When a corresponding groove is cut in the
hollow cylinder or nut of the same diameter as
the bolt, this gives rise to an internal or companion screw or nut, fig. 28.
-46] Virtual Velocity. 29
The vertical distance between any two threads of a screw measured
parallel to the axis is called the pitch, and the angle ace or aee' is called the
inclination of the screw.
In practice, a raised screw is used with its companion in such a manner
that the elevations of the one fitjinto, and coincide with, the depressions 01
the other. The screw is a modification of the inclined plane, 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 = h : b, and the length of the base is the circumference
of the cylinder ; whence P : R = /i : 2nr ; r 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
bookbinders' press, &c., and the principle of the screw may be stated to be
generally that the power of the screw is to 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 slightlyk
displaced, the resolved part of the displacement in the direction of the force
is termed the virtual 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 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 Fig- 29.
number of forces, and the machine or system then re-
ceive 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 dis-
placement is to turn it round the fixed axle ; in the inclined plane the weight
must still continue to rest on the plane ; in the various systems of pulleys
the strings must still continue stretched, and must not alter in length, &c.
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 displacement, the virtual velocities of P and W will be of
opposite signs, and that, neglecting the signs, P x P's virtual velocity = W x W's
virtual velocity. Thus, to take the case of a bent lever, let P and Q be the
forces acting at the extremities 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' perpendicular to P and Q respectively ; then Aa
is the virtual velocity of P, and B^ that of Q, the former being positive and
the latter negative. Let Yp, Yq 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
3O On Matter, Force, and Motion. [46-
right angles; and, therefore, the right-angled triangles AaA', B^B' will
ultimately be similar to the triangles YpA, F^B respectively, whence
BB' = 'FB' "
BB'
FA' * UU F^ = FB-
triangles FAA', FBB' are similar,
as they are both isosceles, and
their vertical angles are equal, so
and
Yp
But the
that
AA'
FA
BB'
FB
whence
P'
P x
Yq
1
]L -s-. Now the denominators of
Fig. 30.
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 = O 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 h ;
then the virtual velocity of the weight is h, and is negative. Now as the
distance between the block and tackle is less than before by the space h, and
as the rope passes over this space n times, in order to keep the rope still
tight the power will have to move through a space equal to nh. This is the
virtual velocity of P, and is positive, and as W = ;zP, 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 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 thus offer a certain resistance to motion ; this is
what is called friction. It must be regarded as a force which continually
acts in opposition to actual or possible motion.
Friction is of two kinds : sliding, 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 rolling iriction, 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.
Friction is directly proportional to the pressure' of the two surfaces
against each other. That portion of the pressure which is required to over-
come friction is called the coefficient 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.
-48]
Resistance to Motion in a Fluid Medium.
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. 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 ; 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 sub-
stances which are not absorbed by the body diminish friction ; but increase
it if they are absorbed. Thus moisture and oil increase, while tallow, soap,
and graphite diminish, the friction of wooden surfaces. In the sliding fric-
tion of cast iron upon bronze the coefficient was found to be 0*25 without
grease ; with oil it was 0-17, fat OTI, soap 0-03, and with a mixture of fat
and graphite 0*02. 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 0*04, hence a horse can draw ten times as great a load on rails as
on an ordinary road.
As rolling friction is considerably less than sliding friction, it is a great
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.
On the other hand, it is sometimes useful to change rolling into sliding fric-
tion, as when drags are placed on carriage wheels.
Without friction on the ground, neither men 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 equivalent
amount of its own motion.
This resistance increases with the surface ot the
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 ; thus in rarefied air 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 iu, fixed to a horizontal
axis, x x; to which also is 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
Fig. 31.
32 On Matter ; Force, and- Motion. [48-
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 veloci-
ties 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
attaining very high speeds in steam-vessels. Use is made, on the other hand,
of this resistance in parachutes (fig. 151) and in the wind-vanes for diminish-
ing the velocity of falling bodies (fig. 55), 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 compared 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 rain-drop falling from a height of 3,000 feet would, 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 appre-
ciable ; with a carriage exposing a surface of 22 square feet, it amounts to
1 6 or 17 pounds when the speed of the train is 16 feet a second or u 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 de-
termined the coefficient of the resistance of water, and found that at 10 it
was equal to o - oi567 gramme on a square centimetre; and for air it was
about ~ as much.
49. Uniformly Accelerated Rectilinear Motion. Let us suppose a
body containing m 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
F = ;/;
consequently, if v is its velocity at the end of / seconds, we have
v=ft. (i)
To determine the space it will describe in / seconds, we may reason as
follows : The velocity at the time / being ft, that at a time t + r will be /
(/ + r). If the body moved uniformly during the time r with the former
velocity it would describe a space s equal to fit ; if with the latter velocity, a
space Sj_ equal to/(/ + r)r. Consequently,
s l : s :\ t + T : t\
therefore, when r is indefinitely small, the limiting values of s and s l are
equal. Now since the body's velocity is continually increasing during the
time T, the space actually described is greater than s, and less than s r But
-49] Uniformly Accelerated Rectilinear Motion. 33
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 v 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 xf~~^
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 a line AC (fig. 32) and at A construct an p- lg 32-
angle CAB, whose tangent equals /; divide
AC into any number of equal parts in D, E, F,...and draw PD, QE, RF,...
BC at right angles to AC, then since PD = AD xf, QE = AE xf, RF = AF xf,
BC = AC xf, &c., PD will represent the velocity of the body at the end of
the time represented by AD, and similarly QE, RF,...BC, will represent the
velocity at the end of the times AE, AF,...AC. Complete the rectangles De,
E/j Yg... 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 CE or AC x AC xf.
Therefore, if AC represents the time / during which the body describes a
space s, we have
Since this equation can be written
we find, on comparison with equation (i), that
7/ 2 = 2/r. (3)
To illustrate these equations, let us suppose the accelerative effect of the
force to be 6 ; that is to say, that, in virtue of the action of the force, the body
acquires in each successive second an additional velocity of 6 ft. 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 ft. per second and will have described 432 ft.
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 \f, \fx 4, fx 9, $fx 16, &c., ft., and consequently during the
first, second, third, fourth, &c., second of the motion will have described /j
i/"* 3> $f* 5> $f* 7, &c-j ft-? namely, spaces in arithmetical progression.
The results of the above' article can be stated in the form of laws which
apply to the state of a body moving from a state of rest under the action of
a constant force :
34 On Matter, Force, and Motion. [49-
I. The velocities are proportional to the times during which the motion
has lasted.
II. The spaces described are proportional to the squares of the times em-
ployed in their description.
III. The spaces described are proportional to the squares of the velocities
acquired during their description.
I V. The 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 :
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 in vacua. Here the force causing
the acceleration is that of gravity, and the acceleration produced is denoted
by the letter g ; it has already been stated (27 and 29) that the numerical
value of g is 32*1912 at London, when the unit of time is a second and the
unit of distance a foot. Adopting the metre as unit of distance the value of
g at 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^ sin x,
in the direction SR, consequently the accelerating force down the plane is
g 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
v =gt sin x,
and will describe a length s of the plane given by the equation
Also, if v is the velocity acquired while describing s feet of the plane,
v~ 2gs sin x.
Hence (fig. 23) if a body slides down the plane from S to R the velocity which
it acquires at R is equal to \/2g . RS sin R or ^/2g . ST ; that is to 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 sub-
stituted 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
-51] Motion of Projectiles. 35
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 ab represent the space
described in any interval ; then, at the end of &
the 2, 3, 4.. .equal interval, the body, in virtue *
of its inertia, will have reached the points c 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 dis-
tances represented on the vertical line ; these are
determined by the successive values of %gt-,
which is the formula for the space described by
a freely falling body (49). 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 b', at the end of the second interval at c f , of
the third at d', &c., the spaces bb', cc', dd'...
being proportional to the squares of ab, 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 regu-
larly curved line of the form known as the parabola.
If the direction in which the body is thrown makes an angle of a with
the horizon (fig. 34), then after / seconds it would have travelled a distance
. 33-
Fig- 34-
ab = vt, where v is the original velocity ; during this time, however, it will have
fallen through a distance bc = %gP\ the height which it will have actually
reached is =bdbc = vt sin a ^gt* \ and the horizontal distance will be
ad=ab cos a = i>t cos a. The range of the body, or the greatest distance
through which it is thrown, will be reached when the height is again = ; that
is, when vt sin a $gt* ^0, from which /-- a . Introducing this value
of/ into the equation for the distance d. we have d= 2v , which
g
by a trigonometrical transformation = c> sm 2a . The greatest height is
g
attained in half the time of flight, or when t = v sin a , from which we get
h =
?/- sin- a
g
It follows from the formula that the height is greatest when sin a is
36 On Matter, Force, and Motion. [51-
greatest, which is the case when it = 90, or when the body is thrown vertically
upwards ; the range is greatest where sin ia is a maximum, that is, when
20 = 90 or =45.
In these formulas it has been assumed that the air offers no resistance.
This is, however, far from the case, and in practice, particularly if the velo-
city of projection is very great, the path differs from that of a parabola. Fig.
34 approximately represents the path, allowing for the resistance of the air.
The divergence from the true theoretical path is the greater from 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 con-
sequence 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. 6, 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 AO, it will move in the direction AR 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 sling.
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 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 centri-
petal or central force ; the reaction of the stone upon the string, which is
equal and opposite to this force, is called its centrifugal force. The amount
of these 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. 35) ; then, had it not been acted on by a force in the
-54]
Motion in cr Vertical Circle.
37
direction ac, it would, in a small succeeding interval of time /, have continued
to move in the direction of the tangent at #, and have passed through a
distance which we will represent by ab. In conse-
quence, however, of this force it has not followed this
direction, but has arrived at the point d on the curve ;
hence the force has made it traverse the distance bd=ae
in this interval. If f be the accelerating force which
draws the body towards the centre, ae= \ft~, and if
ad be very small, it may be taken as equal to ab or z//,
where it is the velocity of the moving body. Now if
an is the diameter of the circle, the triangle adn is
inscribed in a semicircle and is right-angled, whence
ad 1 = ae x an = ae x 2r. Substituting their values for
ad and ae in this equation, we find that v^-f- = \ft- x 2r,
from which /= ; 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 which is
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 gives F =
. To keep the body in a circle an attraction to-
S r
wards the centre is needed, which is constantly equal to
and this attraction is constantly neutralised by the -
Fig- 35-
centrifugal force.
The above expression may be put in a form which is sometimes more con-
venient. If T be the time in seconds required to traverse the circumference
with the velocity v, then v>
from which F = 4 *" ir * r
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 o>, the velocity v of a
point at a distance from the axis is o>r, from which to = -
27T
and f
r T
The existence of centrifugal force may be demonstrated by means of
numerous experiments, such as the centrifugal railway. If a small 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.
54. Motion in a Vertical Circle. Let ACBD be a circle whose plane
is vertical and radius denoted by r. Suppose a point placed at A, and
allowed to slide down the curve, what velocity will it have acquired on
On Matter, Force, and Motion.
[54-
reaching any given point P ? Draw 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 (50) ; if, therefore, v denote the velocity of
the point at P, we shall have
Fig. 36-
Now by similar triangles DCP, PCN we have
DC : CP::CP : CN ;
consequently, if we denote by s the chord CP,
2rNC =s~ ;
in like manner if a denote the chord CA,
= -
2 rMN=^-j 2 ,
therefore
and
Now v will have equal values when ^ 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 s is -zero ; consequently, if V is the velocity acquired by the
body in falling from A to C, we have
V =
and, on the other hand, if the body begins to move from C with a velocity V
it will reach a point A such that the chord AC or a is given by the same
equation. In other words, the velocity at the
lowest point is proportional to the chord of the arc
described.
55. Motion of a Simple Pendulum. By a
simple pendulum is meant a heavy particle sus-
pended 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 reaction 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 poir f moves from A
to B can be easily ascertained when the arc of vibration i*> ^nall ; that is,
when the chord and the arc do not sensibly differ.
Q
Fig- 37-
-56] Motion of a Simple Pendulum. 39
Thus, let AB (fig. 37) equal the arc or chord ACB (fig. 36) ; 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 V or a * / -. At any in-
stant let the point be at Q, 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 O resolved parallel to AB is V cos TQN or
,i . [& cos CQP ; that is, if CP equals s, the velocity of O parallel to AB is
But it 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 * / (a 1 s-} and, therefore, this point
would describe AB in the same time that Q describes the semicircumference
AQB. If then be the required time of an oscillation, we have
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 simple pendulum,
whose time of oscillation at Greenwich is one second ; the formula at once
leads to an accurate detennination of the accelerating force of gravity g ; for
using feet and seconds as our units we have /= i, r= 3-26165, and TT stands
for the known number 3*14159, therefore the formula gives us
g= (3-MI59) 2 * 3-26165 = 32-1912.
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 undergoes
may be graphically represented as follows : Draw a line of indefinite length
and mark off AH (fig. 38) to represent the time of one vibration, HH' to re-
present the time of the second vibration, and so on. During the first vibra-
tion the velocity increases from zero to a 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 time represented
4O On Matter, Force, and Motion. [56-
by AM. If a 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 direction 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 MO. If, then, the curve be continued by a suc-
cession 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. Conical Pendulum. When a point P (fig. 39) is suspended from a
point A as a simple pendulum, it can be caused to describe a horizontal circle
with a uniform velocity V. A point moving in such a manner constitutes
what is called a co?iical pendulum, and admits of many
useful and interesting applications. We will, in this
place, ascertain the relation which exists between the
length r of the thread AP, the angle of the cone PAN
or 6, and the velocity V. Since the point P moves in a
circle whose radius is PN, with a velocity V, a force R
v must act on it in the direction PN given by the equa-
tion (53)
Now the only forces acting are the tension of the thread T along PA,
and the weight of the body M^* vertically ; consequently, their resultant must
be a force R acting along PN. And therefore these forces will be parallel
to the sides of the triangle ANP, so that (35)
therefore
or
Now PN = r sin 6 and PN = tan 6,
AN
therefore
V 2 =gr sin tan 6.
One conclusion from this may be noticed. With centre A and radius
AP, describe the arc PC. Now when the angle PAC is small, the sine, PN,
does not sensibly differ from the chord, nor the cosine, AN, from the radius,
therefore in this case we have
(chdPC)* orV = ch /^
radius V r
On comparing this result with (54) we see that when the angle PAN is
small, the velocity of P moving in a conical pendulum is the same as P
-58] Impulsive Forces. 41
would have at the lowest point C if it oscillated as a simple pendulum ; con-
sequently, if we conceive the point P to be making small oscillations about
the point A, and denote the velocity at the lowest point by V, and if, when
at the extreme point of the arc of vibration, there is communicated to it a
velocity V in a direction at right angles to the plane of vibration, its motion
will be changed into that of a conical pendulum.
58. Impulsive Forces. When a force acts on a body for an inappreci-
ably short time, and yet sensibly changes its velocity, it is termed an instan-
taneous or impulsive 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 a time so short that its duration is nearly,
or quite, insensible. In fact, if M is the mass of the body, and the force
contains M/ units, it will, in a time /, communicate a velocity// ; now, how-
ever small / may be, M/and therefore f may be so large that ft may be of
sensible or even considerable magnitude. Thus if M contain a pound of
matter, and if the force contain ten thousand units, though / were so short
as to be only the j^oth f a second, the velocity communicated by the force
would be one of 10 ft. per second. 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 \ft~ or the ^^ ^ a
foot while 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
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
with contrary signs ; and therefore the sum of the momenta of the two bodies
will remain constant during and at the end of the impact. It is of course
understood that if the two bodies move in contrary directions their momenta
have opposite signs and the sum is an algebraical sum. In order to test the
physical validity of this conclusion, Newton made a series of experiments,
which may be briefly described thus : Two balls A and B 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 ; * u V D * H
both A and B will now move, along the arch \ \
AF and BH respectively ; let A and B come
to their highest points at r and k respectively.
Now if V denote the velocity with which A
reaches the lowest point, v and u the ve-
locities with which A and B leave the lowest
points after impact, and r the radius AC, it Fig. 40.
follows from (54) that
V = chd Ar A* v = chd Ar * , and u = chd
A f s ;
42 On Matter, Force^ and Motion. [58-
therefore if A and B are the masses of the two balls, the momentum at the
instant before impact was A x chd AR, and the momentum after impact was
A x chd Ar+ B x chd B/. Now when the positions of the points R, r, and
k 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 suc-
ceeded equally under every modification, whether A impinged on B at rest
or in motion, and whatever the materials of A and B might be.
59. Direct Collision of Two Bodies. Let A and B be two bodies mov-
ing 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 quite inelastic. In this case, when A
touches B, it will continue to press against B until their velocities are equal-
ised, 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 AJT + B.r
their joint momentum at the end of impact, but their momentum before im-
pact was AV + BU. Whence
an equation which determines x..
ii. Let us suppose the bodies perfectly 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 of that lost while compression took place ;
that is, up to the instant at which their velocities were equalised. But these
are respectively AV A_r and B.r BU ; therefore, if v and u are the required
final velocities,
A?/ = AV-2(AV-A.r) or v= -V + 2.r
Bar = BU + 2(B:r- BU) or u = 2x- U,
hence
(A + B) v = 2BU + (A - B)V
and
(A + B) = 2 AV - (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 u = 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 if carefully performed is a very remarkable experi-
ment.
60. 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
-61] Measure of Work. 43
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 by a horse, whether employed in drawing a vehicle, or in turning a gin ;
or that of a steam-engine, whether it be used to drag a railway-train or to
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 maybe
performed on different materials, with different tools, and with different
degrees of skill.
It is, moreover, easy to see (comp. 52) that any possible change 01
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
accelerated. Hence, what has been said above may be summed up as
follows : When a force produces acceleration, or when it maintains motion
unchanged in opposition to resistance, it is said to do WORK.
61. 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
44 On Matter, Force, and Motion. [61 -
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 move 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 time 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.
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 in a 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 J
the opposite direction to the motion, the component may be considered as a '
resistance and the product is work done against the resistance. Thus, inl
(43), if we suppose a to move up the plane from R to S, the work done by P
is P x RS ; the work done against the resistance W is W sin .r x RS. It willl
be observed that if the forces are in equilibrium during the motion, so that]
the velocity of a is uniform, P equals W sin x, and consequently the work <
done by the power equals that done against the resistance. Also since RSI
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 will not bel
uniform, but accelerated ; the work done upon it will nevertheless still bej
represented by the product of the force into the distance through which itl
acts. In order to ascertain the relation between the amount of work donel
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 throughj
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 (29) thatl
a constant force is measured by the momentum produced by it in a unit ofl
-61] Measure of Work. 45
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 l the velocity at the end,
the momentum produced during the time T is MV X MV, and conse-
quently the momentum produced in a unit of time, or, in other words, the
measure of the force, is
_
The distance S through which the mass M moves while its velocity
changes from the value V to the value V l 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 a uniform rate ; hence,
in the present case, the average velocity is simply the arithmetical mean of
the initial and final velocities, or
Combining this with the last equation, we get as the expression for the
work done by the force F :
or, in words, when a cojistant force acts on a mass so as to change its velocity,
the work done by the force is equal to half the product of the mass into the
change of the square of the velocity.
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 n of very small parts each equal to s,
so that ns = 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 15 F 2 , F 3 . . . . F, be the forces acting
throughout the ist, 2nd, 3rd . . . th interval respectively, and let the
velocity at the end of the same intervals be v lt -z' 2 , v s , . . . . v n ( = Vj),
respectively ; then, for the work done in the successive intervals, we
have
or, for the total work,
46 On Matter, Force, and Motion. [61-
where the quantity of the left-hand side of the equation may also be written
i 0+ ~*~ n ns = YS, if we put F to stand for the average (or arith-
n
metical mean) of the forces F 1} F 2 , &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=|MV 1 2 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 15 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 in 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 ; if the force P
(where P is the constant force with which the string pulls W up the plane)
be greater than W sin x, the body W will move up the incline with a con-
tinually increasing velocity, and 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 v with which W arrives at the top of the incline we
have the equation
(P~-Wsin;r) RS = \W;
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 .r, corresponds to the resultant
force F supposed in the foregoing discussion, and RS to the distance through
which this resultant force acts.
62. Unit of Work, For strictly scientific purposes a unit of work is
taken to be the work done by a unit of force when its point of application
moves through one foot 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 I pound through the height of I 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 per-
fectly 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 kilogrammetre is the unit ; it is the weight of
a kilogramme raised through a height of a metre. This is equal to 7-24
foot-pounds, and one foot-pound = -1381 of a kilogrammetre.
_64] Varieties of Energy. 47
63. Energy. The fact that any agent is capable of doing work is usually
expressed by saying that it possesses Energy, 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 P x 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 conferred upon the weight W a quantity of
energy equal to that which has been expended ; for, in the first place, W
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 W 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
The energy possessed by the mass M in consequence of having been raised
from the ground is commonly distinguished as energy of position vr 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 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. It will be seen, on considering the definition
of work given above, 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 any electrical, magnetic,
or chemical change is produced. This extension of the meaning of the term
work involves a similar extension of the meaning of energy, 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 ; (b] the energy 7 of a charged Leyden jar which,
according to the way in which the jar is discharged, can give rise to changes
48 On Matter, Force, and Motion. [64-
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 is 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 is 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.
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 previous
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 vice 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 j
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 I
invariable. If the combustion take 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. 49
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
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. For instance, 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 (460), 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.
Gravitation and Molecular Attraction. [67-
BOOK II.
GRAVITATION AND MOLECULAR ATTRACTION.
CHAPTER I.
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 ap-
proach each other ; it is a mutual 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 unoccu-
pied by other matter.
A vague hypothesis of the tendency of the matter of the earth and stars
to 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.
Since Newton's time the attraction of matter by matter was experiment-
ally 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 is directly proportional to the product of their masses
and inversely proportional to the square of their distajices 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 increased from i to
2, 3, 4> units, the attraction would be diminished to the 4th,
-68] Terrestrial Gravitation. 5 1
9th, 1 6th, .... 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 mole-
cules, having the masses m and /', at the distance r, would be expressed by
ni in'
r 2
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
gravitation.
At any point of the earth's surface, the direction of gravity that is, the
line which a falling body describes is called the vertical 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 is perpendicular to the
vertical line.
The vertical line at any point of the globe is generally determined by the
phnnb-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, un-
less the direction of the earth's attraction upon it passes
through the point of support, and therefore coincides with
that of the string. . . .
The horizontal plane is also determined with great
ease, since it coincides, as will be afterwards shown, with
the Imel 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 9
deviation of the plumb-line, and is due to the attraction of Flg- 4I<
some great mass of matter in the neighbourhood, swch as a mountain.
Thus, in the case of the mountain of Schehallien, 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 1 1"6 than the angle between the normals of the mean surface
of the earth at those points ; in o.ther 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 result agreeing
D 2 ^^?
rtp* or TH*^<$\
IUII7BRSITT1
Gravitation and Molecular A ttraction.
[68-
pretty closely with that deduced from Cavendish's experiments 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 m m' m"
Fig. 42.
Fig. 43-
m"'. . . (fig. 42) be molecules of any body. The earth's attraction upon
these molecules will constitute a system of parallel forces, having a common
vertical direction, whose resultant, according to (36) will be found by seek-
ing first the resultant of the forces which act on any two molecules, m and
m\ then that of this resultant, and a third force acting on ;", and so on
until we arrive at the final resultant, W, representing the weight of the body,
and applied at a certain point, G. If the body be now turned into the
position shown in fig. 43, the molecules ;;/, ?/z', m". . , will continue to be
acted on by the same forces as before, the resultant of the forces on m and
m' will still pass through the same point o in the line mm', the following re-
sultant will again pass through the same point o' in om", and so on up to the
final resultant P, which will still pass through the same point G, 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 ts 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 ex-
periments intersect each other is the centre of gravity required. For the
-71]
Different States of Equilibrium.
53
Fig. 44.
Fig. 45-
resultant of the earth's attraction being a vertical force applied at the centre
of gravity, the body can only be in equilibrium when this 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.
70. Equilibrium of heavy
bodies. Since the action of gravity
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 resist-
ances 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 equili-
brium 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. 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 stable, unstable, neutral.
A body is said to be in stable equilibrium if it tends to return to its first
position after the equilibrium has been slightly disturbed. Every body is in
this state when its position is such that the slightest alteration of the same
elev*ates 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, b, placed
54
Gravitation and Molecular A ttraction.
[71-
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 suspen-
sion at the toe, and its centre of gravity at a lower
point, g.
A body is said to be in unstable 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
Fig. 46.
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 neutral. In this case an alteration 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 instrument for determining the
relative weights or masses of bodies. There are many varieties.
The ordinary balance (fig. 48) consists of a lever of the first kind, called
the beam, 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, n, commonly called a knife edge, which passes through the beam, and
rests with its sharp edge, or axis of suspension, 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 the graduated arc, a ;
when the beam is perfectly horizontal the needle points to the zero of the
graduated arc.
Since by (40) two equal forces in a lever of the first kind cannot be in
equilibrium unless their leverages are equal, the length of the arms ?zA and
B ought to remain equal during the process of weighing. To secure this
the scales are suspended from hooks, whose curved parts have sharp edges,
and 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.
55
73. Conditions to be satisfied by a balance. A good balance ought
to satisfy the following conditions :
5. The tiuo 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,
weights are placed in the two scales until the beam becomes horizontal ;
the contents of the scales being then interchanged, the beam will remain
B
Fig. 4 8.
horizontal if its arms are equal, but if not, it will descend on the side of the
longer arm.
ii. The 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.
iii. The beam being horizontal, its centre of gravity ought to be in the same
56 Gravitation and M'olecular Attraction. [73-
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).
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, b.
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
Fig. 49.
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 when a
very small difference between the weights in the scales causes a perceptible
deflection of the pointer.
Let A and B (figs. 50 and 51) be the points from which the scale pans are
suspended, and C the axis of suspension of the beam. A, B, and C are
Fig. 50.
supposed 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 O,
the greater is the delicacy 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 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-Q) AC = WxGN
-75]
Physical and Chemical Balances.
Now it is clear that for a given value of CG the angle GCN (that is, ECD,
which measures the delicacy) is great 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 \V is less. Again, for a given value of GN the angle
GCX is greater as CG is less. Hence the means of rendering a balance
delicate are :
i. To make the arms of the balance long.
ii. To make the weight of the beam as small as is consistent with its
rigidity.
iii. To bring tJte 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-
Fig. 52-
ing friction. To secure this advantage the edges from w^hich 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.
75. Physical and cbemical balances. Fig. 52 represents one of the
accurate balances ordinarily used for chemical analysis. Its sensitiveness is
such that when charged with a kilogramme (1,000 grms.) in each scale an
excess of a milligramme (y^oth f a rm -) m either scale produces a very
perceptible deflection of the index.
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
D 3
58 Gravitation and Molecular Attraction. [75-
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 in vacua.
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-established. The sum of these
weights will necessarily 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 determined by placing it suc-
cessively 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 x, and in the other the weight p, required to balance it, let a and b be
the arms of levers corresponding to x and p. 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 bx = ap r Hence abx* = abpp^ from
which x =
-77]
Laws of Falling Bodies.
59
LAWS OF FALLING BODIES.
CHAPTER II.
INTENSITY OF TERRESTRIAL GRAVITY.
PENDULUM.
THE
77. Laws of falling bodies. Since a body falls to the ground in conse-
quence 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; in a vacuum all bodies fall iL'ith
equal rapidity. To demonstrate this by experiment
a glass tube about two yards long (fig. 53) 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, feather, &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 intro-
duced.
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 falling 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 like solids without
separation of their molecules. The water-hammer
illustrates this : the instrument consists 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 blow-pipe. When
such a tube is suddenly inverted, the water falls in
one undivided mass against the other extremity of
the tube, and produces a sharp dry sound, resem-
bling that which accompanies the shock of two solid
bodies. Fi g- 53-
6o
Gravitation and Molecular A ttraction.
[77-
From Newton's law (67) it follows that when a body falls to the earth
the force of attraction which causes it to do so increases as the body
approaches the earth. Unless the
height from which the body falls,
however, be very great, this in-
crease will be altogether inappre-
ciable, 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 ac-
celerated, and would obey the
laws already explained (49).
78. At woods machine.
Several instruments have been
invented for illustrating and ex-
perimentally verifying the laws of
falling bodies. Galileo, who dis-
covered these laws in the early
part of the seventeenth 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.
54. It consists of a stout pillar of
wood, about 2| yards high, at the
top of which is a brass pulley,
whose axle rests and turns upon
four other wheels, called friction
wheels, inasmuch as they serve to
diminish friction. Two equal
weights, M and M', are attached
to the extremities of a fine silk
thread, which passes round the
pulley ; a time-piece, H, fixed to
Fig. 54-
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,
-78] Atwood's Mac/line. 6 1
whose two teeth, as seen in the figure, fit into those of the ratchet wheel.
The axle of this wheel gives motion to the seconds hand of the dial, and
also to an eccentric behind the dial, as shown at E by a 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 pre-
cisely 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 ;;/ 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 ?, 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 \vhich 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 i will fall, the weights M and m 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 ///, the plate z, and the
lever D, be placed as at first ; remove the plate A, and in its place put a ring,
B, so as to arrest the overweight m 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
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 (25) 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 m arrive after
the lapse of two seconds, and putting a ring at B', ascertain by a fourth ex-
periment 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 two seconds. In a 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
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
62 Gravitation and Molecular Attraction. [78-
accelerated motion as enunciated in (49). For example, the spaces OB,
OB', OB", .... described from a state of rest in i, 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 m be changed, the acceleration or velocity BC
acquired per second will also be changed, and we may easily verify the
assertion in (29), 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, if m weighed half an
ounce, and M and M' each 15^ ounces, the acceleration BC would be found
to be six inches ; whilst if in weighed i ounce, and M and M' each 63 .V
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 i : 2 ; while the products of the masses and the accelera-
tions are in the ratio of ( + isf + I5f) x 6 to (i + 63^ + 63^) x 3 ; that is, they
are also in the ratio of i : 2. Now the same result is obtained in whatever
way the magnitudes of m, 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. iviorin's apparatus. The principle of this apparatus, the original
idea of which is due to General Poncelet, is to make the body in falling trace
its own path. Figure 55 gives a view of the whole apparatus, and figure 56
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. If the 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 is a toothed wheel, c,
which turns two endless screws, a and b, one of which turns the cylinder,
and the other two vanes, x and x 1 (fig. 56). At the other end is a ratchet
wheel, in which fits the end 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 is 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 gravity tends
to impart. From this time the motion becomes uniform. This is the case
when the weight Q has traversed about three-quarters its course ; at this
moment the weight P is detached by pulling the cord K, and the pencil then
traces the curve mn.
-80J
The Length of the Compound Pendulum.
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
i, 2, 3, .... in a horizontal direction, the displacements are I, 4, 9 . . . .
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
mn. it is concluded that this curve is a parabola.
80. 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
64 Gravitation and Molecular Attraction. [80--
existence, and any pendulum which does not realise these conditions is
called a compound or physical pendulum. The laws for the time of vibra-
tion of a compound pendulum are the same as those which regulate the
motion of the simple pendulum, though it will be necessary to define ac-
curately what is meant by the length 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 extremi-
ties 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 equidistant from the axis of sus-
pension, constitute a parallel axis known as the axis of oscillation ;
and it is to the distance between these two axes that the term
length of the compound pendulum is applied : we may say, there-
fore, tha.t the length of a compound pendulum is that of the simple
pendulum which would describe its oscillations in tJie 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 compound pendulum.
For this purpose the reversible pendulum devised by Bohnenberger
and Kater may be used. One form of this (fig. 57) is a rod with
the knife-edges a and b turned towards each other. W and V are
lens-shaped masses the relative positions of which may be varied.
By a series of trials a position can be found such that the number
of oscillations of the pendulum in a given time is the same
whether it oscillates about the axis a or the axis b. This being
so, the distance ab represents the length / 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 pen-
dulum.
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 intensity of gravity. The following table gives its
value at the sea level at various places. The accelerative effect of
gravity at these places, according to formula (55), is obtained in
feet and metres, by multiplying the length of the seconds pendulum,
reduced to feet and metres respectively, by the square of 3-14159.
-81]
Verification of the Laws of the Pendulum.
Latitude.
Hammerfest .
7o-4o / N.
Manchester .
53 '29
Konigsberg .
54 -42
Berlin .
52 -30
Greenwich
51 -29
Paris
48 -50
New York
40 '43
Washington .
38 '54
Madras .
13 "4
Ascension
7-56
St. Thomas .
0*25
Cape of Good Hope
33 '55 S.
Length of
Acceleration of Gravity
Pendulum
in
in inches.
feet.
metres.
39-1948
32-2364
9-8258
39T472
32T972
9-8I32
39-I507
32-2002
9-8I42
39-I439
32-1945
9-8I24
39-I398
32-1912
9-8II5
39-I285
32-I8I9
9-8039
39*1012
32-1594
9-8019
39-0968
32-1558
9-8006
39-0268
32-0992
97836
39-0242
32-0939
97817
39-0207
32-0957
97826
39-0780
32-1404
97962
Consequently, \g or the space described in the first second of its motion
by a body falling in vacua from a state of rest (49) is
16-0478 feet or 4-891 metres at St. Thomas,
16-0956 4-905 at London, and
16-1182 ,,4-913 at Hammerfest.
In all calculations, which are used for the sake of illustration, we may
take 32 feet or 9-8 metres as the accelerative
effect due to gravity.
From observations of this kind, after apply-
ing the necessary corrections, and taking into
account the effect of rotation (83), the form of
the earth can be deduced.
8 1. Verification of the laws of the pen-
dulum. In order to verify the laws of the
simple pendulum (55) we are compelled to em-
ploy 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 sus-
pended from a fixed point by means of a very
fine metal wire. A pendulum thus formed os-
cillates 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
Fig. 58.
by causing pendulums, whose lengths are as the numbers i, 4, 9, . . . . to
oscillate simultaneously. The corresponding numbers of oscillations in a given
66
Gravitation and Molecular Attraction.
[81-
time are then found to be proportional to the fractions, i, , f, c.,
which shows that the times of oscillation increase as the numbers i, 2,
3, &c.
By taking several pendulums of exactly equal length, B, C, D (fig. 58),
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 showing that the accelerative effect of gravity on all bodies is the
same at the same place.
By means of an arrangement resembling the above, Newton verified the
fact that the masses of bodies are determined by the balance ; which, it will
be remarked, lies at the foundation of the measure of force (29). For
it will be seen on comparing (54) and (55) with (50) that the law of the
time of a small oscillation is obtained on the supposition that the force of
gravity on all bodies is represented by M^-, in which M is determined by the
balance. In order to verify this, he had made two round equal wooden boxes ;
he filled one 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
boxes by threads eleven feet long, 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 all these bodies had equal weights, and if the
inference, that therefore they had equal masses, had been erroneous, by so
much 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
balance-springs. Pendulums were first applied to
this purpose by Huyghens in 1658, and in the same
year Hooke applied a spiral spring to the balance
of a watch. The manner of employing the pendu-
lum is shown in fig. 59. The pendulum rod passing
between the prongs of a fork a communicates its
motion to a rod b, which oscillates on a horizontal
axis o. To this axis is fixed a piece mn called an
escapement or crutch, terminated by two projections
or pallets, which work alternately with the teeth of
the escapement wheel k. This wheel being acted
on by the weight tends to move continuously, 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 m, and with it the whole of the
clockwork and the weight. If, however, the pen-
dulum moves and takes the position shown by the
dotted line, m is raised, the wheel escapes 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 n ; which
in consequence of the motion of the pendulum will be brought into contact
Fig. 59-
-83] Intensity of Terrestrial Gravitation. 67
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 wheehvork the motion of
the escapement is communicated to the hands of the clock ; and consequently
their motion, also, is regulated by the pendulum.
The pendulum has also been .used for measuring great velocities. A large
block of wood weighing from 3 to 5 tons is coated with iron ; against this
arrangement, which is known as a ballistic-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 velocity, from which the pressure of the
enclosed gases can be deduced, and therefrom the initial velocity of the
shot.
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
' St = T^I " TF> TV* where g is the value of the acceleration of gravity at
K (K + n)
the sea level, g, its value at any height //, and R is the radius of the earth.
From this, seeing that h is very small compared with R, and that therefore
its square may be neglected, we get by simple algebraical transformation
g = -
r 1^
R
But even at the sea level the force of gravity varies in different parts 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, at the centre being greater at
the equator than at the Poles, and as the attraction on a body is inversely
as the square of these distances, calculation shows that the attraction due to
this cause is p^th 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.
ii. 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
68
Gravitation and Molecular A (traction.
[83-
a body in motion tends by reason of its inertia to move in a straight line, it
follows that to make it move in a 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 or accele-
rating force. It appears from calculation that on the equator the -^^ 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 gihth 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 these circles diminish, so
does the centrifugal force until the Pole, where the.
radius is null. Further, on the equator the centrifugal ;
force is directly opposed to gravitation ; in any other ;
latitude only a component of the whole force is thus i
employed. This is seen in figure 60, in which PP'
represents the axis of rotation of the earth and EE' |
the equator. At any given point E on the equator the
centrifugal force is directed along CE, and acts wholly \
in diminishing the intensity of gravitation ; but on any
other point, efore the weights are added.
The cathctometer consists of a strong brass support, K, divided into milli-
metres, and which can be adjusted in a 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 fixing 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 for elasticity of
traction or pressure
The altcratioji in length, within the limits of elasticity, is in proportion
to the length and to the load acting on the body, and is inversely as the section.
It depends, moreover, on the specific elasticity ; that is, on the material of
the body. If this coefficient be denoted by E, and if the length, section,
and load are respectively designated by /, s, and P, then for the alteration in
length, n is altered by a load of a kilogramme. This is called the coefficient of
-city ; it is a very small fraction, and it is therefore desirable to use its
reciprocal, that is I or /A, as the modulus of elasticity ; or the weight in kilo-
mes which applied to a bar would elongate it by its own length, assum-
ing it to be perfectly elastic. This cannot be observed, for no body is
perfectly elastic, but it may be calculated from any accurate observations
by means of the above formula.
The following are the best values for some of the principal substances :
Steel ..... 21,000 Lead ..... 1,800
Wrought Iron . . . 19,000 Wood ..... 1,100
Copper .... 12,400 Whalebone .... 700
Brass ..... 9,000 Ice ...... 236^
Zinc ..... 8,700 Glass ..... 90
Silver .... 7,400
74
Gravitation and Molecular Attraction.
[89-
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 1 5 kilogrammes produces a permanent alteration in length
of j^th, and this is the limit of elasticity. The weight which when applied
to a body of the unit of section just brings about an appreciable permanent
change is a measure of the limit of elasticity. Whalebone, on the contrary,
has only a modulus of 700, and experiences a permanent change 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.
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 ex-
perience 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 that the alteration
in the coefficient of elasticity by heat is the same as that which heat produces
in the coefficient of expansions 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 electricity.
90: Elasticity of Torsion. The laws of the torsion of wires were deter-
mined by Coulomb, by means of an apparatus called the torsion balance
(fig. 63). It consists of a metal wire, clasped
at its upper extremity in a support, A, and
holding at the other extremity a metal sphere,
B, to which is affixed an index, C. Immedi-
ately below this there is a graduated circle, CD.
If the needle is turned from its position of equi-
librium through a certain angle, which is the
angle of torsion, the force necessary to produce
this effect is the force of torsion. 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 direction. The equi-
librium being again destroyed, the wire again
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 subject to the
following laws :
I. The oscj Uations are very nearly isochronous.
'Fig. 63.
-91] Elasticity- of Flexure. 7 5
II. For the same wire, the angle of torsion is proportional to the moment
of the force of torsion.
III. With the same force of torsion, and with wires of the same diameter,
the angles of torsion are proportional to the lengths of the wires.
IV. The same force of torsion being applied to wires of the same length,
the angles of torsion are inversely proportional to the fourth powers of the
diameters.
Wertheim has examined the elasticity of torsion in the case of stout rods
by means of a different apparatus, and finds that it is also subject to these
laws. He has further found that, all dimensions being the same, different
substances undergo different degrees of torsion, and each substance has its
own coefficient of torsion, which is denoted by =.
The laws of torsion may be enunciated in the formula w= 1 in
T r^
which w is the angle of torsion, F the moment of the force of torsion, / the
length of the wire, r its diameter, and - the specific torsion-coefficient.
91. Elasticity of flexure. A solid, when cut into a thin plate, and fixed
at one of its extremities, after having been more or less bent, strives to return
to its original position when left to itself. This property is the elasticity of
flexure, and is very distinct in steel, caoutchouc, wood, and paper.
If a rectangular bar A B be clamped at one end and loaded at the other
(fig. 64), the flexure e is represented by the formula
V
where W is the load, / the length of the bar, b its breadth, h its thick-
ness, and p the modulus of elasticity.
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 de- A <
termine the force of agents -JttS^ -^ [T^ B
in prime movers ; and, as
existing in wool, hair, and
feathers, it is applied to
domestic uses in cushions
and mattresses.
Whatever be the kind
of elasticity, there is, as
has been already said, a
limit to it that is, there
is a molecular displace-
ment, 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 Jiardening,
whether by cold, by means of the draw-plate, by rolling, or by hammering.
E 2
76 Gravitation and Molecular Attraction. [91-
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 annealing, which consists
in raising the body to a temperature lower than that necessary for tempering,
and allowing it to cool slowly. It is by this means that 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. Tenacity 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 : tenacity in the ordinary
sense, or resistance to traction ; relative tenacity, or resistance to fracture ;
reactive tenacity, or resistance to crushing ; sheering tenacity, or resistance
to displacement of particles in a lateral direction ; and torsional 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 is directly 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
one in the ratio of 1 1 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 re-
maining the same.
Tenacity, like elasticity, is different in different directions in bodies. In
wood, for example, both the tenacity and the elasticity are greater in the
direction of the fibres than in a transverse direction. And this difference
obtains in general in all bodies, the texture of which is not the same in all
directions.
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. A strand of wires is stronger than a rod of the same
section.
Wertheim found the following numbers representing the weight in kilo-
-93] Hardness. 77
grammes for the limit of elasticity and for the tenacity of wires, I mm. in
diameter.
The table shows that of all metals cast steel has the greatest tenacity.
Yet it is exceeded by fibres of unspun silk, a thread of which i square milli-
metre in section can carry a load of 500 kilogrammes. Single fibres of cotton
can support a weight of 100 to 300 grammes
300 gramm
over the mouth ; when this is pressed by the hand the same effects are
produced.
Fig. 89.
98 On Liquids. [118-
1 1 8. Swimming-bladder of fishes. Most fishes have an air-bladder
below the spine, which is called the swimming-bladder. The fish can com-
press or dilate this at pleasure by means of a muscular effort, and produce
the same effects as those just described that is, it can either rise or sink in
water.
119. Swimming 1 . The human body is lighter, on the whole, than an
equal volume of water : it consequently floats on the surface, and still better
in sea-water, which is heavier than fresh water. The difficulty in swimming
consists not so much in floating, as in keeping the head above water, so as
to breathe freely. In man the head is heavier than the lower parts, and
consequently tends to sink, and hence swimming is an art which requires to
be learned. With quadrupeds, on the contrary, the head being less heavy
than the posterior parts of the body, remains above water without any effort,
and these animals therefore swim naturally.
SPECIFIC GRAVITY HYDROMETERS.
1 20. Determination of specific gravities. It has been already ex-
plained (24) that the specific gravity of a body, whether solid or liquid, is the
number which expresses the relation of the weight of a given volume of this
body to the weight of the same volume of distilled water at a temperature
of 4. In order, therefore, to calculate the specific gravity of a body, it is
sufficient to determine its weight and that of an equal volume of water, and
then to divide the first weight by the second : the quotient is the specific
gravity of the body.
Three methods are commonly used in determining the specific gravities
of solids and liquids. These are, 1st, the method of the hydrostatic balance ;
2nd, that of the hydrometer ; and 3rd, the specific gravity flask. All three, i
however, depend on the same principle that of first ascertaining the weight ;
of a body, and then that of an equal volume of water. We shall first apply ,
these methods to determining the specific gravity of solids, and then to the
specific gravity of liquids.
121. Specific gravity of solids.- i. Hydrostatic balance. To obtain the;
specific gravity of a solid by the hydrostatic balance (fig. 84), it is first,
weighed in the air, and is then suspended to the hook of the balance and
weighed in water (fig. 90). The loss of weight which it experiences is,
according to Archimedes' principle, the weight of a volume of water equal
to its own volume ; consequently, dividing the weight in air by the loss of.
weight in water, the quotient is the specific gravity required. If P is the
weight of the body in air, P' its weight in water, and D its specific gravity,
p
P P' being the weight of the displaced water, we have D =- f .
It may be observed that though the weighing is performed in air, yet,
strictly speaking, the quantity required is the weight of the body in vacuo :
and when great accuracy is required, it is necessary to apply to the observed
weights a correction for the weights of the unequal volumes of air displaced
by the substance, and the weights in the other scale pan. The water in
which bodies are weighed is supposed to be distilled water at the standard
temperature.
_122] Specific Gravity Bottle.
ii. Xicholsoris hydrometer. The apparatus consists of a hollow metal
cylinder B (fig 91), to which is fixed a cone C, loaded with lead. The
object of the latter is to
bring the centre of gravity
below the metacentre, so
that the cylinder may float
with its axis vertical. At
the top is a stem, termi-
nated by a pan, in which is
placed the substance whose
specific gravity is to be
determined. On the stem
a standard point, kt f a cubic inch of air will equal kgp, where k denotes a
certain quantity to be determined presently, and g the accelerating
force of gravity (80). Hence, if we denote PQ in inches by dx, the pressure
will be diminished by kpg . dx, and we may represent this algebraically by'
the equation
kpg . dx = dp.
By a certain algebraical process this leads to the conclusion that
r i
where X denotes the height of AB, and P and P., the atmospheric pressures
at A and B respectively, the logarithms being what are called ' Napierian
logarithms.' Now, if H and Hj are the heights of the barometer at A and
B respectively, the temperature of the mercury being the same at both sta-
tions, their ratio equals that of P to P 1} and therefore
-172] Determination of Heights by the Barometer. 137
It remains to determine k and g.
(i) Since the force of gravity is different for places in different latitudes,
g will depend upon the latitude (83). It is found that if g is the accelerating
force of gravity in latitude $, and/ that force in latitude 45, then
I +0-00256 COS 2
where/has a definite numerical value.
(2) From what has been stated above it will be seen, that if p is the
density of air at a temperature of / C., under Q, the pressure exerted by
29-92 inches of mercury, we shall have
But it will be afterwards shown that if p is the density of air under the same
pressure O at o C., we shall have
i+at
where a represents the coefficient of expansion of gases. Therefore
^Q_ Pn
i + at
Now if a- is the density of mercury, and if the latitude is 45, we shall
have
= 29-92. a/;
and therefore
f-Pj) I
a- ' 29-92 (I + af)
But p ^-(r is the ratio which the density of dry air at a temperature o C,
in latitude 45, under a pressure of 29-92 inches of mercury, bears to the
density of mercury at o C., and therefore p -*-) (i + Q - lA log
which is La Place's barometric formula. In using it, we must remember
that T and T x are temperatures on the Centigrade thermometer, and that H
and Hj are the heights of the barometer reduced to o C. Thus if h is the
measured height of the barometer at the lower station we have
H - >
6500
If the height to be measured is not great, one observer is enough. For
ater heights the ascent takes some time, and in the interval the pressure
138 On Gases. [172-
may vary. Consequently in this case there must be two observers, one at
each station, who make simultaneous observations.
Let us take the following example of the above formula : Suppose that
in latitude 65 N. at the lower of the two stations the height of the barometer
were 30*025 inches, and the temperature of air and mercury I7'32 C., while
at the upper the height of the barometer was 23-230 inches, and the tempera-
ture of air and mercury was io'55 C. Determine the height of the upper
station above the lower.
(i) Find H and H 1 : viz.
30-025 ( l ~-z-^ - J =2 9'945
28-230 (r-^fU 28-184.
TT
Hence log - - . 1-4763243 1-4500026 = 0-0263217.
(2) Find i+ 2 C I - Tl ) viz. 1-05574.
(3) Find i +0-00256 cos 20.
Since 0*00256 cos 130= 0*00256 cos 50= 0*001645
therefore i +0*00256 cos 20 = o - 998355.
Hence the required height in feet equals
60346 x 0-998355 x 1-05574 x 0-00632 17= 1674
It may be easily proved that if H and H l do not greatly differ, the
TT TT TT
Napierian logarithm of - equals 2 - -A If for instance H equals 30
H j rl + rl j
inches, and H x equals 29 inches, the resulting error would not exceed the
50*00 P ar * f ^ e whole. Accordingly for heights not exceeding 2000 ft. we
may without much error use the formula,
173. Ruhlmann's observations. The results obtained for the differen
in height of places by using the above formula often differ from the true
heights as measured trigonometrically, to an extent which cannot be as-
cribed to errors in observation. The numbers thus found for the heights
of places are influenced by the time of day, and also by the season of year,
at which they are made. Ruhlmann has investigated the cause of this dis-
crepancy by a series of direct barometric and thermometric observations
made at two different stations in Saxony, and also by a comparison of the
continuous series of observations made at Geneva and on the St. Bernard.
Ruhlmann has ascertained thus that the cause of the discrepancy is to be
found in the fact that the mean of the temperatures indicated by the ther-
mometer at the two stations is not an accurate measure of the actual mean
temperature of the column of air between the two stations, a condition
which is assumed in the above formula. The variations in the temperature
.
in-
-173] RitJilinanns Observations. 139
of the column of air are not of the same extent as those indicated by the
thermometer, nor do they follow them so rapidly ; they drag after them as it
were. If the mean monthly temperatures at the two fixed stations are
introduced into the formula, they give in winter heights which are somewhat
too low, and in summer such as are too high. The results obtained by
introducing the mean yearly temperature of the two stations are very near
the true ones.
This influence of temperature is most perceptible in individual obser-
vations of low heights. Thus, using the observed temperatures in the
barometric formula, the error in height of the Uetliberg above Zurich (about
1,700 feet) was found to be 5 \- of the total, while the height of the St. Bernard
above Geneva was found within T |g of the true height.
The reason the thermometers do not indicate the true temperature of the
air is undoubtedly that they are too much influenced by radiation from the
earth and surrounding bodies. The earth is highly absorbent, and becomes
rapidly heated under the influence of the sun's rays, and becomes as rapidly
cooled at night ; the air, as a very diathermanous body, is but little heated
by the sun's rays, and on the contrary is little cooled by radiation during the
night.
140 On Cases. [174-
CHAPTER II.
MEASUREMENT OF THE ELASTIC FORCE OF GASES.
174. Boyle's law. The law of the compressibility of gases was dis-
covered by Boyle in 1662, and afterwards independently by Mariottein 1679.
It is in England commonly called ' Boyle's law,' and, on the Continent,
' Mariotte's law'.' It is as follows :
The temperature remaining the same, the volume of a given qtiantity of
gas is inversely as the pressure which it bears.
This law may be verified by means of an apparatus devised by Boyle
(fig. 141). It consists of a long glass tube fixed to a vertical support ; it is
open at the upper part, and the other end, which is bent into a short vertical
leg, is closed. On the shorter leg there is a scale, which indicates equal
capacities ; the scale against the long leg gives the heights. The zero of
both scales is in the same horizontal line.
A small quantity of mercury is poured into the tube, so that its level in :
both branches is at zero, which is effected without much difficulty after a few
trials (fig. 141). The air in the short leg is thus under the ordinary atmo-
spheric pressure which is exerted through the open tube. Mercury is then
poured into the longer tube until the volume of the air in the smaller tube is
reduced to one-half; that is, until it is reduced from 10 to 5, as shown in
fig. 142. If the height of the mercurial column, CA, be measured, it will be
found exactly equal to the height of the barometer at the time of the experi-
ment. The pressure of the column CA is therefore equal to an atmosphere
which, with the atmospheric pressure acting on the surface of the column at
C, makes two atmospheres. Accordingly, by doubling the pressure, the
volume of the gas has been diminished to one-half.
If mercury be poured into the longer branch until the volume of the
air is reduced to one-third its original volume, it will be found that the
distance between the level of the two tubes is equal to two barometric
columns. The pressure is now three atmospheres, while the volume is
reduced to one-third. Dulong and Petit have verified the law for air up to
27 atmospheres, by means of an apparatus analogous to that which has been
described.
The law also holds good in the case of pressures of less than one at-
mosphere. To establish this, mercury is poured into a graduated tube until
it is about two-thirds full, the rest being air. It is then inverted in a deep
trough M containing mercury (fig. 143), and lowered until the levels of the
mercury inside and outside the tube are the same, and the volume AB noted.
The tube is then raised, as represented in the figure, until the volume of air,
AC, is double that of AB (fig. 144). The height of the mercury in the tube
-174]
Boyle's Law.
141
above the mercury in the trough, CD, is then found to be exactly half the
height of the barometric column. The air, whose volume is now doubled, is
now only under the pressure of half an atmosphere ; for it is the elastic
force of this air which, added to the weight of the column CD, is equivalent
to the atmospheric pressure. Hence the volume is inversely as the pressure.
In the experiment with Mariotte's tube, as the quantity of air remains the
same, its density must obviously increase as its volume diminishes, and vice
Fig. 141.
Fig. 142.
Fig. 143. Fig. 144.
versa. The law may thus be enunciated : ' For the same temperature the
density of a gas is proportional to its pressure? Hence as water is 773
times as heavy as air, under a pressure of 773 atmospheres, air would be as
dense as water.
Boyle's law must not be understood to mean that gases of equal density
have equal elastic force ; different gases of various densities have the same
tension when they are under the same pressure. A given volume of hydrogen
under the ordinary atmospheric pressure has the same elastic force as the
same volume of air, although the latter is 14 times as heavy as the former.
Since, for the same volume, there are the same number of atoms in all gases,
142
On Gases.
[174-
the lighter atoms must possess a greater velocity in order to exert the same
pressure as the same number of atoms of greater mass.
175. Boyle's* law is only approximately true. Until within the last
few years Boyle's law was supposed to be absolutely true for all gases at all
pressures, but Despretz
obtained results incom
patible with the law. He
took two graduated glass
tubes of the same length,
and filled one with air
and the other with the
gas to be examined.
These tubes were placed
in the same mercury
trough, and the whole
apparatus immersed in a
strong glass cylinder filled
with water. By means
of a piston moved by a
screw which worked in a
cap at the top of a cylin-
der, the liquid could be
subjected to an increasing
pressure, and it could be
seen whether the com-
pression of the two gases
was the same or not. The
apparatus resembled that
used for examining the
compressibility of liquids
(fig. 63). In this manner
Despretz found that car-
bonic acid, sulphuretted
hydrogen, ammonia, and
cyanogen are more com-
pressible than air : hydro-
gen, which has the same
compressibility as air up to 15 atmospheres, is then less compressible.
From these experiments it was concluded that the law of Boyle was not
general.
In some experiments on the elastic force of vapours, Dulong and Arago
had occasion to test the accuracy of Boyle's law. The method adopted was
exactly that of Mariotte, but the apparatus had gigantic dimensions.
The gas to be compressed was contained in a strong glass tube, GF (fig.
145), about six feet long and closed at the top, G. The pressure was pro-
duced by a column of mercury, which could be increased to a height of 65
feet, contained in a long vertical tube, KL, formed of a number of tubes
firmly joined by good screws, so as to be perfectly tight.
The tubes KL and GF were hermetically fixed in a horizontal iron pipe
:
Fig- 145-
-175] Boyle's Law. 143
DE, which formed part of a mercurial reservoir, A. On the top of this
reservoir there was a force pump, BC, by which mercury could be forced
into the apparatus.
At the commencement of the experiment, the volume of the air in the
manometer (177) was observed, and the initial pressure determined, by
adding to the pressure of the atmosphere the height of the mercury in K
above its level in H. If the level of the mercury in the manometer had
been above the level in KL, it would have been necessary to subtract tne
difference.
By means of the pump, water was injected into A. The mercury being
then pressed by the water, rose in the tube GF, where it compressed the
air, and in the tube KL, where it rose freely. It was only then necessary
to measure the volume of the air in GF ; the height of the mercury in KL
above the level in GF, together with the pressure of the atmosphere, was
the total pressure to which the gas was exposed. These were all the elements
necessary for comparing different volumes and the corresponding tempera-
tures. The tube GF was kept cold during the experiment by a stream of
cold water.
The long tube was attached to a long mast by means of staples. The
individual tubes were supported at the junction by cords, which passed
round pulleys R and R', and were kept stretched by small buckets, P, con-
taining shot. In this manner, each of the thirteen tubes having been sepa-
rately counterpoised, the whole column was perfectly free notwithstanding its
weight.
Dulong and Arago experimented with pressures up to 27 atmospheres,
and observed that the volume of air always diminished a little more than is
required by Boyle's law. But as these differences were very small, they at-
tributed them to errors of observation, and concluded that the law was per-
fectly exact, at any rate up to 27 atmospheres.
Regnault investigated the same subject with an apparatus resembling
that of Dulong and Arago, but in which all the sources of error were taken
into account, and the observations made with remarkable precision. He found
that air does not exactly follow Boyle's law, but experiences a greater com-
pressibility, which increases with the pressure ; so that the difference between
the calculated and the observed diminution of volume is greater in proportion
as the pressure increases.
Regnault found that nitrogen was like air, but is less compressible.
Carbonic acid exhibits considerable deviation from Boyle's law even under
small pressures. Hydrogen also deviates from the law, but its compressi-
bility diminishes with increased pressure.
Cailletet examined the compressibility of gases by a special method in
which the pressure could be carried as high as 600 atmospheres. His results
confirm those of Regnault as regards hydrogen ; nitrogen was found to
present the curious feature that towards 80 atmospheres it has a maximum
relative compressibility ; beyond this point it gradually becomes less com-
pressible, its compressibility diminishing more rapidly than that of hydrogen.
Carbonic acid deviates less from the law in proportion as the temperature is
higher. This is also the case with other gases. And experiment shows
thai the deviation from the law is greater in proportion as the gas is nearer
144 On Gases. [175-
its liquefying point ; and, on the contrary, the farther a gas is from this
point, the more closely does it follow the law. For gases which are the
most difficult to liquefy, the deviations from the law are inconsiderable, and
may be quite neglected in ordinary physical and chemical experiments,
where the pressures are not great.
176. Applications of Boyle's law, Observations on the volumes of
gases are only comparable when made at the same pressure. Usually,
therefore, in gas analyses, all measurements are reduced to the standard
pressure of 760 millimetres, or 29*92 inches. This is easily done by Boyle's
law, for, since the volumes are inversely as the pressures, V : V = P' : P.
Knowing the volume V at the pressure P, we can easily calculate its volume
V at the given pressure P', for
V'P' = VP; thatis, V' = Y-?.
Suppose a volume of gas to measure 340 cubic inches under a pressure
of 535 mm., what will be its volume at the standard pressure, 760 mm. ?
We have V = 34 -- X 5 ^> = 238 cubic inches.
760
In like manner let it be asked, if D' is the density of a gas when the
barometer stands at H' mm., what will be its density D at the same tem-
perature when the barometer stands at H mm. ?
Let M be the mass of the gas, V 7 its volume in the first case, V its volume
in the second. Therefore,
DV-M-D'V'
_== - = -
D 7 V~ P' H''
Thus, if H' denote 760 mm., we have
IT
Density at H' = (Density at standard pressure) - .
760
177. Manometers. Manometers are instruments for measuring the
tension of gases or vapours. In all such instruments the unit chosen is the
pressure of one atmosphere or 30 inches of mercury at the standard tem-
perature, which, as we have seen, is nearly 15 Ibs. to the square inch.
178. Open-air manometer. The open-air manometer consists of a
bent glass tube BD (fig. 146), 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 pressure 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 I marked
at the level of the mercury, for this represents one atmosphere. From this
point the numbers 2, 3, 4, 5, 6 are marked at each 30 inches, indicating so
many atmospheres, since a column of mercury 30 inches represents a pres-
sure of one atmosphere. The intervals from I 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 height which measures the
-179]
Manometer with Compressed A ir.
tension of the vapour. In the figure the manometer marks 2 atmospheres,
which represents a height -of 30 inches, plus the atmospheric pressure exerted
at the top of the column through the aperture D.
This manometer is only used when the pressures do not exceed 5 to 6
atmospheres. Beyond this, the length of tube necessary makes it very in-
convenient, and the following apparatus is commonly used.
179. Manometer with compressed air. The manometer with com-
pressed air is founded on Boyle's law : it consists of a glass tube closed at
the top, and filled with dry air. It is firmly cemented in
a small iron box containing mercury. By a tubulure, A,
in the side (fig. 146), this box is connected with the closed
vessel containing the gas or vapour whose tension is to
be measured.
In the graduation of this manometer, the quantity of
air contained in the tube is such that when the aperture
A communicates freely with the atmosphere, the level
of the mercury is the same in the tube and in the tubu-
lure. Consequently, at this level, the number i is marked
on the scale to which the tube is affixed. As the pres-
sure acting through the tubulure A increases, the mercury
.
"
Fig. 146.
Fig. 147.
Fig. 148.
rises in the tube, until its weight, added to the tension 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 tension is equal to two atmospheres,
and, together with the weight of the mercury raised in the tube, is there-
H
146
On Gases.
[179
fore more than two atmospheres. The position of the number is a little
below the middle, at such a height that the elastic force of the com-
pressed air, together with the weight of the 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. Sometimes this
manometer is made of one glass tube (as represented in fig. 148). The
principle is obviously the same.
1 80. Volumometer. An interesting application of Boyle's law is met
with in the volumometer. This consists of a glass tube with a cylinder G at
the top (fig. 149), 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 air-tight by the plate, and is raised until the mercury
stands at a height //, above the level Q in the bath. The
original volume of the enclosed air V, which was under the
pressure of the atmosphere, is now increased to V + z/, since
the pressure has diminished by the height of the column of
mercury h. Calling the pressure of the atmosphere at the
time of observation , we shall have V : V + v = b h : b.
Placing now in the cylinder a body K whose volume oc 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,
/Zj, is obtained, and we have (V x] : (V x) + v = b /i 1 : b.
Combining and reducing we get x=(V + v) (i /-). The
Fig. 149. 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.
181. 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. 138). In the same
cistern dips a second tube tn i 08 diameter
38io o""3oo
9540 o""ioo
1 86 Acoustics. [229-
The sound wave of which these numbers represent the limit of distance at
which it is no longer heard, still acts on the membrane at the distances of
4156, 1 1, 430 and 19,851 metres respectively.
According to Regnault the principal cause of this diminution of intensity
is the loss of vis viva against the sides of the tube ; he found also that sounds
of high pitch are propagated in tubes less easily than those of low ones ; a
bass would be heard at a greater distance than a treble voice.
230. Velocity of sound in gases. Since the propagation of sonorous
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 in the act of striking a stone before
hearing the sound.
The velocity of sound in air has often been the subject of experimental
determination.
The most accurate of the direct measurements was made by Moll and
Van Beck in 1823. Two hills, near Amsterdam, Kooltjesberg and Zeven-
boomen, were chosen as stations : their distance from each other as deter-
mined 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, Moll and Van Beck's
results as recalculated by Schroder van der Kolk give 109278 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.
The velocity of sound at zero may be taken at 1093 feet or 333 metres.
This velocity increases with the increase of temperature ; it may be calcu-
lated for an temperature t from the formula,
v= 1093 \f (i +0-003665/)
where 1093 is the velocity in feet at o C., and 0*003665 the coefficient of ex-
pansion for i 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 1040 yards
long, it was heard without alteration at the other end, from which he con-
cluded 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 altera-
tion, except in intensity, which could not be the case if some sounds travelled
more rapidly than others.
-231] Velocity of Sound in Gases. 187
This cannot, however, be admitted as universally true. Earnshaw, by a
mathematical investigation of the laws of the propagation of sound, concludes
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 of 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 Holynead, 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 2000 pounds of gunpowder,
the velocity was 967 feet in a second, while with a charge of 12,000 it was
1 2 10 feet in the same time.
Jacques made a series of experiments by firing different weights of powder
from a cannon and observing the velocity of the report at different
distances from the gun by means of an electrical arrangement. He thus
found that, nearest the gun, the velocity is least, increasing 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
U 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.
231. 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
in which i> represents the velocity of the sound, or the distance it travels in
a second, e the elasticity of the gas, and d its density.
This formula expresses that the velocity of the propagation of sound in
gases is directly as the square root of the elasticity of the gas, and inversely
as the square root of its 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 measure of the elasticity of a gas is the pressure to which it is
subjected : hence, if g be the force of gravity. // the barometric height reduced
to the temperature zero, and 8 the density of mercury, also at zero, then for
a gas under the ordinary atmospheric pressure, and for zero, e =gh '. New-
ton's formula accordingly becomes
1 88 Acoustics. [231-
Now if we suppose the temperature of a gas to increase from o to /, its
volume will increase from unity, at zero, to i + at at /, a being the coefficient
of expansion of the gas. But the density varies inversely as the volume,
therefore d becomes d-*-(i + at}. Hence
Substituting in this formula the values in centimetres and grammes,
=981, ^ = 76, ^/=crooi293, we get for the value v a number 29,795 centi-
metres = 297-95 metres, which is considerably less than the experimental
result. Laplace assigned as a reason for this discrepancy the heat produced
by pressure in the condensed waves ; and, by considerations based on this
idea, Foisson and Biot found that Newton's formula ought to be -written
v= * / L- (i + at} -, ; c being the specific heat of the gas for a constant
pressure, and c' its specific heat for a constant volume (see Book VI.). The
average value of this constant is 1-4, and if the formula be modified by the
introduction of the value \/i'4 the calculated numbers agree with the
experimental results.
The physical reason for introducing the constant * / c - into the equation
for the velocity of sound may be understood from the following considera-
tions : We have already seen (225) that sound is propagated in air by a
series of alternate condensations and rarefactions of the layers. At each
condensation heat is evolved, and this heat increases the elasticity, and thus
the rapidity, with which each condensed layer acts on the next ; but in the
rarefaction of each layer, the same amount of heat disappears as was deve-
loped by the condensation, and its elasticity is diminished by the cooling.
The effect of this diminished elasticity of the cooled layer is the same as if
the elasticity of an adjacent wave had been increased, and the rapidity with
which this latter would expand upon the dilated wave would be greater.
Thus, while the average temperature of the air is unaltered, both the heating
which increases the elasticity, and the chilling which diminishes it, concur in
increasing the velocity.
Knowing the velocity of sound, we can calculate approximately the distance
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 be seen
simultaneously with the explosion. Counting then the number of seconds
which elapse between seeing the flash and hearing the sound, and multiply-
ing this number by 1125, we get the distance in feet at which the gun is
discharged. In the same way the distance of thunder may be estimated.
232. 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, of a second, the velocity of sound or the distance traversed in a
n
second is v = n\. 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
-233] Velocity of Sound m various Gases. 189
of the wave length (275). Hence, if we know the number of vibrations of
the note emitted by any particular pipe, which can be easily ascertained by
means of a syren, and we know the length of this pipe, we can calculate i>.
Taking the temperature into account, Wertheim found in this way 1086
feet for the velocity of sound in air at zero.
Further, since in different gases which have the same elasticity, but differ
in density, 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
This number cannot be universally accurate, for the coefficient differs
somewhat in' different gases. And when pipes were sounded with different
gases, and the number of vibrations of tire notes multiplfed with twice the
length of the pipe, numbers were obtained which differed from those cal-
culated by the above formula. When, however, the calculation was made,
introducing for each gas the special value of c - , the theoretical results agreed
c \
very well with the observed ones.
By the above method the following values have been obtained :
Carbonic acid . . . . . 856 ft. in a second.
Oxygen ........ 104
Air ......... 1093
Carbonic oxide . . . . .1106
Hydrogen . . . . . . .4163
233. Doppler's principle. \Yhen a sounding body approaches the ear,
the tone perceived is somewhat higher than the true one ; but if the source
of sound recedes from the ear, the tone perceived is lower. The truth of
this, which is known as Doppler's principle, will be apparent from the follow-
'ing considerations : When the source of sound and the ear are at rest, the
ear perceives n waves in a second ; but if the ear approaches the sound, or
the sound approaches the ear, it perceives more ; just as a ship 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 w r ave length of the par-
ticular tone is X feet, then there are waves in a second; or also , for
A C
\ = c , where c is the velocity of sound (230). Hence the ear receives not
only the ;/ original waves, but also _f in addition. Therefore the number
of vibrations which the ear actually perceives is
190 Acoustics. [233-
or an ear which approaches a tone ; and by similar reasoning it is
for an ear receding from a tone.
Doppler's principle is also established by laboratory experiments.
Rollmann fixed a long rod on a turning machine, 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 pro-
duced 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.
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 tones compared with stationary ones by musicians. He thus
found both the principle and the formula fully confirmed. 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 loudness, an attentive
ear can detect a difference in pitch on approaching or on leaving the station.
234. Velocity of sound in liquids. The velocity of sound in water.
was investigated in 1827 by Colladon and Sturm. They moored two boats
at a known distance 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 4708 feet in a second
at the temperature 8'i, 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 analogous to that given above (230) as applicable to
gases, that is v = A /^-r ; in which g^ A, and d have their previous signi-
V ?4
ficance ; while p. is the coefficient of the compressibility for the liquid in
question that is, its diminution in volume by a pressure of one atmosphere
and d is the density. In this way were obtained the numbers given in the
following table. As in the case of gases, the velocity varies with the tem-
perature, which is therefore appended in each case :
River water (Seine) . . . I3C. = 4714 ft. in a second.
' .... 30 = 5013
Artificial sea-water . . . . 20 = 4761
Solution of common salt . .18 =5132
chloride of calcium . 23 = 6493
Absolute alcohol .... 23 ^ 3854 ,,
Turpentine ..... 24 3976
Ether ...... = 3801
It will be seen how close is the agreement .between the two values for
-235] Velocity of Sound in Solids. 191
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 uncertainty of the values for their compressibility.
235. 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 3120 feet long,
two sounds were distinctly heard at the other end. The first of these was
transmitted by the tube itself with a velocity x ; 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
3I20_3I20
a x
shows that the velocity of sound in the tube is nearly 9 times as great as
that in air.
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 conductivity 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 of miles by placing one end of the
wire in the ear. The toy telephone also is based on this fact.
The velocity of sound in wire has also been determined theoretically by
Wertheim and others, by the formula v = A /- in which /z is the modulus
V d
of elasticity ^89), while d is the mass in unit volume, which is equal to the
specific gravity, or the weight of unit volume, divided by the acceleration of
gravity, or y
o
This may be illustrated from a determination by Wertheim of the
velocity of sound in a specimen of annealed steel wire, the specific gravity s
of which was 7*631 and its modulus 21,000 (87). That is, a weight of 2 1 ,000
kilogrammes would double unit 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 grammes on a wire one sq. cm. in cross section. Hence
2IaXXX98l = 51958. cm. = ,7047 feet.
The following table gives the velocity in various bodies, expressed in feet
per second :
Caoutchouc
Wax
Lead
Gold
Silver
Pine
Copper
Oak.
'?/
23Q4
Elm ....
I 3ci6
4030
5717
8553
IO9OO
1 1 666
14156
Fir .
Steel wire
Walnut .
Cedar
Iron ....
. 15688
15470
15095
. 16503
. 16822
1 92 Acoustics. [235-
In the case of wood the velocity in the direction of the fibres is greater
than across them.
Mallet has investigated the velocity of the transmission of sound in
various rocks, and finds that it is as follows :
Wet sand 825 ft, in a second
Contorted, stratified quartz and slate rock * , Io88
Discontinuous granite . . . . . 1306
Solid granite 1664
A direct experimental method of determining the velocity of sound in
solids, gases, and vapours will be described farther on (277).
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.
236. 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. 194 represents a series of incident waves reflected from an obstacle,
PO. Taking, for example, the incident wave M C D N, emitted from the
Fig. 194-
centre A, the corresponding reflected wave is represented by the arc, CKD,
of a circle, whose centre a is as far behind the obstacle PO as A is before it
If any point, C, of the reflecting surface be joined to the sonorous centre,
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 C, is the angle of reflection.
The reflection of sound is subject to the two following laws :
I. The angle of reflection is equal to the angle of incidence.
II. The incident sonorous ray and the reflected ray are in the same plane
perpendicular to tJte reflecting surface.
-237] Echoes and ^Resonances. 193
From these laws it follows that the wave which in the figure is propagated
in the direction AC, takes the direction CB after reflection, so that an ob-
server placed at B hears, besides the sound proceeding from the point A, a
second sound, which appears to come from C.
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 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.
237. 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 betaken at 1125 feet in a 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 f eet *
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 dissyllabic, trisyllabic, and so on.
When the distance of the reflecting surface is less than 112-5 f eet tne
direct and the reflected sound are confounded. They cannot be heard
separately, but the sound is strengthened. This is what is often called reso-
nance, and is often observed in large rooms. Bare walls are very reso-
nant ; but tapestry and hangings, which are bad reflectors, deaden the
sound.
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
20 or 30 times. An echo 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 foci like the luminous and calorific
foci produced by concave reflectors. If a 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 any one standing in the
intermediate spaces.
There is a square room with an elliptical ceiling, on the ground floor of
the Conservatoire des Arts et Metiers, in Paris, which presents this pheno-
menon in a remarkable degree when persons stand in the two foci of the
ellipse.
194 Acoustics. [237-
In the whispering gallery 7 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.
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.
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 shadows 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 sonorous
wave passes from a medium of one density into another it undergoes partial
reflection, which, though not strong enough to form an echo, distinctly
weakens the direct sound. This is doubtless the reason, as Humboldt re-
marks, 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 atmo-
sphere in the night with thousands of confused sounds.
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 ; recent re-
searches of Tyndall show that a white fog, or snow, or hail, are not important
obstacles 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 results.
On some days which optically were quite clear, certain sounds could not
be heard at a distance far inferior to that at which they could be heard even
during a thick haze. Tyndall ascribes this result to the presence in the
atmosphere of aqueous vapour, which forms in the air innumerable striae
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 has shown that a medium consisting of
alternate layers of light and heavy gas 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.
-239] Speaking Trumpet. Ear Trumpet. 195
It has long been known that sound is pfropagated 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, the front of a condensed wave
(fig. 192), which was originally vertical, becomes tilted upwards and 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. The
ray which travels with the wind will for similar reasons be refracted down-
wards.
238. Refraction of sound. It will be found in the sequel that refraction
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 between 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 nature of the substance with which the tube was filled.
Accurate measurements showed that the law held that the sines of the angle
of incidence and of refraction are in a constant ratio, which is equal to the
ratio of the velocity of sound in the two media.
Sondhauss has 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. This was filled with carbonic acid,
and a watch 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 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 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 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.
239. Speaking: trumpet. Bar trumpet. These instruments are based
both on the reflection of sound and on its conductibility in tubes.
The speaking trumpet, as its name implies, is used to render the voice
audible at great distances. It consists of a slightly conical tin or brass tube
(fig. 195), very much wider at one end (which is called the belt), and provided
with a mouthpiece at the other. The larger the dimensions of this instrument
the greater is the distance at which the voice is heard. Its action is usually
K2
Acoustics. [239-
ascribed to the successive reflections of sonorous 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
Fig- 195-
this explanation, that the sounds emitted by the speaking trumpet are
not stronger solely in the direction of the axis, out in all directions ; that the
bell would not tend to produce parallelism in the sonorous wave, whereas
it certainly exerts considerable influence in strengthening the sound. It must
be said that no satisfactory explanation has been given of the effect of the bell.
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 extremities, terminating in a bell, 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 developed, are concentrated on
the auditory apparatus, and produce a far greater effect than divergent waves
would have done.
240. Stethoscope. One of the most useful applications of acoustical
principles is the stethoscope. Figs. 196, 197 represent an improved form of
this instrument devised by Konig. Two sheets of caoutchouc, c and \ this means the distinction between the semitones is abolished, so that,
for example, Cfl and Db become the same note. The scale of twelve
notes thus formed is called the chromatic scale. It of course follows that
major triads become slightly dissonant. Thus, in the diatonic scale, if we
reckon C to be i, E is denoted by 1-25003, and G by 1-50000: On the system
of equal temperament, if C is denoted by I, 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 unequal temperament. Of this
class is Kirnberger's, in which nine of the tones are pure.
Although the system of equal temperament has the advantage of afford-
ing, with as small a number of notes as possible, the greatest variety of tones,
yet it has the disadvantage that no chord of an equally-tempered instrument,
such as the piano, is quite 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 much without accompaniment, does the natural pure temperament assert
itself, and thus produce the highest musical effect.
251. Tiie number of vibrations producing each note. The tuning-
fork. Hitherto we have denoted the number of vibrations corresponding to
the note C by ;;/, 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 is 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 one another, 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 F 'g- 2 4-
separately adjusted with .reference to the fundamental note. A tuning-fork
or diapason is an instrument yielding a constant sound, and is used as a
standard for tuning musical instruments. It consists of an elastic steel rod,
206 Acoustics. [251-
bent as represented in fig. 204. It is made to vibrate either by drawing a
bow across the ends, or by striking one of the legs against a hard body, or
by rapidly separating the two prongs by means of a steel rod as shown in
the figure. The vibration produces a note which is always the same for the
same tuning-fork. The note is strengthened by fixing the tuning-fork on a
box open at one end, called a resonance box.
The standard tuning-fork in any country represents its accepted concert
pitch.
It has been remarked for some years that not only has the pitch of the
tuning-fork been getting higher in the large theatres of Europe, but also
that it is not the same in London, Paris, Berlin, Vienna, Milan, &c. This is
a source of great inconvenience both to composers and singers, and a com-
mission was appointed in 1859 to establish in France a tuning-fork of uniform
pitch, and to prepare a standard which would serve as an invariable type.
In accordance with the recommendations of that body, a normal tuning-fork
has been established, which is compulsory on all musical establishments
in France, and a standard has been deposited in the Conservatory of Music
in Paris. It performs 437*5 double vibrations per second, and gives the
standard note a or /#, or the a in the treble stave (252). Consequently, with
reference to this standard, the middle c or do would result from 261 double
vibrations per second.
In England a committee, appointed by the Society of Arts, recommended
that a standard tuning-fork should be one constructed to yield 528 double
vibrations in a second and that this should represent convenient practice is to call the octave, of which the C is produced by an
>L*-eight-foot organ pipe, by the capital letters C, D, E, F, G, A, B ; the next
higher octave by the corresponding small letters, c, d, e,f,g,a,b\ and to
designate the octaves higher than this by the index placed over the letter
thus, ' Marloye, and known as
harp, based on the longitudinal vibration of rods. It consists of
I wooden- pedestal in which are fixed twenty thin deal rods some
232
Acoustics.
[281-
coloured and others white. They are of such a length that the white rods
give the diatonic scale, while the coloured ones give the semitones, and
complete the chromatic scale. The instrument is played by rubbing the
rods in the direction of their length between the finger and thumb, which
have been previously covered with powdered resin. The notes produced
resemble those of a pandsean pipe.
The tuning-fork^ the triangle, and musical boxes are examples of the
transverse vibrations of rods. In musical boxes small plates of steel of
different dimensions are fixed on a rod, like the teeth of a comb. A cylinder
whose axis is parallel to this rod, and whose surface is studded with steel
teeth, arranged in a certain order, is placed near the plates. By means of
a clockwork motion, the cylinder rotates, and the teeth striking the steel
plate set them in vibration, producing a tune, which depends on the arrange-
ment of the teeth on the cylinder.
If a given rod be clamped either in the middle, or at both ends, the
wave-length of the note produced by making it vibrate longitudinally, is
double its own length, and if it be clamped at one end only, and made to
vibrate longitudinally, the wave-length of the sound is four times its own length.
Thus the former case is analogous to an open pipe, and the latter to a
stopped pipe, in respect of the sounds produced.
Stefan has determined the velocity of sound in soft bodies by attaching
them, in the form of rods, to long glass or wooden rods. The compound rod
was made to vibrate and the number of vibrations of the note w r as determined.
Knowing this and also the velocity of sound in the longer rod, the velocity in
the shorter rod was at once obtained. By this method some of the numbers
in the table in article 234 were obtained.
282. Vibrations of plates. In order to make a plate vibrate, it is fixed
in the centre (fig. 237), and a bow rapidly drawn across one of the edges ;
Fig. 237.
Fig. 238.
or else it is fixed at any point of its surface, and caused to vibrate by
rapidly drawing a string covered with resin against the edges of a central
hole (fig. 238).
-283] Vibrations of Membranes. 233
Vibrating plates contain nodal lines (269), which vary in number and
position according to the form of the plates, their elasticity, the mode of
excitation, and the number of vibrations. These nodal lines may be made
visible by covering the plate with fine sand before it is made to vibrate.
As soon as the vibrations commence, the sand leaves the vibrating parts,
and accumulates on the nodal lines, as seen in figs. 237 and 238.
The position of the nodal lines may be determined by touching the
points at which it is desired to produce them. Their number increases with
the number of vibrations ; that is, as the note given by the plates is higher.
The nodal lines always possess great symmetry of form, and the same form
is always produced on the same plate under the same conditions. They
were discovered by Chladni.
The vibrations of plates are governed by the following law : In plates
of the same kind and shape, and giving the same system of nodal lines, the
number of vibrations in a second is directly as the thickness of 'the plate 's, and
inversely as their area.
Gongs and cymbals are examples of instruments in which sounds are
produced by the vibration of metal plates. The glass and the steel harmo-
nicon depend on the vibrations of glass and of steel plates respectively.
283. Vibrations of membranes. In consequence of their flexibility,
membranes cannot vibrate unless they are stretched, like the skin of a drum.
The sound they give is more acute in proportion as they are smaller and
more tightly stretched. To obtain vibrating membranes, Savart fastened
gold-beater's skin on wooden frames.
In the drum, the skins are stretched on the ends of a cylindrical box.
When one end is struck, it communicates its vibrations to the internal
column of air, and the sound is thus considerably strengthened. The cords
stretched against the lower skin strike against it when it vibrates, and pro-
duce the sound characteristic of the drum.
Membranes either vibrate by direct percussion, as in the drum, or they
may be set in vibration by the vibrations of the air, as Savart has observed,
provided these vibrations are sufficiently intense. Fig. 239 shows a mem-
Fig. 239-
brane vibrating under the influence of the vibrations in the air caused by
a sounding bell. Fine sand strewn on the membrane shows the formation
of nodal lines just as upon plates.
There are numerous instances in which solid bodies are set in vibration
234 Acoustics. [283-
by the vibrations of the air. The condition most favourable for the produc-
tion of this phenomenon is, that the body to be set in vibration is under
such conditions that it can readily produce vibrations of the same duration
as those transmitted to it by the air. The following are some of these
phenomena :
If two violoncello strings tuned in unison are stretched on the same
sound-box, as soon as one of them is sounded, the other is set in vibration.
This is also the case if the interval of the strings is an octave, or a perfect
fifth. A violin string may also be made to vibrate by sounding a tuning-
fork.
Two large glasses are taken of the same shape, and as nearly as possible
of the same dimensions and weight, and are brought in unison by pouring
into them proper quantities of water. If now one of them is sounded, the
other begins to vibrate, even if it is at some distance ; but if water be added
to the latter, it ceases to vibrate.
Breguet found that if two clocks, whose time was not very different,
were fixed on the same metallic support, they soon attained exactly the same
time.
Membranes are eminently fitted for taking up the vibrations of the air,
on account of their small mass, their large surface, and the readiness with
which they subdivide. With a pretty strong whistle, nodal lines may be
produced in a membrane stretched on a frame, even at the distant end of a
large room.
The phenomenon so easily produced in easily-moved bodies is also found
in larger and less elastic masses ; all the pillars and walls of a church vibrate
more or less while the bells are being rung.
-284]
Methods of Studying Vibratory Motions.
235
CHAPTER VI.
GRAPHICAL METHOD OF STUDYING MOTIONS.
284. Xiissajous' method of making vibrations apparent. The method
bf Lissajous exhibits the vibratory motion of bodies either directly or by
projection on a screen. It has also the great advantage that the vibratory
motions of two sounding bodies may be compared without the aid of the ear,
so as to obtain the exact relation between them.
This method, which depends on the persistence of visual sensations on
the retina, consists in fixing a small mirror on the vibrating body, so as to
vibrate with it, and impart to a luminous ray a vibratory motion similar to
its own.
Lissajous uses tuning-forks, and fixes to one of the prongs a small
metallic mirror, m (fig. 240), and to the other a counterpoise, n, which is
Fig. 240.
necessary to make the tuning-fork vibrate regularly for a long time. At a
few yards' distance from the mirror there is a lamp surrounded by a dark
chimney, in which is a small hole, giving a single luminous point. The
tuning-fork being at rest, the eye is placed so that the luminous point is seen
at o. The tuning-fork is then made to vibrate, and the image elongates so
Acoustics.
[284-
as to form a persistent Image, m\ which diminishes in proportion as the
amplitude of the oscillation decreases. If, during the oscillation of the mirror,
it is made to rotate by rotating the tuning-fork on its axis, a sinuous line, oix,
is produced instead of the straight line oi. These different effects are ex-
plained by the successive displacements of the luminous pencil, and by the
duration of these luminous impressions on the eye after the cause has
ceased a phenomenon to which we shall revert in treating of vision.
If instead of viewing these effects directly, they are projected on the
screen, the experiment is arranged as shown in fig. 241, the pencil reflected
Fig. 241.
from the vibrating mirror is reflected a second time from a fixed mirror, m t
which sends it towards an achromatic lens, /, placed so as to project the:
images on the screen.
285. Combination of two vibratory motions in the same direction.
Lissajous resolved the problem of the optical combination of two vibratory
motions vibrating at first in the same direction, and then at right angles to
each other.
Fig. 242 represents the experiment as arranged for combining two
parallel motions. Two tuning-forks provided with mirrors are so arranged
that the light reflected from one of them reaches the other, which is almost
parallel to it, and is then sent towards a screen after having passed through
a lens.
If now the first tuning-fork alone vibrates, the image on the screen is the
same as in figure 242 ; but if they both vibrate, supposing they are in unison,
the elongation increases or diminishes according as the simultaneous
motions imparted to the image by the vibrations of the mirrors do or do not
coincide.
-286]
Optical Combination of Vibratory Motions.
237
If the tuning-forks pass their position of equilibrium in the same time
and in the same direction, the image attains its maximum ; and the image
is at its minimum when they pass at the same time but in opposite direc-
tions. Between these two extreme cases, the amplitude of the image varies
according to the time which elapses between the exact instant at which the
tuning-forks pass through their position of rest respectively. The ratio of
Fig. 242.
this time to the time of a double vibration is called a difference of phase of
the vibration.
If the tuning-forks are exactly in unison, the luminous appearance on the
screen experiences a gradual diminution of length in proportion as the ampli-
tude of the vibration diminishes ; but if the pitch of one is very little alte.ed,
Fig. ?43 .
the magnitude of the image varies periodically, and, while the beats resulting
from the imperfect harmony are distinctly heard, the eye sees the concomi-
tant pulsations of the image.
286. Optical combination of two vibratory motions at right angles
to each other. The optical combination of two rectangular vibratory
motions is effected as shown in the figure 243 ; that is, by means of two
tuning-forks, one of \\hich is horizontal and the other vertical, and both
Acoustics.
[286-
provided with mirrors. If the horizontal fork first vibrates alone, a hori-
zontal luminous outline is seen on the screen, while the vibration of the
other produces a vertical image. If both tuning-forks vibrate simultaneously
the two motions combine, and the reflected pencil describes a more or less
complex curve, the form of which depends on the number of vibrations of
the two tuning-forks in a given time. This curve gives a valuable means of
comparing the number of vibrations of two sounding bodies.
Fig. 244.
Fig. 244 shows the luminous image on the screen when the tuning-forks
are in unison ; that is, when the number of vibrations is equal.
The fractions below each curve indicate the differences of phase between
them. The initial form of the curve is determined by the difference of phase.
The curve retains exactly the same form when the tuning-forks are in unison,
provided that the amplitudes of the two rectangular vibrations decrease in
the same ratio.
Fig. 245.
If the tuning-forks are not quite in unison, the initial difference of phase
is not preserved, and the curve passes through all its variations.
Fig. 245 represents the different appearances of the luminous image when
the difference between the tuning-forks is an octave ; that is, when the
-287] The Phonautograph. 239
numbers of their vibrations are as 1:2; and fig. 246 gives the series of
mrves when the numbers of the vibrations are as 3 : 4.
It will be seen that the curves are more complex when the ratios of the
numbers of vibrations are less simple. M. Lissajous has examined these
curves theoretically and has calculated their general equations.
\Yhen these experiments are made with a Duboscq's photo-electrical
apparatus instead of an ordinary lamp, the phenomena are remarkably
brilliant.
287. Leon Scott's Phonauto graph. This apparatus registers not only
the vibrations produced by solid bodies but also those produced by wind
Fig. 247.
instruments, by the voice in singing, and even by any noise whatsoever ; for
instance, that of thunder, or the report of a cannon. It consists of an ellip-
240 Acoustics. [287-
soidal barrel, AB, about a foot and a half long and a foot in its greatest
diameter, made of plaster of Paris. The end A is open, but the end B is
closed by a solid bottom, to the middle of which is fixed a brass tube, a, bent
at an elbow and terminated by a ring on which is fixed a flexible membrane
which by means of a second ring can be stretched to the required amount.
Near the centre of the membrane, fixed by ceiling-wax, is a hog's bristle
which acts as a style, and, of course, shares the movements of the membrane.
In order that the style might not be at a node, M. Scott fitted the stretching
ring with a movable piece, z, which he calls a subdivide^ and which, being
made to touch the membrane first at one point and then at another, enables
the experimenter to alter the arrangements of the nodal lines at will. By
means of a subdivider the point is made to coincide with a loop ; that is, a
point where the vibrations of the membrane are at a maximum.
When a sound is produced near the apparatus, the air in the ellipsoid,
the membrane, and the style will vibrate in unison with it, and it only re-
mains to trace on a sensitive surface the vibrations of the style, and to fix
them. For this purpose there is placed in front of the membrane a brass
cylinder, C, turning round a horizontal axis by means of a handle, m. On
Fig. 248.
Fig. 249.
Fig. 251.
the prolonged axis of the cylinder a screw is cut which works in a nut ; con-
sequently, when the handle is turned, the cylinder gradually advances in the
direction of its axis. Round the cylinder is wrapped a sheet of paper
covered with a thin layer of lampblack.
The apparatus is used by bringing the prepared paper into contact with
the point of the style, and then setting the cylinder in motion round its axis.
So long as no sound is heard the style remains at rest, and merely removes
-288]
Konigs Manometric Flames.
241
the lampblack along a line which is a helix on the cylinder, but which becomes
straight when the paper is unwrapped. But when a sound is heard, the
membrane and the style vibrate in unison, and the line traced out is no
longer straight, but undulates ; each undulation corresponding to a double
vibration of the style. Consequently the figures thus obtained faithfully
denote the number, amplitude, and isochronism of the vibrations.
Fig. 248 shows the trace produced -when a simple note is -sung, and
strengthened by means of its upper octave. The latter note is represented
by the curve of lesser amplitude. Fig. 249 represents the sound produced
jointly by two pipes whose notes differ by an octave. Fig. 250 in its lower
line represents the rolling sound of the letter R when pronounced with a
ring ; and fig. 251 on its lower line represents the sound produced by a tin
plate when struck with the finger.
The upper lines of figs. 250 and 251 are the same, and represent the
perfectly isochronous vibrations of a tuning-fork placed near the ellipsoid.
These lines were traced by a fine point on one branch of the fork, which was
thus found to make exactly 500 vibrations per second. In consequence,
each undulation of the upper line corresponds to the -~~ part of a second ;
and thus these lines become very exact means of measuring short intervals
of time. For example, in fig. 250, each of the separate shocks producing
the rolling sound of the letter R corresponds to about 18 double vibra-
Fig. 252.
tions of the tuning-fork, and consequently lasts about or about ^ f a
second.
288. Xonig's manometric flames. Konig's method consists in trans-
mitting the motion of the sonorous waves which constitute a sound to
M
242 Acoustics. [288-
gas flames, which, by their pulsations, indicate the nature of the sounds.
For this purpose a metal capsule, represented in section at A, fig. 252, is
divided into two compartments by a thin membrane of caoutchouc ; on the
right of the figure is a gas jet, and below it a tube conveying coal gas ; on
Fig 253.
Fig 254.
the left is a tubulure, to which may be attached a caoutchouc tube. The
other end of this may be placed at the node of an organ-pipe (274) or it
terminates in a mouthpiece, in front of which a given note may be sung ;
this is the arrangement represented in fig. 252.
Fig. 255.
Fig. 256.
When the sound waves enter the capsule by the mouthpiece and the
tube, the membrane yielding to the condensation and rarefaction of the
waves, the coal gas in the compartment on the right is alternately contracted
-289] Determination of the^ Intensity of Sounds. 243
and expanded, and hence are produced alternations in the length of the
flame, which are, however, scarcely perceptible when the flame is observed
directly. But to render them distinct they are received on a mirror with
four faces, M, which may be turned by two cog-wheels and a handle. As
long as the flame burns steadily there appears in the mirror, when turned, a
continuous band of light. But if the capsule is connected with a sounding
tube yielding the fundamental note, the image of the flame takes the form
Fig 257
Fig. 258
represented in fig. 253, and that of the figure 254 if the sound yields the
octave. If the two sounds reach the capsule simultaneously the flame has
the appearance of fig. 255 ; in that case, however, the tube leading to the
capsule must be connected by a T-pipe with two sounding tubes, one giving
the fundamental note, and the other the octave. If one gives the funda-
mental note and the other the third, the flame has the appearance of
figure 256.
If the vowel E be sung in front of the mouth-piece first upon c, and
then upon c', the turning mirror gives the flames represented in figs. 257
and 258.
289. Determination of the intensity of sounds. Meyer has devised
a plan by which the intensities of two sounds of the same pitch may be
directly compared. The two sounds are separated from each other by a
medium impervious to sound, and in front of each of them is a resonance
globe '255) accurately tuned to the sound. Each of these resonance globes
is attached by means of caoutchouc tubes of equal length to the two ends of
a U tube, in the middle of the bend of which is a third tube provided with ,1
manometric capsule.
If the resonance globes are each at the same distance from the sounding
bodies, and if the note of only one 01 them is produced, the flame vibrates.
If both sounds are produced, and they are of the same intensity, and in the
same phase, they interfere completely in the tube, so that the flame of the
M 2
244 Acoustics. [289-
manometric capsule is quite stationary, and appears in the turning mirror as
a straight luminous band.
If, however, the sounds are not of the same intensity the interference
will be incomplete, and the luminous band will be jagged at the edge. The
distance of one of the sounds from the resonance globes is altered until the
flame is stationary. The intensities of the two sounds are thus directly as
the squares of their distances from the resonators.
290. Acoustic attraction and repulsion. It was observed by Guyot,
and afterwards independently by Guthrie and by Schellbach, that a sound-
ing body, one in a state of vibration therefore, exercises an action on a
body in its neighbourhood which is sometimes one of attraction and some-
times of repulsion. The vibrations of an elastic medium attract bodies
which are specifically heavier than itself, and repel those which are specific-
ally lighter. Thus a balloon of goldbeater's skin filled with carbonic acid,
is attracted towards the opening of a resonance box on which is a vibrating
tuning-fork ; while a similar balloon filled with hydrogen and tied down by
a thread is repelled. This result always follows, even when the hydrogen
balloon is made heavier than air by loading it with wax.
A light piece of cardboard suspended and held near a tuning-fork moves
towards it when the fork is made to vibrate. If the tuning-fork is suspended
and is then made to vibrate, it moves towards the card if the latter is fixed.
Two suspended tuning-forks in a state of vibration move towards each other.
The flame of a candle placed near the end of a sounding tuning-fork was
repelled if held near it ; if held underneath it was flattened out to a disc.
A gas flame near the end of the tuning-fork was divided into two arms.
Guthrie finds that when one prong of a tuning-fork is enclosed in a tube
provided with a capillary tube dipping into a liquid and is set in vibration
by bowing the free prong, the air around the enclosed prong is expanded,
and he thence concludes that the approach, above described, of a suspended
body to the sounding-fork, is due to the diminution of the pressure of the
air between the fork and the body below that on the other side of the
body.
Light resonators of glass or metal are repelled when brought near the
sounding-box of a tuning-fork, vibrating in unison with the resonators.
When a small mill with four arms, each provided with a small resonator, is
placed near the open end of the sounding-box, the repulsion is so strong as
to produce a uniform rotation.
These phenomena do not seem to be due to the aspirating action of cur-
rents of air, nor are they caused by any heating effect ; and it must be con-
fessed that the phenomena require further elucidation ; they are of special
interest as furnishing a possible clue to the solution of the problem of attrac-
tion in general.
291. Edison's phonograph. Edison has devised an apparatus for re-
producing sound, which is equally remarkable for the simplicity of its con-
struction, and for the striking character of the results which it produces.
Fig. 259 represents a mouthpiece E, which is closed by a thin elastic
metal disc. By means of a spring a small steel point, rounded at the end, is
fixed, at the back of the disc ; this point gently presses against the surface
of tinfoil, to which it transfers the vibrations of the disc by the intervention
-291]
Edison's Phonograph.
24$
of small pieces of india-rubber tubing. Another small piece of tubing helps
to deaden the vibrations of the spring itself. This arrangement is repre-
sented on a larger scale in fig. 260.
Fig. 260.
Fig- 259-
The tinfoil is placed on the circumference of a long cylinder C, on the
surface of which is a very accurately constructed spiral groove, the threads
being about ~ of an inch apart. The cylinder works
on a screw AA', the thread of which is the same as that
on the cylinder ; it is turned by a handle M, the motion
being regulated by a large fly-wheel. There is also
an arrangement \^vm by which the position of the
mouthpiece, and its pressure against the tinfoil, may be
adjusted.
When the disc is made to vibrate, by speaking or
singing into the mouthpiece, while, at the same time, the
cylinder is turned with a uniform motion, a series of dots
or indentations are produced upon the tinfoil, which,
being a non-elastic substance, retains them.
If now the part which the mouthpiece plays be reversed, the indented
tinfoil can be used to reproduce the sound. This is best effected by having
a special mouthpiece of larger size, with a diaphragm of similar construction.
This is so adjusted that the point is made to work along the indentations in
the groove, this sets the diaphragm in vibrations, and these being communi-
cated to the air by the mouthpiece reproduce the sound. For loudness, a
thin elastic membrane is best, while for distinctness, a stouter rigid plate is
preferable.
In this way sound has been reproduced so as to be audible to a large
audience ; the articulation is distinct though feeble ; it reproduces the
quality of the person's voice who speaks into it, but with a nasal intonation.
Speech may thus be treasured up on a sheet of tinfoil and kept for an indefi-
nite period ; the sound may be reproduced more than once by means of its
tinfoil register, but after the second reproduction the strength is greatly
diminished.
If the velocity of rotation is greater than before, the pitch of the speech
is altered ; and if it is not uniform, then, in the case of a song, the reproduc-
tion is incorrect. In order to produce a uniform velocity, clockwork may be
used.
There is great difference in the distinctness with which the various con-
sonants and vowels are reproduced ; the s, for instance, is very difficult
246 Acoustics. [291-
If the phonograph be rotated in the reverse direction, the individual letters
retain their character, but the words as well as the letters are reproduced in
the reverse order.
If the instrument be reset to the starting-point of the phonographic
record of a song, and be again sung into, it will reproduce both series of
sounds, as if two persons were singing at the same time ; and by repeating
the same process, a third or fourth part may be added, or one or more in-
strumental parts.
The impressions on the tinfoil appear at first sight as a series of successive
points or dots, but when examined under a microscope they are seen to have
a distinct form of their own. When a cast is taken by means of fusible
metal, and a longitudinal section made, the outline closely resembles the
jagged edge of a Konig's flame. According to Edison's statement, as
many as 40,000 words can be registered on a space not exceeding 10 square
inches.
The phonograph has been used by Jenkins and King for the analysis of
vocal sounds, for which purpose it is better suited than Konig's flames.
-292] Heat. 247
BOOK VI.
ON HEAT.
CHAPTER I.
PRELIMINARY IDEAS. THERMOMETERS.
292. Heat. Hypothesis as to its nature. In ordinary language the
term heat is used not only to express a particular sensation, but also to de-
scribe that particular state or condition of matter which produces this sensa-
tion. Besides producing this sensation, heat acts variously upon bodies ; it
melts ice, boils water, makes metals red-hot, produces electrical currents,
decomposes compound bodies, and so forth.
Two theories as to the cause of heat have been propounded ; these are
the theory of emission and the theory of undulation.
On the first theory, heat is caused by a subtle imponderable fluid, which
surrounds the molecules of bodies, and which can pass from one body to
another. These heat atmospheres, which thus surrcund the molecules, exert
a repelling influence on each other, in consequence of which heat acts in
opposition to the force of cohesion. The entrance of this substance into our
bodies produces the sensation of warmth, its egress the sensation of cold.
On the second hypothesis the heat of a body is caused by an extremely
rapid oscillating or vibratory motion of its molecules ; and the hottest bodies
are those in which the vibrations have the greatest velocity and the greatest
amplitude. At any given time the whole of the molecules of a body possess
a sum of vis viva which is the heat they contain. To increase their tempera-
.ture is to increase their vis viva ; to lower their temperature is to decrease
their vis viva. Hence, on this view, heat is not a substance but a condition
of matter, and a condition which can be transferred from one body to another.
When a heated body is placed in contact with a cooler one the former cedes
more molecular motion than it receives ; but the loss of the former is the
equivalent of the gain of the latter.
It is also assumed that there is an imponderable elastic ether, which per-
vades all matter and infinite space. A hot body sets this in rapid vibration,
and the vibrations of this ether being communicated to material objects set
them in more rapid vibration ; that is, increase their temperature. Here we
have an analogy with sound ; a sounding body is in a state of vibration, and
its vibrations are transmitted by atmospheric air to the auditory apparatus
in which is produced the sensation of sound.
248 On Heat. [292-
This hypothesis as to the nature of heat is now admitted by the most
distinguished physicists. It affords a better explanation of all the phenomena
of heat than any other theory, and it reveals an intimate connection between
heat and light. It will be subsequently seen that by the friction of bodies
against each other an 'indefinite quantity of heat is produced. Experiment
has shown that there is an exact equivalence between the motion thus de-
stroyed and the heat produced. These and many other facts are utterly in-
explicable on the assumption that heat is a substance, and not a form of motion.
In what follows, however, the phenomena of heat will be considered, as
far as possible, independently of either hypothesis ; but we shall subsequently
return to the reasons for the adoption of the latter hypothesis.
Assuming that the heat of bodies is due to the motion of their particles,
we may admit the following explanation as to the nature of this motion in
the various forms of matter :
In solids the molecules have a kind of vibratory motion about certain
fixed positions. This motion is probably very complex ; the constituents of
the molecule may oscillate about each other, besides the oscillation of the
molecule as a whole ; and this latter again may be a to-and-fro motion, or it
may be a rotatory motion about the centre.
In the liquid state the molecules have no fixed positions. They can
rotate about their centres of gravity, and the centre of gravity itself may
move. But the repellent action of the motion, compared with the mutual
attraction of the molecules, is not sufficient to separate the molecules from
each other. A molecule no longer adheres to particular adjacent ones ; but
it does not spontaneously leave them except to come into the same relation
to fresh ones as to its previous adjacent ones. Thus in a liquid there is a
vibratory, rotatory, and progressive motion.
In the gaseous state the molecules are entirely without the sphere of their
mutual attraction. They fly forward in straight lines according to the ordi-
nary laws of motion, until they impinge against other molecules, or against
a fixed envelope which they cannot penetrate, and then return in an opposite
direction, with, in the main, their original velocity. If the molecules were in
space where no external force could act upon them, they would fly apart,
and disappear in infinity. But if contained in any vessel, the molecules
continually impinge in all directions against the sides, and thus arises the
pressure which a gas exerts on its vessel.
The perfection of the gaseous state implies that the space actually
occupied by the molecules of the gas be infinitely small compared with the
entire volume of the gas ; that the time occupied by the impact of a mole-
cule either against another molecule, or against the sides of the vessel, be
infinitely small in comparison with the interval between any two impacts ;
and that the influence of molecular attraction be infinitely small. When
these conditions are not fulfilled the gas partakes more or less of the nature
of a liquid, and exhibits certain deviations from Boyle's law. This is the
case with all gases ; to a very slight extent with the less easily condensable
gases, but to a far greater extent with vapours and the more condensable
gases, especially near their points of liquefaction.
293. Dynamical theory of gases. We have seen, that in the gaseous
condition, the particles are assumed to fly about in right lines in all possible
-294] Molecular Velocity. 249
directions. A rough illustration of this condition of matter is afforded by
imagining the case of a number of bees enclosed in a box.
Let us suppose a cubical vessel to be filled with air under standard con-
ditions of temperature and pressure. Let the length of the sides be a. We
will for the present suppose that each particle moves freely in the space
without striking against another particle. All possible motions may be con-
ceived to be resolved into motions in three directions which are parallel to
the faces of the cube. Conceive any single particle, of mass m ; it will strike
against one face with such a velocity as not only to annul its own motion,
but to cause it to rebound in the opposite direction with the same velocity ;
hence the measure of the momentum with which it strikes against the side
will be imn. Now by their rapid succession and their uniform distribu-
tion the total action of these separate impacts is to produce a pressure
against the sides of the vessel which is the elastic force of the gas ; and to
measure the pressure on the side, we must multiply the momentum of each
individual impact by the total number of such impacts.
Since the length of the side is #, if there are n molecules in the unit of
space, there will be net" in the volume of the cube, of which will be
moving in a direction parallel to each one of the sides. To get the number of
impacts on one face, we must remember that they succeed each other, after the
interval of time required for a particle to fly to the opposite side and back again.
Hence, u being the velocity, the number of impacts which each particle makes
in the unit of time, a second, will be , and the number of all such which
20.
strike against one side will be ^na~
Now, since each one exerts a pressure represented by 2mu, we shall have
for the total pressure^ on the surface a 2
and therefore the pressure on the unit of surface will be
p = \nmiP.
Now, if N is the number of molecules in the volume z/, N = nv, and
therefore
p = $i mu 1 * ; that is, pv = \Xmir.
But, for any given mass of gas, N, m, and u are constant quantities, and the
product pv must therefore also be constant ; this, however, is Boyle's law (174).
294. Molecular velocity. In the formula p = \nmu*, nm represents the
mass in the unit of volume which we may designate as the density p of the
gas, referred to that of water ; as the pressure p is also capable of direct
measurement, we can calculate the third magnitude u in absolute measure.
The pressure p on a gas is equal to the action of gravity on a column of
mercury of given height h ; so that if d is the density of mercury = I3'596,
and g the acceleration of gravity, p = gh and
M3
250 On Heat. [294-
Now, if o- be the specific gravity of the gas as compared with air, which is
lighter than water, p x 773*3 = o-, or p = - ,
u i = 3* 13-596 x 076x9-81 15x773-3
cr
'which gives u = L.; that is, that for atmospheric air the mean velocity of the
-v/o-
particles is 485 metres in a second. For other gases we have, expressed in
the same units,
0=461
N - 49 2
In a gas the velocities of the particles are unequal ; for, even supposing that
they were all originally the same, it is not difficult to see that they would
soon alter. For imagine a particle to be moving parallel to one side, and to
be struck centrically by another moving at right angles to the direction of
its motion, the particle struck would proceed on its new path with increased
velocity, while the striking particle would rebound in a different direction
with a smaller velocity.
Notwithstanding the accidental character of the velocity of any individual
particle in such a mass of gas as we have been considering, there will, at any
one given time, be a certain average distribution of velocities. Now, from
considerations based on the theory of probabilities, it follows that some
velocities will be more probable than others that there will, indeed, be one
velocity which is more probable than any other. This is called the most
probable velocity. The mean velocity of the particle, as found above, is
not this, nor is it the same as the arithmetical mean of all the velocities ; it
may be defined to be that velocity which, if all the molecules possessed it,
the mean energy of the molecular impacts against the side would be the
same as that which actually exists. This mean velocity is about ~ greater
than the arithmetical mean velocity, and is i| that of the most probable
single velocity.
295. General effects of beat. The general effects of heat upon bodies
may be classed under three heads. One portion is expended in raising the
temperature of the body ; that is, in increasing the vis viva of its molecules.
In the second place, the molecules of bodies have a certain attraction for
each other, to which is due their relative position ; hence a second por-
tion of heat is consumed in augmenting the amplitude of the oscillations,
by which an increase of volume is produced, or in completely altering the
relative positions of the molecules, by which a change of state is effected.
These two effects are classed as internal work. Thirdly, since bodies are
surrounded by atmospheric air which exerts a certain pressure on their sur-
face, this has to be overcome or lifted through a certain distance. The heat
or work required for this is called the external work.
If Q units of heat are imparted to a body, and if A be the quantity of
heat which is equivalent to the unit of work; then if W is the amount of
heat which serves to increase the temperature, I that required to alter the
-29 6] Expansion.
position of the molecules, and if L be the equivalent of the external work,
then
296. Expansion. All bodies expand by the action of heat. As a general
rule, gases are the most expansible, then liquids, and lastly solids.
In solids which have definite figures, we can either consider the expan-
sion in one dimension, or the linear expansion ; in two dimensions, the
superficial expansion ; or in three dimensions, the cubical expansion or the
expansion of volume, although one of these never takes place without the
other. As liquids and gases have no definite figures, the expansions of
volume have in them alone to be considered.
To show the linear expansion of solids, the apparatus represented in fig.
261 may be used. A metal rod, A, is fixed at one end by a screw B, while
Fig. 261.
the other end presses against the short arm of an index, K, which moves on
a scale. Below the rod there is a sort of cylindrical lamp in which alcohol
is burned. The needle K is at first at the zero point, but as the rod becomes
heated, it expands, and moves the needle along the scale.
The cubical expansion of solids is shown by a Gravesande 1 s ring. It con-
sists of a brass ball a (fig. 262), which at the ordinary temperature passes
freely through a ring, m, almost of the same diameter. But when the ball
has been heated, it expands and no longer passes through the ring.
In order to show the expansion of liquids, a large glass bulb provided
with a capillary stem is used (fig. 263). If the bulb and a part of the stem
contain some coloured liquid, the liquid rapidly rises in the stem when heat
is applied, and the expansion thus observed is far greater than in the case
of solids.
The same apparatus may be used for showing the expansion of gases.
Being filled with air, a small thread of mercury is introduced into the capillary
tube to serve as index (fig. 264). When the globe is heated in the slightest
degree, even by approaching the hand, the expansion is so great that the
index is driven to the end of the tube, and is finally expelled. Hence, even
for a very small degree of heat, gases are highly expansible.
In these different experiments the bodies contract on cooling, and when
they have attained their former temperature they resume their original
volume. Certain metals, however, especially zinc, form an exception to this
rule, and it appears to be also the case with some kinds of glass.
252
On Heat.
[297-
MEASUREMENT OF TEMPERATURE. THERMOMETRY.
297. Temperattire. The temperature or hotness of a body, indepen-
dently of any hypothesis as to the nature of heat, may be defined as being
Fig. 262.
Fig. 263. Fig. 264.
the greater or less extent to which it tends to impart sensible heat to other
bodies. The temperature of a body must not be confounded with the quan-
tity of heat it possesses : a body may have a high temperature and yet have
a very small quantity of heat, and conversely a low temperature and yet
possess a large amount of heat. If a cup of water be taken from a bucketful,
both will indicate the same temperature, yet the quantities they possess will
be different. This subject of the quantity of heat will be afterwards more
fully explained in the chapter on Specific Heat.
298. Thermometers. Thermometers are instruments for measuring
temperatures. Owing to the imperfections of our senses we are unable to
measure temperatures by the sensation of heat or cold which they produce
in us, and for this purpose recourse must be had to the physical actions of
heat on bodies. These actions are of various kinds, but the expansion of
bodies has been selected as the easiest to observe. But heat also produces
electrical phenomena in bodies ; and on these the most delicate methods
of observing temperatures have been based, as we shall see in a subsequent
chapter.
Liquids are best suited for the construction of thermometers the ex-
pansion of solids being too small, and that of gases too great. Mercury and
alcohol are the only liquids used the former because it only boils at a very
high temperature, and the latter because it does not solidify at the greatest
known cold.
The mercurial thermometer is the most extensively used. It consists of a
-301]
Graduation of tke TJiermometer.
253
capillary glass tube, at the end of which is blown the bulb, a cylindrical or
spherical reservoir. Both the bulb and a part of the stem are filled with
mercury, and the expansion is measured by a scale graduated either on the
stem itself, or on a frame to which it is attached.
Besides the manufacture of the bulb, the construction of the thermometer
comprises three operations : the calibration of the tube, or its division into
pans of equal capacity, the introduction of the mercury into the reservoir,
and the graduation,
299. Division of the tube into parts of equal capacity. As the in-
dications of the thermometer are only correct when the divisions of the scale
correspond to equal expansions of the mercury in the reservoir, the scale
must be graduated, so as to indicate parts of equal capacity in the tube. If
the tube were quite cylindrical, and of the same diameter throughout, it
would only be necessary to divide it into equal lengths. But as the diameter
of glass tubes is usually greater at one end than another, parts of equal
capacity in the tube are represented by unequal lengths of the scale.
In order, therefore, to select a tube of uniform calibre, a thread of mercury
about an inch long is introduced into the capillary tube, and moved in
different positions in the tube, care being taken to keep it at the same tem-
perature. If the thread is of the same length in every part of the tube, it
shows that the capacity is everywhere the same ;
but if the thread occupies different lengths the
tube is rejected, and another one sought
300. rilling the thermometer. In order to
fill the thermometer with mercury, a small funnel,
C fig. 265), is blown on at the top, and is filled
with mercury ; the tube is then slightly inclined,
and the air in the bulb expanded by heating it
with a spirit lamp. The expanded air partially
escapes by the funnel, and on cooling, the air which
remains contracts, and a portion of the mercury
passes into the bulb D. The bulb is then again
warmed, and allowed to cool, a fresh quantity of
mercury enters, and so on, until the bulb and part
of the tube are full of mercury. The mercury is
then heated to boiling ; the mercurial vapours in
escaping carry with them the air and moisture
which remain in the tube. The tube, being full of
the expanded mercury and of mercurial vapour, is
hermetically sealed at one end. When the ther-
mometer is cold, the mercury ought to fill the bulb
and a portion of the stem.
301. Graduation of the thermometer. The
thermometer being filled, it requires to be gradu-
ated ; that is, to be provided with a scale to which
variations of temperature can be referred. And,
first of all, two points must be fixed which represent identical temperatures
and which can always be easily reproduced.
Experiment has shown that ice always melts at the same temperature
Fig. 265.
254 On Heat. [301-
whatever be the degree of heat, and that distilled water under the same
pressure, and in a vessel of the same kind, always boils at the same tem-
perature. Consequently, for the first fixed point, or zero, the temperature of
melting ice has been taken : and for a second fixed point, the temperature
of boiling water in a metal vessel under the normal atmospheric pressure
of 760 millimetres.
This interval of temperature that is, the range from zero to the boiling
point is taken as the unit for comparing temperatures ; just as a certain
length, a foot or a metre for instance, is used as a basis for comparing
lengths.
302. Determination of the fixed points. To obtain zero, snow or
pounded ice is placed in a vessel in the bottom of which is an aperture by
which water escapes (fig. 266). The bulb and a
part of the stem of the thermometer are immersed
in this for about a quarter of an hour, and a mark
made at the level of the mercury which represents
zero.
The second fixed point is determined by means
of the apparatus represented in the figures 267 and
268, of which 268 represents a vertical section. In
both, the same letters designate the same parts.
The whole of the apparatus is of metal. A central
tube, A, open at both ends, is fixed on a cylindrical
vessel containing water ; a second tube, B, con-
centric with the first, and surrounding it, is fixed
on the same vessel, M. In this second cylinder,
which is closed at both ends, there are three
tubulures, #, E, D. A cork, in which is the ther-
mometer /, fits in a. To E, a glass tube, containing
mercury, is attached, which serves as a manometer
for measuring the pressure of the vapour in the
apparatus. D is an escape tube for the vapour and condensed water.
The apparatus is placed on a furnace and heated till the water boils ;
the vapour produced in M rises in the tube A, and, passing through the two
tubes in the direction of the arrows, escapes by the tubulure D. The
thermometer / being thus surrounded with vapour, the mercury expands, and
when it has become stationary, the point at which it stops is marked. This
is the point sought for. The object, of the second case B, is to avoid the
cooling of the central tubulure by its contact with the air.
The determination of the point 100 (see next article) would seem to
require that the height of the barometer during the experiment should be
760 millimetres, for when the barometric height is greater or less than this
quantity, water boils either above or below 100 degrees. But the point 100
may always be exactly obtained, by making a suitable correction. For
every 27 millimetres difference in height of the barometer there is a differ-
ence in the boiling point of I degree. If, for example, the height of the
barometer is 778 that is, 18 millimetres, or two-thirds of 27, above 760
water would boil at 100 degrees and two-thirds. Consequently ioo| would
have to be marked at the point at which the mercury stops.
Fig. 266.
-303]
Construction ef tJie Scale.
255
Gay-Lussac observed that water boils at a somewhat higher temperature
in a glass than in a metal vessel : and as the boiling point is raised by any
isalts which are dissolved, it has been assumed that it was necessary to use
,a metal vessel and distilled water in fixing the boiling point. Rudberg
showed, however, that these latter precautions are superfluous. The
nature of the vessel and salts dissolved in ordinary water influence the tem-
perature of boiling water, but not that of the vapour which is formed. That
.is to say, that it the temperature of boiling water from any of the above
causes is higher than 100 degrees, the temperature of the vapour does not
exceed 100, provided the pressure is not more than 760 millimetres. Con-
sequently, the higher point may be determined in a vessel of any material
Fig. 268.
/provided the thermometer is quite surrounded by vapour, and does not dip
.in the water.
Even with distilled water, the bulb of the thermometer must not dip in
I the liquid ; for it is only the upper layer that really has the temperature of
.100 degrees, since the temperature increases from layer to layer towards the
i bottom in consequence of the increased pressure.
303. Construction of the scale. Just as the foot-rule which is adopted
as the unit of comparison for length is divided into a number of equal
i divisions called inches for the purpose of having a smaller unit of comparison,
j so likewise the unit of comparison of temperatures, the range from zero to
i the boiling point, must be divided into a number of parts of equal capacity
-called degrees. On the Continent, and more especially in France, this space
I js divided into 100 parts, and this division is called the Centigrade or Celsius
\ scale ; the latter being the name of the inventor. The Centigrade thermo-
meter is almost exclusively adopted in foreign scientific works, and as its use
256 On Heat. [30.3-
is gradually extending in this country, it has been and will be adopte
this book.
The degrees are designated by a small cipher placed a little
above on the right of the number which marks the temperature, and
to indicate temperatures below zero the minus sign is placed before
them. Thus, 15 signifies 15 degrees below zero.
In accurate thermometers the scale is marked on the stem itself
(fig. 269). It cannot be displaced, and its length remains fixed,
as glass has very little expansibility. The graduation is effected
by covering the stem with a thin layer of wax, and then marking
the divisions of the scale, as well . as the corresponding numbers,
with a steel point. The thermometer is then exposed for about ten
minutes to the vapours of hydrofluoric acid, which attacks the glass
where the wax has been removed. The rest of the wax is then re-
moved, and the stem is found to be permanently etched.
Besides the Centigrade scale two others are frequently used
Fahrenheit's scale and Reaumur's scale.
In Reaumur's scale the fixed points are the same as on the
Centigrade scale, but the distance between them is divided into
80 degrees, instead of into 100. That is to say, 80 degrees Reaumur
are equal to 100 degrees Centigrade ; one degree Reaumur is equal
to "0 or | of a degree Centigrade, and one degree Centigrade
equals ~ or | degrees Reaumur. Consequently to convert any
number of Reaumur's degrees into Centigrade degrees (20 for
example), it is merely necessary to multiply them by f (which gives
25). Similarly, Centigrade degrees are converted into Reaumur by
multiplying them by f.
The thermometric scale invented by Fahrenheit in 1714 is still
much used in England, and also in Holland and North America.
The higher fixed point is, like that of the other scales, the tem-
perature of boiling water ; but the null point or zero is the tem-
perature obtained by mixing equal weights of sal-ammoniac and
snow, and the interval between the two points is divided into 212
2&9 ' degrees. The zero was selected because the temperature was the
lowest then known, and was thought to represent absolute cold. When
Fahrenheit's thermometer is placed in melting ice it stands at 32 degrees,
and therefore, 100 degrees on the Centigrade scale are equal to 180 degrees
on the Fahrenheit scale, and thus i degree Centigrade is equal to of a
degree Fahrenheit, and inversely I degree Fahrenheit is equal to f of a
degree Centigrade.
If it be required to convert a certain number of Fahrenheit degrees (95,
for example) into Centigrade degrees, the number 32 must first be subtracted,
in order that the degrees may count from the same part of the scale. The re-
mainder in the example is thus 63, and as I degree Fahrenheit is equal to ' of
a degree Centigrade, 63 degrees are equal to 63 x | or 35 degrees Centigrade.
If F be the given temperature in Fahrenheit degrees and C the corre-
sponding temperature in Centigrade degrees, the former may be converted
into the latter by means of the formula
(F- 3 2)S = C,
-306] Alcohol Thermometers. 257
and conversely, Centigrade degrees may be converted into Fahrenheit by
means of the formula
|C + 3 2 = F.
These formulas are applicable to all temperatures of the two scales pro-
vided the signs are taken into account. Thus, to convert the temperature
of 5 degrees Fahrenheit into Centigrade degrees, we have
In like manner we have, for converting Reaumur into Fahrenheit degrees,
the formula
!R + 3 2 = F>
and conversely, for changing Fahrenheit into Reaumur degrees, the formula
(F- 3 2)J = R.
304. Displacement of zero. Thermometers, even when constructed
with the greatest care, are subject to a source of error which must be taken
into account ; that is, that in course of time the zero tends to rise, the dis-
placement sometimes extending to as much as two degrees ; so that when
the thermometer is immersed in melting ice it no longer sinks to zero.
This is generally attributed to a diminution of the volume of the bulb and
also of the stem, occasioned by the pressure of the atmosphere. It is usual
with very accurate thermometers to fill them two or three years before they
are graduated.
Besides this slow displacement, there are often variations in the position
of the zero, when the thermometer has been exposed to high temperatures,
caused by the fact that the bulb and stem do not contract on cooling to their
original volume (294), and hence it is necessary to verify the position of zero
when a thermometer is used for delicate determinations.
Regnault noticed that some mercurial thermometers, which agree at
o and at 100, differ between these points, and that these differences fre-
quently amount to several degrees. Regnault ascribed this to the unequal
expansion of different kinds of glass.
305. Limits to the employment of mercurial thermometers. Of all
thermometers in which liquids are used, the one with mercury is the most
useful, because this liquid expands most regularly, and is easily obtained
pure, and because its expansion between 36 and 100 is regular', that is,
proportional to the degree of heat. It also has the advantage of having a
very low specific heat. But for temperatures below 36 C. the alcohol
thermometer must be used, since mercury solidifies at -40 C. Above 100
degrees the coefficient of expansion increases and the indications of the
mercurial thermometers are only approximate, the error rising sometimes
to several degrees. Mercury thermometers also cannot be used for tem-
peratures above 350, for this is the boiling point of mercury.
306. Alcohol thermometer. The alcohol thermometer differs from the
mercury thermometer in being filled with coloured alcohol. But as the
expansion of liquids is less regular 1 in proportion as they are near the boiling
point, alcohol, which boils at 78 C., expands very irregularly. Hence,
alcohol thermometers are usually graduated by placing them in baths at
258 On Heat. [306-
different temperatures together with a standard mercurial thermometer, and
marking on the alcohol thermometer the temperature indicated by the
mercury thermometer. In this, manner the alcohol thermometer is com-
parable with the mercury one ; that is to say, it indicates the same tem-
peratures under the same conditions. The alcohol thermometer is especially
used for low temperatures, for it does not solidify at the greatest known cold.
307. Conditions of the delicacy of a thermometer. A thermometer
may be delicate in two ways : I. When it indicates very small changes of
temperature. 2. When it quickly assumes the temperature of the surround-
ing medium.
The first object is attained by having a very narrow capillary tube and
a very large bulb ; the expansion of the mercury on the stem is then limited
to a small number of degrees, from 10 to 20 or 20 to 30 for instance, so that
each degree occupies a great length on the stem, and can be subdivided into
very small fractions. The second kind of delicacy is obtained by making
the bulb very small, for then it rapidly assumes the temperature of the liquid
in which it is placed.
A good mercury thermometer should answer to the following tests :
When its bulb and stem, to the top of the column of mercury, are immersed
in melting ice, the top of the mercury should exactly indicate o C. ; and
when suspended with its bulb and scale immersed in the steam of water
boiling in a metal vessel (as in fig. 267), the barometer standing at 760 mm.,
the mercury should be stationary at 100 C. When the instrument is in-
verted, the mercury should fill the tube, and fall with a metallic click, thus
showing the complete exclusion of air. The value of the degrees should be
uniform : to ascertain this, a little cylinder of mercury may be detached from
the column by a slight jerk, and on inclining the tube it may be made to pass
from one portion of the bore to another. If the scale be properly graduated,
the column will occupy an equal number of degrees in all parts of the tube.
308. Differential thermometer. Sir John Leslie constructed a ther-
mometer for showing the difference of temperature of two neighbouring
places, from which it has received the name differential thermometer.
A modified form of it is that devised by Matthiessen (fig. 270), which has
the advantage of being available for indicating the temperature of liquids.
It consists of a bent glass tube, each end of which is bent twice, and ter-
minates in a bulb ; the bulbs being pendent can be readily immersed in a
liquid. The bend contains some coloured liquid, and in a tube which con-
nects the two limbs is a stopcock, by which the liquid in each limb is easily
brought to the same level. The whole is supported by a frame.
When one of the bulbs is at a higher temperature than the other, the
liquid in the stem is depressed, and rises in the other stem.
The instrument is now only used as a thermoscope ; that is, to indicate a
difference of temperature between the two bulbs, and not to measure its
amount.
309. Breguet's metallic thermometer. Breguet invented a ther-
mometer of considerable delicacy, which depends on the unequal expansion
of metals. It consists of three strips of platinum, gold, and silver, which are
passed through a rolling mill so as to form a very thin metallic ribbon. This
is then coiled in a spiral form, as seen in fig. 271, and one end being fixed to
-310]
Rutherford 's Thermometers.
259
-a support, a light needle is fixed to the other, which is free to move round a
.graduated scale.
Silver, which is the most expansible of the metals, forms the internal face
.of the spiral, and platinum the external. When the temperature rises, the
silver expands more than the gold or platinum, the spiral unwinds itself, and
Fig. 270.
Fig. 271.
"the needle moves from left to right of the above figure. The contrary effect
'is produced when the temperature sinks. The gold is placed between the
other two metals because its expansibility is intermediate between that of the
silver and the platinum. Were these two metals employed alone, their rapid
unequal expansion might cause a fracture. Breguet's thermometer is em-
'pirically graduated in Centigrade degrees, by comparing its indications with
those of a standard mercury thermometer.
On this principle depend several forms of pocket thermometers, and it is
also applied in some registering thermometers.
310. Rutherford's maximum and minimum thermometers. It is
necessary, in meteorological observations, to know the highest temperature
of the day and the lowest temperature of the night. Ordinary thermometers
could only give these indications by a continuous observation, which would be
impracticable. Several instruments have accordingly been invented for this
purpose, the simplest of which is Rutherford's. On a rectangular piece of
plate-glass (fig. 272) two thermometers are fixed, whose stems are bent
horizontally. The one, A, is a mercury, and the other, B, an alcohol
thermometer. In A there is a minute piece of iron wire, A, moving freely in
the tube, which serves as an index. The thermometer being placed hori-
zontally, when the temperature rises the mercury pushes the index before it.
But as soon as the mercury contracts, the index remains in that part of the
tube to which it has been moved, for there is no adhesion between the iron
and the mercury. In this way the index registers the highest temperature
26o
On Heat.
[310-
which has been attained ; in the figure this is 31. In the minimum ther-
mometer there is a small hollow glass tube which serves as index. -When it
is at the end of the column of liquid, and the temperature falls, the column
contracts, and carries the index with it, in consequence of adhesion, until it
has reached the greatest contraction. When the temperature rises the
alcohol expands, and, passing between the sides of the tube and the index,
,n.., 2 P.
Fig. 272.
does not displace B. The position of the index gives therefore the lowest
temperature which has been reached ; in the figure this is 9- degrees below zero.
311. Pyrometers. The name Pyrometers is given to instruments for
measuring temperatures so high that mercurial thermometers could not
be used. The older contrivances for this purpose Wedgwood's, Daniell's
(which in principle resembled the apparatus in fig. 261), Brongiart's, &c.
are gone entirely out of use. None of them give an exact measure of tem-
perature. The arrangements now used for the purpose are either based on
the expansion of gases and vapours, or on the electrical properties of bodies,
and will be subsequently described.
312. Different remarkable temperatures. The following table gives
some of the most remarkable points of temperature. It maybe observed that
it is easier to produce very high temperatures than very low degrees of cold.
Greatest artificial cold produced by a bath of bisulphide of
carbon and liquid nitrous acid I4OC
Greatest cold produced by ether and liquid carbonic acid 1 10
Greatest natural cold recorded in Arctic expeditions . . 587
Mercury freezes . . . . . . . . . 39^4
Mixture of snow and salt . . 20
Ice melts o
Greatest density of water . . . . . . + 4
Mean temperature of London 9-9
Blood heat . . . 36-6
Water boils 100
Mercury boils 350
Sulphur boils . 44
Red heat (just visible) (Daniell) 526
Silver melts ..... 1000
Zinc boils 1040
Cast iron melts . . ..... 153
Highest heat of wind furnace . 1800
-314]
Expansion of Solids.
261
CHAPTER II.
EXPANSION OF SOLIDS.
313. Linear expansion and cubical expansion. Coefficients of ex-
pansion. It has been already explained that in solid bodies the ex-
pansion may be according to three dimensions linear, superficial, and
cubical.
The coefficient of linear expansion is the elongation of the unit of length
of a body when its temperature rises from zero to i degree ; the coefficient of
superficial expansion is the increase of the surface in being heated from zero
to i degree, and the coefficient of cubical expansion is the increase of the unit
of volume under the same circumstances.
These coefficients vary with different bodies, but for the same body the
coefficient of cubical expansion is three times that of the linear expansion, as
is seen from the following considerations: Suppose a cube, the length of
whose side is i at zero. Let k be the elongation of this side in passing from
zero to i degree, its length at i degree will be I + k, and the volume of the
cube, which was i at zero, will be (i + >) 3 , or i +3& + 3&~ + 3 . But as the
elongation k is always a very small fraction (see table, Art. 314), its square k*,
and still more its cube #*, are so small that they may be neglected, and the
value at i degree becomes very nearly i + 3^. Consequently, the increase of
volume is 3^, or thrice the coefficient of linear expansion.
In the same manner it may be shown that the coefficient of superficial
expansion is double the coefficient of linear expansion.
314. Measurement of the coefficient of linear expansion. Lavoisier
and Laplace's method. The apparatus used by Lavoisier and Laplace for
determining the coefficients of linear expansion (fig. 273) consists of a brass
Fig. 273.
trough, placed on a furnace between four stone supports. On the two sup-
ports on the right hand there is a horizontal axis, at the end of which is a
262 On Heat. [314-
telescope ; on the middle of this axis, and at right angles to it, is fixed a
glass rod, turning with it, as does also the telescope. The other two supports
are joined by a cross piece of iron, to which another glass rod is fixed, also
at right angles. The trough, which contains oil or water, is heated by a
furnace not represented in the figure, and the bar whose expansion is to be
determined is placed in it.
Fig. 274 represents a section of the apparatus ; G is the telescope, KH
the bar, whose ends press against the two glass rods F and D. As the rod
Fig. 274.
F is fixed, the bar can only expand in the direction KH, and in order to
eliminate the effects of friction, it rests on two glass rollers. Lastly, the
telescope has a cross-wire in the eyepiece, which, when the telescope moves,
indicates the depression by the corresponding number of divisions on a
vertical scale AB\ at a distance of 220 yards.
The trough is first filled with ice, and the bar being at zero, the division
on the scale AB, corresponding to the wire of the telescope, is read off.
The ice having been removed, the trough is filled with oil or water, which is
heated to a given temperature. The bar then expands, and when its tempe-
rature has become stationary, which is determined by means of thermometers,
the division of the scale, seen through the telescope, is read off.
From these data the elongation of the bar is determined ; for since it has
become longer by a quantity, CH, and the optical axis of the telescope has
become inclined in the direction GB, the two triangles, GHC and ABG,
are similar, for they have the sides at right angles each to each, so that
T-T r* C* 1-F
.- = . In the same way, if HC' were another elongation, and AB' a
AB AG
TT/-'/ /" TT
corresponding deviation, there would still be -.-^ = -.-~ ; from which it fol-
AB AG
lows that the ratio between the elongation of the bar and the deflection of
/ TT
the telescope is constant, for it is always equal to- A ~. A preliminary
AG
TT /"
measurement had shown that this ratio was y ^. Consequently, = 7 J ,
J\LJ
AB
whence HC = - ; that is, the total elongation of the bar is obtained by
744
dividing the length on the scale traversed by the cross-wire by 744. Divid-
ing this elongation by the length of the bar, and then by the temperature of
the bath, the quotient is the dilatation for the unit of length and for a single
degree in other words, the coefficient of linear dilatation.
315. Roy and Ramsden s method. Lavoisier and Laplace's method is
founded on an artifice which is frequently adopted in physical determinations,
-315] Expansion of Solids. 263
and which consists in amplifying by a known amount dimensions which, in
themselves, are too small to be easily measured. Unfortunately this plan is
otten more fallacious than profitable, for it is first necessary to determine the
ratio of the motion measured to that on which it depends. In the present
case it is necessary to know the lengths of the arms of the lever in the
apparatus. But this preliminary operation may introduce errors of such im-
portance as partially to counterbalance the advantage of great delicacy.
The following method, which was used by General Roy in 1787, and which
was devised by Ramsden, depends on another principle. Jt measures the
elongations directly, and without amplifying them ; but it measures them by
means of a micrometer, which indicates very small displacements.
The apparatus (fig. 275) consists of three parallel metal troughs about 6
feet long. In the middle one there is a bar of the body whose expansion is
Fig. 275.
to be determined, and in the two others are cast-iron bars of exactly the
same length as this bar. Rods are fixed vertically on both ends of these
three bars. On the rods in the troughs A and B there are rings with cross-
wires like those of a telescope. On the rods in the trough C are small tele-
scopes also provided with cross-wires.
The troughs being filled with ice, and all three bars at zero, the points of
intersectipn of the wires in the disc, and of the wires in the telescope, are all
in a line at each end of the bar. The temperature in the middle trough is
then raised to 100 C. by means of spirit lamps placed beneath the trough ;
the bar expands, but as it is in contact with the end of a screw, , fixed on
the side, all the elongation takes place in the direction //;//, and, as the cross-
wire n remains in position, the cross-wire m is moved towards B by a quantity
equal to the elongation. But since the screw a is attached to the bar, by
turning it slowly from right to left, the bar is moved in the direction ?nn.
264 On Heat. [315-
and the cross-wire ;;/ regains its original position. To effect this, the screw-
has been turned by a quantity exactly equal to the elongation of the bar,
and, as this advance of the screw is readily deduced from the number of
turns of its thread (n), the total expansion of the bar is obtained, which,
divided by the temperature of the bath, and this quotient by the length of
the bar at zero, gives the coefficient of linear expansion.
316. Coefficients of linear expansion. By one or the other method
the following results have been obtained :
Coefficients of linear expansion for i between o and 100 C.
Pine 0-000003000 Gold . v . . . . 0-000014660
Graphite 0-000007860 Copper 0-000017182
Marble 0-000008490 Bronze 0-000018167
White glass .... 0*000008613 Brass 0-000018782
Platinum 0-000008842 Silver 0-000019097
Untempered steel . . 0-000010788 Tin 0-000^21730
Cast iron 0-000011250 Lead 0-000028575
Sandstone 0-000011740 Zinc 0-000029417
Wrought iron . . . 0*000012204 Sulphur 0-000064130
Tempered steel . . . 0-000012395 Paraffine 0-000278540
From what has been said about the linear expansion (311), the coefficients
of cubical expansion of solids are obtained by multiplying those of linear
expansion by three.
The coefficients of the expansion of the metals vary with their physical
condition, being different for the same metal according as it has been cast
or hammered and rolled, hardened or annealed. As a general rule, opera-
tions which increase the density increase also the rate of expansion. But
even for substances in apparently the same condition, different observers
have found very unequal amounts of expansions ; this may arise in the case
of compound substances, such as glass, brass, or steel, from a want of uniformity
in chemical composition, and in simple bodies from slight differences of
physical state.
The expansion of amorphous solids, and of those which crystallise in the
regular system, is the same for all dimensions, unless they are subject to a
strain in some particular direction. A fragment of such a substance varies
in bulk, but retains the same shape. Crystals not belonging to the regular
system exhibit, when heated, an unequal expansion in the direction of their
different axes, in consequence of which the magnitude of their angles, and
therefore their form, is altered. In the dimetric system the expansion is the
same in the direction of the two equal axes, but different in the third. In
crystals belonging to the hexagonal system the expansion is the same in the
direction of the three secondary axes, but different from that according to
the principal one. In the trimetric system it is different in all three direc-
tions.
To the general law that all bodies expand by heat there is an important
exception in the case of iodide of silver, which contracts somewhat when
heated. It has a negative coefficient of expansion, the value of which is
0-00000139 for i C.
-318] Expansion of Solids. 265
Flzeau has determined the expansion of a great number of crystallised
bodies by an optical method. He placed thin plates of the substance on a
glass plate and let yellow light pass through them. He thus obtained alter-
nately yellow and dark Newton's rings (?.-z>.). On heating, the plate of the
substance expanded, the thin layer of air became thinner, and the position of
the rings was altered. From the alteration in their position the amount of
the expansion could be deduced. Among the results he has obtained is the
curious one, that certain crystallised bodies, such as diamond, emerald, and
cupric oxide, contract on being cooled to a certain temperature, but as the
cooling is continued below this temperature they expand. They have thus
a temperature of maximum density, as is the case with water (329). In the
case of emerald and cuprous oxide this temperature is at 4-2 J , in the case
of diamond at 42-3.
317. The coefficients of expansion increase with tlie temperature.
According to Dr. Matthiessen, who determined the expansion of the metals
and alloys by weighing them in water at different temperatures, the coeffi-
cients of expansion are not quite regular between o and 100. He found
the following values for the linear expansion between o and 100 :
Zinc ..... L t = L (i +0.00002741 / + o-ooopoop235 t*)
Lead ..... L t = L (i +0-00002726 / + 0*0000000074 t)
Silver .... L t = L (i + 0-0000 1809 /-PO'OOOOOOO 135 / 2 )
Copper .... L t = L (i +0-0000 1408 / + 0-0000000264 / 2 )
Gold ..... L t = L (i + -000001358 / + 0-0000000 112 /-)
The same authority found that alloys expand very nearly according to the
following law : ' The coefficients of expansion of an alloy are equal to the
mean of the coefficients of expansion of the volumes of the metals compos-
ing it.'
318. Formulae relative to the expansion of solids. Let / be the length
of a bar at zero, /' its length at the temperature / C., and a its coefficient of
linear expansion. The tables usually give the expansion for i between o
and 100 as in Art. 316, or for 100 ; in this latter case a is obtained by
dividing the number by 100.
The relation existing between the above quantities is expressed by a few
simple formulae.
The elongation corresponding to t is / times a or at for a single unit of
length, or at I for /units. The length of the bar which is /at zero is l+atl
at /, consequently,
This formula gives the length of a body /' at /, knowing its length / at
zero, and the coefficient of expansion a ; and by simple algebraical transforma-
tions we can obtain from it formulae for the length at zero, knowing the
length /' at /, and also for finding a the coefficient of linear expansion,
knowing the lengths I' and / at f and zero respectively.
It is obvious that the formulae for cubical expansion are entirely analo-
gous to the preceding.
The following are examples of the application of these formulae :
(i.) A metal bar has a length I' at f ; what will be its length / at /?
N
266 On Heat. [318-
From the above formula we first .get the length of the given bar at zero,
//
which is -- : by means of the same formula we pass from zero to t' in
I + a/'
multiplying by I + a/, which gives for the desired length the formula
I + /'
(ii.) The density of a body being d at zero, required its density d' at /.
If i be the volume of the body at zero, and D its coefficient of cubical
expansion, the volume at / will be I + D/ ; and as the density of a body is in
inverse ratio of the volume which the body assumes in expanding, we get
the inverse proportion,
d' : d= i : i + D/
d ~ F+~D/ ' ~ T+D7
Consequently, when a body is heated from o to /, its density, and there-
fore its weight for an equal volume, is inversely as the binomial expression,
i +D/.
319. Application of the expansion of solids. In the arts we meet
with numerous examples of the influence of expansion, (i.) The bars of
furnaces must not be fitted tightly at their extremities, but must, at least, be
free at one end, otherwise in expanding they would split the masonry, (ii.)
In making railways a small space is left between the successive rails, for if
they touched, the force of expansion would cause them to curve or would
break the chairs, (iii.) Water-pipes are fitted to one another by means of
telescope joints, which allow room for expansion, (iv.) If a glass is heated
or cooled too rapidly it cracks ; this arises from the fact that glass is a bad
conductor of heat, the sides become unequally heated, and consequently un-
equally expanded, which causes a fracture.
When bodies have been heated to a high temperature, the force pro-
duced by their contraction on cooling is very considerable ; it is equal to
the force which is needed to compress or expand the material to the same
extent by mechanical means. According to Barlow, a bar of malleable iron
a square inch in section is stretched T o^oo tn f ' lts length by a weight of a
ton ; the same increase is experienced by about 9 C. A difference of 45
C. between the cold of winter and the heat of summer is not unfrequently
experienced in this country. In that range, a wrought-iron bar ten inches
long will vary in length by ^th of an inch and will exert a strain, if its ends
are securely fastened, of fifty tons. It has been calculated from Joule's data
that the force exerted by heat in expanding a pound of iron between o and
1 00, during which it increases about ^ of its bulk, is equal to 16,000
foot-pounds ; that is, it could raise a weight of 7 tons through a height of one
foot.
(i.) An application of this contractile force is seen in the mode of secur-
ing tires on wheels. The tire being made red hot, and thus considerably
expanded, is placed on the circumference of the wheel and then cooled.
The tire, when cold, embraces the wheel with such force as not only to
secure itself on the rim, but also to press home the joints of the spokes into
-320]
Compensation* Pendulum.
267
the felloes and nave, (ii.) Another interesting application was made in the
case of a gallery at the Conservatoire des Arts et Metiers in Paris, the walls
of which had begun to bulge outwards. Iron
bars were passed across the building and
screwed into plates on the outside of the walls.
Each alternate bar was then heated by means
of lamps, and when the bar had expanded it
was screwed up. The bars being then allowed
to cool contracted, and in so doing drew the
walls together. The same operation was per-
formed on the other bars.
320. Compensation pendulum. An im-
portant application of the expansion of metals
has been made in the compensation pendulum.
This is a pendulum in which the elongation,
when the temperature rises, is so compensated
that the distance between the centre of sus-
pension and the centre of oscillation (80) re-
mains constant, which, from the laws of the
pendulum (81), is necessary for isochronous
oscillations, and in order that the pendulum
may be used as a regulator of clocks.
In fig. 276, which represents the gridiron
pendulum, one of the commonest forms of
compensation pendulum, the ball, L, instead
of being supported by a single rod, is sup-
ported by a framework, consisting of alternate
rods of steel and brass. In the figure, the
shaded rods represents steel ; including a
small steel rod, b, which supports the whole of
the apparatus, there are six of them. The
rest of the rods, four in number, are of brass.
The rod /, which supports the ball, is fixed at its upper end to a horizontal
cross-piece ; at its lower end it is free, and passes through the two circular
holes in the lower horizontal cross-pieces.
Now it is easy to see from the manner in which the vertical rods are
fixed to the cross-pieces, that the elongation of the steel rods can only take
place in a downward direction, and that of the brass rods in an upward
direction. Consequently, in order that the pendulum may remain of the
same length, it is necessary that the elongation of the brass rods shall tend
to make the ball rise, by exactly the same quantity that the elongation of the
steel rod tends to lower it : a result which is attained when the sum of the
lengths of the steel rods A is to the sum of the lengths of the brass rods B in
the inverse ratio of the coefficients of expansion of steel and brass, a and b ;
that is, in the proportion A : B = b : a.
The elongation of the rod may also be compensated for by means of
compensating strips. These consist of two blades of copper and iron
soldered together and fixed to the pendulum rod, as represented in fig. 277.
The copper blade, which is more expansible, is below the iron. When the
N 2
THK
268 On Heat. [320-
temperature sinks, the pendulum rod becomes shorter, and the ball rises.
But at the same time the compensating strips become curved, as seen in
fig. 278, in con-
sequence of the
copper contract-
ing more than
the iron, and two
metallic balls at
their extremities
become lower. If
they have the
Fig. 277 . Fi g . 27 8. Fig. 279 . P r P er size in
reference to the
pendulum ball, the parts which tend to approach the centre of suspen-
sion compensate those which tend to remove from it, and the centre of
oscillation is not displaced. If the temperature rises, the pendulum ball
descends ; but at the same time the small balls ascend, as shown in fig. 279,
so that there is always compensation.
One of the most simple compensating pendulums is the mercury pen-
dulum, invented by an English watchmaker, Graham. The ball of the pen-
dulum, instead of being solid, consists of a glass cylinder, containing pure
mercury, which is placed in a sort of stirrup, supported by a steel rod.
When the temperature rises the rod and stirrup become longer, and thus
lower the centre of gravity ; but at the same time the mercury expands, and,
rising in the cylinder, produces an inverse effect, and as mercury is much
more expansible than steel, a compensation may be effected without making
the mercurial vessel of undue dimensions.
The same principle is applied in the compensating balances of chronometers
(fig. 280). The motion here is regulated by a balance or wheel, furnished with
a spiral spring not represented in the figure, and the time
of the chronometer depends on the force of the spring, the
mass of the balance, and on its circumference. Now
when the temperature rises the circumference increases,
j[ B and the chronometer goes slower ; and to prevent this,
part of the mass must be brought nearer the axis. The
circumference of the balance consists of compensating
strips BC, of which the more expansible metal is on the
outside, and towards the end of these are small masses
of metal D, which play the same part as the balls in the above case. When
the radius is expanded by heat, the small masses are brought nearer the
centre in consequence of the curvature of the strips ; and as they can be
fixed in any position, they are easily arranged so as to compensate for the
expansion of the balance.
-322]
Expansion of Liquids.
269
CHAPTER III.
EXPANSION OF LIQUIDS.
321. Apparent and real expansion. If a flask of thin glass, provided
with a narrow stem, the flask and part of the stem being filled with some
coloured liquid, be immersed in hot water
(fig. 281), the column of liquid in the stem at
first sinks from b to a, but then immediately
after rises, and continues to do so until the
liquid inside has the same temperature as the
hot water. This first sinking of the liquid is
not due to its contraction ; it arises from the
expansion of the glass, \vhich becomes heated
before the heat can reach the liquid ; but the
expansion of the liquid soon exceeds that of
the glass, and the liquid ascends.
Hence in the case of liquids we must dis-
tinguish between the apparent and the real
or absolute expansion. The apparent expan-
sion is that which is actually observed when
liquids contained in vessels are heated ; the
absolute expansion is that which \vould be
observed if the vessel did not expand ; or, as
this is never the case, it is the apparent ex-
pansion corrected for the simultaneous expansion of the containing vessel.
As has been already stated, the cubical expansion of liquids is alone
considered ; and as in the case of solids, the coefficient of expansion of a
liquid is the increase of the unit of volume for a single degree ; but a
distinction is here made between the coefficient of absolute expansion and the
coefficient of apparent expansion. Of the many methods which have been
employed for determining these two coefficients, we shall describe that of
Dulong and Petit.
322. Coefficient of tbe absolute expansion of mercury. In order to
determine the coefficient of the absolute expansion of mercury, the influence
of the envelope must be eliminated. Dulong and Petit's method depends on
the hydrostatical principle that, in two communicating vessels, the heights
of two columns of liquid in equilibrium are inversely as their densities (108),
a principle independent of the diameters of the vessels, and therefore of
their expansions.
The apparatus consists of two glass tubes, A and B (fig. 282), joined by a
capillary tube, and kept vertical on an iron support, KM, the horizontality
270 On Heat. [322-
of which is adjusted by means of two levelling screws and two spirit levels,
m and n. Each of the tubes is surrounded by a metal case, of which the
smaller, D, is filled with ice ; the other, E, containing oil, can be heated by
the furnace, which is represented in section so as to show the case. Mercury
is poured into the tubes A and B ; it remains at the same level in both, as
Fig 282.
long as they are at the same temperature, but rises in B in proportion as it
is heated, and expands.
Let h and d be the height and density of the mercury in the leg A, at the
temperature zero, and h' and d' the same quantities in the leg B. From the
hydrostatical principle previously cited we have had hd=h' d'. Now from
the problem in Art. 311, d '= , D being the coefficient of absolute
i + D/
expansion of mercury ; substituting this value of (T in the equation, we
have
h'd
, from which we get D
i + D/ ht
The coefficient of absolute expansion of mercury is obtained from this
formula, knowing the heights //' and //, and the temperature / of the bath in
which the tube B is immersed. In Dulong and Petit's experiment this
temperature was measured by a weight thermometer, P (323), the mercury of
which overflowed into the basin, C, and by means of an air thermometer, T
(331).; the heights h' and // were measured by a cathetometer, K (89).
Dulong and Petit found by this method that the coefficient of absolute
expansion of mercury between o and 100 C. is j^~. But they found that
the coefficient increased with the temperature. Between 100 and 200
it is 5/25, and between 200 and 300 it is 5^. The same observation
has been made in reference to other liquids, showing that their expansion
is not regular. It has been found that this expansion is less regular in
proportion as liquids are near a change in their state of aggregation ; that
^frBiiS^?Bii& ______
^
^\^ ~/x *=
J ^Jf^'^L .. *^ *
-325] U'cight Thermometer. 271
is, approach their freezing or boiling points. Dulong and Petit found that
the expansion of mercury between 36 and 100 is practically quite uniform.
Regnault, who has determined this important physical constant, has found
that the mean coefficient between o and 100 is 5.^, between iooand 200,
^Yi? and between 200 and 300, v^.
323. Coefficient of the apparent expansion of mercury. The co-
efficient of apparent expansion of a liquid varies with the nature of the
envelope. That of mercury in glass
was determined by means of the
qpp|ratus represented in fig. 283.
It consists of a glass cylinder to
which is joined a bent capillary
glass tube, open at the end.
The apparatus is weighed first
empty, and then when filled with Fig. 283.
mercury at zero ; the difference
gives the weight of the mercury, P. It is then raised to a known temperature,
/ ; the mercury expands, a certain quantity passes out, which is received in
the capsule and weighed. If the weight of this mercury be /, that of the
mercury remaining in the apparatus will be P p.
When the temperature is again zero, the mercury in cooling produces an
empty space in the vessel, which represents the contraction of the weight of
mercury P /, from / to zero, or, what is the same thing, the expansion
of the same weight from o to / ; that is, the weight p represents the ex-
pansion of the weight P /, for /. If this weight expands in glass by a
quantity p for /, a single unit of weight would expand * , for P and
JL2- for a smgfe degree; consequently, for D', the coefficient of ap-
parent expansion of mercury in glass, we have D' = Dulong
and Petit found the coefficient of apparent expansion of mercury in glass to
berfi*
324. Weight thermometer. The apparatus represented in fig. 283 is
called the weight thermometer, because the temperature can be deduced from
the weight of mercury which overflows.
The above experiments have placed the coefficient of apparent expansion
: we have therefore the equation , p = g^, from which we get
f _ > P ^ a formula which gives the temperature / when the weights P and
p are known.
325. Coefficient of the expansion of glass. As the absolute expansion
of a liquid is the apparent expansion, plus the expansion due to the envelope,
the coefficient of the cubical expansion of glass has been obtained by taking
the difference between the coefficient of absolute expansion of mercury in
glass and that of its apparent expansion. That is, the coefficient of cubical
expansion of glass is
sVi - eiio = IsToo = ' 2 5 8 4
272 On Heat. [325-
Regnault has found that the coefficient of expansion varies with different
kinds of glass, and further with the sha.pe of the vessel. For ordinary
chemical glass tubes, the coefficient is 0-0000254.
326. Coefficients of expansion of various liquids. The apparent ex-
pansion of liquids may be determined by means of the weight thermometer,
and the absolute expansion is obtained by adding to this coefficient the ex-
pansion of the glass.
Total apparent expansions of liquids between o and 100 C.
Mercury .... o-oi|43 Ether o>
Distilled water . . . 0-0406 Fixed oils .... 0-08
Water saturated with salt .0-05 Nitric acid . . . .OTI
Sulphuric acid . . . 0-06 Alcohol. . . , .0-116
Hydrochloric acid . . 0*06 Bisulphide of carbon . .0-128
Oil of turpentine . . 0-07 Chloroform . . . . 0-157
The coefficient of apparent expansion for i C. is obtained by dividing these
numbers by 100 ; but the number thus obtained does not represent the mean
coefficient of expansion of liquids, for the expansion of these bodies increases
gradually from zero. The expansion of mercury is practically constant
between 36 and ico C, while water contracts from zero to 4, and then
expands.
For many physical experiments a knowledge of the exact expansion of
water is of great importance. This physical constant was determined with
great care by Matthiessen, who found that between 4 and 30 it may be
expressed by the formula
V/= i 0-00000253 (/ 4) + 0-0000008389 (/ 4) 2 + o-ooqpoop7i73 (/ 4) 3 ;
and between 30 and 100 by
V/ = 0-999695 +o-ooooo54724/ 2 + 0-000^00^)1 1 26/ 3 .
Many liquids, with low boiling points, especially condensed gases, have very
high coefficients of expansion. Thilorier found that liquid carbonic acid
expands four times as much as air. Drion confirmed this observation, and
has obtained analogous results with chloride of ethyle, liquid sulphurous
acid, and liquid hyponitrous acid.
327. Correction of tne barometric height. It has been already ex-
plained under the Barometer (164), that, in order to make the indications of
this instrument comparable in different places and at different times, they
must be reduced to a uniform temperature, which is that of melting ice.
The correction is made in the following manner :
Let H be the barometric height at /, and // its height at zero, d the
density of mercury at zero, and d' its density at /. The heights H and h
are inversely as the densities dfand d' ; that is, = -. If we call i the volume
H d
of mercury at zero, its volume at t will be i + D/, D being the coefficient
of absolute expansion of mercury. But these volumes, i + D/ and i,
7/
are inversely as the densities d and d' ; that is, = . Consequently,
-330] Maximum Density of Water. 273
H = i +~D? whence ^ = 7~T)7' Replacing D by its value -^^ we have
* '
i + _L 5508 + /'
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.
328. Correction of thermometric readings. If the whole mercury of a
thermometer is noi immersed in the space whose temperature is to be deter-
mined, it is necessary to make a correction, which in the accurate deter-
mination of boiling points, for instance, is of great importance, in order to
arrive at the true temperature which the thermometer should show. That
part of the stem which projects will have a temperature which must be
estimated, and which may roughly be taken as something over that of the
surrounding air.
Supposing, for instance, the reading is 160 and that the whole of the
part over 80 is outside the vessel, while the temperature of the surrounding
air is 15. We will 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 80 x ! 35 = i -66 (taking the coefficient of apparent expansion of mer-
6480
cury) ; so that the true reading is i6r66.
329. 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 o and 10, mercury expands by 0*0015790
of its volume at o ; its compressibility is O'ooooo295 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 o to 10.
330. Maximum density of water. Water presents the remarkable
phenomenon that when its temperature sinks it contracts up to 4 ; but from
that point, although the cooling continues, it expands up to the freezing point,
so that 4 represent the point of greatest contraction of water.
Many methods have been used to determine the maximum density of
water. Hope made the following experiment : He took a deep vessel per-
forated by two lateral apertures, in which he fixed thermometers, and having
filled the vessel with water at o, he placed it in a room at a temperature 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 experi-
ments prove that water is heavier at 4 than at o, for in both cases it sinks
to the lower part of the vessel.
This last experiment may be adapted for lecture illustration by using a
N3
274 On Heat. [330-
cylinder containing water at 15 C., partially surrounded by a jacket con-
taining bruised ice (fig. 284).
Hallstrom 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"i was the temperature at which it
lost most weight, and consequently this
was the temperature of the maximum
density of water.
Uespretz 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 indi-
cated by an ordinary mercury thermo-
meter, found that the water contracted to
the greatest extent at 4, and that this is
therefore 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 radia-
tion. The colder water sinks to the bot-
tom, and a continual series of currents goes on until the whole has a
temperature of 4. The cooling on the surface still continues, but the cooled
layers being lighter remain on the surface, and ultimately freeze. The ice
formed thus protects the water below, which remains 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.
The following table of the density of water at various temperatures is
based on several sets of observations :
Density of water between o and 30.
Fig. 284.
Tempe-
ratures.
Densities.
Tempe-
ratures.
Densities.
Tempe-
ratures.
Densities.
0-99988
II
0-99965
22
0-99785
I
0-99993
12
0-99955
23
0-99762
2
0-99997
13
0-99943
24
0-99738
3
0-99999
H
0-99930
25
0-99704
4
I -00000
15
0-99915
26
0-99089
5
0-99999
16
0-99900
27
0-99662
6
0-99997
I?
0-99884
28
0-99635
7
0-99994
18
0-99800
2 9
0-99607
8
0-99988
19
0-99847
30
0-99579
9
0-99982
20
0-99807
10
0-99974
21
0-99806
-331] Expansion and Density of Gases. 275
CHAPTER IV.
EXPANSION AND DENSITY OF GASES.
331. Gay-Lussacs 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. 285.
Fig. 285.
In a rectangular metal bath, about 16 inches long, was fitted an air ther-
mometer, 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 parts. This was effected by weighing
the bulb and tube full of mercury 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, \ras
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 chloride
of calcium, 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 chloride
276 On Heat. [331-
of calcium tube. The whole of the mercury was displaced, with the ex-
ception 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
stationary. This gave the volume of air at zero ; for 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
a given temperature, and then by the number of units contained in the
volume at zero, the quotient is the coefficient of 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 expansion as air.
II. This coefficient is the same whatever be the pressure supported by the
gas.
These simple laws are not, however, rigorously exact (333) ; they only
express the expansion of gases in an approximate manner. These laws
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.
332. 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 modifications, 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 (318), the volume of
y/
the gas at zero, but still under the pressure H, will be . This pressure
i -i- at
is reduced to the pressure 760 in accordance with Boyle's law (174), by put-
ting V x 760 = V/ x H ; whence V V/t
I +at 760(1 +af)
ii. A volume of gas weighs P' at / ; what will be its weight at zero ?
-333]
Regnaulfs Method.
277
Let P' be the desired weight, a the coefficient of expansion of the gas,
P -i>
337. 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 are substituted. The gas is introduced
by a bent glass tube, the vessel being held either upright or inverted, accord-
ing 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 o C. and 760 millimetres pressure is ^
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.
-337] Density of Gases which attack Metals. 283
Density of gases at zero and at a pressure of 760 millimetres, that of air
being taken as unity.
Air i-oooo Sulphuretted hydrogen . 1-1912
Hydrogen .... 0-0693 Hydrochloric acid . . 1-2540
Ammoniacal gas . . . 0-5367 Protoxide of nitrogen . . 1-5270
Marsh gas .... 9-5590 Carbonic acid . . . i-5 2 9 r
Carbonic oxide . . . 0-9670 Cyanogen .... r86oo
Nitrogen ..... 0-9714 Sulphurous acid . . . 2-2474
Binoxide of nitrogen . . I -0360 Chlorine .... 3'44
Oxygen .... 1-1057 Hydriodic acid . . . 4'443o
Regnault has furnished 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 . . . 1-429802 Carbonic acid . 1-977414
Hydrogen . . 0089578
284 On Heat. [338-
CHAPTER V.
CHANGES OF CONDITION. VAPOURS.
338. Fusion. Iti 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 repulsive force between the
molecules is increased, and ultimately a point is reached at which the mole-
cular attraction is not sufficient to retain the body in the solid state. A new
phenomenon is then produced ; fusion 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 refractory ; that is, incapable of fusion ; but, in pro-
portion as it has been possible to produce higher temperatures, their number
has diminished. Gaudin has 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 blow-pipe, 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 is in-
variable for each substance, if the pressure be constant.
II. Whatever be the inte?isity of the source of heat, from the moment
fusion begins, the temperature of the body ceases to rise, a?id remains con-
stant until the fusioji is complete.
Fusing points of certain substances.
Mercury . . . .-38-8 Sodium 90
Oil of Turpentine . . . 27 Rose's fusible metal . . 94
Bromine . . . . 12-5 Sulphur 114
Ice o Tin 228
Butter + 33 Bismuth 264
Phosphorus . . . -44 Cadmium . . . .321
Spermaceti . . . -49 Lead 335
Potassium . . . .55 Zinc 422
Margaric acid . . -57 Antimony .... 450
Stearine . . . .60 Silver 954
White wax . . . .65 Gold 1250
Wood's fusible metal . .68 Iron 1500
Stearic acid . . . .70 Platinum . . . .1775
-339] Influence of Pressure on the Melting Point.
285
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
solid to the liquid condition. This intermediate 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 their melting points.
The determination of the melting point of a body is a matter of consider-
able importance in fixing the identity of many chemical compounds, and is
moreover a point of frequent practical application in determining the com-
mercial 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 capillary tube, the end of
which is then sealed. This tube is then placed in a bath of clear water in
which is a thermometer, 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 solidifying point
noted ; and the mean of the two is taken as the true melting point.
339. Influence of pressure on the melting point. Thomson and
Clausius have deduced from the principles of the mechanical theory of heat
that, with an increase of pressure, the melting point of a body must w '
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 vis viva of the molecules.
This increase can do more work ; the temperature effusion as well
as the heat of fusion are both increased. Bunsen examined the
influence of pressure on the melting point by means of the ap-
paratus represented in fig. 289, in which acb is a thick tube about
the thickness of a straw in the clear in the parts ca and the bent
part b. The whole tube having been filled with mercury, it was
sealed at #, and then a small quantity was driven out at b and some
of the substance introduced ; the end b was then sealed and a
opened, and the whole tube gently warmed so as to expel some
mercury, upon which a was again hermetically sealed.
When the tube was placed in a bath of warm water a little above
the melting point of the body, the mercury expanded and a pres-
sure resulted which could be accurately measured from the diminu-
tion in volume of the air in ca, which was carefully calibrated for
this purpose. By carefully raising or lowering the instrument in
the water, the pressure could be increased or diminished at will,
then remained to observe the temperature at which the substance solidi-
fied and the corresponding pressure at that moment. In this way Bunsen
found that spermaceti, which melts at 48 under a pressure of I atmosphere,
melts at 51 under a pressure of 156 atmospheres. Hopkins found that
Fig. 289.
It only
286 On Heat. [339^-
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 13 5 and 141.
But in the case of 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 raise ; on the contrary, in melting, it assimilates ex-
ternal 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 differences
of temperature must be but small, for the molecular forces in solids prepon-
derate far over the external pressure ; the internal work is far greater than
the external.
Sir W. Thomson found that pressures of 8*1 and 16*8 atmospheres
lowered the melting point of ice by 0*059 ano ^ O'I26 respectively. These
results justify the theoretical previsions of Prof. J. Thomson, according to
which an increase of pressure of n atmospheres lowers the melting point of
ice by o-oo74;z C.
340. Alloys. Fluxes. Alloys are generally more fusible than any of
the metals of which they are composed ; for instance, an alloy of five parts
of tin and one of lead fuses at 194. The alloy known as Rose's fusible
mental, which consists of 4 parts of bismuth, i part of lead, and i of tin, melts
at 94, and an alloy of i 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 metal, melts
between 66 and 71 C. 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 the chlorides of potassium and of sodium fuses at a lower tem-
perature than either of its constituents ; the same is the case with a mixture
of the carbonates of potassium and sodium, especially when they are mixed
in the proportion of their chemical equivalents.
An application of this property is met with in the case of fluxes, which
are much used in metallurgical operations. They consist of substances
which, when added to an ore, partly by their chemical action, help the reduc-
tion of the substance to the metallic state, and, partly, by presenting a
readily fusible medium, promote the formation of a regulus.
341. Latent beat. Since, during the passage of a body from the solid
to the liquid state, the temperature remains constant until the fusion is 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 latent 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 (461).
An idea of what is meant by latent heat may be obtained from the fol-
lowing 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
-345] Solidification and- Crystallisation. 287
pounded ice 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
\ve shall show how this is determined.
342. Solution. A body is said to dissolve when it becomes liquid in con-
sequence of an affinity between its molecules and those of a liquid. Gum
arabic, sugar, and most salts dissolve in water.
During solution, as well as during fusion, a certain quantity of heat always
becomes latent, and hence it is that the solution 01 a substance usually pro-
duces 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,
and 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.
343. Solidification. Solidification or congelation is the passage of a
body from the liquid to the solid state. This phenomenon is regulated by
the two following laws :
I. Every body, under the same pressure, solidifies at a fixed temperature,
which is the same as that of fusion.
II. From t/u commencement to the end of the solidification, the tempera-
ture of a liquid 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 ab-
sorbed during fusion becomes free at the moment of solidification.
Many liquids, such as alcohol, ether, and bisulphide of carbon, do not
solidify even at the lowest known temperature. Despretz, by the cold pro-
duced by a mixture of liquid protoxide of nitrogen, solid carbonic acid, and
ether, reduced alcohol to such a consistence that the vessel containing it
could be inverted without losing the liquid.
344. Crystallisation. Generally speaking, bodies which pass slowly
from the liquid to the solid state assume regular geometrical forms, such as
the cube, prisms, rhombohedra, &c. ; these are called crystals. If the crys-
tals are formed from a body in fusion, such as sulphur or bismuth, the
crystallisation is said to take place by the dry way. But if the crystallisa-
tion takes place owing to the slow evaporation of a solution of a salt, it is
said to be by the moist 'way. Snow, ice, and many salts present examples
of crystallisation.
345. Retardation of the point of solidification. The freezing point of
pure water can be diminished by several degrees, if the water be previously
288 On Heat. [345-
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. 290, which consists of
a delicate thermometer round the bulb of which is a wider one con-
taining some water. Before melting 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.
The vessel is placed in snow at o and then in alcohol cooled
to -6 or 8. The thermometer sinks a few degrees, but at once
rises to zero when the water in the bulb solidifies. The smaller the
j> quantity of liquid the lower 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
20 mists formed of particles of liquid matter suspended in an atmo-
sphere whose temperature was ioor even 15 below zero.
A very rapid agitation also prevents the formation of ice. The
same is 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. Finally,
Mousson found that a powerful pressure not only retards the
freezing of water, but prevents its complete solidification. In this
case the pressure opposes the tendency of the water to expand
on freezing, and thus virtually lowers the point of solidification.
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
Fig. 290. water f or th e purpose of extracting salt from it. If water con-
tains 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,
and 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 1 8 or 20. Contact with
a fragment of ice immediately set up congelation. Globules of sulphur
(which solidifies at 115) remained liquid at 40 ; and globules of phosphorus
(solidifying point 42) at 20.
When a liquid solidifies after being cooled below its normal freezing
point, the solidification takes place very rapidly, and is accompanied byaj
disengagement 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 hyposulphite of sodium, which melts in its own
-346] Change of Volume on 'Solidification and Liquefaction. 289
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 temperature 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 liquid by the heat of
solidification of that which has solidified.
346. 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. 291 is well
adapted for exhibiting this phenomenon. It consists of a glass
tube ab 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 degrees on the tube c
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 known
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 c 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. Phosphorus, 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 a * the
same temperature when melted. Sulphur expands about 5 per
cent, on liquefying, and stearic acid about 1 1 per cent.
Water presents a remarkable exception ; it expands at the
moment of solidifying, or contracts on melting, by about 10 per
cent. One volume of ice at o gives 0-9178 of water at o, or I
volume of water at o gives 1-102 of ice at the same temperature. Fi
In consequence of this expansion, ice floats on the surface of water.
According to Dufour, the specific gravity of ice is 0-9178 ; Bunsen found for
ice which had been freed from water 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
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 1 3-inch iron bomb-shell
O
290 On Heat. [346-
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. It is possible that under the
great pressure some of the water still remained liquid 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 o, 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.
347. 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 :
the portion which melts robs the rest of the mixture of a large quantity of
sensible heat, which thus becomes latent. In many cases a very consider-
able 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
Sulphate of sodium . . . 8) +iot 17
Hydrochloric acid . . 5 [
Pounded ice or snow 2 ) T . 00
. . . . + 10 to io
Common salt . . . I )
Sulphate of sodium ... 3) + ioto-i 9
Dilute nitric acid . . . 2 )
6\
5 1
4)
Sulphate of sodium . . 6
Nitrate of ammonium . . 5 ... +ioto 26
Dilute nitric acid . . .
Phosphate of sodium . . . 9 ) + 10 to - 20
Dilute nitric acid . . . 4 )
If the substances taken be themselves first 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
-349] Outline's Researches. 291
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
they are intimately mixed. It is also advantageous to use the machines for
a series of successive operations.
348. Guthrie's researches. It appears from recent experiments of
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 is, of course, due to the loss of heat by the thermometer
to 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 be 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 combination with water. That
particular strength of a particular salt, which resists solidification to the
lowest temperature, is called by Guthrie a cryohydrate. It is of such a
strength that when cooled 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 has also shown 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 TENSION.
349. Vapours. We have already seen (146) that vapours are the aeri-
form fluids into which volatile substances, such as ether, alcohol, water, and
mercury, are changed by the absorption of heat. Volatile liquids are those
which thus possess the property of passing into the aeriform state, and fixed
liquids those which do not form vapours at any temperature without under-
o 2
292
On Heat.
[349^
going chemical decomposition, such as the fatty oils. There are some
solids, such as ice, arsenic, camphor, and in general all odoriferous solid
substances, which can directly form vapours without
first becoming liquid.
Vapours are transparent like gases, and generally
colourless ; there are only a few coloured liquids which
also give coloured vapours.
350. 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 boiling to its rapid production in the
mass of the liquid itself. We shall presently see (356)
that at the ordinary atmospheric pressure, ebullition,
like fusion, takes place at a definite temperature. This
is not the case with evaporation, which takes place 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, gives no
vapour below 10, nor sulphuric acid below 30.
351. Elastic force of vapours. Like gases, va-
pours 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 vapours may
be demonstrated by the following experiment : A
quantity of mercury is placed in a bent glass tube (fig.
292), the shorter leg of which is closed ; a few drops of ether are then
passed into the closed leg and the tube immersed in a water bath at a
temperature of about 45. The mercury then sinks slowly in the short
branch, and the space ab 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 d. 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 ab disappears, and the drop of ether is
reproduced. If, on the contrary, the bath be heated still higher, the level of
the mercury descends below , indicating an increase in the elastic force of
the vapour,
352. Formation of vapours in a vacuum. In the previous experiment
the liquid changed very slowly into the vaporous condition ; the same is the
case when a liquid is freely exposed to the air. In both cases the atmo-
sphere is an obstacle to the vaporisation. In a vacuum there is no resist-
ance, and the formation of vapours is instantaneous, as is seen in the
following experiment : Four barometer tubes, filled with mercury, are
immersed in the same trough, fig. 293. One of them, A, serves as a baro-
meter, and a few drops of water, alcohol, and ether are respectively intro-
duced 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 produced by the weight of the liquid, which is an infinitely small
fraction of the weight of the displaced mercury, it must be due to the
Fig. 292.
-353]
Saturated Vapours.
293
ABE C D
formation of some vapour whose elastic force has depressed the mercurial
column.
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 with
ether than with alcohol. We consequently obtain the two following laws for
the formation of vapours :
I. In a vacuum all volatile liquids are instantaneously converted into
vapour.
II. A t the same temperature the vapours of different liquids have differ-
ent elastic forces.
For example, at 20 the tension of ether vapour is 25 times as great as
that of aqueous vapour.
353. Saturated vapours. Maximum of tension. 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 mercurial column is not
depressed to its full extent ; for if some more ether be introduced the
depression increases. By continuing the addition of ether, it 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
tension of the vapour, a limit which, as we
shall presently see (354), varies with the tem-
perature, but which for a given temperature
is independent of the pressure.
To show that, in a closed space, saturated
with vapour and containing liquid in excess,
the temperature remaining constant, there
is a maximum of tension which the vapour
cannot exceed, a barometric tube is used
which dips in a deep bath (fig. 293). 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 mercurial column 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 mercurial column is
constant. The tension 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
294
On Heat.
[353-
vapour is again saturated ; but in both cases the tension and the density of
the vapour remain constant.
354. iron-saturated vapours. From what has been said, vapours pre-
sent 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
exactly resemble gases. For if the experiments (fig. 294) 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 tension dimin-
ishes 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 non-
saturated vapours obey
Boyle's law.
When a non-saturated
vapour is heated, its vol-
ume increases like that of
a gas ; and the number
0-00366, which is the co-
efficient of the expansion
of air, may be taken for
that of vapours.
Hence we see that the
physical properties of un-
saturated vapours are
comparable with those of
permanent gases, and that
the formulas for the com-
pressibility and expan-
sibility of gases (176 and
332) also apply to unsatu-
rated vapours. But it
must not be forgotten that
there is always a limit of
pressure or of cooling at
which unsaturated vapours
pass into a state of satura-
tion, and that they have
then a maximum of ten-
sion an<} density which
Fig. 294.
Fig. 295.
can only be exceeded when the temperature rises while they are in contact
with the liquid.
356] Tension of Aqueous Vapour. 295
355. Tension of aqueous vapour below zero. In order to measure the
elastic force of aqueous vapour below zero, Gay-Lussac used two barometer
tubes filled with mercury, and placed in the same bath (fig. 295). The
straight tube A serves as a barometer ; the other, B, is bent, so that part of
the Torricellian vacuum can be surrounded by a freezing mixture (347).
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 tempera-
ture of the freezing mixture.
At o the depression is ... 4-54 millimetres.
-3
5J ~~ 5 J) V * * 3*1 * 5)
-7 .... 2-67
-10 .... 2-08
-20 .... 0-84
-30 ' ,l ..... 0'36
These depressions, which must be due to the tension of aqueous vapour
in the space BC, show that even at very low temperatures there is always
some aqueous vapour in the atmosphere.
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 lowest
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.
356. Tension of aqueous vapour between zero and one hundred
degrees. i. Daltoris method. Dalton measured the elastic force of aqueous
vapour between o and 100 by means of the apparatus represented in fig.
296. Two barometer tubes, A and B, are filled with mercury, and inverted
in an iron bath full of mercury, and placed on a furnace. The tube A con-
tains a small quantity of water. The tubes are supported in a cylindrical
vessel 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 vaporises, and in proportion as the
tension 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. Regnaulfs method. Dalton's method is wanting in precision, for the
liquid in the cylinder has not everywhere the same temperature, and con-
sequently the exact temperature of the aqueous vapour is not indicated.
Regnault's apparatus is a modification of that of Dalton. The cylindrical
vessel is replaced by a large cylindrical zinc drum, MN (fig. 297), in the bottom
of which are two tubulures. The tubes A and B pass through these tubu-
lures, and are fixed by caoutchouc collars. The tube containing vapour, B,
2 9 6
On Heat.
[356-
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 impregnated with sulphuric acid, which is connected with the air-
pump.
When the flask a 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 vapours. After having vaporised some
Fig. 296.
Fig. 297.
quantity of water, and when it is thought that the air in the tube is withdrawn,
the capillary tube which connects B with the three-way tube is sealed. The
tube B being thus closed, it is experimented with as in Dalton's method.
The drum MN, being filled with water, is gently heated by a spirit lamp,
which is separated from the tubes by a wooden screen. 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
-357]
Tension of Aqueous Vapour.
297
means of this apparatus, the elastic force of vapour between o and 50 has
been determined with accuracy.
357. Tension of aqueous vapour above one hundred degrees. Two
methods have been employed for determining the tension of aqueous vapour
at temperatures above 100 ; the one by Dulong and Arago, in 1830, and the
other by Regnault, in 1844.
Fig. 298 represents a vertical section of the apparatus used by Dulong
and Arago. It consisted of a copper boiler, , with very thick sides, and of
Fig. 298.
about 20 gallons capacity. Two gun-barrels, #, of which only one is seen in
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, /, indicating the temperature of the water and of
the vapour. The tension of the vapour was measured by means of a mano-
meter with compressed air, m, previously graduated (178) and fitted into an
iron vessel, d, 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, , in which
the level was always the same as in the bath. A copper tube, *', connected
the upper part of the vessel, */, with a vertical tube, c, fitted in the boiler.
The tube / 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 b.
The vapour which was disengaged from the tube c exercised a pressure
on the water of the tube / ; this pressure was transmitted to the water and
to the mercury in the 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 tension up to 24 atmospheres, and the tension from thence to 50
atmospheres was determined by calculation.
03
298
On Heat.
[358-
358. Tension of vapour below and above one hundred degrees.
Regnault devised a method by which the tension of vapour may be
measured at temperatures either below or above 100. It depends on the
principle that when a liquid boils, the tension of the vapour is equal to the
pressure it supports (363). If, therefore, the temperature and the corre-
sponding pressure 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 corresponding temperature.
The apparatus consists of a copper retort, C (fig. 299), hermetically sealed
and about two-thirds full of water. In the cover there are four thermometers,
Fig 299.
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
metallic 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 either to an exhaust-
ing or a condensing air-pump, according as the air in the globe is to be
rarefied or condensed. The reservoir K, in which is the globe, contains
water of the temperature of the surrounding air.
If the elastic force of aqueous vapour below 100 is to be measured, the
end H' of the leaden 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.
-358] Tension of Aqueous Vapour. 299
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
tension 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 tension above 100, the tube H' is connected
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 (367), 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 tension
for a given temperature.
The following tables by Regnault give the tension of aqueous vapour
from - 10 to 101 :
Tensions of aqueous vapour from 10 to 104 C.
Tempe-
ratures
Tensions in
millimetres
Tempe-
ratures
Tensions in
millimetres
Tempe-
ratures
Tensions in
millimetres
Tempe-
ratures
Tensions in
millimetres
-10
2-078
12
10-457
29
29782
90
525H5
8
2-456
13
II-062
30
3I-548
91
54578
6
2-890
14
I I -906
31
33-405
92
56676
4
3387
15
12-699
32
35359
93
588-41
2
3-955
16
I3-635
33
37-4IO
94
61074
4-600
17
I4-42I
34
39-565
95
63378
+ I
4-940
18
I5-357
35
4I-827
96
657-54 '
2
5-302
19
16-346
40
54-906
97
682-03
3
5-687
20
I7-39I
45
7I-39I
98
707-26
4
6-097
21
18-495
50
91-982
98-5
720-I5
5
6*534
22
19-659
55
tI7-479
99-o
733-91
6
6- 99 8
23
20-888
60
148791
99'5
746-50
7
7-492
24
22-184
65
186-945
lOO'O
760-00
8
8-017
25
23-550
70
233-093
100-5
77371
9
8-574
26
24-998
75
288-517
icro
787-63
10
9-165
27
26-505
80
354^43
I02'0
8l6-I7
ii
9-792
28
28-101
85
433-4I
104-0
875-69
In the second 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 formulae, but none of the formulae seem to have
the simplicity which characterises a true law.
300
On Heat
[358-
Tensions in atmospheres from 100 to 230-9.
Temperatures
Number
of atmo-
spheres
Temperatures
Number
of atmo-
spheres
Temperatures
Number
of atmo-
spheres
Temperatures
Number
of atmo-
spheres
100-0
I
I70-8
8
198-8
15
2I7- 9
22
112-2
*1
I75-8
9
20I-9
16
220-3
23
120*6
2
180-3
10
204-9
17
222-5
24
J 33'9
3
184-5
ii
2077
18
2247
25
144-0
4
188-4
12
2IO-4
19
226-8
26
152-2
5
I92T
13
2I3-0
20
228-9
27
156-2
6
I95'5
14
2I5-5
21
230-9
28
165-3
7
359. Tension of the vapours of different liquids. Regnault deter-
mined the elastic force, at various temperatures, of a certain number of liquids
which are given in the following table :
Liquids
Tempera-
tures
Tensions in
millimetres
Liquids
Tempera-
tures
Tensions in
millimetres
Mercury .
50
100
o-ii
0'74
Ether . .
-20
68
182
f
o
13
1
60
1728
Alcohol .
50
220
100
4950
I
Bisulphide
100
20
1695
43
132
Sulphurous I
acid 1
-20
60
479
1165
8124
of carbon
60
1164
f
-30
876
I
100
3329
Ammonia \
3163
(
30
8832
360. Tension of the vapours of mixed liquids. Regnault's experiments
on the tension of the vapour of mixed liquids prove that (i.) when two liquids
exert no solvent action on each other such as water and bisulphide of carbon,
or water and benzole the tension of the vapour which rises from them is
nearly equal to the sum of the tensions of the two separate liquids at the
same temperature ; (ii.) with water and ether, which partially dissolve each
other, the tension of the mixture is much less than the sum of the tensions of
the separate liquids, being scarcely equal to that of the ether alone ; (iii.)
when two liquids dissolve in all proportions, as ether and bisulphide of carbon,
or water and alcohol, the tension of the vapour of the mixed liquid is inter-
mediate between the tensions of the separate liquids.
Wiillner has shown that the tension of aqueous vapour emitted from a
saline solution, as compared with that of pure water, is diminished by an
amount proportional to the quantity of anhydrous salt dissolved, when the
salt crystallises without water or yields efflorescent crystals : when the salt is
deliquescent, or has a powerful attraction for water, the reduction of tension
is proportional to the quantity of crystallised salt.
361. Tension in two communicating vessels at different temperatures.
When two vessels containing the same liquid, but at different temperatures,
-362]
Evaporation.
301
are connected with each other, the elastic force is not that corresponding to
the mean of the two temperatures, as would naturally be supposed. Thus,
if there are two globes (fig. 290), one, A, containing water kept at zero by
means of melting ice, the other, B, containing water at 100, the tension, as
long as the globes are not connected, is 4 to 6 millimetres in the first, and
760 millimetres in the second. But when they are connected by opening the
stopcock C, the vapour in the globe B, from its greater tension, passes into
the other globe, and is there condensed, so that the vapour in B can never
reach a higher temperature than that in the globe A. The liquid simply
distils from B towards A without any increase of tension.
From this experiment the general principle may be deduced that when
two vessels containing the same liquid, but at different temperatures, are con-
nected, the tension is identical in both vessels, and is the same as that corre-
sponding to the lower temperature. An application of this principle has been
made by Watt in the condenser of the steam-engine.
362. Evapo-
ration. Causes
which accele-
rate it. Evapo-
ration, as has
been already
stated (349), is the
slow production
of vapour at the
surface of a liquid.
It is in conse-
quence of this
evaporation that
wet clothes dry
when exposed to
the air, and that
open vessels con-
taining water become emptied. The vapours which, rising in the atmo-
sphere, condense, and becoming clouds, fall as rain, are due to the evapora-
tion from the seas, lakes, rivers, and the soil.
Four causes influence the rapidity of the evaporation of a liquid : i. the tem-
perature ; ii. the quantity of the same vapour in the surrounding atmosphere ;
iii. the renewal of this atmosphere ; iv. the extent of the surface of evaporation.
Increase of temperature accelerates the evaporation by increasing the
elastic force of the vapours.
In order to understand the influence of the second cause, it is to be ob-
served that no evaporation could take place in a space already saturated
with vapour of the same liquid, and that it would reach its maximum in
air completely freed from this vapour. It therefore follows that between
these two extremes, the rapidity of evaporation varies according as the
surrounding atmosphere is already more or less charged with the same
vapour.
The effect of the renewal of this atmosphere is similarly explained ; for
if the air or gas, which surrounds the liquid, is not renewed, it soon becomes.
302; On Heat. [362-
saturated, and evaporation ceases. Dalton found that the ratios of the
evaporation in a feeble medium and a strong draught were as 270 : 347 : 424.
He also observed that the quantity evaporated in perfectly dry, almost still
air, in a temperature at 20, was equivalent to o-i of a gramme on a square
decimeter of surface in a minute.
The influence of the fourth cause is self-evident.
363. laws of ebullition. Ebullition, or boiling, is the rapid production
of elastic bubbles of vapour in the mass of a liquid itself.
When a liquid, water for example, is heated at the lower part of a
vessel, the first bubbles are due to the disengagement of air which had
previously been absorbed. Small bubbles of vapour then begin to rise
from the heated parts of the sides, but as they pass through the upper layers,
the temperature of which is lower, they
condense before reaching the surface.
The formation and successive condensa-
tion of these first bubbles occasion the
singing noticed in liquids before they
begin to boil. Lastly, large bubbles rise
and burst on the surface, and this consti-
tutes the phenomenon of ebullition (fig. 30 1 ).
The laws of ebullition have been
determined experimentally, and are as
follows :
I. The temperature of ebullition, or the
boiling point, increases with the pressure.
II. For a given pressure ebullition
begins at a certain temperature, which
varies in different liquids, but which, for
eqtial pressures, is always the same in the
same liquid.
III. Whatever be the intensity of the
source of heat, as soon as ebullition begins,
the temperature of the liquid remains sta-
tionary.
Soiling points under the pressure 0/760 millimetres.
Fig. 301.
Carbonic acid . . . - 82
Chloride of methyle . . -23
Cyanogen , . . . 20
Sulphurous acid . . . 10
Chloride of ethyle . . . + 1 1
Aldehyde . . .21
Ether 37
Bisulphide of carbon . . 47
Acetone .... 56
Bromine .... 58
Methylic alcohol ... 66
Alcohol 78
Benzole ..... 80
Distilled water 100
Acetic acid
Amylic alcohol .
Propionic acid .
Butyric acid
Turpentine
Iodine
Aniline
Phosphorus .
Strong sulphuric acid
Mercury .
Sulphur
Cadmium .
Zinc .
ii 7 c
131
137
156
157
175
182
290
3i8
358
448
860
1040
-364] Theoretical Explanation of Evaporation and Ebullition. 303;
Kopp has pointed out that in homologous chemical compounds the same
difference in chemical composition frequently involves the same difference
of boiling points ; and he has shown that in a very extensive series of
compounds, the fatty acids for instance, the difference of CH 2 is attended by
a difference of 19 C. in the boiling point.
In other series of homologous compounds the corresponding difference irv
the boiling point is 30, and in others 24.
364. Theoretical explanation of evaporation and ebullition. From
what has been said about the nature of the motion of the molecules in liquids
(292), 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 is 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 to momentarily 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 greater the external pressure on the
liquid, and thus we see the dependence of pressure on the temperature of
boiling.
304 On Heat. [365-
365. 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
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
nitrate of potassium 116
carbonate of potassium 135
chloride of calcium 179
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.
Dissolved 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.
M. Donny examined this phenomenon by means of the apparatus depicted in
figure 302. It
A ^ consists of a
glass tube CAB,
bent at one end
and closed at C,
Fig. 302. 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 138 the liquid is suddenly converted
into steam and the water is thrown over into the bulb, which is smashed if
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 beyond
its boiling point without the formation of a trace of vapour. Dufour has
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 ; very commonly globules of 10 millimetres diameter
reached a temperature of 120 or 130, while very small globules of i to 3
millimetres reached the temperature of 175, a temperature at which the
tension 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.
-367] Influence of Pressure on the Boiling Point. 305
Saturated aqueous solutions of sulphate of copper, chloride of sodium,
&c., remained liquid at a temperature far beyond their boiling point, when
immersed in melted stearic acid. In like manner, globules of chloroform
(which boils at 61), suspended in a solution of chloride of zinc, could be
heated to 97 C 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 most recent
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. Nethertheless, 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 bisulphide of carbon 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 bisulphide of carbon, both at the tempera-
ture 45, are mixed together, the mixture at once begins to boil briskly.
366. 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 101 ; and if the glass vessel had been previously cleaned by
means of sulphuric acid and of potass, 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 accompany
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.
367. Influence of pressure on the boiling point. We see from the
table of tensions (358) that at 100, the temperature at which water boils
under a pressure of 760 millimetres, aqueous vapour has a tension exactly
equal to this pressure. This principle is general, and may be thus enunci-
ated : A liquid boils when the tension of its vapour is equal to the pressure
it supports. Consequently, as the pressure increases or diminishes, the
tension of the vapour, and therefore the temperature necessary for ebulli-
tion, must increase or diminish.
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
306
On Heat.
[367-
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. 303. If the bottom
is then cooled 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 which a partial
vacuum is produced.
It is in consequence of this diminu-
tion of pressure that liquids boil on
high mountains at lower temperatures.
On Mont Blanc, for example, water
boils at 84, and at Quito at 90.
On the more rapid evaporation of
water under feeble pressures is based
the use of the air-pump in concentra-
ting those solutions which either can-
not bear a high degree of heat, or
which can be more cheaply evaporated
in an exhausted space. Howard made
a most important and useful applica-
tion of this principle in the manufac-
ture 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 evapo-
rating the juice of certain plants used in preparing medicinal extracts.
On the other hand, ebullition is retarded by increasing the pressure :
under the pressure of two atmospheres, for example, water only boils at i2o-6.
368. Franklin's experiment. The influence of pressure on ebullition
may further be illustrated by means of an experiment originally made by
Franklin. The apparatus consists of a bulb, #, and a tube b, joined by a
tube of smaller dimensions (fig.
304). The tube b is drawn out, and
the apparatus filled with water,
which is then in great part boiled
away by means of a spirit lamp.
When it has been boiled sufficiently
long to expel all the air, the tube b
is sealed. There is then a vacuum
in the apparatus, or rather there is
a pressure due to the tension 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 pressure which drives the water into
the tube , and causes a brisk ebullition.
369. Measurement of heights by the boiling: point. From the con-
nection between the boiling-point of water and the pressure, the heights of
Fig. 303.
Fig. 304.
-370] Formation of Vapour in a Closed Tube. 307
mountains may be measured by the thermometer instead of by the barometer.
Suppose, for example, it is found that water boils on the summit of a
mountain at 90, and at its base at 98 ; at these temperatures the elastic
force or tension of the vapour is equal to that of the pressure on the liquid ;
that is, to the pressure of the atmosphere at the two places respectively.
Now the tensions of aqueous vapour for various temperatures have been
determined, and accordingly the tensions corresponding to the above tem-
peratures 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 (171). An ascent of about 1080 feet produces a diminution of
i C. in the boiling point.
The instruments used for this purpose are called thermo-barometers or
hypsometerS) and were first applied by Wollaston. They consist essentially
of a small metallic vessel for boiling water, fitted with very delicate ther-
mometers, which are only graduated from 80 to 100; so that each degree
occupying a considerable space on the scale, the loths, and even the icoths,
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 10 feet.
370. Formation of vapour in a closed tube. We have hitherto con-
sidered vapours as being produced in an indefinite space, or where they
could expand freely, and it is only under this condition that ebullition can
take place. In a closed vessel the vapours produced finding no issue, their
tension and their density increase with the temperature, but the rapid dis-
engagement of vapour which constitutes ebullition is impossible. Hence,
while the temperature of a liquid in an open vessel can never exceed that of
ebullition, in a closed vessel it may be much higher. The liquid state has,
nevertheless, a limit ; for, according to experiments by Cagniard-Latour, if
either water, alcohol, or ether be placed in strong glass tubes, which are
hermetically sealed after the air has been expelled by boiling, and if then
these tubes are exposed to a sufficient degree of heat, a moment is reached
at which the liquid suddenly disappears, and is converted into vapour at 200,
occupying a space less than double its volume in the liquid state, its tension
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 in the glass, be
heated, it is completely vaporised at about the temperature of melting
zinc.
When chloride of ethyle is heated in a very thick sealed tube, the upper
surface ceases to be distinct at 170, and is replaced by an ill-defined
nebulous zone. As the temperature 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 the oppo-
site order. Similar appearances are observed on heating ether in a sealed
tube at 190.
Andrews has observed that when liquid carbonic acid was heated in a
closed tube to 31 C the surface of demarcation between the liquid and the
308
On Heat.
[370-
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 striae throughout its whole mass.
Above 30 no apparent liquefaction of carbonic anhydride, or separation into
two distinct forms of matter, could be effected, not even when the pressure
of 400 atmospheres was applied. It would thus seem that there exists for
every liquid a temperature, the critical point or critical temperature. While
below this critical point a sudden transition from gas to liquid is accom-
panied 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 con-
nected 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 condensation is only possible at
a temperature below the critical point, and it is not surprising, therefore,
that mere pressure, however great, should fail to liquefy many of the bodies
which usually exist as gases.
371. Papin's dig-ester. Papin appears to have been the first to study
the effects of the production of vapour in closed vessels. The apparatus
which bears his name consists of a cylin-
drical iron vessel (fig. 305), 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. At the bottom of a cylindrical
cavity, which traverses the cylinder S,
and the tubulure 0, the cover is perforated
by a small orifice in which there is a rod
n. This rod presses against a lever, A,
movable at a, and the pressure may be
regulated by means of a weight movable
on this lever. The lever is so weighted,
that when the tension in the interior is
equal to 6 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 tension of the vapour increased to several atmo-
spheres, according to the weight on the lever.
We have seen that water boils at much lower temperatures on high
mountains (367) ; 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.
Papin's digester is used in extracting gelatine. When bones are digested
Fig. 305-
-372] Latent Heat of Vapour. 309
in this apparatus they are softened so that the gelatine which they contain
is dissolved. The use of the digester is extending in Germany ; 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.
372. latent heat of vapour. As the temperature of a liquid remains
constant during ebullition, whatever be the source of heat (363), it follows
that a considerable quantity of heat becomes absorbed in ebullition, the
only effect of which is to transform the body from the liquid to the gaseous
condition. 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
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 of a few liquids, may be here given :
Water 536 Bisulphide of carbon . . 87
Alcohol 208 Turpentine . . . .74
Acetic acid . . . .102 Bromine 49
Ether 90 Iodine 24
The meaning of these numbers is, 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 the boiling point to that of vapour at the same temperature, as would raise
a pound of water through 536 degrees, or 536 pounds of water through one
degree ; or that the conversion of one pound of vapour of alcohol at 78 into
liquid alcohol of the same temperature would heat 208 pounds of water
through one degree.
Watt, who investigated the subject, found that the whole quantity of heat
necessary to raise a given 'weight of water from zero at any temperature and
then to evaporate it entirely, 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 evapo-
rated under a pressure of 1 5 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 T >
in which Q is the total quantity of heat, and T the temperature of the water
3io
On Heat.
[372-
during evaporation, while the numbers are constant quantities. The total
quantity of heat necessary to evaporate water at 100 is 606-5 + ('3O5 * 100)
= 637 ; at 120 it is 643 ; at 150 it is 651 ; and at 180 it is 661.
Thus the heat required to raise a pound of water from zero and convert
it into steam at 100 represents a mechanical work of 885430 units, which
would be sufficient to raise a ton weight through a height of nearly 400 feet.
The total heat of the evaporation of ether is expressed by a formula
similar to that of water, namely, Q = 64 + 0-045/5 and that for chloroform
A
373. Cold due to evaporation. Mercury frozen. Whatever be the
temperature at which a vapour is produced, an absorption of heat always
takes place. If, therefore, a liquid evaporates, and does not receive from
without a quantity of heat equal to that which is expended in producing the
vapour, its temperature sinks, and the cooling is greater in proportion as the
evaporation is more rapid.
Leslie succeeded in freezing water by means of rapid evaporation.
Under the receiver of the air pump is placed a vessel containing strong sul-
phuric acid, and above it a thin metal capsule, A (fig. 306), containing a small
quantity of water. By
exhausting the receiver
the water begins to
boil (360), and since the
vapours are absorbed
by the sulphuric acid
as fast as they are
formed, a rapid evapo-
ration is produced,
which quickly effects
the freezing of the
water.
This experiment is
best performed by
using, instead of a thin
metallic vessel, a watch
glass, coated with lampblack and resting on a cork. 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 advantageously be
used.
The same result is obtained by means of Wollaston's cryophorus (fig.
307), 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 introduced into the bulb A, the other is immersed in a
freezing mixture. The vapours in the tube are 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 temperature
is so much reduced that it freezes.
? 306.
Fi.
-374] Carres Apparatus for Freezing Water. 311
By using liquids more volatile than water, more particularly liquid sul-
phurous acid, which boils at 10, or still better, chloride of methyle, which
is now prepared industrially in large quantities, a degree of cold is obtained
sufficiently intense to freeze mercury. The experiment may be made by cover-
ing 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.
Thilorier, by directing a jet of liquid carbonic acid on the bulb of an
alcohol thermometer, obtained a cold of - 100 without freezing the alcohol.
We have already seen, however (343), that with a mixture of solid carbonic
acid, liquid protoxide of nitrogen and ether, Despretz obtained a sufficient
degree of cold to reduce alcohol to the viscous state.
By means of the evaporation of bisulphide of carbon 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 bisulphide
of carbon, is placed on the water. The evaporation of the bisulphide is ac-
celerated 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 anaesthesia also depends
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 ap-
paratus 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
temperatures, when we are in an atmosphere saturated by moisture, in which
no evaporation takes place.
374. Carre'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 vaporisation.
This property of liquids has been utilised by M. Carre\ in freezing water
by the distillation of ammonia. The apparatus consists of a cylindrical
boiler C (figs. 308, 309), and of a slightly conical vessel A, which is the freezer.
These two vessels are connected by a tube, ?//, and a brace, , binds them
312
On Heat.
[374-
firmly. They are made of strong galvanised iron plate, and can resist a
pressure of seven atmospheres.
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 /. 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 commu-
nication with the boiler by means of the tube m. 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 comprehends 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
Fig. 308.
Fig. 309.
in the water of the boiler is disengaged, and, in virtue of its own pressure, is
liquefied in the freezer, along with about a tenth of its weight of water. This
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. 309), and the freezer outside, care being taken to
surround it with very 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 dissolved ; the pressure thus being diminished,
the ammonia which has been liquefied in it is converted into the gaseous
form, and now distils from A towards C, to redissolve 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,
-374]
Carrt ' s Apparatus for Freezing Water.
313
alcohol is poured between them. In about an hour and a quarter a perfectly
compact cylindrical 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.
Carre has constructed an ice-making machine which is an industrial
application of Leslie's experiment (373), 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. 310). At one end is a funnel E, by which strong sulphuric acid can be
introduced ; at the other is a tubulure ;;/, to which is screwed a dome d that
supports a series of obstacles intended to prevent any sulphuric acid from
spirting into m and b. There are, moreover, on the receiver a wide tube //,
closed by a thick glass disc O, and a long tube //, to the top of which is fitted
the bottle C con-
taining water to be
frozen. The dome
d, the disc O, and
the stopper i of the
funnel E are all
sealed with wax.
On the side of
the receiver is an
air-pump P, con-
nected with it by a
tube , and worked
by a handle M. To
this handle is at-
tached a rod /,
whi ch by the
mechanism repre-
sented on the left
of the figure works
a stirrer A in the
sulphuric acid. A
lever x connected
with a horizontal
axis which tra-
verses a small stuff- Fig. 310.
ing-box n, trans-
mits its backward and forward motion to the rod e and to the stirrer. This
and the stuffing-box n are fitted in a tubulure on the side of the tubulure /;/.
The smallest size which Carr 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
314 On Heat. [374-
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.
375. Liquefaction of vapours. The liqti ef action or condensation of
vapours is their passage from the aeriform to the liquid state. Condensa-
tion may be due to three causes cooling, compression, or chemical affinity.
For the first two causes the vapours must be saturated (354), while the
latter produces the liquefaction of the most rarefied vapours. Thus, a large
number of salts absorb and condense the aqueous vapour in the atmosphere,
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.
376. Distillation. Stills. Distillation is an operation by which a
volatile liquid may be separated from substances which it holds in solution
Fig. 311.
or by which two liquids of different volatilities may be separated. The
operation depends on the transformation of liquids into vapours by the
action of heat, and on the condensation of these vapours by cooling.
The apparatus used in distillation is called a stilL Its form may vary
greatly, but it consists essentially of three parts : ist, the body, A (fig. 311),
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
-378] Apparatus for determining Alcoholic Value of Wines. 315
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 col-
lected 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 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.
377. Xiiebig's condenser. In distilling smaller quantities of liquids,
or in taking the boiling point of a liquid, so as not to lose any of it, the
Fig. 312-
apparatus known as Liebig's condenser is extremely useful. It consists of a
glass tube, //(fig. 312), about thirty inches long, fittedin a copper or tin 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 the
lower part of the condenser by a funnel and tube f, and flowing out from the
upper part of the tube g. 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 extremity of the con-
densing tube.
378. Apparatus for determining: tne alcoholic value of wines. One
of the forms of this apparatus consists of a glass flask resting on a tripod,
and heated by a spirit lamp (fig. 313). By means of a caoutchouc tube this
is connected with a worm placed in a copper vessel filled with cold water,
and below which is a test-glass for collecting the distillate. On this are
P 2
3 i6
On Heat.
[378-
three divisions, one , which measures the quantity of wine taken ; the two
others indicating 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 over is a mixture of alcohol and
water ; for ordinary wines, such as clarets and hocks, about one-third is dis-
tilled over, and for wines richer in spirit, such as sherries and ports, one-half
must be distilled ; experiment has shown that under these circumstances all
the alcohol passes over in the distillate. The measure is then filled up with
distilled water to
a ; this gives the
mixture of alco-
hol and water of
the same volume
as the wine
taken, free from
all solid matters,
such as sugar,
colouring mat-
ter, and acid, but
containing all
the alcohol. The
specific gravity
of this distillate
is then taken by
means of an al-
coholometer
(129), and the
number thus ob-
tained corresponds to a certain strength of alcohol as indicated by the
tables.
379. 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 tension in the vessel. If a gas, sul-
phurous acid, for example, be generated in the
flask m (fig. 314), and be passed into water in the
vessel A, as long as the gas is given off freely, its
tension 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
cooled or the gas being disengaged too slowly,
the external pressure prevails, and when it exceeds the internal tension 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.
Fig. 3M-
-380] Liquefaction of Gases. 317
These are tubes which prevent absorption by allowing air to enter in
proportion as the internal tension decreases. The simplest is a tube C o
(fig. 315,) passing through the cork which closes the flask M, in which the gas
is generated, and dipping in the liquid. When the tension of the 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 C0, depresses it to the same extent, assuming that
the liquid has the same density as the water in E. Now as the distance or
is less than the height DH, air enters by the aperture 0, before the water in
the bath can rise to A, and no absorption takes place.
Fig. 316 represents another kind of safety tube. It has a bulb a, con-
taining a certain quantity of liquid, as does also id. When the tension of
the gas in the retort M exceeds the atmospheric pressure, the level in the
leg id rises higher than in the bulb a ; if the gas has the tension of one atmo-
sphere, the level is the same in the tube as in the bulb. Lastly, if the
tension of the gas is less than the atmospheric preieure, the level sinks in
the leg di ; and, as care is taken that the height ia is less than b h, as soon
as the air which enters through c reaches the curved part *, it raises the
column / a, and passes into the retort before the water in the cylinder can
Fig- 3*5- Fig. 316.
reach b ; the tension in the interior is then equal to the exterior pressure,
and no absorption takes place.
380. liquefaction of gases. We have already seen that a saturated
vapour, the temperature of which is constant, is liquefied by increasing the
pressure, and that, the pressure remaining constant, it is brought into the
Liquid state by diminishing the temperature.
Unsaturated vapours behave in all respects like gases. And it is natural
to suppose that what are ordinarily called permanent gases are really un-
saturated vapours. For the gaseous form is accidental, and is not inherent
in the nature of the substance. At ordinary temperatures sulphurous acid is
a gas, while in countries near the poles it is a liquid ; in temperate climates
ether is a liquid, at a tropical heat it is a gas. And just as unsaturated
vapours may be brought to the state of saturation, and then liquefied, by
suitably diminishing the temperature or increasing the pressure, so by the
318 On Heat. [380-
same means gases may be liquefied. But as they are mostly very far re-
moved from this state of saturation, 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.
The late researches of Cailletet and Pictet have
shown that the distinction permanent gas no
longer exists, now that all are liquefied.
Faraday was the first to liquefy some of the
gases. His method consists in enclosing in a
bent glass tube (fig. 317) substances by whose
chemical action the gas to be liquefied is pro-
duced, and then sealing the shorter leg. In
proportion as the gas is disengaged its pressure
increases, and it ultimately liquefies and collects
Fig. 317. in the shorter leg, more especially if its conden-
sation is assisted by placing the shorter leg in a
freezing mixture. A small manometer may be placed in the apparatus to
indicate the pressure.
Cyanogen gas is readily liquefied by heating cyanide of mercury in a
bent tube of -this description ; and carbonic acid by heating bicarbonate
of sodium ; other gases have been condensed by taking advantage of special
reactions, the consideration of which belongs rather to chemistry than to
physics. For example, chloride of silver absorbs about 200 times its volume
of ammoniacal gas ; when the compound thus formed is placed in a
freezing tube and gently heated, while the shorter leg is immersed in a
freezing mixture, a quantity of liquid ammoniacal gas speedily collects in the
shorter leg.
381. Apparatus to liquefy and solidify gases. Thilorier first con-
structed 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 con-
denses. The use of this apparatus is not free from danger : many acci-
dents 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. 319, and a section on a larger scale in fig. 318. 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 ;, into a cylindrical copper case C,
which surrounds the force-pump, from whence it escapes through the
tube ??, and the stopcock o. The whole arrangement rests on an iron
frame, PQ.
-381]
Apparatus to Liquefy and Solidify Gases.
319
The gas to be liquefied is previously collected in air-tight bags, R, from
whence it passes into a bottle, V, containing some suitable drying substance ;
it then passes into the condensing pump through the vulcanised india-rubber
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. 318). In order to collect some of the
Fig. 319.
liquid gas, the reservoir is inverted, and on turning the stopcock r, the liquid
escapes by a small tubulure jr.
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.
Solid carbonic acid evaporates very slowly. By means of an alcohol
thermometer its temperature has been found to be about 90. A small
quantity placed on the hand does not produce the sensation of such great
320 On Heat. [381-
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 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
protoxide of nitrogen. The gas once liquefied only evaporates slowly, and
produces a temperature of 88 below zero. 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 protoxide of nitrogen.
Protoxide of nitrogen is readily decomposed by heat, and has the pro-
perty 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 i-s thrown on liquid protoxide of nitrogen
it continues to burn with a brilliant light.
The cold produced by the evaporation of ether (373) has been used by
Loir and Drion in the liquefaction of gases. 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 ammoniacal gas 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.
382. Cailletet's and Pictet's researches. Cailletet and Pictet, working
independently, but simultaneously, have effaced the old distinction between
permanent and non-permanent gases, by effecting the condensation of the
gases oxygen and hydrogen, and other gases hitherto supposed to be in-
coercible. This has been accomplished by means of powerful material
appliances directed with great skill and ingenuity.
The essential parts of Cailletet's apparatus are represented in fig. 320.
The gas to be condensed is contained in the tube T P, which is fitted,
by means of a bronze screw, A, into a strong wrought-iron mercury
bath, B. By means of a screw, R E, and a tube, U, this is connected with a
hydraulic or a screw press not represented in the figure. The capillary part,
P, of the tube T, is placed in a vessel M, in which it can be surrounded
by a freezing mixture, and this again is surrounded by a stout safety bell
jar, C.
When a pressure of 250 to 300 atmospheres is applied by means of the
hydraulic press, after waiting until the heat due to the compression has dis-
appeared, if a screw arranged in the press is suddenly opened, the pressure
being diminished, the cold produced by the sudden expansion of the gas in
the tube T P is so great as to liquefy a portion of the rest, as is shown by
the production of a mist.
-382] Cailletefs and Pictet 's Researches. 3 2 \
This observation was first made with binoxide of nitrogen, but similar
results have been obtained with marsh gas, carbonic acid, and oxygen.
The principle of Pictet's method is that of
liberating the gas under great pressure combined
with the application of great degrees of cold. The
essential parts of the apparatus are the following :
Two double-acting pumps, A and B (fig. 321), are so
coupled together that they cause the evaporation
of liquid sulphurous acid contained in the annular
receiver C. By the play 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 sul-
phurous acid is reduced to 65. Its function is
to produce a sufficient quantity of liquid carbonic
acid, which is then submitted to a perfectly ana-
logous process of rarefaction and condensation.
This is effected by means of two similar pumps, E
and F. The carbonic acid gas, perfectly pure and
dry, is drawn from a reservoir through a tube not
represented in the figure, and is forced into the
condenser K, which is cooled by the liquid sul-
phurous acid, to a temperature of 65, and is there
liquefied.
H is a tube of stout copper in connection with
the condenser K by a narrow tube k. When a sufficient quantity of car-
bonic 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. This retort
is closed by a strong copper tube in which the actual condensation is effected,
near the end of which is a specially-constructed manometer R, and which is
closed by a stopcock X.
When the four pumps are set in action, for which a steam engine of 1 5
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
of 500 atmospheres, and then sinks to 320. This diminution is due to the con-
densation of gas, and at this stage the tube contains liquefied oxygen. If the
cock N is opened, the gas issues with violence, having the appearance 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
again, and again becomes stationary, proving that the gas is once more
being condensed.
P3
322
On Heat.
[382-
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 gas.
For hydrogen the gas was disengaged by heating a mixture of potassic
formate and hydrate. When the pressure had reached 650 atmospheres,
and the cock was opened, a steel-blue jet issued from the aperture with a
brisk noise. This suddenly became intermittent, and resembled a shower of
hailstones. As the separate granules struck the ground, they produced a loud
noise, and Pictet considers that in all probability the hydrogen in the interior
was frozen.
MIXTURES OF GASES AND VAPOURS.
383. Laws of the mixture of gases and vapours. Every mixture of a
gas and a vapour obeys the following two laws :
I. The tension, 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 is a vacuum.
II. The tension of the mixture of a gas and a vapour is equal to the
sum of the tensions which each would possess if it occupied the same space
alone.
These are known as Daltoils 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. 322), to which two stopcocks, b and d, are
cemented. The lower stopcock is provided with a tubulure, which connects
-383]
Mixtures of Gases and Vapours.
323
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 b and d are 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. Mercury is ac-
cordingly poured into the tube B until it is at
the same level in both tubes. The globe is
then removed, and replaced by a funnel C, pro-
vided with a stopcock a of a peculiar construc-
tion. It is not perforated, but has a small
cavity, as represented in //, 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 b 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
is allowed to fall drop by drop until the air in
the tube is saturated, which is the case when
the level k of the mercury ceases to sink (353).
As the tension 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 k,
there is a difference B .
fig- 346 gives a T\^~S. '-''-''- c
medial section, 1 5\^_
which is called
the principal sec-
tion. The centre Fig> 346>
C of the sphere
to which the mirror belongs is called the centre of cuivature ; the point A,
the middle of the reflector, is the centre of the figure ; the 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 emanate from it may be con-
sidered as parallel. From the hypothesis that the mirror is composed of
an infinitude 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.
420. 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. 347), 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 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 (419), and impinging on the other mirror, N, are reflected
so that they coincide in the focus B. That this is so is proved by the fact
356
On Heat.
[420-
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.
In consequence of the high temperature produced in the foci of concave
mirrors they have been called burning mirrors. It is stated that Archi-
medes 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 of a
number of silvered 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
and a hot summer's sun Buffon ignited a plank of tarred wood at a distance
of 70 yards.
421. Reflection in a vacuum. Heat is reflected in a vacuum as well as
in air, as is seen from the following experiment (fig. 348), 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
thermometer, and in the focus of the other a platinum wire made incan-
-423]
Reflecting Power.
357
Fig. 348.
descent by means of a galvanic current. The thermometer was immedi-
ately seen to rise several degrees, which could only be due to reflected heat,
for the thermometer did not show any
increase of temperature if it were not
exactly in the focus of the second re-
flector.
422. Apparent reflection of cold.
If two mirrors are arranged as repre-
sented in fig. 347, 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 differential
thermometer placed in the focus of the
second reflector would exhibit a decrease
in temperature of several degrees. This
appears at first to be caused by the
emission of frigorific rays from ice. It
is, however, easily explained from what
has been said about the mobile equi-
librium of temperature (415). There is
still an exchange of temperature, but here
the thermometer is the warmest body. As the rays which the thermometer
emits are more intense than those 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.
423. Reflecting: power. The reflecting 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. 349. The source of heat is a
cubical canister, M, now known as Leslies 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, in 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 what has been said on the application of Newton's
law to the differential thermometer, 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 i
and a plate of lead 6, it follows that the quantity of heat reflected by the
latter is six times as great as that reflected by the former. For the heat
353
On Heat.
[423-
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 100 :
Polished brass
Silver .
Steel .
Lead
100 Indian ink
90 Glass
70 Oiled glass
60 Lampblack
13
10
5
o
The numbers only represent the relative reflecting power as compared
with that of brass. Their absolute power is- the relation of the quantity of
heat reflected to the quantity of heat received. Desains and De la Provostaye,
who examined the absolute reflecting power of certain metals, obtained
the following results by means of Melloni's thermo-multiplier (412), the heat
being reflected at an angle of 50 :
Silver plate
Gold .
Brass
Platinum .
0-97 Steel
0-95 Zinc
o % 93 Iron
0*83 Cast iron
0-82
0-8 1
077
074
424. Absorbing- power. The absorbing power of a body is its property
of allowing a greater or less quantity of incident heat 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 versa.
-425] Radiating Power. 359
It was formerely 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 ist, one which is absorbed; 2nd, another
which is reflected regularly that is, according to laws previously demon-
strated (417) ; 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 (423).
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,
however, 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 observation. But we shall presently show (426) how the com-
parative 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 thermo-multiplier the following relative absorbing
powers :
Lampblack .... 100 Indian ink 85
White lead . . . . 100 Shellac 72
Isinglass 91 Metals 13
425. Radiating: power. The radiating or emissive 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. 349 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, and representing the heat emitted by lampblack as 100, Leslie
formed the following table of radiating powers :
Lampblack . . . .100 Tarnished lead . . . .45
White lead . . . .100 Mercury 20
Paper 98 Polished lead . . . .19
Ordinary white glass . . 90 Polished iron . . . .15
Isinglass 80 Tin, gold, silver, copper, c. .12
On Heat. [425-
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 thermo-multiplier. They found in this
manner the following numbers compared with lampblack as 100 :
Platinum foil .
Burnished platinum
Silver deposited chemically
Copper foil
Gold leaf
Pure silver laminated
burnished
deposited chemi-
cally and bur-
nished
3-00
2-50
10-80
9-50
5-36
4-90
4-28
It appears, therefore, that the radiating power found by Leslie for the
metals is too large.
426. Identity of the absorbing and radiating: powers. The absorb-
ing 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, 1 5 for ex-
ample ; the globe was kept at zero by surrounding it with ice, and having
been exhausted by means of a tubulure connected with the 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 1 5, 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 sur-
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. 350 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 of the two
faces opposite each other, one is black and the other white ; hence when
the cylinder A is filled with hot water, its white face radiates towards the
-427] Radiating Power. 361
black face of B, and its black face towards the white face of C. Under
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 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 replacing the two white faces by discs
of paper, glass, porcelain, c.
427. 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 increases it diminishes the radiating
and absorbing powers, and vice versA.
It has been already stated that these different 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 nature of the source of heat.
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 internal 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,
whatever the number. The thickness of the 16 layers was calculated to be
0-04 mm. With reference to metals, gold leaves of 0*008, 0-004, an d 0-002
of a millimetre in thickness, having been successively 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 radiat-
ing layer of metal is without influence.
The absorbing power is greatest when the rays are at right angles ; and
it diminishes in proportion as the incident rays deviate from the normal.
This is one of the reasons 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
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
R
362
On Heat.
[427-
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.
428. Ittelloni'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 described, science is indebted mainly to Leslie. But
since his time the discovery of other and far more delicate modes of de-
tecting and measuring heat has not only extended and corrected our pre-
vious knowledge, 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 (412).
In his experiments Melloni used five sources of heat ist, a Locatelli's
lamp one, that is, without a glass chimney, but provided with a reflector
, or what may be called a Torricellian
vacuum, the viscosity is practically constant, only diminishing from 0-126 to
O'ii2. It now begins to fall off, and at a pressure of O'oooo76 mm> it has
diminished to O-QI, or about i. Simultaneously with this decrease in
viscosity the force of repulsion excited by a standard light on a blackened
surface varies. It incr-eases as the pressure diminishes until the exhaus-
tion is about 0'05 mm ', and attains its maximum at about cro3 ram -. It then
sinks very rapidly until it is at O'oooo76 mm> , when it is less than ~ of its
maximum.
The viscosity varies in different gases ; it is considerably less in hydrogen
than in air ; and hence it is not necessary to drive the exhaustion so far to
produce a considerable degree of repulsion.
The researches of Crookes have opened the way to an entirely new field
of experimental inquiry into the phenomena which occur in what is called the
ultra-gaseous state of matter, or that in which the rarefaction of gases is
pushed to its utmost limits. This state in which molecular, as distinguished
from molar, actions come into play, has been aptly termed Crooked s vacuum
A further account of the researches requires too great an amount of detail
for the purposes of this work ; and it must also be added that the explana-
tions which have been given are still not beyond the range of controversy.
-448] Specific Heat. 385
CHAPTER IX.
CALORIMETRV.
447. Calorimetry. Thermal unit. The object of calorimetry is to
measure the quantity of heat which a body parts with or absorbs, when its
temperature sinks or rises through a certain number of degrees, or when it
changes its condition.
Quantities of heat may be expressed by any of its directly measurable
effects, but the most convenient is the alteration of temperature, and quan-
tities of heat are usually defined by stating the extent to which they are
capable of raising a known weight of a known substance, such as water.
The unit chosen for comparison, and called the thermal unit, is not every-
where the same. In France it is the quantity of heat necessary to raise the
temperature of one kilogramme of water through one degree Centigrade ; this
is called a calorie. In this book we shall adopt, as a thermal unit, the
quantity of heat necessary to raise one pound of water through one degree
Centigrade : I calorie = 2'2 thermal units, and I thermal unit =0*45 calorie.
On the centimetre-gramme-second system of units the heat required to
raise one gramme of water through one degree is taken as the unit. This is
called the gramme degree.
448. Specific beat. When equal weights of two different substances, at
the same temperature, placed in similar vessels, are subjected for the same
length of time to the heat of the same lamp, or are placed at the same
distance in front of the same fire, it is found that their temperatures will vary
considerably ; thus mercury will be much hotter than water. But as, from
the conditions of the experiment, they have each been receiving the same
amount of heat, it is clear that the quantity of heat which is sufficient to
raise the temperature of mercury through a certain number of degrees, will
only raise the temperature of the same quantity of water through a less
number of degrees ; in other words, that it requires more heat to raise the
temperature of water through one degree than it does to raise the temperature
of mercury by the same extent. Conversely, if the same quantities of water
and of mercury at 100 C.,be allowed to cool down to the temperature of the
atmosphere, the water will require a much longer time for the purpose than
the mercury : hence, in cooling through the same number of degrees, water
gives out more heat than does mercury.
It is readily seen that all bodies have not the same specific heat. If a
pound of mercury at 100 is mixed with a pound of water at zero, the tem-
perature of the mixture will only be about 3 ; that is to say, that while the
mercury has cooled through 97, the temperature of the water has only been
raised 3. Consequently the same weight of water requires about 32 times as
much heat as mercury does to produce the same elevation of temperature.
S
386 On Heat. [449-
If similar experiments are made with other substances it will be found
that the quantity of heat required to effect a certain change of temperature
is different for almost every substance, and we speak of the specific heat, or
calorific capacity, of a body as the quantity of heat which it absorbs when its
temperature rises through a given range of temperature, from zero to i for
example, compared with the quantity of heat which would be absorbed,
under the same circumstances, by the same weight of water ; that is, water
is taken as the standard for the comparison of specific heats. Thus, to say
that the specific heat of lead is 0-0314, means that the quantity of heat
which would raise the temperature of any given weight of lead through i
C. would only raise the temperature of the same weight of water through
0-0314 C.
Temperature is the ins viva of the smallest particles of a body ; in
bodies of the same temperature the atoms have the same vis viva, the
smaller mass of the lighter atoms being compensated by their greater
velocity. The heat absorbed by a body not only raises its temperature that
is, increases the vis viva of the progressive motion of the atoms but in over-
coming the attraction of the atoms it moves them further apart, and, along
with the expansion which this represents, some external pressure is overcome.
In the conception of specific heat is included, not merely that amount of heat
which goes to raise the temperature, but also that necessary for the internal
work of expansion, and that required for the external work. If these latter
could be separated we should get the true heat of temperature, that which is
used solely in increasing the vis viva of the atoms. This is sometimes
called the true specific heat.
Three methods have been employed for determining the specific heats of
bodies : (i.) the method of the melting of ice, (ii.) the method of mixtures,
and (iii.) that of cooling. In the latter, the specific heat of a body is deter-
mined by the time which it takes to cool through a certain temperature.
Previous to describing these methods, it will be convenient to explain the
expression for the quantity of heat absorbed or given out by a body of known
weight and specific heat, when its temperature rises or falls through a certain
number of degrees.
449. Measure of tbe sensible heat absorbed by a body. Let m be
the weight of a body in pounds, c its specific heat, and / its temperature.
The quantity of heat necessary to raise a pound of water through one degree
being taken as unity, m of these units would be required to raise m pounds
of water through one degree, and to raise it through t degrees, / times as
much, or mt. As this is the quantity of heat necessary to raise through /
degrees m pounds of water, whose specific heat is unity, a body of the same
weight, only of different specific heat, would require mtc. Consequently,
when a body is heated through / degrees, the quantity of heat which it
absorbs is the product of its weight, into the range of temperature, into its
specific heat. This principle is the basis of all the formulae for calculating
specific heats.
If a body is heated or cooled from t to f degrees, the heat absorbed or
disengaged will be represented by the formula
m(t' -f}c, or jn(t-f)c.
-450]
MetJiod of the Fusion of Ice.
387
= %Q P we have
450. Method of the fusion of ice. This method of determining specific
heats is based on the fact that to melt a pound of ice 80 thermal units are
necessary, or more exactly 79*25. Black's calorimeter (fig. 361) consists of
a block of ice in which a cavity is made,
and which is provided with a cover of ice.
The substance whose specific heat is to be
determined is heated to a certain tempera-
ture, and is then placed in the cavity, which
is covered. After some time the body be-
comes cooled to zero. It is then opened, and
both the substance and the cavity wiped dry
with a sponge which has been previously
weighed. The increase of weight of this
sponge obviously represents the ice which Fig 361.
has been converted into water.
Now, since one pound of ice at o in melting to water at o absorbs 80
thermal units, P pounds absorbs 80 P units. On the other hand this quan-
tity of heat is equal to the heat given out by the body in cooling from / to
zero, which is ;;//r, for it may be taken for granted that in cooling from / to
zero a body gives out as much heat as it absorbs in being heated from zero
to /. Consequently from
8oP
;///'
It is difficult to obtain blocks of ice as large and pure as those used
by Black in his experiments, and Lavoisier and Laplace replaced the block
of ice by a more complicated
apparatus which is called the
ice calorimeter. Fig. 362
gives a perspective view of it,
and fig. 363 represents a sec-
tion. It consists of three
concentric tin vessels ; in the
central one is placed the body
M, whose specific heat is to
be determined, while the two
others are filled with pounded-
ice. The ice in the com-
partment A, is melted by the
heated body, while the ice in
the compartment B cuts off
the heating influence of the
surrounding atmosphere.
The two stopcocks E and D Fig. 362. Fig. 363.
give issue to the water which
arises from the liquefaction of the ice.
In order to find the specific heat of a body by this apparatus, its weight,
;;/, is first determined ; it is then raised to a given temperature, /, by keeping
it for some time in an oil or water bath, or in a current of steam. Having
been quickly brought into the central compartment, the lids are replaced
S 2
3 88
On Heat.
[450-
and covered with ice, as represented in the figure. The water which flows
out by the stopcock D is collected. Its weight, P, is manifestly that of the
melted ice. The calculation is then made as in the preceding
case.
There are many objections to the use of this apparatus.
From its size it requires some quantity of ice, and a body, M,
of large mass ; while the experiment lasts a considerable time.
A certain weight of the melted water remains adhering to the
ice, so that the water which flows out from D does not exactly
represent the weight of the melted ice.
451. Bunsen's ice calorimeter. On the very considerable
diminution of volume which ice experiences on passing into
water (347), Bunsen has based a calorimeter which is particu-
larly suitable when only small quantities of a substance can
be used in determinations. A small test tube a (fig. 364)
intended to receive the substance experimented upon is fused
in the wider tube B. The part ab contains pure freshly
boiled-out distilled water, and the prolongation of this tube
BC, together with the capillary tube d, contains pure mercury.
This tube d is firmly fixed to the end of the tube C ; it is
|B graduated, and the value of each division of the graduation is
specially determined by calibration. When the apparatus is
immersed 'in a freezing mixture, the water in the part ab
Fig. 364. freezes. Hence, if afterwards, while the apparatus is protected
against the access of heat from without, a weighed quantity of
a substance at a given temperature is introduced into the tube, it imparts
its heat to this in sinking to zero. In doing so it melts a certain quantity
of ice, which is evidenced by a cor-
responding depression of the mercury
in the tube d. Thus the weight of
ice melted, together with the weight
and original temperature of the sub-
stance experimented upon, furnish all
the data for calculating the specific
heat.
For heating the substance in this,
and also in other calorimetrical ex-
periments, the apparatus fig. 365 is
well adapted. The cylindrical metal
vessel G is narrower at the top, and
a glass test tube R is fitted into a
cork which closes G. In this glass tube,
which is also closed by a cork K, the
substance is placed which is to be
heated. The greater part of the vessel
is covered by a thick mantle of felt, B.
The water in the vessel is boiled, the
steam emerging at d, until the substance has acquired the temperature of
boiling water, for which about twenty minutes is required. The mantle and
Fig. 365-
-453] Corrections. 389
the lamp having been taken away, the tube R is rapidly removed, and its
contents tipped into the tube d of the calorimeter (fig. 364).
For this mode of determining the specific heat a new determination of
the latent heat of ice was made, and was found to be 80-025. It was also
in connection with these experiments that Bunsen made his determination
of the specific gravity of ice, which he found to be in the mean 0*91 674.
By the above method Bunsen determined the specific heat of several of
the rare metals for which a weight of only a few grains could be used.
452. Method of mixtures. In determining the specific heat of a solid
body by this method, it is weighed and raised to a known temperature, by
keeping it, for instance, for some time in a closed place heated by steam ;
it is then immersed in a mass of cold water, the weight and temperature of
which are known. From the temperature of the water after mixture the
specific heat of the body is determined.
Let M be the weight of the body, T its temperature, c its specific heat ;
and let m be the weight of the cold water, and / its temperature.
As soon as the heated body is plunged into the water, the temperature of
the latter rises until both are at the same temperature. Let this temperature
be 9. The heated body has been copied by T - 6 ; it has, therefore, lost a
quantity of heat, M(T 6}c. The cooling water has, on the contrary, ab-
sorbed a quantity of heat equal to m (6 - /), for the specific heat of water is
unity. Now the quantity of heat given out by the body is manifestly equal
to the quantity of heat absorbed by the water; that is, M(T &]c = m(6 /),
from which
An example will illustrate the application of this formula. A piece of
iron weighing 60 ounces, and at a temperature of 100 C., is immersed in
1 80 ounces of water, whose temperature is 19 C. After the temperatures
have become uniform, that of the cooling water is found to be 22 C. What
is the specific heat of the iron ?
Here the weight of the heated body, M, is 60, the temperature, T, is 100,
c is to be determined ; the temperature of mixture, 0, is 22, the weight of
the cooling water is 180, and its temperature 19. Therefore
_ 180(22- 19) _ 9 __. ITC -
'-60(100-22) -T8- 01153 '
453. Corrections. The vessel containing the cooling water is usually
a small cylinder of silver or brass, with thin polished sides, and is supported
by some badly conducting arrangement. It is obvious that this vessel, which
is originally at the temperature of the cooling water, shares its increase of
temperature, and in accurate experiments this must be allowed for. The
decrease of temperature of the heated body is equal to the increase of
temperature of the cooling water, and of the vessel in which it is contained.
If the weight of this latter be ;', and its specific heat c', its temperature, like
that of the water, is / : consequently the previous equation becomes
M 0-1318 at 33, 0*2218 at 140, and 0-3026 at 247.
Although the specific heat increases thus rapidly between 50 and 2 50,
beyond that point the rate of increase is slower ; and beyond 600, or at an
incipient red heat, it seems to be pretty constant, or at any rate to exhibit
no greater variations with the temperature than are afforded by other sub-
stances. Thus, while at 600 the specific heat is 0-441, at 985 it is 0-459.
Graphite also has at 22 the specific heat 0-168 ; this increases, but at a
gradually diminishing rate, to 642, where its specific heat is 0-445. Like
diamond, an incipient red heat seems to be a limiting temperature beyond
which graphite exhibits only the ordinary variation with the temperature.
Weber has also found that, in their thermal deportment, there are only two
essentially different modifications of carbon the transparent one (diamond),
and the opaque ones (graphite, dense amorphous carbon, and porous amor-
phous carbon).
Crystallised boron is similar in its deportment to carbon ; its specific heat
increases from 0-1915 at 40 to 0*2382 at 27, and to 0-3663 at 233. The
rate of increase is very rapid up to 80 ; it increases beyond that temperature,
but at a gradually diminished rate, and, no doubt, tends to an almost constant
value of 0-5.
The specific heat of silicon also varies with the temperature ; between
40 and 200 it increases from 0-136 to 0-203 '> t^ e rate f increase is less
rapid with higher temperatures, being at 200 only what it is at 10. At
200 it reaches its limiting value.
The specific heat of substances is greater in the liquid than in the solid
state, as will be seen by the following table :
S3
394 On Heat. [457-
Solid Liquid
Water ....... 0-489 rooo
Bromine ....... 0-084 o-iio
Mercury ....... 0*031 0-033
Phosphorus ...... 0-190 0*202
Tin ........ 0-056 0-064
Lead ........ 0*031 0*040
It also differs with the allotropic modification ; thus the specific heat of
red phosphorus is 0*19, and that of white 0*17; of crystallised arsenic
0*083, an d of amorphous 0*058 ; of crystallised selenium 0-084, an d of
amorphous 0-0953* of wood charcoal 0*241 * of graphite 0*202; and of
diamond 0*147.
Pouillet used the specific heat of platinum for measuring high degrees of
heat. Supposing 200 ounces of platinum had been heated in a furnace, and
had then been placed in 1000 ounces of water, the temperature of which it
had raised from 13 to 20. From the formula we have M =200, m = 1000 ;
6 is 20, and /is 13. The specific heat of platinum is 0*033, an d we have,
therefore, from the equation
T = ^(-0 + M = 7000+ I3 2 = 733 = Tn o n o
M^ 6-6 6*6 "
It is found, however, that the mean specific heat of platinum at tempera-
tures up to about 1200 is 0*0377 ; if this value, therefore, be substituted for
c in the above equation, we have
7'54
By this method, which requires great skill in the experimenter, Pouillet
determined a series of high temperatures. He found, for example, the tem-
perature of melting iron to be 1500 to 1600 C.
458. Dillon? and Petit's law. A knowledge of the specific heat of
bodies has become of great importance, in consequence of Dulong and Petit's
discovery of the remarkable law, that the product of the specific heat of any
solid element into its atomic weight is approximately a constant number, as
will be seen from the following table :
Aluminium
Specific
heat
. 0-2143
O*O r; I T,
Atomic
weight
27-4
122
Atomic
heat
5*8 7
6*26
Arsenic
Bismuth .
Bromine .
. 0-0822
. 0-0308
. 0-0843
O-Oi;67
75
210
80
I 12
6-17
6-47
674
6'35
Cobalt
Copper
Gold .
Iodine
. 0-1067
0-0939
. 0-0324
0-0541
5 8*7
63-5
197
127
6*26
5'99
6*38
6*87
Iron .
. 0*1138
56
6-37
-458] Dnlong and Petit' s Law. 395
Specific Atomic Atomic
neat weight heat
Lead 0-0314 207 6-50
Magnesium .... 0-2475 2 4 5 '94
Mercury 0-0332 200 6-64
Nickel 0-1092 587 6-41
Phosphorus .... 0-1740 31*0 5-39
Platinum . . . . . 0-0524 I97'5 6-40
Potassium . . . .0-1655 39' * 6-47
Silver 0-0570 108-0 6- 1 6
Sulphur 0-178 32 570
Tin ". 0-0555 1'8 6-55
Zinc 0-0956 65-2 6-23
It will be seen that the number is not a constant, varying as it does
between 5-39 and 6-87. These variations may depend partly on the difficulty
of getting the elements in a state of perfect purity, and partly on errors in-
cidental to the determination of the specific heats, and of the atomic weights.
Again, the specific heats of bodies vary with the state of aggregation of the
bodies, and also with the temperatures at which they are determined ; some,
such as potassium, have been determined at temperatures very near their
fusing points ; others, like platinum, at temperatures much removed from
them. A main cause, therefore, of the discrepancies is doubtless to be found
in the fact that all the determinations have not been made under corre-
sponding physical conditions.
According to modern views, the heat imparted to a body is partly ex-
pended in external work, which in the case of a solid would be extremely
small, being only that required for the pressure of the atmosphere raised
through a distance representing the expansion ; secondly, the internal work,
or the heat used in overcoming the attraction of the atoms, and forcing
them apart ; and thirdly, there is the true specific heat, or the heat applied in
increasing the temperature that is, in increasing the vis viva of the molecules
(448). By far the most considerable of these is the latter ; the amount of
heat consumed in the two former operations is small, and the variations
with different bodies must be inconsiderable. Until, however, the relation
between the various factors is made out, absolute identity in the numbers
for the atomic specific heat cannot be expected. Weber holds that even
when due allowance has been made for these circumstances, the variations
are too great to be accounted for, and he considers that they point for their
explanation to an alteration in the constitution of the atom, and render
probable a changing valency of the atom of carbon.
The atomic weights of the elements represent the relative weights of equal
numbers of atoms of these bodies, and the product, /<:, of the specific heat,
c, into the atomic weight, p, is the atomic heat, or the quantity of heat
necessary to raise the temperature of the same number of atoms of different
substances by one degree ; and Dulong and Petit's law may be thus ex-
pressed : the same quantity of heat is needed to heat an atom of all simple
bodies to the same extent.
The atomic heat of a body, when divided by its specific heat, gives the
atomic weight of a body. Regnault has even proposed to use this relation
396 On Heat. [458-
as a means of determining the atomic weight, and it certainly is of great
service in deciding on the atomic weight of a body in cases where the
chemical relations permit a choice between two or more numbers.
In compound bodies the law also prevails : the product of the specific
heat into the equivalent is an almost constant number, which varies, how-
ever, with different classes of bodies. Thus, for the class of oxides of the
general formula RO, it is ii'3o; for the sesquioxides R 2 O 3 , it is 27*15;
for the sulphides RS, it is 18-88 ; and for the carbonates RCO 3 , it is 21-54.
The law, which is known as Naumanrfs /aw, may be expressed in the
following general manner : With compounds of the same formula, and of a
similar chemical constitution, the product of the atomic weight into the
specific heat is a constant quantity. This includes Dulong and Petit's law as
a particular case.
459. Specific heat of compound bodies. In order to deduce the specific
heat of the compound from that of its elements, Wcestyn has made the
following hypothesis : he assumes that an element, in entering into com-
bination with others to form a compound body, retains its own specific heat,
so that if p, p' ', p" .... represent the atomic weights of the elements, and
P that of the compound ; c, c', c", . . . . C, the corresponding specific heats,
while n, n', n", .... are the numbers of atoms of these simple bodies which
make up the molecule of the compound, the relation obtains :
The numbers obtained by calculating, on this hypothesis, the specific
heats of the sulphides, iodides, and bromides, agree with experimental
results.
460. Specific beat of gases. The specific heat of a gas may be re-
ferred either to that of water or to that of air. In the former case, it repre-
sents the quantity of heat necessary to raise a given weight of the gas through
one degree, as compared with the heat necessary to raise the same weight
of water one degree. In the latter case it represents the quantity of heat
necessary to raise a given volume of the gas through one degree, compared
with the quantity necessary for the same volume of air treated in the same
manner.
De la Roche and Berard determined the specific heats of gases in re-
ference' to water by causing known volumes of a given gas under constant
pressure, and at a given temperature, to pass through a spiral glass tube
placed in water. From the increase in temperature of this water, and from
the other data, the specific heat was determined by a calculation analogous
to that given under the method of mixtures. They also determined the
specific heats of different gases relatively to that of air, by comparing the
quantities of heat which equal volumes of a given gas, and of air at the same
pressure and temperature, imparted to equal weights of water. Subsequently
to these researches, De la Rive and Marcet applied the method of cooling to
the same determination ; and more recently Regnault made a series of in-
vestigations on the calorific capacities of gases and vapours, in which he
adopted, but with material improvements, the method of De la Roche and
Berard. He thus obtained the following results for the specific heats of the
various gases and vapours, compared first with an equal weight of water
Vapours
-460] Specific Heat of Gases. 397
taken as unity ; secondly, with that of an equal volume of air, referred, as
before, to its own weight of water taken as unity :
Specific weights
Equal Equal
weights volumes
Air 0-2374 0-2374
(Oxygen 0-2175 0-2405
Simple ] Nitrogen 0-2438 0-2370
gases 1 Hydrogen 3-4090 0-2359
I Chlorine 0-1210 0-2962
/ Binoxide of nitrogen . . . 0-2315 0-2406
I Carbonic oxide .... 0-2450 0*2370
Compound Carbonic acid .... 0-2163 0*3307
gases ~ Hydrochloric acid .... 0-1845 0-2333
I Ammonia ..... 0-5083 0*2966
\Olefiantgas 0-4040 0-4106
Water 0-4805 0-2984
Ether 0-4810 1-2296
Alcohol 0-4534 0-7171
Turpentine 0-5061 2*3776
Bisulphide of carbon . . . 0-1570 0-4140
Benzole 0-3754 1-0114
In making these determinations the gases were under a constant pressure,
but variable volume ; that is, the gas as it was heated could expand, and
this is called the specific heat under constant pressure. But if the gas when
being heated is kept at a constant volume, its pressure or elastic force then
necessarily increasing, it has a different capacity for heat ; this latter is
spoken of as the specific heat under constant volume. That this latter is less
than the former is evident from the following considerations :
Suppose a given quantity of gas to have had its temperature raised /,
while the pressure remained constant, this increase of temperature will have
been accompanied by a certain increase in volume. Supposing now that
the gas is so compressed as to restore it to its original volume, the result of
this compression will be to raise its temperature again to a certain extent,
say /'. The gas will now be in the same condition as if it had been heated
and not been allowed to expand. Hence, the same quantity of heat which
is required to raise the temperature of a given weight of gas, /, while the
pressure remains constant and the volume alters, will raise the temperature
/ -r /' degrees if it is kept at a constant volume but variable pressure. The
specific heat, therefore, of a gas at constant pressure, c, is greater than the
specific heat under constant volume, c^ and they are to each other as / + f : /,
It is not possible to determine by direct means the specific heat of gases
under constant volume with much approach to accuracy ; and it has always
been determined by some indirect method, of which the most accurate is
based on the theory of the propagation of sound (229). A critical comparison
of the most accurate recent determinations gives the number 1-405 for the
value of c .
398 On Heat. [461
461. Latent heat of fusion. Black was the first to observe that during
the passage of a body from the solid to the liquid state, a quantity of heat
disappears, so far as thermometric effects are concerned, and which is ac-
cordingly said to become latent.
In one experiment he suspended in a room at the temperature 8-5 two
thin glass flasks, one containing water at o, and 'the other the same weight
of ice at o. At the end of half an hour the temperature of the water had
risen 4, that of the ice being unchanged, and it was io hours before the
ice had melted and attained the same temperature. Now the temperature
of the room remained constant, and it must be concluded that both vessels
received the same amount of heat in the same time. Hence 21 times as
much heat was required to melt the ice and raise it to 4 as was sufficient to
raise the same weight of water through 4. So that the total quantity of
heat imparted to the ice was 21 x4 = 84 ; and as of this only 4 was used
in raising the temperature, the remainder, 80, was used in simply melting
the ice.
He also determined the latent heat by immersing 119 parts of ice at o
in 135 parts -of water at 877 C. He thus obtained 254 parts of water at
11-6 C. Taking into account the heat received by the vessel in which the
liquid was placed, he obtained the number 79*44 as the latent heat of liquidity
of ice.
We may thus say
Water at o = Ice at o + latent heat of liquefaction.
The method which Black adopted is essentially that which is now used
for the determination of latent heats of liquids ; it consists in placing the
substance under examination at a known temperature in the water (or other
liquid) of a calorimeter, the temperature of which is sufficient to melt the
substance if it is solid, and to solidify it if liquid ; and when uniformity of
temperature is established in the calorimeter, this temperature is determined.
Thus, to take a simple case, suppose it is required to determine the latent
heat of the liquidity of ice. Let M be a certain weight of ice at zero, and m
a weight of water at t sufficient to melt the ice. The ice is immersed in
the water, and as soon as it has melted the final temperature 6 is noted.
The water, in cooling from / to 0, has parted with a quantity of heat,
m(t 6}. If .r be the latent heat of the ice, it absorbs, in liquefying, a quantity
of heat, MX- ; but, besides this, the water which it forms has risen to the
temperature $, and to do so has required a quantity of heat, represented by
M#. We thus get the equation
from which the value of x is deduced.
By this method Desains and De la Provostaye found that the latent heat
of the liquefaction of ice is 79*25 ; that is, a pound of ice, in liquefying,.
absorbs the quantity of heat which would be necessary to raise 79*25 pounds
of water i, or, what is the same thing, one pound of water from zero to
79-25 (vide 451).
This method is thus essentially that of the method of mixtures ; the same
apparatus may be used, and the same precautions are required, in the two
cases. In determining the latent heat of liquidity of most solids, the differ-
461]
Latent Heat of Fusion.
399
ent specific heats of the substance in the solid and in the liquid state require
to be taken into account. In such a case, let ;;/ be the weight of the water
in the calorimeter (the water equivalents of the calorimeter and thermometer
supposed to be included) ; M the weight of the substance worked with ; / the
original and 6 the final temperature of the calorimeter ; T the original tem-
perature of the substance ; C its melting (or freezing) point ; C the specific
heat of the substance in the solid state between the temperature C and 6 ; c
its specific heat in the liquid state between the temperatures T and C ; and
let L be the latent heat sought.
If the experiment be made on a melted substance which gives out heat
to the calorimeter and is thereby solidified (it is taken for granted that a
body gives out as much heat in solidifying as it absorbs in liquefying), it is
plain that the quantity of heat absorbed by the calorimeter, m(6 - /), is made
up of three parts : first, the heat lost by the substance in cooling from its
original temperature T to the solidifying point C ; secondly, the heat given
out in solidification, L ; and, thirdly, the heat it loses in sinking from its
solidifying point C to the temperature of the water of the calorimeter.
That is
whence,
m(e -
L + 1 thermal units will be needed. Hence the total
heat which it absorbs is 8oM + 5M = 85M. On the other hand, the heat
given up by the water in cooling from 20 to 5 is 9 x (205) = 135. Con-
sequently,
85 M - 135 ; from which M = 1-588 pounds.
II. What weight of steam at 100 is necessary to raise the temperature
of 208 pounds of water from 14 to 32 ?
Let p be the weight of the steam. The latent heat of steam is 540, and
consequently^ pounds of steam in condensing into water give up a quantity
of heat, 540^, and form p pounds of water at 100. But the temperature
of the mixture is 32, and therefore p gives up a further quantity of heat
p(\oo 32) = 68/, for in this case c is unity. The 208 pounds of water in
being heated from 14 to 32 absorb 208(32 - 14) = 3744 units. Therefore
+ 68/fr - 3744 ', from which p = 6'i 58 pounds.
404
On Heat.
[465-
CHAPTER X.
STEAM ENGINES.
465. Steam engines. Steam engines are machines in which the elastic
force of aqueous vapour is used as the motive power. In the ordinary engines
the alternate expansion and condensation of steam imparts to a piston ah
alternating rectilinear motion, which is changed into a circular motion by
means of various mechanical arrangements.
Every steam engine consists essentially of two distinct parts : the ap-
paratus in which the steam is produced, and the engine proper. We shall
first describe the former.
466. Steam boiler. The boiler is the apparatus in which steam is gene-
rated. Fig. 371 represents a side view, and fig. 372 a cross section of a
Fig. 371.
cylindrical boiler, such as are used for fixed engines ; those of locomotives
and of steam vessels are very different.
-466]
Steam Boiler.
405
It is a long wrought-iron cylinder, PQ, with curved ends, beneath which
there are two smaller cylinders, BB, of the same material, and communicating
with the boiler by two tubes. Only one of these cylinders is represented in
fig. 371. They are called heaters, and are quite full of water, while the
boiler is only about half full.
In order to multiply the heating surface, and utilise all the heat carried
off by the products of combustion, the latter are made to circulate through
brick conduits which surround the sides of the heaters and of the boiler.
These conduits, which are called flues, divide the furnace.into two horizontal
compartments, FF and DCD (fig. 372). The upper compartment is more-
over divided into three distinct flues, D, C, D, by two vertical divisions
which are not represented in the drawing, and which correspond to the two
sides of the boiler. The flame and the products of combustion, which first
sweep below the heaters from back to front, return in the opposite direction
by the central flue C ; then, dividing, they pass by the lateral flues into the
chimney K, where they are lost in the atmosphere.
Explanation of Figitres 37 1 and 372.
E. Float of the safety whistle, s.
FF. Furnace.
F'. Float, to show the level of the water in the boiler. It consists of a
rectangular piece of stone partially immersed in water, as seen through the
space which is represented as left open.
This stone, which is suspended at one
end of a lever, is kept poised by the loss *
of weight which it sustains by immersion
in the water, and by a weight, a, at the
other end of the lever. As long as the
water is at the desired height, the lever
which sustains the float remains horizontal ;
but it sinks when there is too little water,
and rises in the contrary direction when
there is too much. Guided by these in-
dications, the stoker can regulate the
supply of water.
K. Chimney, which has usually a great
height, so as to increase the draught.
S. Safety valve described under Papin's
digester (373).
T. Man-hole, an aperture by which -&*
the boiler can be repaired and cleansed.
This is self-closing, and consists of a cover
fitting against the inside edges. It is kept in position by a screw, which also
presses it strongly against the sides. Thus the greater the internal pressure,
the more firmly is the cover pressed against the sides, and the more com-
pletely does it close, a. Counterpoise of the float.
m. Tube which leads the steam to the tube c of the valve chest (fig. 372)
n. Tube for the admission of feed water for the boiler.
Fig. 372-
406
On Heat.
[466-
s. Safety whistle so called because it gives a whistle when there is not
enough water in the boiler a circumstance which might produce an accident.
As long as the level of the water is not too low in the boiler, the steam does
not pass into the whistle ; but if the level sinks below a certain point, a small
float, E, which closes the bottom of the whistle sinks, and the steam escapes ;
in so doing it grazes against the edge of a thin metal plate, which it sets in
vibration, and produces a sharp and loud sound. This steam whistle is
the sound frequently heard upon railways ; it is used as a signal in locomo-
tives.
467. Double action or Watt's engine. In the double-acting steam en-
gine, the steam acts alternately above and below the piston. It is also known
as Watfs engine, from its illustrious inventor.
We shall first give a general idea of this engine, and shall then describe
each part separately. On the left of the fig. 373, is the cylinder which receives
the steam from the boiler. A part of its side is represented as being left
open, and a piston, P, can be seen, which is moved alternately up and down
by the pressure of the steam above or below the piston. By the piston rod
A this motion is transmitted to a huge iron lever, L, called the beam, which
is supported by four iron columns. The beam transmits its motion to a
-467] Double Action or Watt's Engine. 407
connecting rod, I, working on a crank, K, to which it imparts a continuous
rotatory motion. The crank is fixed to a horizontal shaft, which turns with
it, and, by means of wheels or endless bands, this shaft sets in motion various
machines, such as spinning frames, saw mills, lathes, &c.
On the left of the cylinder is a valve chest, where, by a mechanism which
will presently be described, the steam passes alternately above and below
the piston. Now, after its action on either face of the piston, it must dis-
appear, for otherwise a pressure would be exerted in two opposite directions
and the piston would remain at rest. To effect this the steam, after it has
acted on one side of the piston, passes into a vessel, O, called the condenser,
into which cold water is injected. It is almost completely condensed there,
and consequently the pressure ceases in that part of the cylinder which is
in communication with the condenser, and as there is now pressure on only
one face of the piston, it either rises or sinks.
The use of the condenser depends upon Watt's law of vapours (360),
that when two vessels communicating with each other, and containing
saturated vapour, are at different temperatures, the tension is the same
in both vessels, and is that corresponding to the temperature of the colder
vessel.
The injected water is rapidly heated by the condensation of the steam,
and must be constantly renewed. This is effected by means of two pumps ;
one M, is called the air pump, and draws, from the condenser, the heated
water which it contains, and also the air which was dissolved in the water of
the boiler, and which passes with the steam into the cylinder and condenser ;
the other, R, is called the cold -water pump, and forces cold water from a
well, or from a river, into the condenser.
A third pump, Q, which is called \hzfeed pump, utilises the heated water
by forcing it from the condenser into the boiler.
Double-acting Steam Engine.
A. Piston rod connected with a parallel motion, and serving to transmit
to the beam the upward and downward motion of the piston.
B. Rod fixed to the cylinder, or elsewhere, and supporting the guiding
arm or radius rod, C.
DDDE. Rods forming at the end of the beam a parallel motion, to which
is fixed the piston rod, and the object of which is to guide the motion of this
rod in a straight line. F. Rod of the air pump, which removes from the
condenser the air and heated water which it contains.
G. Rod of the feed pump, which forces into the boiler through the tube S
the heated water pumped from the condenser. H. Rod of the cold water
pump, which supplies the cold water necessary for condensation.
I. Connecting rod, which transmits the motion of the beam to the crank.
K. Crank, which imparts the motion of the rod to the horizontal shaft.
L. Beam, which moves on an axle in its middle, and transmits the motion
of the piston to the connecting rod I. M. Cylinder of the air pump, in
connection with the condenser O. N. Reservoir for the hot water pumped
by the air pump from the condenser. O. Condenser into which cold water
is injected to condense the steam after it has acted on the piston.
408
On Heat.
[467-
P. Metal piston, moving in a cast-iron cylinder ; this piston receives
the direct pressure of the steam, and transmits the motion to all parts of the
machine. Q. Feeding force pump, which sends the water into the boiler.
R. Cold water pump. S. Pipe by which the hot water from the feed pump
passes into the boiler. T. Pipe by which cold water from the reservoir of
the pump, R, passes into the condenser. U. Pipe by which the steam from
the cylinder passes into the condenser after acting on the piston.
V. Large iron wheel, called the_/?y wheel, which, by its inertia, serves to
regulate the motion, especially when the piston is at the top or bottom of its
course, and the crank K at its dead points. Y. Bent lever which imparts the
motion of the eccentric e to the slide valve b. Z. Eccentric rod.
a. Aperture which communicates both with the upper and lower part of
the cylinder, according to the position of the slide valve, and by which steam
passes into the condenser through the tube U. b. Rod transmitting the
motion of the slide 'valve, by which steam is alternately admitted above
and below the piston, c. Aperture by which steam reaches the valve chest.
d. Stuffing box, in which the piston rod works without giving exit to the
steam, e. Eccentric, fixed to the horizontal shaft, and rotating in a collar,
to which the rod Z is attached, m. Rod which connects the rod of the slide
valve b to the bent lever Y, and to the eccentric.
The lower part of the figure does not exactly represent the usual arrange-
ment of the pumps. The drawing has been modified in order more clearly
to show how these parts work, and their connection with each other.
374-
468. Distribution of the steam. Eccentric. Fig. 374 represents the
details of the valve chest or arrangement for the distribution of steam. The
-469] Single-acting Engine. 409
steam from the boiler passes by a pipe, c, into a cast-iron box on the side of
the cylinder. In the sides of the cylinder there are three openings or ports
u, n, and a, of which u communicates by an internal conduit with the upper
part of the cylinder, and n with the lower part. A slide, /, works over these
three orifices. It is fixed to a vertical rod, , which is jointed at ;;/ to a larger
rod, d, and receives an upward and downward motion from the bent lever
yoS, attached to the eccentric rod. When the slide is at the top of its course,
as shown in the figune, the steam passes through n into the lower part of the
cylinder, while the steam cannot pass through the orifice u, for it is covered
by the slide. But the steam which is above the piston passes through u and
through a into the hole r, from which it enters the condenser. The piston
is then only pressed upwards, and therefore ascends. When the slide is at
the bottom of its course, the steam enters the cylinder by the aperture u, and
passes from the lower part of the cylinder into the condenser by n and a.
The piston consequently descends, and this motion goes on for each dis-
placement of the slide.
The upward and downward motion of the slide is effected by means of
the eccentric. This is a circular piece, E, fixed to the horizontal shaft, A, but
in such a manner that its centre does not coincide with the axis of this shaft.
The eccentric works with gentle friction in a collar, C, to which the rod ZZ
is fixed. The collar, without rotating, follows the motion of the eccentric,
and receives an alternating motion in a horizontal direction, which it com-
municates to the lever S0y, and from thence to the slide.
469. Single-acting engine. In a single-acting engine the steam only
acts on the upper face of the piston ; a counterpoise fixed to the other end
of the beam makes the piston rise. These engines were first constructed by
Watt for pumping water from mines, and are still used for this purpose in
Cornwall, and also for the supply of water to towns. They are preferred for
these purposes from their simplicity, but for other applications they have
been superseded by the double-acting engine.
Fig. 375 represents a section. The beam B B is of wood, with wooden
segments at each end, to which chains are attached. One of these chains is
connected with the piston P, and the other with the pump Q. On the right
of the cylinder A is a valve chest, C, into which steam passes from the boiler
by the tube T. There are three valves, m, n, and o, on a vertical rod. The
valves m and o open upwards, the valve n downwards.
When m and o are open, as shown in the drawing, the steam passes
through the tube T, over the piston, while the steam which is below is forced
into the condenser through the tube M. The piston therefore descends.
The rod, on which are the valves m, n, and o, is connected with a bent lever,
dck, moving on a joint c. This bent lever closes and opens the valves. For
this purpose there are two catches, b and a, on a rod, F, connected with the
beam, by means of which the rod works against the end of the bent lever.
From the arrangement of the valves, as represented in the drawing, the piston
sinks and carries with it the rod F, and, consequently, the catch strikes
against the lever, and makes it sink at the same time as the rod dmo ; the
valves m and o then close, while n opens.
The communication with the boiler as well as with the condenser is now
cut off, and the steam which has made the piston sink, passes below by the
T
4io
On Heat.
[469-
pipe C. As it presses equally on both faces, the piston would remain at
rest, but it rises in consequence of the traction of the weight Q. Very little
force is necessary for this ; for the pump, the rod of which is fixed to the
weight Q, only requires power when its piston rises. When the piston P is
at the top of its course, the catch a strikes in turn against the lever k, raises
the rod dmo, the steam again passes to the top of the piston, which again
descends, and so on.
470. locomotives. Locomotive engines, or simply locomotives, are
steam-engines which, mounted on a carriage, propel themselves by trans-
Fig- 375-
mitting their motion to wheels. The principal parts are \heframework, the
fire box, \htcasing of the boiler, the smoke box, the steam cylinders, the driving
wheels, and \^& feed pump.
The framework is of oak, and rests on the axles of the wheels. Fig. 376
represents the driver of the locomotive in the act of opening the regulator
valve I, placed in the upper part of the steam dome. In the lower part of
this is the fire box, from whence the flame and the products of combustion
pass into the smoke box, Y, and then into the chimney Q, after having pre-
viously traversed i2$brassjire tubes which pass through the boiler. The
boiler, which connects the fire box with the smoke box, is made of iron, and
is cylindrical. It is cased with staves of mahogany, which, being a bad con-
ductor, prevents its cooling too rapidly. The steam passes from the boiler
-470] Locomotives. 4 1 1
into two cylinders, placed on either side of the smoke box. There, by
means of a steam chest similar to that already described, it acts alternately
on the two faces of the piston, the motion of which is transmitted to the
axle of the large driving wheels. This arrangement of the slide valve is not
seen in the drawing, because it is placed under the frame between the two
cylinders. After having acted on the pistons, the steam is forced through
the blast pipe E into the chimney, thus increasing the draught.
T 2
4 I2 On Heat. [470-
The motion of the pistons is transmitted to the two large driving wheels
by two connecting rods, which, by means of cranks, connect the piston
rods with the axles of the wheels. The alternating motion of the slide
valve is effected by means of eccentrics placed on the axles of the large
wheels. The feeding or supply of water to the boiler is obtained by means
of two pumps, placed under the frame, and moved by eccentrics. These
pumps suck the water from a reservoir placed on the tender, which is a
carriage attached to the locomotive for carrying the necessary water and
coal.
Explariation of Figure 376.
A. Copper tube, into which steam passes by the extremity I, and which,
dividing at the other end into two branches, conveys the steam to the two
cylinders which contain the pistons. B. Handle of the lever by which the
motion is reversed. It imparts motion to a rod, C, which communicates
with the steam chest. C. Rod by which the motion is reversed. D. Lower
part of the fire box and ash pan. E. Escape pipe for the steam after acting
on the pistons. F. Iron cylinder containing a piston, P. There is one of
these on each side of the engine, and the one in front is represented as being
left open in order that the piston may be seen.
G. Rod which opens the regulator valve I, in order to allow the steam to
pass into the tube A. In the drawing the driver holds in his hand the lever
which moves this rod. H. Cock for blowing off water from the boiler.
I. Regulator valve, which is opened and closed by hand, so as to regulate
the quantity of steam passing into the cylinders.
K. Large rod connecting the head of the piston rod with the crank M of
the driving wheel. L. Lamp. M. Crank, which transmits the motion of
the piston to the axle of the large wheel. N. Coupling iron, by which the
tender is attached. O. Fire door. P. Metallic piston, the rod of which is
connected with the rod K. Q. Chimney. R, R. Feed pipes, through which
the water in the tender passes to two force pumps, which are not shown in
the drawing. S. Guard for removing obstructions on the rails. T, T.
Springs on which the engine rests. U, U. Iron rails fixed in chairs on wooden
sleepers. V. Frame of the stuffing box of the cylinder. X, X. Cylindrical
boiler, covered with mahogany staves, which, from their bad conductivity,
hinder the loss of heat. The level of the water is just below the tube A.
In the water are the tubes #, through which the smoke and flames pass
into the smoke box. Y. Smoke box in which the fire tubes a terminate.
Z, Z. Fire box, with dome, into which the steam passes.
a. Brass tubes, of which there are 125, open at both ends, and terminating
at one end in the fire box, and at the other in the smoke box. . These tubes
transmit to the water the heat of the fire.
bb. Toothed segment, placed on the side of the fire box, and in which
the arm of the lever B works. When the handle is pushed forward or pulled
back as far as it can go, the engine is in full forward or backward gear re-
spectively ; the intermediate teeth give various rates of expansion in back-
ward and forward motion, the middle tooth being a dead point, e. Cases
containing springs by which the safety valves i are regulated, g. Signal
whistle, i. Safety valves, m, m. Steps, n. Glass tube, showing the height
-472]
Reaction Mac/lines. Eolipyle.
413
of water in the boiler. ?, r. Guiding rods, for keeping the motion of the
pistons in a straight line. /, /. Blowing-off taps, for use when the pistons
are in motion. i>. Rod by which motion is transmitted to these taps.
471. Reaction machines. Eolipyle. In reaction machines steam acts
by a reactive force like water in a hydraulic tourniquet (217). The idea of
these machines is by no means new ; Hero of Alexandria, who invented the
fountain which bears his name, described the apparatus which is represented
in fig. 377, known as the reaction machine.
It consists of a hollow metal sphere which rotates on two pivots. At
the ends of a diameter are two tubulures, pierced laterally in opposite
directions by ori-
fices through which
vapour escapes.
Water is introduced
into this apparatus
by heating it, and
then allowing it to
cool in cold water.
If the apparatus be
then heated to boil-
ing, the vapour dis-
engaged imparts to
it a rotatory motion,
which is due to the
pressure of the va-
pour on the side
opposite to that
from which it es-
Fig. 377-
ISumerous at-
tempts have been made to use this reactive force of the vapour on a large
scale as a motive force, and endeavours have also been made to cause
steam to act by impulse by directing a jet of steam on the float board of
a paddle-wheel ; but in both cases the steam exerts by no means so great
an effect as is obtained when it acts by expansion on a piston.
472. Various kinds of steam engines. A low-pressure engine is one in
which the pressure of the vapour does not much exceed an atmosphere ; and
a high-pressure engine is one in which the pressure of the steam usually
exceeds this amount considerably. Low-pressure engines . are mostly con-
densing engines ; in other words, they generally have a condenser where the
steam becomes condensed after having acted on the piston ; on the other
hand, high-pressure engines are frequently without a condenser ; the loco-
motive is an example.
If the communication between the cylinder and boiler remains open
during the whole motion of the piston, the steam retains essentially the same
elastic force, and is said to act without expansion ; but if, by a suitable
arrangement of the slide valve, the steam ceases to pass into the cylinder
when the piston is at \ or f of its course, then the vapour expands ; that is
to say, in virtue of its elastic force, which is due to the high temperature, it
On Heat. [472-
still acts on the piston and causes it to finish its course. Hence a distinction
is made between expanding and non-expanding engines.
473. Work of an engine. Horse-power. The work of an engine is
measured in practice by the
Mean pressure on piston x area of piston x length of stroke.
In England the unit of work is the foot-pound '; that is, the work performed
in raising a weight of one pound through a height of a foot. Thus, to raise
a weight of 14 pounds through a height of 20 feet would require 280 foot-
pounds. On the Continent the kilogrammetre is used ; that is, the work
performed in raising a kilogramme through a metre. This unit corresponds
to 7*233 foot-pounds.
The rate of work in machines is the amount of work performed in a given
time ; a second or an hour, for example. In England the rates of work are
compared by means of horse-power, which is a conventional unit, and repre-
sents 550 foot-pounds in a second. In France a similar unit is used called
the cheval vapeur, which represents the work performed in raising 75 kilo-
grammes through one metre in a second. It is equal to about 542 foot-
pounds per second. Suppose, for instance, that a steam-engine works under
a pressure of i| atmospheres, the pressure in the condenser being f an at-
mosphere. If the area of the piston is 50 square inches, the length of the
stroke 2 1 inches, and the number of up and down strokes 60 in a minute ;
then, taking an atmosphere as representing 14 pounds on a square inch,
we shall have 14 x 50 x 175 x 120= 147,000 foot-pounds in a minute.
The useful effect of a machine is only about o - 5 to 07 of the theoretical
effect as thus calculated, the rest is consumed in the unavoidable friction
of the machine, in working the pumps, &c. If in our case we allow ~ for
this loss we shall have 88,200 foot-pounds in a minute as the available useful
effect = 1, 470 foot-pounds in a second, or nearly 2| horse-power. If the work
of a steam-engine be calculated from the heat known to be produced from
a given weight of fuel (484), the discrepancy is far greater. The best Cornish
engines do not give more than 14 per cent, of the theoretical yield of the
combustible.
474. Kirn's experiments. Hirn made an important series of experiments
in order to determine the mechanical equivalent of heat by means of the
steam-engine (497). On the one hand, steam of known temperature and
pressure was allowed to act upon the steam-engine, which was one of 100
horse-power. The amount of heat contained in the steam could be readily
calculated. The amount of work which the engine performed was also de-
termined by means of a dynamometer. The steam was ultimately condensed
in the condenser, and the amount of heat produced there could readily be
measured by known calorimetrical methods. It was found in all cases to be
less than that which originally passed into the engine, and the difference re-
presented the amount of heat \\hich had been converted into work in the
engine ; in Hirn's experiments, for every unit of heat which had disappeared,
1,354 units of work had been performed a result, considering the difficulty
of the experiments, closely agreeing with the best determinations (497).
475. Hot air and gras engines. Numerous attempts have been made
to replace the expansive force of steam by that of heated air. Yet they
-476]
TJiermomotive Wheel.
415
have hitherto not been completely successful, owing to practical difficulties ;
for either the temperature had to be so high that it was impossible to keep
the valves and the stuffing-boxes tight, or else it was necessary greatly to
increase the dimensions of the cylinder, in comparison with those of steam-
engines of the same power.
In some forms of gas-engines a mixture of coal gas and of atmospheric
air contained in a cylinder is ignited by the electrical spark, and the
expansive force of the heated gas thus produced moves the piston. As the
combustion of the gaseous mixture takes place within the cylinder itself,
the loss of heat is the smallest. They have, moreover, the advantage of
requiring no special fire, but can be set up and worked in any space pro-
vided with gas. Yet these engines have hitherto only succeeded on a small
scale.
It is shown by mathematical analysis that the greatest theoretical effi-
ciency of any heat-engine may be expressed by the formula
t,
Q
where q is the quantity of heat actually utilised, and Q that brought into play,
while T and Tj are the temperatures of the source and of the condenser,
these temperatures being what are called absohtte. It will thus be seen that
it is desirable to extend the limit between the two temperatures ; and it is
probably in the extension of the use of superheated steam that most pro-
gress in the perfectionment of steam-engines is to be anticipated. This
behaves as a gas, and has not the disadvantage of oxidising the metals.
476. Thermomotive wheel. This is an interesting example of the con-
version of heat into motion. It consists (fig. 378) of a series of tubes aa, bb,
cc, bent at the ends, on
which bulbs are blown,
which are covered with
muslin. The bulbs
themselves contain
ether. The tubes pass
through a nave, which
has an axis d, resting
on a support on the
top of a reservoir e
containing water. All
the bulbs having been
wetted, three of them
will be in the air and
the others in water.
From those in air the
water in the muslin will
evaporate, and the ether inside will condense, and fresh vapour be formed
from the immersed bulb. This will continue to collect and condense
in the upper bulb, which will sink, and the other bulb rise, and so on with
the other tubes, and this continues with such regularity that Bernardi, the
inventor, has been able to drive a small clock by its means.
Fig- 378.
4 i 6 On Heat. [477-
CHAPTER XI.
SOURCES OF HEAT AND COLD.
477. Different sources of heat. The following different sources of heat
may be distinguished : i. the mechanical sources, comprising friction, percus-
sion, and pressure ; ii. the physical sources that is, solar radiation, terres-
trial heat, molecular actions, changes of condition, and electricity ; iii. the
chemical sources^ or molecular combinations, and more especially combus-
tion.
In what follows it will be S9en that heat may be produced by reversing
its effects ; as, for instance, when a liquid is solidified or a gas compressed
(479) ; though it does not necessarily follow that in all cases the reversal of
its effects causes heat to be produced instead 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.
478. 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 26| pounds
of water from zero to 100, which represents 2,650 thermal units (447). .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 10 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.
The luminosity of aerolites is considered to be due to their friction against
-479] Heat due to Pressure and Percussion. 417
the air, and to their condensation of the air in front of them (479), their
velocity attaining as much as 1 50 miles in a second.
Tyndall has devised an experiment by which the great heat developed by
friction is illustrated in a striking manner. A brass tube (fig. 379), about
7 inches in length and \ of "an inch in diameter, is fixed on a small wheel.
By means of a cord passing round a much larger wheeJ, this tube can be
rotated with any desired velocity. The tube is three parts full of water, and
is closed by a cork. In making the experiment, the tube 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.
479. Heat due to pressure and percussion. If a body be so com-
pressed that its density is increased, its temperature rises according as the
Fig- 379-
volume diminishes. Joule has verified this in the case of water an'd 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 metallic pillars, heat is evolved, and
absorbed when they are removed. So in like manner the stretching of a
metallic wire is attended with a diminution of temperature.
The production of heat by the compression of gases is easily shown by
means of the pneumatic syringe (fig. 380). 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 witk
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 inflammation of the cotton in this experiment
indicates a temperature of at least 300.
A curious application of the pneumatic syringe is met with in the American
4 i 8 On Heat. [479-
poivder 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, condenses the air, producing so much heat that the powder is ex-
ploded. The force of the gases projects the rammer into its original posi-
tion 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.
The elevation of temperature produced by the compression in the above
experiment is sufficient to effect the combination, and therefore the detona-
tion, of a mixture of hydrogen and oxygen.
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 has 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. The heat is not simply due to an approximation of the molecules
that is, to an increase in density but arises from a vibratory motion im-
parted to them ; for lead, which does not increase in density by hammering,
nevertheless becomes heated.
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 vis viva is converted into heat. This holds equally whatever be the
cause to which the motion is due : whether it be that acquired by a 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 vis viva of any moving body
mv
is expressed by or in foot-pounds
, where p is
the weight in
pounds, v 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 . ^ . Suppose, for instance, a lead ball weighing a pound be fired
2-x 1390
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
= 40,000 foot-pounds. Some of this will have
its vis viva will be
2x32
-480] Solar Radiation. 419
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
and the target, then, since 40,000 foot-pounds is the equivalent of 287
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
i xo-o3i4x/= 14-3 or / = 457,
which is a temperature considerably above that of the melting point of lead
(338).
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 has 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.
480, Solar radiation. The most intense of all sources of heat is the sun.
Different attempts have been made to determine the quantity of heat which
it emits. Pouillet, from experiments made by means of an apparatus which
he calls a pyroheliometcr, calculated 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. The heat emitted by the sun is equal to that pro-
duced 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
solar radiation, and from the distance which separates the earth from the
sun, the quantity of heat which the earth receives can only be 1|38I| J UO|000 of the
heat emitted by the sun.
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 a 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 meteoric stone
r>r 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
420 On Heat. [480-
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 Sir W.
Thomson has proved that a fall of 0-3 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 observations.
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 of
degrees Centigrade ; and a contraction of ^Q~ of its mass would be sufficient
to supply the heat radiated by the sun in 2,000 years. This amount of con-
traction could not be detected even by the most refined astronomical
methods.
481. Terrestrial beat. Our globe possesses a heat peculiar to it, which
is called the terrestrial heat. The variations of temperature which occur at
the surface gradually penetrate to a certain depth, at which their influence
becomes too slight to be sensible. It is hence concluded that the solar heat
does not penetrate below a certain internal layer, which is called the layer of
constant temperature : its depth below the earth's external surface varies, of
course, in different parts of the globe ; at Paris it is about 30 yards, and the
temperature is constant at ir8 C.
Below the layer of constant temperature, the temperature is observed to
increase, on the average, i C. for every 90 feet. The most rapid increase
is at Irkutsk in Siberia, where it is i for 20 feet, and the slowest in the mines
at Mansfield, where it is about i 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 temperature of a corresponding layer would be 100, 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 thickness of this crust is not believed to be more than 40 to 50
miles, and the interior is probably still in a liquid state. The cooling must
be very slow, in consequence of the imperfect conductivity of the crust. For
the same reason the central heat does not appear to raise the temperature
of the surface more than ^ of a degree.
482. Heat produced by absorption and Imbibition. Molecular phe-
nomena, such as imbibition, absorption, capillary actions, are usually accom-
panied by disengagement of heat. Pouillet found that whenever a liquid is
poured on a finely-divided solid, an increase of temperature is produced
which varies with the nature of the substances. With inorganic substances,
such as metals, the oxides, the earths, the increase is T 4 5 of a degree ; but
with organic substances, such as sponge, flour, starch, roots, dried mem-
branes, the increase varies from I to 10 degrees.
-483]
Chemical Combination. Combustion.
421
The absorption of gases by solid bodies presents the same phenomena.
Diibereiner 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 intense combustions.
Spongy platinum produces the same effect. A jet
of hydrogen directed on it takes fire.
The apparatus known as Dobereiner's Lamp
depends on this property of finely -divided platinum.
It consists of two glass vessels (fig. 381). 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 gene-
rated, 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. On a copper tube,
H, fixed in the side of the vessel B, there is a small
cone, #, 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
increase 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 has 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
protoxide of nitrogen, 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 solidifi-
cation 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 due to that
produced by the liquefaction of the gas, and to the heat due to the imbibition
in the charcoal of the liquid so produced.
The heat produced by the changes of condition has been already treated
of in the articles Solidification and Liquefaction ; the heat produced by elec-
trical action will be discussed under the head of Electi icity.
Fig. 381.
CHEMICAL SOURCES.
483. Chemical combination. Combustion. Chemical combinations
are usually accompanied by a certain elevation of temperature. When these
combinations take place slowly, as when iron oxidises in the air, the heat
produced is imperceptible ; but if they take place rapidly, the disengagement
422 On Heat. [483-
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 of light
and heat. In ordinary combustion in lamps, fires, candles, the carbon and
hydrogen of the coal, or of the oil, &c., combine with 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 flame
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, have a 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 arrangement 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, gives the greatest heat.
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 likened by
Tyndall to the action of meteorites which fall into the sun.
484. Heat disengaged during- combustion. Many physicists, more
especially Lavoisier, Rumford, Dulong, Despretz, Hess, Favre and Silber-
mann and Andrews, have investigated the quantity of heat disengaged by
various bodies in chemical combinations.
In these experiments Lavoisier used the ice calorimeter already described.
Rumford used a calorimeter known by his name, which consists of a rect-
angular copper canister filled with water. In this 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 its temperature the quantity
of heat evolved is calculated. Despretz and Dulong successively modified
Rumford's calorimeter by allowing the combustion to take place, not
-485] Animal Heat. 423
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 serpentine form in the mass of the
liquid to be heated. Favre and Silbermann have improved this calorimeter
very greatly (463), not only by avoiding or taking account of all possible
sources of error, but by arranging it for the determination of the heat evolved
in other chemical actions than those of ordinary combustion.
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 one degree Centigrade, the follow-
ing table gives the thermal units in round numbers disengaged by a pound
of each of the substances in burning in oxygen :
Hydrogen .... 34462 Diamond .... 7770
Marsh gas .... 13063 Absolute alcohol . . .7180
Olefiant gas .... 11858 Coke 7000
Oil of turpentine . . . 10852 Phosphorus .... 5750
Olive oil .... 9860 Wood, dry .... 4025
Ether 9030 Bisulphide of carbon . . 3401
Anthracite .... 8460 Wood, moist. . . .3100
Charcoal .... 8080 Carbonic oxide . . . 2400
Coal 8000 Sulphur .... 2220
Tallow 8000 Iron 1576
Bunsen's calorimeter (451) has been used for studying the heat produced
in chemical reactions for cases in which only very small quantities are
available.
The experiments of Dulong, of Despretz, and of Hess prove that a body
in burning always produces the same quantity of heat in reaching the same
degree of oxidation, whether it attains this at once or only reaches it after
passing through intermediate stages. Thus a given weight of carbon gives
out the same amount of heat in burning directly to carbonic acid as if it
were first changed into carbonic oxide, and then this were burnt into carbonic
acid.
485. Animal heat. In all the organs of the human body, as well as
those of all animals, processes of oxidation are continually going on. Oxygen
passes through the lungs into the blood, and so into all parts of the body. In
like manner the oxidisible 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, &c. Oxidation in the muscle produces motions of the
molecules, which are changed into contraction of the muscular fibres ; aH
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 muscle and of the sinews in their sheaths,
and of the bones in their sockets. Hence the heat produced by the body
424 On Heat. [485-
when at work is greater than when at rest. The blood distributes heat
uniformly through the body, which in a normal condition has a temperature
of 37'5- The blood of mammalia has the same temperature, that of birds is
somewhat higher. In fever the temperature rises to 42-44, and in cholera,
or when near death, sinks to 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 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 oxida-
tion of nitrogenous matter ; moreover, the organism while at rest produces
less carbonic acid, and requires less oxygen than when it is at work j 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 also ascribed to
the oxidation of organic matter.
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 re-
appears during the combustion of wood or of the coal arising from its de-
composition.
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 appreci-
able increase of temperature.
HEATING.
486. Different kinds of heating-. Heating 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.
We may distinguish five kinds of heating, according to the apparatus
used : ist, heating with an open fire ; 2nd, heating with an enclosed fire, as
with a stove ; 3rd, heating by hot air ; 4th, heating by steam ; 5th, heating
by the circulation of hot water.
487. Fire-places. Fire-places are open hearths built against a wall
under a chimney, through which the products of combustion escape.
However much they may be improved, fire-places 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 temperature 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 'fire-places should be adopted in cases where the smallest
quantity of heat was to be obtained from a given quantity of fuel.' Not-
-488] Draught of Fire-places. 425
withstanding 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.
488. Draught of fire-places __ The
draught of a fire is the upward current in the
chimney caused by the ascent of the pro-
ducts 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
substances 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. 383, 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 determined theoreti-
cally by the formula
Fig. 382.
in which g is the acceleration of gravity, a the coefficient of the expansion
of air, h the height of the chimney, f the mean temperature of the air in-
side 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, the flame will be turned from the room towards 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
conditions :
i. The section of the chimney ought not to be larger than is necessary to
allow an exit for the products of combustion ; otherwise ascending and de-
scending currents are produced in the chimney, which cause it to smoke. It
is advantageous to place on the 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.
426 On Heat. [488-
iii. The external air ought to pass into the chamber with sufficient rapidity
to supply the wants of the fire. In an hermetically-closed room the com-
bustibles 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
the space between them containing air.
489. Stoves. Stoves are apparatuses for heating with a detached fire,
placed in the room to be heated, so that the 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 fire-places,
for the ventilation is very bad, more especially where, as in Sweden and in
Germany, the stoves are fed from the outside of the room. These stoves
also emit a bad smell, probably arising from the decomposition of organic
substances 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, heat more slowly, but more pleasantly, and they retain the
heat longer.
490. Heating: by steam. Steam, in condensing, gives up its latent heat
of vaporisation, and this property has been used in heating baths, workshops,
public buildings, hothouses, &c. For this purpose steam is generated in
boilers similar to those used for steam-engines, and is then made to circulate
in pipes placed in the room to be heated. The steam condenses, and in
doing so imparts to the pipes its latent heat, which becomes free, and thus
heats the surrounding air.
491. Heating: by not air. Heating by hot air consists in heating the
air in the lower part of a building, from whence it rises to the higher parts
in virtue of its lessened density. The apparatus is arranged as represented
in fig. 383.
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
chimney. These apparatuses are more economical than open fire-places, but
they are less healthy, unless special provision is made for ventilation.
493]
Various Sources of Cold.
427
492. 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.
Figure 384 represents an
apparatus for heating a
building of several stories.
The heating apparatus,
which is in the basement,
consists of a bell -shaped
boiler, o o, with an internal
flue, F. A long pipe, M, fits
in the upper part of the
boiler, and also in the reser-
voir Q, placed in the upper
part of the building to be
heated. At the top of this
reservoir there is a safety
valve, j, by which the pres-
sure of the vapour in the
interior can be regulated. F i g . 3 g 3>
The boiler, the pipe M,
and a portion of the reservoir Q, being filled with water, as it becomes
heated in the boiler, an ascending 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 , d, /, filled with
water. The water from these passes again through pipes into other re-
ceivers, a, c, e, 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
increase of temperature to 3,200 cubic feet of air (460). In the interior of the
receivers, #, , $ and S be the areas
of the two screens. If
a be the total quantity of
light which is emitted by
the source in the direc-
tion of the cone ALB,
the intensity of the light
Fig. 397 . on the screen CD that
is, the quantity which
falls on the unit of surface is *, and the intensity on the screen AB is a .
Now, as the triangles ALB and CLD are similar, the diameter of AB is
-509] Photometers. 445
double that of CD ; and as the surfaces of circles are as the squares of their
diameters, the surface S is four times j, consequently the intensity is one-
o
fourth that of f .
s
The same law may also be demonstrated by an experiment with the
apparatus represented in fig. 399. It is made by comparing the shadows
of an opaque rod cast upon a glass plate, in one case by the light of a single
candle, and in another by that of a lamp equalling four candles, placed at
double the distance of the first. In both cases the shadows have the same
intensity.
Figure 397 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, at any rate in a
vacuum, for in air and in other transparent media the intensity of light de-
creases in consequence of absorption, but far more slowly 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. 398) be a pencil of parallel
rays falling obliquely on a surface,
AB, and let om be the normal to
this surface. If S is the section
of the pencil, a the total quan-
tity of light which falls on the
surface AB, and I that which falls
on the unit of surface that is, the
intensity of illumination we have
I = ^. But as S is only the projection of AB on a plane perpendicular to
the pencil, we know from trigonometry that S=AB cos a, from which
AB _ This value, substituted in the above equation, gives I = "
cos a ; 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 in-
clined to the surface which emits them. In this respect they correspond to
the third law of the intensity of radiant heat.
509. Photometers. A photometer is an apparatus for measuring the
relative intensities of different sources of light.
Rumfords pJiotomcter. This consists of aground glass screen, in front
of which is fixed an opaque rod (fig. 399) ; 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. The
shadows 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
446
On Light.
[509-
illuminated by the candle, and that thrown by the candle is illuminated
by the lamp, the illumination 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 distances are then directly proportional to the squares
of their distances from the shadows ; that is to say, that if the lamp is three
Fig. 399-
times the distance of the candle, its illuminating power is nine times as
great.
For if i and i' are the intensities of the lamp and the candle at the unit
of distance, and d and d' 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 candle 4,7, at the distanced. On the screen
d~ d *
these two intensities are equal ; hence 4* = -fo or -.,- = > which was to be
d" a'~ i a*
proved.
Bunserts 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
Fig. 400.
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 in-
tensity of illumination on both sides is the same. Bunsen's photometer
depends on an application of this principle. Its essential features are re-
presented in fig. 400. A circular spot is made on a paper screen by means
-510] Relative Intensities of Various Sources of Light. 447
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 is a sperm
candle of six to the pound, and burning 120 grains in an hour. The light to
be tested, a petroleum lamp or a gas burner consuming a certain volume 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 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.
By this kind of determination the 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 different 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 illuminating power of coal gas and of other
artificial lights.
WheatstonJs photometer. The principal part of this instrument is a
steel bead, P (fig. 401), fixed on the edge of a disc, which rotates on a
pinion, o, working in a larger toothed F
wheel. The wheel fits in a cylin-
drical brass box, which is held in one
hand, while the other works a handle, '^^^M iff
A, which turns a central axis, the
motion of which is transmitted by a
spoke, a, to the pinion o. In this
way the latter turns on itself, and
, . , j , rig. 401. rig. 402.
at the same time revolves round the
circumference of the box ; the bead shares the double motion, and con-
sequently describes a curve in the form of a rose (fig. 402).
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 bead give rise to two luminous bands, arranged as represented in
fig. 402. 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.
5 10. 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 5,000
million times as bright as Jupiter, and 80 billion times as bright as Neptune.
Its light is estimated to be equal to that of 5,500 wax candles at a distance of
i foot. According to Fizeau and Foucault the electric light produced by 50
Bunsen's cells is about \ as strong as sunlight.
A difference in the strength of light or shadow is perceived when the
duller light is -|j of the brightness of the other, and both are near together,
especially when the shadow is moved about.
448
On Light.
[511-
CHAPTER II.
REFLECTION OF LIGHT. MIRRORS.
511. Xiaws of the reflection of light. When a luminous ray meets a
polished surface, it is reflected according to the following two laws, which,
as we have seen, also prevail for heat :
I. The angle of reflection is equal to the angle of incidence.
II. The incident and the reflected ray are both in the same plane, ivhicli
is perpendicular to the reflecting surface.
The words are here used in the same sense as in article 411, and need
no further explanation.
First proof. The two laws may be demonstrated by the apparatus
represented in fig. 403. 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, ;;z, placed
horizontally in the centre of the circle.
In making the experiment, a pencil
of solar light, S, is caused to impinge
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 m. The luminous
pencil then experiences a second re-
flection in a direction ;P, which is
ascertained by moving P until an
image of the aperture is found in its centre. The number of degrees com-
prised in the arc AN is then read off, and likewise that in AP ; these being
equal, it follows that the angle of reflection AwP is equal to the angle of
incidence AmM.
The second law follows from the arrangement of the apparatus, the plane
of the rays Mm and mP being parallel to the plane of the graduated circle,
and, consequently, perpendicular to the mirror m.
-513] Formation of Images by Plane Mirrors. 449
Second proof . The law of the reflection of light may also be demon-
strated by the following experiment, which is susceptible of greater accuracy
than that just described : In the centre of a graduated circle, M (fig. 404),
placed in a vertical position, there is a small telescope movable in a plane
parallel to the limb ; at a 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 direction
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.
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.
512. Mirrors. Images. Mirrors are bodies with polished surfaces,
which show by reflection objects presented to them. The place at which
objects appear is their image. According to their shape, mirrors are divided
into plane, concave, convex, spherical, parabolic, conical, &c.
513. Formation of image* 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 before
a plane mirror. MN (fig. 405), will be considered. Any 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.
If, now, a perpendicular, AN, be let fall from the point A on the mirror,
450 On Light. [513-
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 EN a, which are
equal, for they have the side BN common to both, and the angles ANB,
ABN, equal to the angles rCT : : therefore CL x LM = CL x /M. \
If the arc AM does not exceed 5 or 6 degrees, the lines ML and M/ are
approximately equal to AL and A/ ;
that is, to/ and/'.
Further, C/=CA-A/=R-/',
and also CL = AL-AC=/-R.
The values substituted in the
preceding equations give
(R
From which transposing and reducing we have
' = 2//' '. (i)
If the terms of this equation be all divided by//'R, we obtain
= K ' ' ' "
which is the usual form of the equation.
From the equation (i) we get
/'--^- (3)
. 2/-R U;
which gives the distance of the image from the mirror, in terms of the
distance of the object, and of the radius of curvature.
531: Discussion of the formulae for mirrors. We shall now in-
vestigate the different values of /', according to the values of p in the
formula (3).
i. Let the object be placed at an infinite distance on the axis, in which
case the incident rays are parallel. To obtain the value of/', both terms of
the fraction (3) must be divided by /, which gives
'- K
,-* .... (4)
p TD
as p is infinite, --is zero, and we have/' = ; that is, the image is formed
in the principal focus, as ought to be the case, for the incident rays are
parallel to the axis.
ii. If the object approaches the mirror, p decreases, and as the denomi-
nator of the formula (4) diminishes, the value of/ 7 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
p is > R, we have ^ > ?and < R.
2-5 2
p
iii. When the object coincides with the centre, p = R, and, consequently,
p' = R ; that is, the image coincides with the object.
iv. When the luminous object is between the centre and the principal
-533] Spherical Aberration. Caustics. 463
focus, /R; that is, the image is
formed on the other side of the centre. When the object is in the focus,
p ID
p = v which gives/'-- -= ; 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
D
get p <[ ; p' is then negative, because the denominator of the formula (4)
is negative. Therefore, the distance p' 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.
Making/' negative in the formula (2), it becomes I . 1 - = 3.- in this
P P R
form it comprehends all cases of virtual images in concave mirrors.
In the case of concave mirrors, the image is always virtual (525) ; /' 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
P'
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.
It must be observed that the preceding formulae are not rigorously true,
inasmuch as they depend upon the assumption that the lines LM and /M
(fig. 423) 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.
532. Calculation of the magnitude of images. By means of the above
formulas 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. 424), bd its
image, and if the distance
A and the radius AC be
known, A0 can be calculated
by means of formula (3) of
article 530. A0 known, oC *i g . 424 .
can be calculated. But as
the triangles BCD and dCb are similar, their bases and heights are in thfe
proportion bd : BD =C0 : CK, or
Length of the image : length of the object
= Distance from image to centre : distance from the object to the centre.
533. spherical aberration. Caustic*. In the foregoing theory of the
foci and images, of spherical mirrors, it has already been observed that the
464 On Light. [533-
reflected rays only pass through a single point when the aperture of the
mirror does not exceed 8 or 10 degrees (531). 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 neighbourhood of the centre of
the mirror. Hence arises a want of precision in these images, which is called
spherical aberration by reflection, to distinguish it from the spherical aber-
ration by refraction, which occurs in the'case of lenses.
Every reflected ray cuts the one next to it (fig. 425), and their points of
intersection form in space a curved surface, which is called the caustic by
reflection. The curve FM repre-
sents one of the branches of a
section of this surface made by the
plane of the paper. When the
light of a candle is reflected from
the inside of a cup or tumbler, a
section of the caustic surface can
be seen by partly filling the cup or
tumbler with milk.
534. Applications of Mirrors. Beliostat. 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. The
solar light can only be sent in a constant direction by making the mirror
moveable. 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. This apparatus is called the heliostat. We have already seen an
application of this in the heliograph (523). The reflection of light is also
used to measure the angles of crystals by means of the instruments known
as reflecting goniometers.
Concave spherical mirrors are also often used. They are applied for
magnifying mirrors, as in a shaving mirror. They have been employed for
burning mirrors, and are still used in
telescopes. They also serve as reflec-
tors, for conveying light to great dis-
tances, by placing a luminous object
in their principal focus. For this
purpose, however, parabolic mirrors
are preferable.
While the images of objects seen
in concave or convex mirrors appear
smaller or larger, but otherwise similar
geometrically, this is not the case with
cylindrical or with conical mirrors.
Objects seen in such mirrors appear
ludicrously distorted. From the laws of reflection the shape of such a
distorted figure can be geometrically constructed. In like manner distorted
images of objects can be constructed which, seen in such mirrors, appear
in their normal proportions. ' They are called anamorphoses.
-535] Parabolic Mirrors. 465
535. Parabolic mirrors. Parabolic mirrors are concave mirrors, whose
surface is generated by the revolution of the arc of a parabola, AM, about
its axis, AX (fig. 426).
It has been already stated that in spherical mirrors the rays parallel to
the axis converge only approximately 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 re-
flectors. It is a property of a parabola 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 tangent TT' at this point. Hence all
rays parallel to the axis after reflection meet in
the focus of the mirror F ; and conversely, when
a 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 (508) that it is the
divergence of the luminous rays which princi-
pally 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
through the focus, and are then united at their
intersections as shown in figure 427, so that
their foci coincide, a system of reflectors is obtained with which a single
lamp illuminates in two directions at once. This arrangement is used in
lighting staircases and passages.
*3
466 On Light. [536-
CHAPTER III.
SINGLE REFRACTION. LENSES.
536. Phenomenon of refraction. Refraction is the deflection or bending 1
which luminous rays experience in passing obliquely from one medium to
another : for instance, from air into water. We say obliquely, because if the
incident ray is perpendicular to the surface separating the two media, it is
not bent, and continues its course in a right line.
The incident ray being represented by SO (fig. 428), the refracted ray is
the direction OH which light takes in the second medium ; and of the angles
SOA and HOB, which these rays form with the line AB, at right angles to
the surface which separates the two media, the first'
is the angle of incidence, and the other the angle of
refraction. According as the refracted ray ap-
proaches 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 a refracting surface
does not completely pass into it ; one part is re-
Fig. 4 2b. fleeted and scattered (518), 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 least.
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 single refraction.
537. Itaws 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 line of
the incident angle bears to the sine of the angle of refraction is constant for
the same two media, but varies with different media.
II. The incident and the refracted ray are in the same plane, which is
perpendicular to the surface separating the two media.
These have been known as Descartes' laws ; they are, however, really
due to Willibrod Snell, who discovered them in 1620 ; they are demon-
strated by the same apparatus as that used for the laws of reflection (gn).
The plane mirror in the centre of the graduated circle is replaced by a
-639]
Effects produced by Refraction.
467
semi-cylindrical glass vessel, filled with water to such a height that its
level is exactly the height of the centre (fig. 429). 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 then its direction is at right angles to the curved sides of the
vessel. In order to observe the course
of the refracted ray, it is received on a
screen, P, which is moved until the
image of the aperture in the screen N
is formed in 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, moveable so as to be always hori-
zontal, and hence perpendicular to the
diameter AD.
On reading off the length of 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 refrac-
tion 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 graduated limb is perpendicular to the surface
of the liquid in the semi-cylindrical vessel.
538. Index of refraction. The ratio between the sines of the incident
and refracted angle is called index of refraction or refractive index. It
varies with the media ; for example, from air to water it is f, and from air to
glass it is f.
If the media is 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 in a
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
4, and from glass to air f.
539. 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. 430) 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 intersect approximately in the point L',
placed on the perpendicular L'K. The eye receiving these rays sees the
object L at L'. The greater the obliquity of the rays LA, LB . . . the higher
the object appears.
It is for the same reason that a stick plunged obliquely into water appears
bent (fig. 431), the immersed part appearing raised.
Fig. 429
4 68
On Light.
[539-
Owing to an effect of refraction, stars are visible to us even when they are
below the horizon. For as the layers of the atmosphere are denser in pro-
portion as they are nearer the earth, and as the refractive power of a gas
Fig. 430.
Fig. 432.
increases with its density (550), it follows that on entering the atmosphere
the luminous rays become bent, as seen in fig. 432, describing a curve
before reaching the 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.
Another 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 it is just not visible. If now, the position of the eye remaining
unaltered, water be poured into the basin, the coin becomes visible. A con-
sideration of fig. 430 will suggest the explanation of this phenomenon.
540. Total reflection. Critical angle. When a luminous ray 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 pro-
pagated in a mass
of water from S to
O (fig. 433), there
is always a value
of the angle of in-
cidence SOB, such
that the angle of refraction, AOR, is a right angle, in which case the re-
fracted ray emerges parallel to the surface of the water.
This angle, SOB, is called the critical angle, since for any greater angle,
FOB, the incident ray cannot emerge, but undergoes an internal reflection,
which is called total reflection, because the incident light is entirely reflected.
From water to air the critical angle is 48 35' ; 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 rilled with
water (fig. 434) ; the surface of the liquid is then looked at as shown in the
figure, and an image at the object A is seen at a, formed by the rays reflected
at m, in the ordinary manner of a mirror.
Fig. 432
Fig. 434.
-541] Mirage. 469
Similar effects of the total reflection of the images of objects contained
in aquaria are frequently observed, and add much to the interest of their
appearance.
In total reflection there is no loss of light from absorption or transmission,
and accordingly it produces the greatest brilliancy. If a test tube half full
of water be placed in water, the empty part shines as brilliantly as pure
mercury. Bubbles, again, in water glisten like pearls, and cracks in trans-
parent 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 more
frequent and more brilliant the smaller the limiting angle ; the lustre of dia-
mond therefore is the most brilliant,
541. Mirage. The mirage is an optical illusion by which inverted images
of distant objects are seen as if below the ground or in the atmosphere. This
phenomenon is of most frequent occurrence in hot climates, and more
especially on the sandy plains of Egypt. The ground there has often the
435-
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 a luminous ray
from an elevated object, A (fig. 435), traverses layers which are gradually less
refracting ; for, as will be shown presently (550), the refracting power of a
gas diminishes with lessened density. The angle of incidence accordingly
increases from one layer to the other, and ultimately reaches the critical
angle, beyond which internal reflection succeeds to refraction (540). The
ray then rises, as seen in the figure, and undergoes a series of successive
refractions, but in the direction contrary 7 to the first, for it now passes through
layers which are gradually more refracting. The luminous ray 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.
470
On Light.
[541-
The effect of the mirage may be illustrated artificially, as Dr. Wollaston
showed, .by looking along the side of a red-hot poker at a word or object ten
or twelve feet distant. At a distance less than three-eighths of an inch from
the line of the poker, an inverted image was seen, and within and without
that an erect image. A more convenient arrangement than a red-hot poker
is a flat box closed at the top and filled with red-hot charcoal.
Mariners sometimes see images in the air of the shores or of distant
vessels. This is due to the same cause as the mirage, but in a contrary
direction, only occurring when the temperature of the air is above that of the
sea, for then the inferior layers of the atmosphere are denser, owing to their
contact with the surface of the water. Scoresby observed several such
cases in the Polar Seas.
TRANSMISSION OF LIGHT THROUGH TRANSPARENT MEDIA.
; 542. Media with parallel faces. When light traverses a medium with
parallel faces the emergent rays are parallel to the incident rays.
Let MN (fig. 436) be a glass plate with parallel faces, let SA be the
incident and DB the emergent ray, i and r the angles of incidence and of
refraction at the entrance of the ray, and,
lastly, i f and r' the same angles at its emer-
gence. At A the light undergoes a first
refraction, the index of which is s ? n z (537).
sin r '
At D it is refracted a second time, and the
index is then
But we have seen that
Fig. 436.
sin r'
the index of refraction of glass to air is the re-
ciprocal of its refraction from air to glass; hence
s iHJi = s ' in _ r
sin r' sin t
But as the two normals AG and DE are parallel, the angles r and i f are
equal, as being alternate interior angles. As the numerators in the above
equation are equal, the denominators must be also equal ; the angles r' and
i are therefore equal, and hence DB is parallel to SA.
543. Prism. In optics a prism 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 refract-
ing angle. Every sec-
tion perpendicular to the
edge is called a prin-
cipal section.
The prisms used for
experiments are gene-
Fig. 437 . Fig. 43 8. rally right triangular
prisms of glass, as
shown in fig. 437, and their principal section is a triangle (fig. 438). In this
section the point A is called the summit of the prism, and the right line BC
-544] Path of Rays in Prisms. Angle of Deviation. 471
is called the base ; these expressions have reference to the triangle ABC, and
not to the prism.
544. Path of rays in prisms. 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. 438) in the same plane as the principal sec-
tion ABC of a prism, and let OD be an incident ray. This ray is refracted
at D, and approaches the normal, because it passes into a more highly re-
fracting medium. At K it experiences a second refraction, but it then de-
viates 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 is 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 the angle of deviation.
39- Fig- 440-
Besides this, objects seen through a prism appear in all the colours of
the rainbow ; this phenomenon will be described under the name of dis-
persion.
This angle increases with the refractive index of the material of the prism,
and also with its refracting angle. It also varies with the angle 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.
That the angle of deviation increases with the refractive index may be
shown by means of the polyprism. This name is given to a prism formed
of several prisms of the same angle connected at their ends (fig. 439). These
prisms are made of substances unequally refringent, such as flint glass, rock
crystal, or crown glass. If any object a line, for instance be looked at
through the polyprism, its different parts are seen at unequal heights. The
472
On Light.
[544-
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. 440) 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.
545. Application of right-angled prisms in reflectors. Prisms whose
principal section is an isosceles right-angled triangle afford an important
application of total reflection (540). For
let ABC (fig. 441) 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
Fi - 44*. angle of glass, which is 41 48' (540). The
ray OH undergoes, therefore, at H total reflection, which imparts to it a
direction HI perpendicular to the second face AC. Thus the hypothenuse
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 fre-
quently used in optical instruments.
546. Conditions of emergence in
prisms. In order that any luminous
rays 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 criti-
cal angle of the substance of which
the prism is composed. For if LI
(fig. 442) 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 (540). But as the inci-
dent angle LIN increases, the angle EIP also increases, while IEP dimin-
ishes. 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.
Let LI be now parallel to AB, the angle r is then equal to the critical
angle / of the prism because it has its maximum value. Further, the angle
EPK, the exterior angle of the triangle IPE, is equal to r + i' but the angles
EPK and A are equal, because their sides are perpendicular, and therefore
Fig. 442-
-547] Minimum Deviation. 473
A = r+* v ; therefore also A = / + *', for in this case r = l. Hence, if A = 2/
or is >2/, we shall have i'^l or >/, and therefore the ray would not emerge
at the second face, but would undergo internal reflection, and would 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 /' con-
tinually increases. 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', twice this angle is less than 90,
and, accordingly, objects cannot be seen through a glass prism whose refract-
ing angle is a right 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
within the angle NIA.
547. Minimum deviation. When a pencil of solar light passes through
an aperture A, in the side of a dark chamber (fig. 443), the pencil is projected
in a straight line AC,
on a distant screen.
But if a vertical prism
be interposed be-
tween the aperture
and the screen, the
pencil is deviated to-
wards the base of the
prism, and the image
is projected at D, at
some distance from
the point C. If the Fig . 443 .
prism be turned so
that the incident angle decreases, the luminous disc 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 demonstrated mathematically that
this minimum dmiation 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 least, as the angle of emergence Y* is equal to the incident angle
/ (fig. 442), r must =/'. But it has been shown above (546) that A. = r+i' ;
consequently,
A = 2;- (I)
If the minimum angle of deviation LD/ be called d, this angle being ex
terior to the triangle DIE, we readily obtain the equation
474
On Light.
[547-
whence and the right line which
passes through these two
centres is the principal axis. In a plano-concave or plano-convex lens, the
-552] Foci in Double Convex Lenses. 477
principal axis is the perpendicular let fall from the centre of the spherical
face on the plane face.
In order to compare the path of a luminous ray in a lens with that in a
prism, the same hypothesis is made as for curved mirrors (525) ; that is, the
surfaces of these lenses are supposed to be formed of an infinity of small
plane surfaces or elements ; the normal at any point is then the perpen-
dicular to the plane of the corresponding element. It is a geometrical
principle, 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 convergence, which are inclined to
each other, and thus produce the effect of a prism. Pursuing this com-
parison, the three lenses A, B, and C may be compared to a succession of
prisms having their summits outwards, and the lenses D, E, and F to a
series having their summits inwards ; from this we see that the first ought
to condense 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 (536).
552. 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.
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.
448. 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 to-
wards 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 calculation 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 dis-
tance FA is the
principal focal
distance. It is
constant in the
same lens, but
varies with the
radii of curvature
and the index of
refraction. In or-
dinary 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 case in which the luminous point is outside
478 On Light. [552-
the principal focus, but so near that all incident rays form a divergent pencil
as shown in fig. 449. The luminous point 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, LB, greater than the angle
SBn ; consequently, after traversing the lens, the ray cuts the axis at a
point, /, which is more distant than the principal focus F. As all rays from
the point L intersect approximately in the same point /, this latter is the con*
jugate 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 /, which is of such a nature that, if the luminous point is moved to/,
the focus passes to L.
According as the luminous point comes nearer the lens, the convergence
of the emergent rays decreases, and the focus / becomes more distant ; when
the point L coin-
cides with the prin-
cipal 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. 450.
Virtual foci. A double convex lens has a virtual focus when the luminous
object is placed between the lens and the principal focus, as shown in fig.
451. In this case the inci-
dent 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 can-
not produce a real focus, but their prolongations intersect in some point,
/, on the axis, and this point is the virtual focus of the point L (514).
553. Foci in doable concave lenses. In double concave lenses there
are only virtual foci, whatever the distance of the object. Let SS' be any
pencil of rays parallel to the axis (fig. 452), any ray, SI, is refracted at the
point of incidence, I, and approaches the normal CI. At the point of emer-
gence 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
-555] Optical Centre, Secondary Axis. 479
no real focus, but the prolongations of these rays cut one another in a point
F, which is the principal virtual focus.
In the case in which the rays proceed from a point, L (fig. 453), on the
Fig 452. *'ig 453-
axis, it is found by the same construction that a virtual focus is formed at /,
which is between the principal focus and the lens.
5 54. 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 conrerge
is readily seen ; it is the principal focus.
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 calcu-
lated from the dioptric formula (561).
With a double concave lens, the face ab (fig. 454) is covered with an
opaque substance, such as lampblack, two small apertures, a and b, being
left in the same principal section, and
at an equal distance from the axis ; a
pencil of solar light is then received
on the other face, and the screen
P, which receives the emergent
rays, is moved nearer to or farther
from the 'ens, until A and B, the
spots of light from the small aper-
tures a and b, are distant from each
other by twice ab. The distance *ig-454-
DI is then equal to the focal distance FD, because the triangles at> and
FAB are similar. Another method of determining the focus of a concave
lens is given in article 560.
555. Optical centre, secondary axis. In every lens there is a point
called the optical centre, which is situated 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. 455) be drawn to the
two surfaces of a double convex lens. Since the two plane elements of the
lens 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
that after refraction it takes the direction AA' will emerge parallel to its first
480 On Light. [555-
direction (542) ; 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 CO A and C / OA / are equal,
and therefore that OC = OC', which gives the point O. If the curvatures are
unequal, the triangles CO A and CO'A' 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
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. 456), which passes through the optical centre
without passing through the centres of curvature, is a secondary axis. From
Fig- 455- Fig. 456.
this property of the optical centre, every secondary axis represents a luminous
rectilinear ray passing through this point, for, from the slight thickness of the
lenses, 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. 436).
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. 456), 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 prin-
ciple is the foundation of what follows as to the formation of images.
556. Formation of images in double convex lenses. In 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 re-
solves itself into de-
termining the position
of a series of points,
Fig. 457 . j as was the case with
mirrors (528).
i. Real image. Let AB (fig. 457) be placed beyond the principal focus. If
a secondary axis, Aa, be drawn from the outside point A, any ray, AC, from
-556] Formation of Images in Double Convex Lenses. 481
this point, will be twice refracted at C and D, and both times in the same
direction, approaching the secondary axis, which it cuts at a. From what
has been said in the last paragraph, the other rays from the point A will inter-
sect in the point a, which is accordingly the conjugate focus of the point A.
If the secondary axis be drawn froVn the point B, it will be seen, in like
manner, that the rays from this point intersect in the point b ; and as the points
between A and B have their foci between a and b, a real but inverted image
of AB will be formed at ab.
In order 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 ab were the luminous or illuminated object which emitted
rays, its image would be formed at AB. Two consequences important for
the theory of optical instruments follow from this : that 1st, If an object, even
a very large one, is at a sufficient distance from a double convex lens, the real
and inverted image which is obtained of it is very small, it is near the prin-
cipal focus, but somewhat farther from the lens than this is ; 2nd, If a very
small object be placed near the principal focus, but a little in front of it, the
image u'hich is formed is at a great distance, it is 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.
ii. Virtual image. There is another case in which the object AB (fig. 458)
is placed between the lens and its principal focus. If a secondary axis, O#
be drawn from the
point A, every ray,
AC, after having
been twice refrac-
ted on emerging,
diverges from this
axis, since the
point A is at a less
distance than the
principal focal dis-
tance (552). 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
b. There is, therefore, an image of AB, at ab. This is a virtual image, it
is erect, and larger than the object.
The magnifying power is greater in proportion as the lens is more con-
vex, and the object nearer the principal focus. We shall presently show how
the magnifying power may be calculated by means of the formulae relating
to lenses (561). Double convex lenses used in this manner as magnifying
glasses, are called simple microscopes.
Y
482 On Light. [557-
557. Formation of images in double concave lenses. Double con-
cave lenses, like convex mirrors, only give virtual images, whatever the
distance of the object.
Let AB (fig. 459) be an object placed in front of such a lens. If the
secondary axis AO be drawn from the
point A, all rays, AC, AI, from this
point are twice refracted in the same
direction, diverging from the axis
AO ; so that the eye, receiving the
emergent rays DE and GH, supposes
them to proceed from the point where
their prolongations cut the secondary
axis AO in the point a. In like
manner, drawing a secondary axis
Fl . from the point B, the rays from this
* 459' . - . - r _
point form a pencil of divergent rays
the directions of which, prolonged, intersect in b. Hence the eye sees at
ab a virtual image of AB, which is always erect, and smaller than the object.
558. 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 ioor 12.
Where, however the aperture is larger, the rays which traverse the lens
near the edge are refracted to a point F nearer the lens than the point G,
which is the focus of
the rays which pass
near the axis. The
phenomenon thus pro-
duced is named sphe-
rical aberration by
refraction ; it is ana-
logous to the spherical
aberration produced
by reflection (533).
The luminous sur-
faces formed by the
Fig. 460 intersection of the re-
fracted 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 object will be sharply defined in the centre, but indistinct at
the edges ; and, vice versa, if the image is sharp at the edges, it will be
indistinct in the centre. This defect is very objectionable, more especially in
lenses used for photography. It is partially obviated by placing before the
lenses diaphragms, provided with a central aperture, called stops, which
admit the rays passing near the centre, but cut off those which pass near the
^559] Formula Relating to Lenses. 483
edges. The image thereby becomes sharper and more distinct, though the
illumination is less.
If a screen be held between the light and an ordinary 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 ascer-
tained 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
r _ 4 2/z 2 + n
r^ 2n* + n
are most free from spherical aberration, and are called lenses of best form
in this formula r is the radius of curvature of the foci turned to the parallel
rays, and r^ that of the other face, while n is the refractive index. Thus,
with a glass whose refractive index is ^,^ = 6^ Spherical aberration is 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 (560). Lenses which are free from spherical aberration
are called aplanatic.
559. Formulae relating: to lenses. In all lenses, the relations between
the distances of the image and object, the radii of curvature, and the refrac-
Fig. 461.
tive index, may be expressed by a formula. In the case of a double convex
lens, let P be a luminous point, situate on the axis (fig. 461), let PI be an
incident ray, IE its direction within the lens, EP' the emergent ray, so that P
is the conjugate focus of P. Further, let C'l and CE be the normals to the
points of incidence and emergence, and I PA be put equal to a, EP'A' = P
ECA' = y , IC'A = S, NIP-/, ElO-r, IEO-/', N'EP'-r.
Y 2
484 On Light. [559-
Because the angle i is the exterior angle of the triangle PIC', and the
angle r' the exterior angle of the triangle CEP 7 , therefore, / = a + S, and
^ = y + /3, whence
2-j-r' = a + + y + S . , , . . (i)
But at the point I, sin i = n sin r, and at the point E, sin r' ' = n sin i (538), n
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 /, r, i', and r' ; whence, in the above formula, we may replace the sines
by their angles, which gives i=*nr and r / = z v , from which i + r 1 ' = n (r + z'),
Further, because the two triangles IOE and COC' have a common equal
angle O, therefore r-t-z' = y + S, from which z + r' = n (y + 8). Introducing
this value into the equation (i) we obtain
n (y + S) = a + /3 + y + S, from which (n i) (y + S)=a + /3. . (2)
Let CA' be denoted by R, C'A by R', PA by /, and P'A' by /'. Then
with centre P and radius PA describe the arc A'
whence = * where AB = O is the magnitude of the object and ab = \
O p
that of the image ; while p and p' are their respective distances from the
lens. Replacing p' by its value from the equation + = where the
image is real, or from the equation _I -L = * where it is virtual, we shall
P P' f
obtain the different values of the ratio for various positions of the object.
In the first case we have v_ m_f.
Thus if p>2f I>O
p = 2 f 1 =
P<2f I>0
In the second case when the image is virtual we shall have
_- = J- . so that in all cases I > O.
O f-p
By using the above formula we may easily deduce the focal length of a
convex lens, where direct sunlight is not available. For if it be placed in
front of a scale, and if a screen be placed on the other side, then, by altering
the relative positions of the lens and the screen, a position may be found by
486
On Light.
[561-
Fig. 462.
trial, such that an image of the object is formed on the screen of exactly the
same size. Dividing now by 4, the total distance between the object and the
screen, we get the focal distance of the lens.
562. Determination of refractive index. By measurements of focal
distance the refractive index of a liquid 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 f, and
known curvature r, is pressed against a drop of the liquid
in question on a glass plate (fig. 462). The liquid forms
thereby a plano-concave lens, whose radius of curvature is r.
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
i _ i _ I
T"7 7"
while from the formula __ = ( i) we get the value of n.
563. Laryngoscope. As an application of lenses may be adduced the
laryngoscope, which is an instrument invented to facilitate the investi-
gation of the larynx and the other cavities of the mouth. It consists of a
plane convex lens L, and a concave reflector M, both fixed to a ring which
can be adjusted to any convenient lamp (fig. 463). The flame of a lamp is
Fig. 463.
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 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.
-564] Decomposition of White Light. 487
CHAPTER IV.
DISPERSION AND ACHROMATISM.
564. Decomposition of wbite light. Solar spectrum. The pheno-
menon of refraction is by no means so simple as we have hitherto assumed ;
when white light, or that which reaches us from the sun, passes from one
medium into another, // is decomposed into several kinds of light, a phenor
menon to which the name dispersion is given.
In order to show that white light is decomposed by refraction, a pencil of
solar light SA (fig. 464) is allowed to pass through a small aperture in the
window shutter of a dark
chamber. This pencil
tends to form a round
and colourless image of
the sun at K ; but if a
flint glass prism, ar-
ranged horizontally, be
interposed in its path,
the beam, on emerging
from the prism, becomes
refracted towards its
base, and produces on
a distant screen a ver-
tical band rounded at
the ends, coloured in all Fig 464.
the tints of the rainbow,
which is called the solar spectrum, see Plate I. In this 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
violet, indigo, blue, green, yellow, orange, red ; they are arranged in this
order in the spectrum, the violet being the most refrangible, and the red trie
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 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 dispersion, and the ratio of
this angle to the mean deviation of the two rays is called the dispersive power.
488 On Light. [564-
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 ; f r crown glass it is 0-0246 ; for 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.
565. Production of a pure solar spectrum. In the above experiment,
when the light is admitted through a wide slit, the spectrum formed is built
up of a series of overlapping spectra, and the colours are confused and indis-
tinct. In order to obtain a pure spectrum, the slit, in the shutter of the dark
room through. which light enters, should be from 15 to 25 mm. in height and
from i to 2 mm. in breadth. The sun's rays are directed upon the slit by a
mirror, or still better by a helibstat (534). 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 (561). 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 free from striae, and should be placed so that it
produces the minimum deviation.
566. The colours of the spectrum are simple, and unequally refran-
gible. If one of the colours of the spectrum be isolated by intercepting the
others by means of a screen E, as shown in fig. 465, and if the light thus in-
tercepted be allowed to
pass through a second
prism, B, a refraction will
be observed, but the light
remains unchanged ; that
is, the image received on
the screen H is violet if
the violet pencil has
Fig 465 . been allowed to pass,
blue if the blue pencil,
and so on. Hence the colours of the spectrum are simple ; that is, they
cannot be further decomposed by the prism.
Moreover, the colours of the spectrum are unequally refrangible ; that
is, they possess different refractive indices. 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 re-
flected, is least refrangible. But the unequal refrangibility of simple colours
-566] The Colours of the Spectrum are unequally Refrangible. 489
may be shown by numerous experiments, of which the two following may be
adduced :
i. Two narrow strips of coloured paper, one red and the other 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. 466), in a horizontal position, a pencil
Fig. 466.
of white light, S, is received, which, if it had merely traversed the prism A,
would form the spectrum rz/, on a distant screen. But if a second prism, B.
be placed in a vertical position behind the first, in such a manner that the
refracted pencil passes through it, the spectrum rv becomes deflected towards
the base of the vertical prism ; but, instead of being deflected in a direction
parallel to jtself, as would be the case if the colours of the spectrum were
equally refracted, it is obliquely refracted in the direction r'l/^ proving that
from red to violet the colours are more and more refrangible.
These different experiments show that the refractive index differs in
different colours ; even rays which are to perception undistinguishable have
not the same refractive index. In the red band, for instance, the rays at the
Fig. 467.
4 68.
extremity of the spectrum are less refracted than those which are nearer the
orange zone. In determining indices ol refraction (540), it is usual to take,
as the index of any particular substance, the refrangibility of the yellow ray
in a prism formed of that substance.
490
On Light.
[567-
567. Decomposition of white ligrlit. 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 :
i. If the spectrum produced by one prism be 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. 468, 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.
ii. If the spectrum falls upon a double
convex lens (fig. 467), a white image of the
sun will be formed on a white screen placed
in the focus of the lens ; a glass globe
Figt 4&9 filled with water produces the same effect as
the lens,
iii. When the spectrum falls upon a concave mirror, a white image is
formed on a screen of ground glass placed in its focus (fig. 469).
iv. Light may be recomposed by means of a pretty experiment, which
consists in receiving the seven colours of the spectrum on seven small glass
Fig. 470.
mirrors with plane faces, and which can be so inclined in all positions that
the reflected light may be transmitted in any given direction (fig. 470).
When these mirrors are suitably arranged, the seven reflected pencils may
be caused to fall on the ceiling in such a manner as to form seven distinct
images red, orange, yellow, &c. When the mirrors are moved so that
the separate images become superposed, a single image is obtained, which
is white.
v. By means of Newtorts disc, fig. 471, 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
-568] Newton's Tlieory of the Composition of Light. 491
relative dimensions and tints are such as to represent five spectra T(fig. 472).
When this disc is rapidly rotated, the effect is the same as if the retina re-
ceived 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. 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
maybe mixed with each other. With a rapid rotation the disc (fig. 471)
Fig. 471.
is nearly white. It is not quite so, for the colours cannot be exactly arranged
in the same proportion as those in which they exist in the spectrum, and
pigment colours are not pure. A similar explanation applies to the experi-
ment of the oscillating prism.
568. 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 simple or primitive lights. Owing to the difference in re-
frangibility 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 7 , the spectrum is made up of an infinite
number of simple colours, which pass into one another by imperceptible
gradations of colour and refrangibility.
492 On Light [569-
569. Colour of bodies. The natural colour of bodies results from the
fact that of the coloured rays contained in white light, one portion 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 which bodies reflect or transmit some colours and absorb others.
Thus a body appears yellow, because it absorbs all colours with the ex-
ception of yellow. In like manner, a solution of ammoniacal oxide of
copper 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.
Hence bodies have no colour of their own ; with the nature of the in-
cident light the colour of the body changes. Thus, if in a dark room a white
body be successively illuminated by each of the colours of the spectrum, it
has no special colour, but appears red, orange, green, &c., according to the
position in which it is placed. If homogeneous light falls 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. In the 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 well 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 gas has a reddish
tint.
570. 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 position of the retina. This new im-
pression is single ; it cannot be resolved into
its components ; in this respect it differs from
P y'^ a complex sound, in which the ear, by practice,
can learn to distinguish the constituents. Mixed
colours may be produced by looking in an
oblique direction through a vertical glass plate
^ P (fig. 473) at a coloured wafer b, while, at the
~ F same time, a wafer of another colour g sends
its light by reflection towards the observer's
eye ; if g is placed in a proper position its image exactly coincides with
that of b. The method of the colour disc (567) affords another means of
producing mixed colours.
If in any of the methods by which the impression of mixed spectral
colours is produced, one or more colours be 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. 467 the red rays are cut off from the lens L, the light on the focus is no
-571] Spectral Colours and Pigment Colours. 493
longer white but greenish blue. In like manner if the violet, indigo, and
blue of the colour disc be suppressed, the rest seems yellow, while the
mixture of that which has been taken out is a bluish violet. Hence white
can always be compounded of two tints ; and two tints which together give
white are called complementary colours. Thus of spectral tints red and
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. 474), at right
Fig. 474-
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
vertical. When this is 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 where this is the case two homogeneous spectral
colours mix. Thus at I 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 are given 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.
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.
571. Spectral colours and pigment colours. A distinction must be
made between spectral 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
colours, and not of addition. For in the mixture the pigment blue 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 : these are red, the com-
plementary 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 comple-
mentary colours were mixed. But a mixture of greenish blue and of greenish
yellow is green. Hence it follows that from a mixture of red, green, and
violet, white must be formed. This may easily be ascertained to be the case,
494
On Light.
[571-
by means of a colour disc on which are these three colours in suitable pro-
portions.
Violet
Blue
Green
Yellow
Red
Red
Purple
Rose
Dull
yellow
Orange
Red
Yellow
Rose
White
Yellowish
green
Yellow
Green
Pale blue
Bluish
green
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 fundamental 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 tint 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 intensity which depends on the amplitude of
vibration.
57 2 - 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 oi
great importance to procure homogeneous or monochromatic light. Common
salt in the flame of a Bunsen's lamp gives a yellow of great purity. For red
light, ordinary light is transmitted through glass coloured with suboxide of
copper, which absorbs nearly all the rays excepting the red. A very pure
blue is obtained by transmitting ordinary light through a glass trough con-
taining an ammoniacal solution of sulphate of copper, and a nearly pure
red by transmitting it through a solution of sulphocyanide of iron.
573. 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 light in the yellow part of the spectrum has the
greatest intensity, and that in the violet the least.
Heating effects. It was long known that the various parts of the spectrum
differed in their calorific effects. Leslie found that a thermometer placed in
-573] Chemical Properties of the Spectrum. 495
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 those different effects depend on the nature of a prism : 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 himself
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 acts as a chemical
agent. For instance, chloride of silver 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
chloride of silver 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
invisible and more highly refrangible rays. These are the chemical or
actinic rays.
The most remarkable chemical action which light exerts is in the growth
of plant life. The vast masses of carbon accumulated in the vegetable
world, owe their origin to the carbonic acid present in the atmosphere.
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 gaseous form.
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 others
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 exciting rays^ and the latter
496 On Light. [573-
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 light. Becquerel found
that the phosphorogenic spectrum extended from indigo to beyond the
violet.
574. 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 1 802 ;
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,
one constructed by the
late Earl of Rosse. This magnificent instrument has a focal distance of 53
feet, the diameter of the spectrum 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.
602. Camera obscura. The camera obscura (dark chamber) is, as its
name implies, a closed space impervious to light. There is, however, a small
aperture by which luminous rays enter, as shown in fig. 505. The rays, pro-
ceeding from external objects, and entering by this aperture, form on the
opposite side an image of the object in its natural colours, but of reduced
dimensions, and in an inverted position.
526
On Light.
[602-
Porta, a Neapolitan physician, the inventor of this instrument, found that
by fixing a double convex lens in the aperture, and placing a white screen in
the focus, the image was much brighter and more definite.
Fig. 505 represents a camera obscura, such as is used for drawing. It
consists of a rectangular wooden box, formed of two parts which slide in and
out. The luminous rays, R, pass into the box through a lens B, and form an
image on the opposite side, O, which is at the focal distance of the lens.
But the rays are reflected from a glass mirror, M, inclined at an angle of 45,
and form an image on the ground-glass plate, N. When a piece of tracing
paper is placed on this screen, a drawing of the image is easily made. A
wooden door, A, cuts off extraneous light.
The box is formed of two parts, sliding one within the other, like the
joints of a telescope, so that, by elongating it more or less, the reflected
image may be made to fall exactly
on the screen, N, at whatever dis-
tance the object may be situated.
Fig. 506 shows another kind of
camera obscura which is occasionally
erected in summer-houses. In a
brass case, A, there is a triangular
prism, P (fig. 507), which acts both
as condensing lens and as mirror.
One of its faces is plane, but the
others have such curvatures that the
combined refractions on entering
and emerging from the prism pro-
duce the effect of a meniscus lens.
Hence rays from an object, AB,
after passing into the prism and un-
dergoing total reflection from the
face, cd, form at ab a real image of
AB.
In fig. 506, the small table B
corresponds to the focus of the prism
in the case, A, and an image forms
on a piece of paper placed on the
table. The whole is surrounded by
a black curtain, so that the observer can place himself in complete dark-
ness. .
603. Camera luclda. The camera lucida is a small instrument depend-
ing on internal reflection, and serves for taking an outline of any object. It
was invented by Wollaston in 1804. It consists of a small four-sided glass
prism, of which fig. 508 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 67^.
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 per-
pendicular on this face, pass into the prism without any appreciable refrac-
tion, and are totally reflected from BC ; for as the line ab is perpendicular to
-604]
Magic Lantern.
527
Fig. 507.
BC, and nL to AB, the angle anL will equal the angle B ; that s, it will con-
tain 67 , and this being greater than the critical angle of glass (540), the ray
Ln will undergo total reflection. The rays are again
totally reflected from 0, and emerge near the summit, A
D, in a direction almost perpendicular to the face I
DA, so that the eye which receives the rays sees at K~
L' an image of the object L. If the outlines of the
image are traced with a pencil, a very correct design
is obtained ; but unfortunately there is a great diffi-
culty in seeing both the image and the point of the
pencil, for the rays from the object give an image
which is farther 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 aper-
ture 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. 509, is preferable to that of
\Vollaston, 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 con-
sists of a rectangular
glass prism, ABC,
having one of its per-
pendicular faces turn-
ed towards the object
to be depicted, while
the other is at right
angles to an inclined
plate of glass, inn.
The rays, LI, pro-
ceeding from the ob
Fig. 508. Fig. 509.
ject, 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 mn at H, and form a vertical 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.
604. Magric lantern. This is an apparatus by which a magnified image
of small objects may be projected on a white screen in a dark room. It
consists of a tin-plate box, in which there is a lamp placed in the focus of a
concave mirror, A (fig. 511). The reflected rays fall upon a condensing lens, B,
(fig. 510), which concentrates them on the figure painted on a glass plate, V.
There is a double convex lens, C, at a distance from V of rather more than
its focal distance, and, consequently, a real and very much magnified image
of the figure on the glass is produced on the screen (556).
Dissolving views are obtained by arranging two magic lanterns, which
are quite alike, with different pictures, in such a manner that both pictures
5 28
On Light.
[604-
are produced on exactly the same part of a screen. The object-glasses of
both lanterns are closed by shades, which are so arranged that according as
one is raised the other is lowered, and vice versa. In this way one picture is
gradually seen to change into the other.
The magnifying power of the magic lantern is obtained by dividing the
distance of the lens C from the image by its distance from the object. If
Fig. 510.
Fig. 511.
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.
605. Solar microscope. The solar microscope is in reality a magic
lantern illuminated by the sun's rays ; it serves to produce highly magnified
Fig. 512.
images ot very small objects. It is worked in a dark room ; fig. 512 re-
presents it fitted in the shutter of a room, and fig. 513 gives the internal
details. - -
-606]
Photo-electric Microscope.
529
The sun's rays fall on a plane mirror, M, placed outside the room, and
are reflected towards a condensing lens, /, and from thence to a second lens,
(fig- 5 r 3) by which they are concentrated at its focus. The object to be
magnified is at this point ; it is placed between two glass plates, which, by
means of a spring, , are kept in a firm position between two metal plates,
;//. The object thus strongly illuminated is very near the focus of a
system of three condensing lenses, JT, which forms upon a screen at a
suitable distance an inverted and greatly magnified image, ab. The distance
of the lenses, o and x, from the object is regulated by means of screws, C
and D.
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
Fig. 513-
ahvays in the direction of the axis of the microscope. The most exact
apparatus for this purpose is the heliostat (534) ; but as this instrument is
very expensive, the object is usually attained by inclining the mirror to a
greater or less extent by means of an endless screw B, and at the same time
turning the mirror itself round the lens, /, by a knob, A, which moves in a
fixed slide.
The solar microscope labours under the objection of concentrating great
heat on the object, which soon alters it. This is partially obviated by
interposing a layer of a saturated solution of alum, which, being a power-
fully athermanous substance (434), cuts off a considerable portion of the heat.
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 r \ or ^ 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 photo-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 are all achromatic.
The solar microscope furnishes the means of exhibiting to a large audience
many curious phenomena, such, for instance, as the circulation of blood in
the smaller animals, the crystallisation of salts, the occurrence of animalculae
in water, vinegar, &c. &c.
606. Photo-electric microscope. This is nothing more than the solar
microscope, which is illuminated by the electric light instead of by the sun's
A A
530
On Light.
[606-
rays. The electric light, by its intensity, its steadiness, and the readiness
with which it can be procured at any time of the day, is far preferable to the
solar light. The photo-electric microscope alone will be described here :
the electric light will be considered under the head of Galvanism.
Fig. 514 represents the arrangement devised by Duboscq. A solar
microscope, ABD, identical with that already described, is fixed on the
outside of a brass box. In the interior are two charcoal points which do
not quite touch, the space between them being exactly on the axis of the
lenses. The electricity of one end of a powerful battery reaches the charcoal
Fig 514-
a, by means of a copper wire, K ; while the electricity from the opposite end
of the battery reaches c 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
-607]
Lighthouse Lenses.
531
image of the object placed between two plates of glass is produced on the
screen.
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 photo-
genic apparatus. The microscope can be replaced by the head-pieces 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 oxy-hydrogen or Drummond's light, which is obtained by
heating a cylinder
of lime in the flame
produced by the
combustion of a
mixture of hydro-
gen or of coal gas
with oxygen gab.
607. ! i gr n t-
house lenses.
Lenses of large
dimensions are
very difficult of
construction ; they
further produce a
considerable sphe-
rical aberration,
and their thick-
ness causes the
loss of much light.
In order to avoid
these inconveni-
ences, echelon len-
ses have been con-
structed. They
consist of a plano-
convex lens, C
(figs. 515 and 516),
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 faces on the other side have such a curvature that the
foci of the different segments coincide in the same point. These rings form,
together with the central lens, a single lens, a section of which is represented
A A 2
532 On Light. [607-
in fig. 516. The drawing was made from a lens of about 2 feet in diameter,
the segments of which are formed of a single 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 calorific focus is identical with that of
the luminous focus.
Formerly parabolic mirrors were used in sending the light of beacons
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
peculiar construction, which gives as much light as 20 moderators. The
light is placed in the principal focus of the lens so that the emergent rays
form a parallel beam (fig. 450), which loses intensity only by passing through
the atmosphere, and can be seen at a distance of above 40 miles. In order
that all points of the horizon may be successively illuminated, the lens
is continually moved round the lamp by a clockwork 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 disap-
pears 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 been substituted for that of
oil lamps ; a description of the apparatus will be given in a subsequent
chapter.
PHOTOGRAPHY.
608. Photography is the art of fixing the images of the camera obscura
on substances sensitive to light. The various photographic processes may
be classed under three heads : photography on metal, photography on paper,
and photography on glass.
Wedgwood was the first to suggest the use of chloride of silver in fixing
the image, and Davy, by means of the solar microscope, obtained images of
small objects on paper impregnated with chloride of silver ; but no method
was known of preserving the images thus obtained, by preventing the further
action of light. Niepce, in 1814, obtained permanent images of the camera
by coating glass plates with a layer of a varnish composed of bitumen dis-
solved in oil of lavender. This process was tedious and inefficient, and it
was not until 1839 that the problem was solved. In that year, Daguerre
described a method of fixing the images of the camera, which, with the sub-
sequent improvements of Talbot and Archer, has rendered the art of photo-
graphy one of the most marvellous discoveries ever made, either as to the
beauty and perfection of the results, or as to the celerity with which they are
produced.
-608]
PhotograpJiy.
S33
In Daguerre's process, the Dagucrrotype, the picture is produced on a
plate of copper coated with silver. This is first very carefully polished an
operation on which much of the success of the subsequent operations depends.
It is then rendered sensitive by exposing it to the action of iodine vapour,
which forms a thin layer of iodide of silver on the surface. The plate is now
fit to be exposed in the camera ; it is sensitive enough for views which re-
quire an exposure of ten minutes in the camera, but when greater rapidity is
required, as for portraits, &c., it is further exposed to the action of an accele-
rator, such as bromine or hypobromite of calcium. All the operations must
be performed in a room lighted by a candle, or by the daylight admitted
through yellow glass, which cuts off all chemical rays. The plate is preserved
from the action of light by placing it in a small wooden case provided with
a slide on the sensitive side.
The third operation consists in exposing the sensitive plate to the action
of light, placing it in that position in the camera where the image is produced
with greatest delicacy. For
photographic purposes a I9Q1 \.
camera obscura of peculiar
construction is used. The
brass tube A (fig. 517), con-
tains an achromatic con-
densing lens, which can be
moved by means of a rack-
work motion, to which is
fitted a milled head, D. At
the opposite end of the box
is a ground-glass plate, E,
which slides in a groove, B,
in which the case containing
the plate also fits. The
camera being placed in a
proper position before the object, the sliding part of the box is adjusted
until the image is produced on the glass with the utmost sharpness ; this is
the case when the glass slide is exactly in the 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 time, the
duration of which varies in different cases, and can only be hit exactly
by great practice. The plate is then removed to a dark room. No change
is perceptible to the eye, but those parts on which the light has acted have
acquired the property of condensing mercury : the plate is next placed
in a box and exposed to the action of mercurial vapour at 60 or 70 de-
grees.
The mercury is deposited on the parts affected, in the form of globules
imperceptible to the naked eye. The shadows, or those parts on which
the light has not acted, remain covered with the layer of iodide of silver.
This is removed by treatment with hyposulphite of sodium, which dis-
solves iodide of silver without affecting the rest of the plate. The plate is
next immersed in a solution of chloride of gold in hyposulphite of sodium
Fig. 517-
534
On Light.
[608-
which dissolves the silver, while some gold combines with the mercury
and silver of the parts attacked, and greatly increases the intensity of the
lustre.
Hence the light parts of the image are those on which the mercury
has been deposited, and the shaded those on which the metal has retained
its reflecting lustre.
Fig. 518 represents a section of the camera and the object-glass. At first
it consisted of a double convex lens, but now double achromatic lenses, LL',
Fig. 518.
are used as object-glasses. They act more quickly than objectives with a
single lens, have a shorter focus, and can be more easily focussed by moving
the lens, L', by means of the rack and pinion, D.
609. Photographs on paper. In Daguerre's process, which has just
been described, the images are produced directly on metal plates. With
paper and glass, photographs of two kinds may be obtained : those in which
an image is obtained with reversed tints, so that the lightest parts have be-
come the darkest on paper, and vice versa ; and those in which the lights
and shades are in their natural position. The former are called negative,
and the latter positive pictures.
A negative may be taken either on glass or on paper ; it serves to produce
a positive picture.
Negatives on glass. A glass plate of the proper size is carefully cleaned
and coated with a uniformly thick layer of collodion impregnated with iodide
of potassium. The plate is then immersed for about a minute in a bath of
nitrate of silver containing 30 grains of the salts in an ounce of water. This
operation must be performed in a dark room. The plate is then removed,
allowed to drain, and when somewhat dry, placed in a closed flame, and
afterwards exposed in the camera, for a shorter time than in the case of a
Daguerrotype. On removing the plate to a dark room, no change is visible,
but on pouring over it a solution called the developer, an image gradually
appears. The principal substances used for developing are protosulphate
of iron and pyrogallic acid. The action of light on iodide of silver appears
to produce some molecular change, or else some actual chemical decom-
position, in virtue of which the developers have the property of reducing
to the metallic state those parts of the iodide of silver which have been most
acted upon by the light. When the picture is sufficiently brought out, water
is poured over the plate, in order to prevent the further action of the deve-
-611] Photographs on Albumenised Paper and Glass. 535
loper. The parts on which light has not acted are still covered with iodide
of silver, which would be affected if the plate were now exposed to the light.
It is, accordingly, washed with solution of hyposulphite of sodium, which
dissolves the iodide of silver and leaves the image unaltered. The picture
is then coatecl with a thin layer of spirit varnish, to protect it from mechanical
injury.
When once the negative is obtained, it may be used for printing an in-
definite number of positive pictures. For this purpose paper is impregnated
with chloride of silver, by immersing it first in solution of nitrate of silver and
then in one of chloride of sodium ; chloride of silver is thus formed on the
paper by double decomposition. The negative is placed on a sheet of this
paper in a copying frame, and exposed to the action of light for a certain
time. The chloride of silver becomes acted upon the light parts of the
negative being most affected, and the dark parts least so. A copy is thus
obtained, on which the lights of the negative are replaced by shades, and
inversely. In order to fix the picture, it is washed in a solution of hyposul-
phite of sodium, which dissolves the unaltered chloride of silver. The
picture is afterwards immersed in a bath of chloride of gold, which gives it
tone.
6 10. Positives on glass. Very beautiful positives are obtained by pre-
paring the plates as in the preceding cases ; the exposure in the camera,
however, is not nearly so long as for the negatives. The picture is then
developed by pouring over it a solution of protosulphate of iron, which pro-
duces a negative image ; and by afterwards pouring a solution of cyanide of
potassium over the plate, this negative is rapidly converted into a positive.
It is then washed and dried, and a coating of varnish poured over the
picture.
6n. Photographs on albumenised paper and glass. In some cases,
paper impregnated with a solution of albumen containing iodide of potassium
is used instead of collodion, over which it has the advantage that it can be
prepared for some time before it is used, and that it produces certain effects
in the middle tints. It has the disadvantage of not being nearly so sensitive.
It requires, therefore, longer exposure and is unsuitable for portraits, but in
some cases can be advantageously used for views.
536
On Light.
[612-
CHAPTER VI.
THE EYE CONSIDERED AS AN OPTICAL INSTRUMENT.
6 1 2. Structure of the human jye. The eye is the organ of vision ;
that is to say, of the phenomenon by virtue of which the light emitted
or reflected from bodies excites in us the sensation which reveals their pre-
sence.
The eye is placed in a bony cavity called the orbit ; it is maintained
in its position by the muscles which serve to move it, by the optic nerve,
the conjunctiva, and the eyelids.
Its size is much the same in all
persons : it is the varying aper-
ture of the eyelids that makes
the eye appear larger or smaller.
Fig. 519 represents a trans-
verse section of the eye from
back to front. The general
shape is that of a spheroid, the
curvature of which is greater in
the anterior than in the posterior
part. It is composed of the
following parts : the cornea, the
sclerotica, the iris, the pttpil,
the aqueotis humour, the crys-
talline, the vitreous body, the
hyaloid membrane, the choroid, the retina, and the optic nerve.
Cornea. The cornea, a, is a transparent membrane situated in front of
the ball of the eye. In shape it resembles a small watch-glass, and it fits
into the sclerotica, i ; in fact, these membranes are so connected that some
anatomists have considered them as one and the same, and have distin-
guished them by calling the cornea the transparent, and the sclerotica the
opaque cornea.
Sclerotica. The sclerotica, i, or sclerotic coat, is a membrane which,
together with the cornea, envelopes all parts of the eye. In front there is
an almost circular aperture into which the cornea fits ; a perforation behind
gives passage to the optic nerve.
Iris. The iris, d, is an annular, opaque diaphragm, placed between the
cornea and the crystalline lens. It constitutes the coloured part of the eye,
and is perforated by an aperture called \he pupil, which in man is circular.
In some animals, especially those belonging to the genus felts, it is narrow
and elongated in a vertical direction ; in the ruminants it is elongated in a
-612] Structure of the Human Eye. 537
transverse direction. It is a contractile membrane, and its diameter varies
in the same individual between 0-12 and 0*28 of an inch; but these limits
may be exceeded. The luminous rays pass into the eye through the pupil.
The pupil enlarges in darkness, but contracts under the influence of a bright
light. These alterations of contraction and enlargement take place with
extreme rapidity ; they are very frequent, and play an important part in the
act of vision. The movements of the iris are involuntary.
It appears from this description that the iris is a screen with a variable
aperture, whose function is to regulate the quantity of light which penetrates
into the eye ; for the size of the pupil diminishes as the intensity of light
increases. The iris serves also to correct the spherical aberration, as it
prevents the marginal rays from passing through the edges of the crystalline
lens. It thus plays the same part with reference to the eye that a stop does
in optical instruments (558).
Aqueous humour. Between the posterior part of the cornea and the
front of the crystalline there is a transparent liquid called the aqueous hu-
mour. The space, ^, occupied by this humour is divided into two parts by
the iris : the part <, between the cornea and the iris, is called the anterior
chamber ; the part c, which is between the iris and the crystalline, is the
posterior chamber.
Crystalline lens. This is a double convex transparent body placed im-
mediately behind the iris ; the inner margin of which is in contact with
its anterior surface, though not attached to it. The lens is enclosed in a
transparent membrane, called its capsule } it is less convex on its anterior
than on its posterior surface, and is composed of almost concentric layers,
which decrease in density and refracting power from the centre to the cir-
cumference.
To the anterior surface of the capsule, near its margin, is fixed a firm
transparent membrane, which is attached behind to the front of the hyaloid
membrane, and is known as the suspensory ligament. This ligament exerts
attraction, all round, on the front surface of the lens, and renders it less
convex than it would otherwise be, and its relaxation plays an important
part in the adaptation of the eye for sight at different distances.
Vitreous body. Hyaloid membrane. The vitreous body, or vitreous
humour, is a transparent mass resembling the white of an egg, which occu-
pies all the part of the ball of the eye //, behind the crystalline. The vitreous
humour is surrounded by the hyaloid membrane, /, which lines the posterior
face of the crystalline capsule, and also the interior face of another mem-
brane called the retina.
Retina. Optic neme. The retina, m, is a membrane which receives the
impression of light, and transmits it to the brain by the intervention of a
nerve, , called the optic nerve, which, proceeding from the brain, pene-
trates into the eye, and extends over the retina in the form of a nervous
network. The nerve-fibres themselves are not sensitive to light, but are
only stimulated by it indirectly through the intervention of certain structures
called the rods and cones. Where the optic nerve enters, there are no rods
or cones ; this part of the retina therefore is insensitive to light and is called
the punctum cacum.
The only property of the retina and optic nerve is that of receiving and
A A 3
538 On Light. [612-
transmitting to the brain the impression of objects. These organs have been
cut and pricked without causing any pain to the animals submitted to these
experiments ; but there is reason to believe that irritation of the optic nerve
causes the sensation of a flash of light.
Choroid, The choroid, k, is a membrane between the retina and the
sclerotica. It is completely vascular, and is covered on the internal face
by a black substance which resembles the colouring matter of a negro's
skin, and which absorbs all rays not intended to co-operate in producing
vision.
The choroid elongates in front, and forms a series of convoluted folds,
called ciliary processes, which penetrate between the iris and the crystalline
capsule, to which they adhere, forming round it a disc, resembling a radiated
flower. By its vascular tissue, the choroid serves to carry the blood into
th'e interior of the eye, and especially to the ciliary processes.
613. Refractive indices of the transparent media of the eye. The
refractive indices from air into the transparent parts of the eye were deter-
mined by Brewster. His results are contained in the following table, com-
pared with water as a standard :
Water . . . . . . . . . . 1*3358
Aqueous humour . . . . . . . . . 1*3366
Vitreous humour i'3394
Exterior coating of the crystalline ..... 1*3767
Centre of the crystalline i'399o
Mean refraction of the crystalline 1*3839
614. Curvatures and dimensions of various parts of the human eye.
Radius of curvature of the sclerotica 0-40 to 0-44 in.
cornea 0*28 to 0-32
anterior face of the crystalline . 0*28 to 0-40
posterior face of the crystalline . 0*20 to 0*24 ,,
Diameter of the iris 0-44 to 0*48
pupil 0-12 to 0*28
crystalline . 0*40
Thickness of the crystalline . . . . . . . 0*20
Distance from the pupil to the cornea 0*08
Length of the axis of the eye 0*88 to 0*96
615. Path of rays in the eye. From what has been said as to the
structure of the eye, it may be compared to a camera obscura (602), of which
the pupil is the aperture, the crystalline is the condensing lens, and the
retina is the screen on which the image is formed. Hence, the effect is the
same as when the image of an object placed in front of a double convex lens
is formed in its conjugate focus. Let AB (fig. 520) be an object placed
before the eye, and let us consider the rays emitted from any point of the
object, A. Of all these rays, those which are directed towards the pupil are
the only ones which penetrate the eye, and are operative in producing
vision. These rays, on passing into the aqueous humour, experience a first
refraction which brings them near the secondary axis Aa, drawn through
-617]
Optic Axis, Optic Angle, Visual Angle.
539
the optic centre of the crystalline ; they then traverse the crystalline, which
again refracts them like a double convex lens, and, having experienced a
Fig. 520.
final refraction by the vitreous humour, they meet in a point, , and form
the image of the point, A. The rays issuing from the point B form in like
manner an image of it at the point b, so that a very small, real, and inverted
image is formed exactly on the retina, provided the eye is in its normal
condition.
6 1 6. Inversion of images. In order to show that the images formed
on the retina are really inverted, the eye of an albino or any animal with
pink eyes may be taken ; this has the advantage that, as the choroid is
destitute of pigment, light can traverse it without loss. This is then deprived
at its posterior part of the cellular tissue surrounding it, and fixed in a hole
in the shutter of a dark room ; by means of a lens it may be seen that the
inverted images of external objects are depicted on the retina.
The inversion of images in the eye has greatly occupied both physicists
and physiologists, and many theories have been proposed to explain how it
is that we do not see inverted images of objects. The chief difficulty seems
to have arisen from the conception of the mind or brain as something
behind the eye, locking into it, and- seeing the image upon the retina ;
whereas really this image simply causes a stimulation of the optic nerve,
which produces some molecular change in some part of the brain, and it is
only of this change, and not of the image, as such, that we have any con-
sciousness. The mind has thus no direct cognisance of the image upon the
retina, nor of the relative positions of its parts, and, sight being supple-
mented by touch in innumerable cases, it learns from the first to associate
the sensations brought about by the stimulation of the retina (although due
to an inverted image) with the correct position of the object as taught by touch.
617. Optic axis, optic angle, visual angle. The principal optic axis
of an eye is the axis of its figure ; that is to say, the straight line in reference
Fig. 511.
to which it is symmetrical. In a well-shaped eye it is the straight line
passing through the centre of the pupil and of the crystalline, such as the
540 On Light. [617-
line O of propagation of the wave in
two media will be different.
While the plane wave moves from n to K, the corresponding wave starting
from m reaches the surface of a sphere the radius of which is less than K,
if the second medium is more strongly refracting than the first. The incident
wave in like manner reaches m f and n f simultaneously, and while n moves to
K, m' moves to 0', the surface of a sphere the radius of which, m'o', is to mo
as n' is to nK. All the elementary waves proceeding from points interme-
diate to n and K which arise from the same incident wave, all touch one
and the same plane Ko'o, and the refracted ray proceeds in the new medium
perpendicular to this tangent plane.
Now nK and mo represent the velocities of light in the unit of time in the
two media respectively ; let mK be taken as unit of length, then
72 K = sin nmK and mo = sin mK0.
Now mnK is the angle of incidence of the ray, and mKo is the angle of 1
refraction; and nK and mo are the velocities of light in the two media
respectively ; hence we see that these velocities are to each other in the
same ratio as the sines of the angles of incidence and refraction ; a conclu-
sion which agrees with the results of direct observation (506) and forms a
beautiful confirmation of the truth of the undulatory theory.
DOUBLE REFRACTION.
639. Double refraction. It has been already stated (536), that a large
number of crystals possess the property of double refraction, in virtue of
which a single incident ray in passing through any one of them is divided
-640] Uniaxial Crystals. 559
into two, or undergoes bifurcation, whence it follows that, when an object
is seen through one of these crystals, it appears double. The fact of
the existence of double refraction in Iceland spar was first stated by
Bartholin in 1669, but the law of double refraction was first enunciated
exactly by Huyghens in his treatise on light written in 1678 and published
in 1690.
Crystals which possess this peculiarity are said to be double refracting.
It is found to a greater or less extent in all crystals which do not belong to
the cubical system. Bodies which crystallise in this system, and those
which, like glass, are destitute of crystallisation, have no double refraction.
The property can, however, be imparted to them when they are unequally
compressed, or when they are cooled quickly after having been heated, in
which state glass is said to be unannealed. Of all substances, that which
possesses it most remarkably is Iceland spar or carbonate of calcium. In
many substances, the power of double refraction can hardly be proved to
exist directly by the bifurcation of an incident ray ; but its existence is shown
indirectly by their being able to depolarise light (665).
Fresnel has explained double refraction by assuming that the ether in
double refracting bodies is not equally elastic in all directions ; from which
it follows that the vibrations, in certain directions at right angles to each
other, are transmitted with unequal velocities ; these directions being depen-
dent on the constitution of the crystal. This hypothesis is confirmed by the
property which glass acquires of becoming double refracting by being un-
annealed and by pressure.
640. Uniaxial crystals. In all double refracting crystals there is one
direction, and in some a second direction possessing the following property :
When a point is looked at through the crystal in this particular direction, it
does not appear double. The lines fixing these directions are called optic
axes ; and sometimes, though not very properly, axes of double refraction.
A crystal is called uniaxial when it has one optic axis ; that is to say, when
there is one direction within the crystal along
which a ray of light can proceed without
bifurcation. When a crystal has two such
axes, it is called a biaxial crystal.
The uniaxial crystals most frequently
used in optical instruments are Iceland spar,
quartz, and tourmaline. Iceland spar crystal-
lises in rhombohedra, whose faces form with
each other angles of 105 5' or 74 55'. It
has eight solid angles (see fig. 534). Of Flg ' 534 *
these, two, situated at the extremities of one of the diagonals, are severally
contained by three obtuse angles. A line drawn within one of these two
angles in such a manner as to be equally inclined to the three edges contain-
ing the angle is called the axis of the crystal. If all the edges of the crystal
were equal, the axis of the crystal would coincide with the diagonal, ab.
Brewster showed that in all uniaxial crystals the optic axis coincides with
the axis of crystallisation.
The principal plane with reference to a point of any face of a crystal,
whether natural or artificial, is a plane drawn through that point at right
560 On Light. [640-
angles to the face and parallel to the optic axis. If in fig. 534 we suppose
the edges of the rhombohedron to be equal, the diagonal plane abed contains
the optic axis (ab), and is at right angles to the faces aedfand chbg', conse-
quently, it is parallel to the principal plane at any point of either of those
two faces. For this reason abed is often called the principal plane with
respect to those faces.
641. Ordinary and extraordinary ray. Of the two rays into which an
incident ray is divided on entering a uniaxial crystal, one is called the,
ordinary and the other the extraordinary ray. The ordinary ray follows
the laws of single refraction ; that is, with respect to that ray the sine of the
angle of incidence bears a constant ratio to the sine of the angle of refraction,
and the plane of incidence coincides with the plane of refraction. Except
in particular positions, the extraordinary ray follows neither of these laws.
The images corresponding to the ordinary and extraordinary rays are called
the ordinary and extraordinary images respectively.
If a transparent specimen of Iceland spar be placed over a dot of ink,
on a sheet of white paper, two images will be seen. One of them, the
ordinary image, will seem slightly nearer to the eye than the other, the extra-
ordinary image. Suppose the spectator to view the dot in a direction at
right angles to the paper, then, if the crystal, with the face still on the paper,
be turned round, the ordinary image will continue fixed, and the extraordinary
image will describe a circle round it, the line joining them being always in
the direction of the shorter diagonal of the face of the crystal, supposing its
edges to be of equal length. In this case it is found that the angle between,
the ordinary and extraordinary ray is 6 12'.
642. The laws of double refraction in a uniaxial crystal. These
phenomena are found to obey the following laws :
i. Whatever be the plane of incidence, the ordinary ray always obeys the
two general laws of single refraction (537). The refractive index for the
ordinary ray is called the ordinary refractive index.
ii. In every section perpendicular to the optic axis the extraordinary ray
also follows the laws of single refraction. Consequently in this plane the
extraordinary ray has a constant refractive index, which is called the ordinary
refractive index.
iii. In every principal section the extraordinary ray follows the second
law only of single refraction ; that is, the planes of incidence and refraction
coincide, but the ratio of the sines of the angles of incidence and refraction
is. not constant. ..,
iv. The velocities of light along the rays are unequal. It can be shown
that the difference between the squares of the reciprocals of the velocities
along the ordinary and extraordinary rays is proportional to the square of the
sine of the angle between the latter ray and the axis of the crystal.
There is an important difference between the velocity of the ray and the
velocity of the corresponding plane wave. If the velocities of the plane
waves corresponding to the ordinary and extraordinary rays are considered,
the difference between the squares of these velocities is proportional to the
square of the sine of the angle between the axis of the crystal, and the normal
to that plane wave which corresponds to the extraordinary ray. The normal
and the ray do not generally coincide.
-644] Double Refraction in Biaxial Crystals. 561
Huyghens gave a very remarkable geometrical construction, by means of
which the directions of the refracted rays can be determined when the direc-
tions of the incident ray and of the axis are known relatively to the face of
the crystal. This construction was not generally accepted by physicists
until Wollaston and subsequently Malus showed its truth by numerous exact
measurements.
643. Positive and negative uniaxial crystal. The term extraordinary
refractive index has been defined in the last article. For the same crystal
its magnitude always differs from that of the ordinary refractive index ; for
example, in Iceland spar the ordinary refractive index is 1-654, while the
extraordinary refractive index is 1-483. In this case the ordinary index
exceeds the extraordinary index. When this is the case, the crystal is said
to be negative. On the other hand, when the extraordinary index exceeds
the ordinary index, the crystal is said to be positive. The following list gives
the names of some- of the principal uniaxial crystals :
Negative Uniaxial Crystals.
Iceland spar Ruby Pyromorphite
Tourmaline Emerald Ferrocyanide of potassium
Sapphire Apatite Nitrate of sodium
Positive Unia.vial Crystals.
Zircon Apophyllite Titanite
Quartz Ice Boracite
644. Doable refraction in biaxial crystals. A large number of
crystals, including all those belonging to the trimetric, the monoclinic, and
the triclinic systems, possess two optic axes ; in other words, in each of these
crystals there are two directions along which a ray of light passes without
bifurcation. A line bisecting the acute angle between the optic axes is
called the medial line ; one that bisects the obtuse angle is called the sup-
plementary line. It has been found that the medial and supplementary
lines and a third line at right angles to both are closely related to the funda-
mental form of the crystal to which the optic axes belong. The acute angle
between the optic axes is different in different crystals. The following
table gives the magnitude of this angle in the case of certain crystals :
Nitre . . . 5 20' Anhydrite . . .28 7'
Strontianite . . 6 56 Heavy spar . . . 37 42
Arragonite . . . 18 18 Mica . . . . 45 o
Sugar . . . . 50 o Epidote . . . . 14 19
Selenite . . . . 60 o Sulphate of iron . . 90 o
When a ray of light enters a biaxial crystal, and passes in any direction
not coinciding with an optic axis, it bifurcates ; in this case, however,
neither ray conforms to .the laws of single refraction, but both are extra-
ordinary rays. To this general statement the following exception must be
made : In a section of a crystal at right angles to the medial line one ray
follows the law of ordinary refraction, and in a section at right angles to
the supplementary line the other ray follows the laws of ordinary refraction.
BB 3
5 62
On Light.
[645-
INTERFERENCE AND DIFFRACTION.
645. Interference of light. The name interference is given to the
mutual action which two luminous rays exert upon each other when they are
emitted from two neighbouring sources, and meet each other under a very
small angle. This action may. be observed by means of the following ex-
periment : In the shutter of a dark room two very small apertures of the
same diameter are made close to each other. The apertures are closed
by pieces of coloured glass red, for example by which two pencils of
homogeneous light are introduced. These two pencils form two divergent
luminous cones, which meet at a certain distance ; they are received on a
white screen a little beyond the place at which they meet, and in the segment
common to the two discs which form upon this screen some very well-defined
alternations of red and black bands are seen. If one of the two apertures
be closed, the fringes disappear, and are replaced by an almost uniform red
tint. From the fact that the dark fringes disappear when one of the beams
is intercepted, it is concluded that they arise from the interference of the two
pencils which cross obliquely.
This experiment was first made by Grimaldi, but was modified by
Young. Grimaldi had drawn from it the conclusion that light added to light
Fig- 535-
produced darkness. The full importance of this principle remained for
a long time unrecognised, until hese inquiries were resumed by Young
and Fresnel, of whom the latter, by a modification of Grimaldi's experi-
ment, rendered it an experimentum cruets of the truth of the undulatory
hypothesis.
In Grimaldi's experiment diffraction (646) takes place, for the luminous
rays pass by the edge of the aperture. In Fresners experiment the two
pencils interfere without the possibility of diffraction.
Two plane mirrors, AB and BC (fig. 535), of metal, are arranged close to
-645] Interference of Light. 563
each other, so as to form a very obtuse angle, ABC, which must be very
little less than 180. A pencil of red light, which passes into the dark
chamber, is brought by means of a lens, L, to a focus F. On diverging from
F the rays fall partly on AB, and partly on BC. If BA is produced to P and
FPF,- is drawn at right angles to AP, and if PF X is made equal to PF, then
the rays which fall on AB will, after reflection, proceed as if they diverged
from F r If a similar construction is made for the rays falling on BC, they
will proceed after reflection as if they diverged from F 2 . A little considera-
tion will show that F, and F 7 are very near each other. Suppose the re-
flected rays to fall on a screen SS! placed nearly at right angles to their
directions. Every point of the screen which receives light from both pencils
is illuminated by both rays, viz. one from F,, the other from F 2 ; thus the
point H is illuminated by two rays, as also are K and I. Now the combined
action of these two pencils is to form a series of parallel bands alternately
light and dark on the screen at right angles to the plane of the paper. This
is the fundamental phenomenon of interference ; and that it results from the
joint action of the tiuo pencils is plain, for if the light which falls upon either
of the mirrors is cut off, the dark bands disappear.
This remarkable experiment is explained in the most satisfactory manner
by the undulatory theory of light. The explanation exactly resembles that
already given of the formation of nodes and loops by the combined action of
two aerial waves (262) ; the only difference being that in that case the vibrating
particles were supposed to be particles of air, whereas, in the present case, the
vibrating particles are supposed to be those of the luminiferous ether. Con-
sider any point K on the screen, and first let us suppose the distance of K from
F, and F 2 to be equal. Then the undulations which reach K will always be
in the same phase, and the particle of ether at K will vibrate as if Ahe light
came from one source : the amplitude of the vibration, however, will be
increased in exactly the same manner as happens at a loop or ventral point ;
consequently at K the intensity of the light will be increased. And the
same will be true for all parts on the screen, such that the difference between
their distances from the two images equals the length of one, two, three, &c.,
undulations. If, on the other hand, the distances of K from Fj and F 2 differ
by the length of half an undulation, then the two waves would reach K in
exactly opposite phases. Consequently, whatever velocity would be com-
municated at any instant to a particle of ether by the one undulation, an
exactly equal and opposite velocity would be communicated by the other
undulation, and the particle would be permanently at rest, or there would be
darkness at that point ; this result being produced in a manner precisely
resembling the formation of a nodal point already explained. The same
will be true for all positions of K, such that the differences between its
distances from F, and F 2 is equal to three halves, or five halves, or seven
halves, &c., of an undulation. Accordingly, there will be on the screen a
succession of alternations of light and dark points, or rather lines for what
is true of points in the plane of the paper (fig. 534) will be equally true of
other points on the screen which is supposed to be at right angles to the
plane of the paper. Between the light and dark lines the intensity of the
light will vary, increasing gradually from darkness to its greatest intensity,
and then decreasing to the second dark line, and so on.
564
On Light.
[645-
If instead of red light any other coloured light were used for example,
violet light an exactly similar phenomenon would be produced, but the dis-
tance from one dark line to another would be different. If white light were
used, each separate colour tends to produce a different set of dark lines.
Now these sets being superimposed on each other, and not coinciding, the
dark lines due to one colour are illuminated by other colours, and instead of
dark lines a succession of coloured bands is produced. The number of
coloured bands produced by white light is much smaller than the number of
dark lines produced by a homogeneous light ; since at a small distance from
the middle band the various colours are completely blended, and a uniform
white light produced.
646. Diffraction and fringes. Diffraction is a modification which light
undergoes when it passes the edge of a body, or when it traverses a small
aperture a modification in virtue of which the luminous rays appear to
become bent, and to penetrate into the shadow.
This phenomenon may be observed in the following manner : A beam of
solar light is allowed to pass through a very small aperture in the shutter of
a dark room, where it is received on a condensing lens, L (fig. 536), with a
Fig. 536.
short fooal length. A red glass is placed in the aperture so as only to allow
red light to pass. An opaque screen, ^, with a sharp edge a a razor, for
instance is placed behind the lens beyond its focus, and intercepts one por-
tion of the luminous cone, while the other is projected on the screen , of
which B represents a front view. The following phenomena are now seen :
Within the geometrical shadow, the limit of which is represented by the line
ab, a faint light is seen, which gradually fades in proportion as it is farther
from the limits of the shadow. In this part of the screen which, being above
the line ab, might be expected to be uniformly illuminated a series of alternate
dark and light bands or fringes are seen parallel to the line of shadow, which
gradually become more indistinct and ultimately disappear. The limits
between the light and dark fringes are not quite sharp lines ; there are parts
of maximum and minimum intensity which gradually fade oft into each
other.
All the colours of the spectrum give rise to the same phenomenon, but
the fringes are broader in proportion as the light is less refrangible. Thus,
with red light they are broader than with green, and with green than with
violet. Hence, with white light, which is composed of different colours, the
dark spaces of one tint overlap the light spaces of another, and thus a series
of prismatic colours will be produced.
If, instead of placing the edge of an opaque body between the light and
the screen, a very narrow body be interposed, such as a hair or a fine metallic
wire, the phenomena will be different Outside the space corresponding to
-647]
Gratings.
565
fiiiiiifft
iiiiiiiii
the geometrical shadow, there is a series of fringes, as in the former case.
Hut within the shadow also there is a series of alternate light and dark bands.
They are called interior fringes, and are much narrower and more numerous
than the external fringes.
When a small opaque circular disc is interposed, white light being used,
its shadow on the screen shows in the middle a bright spot surrounded by a
series of coloured concentric rings ; the bright spot is of various colours
according to the relative positions of the disc and screen. The haloes
sometimes seen round the sun and moon belong to this class of phenomena.
They are due, as Fraunhofer showed, fo the diffraction of light by small
globules of fog in the atmosphere. Fraunhofer even gave a method of
estimating the mean diameter of these globules from the dimensions of the
haloes. A beautiful phenomenon of the same kind is produced by looking
at a flame through lycopodium powder strewed on glass.
647. Gratings. Phenomena of diffraction of another class are produced
by allowing the pencil of light from the luminous point to traverse an aper-
ture in the form of a narrow slit in an opaque screen. The diffracted light
may be received on a sheet of
white paper, but the images
are much better seen through
a small telescope placed behind
the aperture. If the aperture
is very small, the telescope
may be dispensed with, and
the figure may be viewed by
placing the aperture before the F - .
eye. If now monochromatic
light, red for instance (572), be allowed to fall through such a narrow slit,
a bright band of red light is seen, and right and left of it a series of
similar bands gradually diminishing in brightness and separated by dark
bands.
The breadth of these bands differs with the nature of the light, being
narrower and nearer together in violet than in green, and these again nar-
rower and nearer than in red, as shown in fig. 537. If ordinary white light
be used, then the colours are not exactly superposed, but a series of equi-
distant spectra are formed on each side of the bright line, with their violet
side turned inwards.
In order to explain this, let us refer to fig. 538, which represents the
formation of the first dark band. When light is incident on the slit, AB, the
particles of ether there, which we will represent by the dotted lines, will be
set in vibration, and each point will become the centre of a new series of
oscillations. Consider now the undulations which constitute a ray pro-
ceeding at right angles to the plane of the slit : all such undulations will
form a band of light on the screen MN. Those which are not parallel
but proceed at equal inclinations, and meet at the point r, will be in the
same phase and will reinforce each other, and the line of maximum bright-
ness will be at r. Consider, however, a pencil of rays which proceeds from
the slit in an oblique direction and which meets the screen, or the retina, in
the point s, and let us suppose that the difference between the lengths of the
566
On Light.
[647-
paths of the undulations proceeding from the edges b and a that is, bs and
as is equal to the length of an undulation. Make sc = sb and join be ; then
ac is the length of the undulation.
Let us suppose that the whole set of undulations which proceeds from
the slit ab is divided at d into two equal groups of undulations. Then a
little consideration will show that at any part of the path there will be a
difference of phase of half an undulation between the ray from the margin
a, and that from the centre d ; and to each
undulation constituting the group on the
left there will be a corresponding one
among the groups on the right, which just
differs from it by half an undulation ; the
general effect will be that the group on the
left will be half an undulation behind the
group on the right, and both arriving at the
screen in opposite phases neutralise each
other and produce darkness.
When the difference between the paths
of the marginal undulations is equal to half
a wave-length, a partial destruction of light
takes place ; the luminous intensity cor-
responding to this obliquity is a little less
than half that of the undiffracted light.
M. ^ * K If the marginal distance is one and a half
Fig 53 g undulations, we can, as before, conceive
the whole pencil divided into three parts,
of whicji two will neutralise each other, and the third only will be effective.
There will be a luminous band, but one of less intensity. In like manner
where the marginal undulations differ by two whole wave-lengths, they will
again extinguish each other, and a dark band will be the result. Thus there
will be formed a series of alternate dark and bright bands of rapidly diminish-
ing intensity. In general, when the difference of path of the rays proceeding
from the margin of the slit amounts to n wave-lengths, n being any whole
number, we have a dark band, and when it amounts to n + wave-lengths, a
bright band.
The phenomena of diffraction produced when other than straight lines are
used are often of great beauty. They have been more particularly examined
by Schwerdt, and the whole of the phenomena are in exact accordance with
the undulatory theory, though the explanation is in many cases somewhat
intricate. The theory renders it possible to predict the appearance which
any particular aperture will produce, just as astronomy enables us to foretell
the motions of the heavenly bodies. Some of the simpler forms such as
straight lines, triangles, squares may be cut out of tinfoil pasted on glass,
and apertures of any form may be produced with great accuracy by taking
on glass a collodion picture of a sheet of paper, on which the required shapes
are drawn in black.
Looking through any of these apertures at a luminous point, we see it sur-
rounded with coloured spectra of very various forms, and of great beauty.
The beautiful colours seen on looking through a bird's feather at a distant
-648] Diffraction Spectra. 567
source of light, and the colours of striated surfaces, such as mother-of-pearl,
are due to a similar cause.
648. Diffraction Spectra. The most important of these figures are the
gratings proper, which may be produced by arranging a series of fine wires
parallel to each other, or by careful ruling on a piece of smoked glass, or by
photographic reduction. Nobert has made such gratings by ruling lines on
glass with a diamond, in which there are no less than 12,000 lines in an inch
in breadth. Dr. Stone has constructed such gratings for reflection, by ruling
lines on plates of nickel ; this metal has the advantage of hardness, non-
liability to tarnish, and great reflecting power.
If a grating be used instead of a single slit, as above described, the
phenomena are in general the same, though of greater intensity. With
homogeneous light and such a grating, there is seen, on each side of the
central bright line, a series of sharply defined narrow bands and lines of
light, gradually increasing in breadth and diminishing in intensity as their
distance from the central line increases. If white light be used there is seen
then in the centre, the white band, and on each side of it a sharply defined
isolated spectrum with the violet edges inwards. Next to this, and separated
by a dark interval, is on each side a somewhat broader but similar spectrum,
and then follow others which become fainter and broader and overlap
each other. The brightness and sharpness of these spectra depend on the
closeness of the lines, and on the opacity of the intermediate space. In
those which are ruled by diamond on glass, the parts scratched represent
the opaque parts.
The spectra produced by means of a grating are known as interference or
diffraction spectra. Very accurate gratings can now be easily and cheaply
prepared by means of photography, and their use for scientific purposes is
extending.
For objective representation the image of a slit in a dark shutter,
through which the sunlight enters, is focussed by means of a convex lens
on a screen at a distance, and then a grating is placed in the path of the
rays.
There are many points of difference between these spectra and those
produced by the prism, and for scientific work the former are preferable.
A diffraction spectrum is the purer the greater the number of lines in the
grating, provided they are equidistant. The spectra are, however, not more
than i as bright as prismatic spectra ; and to obtain the maximum bright-
ness the opaque intervals should be as opaque and the transparent ones as
transparent as possible.
On the other hand, in diffraction spectra, the colours are uniformly dis-
tributed in their true order and extent according to the difference in their
wave-lengths, and according therefore to a property which is inherent in the
light itself; while in prismatic spectra the red rays are concentrated, and
the violet ones dispersed. In diffraction spectra the centre is the brightest
part.
Diffraction spectra have, moreover, the advantage of giving a far larger
number of dark lines, and of giving them in their exact relative positions.
Thus, in a particular region in which Angstrom had mapped 118 lines,
Draper, by means of a diffraction spectrum, was able to photograph at least
568 On Light. [648-
293. Diffraction spectra also extend farther in the direction of the ultra-
violet, and give more dark lines in that region.
649. Determination of wave-length. The relative positions of these
bright and dark lines furnish a means of calculating the wave-length or
length of undulation of any particular colour. We must first of all know
the distance rs of the first dark band from the bright one. The bands are
not uniform in brightness or darkness, but there is in each case a position of
maximum intensity, and it is from these that the distances are measured.
If the bands are viewed through a telescope the angle is observed through
which the axis must be turned from the position in which the cross wire
coincides with the centre of the bright band to that in which it coincides
with the centre of the dark band. From the angle, which can be very ac-
curately measured, the distance is easily calculated. When the diffraction
bands are received on a screen the distance may be directly measured, and
most accurately by taking half the distance between the centres of the first
pair of dark bands.
We have thus the similar triangles abc, and rds, in which ac \ bt = rs : rd
(fig. 538). Now be may be taken equal to ab, the width of the slit, which can
be measured directly with great accuracy by means of a micrometric screw
(u), and rd'is the distance of the screen. Hence
rs x ab
ac = .
rd
Now ac, the difference between as and sc, is equal to the length of an undu-
lation of this particular colour. In one experiment with red light the width
of the slit ab was 0*015 m -> tne distance rs 0-15 in., and the distance of the
screen 93 in., which gave ac= 5 t ? 0*000024 m - as the wave-length
of red light. Using blue light the distance of rs was found to be OT, which
gives 0*000016.
Knowing the length of the undulations, we can easily calculate their
number in a second, //, from the formula n= (232), where v is the velocity
of light. Taking this at 186,000 miles, we get for the red corresponding to
the dark line B 434,420,000,000,000 as the number of oscillations in a. second,
and for the H in the violet 758,840,000,000,000 undulations.
If, instead of a single slit, gratings be used, we have the possibility of
more accurate results, for the contrast is greater, and thus the distance is
more easily determined. The breadth of the slit is then easily calculated if
we know the number of lines in a given space.
650. Colours of thin plates. Newton's rings. All transparent bodies,
solids, liquids, or gases, when in sufficiently fine laminae, appear coloured
with very bright tints, especially by reflection. Crystals which cleave easily,
and can be obtained in very thin plates, such as mica and selenite, show this
phenomenon, which is also well seen in soap-bubbles and in the layers of air
in cracks in glass and in crystals. A drop of oil spread rapidly over a large
sheet of water exhibits all the colours of the spectra in a constant order. A
soap-bubble appears white at first, but, in proportion as it is blown out,
brilliant iridescent colours appear, especially at the top, where it is thinnest.
-651] Explanation of Newton* s Rings. 569
These colours are arranged in horizontal zones around the summit, which
appears black when there is not thickness enough to reflect light, and the
bubble then suddenly bursts.
Newton, who first studied the phenomena of the coloured rings in soap-
bubbles, wishing to investigate the relation between the thickness of the
thin plate, the colour of the
rings, and their extent, pro-
duced them by means of a "^^v^^^^^MM'MM^^'
layer of air interposed be- r "~"~~ . """ ;
tween two glasses, one plane
and the other convex, and
with a very long focus (fig.
539). The two surfaces being cleaned and exposed to ordinary light in
front of a window, so as to reflect light, there is seen at the point of contact
a black spot surrounded by six or seven coloured rings, the tints of which
become gradually less strong. If the glasses are viewed by transmitted
li.L, r ht, the centre of the rings is white, and each of the colours is exactly
complementary of that of the rings by reflection.
With homogeneous light, red for example, the rings are successively
black and red ; the diameters of corresponding rings are less as the colour
is more refrangible, but with white light the rings are of the different colours,
of the spectrum, which arises from the fact that, as the rings of the different
simple colours have different diameters, they are not exactly superposed, but
are more or less separated.
If the focal length of the lens is from three to four yards, the rings can be
seen with the naked eye ; but if the length is less, the rings must be looked
at \vith a lens.
651. Explanation of Newton's rings. Newton's rings, and all pheno-
mena of thin plates, are simple cases of interference.
In fig. 540, let MNOP represent a thin plate of a transparent body, on,
which a pencil of parallel rays of homogeneous light, ab, impinges : this will,
be partially reflected in the direction be, and partially
refracted towards d. But the refracted ray will un-
dergo a second reflection at the surface, OP ; the re-
fleeted ray will emerge at e in the same direction as
the pencil of light reflected at the first surface ; and
consequently the two pencils be and ej "will destroy or
augment each others effect according as they are in
the same or different phases. We shall thus have an ' //
effect produced similar to that of the fringes.
It is usual to speak of the successive rings as the *' y
first, second, third, &c. By theyfrj-/ ring is understood Fit?. 540.
that of least diameter. Knowing the radius of any
particular ring, p, and the radius of curvature, R, of the lens, the thickness, d,
of the corresponding layer of air is given approximately by the formula
'-
Newton found that the thicknesses corresponding to the successive dark
rings are proportional to the numbers o, 2, 4, 6, , while for the
570 On Light. [651-
bright rings the thicknesses were proportional to I, 3, 5 He found
that for the first bright ring the thickness was jy/ooo of an incn - when the
light used was the brightest part of the spectrum ; that is, the part on the
confines of the orange and yellow rays.
POLARISATION OF LIGHT.
652. Polarisation by double refraction. It has been already seen that,
when a ray of light passes through a crystal of Iceland spar (641), it becomes
divided into two rays of equal intensity ; viz. the ordinary ray, and the ex-
traordinary ray. These rays are found to possess other peculiarities, which
are expressed by saying they are polarised ; namely, the ordinary ray in a
principal plane, and the extraordinary ray in a plane at right angles to a
principal plane. The phenomena which are thus designated may be de-
scribed as follows : Suppose a ray of light which has undergone ordinary
refraction in a crystal of Iceland spar to be allowed to pass through a second
crystal, it will generally be divided into two rays ; namely, one ordinary, and
the other extraordinary, but of unequal intensities. If the second crystal
be turned round until the two principal planes coincide that is, until the
crystals are in similar or in opposite positions then the extraordinary ray
disappears, and the ordinary ray is at its greatest intensity ; if the second
crystal is turned farther round, the extraordinary ray reappears, and increases
in intensity as the angle increases, while the ordinary ray diminishes in in-
tensity until the principal planes, are at right angles to each other, when the
extraordinary ray is at its greatest intensity, and the ordinary ray vanishes.
These are the phenomena produced when the ray which experienced ordi-
nary refraction in the 'first crystal passes through the second. If the ray
which has experienced extraordinary refraction in the first crystal is allowed
to pass through the second crystal, the phenomena are similar to those above
described ; but when the principal planes coincide, an extraordinary ray alone
emerges from the second crystal, and when the planes are at right angles, an
ordinary ray alone emerges.
These phenomena may also be thus described : Let O and E denote
the ordinary and extraordinary rays produced by the first crystal. When
O enters the second crystal, it generally gives rise to two rays, an ordinary
(O0), and an extraordinary (O), of unequal intensities. When E enters the
second crystal, it likewise gives rise to two rays, viz. an ordinary (E#) and
an extraordinary (E^), of unequal intensities, the intensities varying vrith
the angle between the principal planes of the crystals. When the principal
planes coincide, only two rays, viz. Oo and E^, emerge from the second
crystal, and when the planes are at right angles, only two rays, viz. Oe and
E0, emerge from the second crystal. Since O gives rise to an ordinary ray
when the principal planes are parallel, and E gives rise to an ordinary ray
when they are at right angles, it is manifest that O is related to the principal
plane in the same manner that E is related to a plane at right angles to a
principal plane.
This phenomenon, which is produced by all double refracting crystals,
was observed by Huyghens in Iceland spar, and in consequence of a sug-
gestion of Newton's was afterwards called polarisation. It remained, how-
ever, an isolated fact until the discovery of polarisation by reflection recalled
-654] Angle of Polarisation. 571
the attention of physicists to the subject. The latter discovery was made
by Malus in 1808.
653. Polarisation by reflection. When a ray of light, ab (fig. 541), falls
on a polished unsilvered glass surface, fghi^ inclined to it at an angle of
3 5 25', it is reflected, and the reflected ray is
polarised in the plane of reflection. If it were
transmitted through a crystal of Iceland spar,
it would be transmitted without bifurcation,
and undergo an ordinary refraction, when the
principal plane coincides with the plane of re-
flection ; it would also be transmitted without
bifurcation, but undergo extraordinary refrac-
tion, when the principal plane is at right angles
to the plane of reflection ; in other positions
of the crystal it would give rise to an ordinary
and an extraordinary ray of different intensi-
ties, according to the angle between the plane
of reflection and the principal plane of the
crystal. The peculiar property which the light
has acquired by reflection at the surface fghi
can also be exhibited as follows : Let the
polarised ray be be received at <:, on a second surface of unsilvered glass, at
the same angle, viz. 35 25'. If the surfaces are parallel, the ray is reflected ;.
but if the second plate is caused to turn round cb, the intensity of the re-
flected ray continually diminishes, and when the glass surfaces are at right
angles to each other, no light is reflected. By continuing to turn the upper
mirror the intensity of the reflected ray gradually increases, and attains a
maximum value when the surfaces are again parallel.
The above statement will serve to describe the phenomenon of polarisa-
tion by reflection so far as the principles are concerned ; the apparatus best
adapted for exhibiting the phenomenon will be described farther on.
654. Angle of polarisation. The polarising angle of a substance is the
angle which the incident ray must make with the normal to a plane polished
surface of that substance in order that the polarisation be complete. For
glass this angle is 54 35', and if in the preceding experiment the lower
mirror were inclined at any other angle than this, the light would not be
completely polarised in any position ; this would be shown by its being
partially reflected from the upper surface in all positions. Such light is said,
to be partially polarised. The polarising angle for water is 52 45' ; for
quartz, 57 32' ; for diamond, 68 ; and it is 56 30' for obsidian, a kind of
volcanic glass which is often used in these experiments.
Light which is reflected from the surface of water, from a slate roof, from
a polished table, is all more or less polarised. The ordinary light of the at-
mosphere is frequently polarised, especially in the earlier and later periods of
the day, when the solar rays fall obliquely on the atmosphere. Almost all
reflecting surfaces may be used as polarising mirrors. Metallic surfaces
form, however, an important exception.
Brewster has discovered the following remarkably simple law in reference
to the polarising angle :
572 On Light. [654-
The polarising angle of a substance is that angle of incidence for whicJi
the reflected polarised ray is at right angles to the refracted ray.
Thus, in fig. 542, if si is the incident, ir
the refracted, and if the reflected ray, the
polarisation is most complete when fi is at
right angles to ir.
The plane of polarisation is the plane of
reflection in which the light becomes polar-
ised ; it coincides with the plane of inci-
dence, and therefore contains the polarising
angle.
655. Polarisation by single refraction.
When an unpolarised luminous ray falls
Fig. 542. upon a glass plate placed at the polarising
angle, one part is reflected ; the other part
in passing through the glass becomes refracted, and the transmitted light
is now found to be partially polarised. If the light which has passed
through one plate, and whose polarisation is very feeble, be transmitted
through a second plate parallel to the first, the effects become more marked,
and by ten or twelve plates are tolerably complete. A bundle of such plates,
for which the best material is the glass used for covering microscopic
objects, fitted in a tube at the polarising angle, is frequently used for exam-
ining or producing polarised light.
If a ray of light fall at any angle on a transparent medium, the same
holds good with a slight modification. In fact, part of the light is reflected
and part refracted, and both are found to be partially polarised, equal quan-
tities in each being polarised, and their planes of polarisation being at right
angles to each other. It is, of course, to be understood that the polarised
portion of the reflected light is polarised in the plane of reflection, which is
likewise the plane of refraction.
656. Polarising- instruments. Every instrument for investigating the
properties of polarised light consists essentially of two parts one for polaris-
ing the light, the other for ascertaining or exhibiting the fact of light having
undergone polarisation. The former part is called the polariser, the latter
the analyser. Thus in art. 652 the crystal producing the first refraction is
the polariser, that producing the second refraction is the analyser. In art.
653 the mirror at which the first reflection takes place is the polariser, that
at which the second reflection takes place is the analyser. Some of the
most convenient means of producing polarised light will now be described,
and it will be remarked that any instrument that can be used as a polariser
can also be used as an analyser. The experimenter has therefore considerable
liberty of selection.
657. Worremberg's apparatus. The most simple but complete instru-
ment for polarising light is that invented by Norremberg. It may be
used for repeating most of the experiments on polarised light.
It consists of two brass rods b and d (fig. 543), which support an unsil-
vered mirror, n, of ordinary glass, movable about a horizontal axis. A small
graduated circle indicates the angle of inclination of the mirror. Between
the feet of the two columns there is a silvered glass, p, which is fixed and
-658] Tourmaline. 5/3
horizontal. At the upper end of the columns there is a graduated plate, /,
in which a circular disc, o, rotates. This disc, in which there is a square
aperture, supports a mirror of black glass, ///, which is inclined to the vertical
at the polarising angle. An annular disc, , can be fixed at different heights
on the columns by means of a screw. A second ring, #, may be moved
around the axis. It supports a
black screen, in the centre of
which there is a circular aper-
ture.
When the mirror n makes
with the vertical an angle of 35
25', which is the complement of
the polarising angle for glass,
the luminous rays, Sw, which
meet the mirror at this angle,
become polarised, and are re
fleeted in the direction np to-
wards the mirror/, which sends
them in the direction ' nr. After
having passed through the glass,
/;, the polarised ray falls upon
the blackened glass /;/ under an
angle of 35 25', because the
mirror makes exactly the same
angle with the vertical. But if
the disc, 0, to which the mirror,
;//, is fixed, be turned horizon-
tally, the intensity of the light
reflected from the upper mirror
gradually diminishes, and totally
disappears when it has been
moved through 90. The posi-
tion is that represented in the
diagram : the plane of incidence
on the upper mirror is then perpendicular to the plane of incidence, S;//, on
the mirror n. When the upper mirror is again turned, the intensity of the
light increases until it has passed through 180, when it again reaches a
maximum. The mirrors /// and n are then parallel. The same phenomena
are repeated as the mirror /// continues to be turned in the same direction,
until it again comes into its original position ; the intensity of the reflected
light being greatest when the mirrors are parallel, and being reduced to
zero when they are at right angles. If the mirror m is at a greater or less
angle than 35 25', a certain quantity of light is reflected in all positions of
the plane of incidence.
658. Tourmaline. The primary form of this crystal is a regular hex-
agonal prism. Tourmaline, as already stated, is a negative uniaxial crystal,
and its optic axis coincides with the axis of the prism. For optical purposes
a plate is cut from it parallel to the axis. When a ray of light passes
through such a plate, an ordinary ray and an extraordinary ray are produced
Fig- 543-
574 On Light. [658-
polarised in planes at right angles to each other ; viz. the former in a plane
at right angles to the plate parallel to the axis, and the latter in a plane at
right angles to the axis. The crystal possesses, however, the remarkable
property of rapidly absorbing the ordinary ray ; consequently, when a plate
of a certain thickness is used, the extraordinary ray alone emerges in
other words, a beam of common light emerges from the plate of tourmaline
polarised in a plane at right angles to the axis of the crystal. If the light
thus transmitted be viewed through another similar plate held in a parallel
position, little change will be observed excepting that the intensity of the
transmitted light will be about equal to that which passes through a plate of
double the thickness ; but if the second tourmaline be slowly turned, the
light will become feebler, and will ultimately disappear when the axes of the
two plates are at right angles.
The objections to the use of the tourmaline are that it is not very trans-
parent, and that plates of considerable thickness must be used if the polarisa-
tion is to be complete. For unless the ordinary ray is completely absorbed
the emergent light will be only partially polarised.
Herapath discovered that sulphate of iodoquinine has the property of
polarising light in a remarkable degree. Unfortunately, it is a very fragile
salt, and difficult to obtain in large crystals.
659. Double refracting- prisms of Iceland spar. When a ray of light
passes through an ordinary rhombohedron of Iceland spar, the ordinary and
extraordinary rays emerge parallel to the original ray, consequently the
separation of the rays is proportional to the thickness of the prism. But if
the crystal is cut so that its faces are inclined to each other, the deviations
of the ordinary and extraordinary rays will be different, they will not emerge
parallel, and their separation will be greater as their distance from the prism
increases. The light, however, in passing through the prism becomes de-
composed, and the rays will be coloured. It is therefore necessary to achro-
matise the prism, which is done by combining it with a prism of glass with
its refracting angle turned in the contrary direction (fig. 545). In order to
obtain the greatest amount of divergence, the refracting edges of the prism
should be cut parallel to the optic axis, and this i^ always done.
Let us suppose that a ray of polarised light passes along
the axis of the cylinder (fig. 545), and let us suppose that the
cylinder is caused to turn slowly round its axis ; then the
resulting phenomena are exactly like those already described
(643). Generally there will be an ordinary and extraordinary
ray produced, whose relative intensities will vary as the tube
is turned. But in two opposite positions the ordinary ray
Fig 545 alone will emerge, and in two others at right angles to the
former the extraordinary ray will alone emerge. When the
ordinary ray alone emerges, the principal plane of the crystal that is, a
plane at right angles to its face, and parallel to its refracting edge coincides
with the original plane of polarisation of the ray. Consequently, by means
of the prism, it can be ascertained both that the ray is polarised, and like-
wise the plane in which it is polarised.
660. Nicol's prism. The Nicol's prism is one of the most valuable
means of polarising light, for it is perfectly colourless, it polarises light com-
-661] Physical Theory of Polarised Light. 575
pletely, and it transmits only one beam of polarised light, the other being
entirely suppressed.
It is constructed out of a rhombohedron of Iceland spar, about an inch
in height and \ of an inch in breadth. This is bisected in the plane which
passes through the obtuse angles as shown in fig. 547 ; that is, along the
plane abed (fig. 534). The two halves are then again joined in the same
order by means of Canada balsam.
The principle of the Nicol's prism is this : The refractive index of Canada
balsam, i -549, is less than the ordinary index of Iceland spar 1*654, but greater
Fig. 546. Fig. 547.
than its extraordinary index 1*483. Hence, when a luminous ray SC (fig.
547) enters the prism, the ordinary ray is totally reflected on the surface, ab,
and takes the direction GfO, by which it is refracted out of the crystal,
while the extraordinary ray, C
is a double refracting achromatic prism, which can be turned about the axis
of the apparatus by means of a button ;/. The latter is fixed to a limb <;, on
-677] Rotatory power of Liquids. 587
which is a vernier, to indicate the number of degrees turned through. Lastly,
from the position of the mirror ;//, the plane of polarisation, S02 94
Naples 1805 40*50 1*274
Paris 1800 48*52 i'348
Berlin 1829 52-51 1-366
Petersburg .... 1828 59-66 1-410
Spitzbergen .... 1823 79'4O 1*567
According to Gauss the total magnetic action of the earth is the same as
that which would be exerted if in each cubic yard there were eight bar mag-
nets each weighing a pound.
The lines connecting places of equal intensity are called isodynamic lines.
They are not parallel to the magnetic equator, but appear to have about
the same direction as the isothermal lines. According to Kuppfer, the
intensity appears to diminish as the height of the place is greater ; a needle
which made one oscillation in 24" vibrated more slowly by o-oi /r at a height
of i,ooo feet ; but, according to Forbes, the intensity is only ^^ less at a
height of 3,000 feet. There is, however, some doubt as to the accuracy
of these observations, owing to the uncertainty of the correction for tem-
perature.
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 1 1 in the morning.
It is probable, though it has not yet been ascertained with certainty, that
the intensity undergoes secular variations. From measurements made at
Kew, it appears that, on the whole, the total force experiences a very slight
annual increase (692).
702. Magnetic observatories. During the last few years great attention
has been devoted to the observation of the magnetic elements, and obser-
vatories 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. And in study-
ing the variations of the declination, &c., the mean of a great number of
observations must be taken, so as to eliminate the 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
D D 3
6 io On Magnetism. [702-
is covered with sensitive photographic paper, and is rotated uniformly by
clockwork. .
If now the magnet is quite stationary, and 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.
Knowing 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 (522).
The observations made in the English magnetic observatories were
reduced by Sabine, and revealed some curious facts in reference to the
magnetic storms (694). 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, a German astronomer, who had
studied the subject many years, has found that the spots on the sun, seen on
looking at it through a coloured glass, vary in their number, size, and fre-
quency, but attain their maximum between 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 simultaneous perturbation of the magnetic needle was observed in
the observatory at Kew : subsequent examination of magnetic observations
in various parts of the world showed that within a few hours one of the most
violent magnetic storms ever known had prevailed.
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.
-704]
The Torsion Balance.
611
CHAPTER III.
LAWS OF MAGNETIC ATTRACTIONS AND REPULSIONS.
703. x,aw of decrease with distance. Coulomb discovered the remark-
able law in reference to magnetism, that magnetic attractions and repul-
sions are inversely as the squares of the distances. He proved this by
means of two methods : (i.) that of the torsion balance, and (ii.) that of
oscillation.
704. i. The torsion balance. This apparatus depends on the principle
that, when a wire is twisted through a certain space, the angle of torsion is
proportional to the force of torsion
(90). It consists (fig. 529) of a
glass case closed by a glass top,
with an aperture 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 : d, which is '
fixed, is divided on the edge into
360, while on one e, which is move-
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, ab. On the side of Fi s- 579-
the case there is a graduated scale, which indicates the angle of the needle
ad, 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, ab, being
now replaced, is exactly in the magnetic meridian, and the wire exerts no
torsion.
Before introducing the magnet, A, it is necessary to investigate the action
612 On Magnetism. [704-
of the earth's magnetism on the needle ab, when the latter is removed out of
the magnetic meridian. This will vary with the dimensions and force of the
needle, with the dimensions and nature of the particular wire used, and with
the intensity of the earth's magnetism in the place of observation. Accord-
ingly, the piece E is turned until ab makes a certain angle with the magnetic
meridian. Coulomb found in his experiments that E had to be turned 36
in order to move the needle through i ; that is, the earth's magnetism was
equal to a torsion of the wire corresponding to 35. As the 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 counterbalanced those forces must be equal to
864. The disc was then turned until ab made an angle of 12. To effect
this, eight complete rotations of the disc were necessary. The total force
which now tended to bring the needle into the magnetic meridian was com-
posed of: ist, 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
12 . 3312
Now, 3312 is very nearly four times 864 ; hence, for half the distance the
repulsive force is four times as great.
705. ii. 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 oscillations
consists in causing a magnetic needle to oscillate first under the influence
of the earth's magnetism alone, and then successively under the combined in-
fluence 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 under the influence of the earth's magnetism alone. A magnetic bar
about 2 feet long was then placed vertically in the plane of the magnetic
meridian, so that its north pole was downwards and its south pole presented
to the north pole of the oscillating needle. He found that at a distance of 4
inches the needle made 41 oscillations in a minute, and at a distance of 8
inches 24 oscillations. Now, from the laws of the pendulum (55), the
intensity of the forces are inversely as the squares of the times of oscillations.
Hence, if we call M the force of the earth's magnetism, ;the attractive force
of the magnet at the distance of 4 inches, m f at the distance of 8 inches, we
have
-706] Magnetic Curves. 613
M : M 4 m = 1 5- : 41-, and
M : M + /w'=i5 2 : 24,
eliminating M
AV : ;//' = 41 1 5 2 : 24- 1 5- - 1456 1351=4: i nearly,
or ;;/ : /;/' = 4 : i.
In other words, the force acting at 4 inches is quadruple that which acts at
double the distance.
The above results do not quite agree with the numbers required by the
law of inverse squares. But this could only be expected to apply in the case
in which the repulsive or attractive force is exerted between two points, and
not, as is here the case, between the resultant of a system of points. And it
is to this fact that the discrepancy between the theoretical and observed
results is due.
When a magnet acts upon a mass of soft iron, the law of the variation
with the distance is modified. The attraction in this case is inversely pro-
portional to the distance between the magnet and the iron.
\Yhen the distance between the magnet and the iron is small, Tyndall
found that the attraction is directly proportional to the square of the strength
of the magnet ; but when the iron and the magnet are in contact, then the
attraction is directly proportional to the strength of the magnet.
Fig. 580.
706. Magnetic curves. If a stout sheet of paper stretched on a frame
be held over a horse-shoe magnet, and then some very fine iron filings be
strewn on the paper, on tapping the frame the filings will be found to
arrange themselves in thread-like curved lines, stretching from pole to pole
(fig. 580). These lines form what are called magnetic curves. The direction of
the curve at any point represents the direction of the magnetism at this point.
To render these curves permanent, the paper on which they are formed
should be v/axed ; if then a hot iron plate be held over them, this melts the
wax, which rises by capillary attraction (132) between the particles of filings,
and on subsequent cooling connects them together.
These curves are a graphic representation of the law of magnetic attrac-
tion and repulsion with regard to distance ; for under the influence of the
614
On Magnetism.
[706-
two poles of the magnet, each 'particle itself becomes a minute magnet, the
poles of which arrange themselves in a position dependent on the resultant
of the forces exerted upon them by the two poles, and this resultant varies
with the distance of the two poles respectively. A small magnetic needle
placed in any position near the magnet will take a direction which is the
tangent to the curve at this place.
707. Magnetic field. The space in the immediate neighbourhood of
any magnet undergoes some change, in consequence of the presence of this
magnet, and such a space is spoken of as a magnetic field ; the effect pro
duced by the magnet is often said to be due to the magnetic field. Magnets
of different powers produce magnetic fields of different intensity.
The direction which represents the resultant of the magnetic forces in a
magnetic field is spoken of as the direction of the lines of force of this field.
In the above figure the magnetic curves represent the direction of the lines
of force in the field due to the two poles.
A uniform magnetic field is one in which the lines of force are parallel.
This is practically the case with a small portion of a field at some distance
from a long thin magnet of uniform magnetisation. The dipping-needle,
when free to oscillate in a vertical plane in the magnetic meridian, represents
the direction of the lines of force due to the terrestrial magnetic field. The
field due to this in any one place is uniform.
708. Total action of two magnets on each other. In the above case
of the torsion balance one pole of the magnet to be tested was at so great
a distance that it could not appreciably modify the influence of the other.
When, however, the conditions are such that both poles act, then they follow
a different law, as will now be demonstrated.
Let ns (fig. 581) be a small magnetic needle, free to move in a horizontal
plane, and let NS be a bar magnet placed at right angles to the magnetic
meridian, at a distance which is great compared with its
own dimensions, and so that the straight line drawn through
its middle point and that of the needle coincides with the
magnetic meridian. The two poles S and s will repel each
other in the direction sa : if mm, is the repellent force
which these two poles would exert at the unit distance, then
mn *i is the force which they would exert at the distance
Sj = r ; let this force be represented in direction and strength
by the line sa. Similarly, the pole N will act on j, with a
force represented by the line sc ; S and N being at the same
distance r from s y sa and sc are equal, and their resultant
may be represented by the line sb. From the similarity of
the triangles bsa and NSj we have the proportion Sj : SN =
-as : bs ; if / is the value of the resultant &r, that is the total
action of the magnet SN on the pole j, and if / be half the
length of the magnet SN, we have r : 2 /= - :/ from
Fig. 581.
which /= ; that is, the total action of the magnet NS upon another is
inversely as the cube of the distance r.
-709] Determination of Magnetism in Absolute Measure. 615
If the two magnets be placed as represented in fig. 582, the needle
being in the magnetic meridian, and the deflecting magnet at right angles
thereto, and so that the prolongation of its axis bisects the needle, then if
;//;>>/! is the force with which the pole N attracts the pole s at the unit dis-
tance, ;;/ and ;;/, being the strength of the poles in the bar magnet, and the
magnetic needle respectively ; the attracting force at the distance N.y will
be /"-' , / being as before the half-
(r + /)
length of the magnet, and r the dis-
tance of the pole s from the middle
of the magnet NS ; in like manner
the repellent force with which S acts
upon s will be ~ ^. If ns is small
v /
compared with the distance of the bar magnet NS, the direction of these
forces may be assumed to be parallel, and at right angles to ns. Since S
is nearer than N the repulsion will predominate, and the total force with
which the magnet NS acts on the pole s is
F _ mm, _
which, assuming that / is so small in comparison with r that its square and
higher powers may be neglected, gives approximately
-p _ 4 mm, I
-75
so that compared with the first position of the magnet
F-2/
709. Determination of magnetism in absolute measure. The com-
parisons of the intensity of the earth's magnetism in different places (701) are
only relative. Of late years much attention has been devoted to the method
of expressing not only this, but all other magnetic forces in what is called
absolute measure. This term is used as opposed to relative, and does not
imply that the measure is absolutely accurate, or that the units of comparison
employed are of perfect construction ; it means that the measurements,
instead of being a simple comparison with an arbitrary quantity of the same
kind as that measured, are referred to the fundamental units of time, space,
and mass (21).
The manner in which this oetermination is made in the case of magnetism,
depends essentially on the observation of the oscillation of a horizontal bar
magnet under the influence of the earth's magnetism ; and in the second
place, on observing the deflection of a magnetic needle under the influence
of this same magnet.
When a bar magnet suspended by a thread without torsion, free to oscil-
late in a horizontal plane, is deflected from its position of equilibrium and
then left to itself, it vibrates backwards and forwards through its position of
equilibrium, making oscillations which, if small, are isochronous like those of
the pendulum. The number of these oscillations in a given time depends on the
mass and dimensions of the bar, on its magnetic power, and on the intensity of
6i6 On Magnetism. [709
the earth's magnetism in the place of observation. The time, /, of a complete
/ /
oscillation of such a magnet is represented by the formula / = 27r A / - ;
V -H- M
where k is the moment of inertia of the magnet ; that is, the mass which must
be concentrated at the unit of distance from the centre of suspension, to
present the same resistance to change of angular velocity about this centre
as the magnet itself actually does. The moment of inertia of a magnet
may be determined theoretically if it be homogeneous in structure, and of a
regular geometrical shape ; or it may be determined experimentally by first
observing the time of oscillation of the magnet under the influence of the
earth's magnetism, and then the time when it has been loaded with a mass
the inertia of which is known, and which does not alter the magnetic moment
of the bar. M is the magnetic moment of the bar itself, and H is the force
of the earth's manetism. Hence
(i).
This expression gives the force which, applied in opposite directions at
the ends of a lever of unit length, placed at right angles to the direction of
this force, would have the same effect in tending to turn the lever, as the
magnetic force of the earth has in tending to turn the magnet about a vertical
axis when it is set at right angles to the magnetic meridian.
Now the value of HM depends on the nature of the bar, and on the force
of the earth's magnetism in the place in question. If the bar were magne-
tised more or less strongly, or if the same bar were removed to a different
locality, the product would have a different value. We must, therefore, find
some independent relation between H and M, which will give rise to a new
equation, and thus M, the magnetic moment of the bar, would be got rid of,
and an absolute value be obtained for H.
Such a relation exists in the deflection from the magnetic meridian, which
a bar magnet produces in a magnetic needle.
If in the formula in the preceding article we put M = 2ml, then 2 ;; * =
the + or force acting on either pole of the magnetic needle, and, as both
poles are acted on, the magnet will be subject to the action of a couple, the
moment of which will be expressed by --| 2/' cos a ; where a is the angle
of deflection, /' the half-length of the small magnetic needle ; let M' = 2m' I'.
In like manner the earth's magnetism will act upon the magnetic needle
with a couple the moment of which is expressed by H;;z' 2/' sin a = HM'
sin a. Now when the needle is in equilibrium these forces are equal ; that
is
2M a M/ cos a-HM' sina,
from which ^=- = r* tan a (2).
Jri
Combining (i) and (2) we get the expression
TT 77 / k
~/VVtan
709] Determination of Magnetism in Absolute Measure. 617
an expression which involves no other physical units than those of length
(involved in k and r), mass (involved in ), and time (involved in /), so that
the value of H can be expressed in absolute measure.
The value for H in this expression only gives the horizontal compo-
nent of the earth's magnetism ; the total force is obtained by dividing the
value of H by the cosine of the angle of dip for the place and time of obser-
vation.
The numerical value of H will depend, moreover, on the units taken. On
the centimctre-gramme-second system the unit offeree is called a dyne. It is
the force which acting upon a gramme for a second generates a velocity of a
centimetre per second. The value of H at Greenwich for the year 1877, ex-
pressed in this unit, is 0-18079 of a dyne ; that is, the horizontal component
of the earth's magnetism at this place acting on the unit of magnetism, asso-
ciated with one gramme of matter, would produce a velocity of 0-18079
c entimetres at the end of a second. The angle of dip at this time and place
being 67 37', we get the total force = 0-4745 units. If British units namely,
the foot, grain, second be employed, the unit of force is that which by acting
for a second on a grain gives to it a velocity of a foot per second, and the
unit magnetic pole is such that if placed one foot from a second equal pole
it will repel it with a force equal to the unit just defined. To convert the
value of H when expressed in centimetres, grammes, and seconds into the
equivalent value referred to British units, we must multiply by 21-69. ^ n like
manner to convert magnetic forces referred to British units into the corre-
sponding values expressed in centimetres, grammes, and seconds we must
multiply by 0*0461 = ^r~-
6 1 8 On Magnetism. [710-
CHAPTER IV.
PROCESSES OF MAGNETISATION.
710. Magnetisation. The various sources of magnetism are the in-
fluence of natural or artificial magnets, terrestrial magnetism, and electricity.
This last method will be described under voltaic electricity. The three prin-
cipal methods of magnetisation by magnets are known by the technical names
of single touch, separate touch, and double touch.
711. Method of single touch. This consists in moving the pole of a
powerful magnet from one end to the other of the bar to be magnetised, and
repeating this operation several times always in the same direction. The
neutral magnetism is thus gradually decomposed throughout all the length of
the bar, and that end of the bar which was touched last by the magnet is of
opposite polarity to the end of the magnet by which it has been touched.
This method only produces a feeble magnetic power, and is, accordingly, only
used for small magnets. It has further the disadvantage of frequently deve-
loping consequent poles.
712. Method of separate touch. This method, which was first used by
Dr. Knight in 1745, consists in placing the two opposite poles of two magnets
of equal force in the middle of the bar to be magnetised, and in moving each
of them simultaneously towards the opposite ends of the bar. Each magnet
is then placed in its original position, and the operation repeated. After
several frictions on both faces of the bar it is magnetised.
In Knight's method the magnets are held vertically. Duhamel improved
the method by inclining the magnets, as represented in fig. 583 ; and still
more, by placing the bar to be magnetised on the opposite poles of two fixed
magnets, the action of which strengthens that of the movable magnets. The
relative position of the poles of the magnets is indicated in the figure. This
method produces the most regular magnets.
713. Method of double touch. In this method, which was invented by
Mitchell, the two magnets are placed with their poles opposite each other in
the middle of the bar to be magnetised. But, instead of moving them in
opposite directions towards the two ends, as in the method of separate touch,
they are kept at a fixed distance by means of a piece of wood placed between
them (fig. 583), and are simultaneously moved first towards one end, then
from this to the other end, repeating this operation several times, and finish-
ing in the middle, taking care that each half of the bar receives the same
number of frictions.
Epinus, in 1758, improved this method by supporting the bar to be mag-
netised, as in the method of separate touch, on the opposite poles of two
powerful magnets, and by inclining the bars at an angle of 15 to 20. In
-715]
Magnetism of Iron Ships.
619
practice, instead of two bar magnets, it is usual to employ a horse-shoe
magnet, which has its poles conveniently close together.
By this method of double touch, powerful magnets are obtained, but they
Fig. 583-
have frequently consequent poles. As this would be objectionable in com-
pass needles, these are best magnetised by separate touch.
714. Magnetisation by the action of tne earth. The action of the
earth on magnetic substances resembles that of a magnet, and hence the
terrestrial magnetism is constantly tending to separate the two magnetisms
which are in the neutral state in soft iron and in steel. But, as the coercive
force is very considerable in the latter substance, the action of the earth is
inadequate to produce magnetisation, except when continued for a long time.
This is not the case with perfectly soft iron. When a bar of this metal is
held in the magnetic meridian parallel to the inclination, the bar becomes at
once endowed with feeble magnetic polarity. The lower extremity is a north
pole, and if the north pole of a small magnetic needle be approached, it will
be repelled. This magnetism is of course unstable, for if the bar be turned
the poles are inverted, as pure soft iron is destitute of coercive force.
\Vhile the bar is in this position, a certain amount of coercive force may
be imparted to it by giving it several smart blows with a hammer, and the
bar retains for a short time the magnetism which it has thus obtained. But
the coercive force thus developed is very small, and after a time the mag-
netism disappears.
If a bar of soft iron be twisted while held vertically, or, better, in the
plane of the dip, it acquires a feeble permanent magnetism.
It is this magnetising action of the earth which develops the magnetism
frequently observed in steel and iron instruments, such as fire-irons, rifles,
lamp-posts, railings, gates, lightning-conductors, c., which remain for some
time in a more or less inclined position. They become magnetised with their
north pole downward, just as if placed over the pole of a powerful magnet.
The magnetism of native black oxide of iron has doubtless been produced by
the same causes ; the very different magnetic power of different specimens
being partly attributable to the different positions of the veins of ore with
regard to the line of dip. The ordinary irons of commerce are not quite pure,
and possess a feeble coercive force ; hence a feeble magnetic polarity is
generally found to be possessed by the tools in a smith's shop. Cast iron,
too, has usually a great coercive force, and can be permanently magnetised.
The turnings, also, of wrought iron and of steel produced by the powerful
lathes of our ironworks are found to be magnetised.
715. Magnetism of iron snips. The inductive action of terrestrial
magnetism upon the masses of iron always found in ships exerts a disturb-
62O On Magnetism. [715-
ing action upon the compass needle. The local attraction, as it is called,
may be so considerable as to render the indications of the needle almost
useless if it be not guarded against. A full account of the manner in
which local attraction is produced, and in which it is compensated, is in-
consistent with the limits of this book, but the most important points are
the following :
i. A vertical mass of soft iron in the vessel, say in the bows, would
become magnetised under the influence of the earth ; in the northern hemi-
sphere, the lower end would be a north pole, and the upper end a south
pole ; and as the latter may be assumed to be nearer the north pole of the
compass needle, it would act upon it. So long as the vessel was sailing in
the magnetic meridian this would have no effect ; but in any other direction
the needle would be drawn out of the magnetic meridian, and a little con-
sideration will show that when the ship was at right angles to the magnetic
meridian the effect would be greatest. This vertical induction would dis-
appear twice in swinging the ship round, and would be at its maximum
twice ; hence the deviation due to this cause is known as semicircular
deviation.
ii. Horizontal masses again, such as deck-beams, are also acted upon
inductively by the earth's magnetism, and their induced magnetism exerts
a disturbing influence upon the magnetic needle. The effect of this hori-
zontal induction will disappear when the ship is in the magnetic meridian
and also when it is at right angles thereto. In positions intermediate to the
above the disturbing influence will attain its maximum. Hence in swinging
a ship round there would be four positions of the ship's head in which the
influence would be at a maximum, and four in which it would be at a mini-
mum. The effect of horizontal induction is accordingly spoken of as quad-
rantal deviation.
The influence of both these causes, vertical and horizontal induction,
may be remedied in the process of ' swinging the ship.' This consists in
comparing the indications of the ship's compass with those of a standard
compass placed on shore. The ship is then swung round in various posi-
tions, and by arranging small vertical and horizontal masses of soft iron in
proximity to the steering compass, positions are found for them in which the
inductive action of the earth upon them quite neutralises the influence of the
earth's magnetism upon the ship ; and in all positions of the ship, the com-
pass points in the same direction as the one on shore.
iii. The extended use of iron in ship-building, more especially when the
frames are entirely of iron, has increased the difficulty. In the process of
building a ship, the hammering and other mechanical operations to which
it is subject, while under the influence of the earth's magnetism, will cause
it to become to a certain extent permanently magnetised. The distribution
of the magnetism, the direction of its magnetic axis, will depend on the
position in which it has been built ; it may or may not coincide with the
direction of the keel. The vessel becomes in short a huge magnet, and will
exert an influence of its own upon the compass quite independently of ver-
tical or horizontal induction. The influence is semicircular ; that is, it dis-
appears when the magnetic axis of the ship is in the magnetic meridian, and
is greatest at right angles to it. It may be compensated by two permanent
-717] Magnetic Battery. 62 1
magnets placed near the compass in suitable positions found by trial during
the process of swinging the ship. Supposing the inherent magnetism of the
ship to have the power of drawing the compass a point to the east, the com-
pensating magnets may be so arranged as to tend to draw it a point to the
west, and thus keep it in the magnetic meridian. If, however, the inherent
magnetism be destroyed, from whatever cause, it is clear that the magnets
will now draw it aside a point too much to the west. This is the source of a
new difficulty. It has been found that a ship which at the time of sailing
was properly compensated, would, on returning from a long voyage, have its
compasses over-compensated. The buffeting which the ship had experienced
had destroyed its inherent magnetism, and numerous instances are known
where the loss of a vessel can be directly traced to this cause. Fortunately,
it has been found that after some time a ship's magnetic condition is virtu-
ally permanent, and is unaltered by any further wear and tear. The magne-
tism which it then retains is called its permanent magnetism, in opposition
to the sub-permanent which it loses.
The difficulty of adequately compensating compasses, which is greatly
increased by the armour-plated and turret ships now in use, has induced one
school to throw over any attempt at correction ; but by careful observation
of the magnetic condition of a ship, and tabulating the errors to construct a
table, and comparing this with the indications of the compass at any one
time, the true course can be made out.
In the Royal Navy, the plan now adopted is to combine both methods :
compensate the errors to a considerable extent, and then construct a table
of the residual errors.
716. Magnetic saturation. Experiment has shown that to a certain
extent the magnetic force which can be imparted to a steel bar increases with
the magnetising force used. It depends also on the number of strokes or
movements of the magnetising magnets or coils ; on the form and dimensions
of the bar, on its density, on the quantity of carbon it contains, on its hard-
ness, and on the manner in which it is tempered. Yet there is a limit to the
magnetic force which can be imparted to iron or steel, and when this is at-
tained, the bar is said to be saturated or magnetised to saturation. A bar
may indeed be magnetised beyond this point, but this excess is temporary ;
it gradually diminishes until the magnet has sunk to its point of saturation.
This is intelligible, for the magnetisms once separated tend to reunite,
and when their attractive force is equal to that which opposes their separa-
tion that is, the coercive force of the metal equilibrium is attained, and
the magnet is saturated. Hence, more magnetism ought to be developed
in bars than they can retain, in order that they may decline to their perma-
nent state of saturation. To increase the magnetism of an unsaturated bai,
a less feeble magnet must not be used than that by which it was originally
magnetised.
717. Magnetic battery. A magnetic battery or magazine consists of
a number of magnets joined together by their similar poles. Sometimes
they have the form of a horse-shoe, and sometimes a rectilinear form. The
batter)' represented in fig. 584 consists of five superposed steel plates. That
in fig. 585 consists of twelve plates, arranged in three layers of four each.
The horse-shoe form is best adapted for supporting a weight, for then both
622
On Magnetism. [717-
In both the bars are magnetised separately, and
poles are used at once.
then fixed by screws.
The force of a magnetic battery consisting of n similar plates equally
magnetised, is not n times as great as that of a single one, but is somewhat
smaller. These magnets mutually en-
feeble each other ; manifestly because,
for instance, each north pole evokes
south magnetism in the adjacent north
pole, and thereby diminishes some of its
north polarity. The magnetism of a
plate which has formed part of such a
battery will be found to be materially
less than it was originally.
Thus Jamin found that six equal plates
which had each the portative force 18
kilos, only lifted 64 kilos when arranged
as a battery, instead of 108 ; and when
removed from the battery, each of them
had only the portative force 9 to 10 kilos.
The force is increased by making the
lateral plates I or 2 centimetres shorter
than the one in the middle (fig. 584).
718. Armatures. When even a steel
bar is at its limit of saturation, it gradu-
ally loses its magnetism. To prevent
this, armatures or keepers are used ;
Fig. .584-
these are pieces of soft iron, A and B (fig. 585), which are placed in contact
with the poles. Acted on inductively, they become powerful temporary
magnets, possessing opposite polarity to that of the inducing pole ; they
Fig 585-
thus react in turn on the permanent magnetism of the bars, preserving and
even increasing it.
When the magnets are in the form of bars, they are arranged in pairs,
as shown in fig. 586, with opposite poles in juxtaposition, and the circuit is
Fig. 586.
completed by two small bars of soft iron, AB. Movable magnetic needles,
if not clamped down, set spontaneously towards the magnetic poles of the
earth, the influence of which acts as a keeper.
-719] Portative Force. Power of Magnets. 623
A horse-shoe magnet has a keeper attached to it, which is usually ar-
ranged so as to support a weight. The keeper becomes magnetised under
the influence of the two poles, and adheres with
great force : the weight which it can support being
more than double that which a single pole would
hold.
In respect to this weight, a singular and hitherto
inexplicable phenomenon has been observed. When
contact is once made, and the keeper is charged with
its maximum weight, any further addition would
detach it ; but if left in contact for a day, an addi-
tional weight may be added without detaching it, and
by slightly increasing the weight every day it may
ultimately be brought to support a far greater load
than it would originally. But if contact be once
broken, the weight it can now support does not much
exceed its original charge.
It is advantageous that the surface of the magnet
and armatures which are in contact should not be Fi s- 587.
plane but slightly cylindrical, so that they touch along a line.
In providing a natural magnet with a keeper, the line joining the two
poles is first approximately determined by means of iron filings. Two poles
of soft iron (fig. 587), each terminating in a massive shoe, are then applied
to the faces corresponding to the poles. Under the influence of the natural
magnet, these plates become magnetised, and if the letters A and B repre-
sent the position of the poles of the natural magnet, the poles of the arma-
ture are a and b.
719. Portative force. Power of magnets. The portative force is
the greatest weight which a magnet can support. Hacker found that the
portative force of a saturated horse-shoe magnet, which, by repeatedly de-
taching the keeper, had become constant, may be represented by the formula
in which P is the portative force of the magnet,^ its own weight, and a a
coefficient which varies with the nature of the steel and the mode of mag-
netising. Hence a magnet which weighs 1,000 ounces only supports 25
times as much as one weighing 8 ounces or y| s as heavy, and 125 such bars
would support as much as one which is as heavy as all together. It appears
immaterial whether the section of the bar is quadratic or circular, and the
distance of the legs is of inconsiderable moment ; it is important, however,
that the magnet be suspended vertically, and that the load be exactly in the
middle. In Hacker's magnets the value of a was 10-33, while in Logemann's
it was 23. By arranging together several thin magnetised plates Jamin
constructed bar magnets which support 1 5 times their own weight.
The strength of two bar magnets may be compared by the following
simple method, which is known as Kiilp's compensation method: A small
magnetic compass needle is placed in the magnetic meridian. One pole of
one of the magnets to be tested is then placed at right angles to the mag-
netic meridian in the same plane as the needle, and so that its axis prolonged
624 On Magnetism. [719-
would bisect the needle. The compass needle is thereby deflected through
a certain angle. The similar pole of the other magnet is then placed
similarly on the other side of the needle, and a position found for it in
which it exactly neutralises the action of the first magnet ; that is, when
the needle is again in the magnetic meridian. If the magnets are not too
long, compared with their distance from the needle, their strengths are ap-
proximately as the cubes of the distance of the acting poles from the mag-
netic needle.
720. Circumstances which influence the power of magnets. All bars
do not attain the same state of saturation, for their coercive force varies
Twisting or hammering imparts to iron or steel a considerable coercive force
But the most powerful of these influences is the operation of tempering (95).
Coulomb found that a steel bar tempered at dull redness and magnetised to
saturation, made ten oscillations in 93 seconds. The same bar tempered at
a cherry -red heat, and similarly magnetised to saturation, only took 63
seconds to make ten oscillations.
Hence it would seem, that the harder the steel the greater is its coercive
force ; it receives magnetism with much greater difficulty, but retains it more
effectually. It appears from Jamin's experiments that no general rule of this
kind can be laid down ; for each specimen of steel there seems, according
to the proportion of carbon which it contains, to be a certain degree of
tempering which is most favourable for the development of permanent
magnetisation.
Very hard steel bars have the disadvantage of being very brittle, and in
the case of long thin bars a hard tempering is apt to produce consequent
*poles. Compass needles are usually tempered at the blue heat that is, about
300 C. by which a high coercive force is obtained without great fragility.
Steel is magnetised with difficulty even when placed for some time in a coil
through which a powerful current is passing ; iron under these circum-
stances is magnetised at once. If a short coil covering only a portion of the
steel bars be moved backwards and forwards the magnetisation is more
complete.
The hardness of steel, and the proportion of carbon which it contains, exert
an important influence on the degree to which it can be magnetised. For
the same degree of hardness, the magnetisation increases with the proportion
of carbon in the steel, and more markedly the smaller this proportion ; with
the same proportion of carbon it increases with the hardness of the steel. It
appears that the compound of iron and carbon in steel is the carrier of the
permanent magnetism, and the interjacent particles of iron the carriers of
the temporary magnetism. Holtz magnetised plates of English corset steel
to saturation and determined their magnetic moment ; they were then placed
in dilute hydrochloric acid, by which the iron was eaten away, and the
magnetic moment determined when the plate had been magnetised to satura-
tion after each such treatment. It was thus found that, with a diminution
in the proportion of iron, there was an increase in the magnetic moment for
the unit of weight. Holtz found, however, that pure iron prepared by elec-
trolysis can acquire permanent magnetism.
Jamin investigated the distribution of force in magnets by suspending
from one arm of a delicate balance a small iron ball, and then ascertaining
-720] Power of Magnets. 62$
what force applied at the other arm, was required to detach the ball when
placed in contact with various positions of the magnet to be investigated.
Taking thus a thin plate magnetised to saturation, it was found that the
magnetism increased with the thickness, but did not materially vary with
the breadth of the plate. The magnetic force was developed almost ex-
clusively at the ends. The curve representing the magnetic force (721)
was convex towards the poles at the ends. If now several similar plates are
superposed, the corresponding curves become steeper and prolonged towards
the middle ; the magnetic force thus becomes increased. When the curves
run into each other in the middle the maximum of the combination is reached ;
any additional plates produce no increase in the strength. Steel bars may
also be magnetised so as to show the same curves, and such bars and com-
binations of plates are called by Jamin normal magnets.
Jamin found that magnetisation extends deeper in a bar than has been
usually supposed ; in soft and annealed steel it penetrates deeply. The
depth diminishes with the hardness of the steel and the proportion of carbon
it contains. If plates of varying thickness are so thin that the magnetisation
can entirely penetrate them, the thicker of these plates are more strongly mag-
netised by the same force, for the magnetisation extends through a thicker
layer than the thinner ones ; if, however, the plates are very thick, they are
magnetised to the same extent by one and the same force. With equal bars
the thickness of the magnetic layer varies with the strength of the magnetising
force. Jamin proved this by placing the plates in sulphuric acid ; he found
magnetism in bars which had been exposed to the stronger force, while those
which had been more feebly magnetised showed none when they had been
eaten away by the acid to the same extent. He thus showed that the
magnetism which had penetrated was as strong as that on the surface.
Xoltz has made some experiments on the influence of solid bars as against
hollow tubes in the construction of permanent steel magnets. The latter
are to be preferred ; they are decidedly cheaper, as they need not be bored,
but may be bent from steel plates. A bar and a tube of the same steel,
125 mm. in length by 13 mm. diameter, and the tube 175 mm. thick, were
magnetised to saturation, and their magnetic moments determined by the
method of oscillation (705) the tube being loaded with copper. The mag-
netism of the tube was to that of the bar as i'6 : i. The tubes also retained
their magnetisation better. After the lapse of six months the ratio of the
magnetisation of the tube was to that of the bar as 27 : i. A magnetised
steel tube filled with a soft iron core had scarcely any directive force.
Temperature. Increase of temperature always produces a diminution of
magnetic force. If the changes of temperature are small, those of the atmo-
sphere for instance, the magnet is not permanently altered. Kuppfer allowed
a magnet to oscillate at different temperatures, and found a definite decrease
in its power with increased temperature, as indicated by its slower oscillations.
In the case of a magnet 2 inches in length, he observed that with an increase
of each degree of temperature the duration of 800 oscillations was 0-4"
longer. If n be the number of oscillations at zero, and n^ the number at /,
then
n = n l (\-ct],
where c is a constant depending in each case on the magnet used. This
E E
626 On Magnetism. [720-
formula has an important application in the correction of the observations of
magnetic intensity which are made at different places and at different tem-
peratures, and which, in order to be comparable, must first be reduced to a
uniform temperature.
When a magnet has been more strongly heated, it does not regain its
original force on cooling to its original temperature, and when it has been
heated to redness, it is demagnetised. This was first shown by Coulomb,
who took a saturated magnet, progressively heated it to higher tem-
peratures, and noted the number of oscillations after each heating.
The higher the temperature to which it had been heated the slower its
oscillations.
A magnet heated to bright redness loses its magnetism so completely
that it is quite indifferent, not only towards iron, but also towards another
magnet, and this holds so long as this high temperature continues. Incan-
descent iron also does not possess the property of being attracted by the
magnet. Hence there is in the case of iron a magnetic limit, beyond which
it is unaffected by magnetism. Such a magnetic limit exists in the case of
other magnetic metals. With cobalt, for instance, it is far beyond a white
heat, for at the highest temperatures hitherto examined it is still magnetic ;
the magnetic limit of chromium is somewhat below red heat ; that of nickel
at about 350 C. and of manganese at about 15 to 20 C.
A change of temperature whether from 16 to 100, or from 100 to 16,
increases the strength of temporary or induced magnetism both in the case
of iron and of steel.
Percussion and Torsion. When a steel bar is hammered while being
magnetised it acquires a much higher degree of magnetisation than it would
without this treatment. Conversely when a magnet is let fall, or is otherwise
violently disturbed, it loses much of its magnetisation. Torsion exerts a
great influence on the magnetisation of a bar, and the interesting phenomenon
has been observed that torsion influences magnetism in the same manner
as magnetism does torsion. Thus the permanent magnetisation of a steel bar
is diminished by torsion, but not proportionally to the increase of torsion.
In like manner the torsion of twisted iron wires is diminished by their being
magnetised, though less so than in proportion to their magnetisation. Re-
peated torsions in the same direction scarcely diminish magnetisation, but
a torsion in the opposite direction produces a new diminution of the magne-
tism. In a perfectly analogous manner, repeated magnetisations in the same
sense scarcely diminish torsion, but a renewed magnetisation in the opposite
direction does so.
721. Distribution of free magnetism. Coulomb investigated the dis-
tribution of magnetic force by placing a large magnet in a vertical position
in the magnetic meridian ; he then took a small magnetic needle, and, having
ascertained the number of its oscillations under the influence of the earth's
magnetism alone, he presented it to different parts of the magnet. The
oscillations were fewer as the needle was nearer the middle of the bar, and
when they had reached that position their number was the same as under
the influence of the earth's magnetism alone. For saturated bars of more
than 7 inches in length the distribution could always be expressed by a
curve whose abscissae were the distances from the ends of the magnet, and
-722] Mayer's Floating Magnets. 627
whose ordinates were the force of magnetism at these points. With magnets
of the above dimensions the poles are at the same distance from the end ;
Coulomb found the distance to be r6 inch in a bar 8 inches long. He also
found that, with shorter bars, the distance of the poles from the end is | of
the length ; thus with a bar of three inches it would be half an inch. These
results presuppose that the other dimensions of the bar are very small as
compared with its length, that it has a regular shape, and is uniformly
magnetised. When these conditions are not fulfilled, the positions of the
poles can only be determined by direct trials with a magnetic needle. With
lozenge-shaped magnets the poles are nearer the middle. Coulomb found
that these lozenge-shaped bars have a greater directive force than rectangular
bars of the same weight, thickness, and hardness.
722. Mayer's floating: magnets. The reciprocal action of magnetic
poles may be conveniently illustrated by an elegant method devised by
Prof. A. M. Mayer. Steel sewing-needles are magnetised so that their
points are north poles, and their eyes, which are thus south poles, just
project through minute cork discs, so that when placed in water the magnets
float in a vertical position. If the north pole of a strong magnet is brought
near a number of these floating magnets they are attracted by it, and take up
definite positions, forming figures which depend on the reciprocal repulsion
of the floating magnets, and on their number. Some of them are repre-
sented in fig. 588. The more complex produce more than one arrange-
6a 63
*
ment which are not equally stable, the letters
silk or flannel. On approaching the metal to an electrical pendulum (fig.
589). the pith ball will be attracted. If the metal is held in the hand electri-
city is indeed produced by friction but it immediately passes through the
body into the ground.
If, too, the cap of a gold-leaf electroscope be briskly flapped with a dry
silk handkerchief, the gold leaves will diverge.
727. Distinction of tne two kinds of electricity. If electricity be
developed on a glass rod by friction with silk, and the rod be brought near
an electrical pendulum, the ball will be attracted to the glass, and after
momentary contact will be again repelled. By this contact the ball becomes
electrified, and so long as the two bodies retain their electricity, repulsion
follows whenever they are brought near each other. If a stick of sealing-wax
electrified by friction with flannel or silk be approached to another electrical
pendulum, the same effects will be produced the ball will fly towards the
wax, and after contact will be repelled. Two bodies, which have been
charged with electricity, repel one another. But the electricities respectively
developed in the preceding cases, are not the same. If, after the pith ball
had been touched with an electrified glass rod, an electrified stick of sealing-
wax, and then an electrified glass rod, be alternately approached to it, the
pith ball will be attracted by the former and repelled by the latter. Simi-
larly, if the pendulum be charged by contact with the electrified sealing-
wax, it will be repelled when this is approached to it, but attracted by the
approach of the excited glass rod.
On experiments of this nature, Dufay first made the observation that
there are two different electricities : the one developed by the friction of
glass, the other by the friction of resin or shellac. To the first the name
I'itreons electricity is given ; to the second the name resinous electricity.
632 Frictional Electricity. [728-
728. Theories of electricity. Two theories have been proposed to
account for the different effects of electricity. Franklin supposed that there
exists a peculiar, subtle, imponderable fluid, which acts by repulsion on its
own particles, and pervades all matter. This fluid is present in every sub-
stance in a quantity peculiar to it, and when it contains this quantity it is in
the natural state, or in a state of equilibrium. By friction certain bodies
acquire an additional quantity of the fluid, and are said to be positively
electrified ; others by friction lose a portion, and are said to be negatively
electrified. The former state corresponds to vitreous electricity, and the
latter to resinous electricity. Positive electricity is represented by the
sign + , and negative electricity by the sign ; a designation based on
the algebraical principle, that when a plus quantity is added to an equal
minus quantity zero is produced. So when a body containing a quantity of
positive electricity is touched with a body possessing an equivalent quantity
of negative electricity, a neutral or zero state is produced.
The theory of Symmer assumes that every substance contains an indefinite
quantity of a subtle, imponderable matter, which is called the electric fluid.
This fluid is formed by the union of two fluids \hepositive and the negative.
When they are combined they neutralise one another, and the body is then
in the natural or neutral state. By friction, and by several other means,
the two fluids may be separated, but one of them can never be excited
without a simultaneous production of the other. There may, however, be a
greater or less excess of the one or the other in any body, and it is then said
to be electrified positively or negatively. As in Franklin's theory, vitreous
corresponds to positive and resinous to negative electricity. This distinction
is merely conventional : it is adopted for the sake of convenience, and there
is no other reason why resinous electricity should not be called positive
electricity.
Fluids of the same name repel one another, and fluids of opposite kinds
attract each other. The fluids can circulate freely on the surface of certain
bodies, which are called conductors, but remain confined to certain parts of
others, which are called nonconductors.
It must be added that this theory is quite hypothetical ; but its general
adoption is justified by the convenient explanation which it gives of electrical
phenomena.
729. Action of electrified bodies on each other. Admitting the two-
fluid hypothesis, the phenomena of attraction and repulsion may be enunciated
in the following law :
Two bodies charged with the same electricity repel each other; two bodies
charged with opposite electricities attract each other.
These attractions and repulsions take place in virtue of the action which
the two electricities exert on themselves, and not in virtue of their action on
the particles of matter.
730. I,aw of the development of electricity by friction. Whenever
two bodies are rubbed together, the neutral electricity is decomposed. Two
electricities are developed at the same time and in equal quantities one
body takes positive and the other negative electricity. This may be proved
by the following experiment devised by Faraday : A small flannel cap
provided with a silk thread (fig. 592) is fitted on the end of a stout rod of
-731] Development of Electricity by Pressure and Cleavage. 633
shellac, and rubbed round a few times. When the cap is removed by means
of a silk thread, and presented to a pith-ball pendulum charged with positive
electricity, the latter will be repelled, proving that the
flannel is charged with positive electricity ; while if the
shellac is presented to the pith ball, it will be attracted,
showing that the shellac is charged with negative
electricity. Both electricities are present in equal
quantities ; for if the rod be presented to the electro-
scope before removing the cap, no action is observed.
The electricity developed on a body by friction
depends on the rubber as well as the body rubbed.
Thus glass becomes negatively electrified when rubbed
with cat ; s skin, but positively when rubbed with silk.
In the following list the substances are arranged in such an order that each
becomes positively electrified when rubbed with any of the bodies following,
but negatively when rubbed with any of those which precede it :
Fig 5Q2>
1. Cat's skin. 5. Glass.
2. Flannel. 6. Cotton.
3. Ivory. 7. Silk.
4. Rock crystal. 8. The hand.
9. Wood. 13. Resin.
10. Metals. 14. Sulphur.
11. Caoutchouc. 15. Gutta-percha.
12. Sealing-wax. 16. Gun-cotton.
The nature of the electricity set free by friction depends also on the
degree of polish, the direction of the friction, and the temperature. If two
glass discs of different degrees of polish are rubbed against each other, that
which is most polished is positively, and that which is least polished is
negatively electrified. If two silk ribbons of the same kind are rubbed across
each other, that which is transversely rubbed is negatively and the other
positively electrified. If two bodies of the same substance, of the same
polish, but of different temperatures, are rubbed together, that which is most
heated is negatively electrified. Generally speaking, the particles which are
most readily displaced are negatively electrified.
Poggendorff has observed that many substances which have hitherto been
regarded as highly negative, such as gun-paper, gun-cotton, and ebonite, yield
positive electricity when rubbed with leather coated with amalgam.
731. Development of electricity by pressure and cleavage.
Electrical excitement may be produced by other causes than friction. If a
disc of wood, covered with oiled silk, and a metal disc, each provided with
an insulating handle, be pressed together, and then suddenly separated, the
metal disc is negatively electrified. A crystal of Iceland spar pressed be-
tween the fingers becomes positively electrified, and retains this state for
some time. The same property is observed in several other minerals, even
though conductors, provided they be insulated. If cork and caoutchouc be
pressed together, the first becomes positively and the other negatively
electrified. A disc of wood pressed on an orange and separated carries
away a good charge of electricity if the contact be rapidly interrupted.
But if the disc is slowly removed the quantity is smaller, for the two fluids
recombine at the moment of their separation. For this reason there is no
apparent effect when the two bodies pressed together are good conductors.
Cleavage also is a source of electricity. If a plate of mica be rapidly
EE3
634 Frictional Electricity. [731-
split in the dark, a slight phosphorescent light is perceived. Becquerel
fixed glass handles to each side of a plate of mica, and then rapidly sepa-
rated them. On presenting each of the plates thus separated to an electro-
scope, he found that one was negatively and the other positively electrified
If a stick of sealing-wax be broken, the ends exhibit different electricities.
All badly conducting crystalline substances exhibit electrical indications
by cleavage. The separated plates are always in opposite electrical condi-
tions, provided they are not good conductors : for if they were, the separa-
tion would not be sufficiently rapid to prevent the recombination of the two
electricities. To the phenomena here described is due the luminous appear-
ance seen in the dark when sugar is broken.
732. Pyroelectricity. Certain minerals, when warmed, acquire electri-
cal properties ; a phenomenon to which the name pyroelectricity is given.
It is best studied in tourmaline, in which it was first discovered from the
fact that this mineral has the power of first attracting and then repelling hot
ashes when placed among them.
To observe this phenomenon, a crystal of tourmaline is suspended hori-
zontally by a silk thread, in a glass cylinder placed on a heated metal plate.
On subsequently investigating the electric condition of the ends by approach-
ing to them successively an electrified glass rod, one end will be found to be
positively electrified, and the other end negatively electrified, and each end
shows this polarity as long as the temperature rises. The arrangement of
the electricity is thus like that of the magnetism in a magnet. The points
at which the intensity of free electricity is greatest are" called the poles, and
the line connecting them is the electric axis. When a tourmaline, while
thus electrified, is broken in the middle, each of the pieces has its two
poles.
These polar properties depend on the change of temperature. When a
tourmaline, which has become electrical by being warmed, is allowed to cool
regularly, it first loses electricity, and then its polarity becomes reversed ;
that is, the end which was positive now becomes negative, and that which
Avas negative becomes positive, and the position of the poles now remains
unchanged so long as the temperature sinks. Tourmaline only becomes
pyroelectric within certain limits of temperature ; these vary somewhat with
the length, but are usually between 10 and 150 C. Below and above these
temperatures it behaves like any other body, and shows no polarity.
The name analogous pole is given to that end of the crystal which shows
positive electricity when the temperature is rising, and negative electricity
when it is sinking ; antilogous pole to that end which becomes negative by
being heated, and positive by being cooled.
The phenomena of pyroelectricity are intimately connected with the
crystalline form of the mineral ; and are only seen in those crystals whose
forms are hemihedral, or which are differently modified at the ends of their
crystallographical principal axis.
Besides tourmaline the following minerals are found to be pyroelectric :
boracite, topaz, prehnite, silicate of zinc, scolezite, axenite. And the follow-
ing organic bodies are pyroelectric : cane-sugar, Pasteur's salt (racemate of
sodium and ammonium), tartrate of potassium, &c.
-734] Laws of Electrical Attractions and Repulsions. 635
CHAPTER II.
QUANTITATIVE LAWS OF ELECTRICAL ACTION.
733. Electrical quantity. In the experiment with the flannel cap ab,
described above (730), each time the experiment is made, equal quantities of
neutral fluid are decomposed into positive electricity, which remains on the
flannel, and negative electricity, which remains on the sealing-wax. The
flannel, with its charge of electricity, may be detached, and if we work under
precisely uniform conditions, equal quantities of electricity can thus be
separated.
If \ve fill water from a constant source into a cask by means of a measure,
the quantity added would be directly proportional to the number of such
measures. Now, although in the above experiment the quantities of elec-
tricity produced each time are equal, yet when the flannel cap is applied
each time to an insulated conductor it does not necessarily follow that the
quantity of electricity imparted each time
is directly proportional to the number of
such applications.
734, Saws of electrical attractions
and repulsions. The laws which regu-
late the attractions and repulsions of
electrified bodies may be thus stated :
I. The repulsions or attractions be~
f-i'een two electrified bodies are in the
inverse ratio of the squares of their dis-
tance.
I 1. The distance remaining the same,
the force of attraction or repulsion between
t'i'o electrified bodies is directly as the pro-
duct of the quantities of electricity U'ith
ichich they are charged.
These laws were established by Cou-
lomb, by means of the torsion balance,
used in determining the laws of magnetic
attractions and repulsions (704), modified
in accordance with the requirements of the
case. The wire, on the torsion of which Fig. 593.
the method depends, is so fine that a foot
weighs only ^ of a grain. At its lower extremity there is a fine shellac rod,
n P (fig- 593)> at one en d of which is a small disc of copper foil, n. Instead of
the vertical magnetic needle, there is a glass rod, *, terminated by a gilt
.636 Frictional Electricity. [734-
pith ball, ;;z, which passes through the aperture r. The scale oc is fixed
round the sides of the vessel, and during the experiment the ball m is
opposite the zero point o. The micrometer consists of a small graduated
disc, , moveable independently of the tube, d, and of a fixed index, , which
shows by how many degrees the disc is turned. In the centre of the disc
there is a small button /, to which is fixed the wire which supports np.
i. The micrometer is turned until the zero point is opposite the index,
and the tube d is turned until the knob n is opposite zero of the graduated
circle : the knob m is in the same position, and thus presses against n. The
knob m is then removed and electrified, and replaced in the apparatus,
through the aperture r. As soon as the electrified knob m touches ;z, the
latter becomes electrified, and is repelled, and after a few oscillations re-
mains constant at a distance at which the force of repulsion is equal to the
force of torsion. In a special experiment Coulomb found the angle of tor-
sion between the two to be 36 ; and as the force of torsion is proportional
to the angle of torsion, this angle represents the repulsive force between m
and n. In order to reduce the angle to 1 8 it was necessary to turn the disc
through 126. The wire was twisted 126 in the direction of the arrow at
its upper extremity, and 18 in the opposite direction at its lower extremity,
and hence there was a total torsion of 144. On turning the micrometer in
the same direction, until the angle of deviation was 8^, 567 of torsion was
necessary. Hence the whole torsion was 575^. Without sensible error
these angles of deviation may be taken at 36, 18, and 9, and on comparing
them with the corresponding angles of torsion 36, 144, and 576, we see
that while the first are as
i : i : i
the latter are as
i :4 : 16;
that is, that for a distance % as great the angle of torsion is 4 times as
great, and that for a distance \ as great the repulsive force is 16 times as great.
In experimenting with this apparatus, the air must be thoroughly dry, in
order to diminish, as far as possible, loss of electricity. This is- effected by
placing in it a small dish containing chloride of calcium.
The experiments by which the law of attraction is proved are made in
much the same manner, but the two balls are charged with opposite electri-
cities. A certain quantity of electricity is imparted to the moveable ball, by
means of an insulated pin, and the micrometer moved until there is a certain
angle below. A charge of electricity of the opposite kind is then imparted
to the fixed ball. The two balls tend to move towards each other, but are pre-
vented by the torsion of the wire, and the moveable ball remains at a distance
at which there is equilibrium between the force of attraction, which draws the
balls together, and that of torsion, which tends to separate them. The mi-
crometer screw is then turned to a greater extent, by which more torsion
and a greater angle between the two balls are produced. And it is from the
relation which exists between the angle of deflection on the one hand, and
the angle which expresses the force of torsion on the other, that the law of
attraction has been deduced.
ii. To prove this second law let a charge be imparted to m n being in
contact with it becomes charged and is repelled to a certain distance. The
-735]
Distribution of Electricity.
637
angle of deflection being noted, let the ball m be touched by an insulated
but unelectrified ball of exactly the same size and kind ; in this way half its
charge is removed, and the angle of deflection will now be found to be only
half its original amount. In like manner if either ;;/ or the moveable body
be now again deprived of half its electricity, the deflection will be a quarter
of what it originally was, and so on.
The two laws are included in the formula F = ~ , where F is the force,
e and e the quantities of electricity on any two surfaces, and d the distance
between them. If e and e' are of opposite electricities the action is one of
attraction, while if they are the same it is a repulsive action.
On the centimetre-gramme-second system the unit quantity of electricity
is that amount which, acting, at a distance of one centimetre across air, on
a quantity of electricity equal to itself, would repel it with a force equal to
one dyne (709).
735. Distribution of electricity. When an insulated sphere of con-
ducting material is charged with electricity, the electricity passes to the
surface of the sphere, and forms an extremely thin layer. If, in Coulomb's
balance, the fixed ball be replaced by another electrified sphere, a certain
repulsion will be observed. If then this sphere be touched with an insulated
sphere identical with the first, but in the neutral state, the first ball will be
found to have lost half its electricity, and only half the repulsion will be
observed. By repeating this experiment with spheres of various substances
solid and hollow, but all having the same superficies, the result will be
the same, excepting that, with imperfectly conducting materials, the time
required for the distribution will be greater. From this it is concluded that
the distribution of electricity depends on the extent of the surface, and not
on the mass, and, therefore, that electricity does not penetrate into the
interior, but is confined to the surface. This
conclusion is further established by the following-
experiments :
i. A thin hollow copper sphere provided
with an aperture of about an inch in diameter
(fig. 594), and placed on an insulating support,
is charged in the interior with electricity. When
the carrier or proof plane (a small disc of copper
foil at the end of a slender glass or shellac rod)
is applied to the interior, and is then brought
near an electroscope, no electrical indications
are produced. But if the proof plane is applied
to the electroscope after having been in contact
with the exterior, a considerable divergence
ensues.
The action of the proof plane as a measure of
the quantity of electricity is as follows : When
it touches any surface the proof plane becomes
confounded with the element touched ; it takes
in some sense its place relatively to the electricity, or rather, it becomes
itself the element on which the electricity is diffused. Thus when the proof
Fig- 594-
6 3 8
Frictional Electricity.
[735-
plane is removed from contact we have In effect cut away from the surface,
an element of the same thickness and the same extent as its own, and have
any of the electricity which
595-
transferred it to the balance without its losim
covered it.
ii. A hollow globe, fixed on an insulating support, is provided with two
hemispherical enve-
lopes \vhich fit closely,
and can be separated
by glass handles. The
interior is now elec-
trified, and the two
hemispheres brought
in contact. On then
rapidly removing them
(fig- 595)> the cover*
ings will be found to
be electrified, while the
sphere is in its natural
condition.
iii. The distribu-
tion of electricity on
the surface may also
be shown by means of
the following appara-
tus : It consists of a
metallic cylinder on
insulated supports, on
which is fixed a long 1
5g6< strip of tin foil which
can be rolled up by
means of a small insulating handle (fig. 596). A quadrant electrometer
is fitted in metallic communication with the cylinder. When the sphere
-736]
Electric Density.
639
is rolled up, a charge is imparted to the cylinder, by which a certain
divergence is produced. On unrolling the tinfoil, this divergence gradually
diminishes, and increases as it is again rolled up. The quantity of electri-
city remaining the same, the electrical force, on each unit of surface, is
therefore less as the surface is greater.
iv. The following ingenious experiment by Faraday further illustrates
this law : A metal ring is fitted on an insulated support, and a conical
gauze bag, such as is used for catching butterflies, is fitted to it (fig. 597).
By means of a silk thread, the bag can be
drawn inside out. After electrifying the bag,
it is seen by means of a proof plane that the
electricity is on the exterior; but if the positions
are reversed by drawing the bag inside out,
so that the interior has now become the ex-
terior, the electricity will still be found on the
exterior.
v. The same point maybe further illustrated
by an experiment due to Terquem. A bird-cage,
preferably of metal wire, is suspended by insu-
lators, and contains either a gold-leaf electro-
scope or pieces of Dutch metal, feathers, pith
balls, &c. When the cage is connected with
an electrical machine, the articles in the interior
are quite unaffected, although strong sparks
may be taken from the outside. Bands of paper
Fig. 597-
may be fixed to the inside ; while those fixed to the outside diverge widely.
A bird in the inside is quite unaffected by the charge or discharge of the
electricity of the cage.
The property of electricity, of accumulating on the outside of bodies,
is ascribed to the repulsion which the particles exert on each other. Electri-
citv tends constantly to pass to the surface of bodies, whence it continually
tends to escape, but is prevented by the resistance of the feebly conducting
atmosphere.
To the statement that electricity resides on the surface of bodies, two ex-
ceptions may be noted. When two opposite electricities are discharged
through a wire a phenomenon which, when continuous, forms an electrical
current the discharge is effected throughout the whole mass of the conductor.
Also a body placed inside another may, if insulated from it, receive charges
of electricity. On this depends the possibility of electrical experiments in
ordinary rooms.
736. Electric density. On a metallic sphere the distribution of the
electricity will be uniform in ever}" part, simply from its symmetry. This
can be demonstrated by means of the proof plane and the torsion balance.
A metallic sphere placed on an insulating support is electrified, and
touched at different parts of its surface with the proof plane, which each
time is applied to the moveable needle of the torsion balance. As in all
cases the torsion observed is sensibly the same, it is concluded that the
proof plane each time receives the same quantity of electricity. In the
case of an elongated ellipsoid (fig. 598) it is found that the distribution
of electricity is different at different points of the surface. The electricity
640
Frictional Electricity.
[736-
accumulates at the most acute points. This is demonstrated by succes-
sively touching the ellipsoid at different parts with the proof plane, and
then bringing this
into the torsion
balance. By this
means Coulomb
found that the
greatest deflection
was produced when
the proof plane had
been in contact
with the point a,
and the least by
contact with the
middle space e.
The electric den-
. sity or electric
thickness is the
term used to ex-
press the quantity of electricity found at any moment on a given surface.
If S represents the surface and Q the quantity of electricity on that surface,
then, assuming that the electricity is equally distributed, its electrical density
is equal to 2|.
Coulomb found, by quantitative experiments, that in an ellipsoid the
density of the electricity, at the equator of the ellipsoid, is to that at the ends
in the same ratio as the length of the minor to the major axis. On an insu-
lated cylinder, terminated by two hemispheres, the density of the electrical
layer at the ends is greater than in the middle. In one case, the ratio of
the two densities was found to be as 2-3 : i. On a circular disc the density
is greatest at the edges.
737. Force outside an electrified body. The force F which a sphere,
charged with a quantity of electricity Q, exerts on a point at a distance d
from its centre, is ~ ; this is equal to - if S is the area of the sphere, and
d~ d
p the density of electricity on the unit of surface. Now the area of the
sphere is 4?rR 2 , and if the distance d is equal to the radius R then the force
at the surface is ^^>- 2 4 7r P-
This holds also if the point considered is at a very small distance just
outside the sphere. Let a small segment ab be cut in a sphere (fig. 599).
Then its action on a point p just inside the sphere will be exactly neutralised
by the action of the rest of the sphere acb on this point, since there is no
electrical force inside a sphere (735) ; that is, the action of the two portions
is equal, but in opposite directions. Now for a point p , just outside the
sphere, the actions will also be equal, but in the same directions. But the
total action of the whole sphere is 4rrp ; hence the action of each portion is
half of this ; that is, 2?rp.
-738] Potential. 641
It may be shown in like manner that the whole force of any closed
conductor is 4717).
On an insulated conductor, where the electricity is in equilibrium, a
particle of electricity will have no tendency to move along the surface, for
otherwise there would be no equilibrium. But the
electricity does exert a pressure on the external non-
conducting medium, which is always directed outwards,
and is called the electrical tension or pressure.
The amount of this pressure is 27rp 2 for the unit
area, p being the electrical density at the point con-
sidered. The effect of this, for instance, on a soap-
bubble, if electrified with either kind of electricity,
would be to enlarge it. In any case the electrification
would constitute a deduction from the amount of atmo- Fig. 599-
spheric pressure which the body experiences when unelectrified.
The term electric density and electrical tension are often confounded.
The latter ought rather to be restricted, as Maxwell proposed, to express the
state of strain or pressure exerted upon a dielectric in the neighbourhood of
an electrified body ; a strain which, if continually increased, tends to disrup-
tive discharge. Electric tension may thus be compared to the strain on a
rope which supports a weight ; and the dielectric medium which can support
a certain tension and no more is said to have a certain strength, in the same
sense as a rope which bears a certain weight without breaking is said to
have a certain strength.
738. Potential In the experiment (fig. 598), instead of applying the
test sphere directly to the large sphere, let the two be placed at a consider-
able distance from each other, and let them be connected by a long thin wire,
and then, detaching the small sphere, let the quantity upon it be measured
by the torsion balance ; the angle of deflection will show that this quantity is
the same whatever part of the large sphere be touched, as must indeed be
the case, owing to symmetry' ; but the amount of this charge will be mate-
rially different from that in which the small sphere is placed in direct contact
with the larger one. Hence the quantity of electricity removed differs ac-
cording to the mode in which connection is made.
If now this experiment be repeated with the ellipsoid, it will be found
that whatever point of this is put in distant connection with the proof sphere
by the long wire, the charge which the small sphere acquires is everywhere
the same ; although, as we have seen, the proof sphere would remove very
different quantities of electricity according to the part where it touches.
Here, then, we are dealing with experimental facts which our previous
notions are insufficient to explain. It is manifest that the difference in the
results depends neither on the total charge nor on the density. We require
the introduction of a new conception, which is that of electrical potential.
Introduced originally into electrical science by Green, out of considerations
arising from the mathematical treatment of the subject, the use of the term
potential is justified and recommended by the clearness with which it brings
out the relations of electricity to work.
We have already seen, that in order to lift a certain mass against the
attraction of gravitation (60-63) there must be a definite expenditure of work,
642 Frictiondl Electricity. [738 -
and the equivalent of this work is met with in the energy which the lifted
mass retains, or what is called the potential energy of position.
Let us now suppose that we have a large insulated metal sphere charged
with positive electricity, and that, at a distance which is very great in com-
parison with the size of the sphere, there is a small insulated sphere charged
with the same kind of electricity. If now we move the small sphere to any
given point nearer the larger one, we must do a certain amount of work upon
it to overcome the repulsion of the two electricities.
The work required to be done against electrical forces, in order to move
the unit of positive electricity from an infinite distance to a given point in
the neighbourhood of an electrified conductor, is called \}\Q potential at this
point. If, in the above case, the larger sphere were charged with negative
electricity, then instead of its being needful to do work in order to bring a
unit of positive electricity towards it, work would be done by electrical at-
traction, and the potential of the point near the charged sphere would thus
be negative.
The potential at any point may also be said to be the work done
against electrical force, in moving unit charge of negative electricity from
that point.
The amount of work required to move the unit of positive electricity
against electrical force, from any one position to any other, is equal to the
excess of the electrical potential of the second position over the electrical
potential of the first. This is, in effect, the same as what has been said
above, for at an infinite distance the potential is zero.
We cannot speak of potential in the abstract, any more than we can
speak of any particular height, without at least some tacit reference to a
standard of level. Thus, if we say that such and such a place is 300 feet
high, we usually imply that this height is measured in reference to the level
of the sea. So, too, we refer the longitude of a place to some definite
meridian, such as that of Greenwich, either expressly or by implication.
In like manner we cannot speak of the potential of a mass of electricity
without, at least, an implied reference to a standard of potential. This
standard is usually the earth, which is taken as being zero potential. If we
speak of the potential at a given point, the difference between the potential
at this point and the earth is referred to.
If in the imaginary experiment described above, we move the small sphere
round the large electrified one always at the same distance, no work is done
by or against it for the purpose of overcoming or of yielding to electrical
attractions or repulsions, just as if we move a body at a certain constant level
above the earth's surface, no work is done upon it as respects gravitation.
An imaginary surface drawn in the neighbourhood of an electrified body,
such that a given charge of electricity can be moved from any one point of
it to any other, without any work being done either by or against electrical
force, is said to be an equipotential surface. Such a surface may be de-
scribed as having everywhere the same electrical level ; and the notion of
bodies at different electrical levels, in reference to a particular standard, is
the same as that of bodies at different potentials.
As water only flows from places at a higher level to places at a lower
level, so also electricity only passes from places at a higher to places at a
-739] Electrical Capacity. 643
lower potential. If an electrified body is placed in conducting communica-
tion with the earth, electricity will flow from the body to the earth, if the
body is at a higher potential than the earth ; and from the earth to the body,
if the body is at a lower potential. If the potential of a body is higher than
that of the earth, it is said to have a positive potential ; and if at a lower
potential, a negative potential. A body charged with/ra negative electricity
is one at lower potential than the earth ; one charged with free positive
electricity is at a higher potential.
739. Electrical capacity. The capacity of any conductor may be
measured by the quantity of electricity which it can acquire when placed
in contact with a body which charges it to unit electrical potential.
We may illustrate the relation between capacity and potential by refer-
ence to the analogous phenomenon of heat. In the interchange of heat
between bodies of different temperatures the final result is that heat only
passes from bodies of higher to bodies of lower temperature. So also elec-
tricity only passes from bodies of higher to bodies of lower potential.
Potential is, as regards electricity, what temperattire is as regards heat, and
might indeed be called electrical temperature. We may have a small
quantity of heat at a very high temperature. Thus a short thin wire heated
to incandescence has a far higher heat potential or temperature than a
bucket of warm water. But the latter will have a far larger quantity. A
flash of lightning represents electricity at a very high potential, but the
quantity is small.
The relation between electrical potential and density may be further
illustrated by reference to the head of water in a reservoir. The pressure
is proportional to the depth ; the potential is everywhere the same. For
suppose we want to introduce an additional pound of water into the reservoir,
the same amount of work is required whether the water be forced in at the
bottom or be poured in at the top.
If a hole be made very near the top of the reservoir, a quantity of water
in falling to the ground would generate an amount of heat proportional to
the fall. If the same quantity escaped through a hole near the bottom, it
would not produce so much heat by direct fall ; but it will possess a certain
velocity, the destruction of which will produce a quantity of heat, which,
added to that produced by the fall, will give exactly as much as the other.
When the charge or quantity of electricity imparted to a body increases,
the potential increases in the same ratio ; so that, calling Q the quantity of
electricity, C the capacity, and V the potential, we have
Q = CV.
Now for a sphere whose radius is R the potential V = i from which we
R
get C = R ; that is, that the capacity of a sphere is equal to its radius.
While there is a close analogy between heat and electricity, as regards
capacity, there are important differences ; thus the capacity of a body for heat
is influenced by the temperature (457), while the capacity of a body for
electricity does not depend on the potential. Again, the calorific capacity
depends solely on the mass of a body, and in bodies of the same material and
shape is proportional to the cube of homologous dimensions ; the capacity
644 Frictional Electricity. [739-
for electricity is directly proportional to such dimensions. Calorific capacity
is proportional to a specific coefficient, which varies with the material, but
is independent of its shape, while electrical capacity varies with the shape of
a body, but not with its material, provided the electricity can move freely
upon it.
If we have a series of bodies at a considerable distance from each other,
whose capacities and potentials are respectively <:, c\ c", c., and v, v', v", &c.,
then, if they are all connected by fine wires of no capacity, they all instantly
acquire the same potential V, which is determined by the equation
cv + c'v' -f c"v"
c + c' -t c' f
The analogy of this to the equalisation of temperature which takes place
when bodies at different temperatures are mixed together is directly apparent
(449). It may be further illustrated by supposing a series of tubes of different
diameters, and connected by very narrow tubes, but in which are stopcocks
to cut off communication. If, while in this state, water be poured into the
tubes to different heights, it will be manifest that they will hold very various
quantities of water. If, however, the stopcocks are opened, the tubes will
still contain quantities of water proportional to their capacities, but the level
or potential in all will be the same.
740. Measurement of capacity and potential. We may use Cou-
lomb's balance for the purpose of measuring the capacity C, or the potential
V, of a body charged with electricity. For this purpose the body in question
is placed, by means of a long fine wire of no capacity, in distant contact with
a small neutral insulated sphere of known radius r. This small sphere is
then applied to the torsion balance, and its charge g = rv'\s measured. Now,
since the original charge on the sphere is O = CV, after contact with the
small sphere, which is neutral, the system will have a new potential or elec-
trical level, v, such that CV = (C + r) v. Restoring now the small sphere to
the neutral state, and repeating the experiment and the measurement, we shall
then get a second value rz/', from which we have the equation Cz/ = (C - r} z/.
Combining and reducing, we get the ratio V = %-, which, seeing that rv and
rv' are numerical values, leads directly to the desired result.
In like manner it is easy to determine the capacity by obvious transform-
ations of these equations.
It will thus be seen that this process of determining potential is ana-
logous to that of determining temperature by means of a thermometer ; and
the proof sphere plays the part, as it were, of an electrical thermometer.
It may be observed that in the case of heat we pass from the conception
of temperature to that of quantity of heat, while with electricity, starting with
the fact of quantity, or charge of electricity, we arrive at the conception of
potential of electricity.
741. Potential of a sphere. If q, q\ and ^ r 'are any masses of electri-
city on the surface of an insulated conducting sphere, and d, d\ and d" their
respective distances from any point of the interior of the sphere, then ?,
-742] Loss of Electricity. 645
and 9 are the values of the potentials z/, z>', and v" which they would
a'
severally produce at this point. Let the point in question be the centre,
and let O be the sum of the whole quantities ; then V, the potential of the
sphere, equals A R being the radius.
R
If there be a sphere, or uniform spheroidal shell of matter, which acts
according to the inverse square of the distance, then 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 out-
side a sphere possessing a uniform charge, we need only consider its dis-
tance from the centre, and for such a case we may write the value of the
potential V ~.
If a charge of electricity, Q, be imparted to two insulated conducting
spheres whose radii are respectively r and r\ 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
q and q' ; that is,
and of negative electricity on the corresponding outsides of
m ( i - ;;z n )
m + nr + ?/r + m + . . . mr =
I //2
Thus, if there be six jars and m = 0-9, the quantity of positive electricity
developed by the unit charge is 4-69.
777. Measurement of the cliarg-e of a "battery, lane s electro-
meter. When the outer and inner coatings of a charged Leyden jar
are gradually brought nearer each other, at a certain distance a spontaneous
discharge ensues. The distance
is called the striking distance.
It is inversely proportional to
the pressure of the air and
directly proportional to the elec-
tric density of that point of the
inner coating at which the dis-
charge takes place. As the
density of any point of the inner
coating, other things remaining
~ ~ the same, is proportional to the
entire charge, the striking dis-
tance is proportional to the quantity of electricity in a jar. The measure-
ment 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
apparatus, c (fig. 639), consists of an ordinary Leyden jar, near which there
is a vertical metallic support. At the upper end is a brass rod, with a knob
at one end, which can be placed in metallic connection with the outside of
the jar : the rod being moveable, the knob can be kept at a measured dis-
tance from the knob of the inner coating. Fig. 639 represents the operation
of measuring the charge of a jar by means of this apparatus. The jar $,
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 c,
the outer coating of which is in connection with the ground, or still better
with a system of gas or water pipes ; a is the conductor of the machine.
When the machine is worked, positive electricity passes into the jar b ; a pro-
portionate quantity of positive electricity is repelled from its outer coating,
passes into the inner coating of the electrometer, and there produces a
charge. 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.
-779] Volte! s Condensing Electroscope. 68 1
Harris's unit jar (fig. 640) is an application of the same principle, and is
very convenient for measuring quantities of electricity. It consists of a small
Leyden phial, 4 inches in length and
of an 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 / p. When the
accumulation of electricity in the interior
has reached a certain height depending on the distance of the two balls ;//
and /;, a discharge ensues, and marks a certain quantity of electricity received
as a charge by the battery, in terms of the small jar.
778. Xiaws of electric charge. Harris, by means of experiments with
the unit jar suitably modified, and Riess, by analogous arrangements, have
found, by independent researches, that for small distances the striking dis-
tance is directly proportional to the quantity of electricity, and inversely
proportional to the extent of coated surface ; in other words, it is proportional
to the electric density. Thus, taking the surface of one jar as unity, if a
battery of six Leyden jars charged by 100 turns of the machine has a striking
distance of 9 millimetres, a battery of four similar jars charged by 120 turns
will have the striking distance of 16-2 millimetres. For
': 9 =^.-^=.6-2
6 4
The charge also depends on the nature of the glass, or other dielectric, of
which the jar is made ; and, further, is stated by Wheatstone to be inversely
proportional to the square of the thickness of the dielectric. Riess has also
found that when a battery or jar is discharged in the striking distance, a
charge still remains ; for when the coatings are brought nearer, a similar dis-
charge may be taken, and so on. The amount of this residual charge, when
the discharge takes place at the greatest striking distance, is always in the
same proportion to the entire charge. In Riess's experiments, 0*846 or }} of
the total charge disappeared, and only ^ remained.
779. Volta's condensing: electroscope. The condensing electroscope
invented by Volta is a modification of the ordinary gold-leaf electroscope
(751). 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. 641).
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 ground by touching it with the finger. The electricity of
the body, being diffused over the collecting plate, acts inductively through
the varnish on the neutral fluid of the other plate, attracting the opposite
electricity, but repelling that of like kind. The two electricities thus become
G G 3
682
Frictional Electricity.
[779-
accumulated on the two plates just as in a condenser, but there is no diver-
gence 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
divergence; but if the upper plate be raised (fig. 642) 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 the apparatus is in-
creased by adapting to the foot of the apparatus two metallic rods, termi-
nating 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 be replaced by two
Fig. 641.
Fig. 642.
Bohnenberger's dry piles, one of which presents its positive and the other its
negative pole. Instead of two gold leaves there 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.
780. Thomson's quadrant electrometer. Sir William Thomson has
devised a new and delicate form of electrometer, by which accurate measure-
ments of the amount of electrical charge may be made. The principle of
this instrument may be understood from the following description of a form
of it constructed for lecture purposes by Messrs. Elliott.
A light flat broad aluminium needle (fig. 643) hangs by a very fine wire
from the inner coating of a charged Leyden jar, the outer coating being in
conducting communication with the earth. The whole apparatus is enclosed
within a glass shade, and the air is kept dry by means of a dish of sulphuric
-781]
Thomson's Absolute Electrometer.
683
acid ; there is, therefore, very little loss of electricity, and the needle remains
at a virtually constant charge.
The needle is suspended over
four quadrantal metal plates, in-
sulated from each other and from
the ground by resting on glass
rods. The alternate quadrants
are in conducting communication
with each other by means of wires.
If now all the quadrants are in the
same electrical condition, the needle
will be at rest when it is directly
over one of the diametrical slits.
But if the two pairs of quadrants
are charged with opposite kinds of
electricity, as when, for instance,
they are connected with the two
poles of an insulated voltaic cell by
means of the knobs, then each end
of the needle will be repelled by the
pair of quadrants which are electri-
fied like itself, and will be attracted
by the other pair. 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 (520).
781. Thomson's absolute electrometer. Another class of electro-
meters, also invented by Sir W. Thomson, have the advantage of furnishing
a direct measure of electrical constants in absolute measure. Fig. 644
represents the essential features of a modified form of the electrometer,
which has been devised by Professor Foster for class experiments.
Two plane metal discs A and B, about 10 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 c ; this is suspended by insulating threads from one end of
the arm a b of a balance, at the other end of which is a counterpoise, or a
scale pan p. At the end of the arm is a fork, across which is stretched a
line 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 the posi-
tion of which 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 electricity, while the other can be kept at
any potential.
684
Friciional Electricity.
[781-
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
it be electrified to a given
potential, while the other
plate is connected with the
earth, then the body charged
with electricity of higher po-
tential 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
scale pan, and the additional force thus applied is a measure of the attractive
force.
Now it can be shown that the attractive force between any two plates
electrified to different potentials is proportional to the square of the differ-
ence of potentials, provided the distance between them is small in comparison
with their area, and that the portions of the plates opposite each other are
at some distance from the edge. These conditions are fulfilled in the above
case. If S is the area of the disc, of the distance of the plates, V- V a the
difference of potentials, and F the force required to balance a certain attrac-
tion, then
F _(v-v-)'s
^O; this is and V
Now as F is expressed by a weight, and S and ^/are measures of length, we
have a means of expressing difference of potentials in absolute measure (709).
It is also clear that the experiments may be modified by making the
weight constant, and the distance variable. By means of micrometric
arrangements the distance of the plates may be varied and measured with
very great accuracy.
782. Potential of a leyden jar. Let us suppose A (fig. 645) to represent
an insulated metal sphere, and let us consider it placed in conducting com-
munication with a source of, say, positive electricity, which is supposed to be
at a constant potential V. Then its potential V is " , and its charge q = VR,
R
R being the radius of the sphere A,
Suppose now it be possible to surround this sphere by an external con-
ducting shell, B, which is in connection with the ground ; movements of
electricity will take place ; a new equilibrium will be established, and there
will now be two electrical layers one on the sphere A, and the other on the
-782] Potential of a Ley den Jar. 68 5
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 sphere, then Q is that on the
outer.
The charge of the original sphere is at
first not altered by this operation, but its
potential is less, its capacity being now
greater, and, as it is in contact with the
source, which is constant, it receives fresh
charges of electricity until it is again at the
potential of the source V.
Now let us suppose that the insulating
layer which separates the inner from the
outer coating is air, and that its thickness is
/ ; then the potential V of the whole system is Fig. 645.
made up of two parts Q,the first due to the elec-
trical charge of the inner sphere V- + ^, and the second due to the charge
of theouter sphere =-S; that is, V = Q - 1 - ^= , R l' or Q
ff R' R
Now, the charge of the insulated sphere q = VR ; hence i = . But
Q K
R' R is the thickness of the insulator, which, for the sake of simplicity, we
O R r
will suppose is air, and, calling this /, we have - = ; that is, that the
charge is inversely as the thickness.
It is to be observed that the results here obtained apply strictly only to
the supposed case in which the inner conductor is completely surrounded by
the outer one, which is not the case with the ordinary form of a Leyden
jar. It may, however, be applied to them if we compare homologous jars ;
in the above formula Q = , if R and R' are nearly equal, then Q =
Kj K /
^ - where S is the surface and / the thickness of the insulating coat-
47r/ 4irt
c
ing. In this formula is a constant for a Leyden jar of given dimen-
47J-/
sions, and represents the capacity of the jar.
If instead of air there be a solid or liquid dielectric, whose specific induc-
tive capacity is AC, the formula becomes Q= = *. If the dielectric be
"
K
partly air and partly some other material such as glass, then if the thick-
VS
ness of this latter is 6, Q - . The expression 6 is sometimes
written /', and represents the thickness of the layer of air equivalent to it in
specific inductive capacity. It is also called the reduced thickness.
686 Fractional Electricity. [783-
THE ELECTRIC DISCHARGE.
783. Effects of the electric discharge. The recombination of the two
electricities which constitutes the electrical discharge may be either con-
tinuous or sudden : continuous, 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, as when the opposite electricities accumulate on the surface of two
adjacent conductors, till their mutual attraction is strong enough to over-
come 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 has shown that the discharge of a battery does not consist in a
simple union of the positive and 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. By observations of
the image of the spark in a rotating mirror, and of the luminous phenomena
at the positive and negative poles when the discharge takes place in highly
rarefied gases, as well as by the manner in which a magnet affects the pheno-
mena of discharge, Feddersen and Paalzow have shown that the discharge
consists of a series of oscillating currents alternating in opposite directions.
As the resistance of the circuit increases, the number of these alternating
discharges decreases, but at the same time their duration is greater. With
very great resistance as, for instance, when a wet thread is interposed the
alternating discharge becomes a single one.
784. Work effected by the discharge of a leyden jar. The work
CV 2 O 2
required to charge a Leyden jar is W = ^QV= = -^- , and from the
principle of the conservation of energy, this stored-up energy reappears when
the jar is discharged. This occurs 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
discharged 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 = ^Vnq = ^VQ ; that is, the energy
of a battery of n equal jars is the same as that of a single jar of the same
thickness but of n times the surface.
Let us consider two similar Leyden jars having respectively the capaci-
ties c and c', and let one of them be charged to potential V and let the other
-786] Luminous Effects. 687
remain uncharged. Suppose now that the inner and outer coatings of the
jars are respectively connected with each other. Then the energy of the
charged jar alone is W- J 9* , and when it is connected with the other the
original charge will spread itself over the two, so that the energy of the
charge in the two jars is W = Q* Hence \V : W = c + ^ : c ; and there-
fore since c + c* is always greater than r, there must be a loss of energy. In
point of fact, when a charged jar is connected with an uncharged one, a spark
passes which is the equivalent of this loss of energy.
It follows further that whenever two jars at different potentials are united
there is always a loss of energy.
The phenomena of the discharge are conveniently divided into the
physiological, luminous, mechanical, magnetical, and chemical effects.
785. Physiological effects. The physiological effects are those pro-
duced on living beings, or on those recently deprived of life. In the first
case they consist of a violent excitement which the electricity exerts on
the sensibility and contractility of the organic tissues through which it passes ;
and in the latter, of violent muscular convulsions which resemble a return
to life.
The shock from the electrical machine has been already noticed (770).
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 trie extremities. The Abbd Nollet dis-
charged a Leyden jar through an entire regiment of 1,500 men, who all
received a violent shock in the arms and shoulders.
With large Leyden 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 batter)' of about 4^ square yards coating.
786. Luminous effects. The recombination of two electricities of high
potential (738) is always accompanied by a 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 atmospheric air at the ordinary pressure the electric spark is
white and brilliant ; in rarefied air it is reddish ; and in vacuo it is violet.
In oxygen, as in air, the spark is white ; in hydrogen it is reddish, and green
688
Frictional Electricity.
[786-
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. Generally
speaking, the higher the potential the greater is the lustre of the spark.
It is asserted by Fusinieri that in the electric spark there is always a
transfer of material particles in a state of extreme tenuity, in which case
the modifications in colour must be due to the transport of ponderable
matter.
When the spark is viewed through a prism, the spectrum obtained is full
of dark lines (578), the number and arrangement of which depend on the
material of which the poles are made.
787. Spark and brush discharge. The shapes which luminous electric
phenomena assume may be classed under two heads the spark 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 of these depends on the nature of the con-
ductor and on the nature of the conductors in its vicinity ; and small altera-
tions 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 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 arrangement 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 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, issues from a conductor,
Fig. 646.
-789] Luminous Tube, Square, and Bottle. 689
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.
788. Electric egrgr. The influence of the pressure of the air on the
electric light may be studied by means of the electric egg. This consists of
an ellipsoidal glass vessel (fig. 646), with metal caps at each end. The
lower cap is provided with a stopcock, 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 in a 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 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 fluid of the
upper cap with the negative of the lower. If the air be gradually allowed
to enter by opening the stopcock, the light now appears white and brilliant,
and is only seen as an ordinary intermittent spark.
Some beautiful effects of the electric light are obtained by means of
Geissler's tubes, which will be noticed under Dynamical Electricity.
789. Luminous tube, square, and bottle. The luminous tube (fig. 647)
is a glass tube about a yard long, round which are arranged in a spiral form
Fig. 647.
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 simultaneously at each interval, and pro-
duce a brilliant luminous appearance, especially in the dark.
The luminous pane (fig. 648) 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 lower part with the
ground. When the machine is in operation, a spark appears at each
interval, and reproduces in luminous flashes the object represented on the
glass.
The luminous jar (fig. 649) is a Leyden jar whose outer coating consists
of a layer of varnish strewed over with metallic powder. A strip of tin fitted
6go
Frictional Electricity.
[789-
on the bottom is connected with the ground by means of a chain ; a second
band at the upper part of the coating has a projecting part, and the rod of
the bottle is curved so that the
knob is about f of an inch from
the projection. This jar is sus-
pended from the machine, and,
as rapidly as this is worked,
large and brilliant sparks pass
between the knob and the outer
coating, illuminating the outside
of the apparatus.
790. Heating 1 effects. Be-
sides being luminous, the electric
spark is a source of intense
heat. When it passes through
inflammable liquids, as ether or
alcohol, it inflames them. An
arrangement for effecting this is
represented in fig. 650. 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 quan-
tity 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 a
machine which is then worked, while he presents the other to the jet of gas
issuing from a metallic burner. The spark which passes ignites the gas.
When a battery is discharged through an iron or steel wire it becomes
heated, and even made incandescent or melted, if the discharge is very
powerful.
If, in discharging a jar, the discharge does no other work, then the whole
of the energy of the charge (784) appears in the form of heat ; and if we
divide this by Joule's equivalent (497), we have the total heating due to
any charge.
The laws of this heating effect have been investigated independently by
Harris and by Riess by means of the electric thermometer. This is essentially
an air thermometer, across the bulb of which is a fine platinum wire. When
a discharge is passed through the wire it becomes heated, expands the air
in the bulb, and this expansion is indicated by the motion of the liquid along
the graduated stem of the thermometer. In this way it has been found that
the increase in temperature 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 given (784). Riess has also found that with the same
charge, but with wires of different dimensions, the rise of temperature is in-
-790]
Magnetic Effects.
691
verse/}' as the fourth power of the diameter. Thus, compared with a given
wire as unity, the rise of temperature in a wire of double or treble the
diameter would be j 1 ^ or / T as small ; but
as the masses of these wires are four and
nine times as great, the heat produced would
be respectively \ and \ as great as in a wire
of unit thickness.
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 be interposed in the circuit, a spark
Fig. 649.
Fig. 650.
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 has shown 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 ; we have here, probably, something analogous to the heating pro-
duced in iron when it is rapidly magnetised and demagnetised.
Duter has found that when a Leyden jar is discharged, the insulating
plate undergoes a mechanical expansion which he considers can neither be
due to a heating effect nor to electrical pressure, but which he ascribes to a
special electrical effect. For one and the same dielectric it appears directly
proportional to the square of the potential and inversely as the thickness.
692
Frictional Electricity.
[791-
791. 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 with less powerful discharges, a
steel bar or needle may be magnetised by placing it inside a tube on which
is coiled a fine insulated copper wire. On passing the discharge through
this wire the steel becomes magnetised.
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.
792. Mechanical effects. The mechanical effects are the violent lacera-
tions, fractures, and sudden expansions which ensue when a powerful dis-
charge is passed through a badly conducting substance. Glass is perforated,
wood and stones are frac-
tured, and gases and
liquids are violently dis-
turbed. The mechanical
effects of the electric
spark may be demon-
strated by a variety of ex-
periments.
Fig. 651 represents an
arrangement for peforat-
ing a piece of glass or
card. It consists of two
glass columns, with a
horizontal cross-piece, in
which is a pointed con-
ductor, B. The piece of
glass, A, is placed on an
insulating glass support,
in which is placed a
second conductor, ter-
minating 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 only succeeds with a single jar
when the glass is very thin ; otherwise a battery must be used.
The perturbation and sudden expansion which the discharge produces
may be illustrated by means of Kinnersley's thermometer. This consists of
two glass tubes (fig. 652), which fit into metallic caps, and communicate with
each other. At the top of the large tube is a rod terminating 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.
Fig. 651.
-793]
Chemical Effects.
693
When the electric shock 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 is not due to
an increase of temperature.
For the production of mechanical effects the universal discharger (fig. 622)
is of great service. A piece of wood, for instance, placed on the table
between the two conductors, is
split when the discharge passes.
793. Chemical effects. -
The chemical effects are the
decompositions and recombina-
tions effected by the passage of
the electric discharge. When
two gases which act on each
other are mixed in the propor-
tions 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 elec-
tric sparks was passed through
moist air, its volume dimin-
ished, and blue litmus intro-
duced into the vessel was
reddened. This, Cavendish
discovered, was due to the for- Fi s- 6 5 2 -
mation of nitric acid.
Several compound gases are decomposed by the continued action of the
electric spark. With olefiant gas, sulphuretted hydrogen, and ammonia, the
decomposition is complete ; while carbonic acid is partially decomposed
Fig. 653.
Fig. 654.
into oxygen and carbonic 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 demonstrated by means of a solution of iodide of potassium.
Frictional Electricity.
[793-
A small lozenge-shaped piece of filtering paper, impregnated with iodide of
potassium, is placed on a glass plate, and one corner connected with the
ground. When a few sparks from a conductor charged with positive elec-
tricity 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. 653), in
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 A and B. The vessel is held as represented in fig. 654, and brought
near the machine. The knob A becomes negatively, and B positively, elec-
trified by induction from the machine, and a spark passes between the con-
ductor 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 accom-
panied 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 proper-
ties. The odour is perceived when elec-
tricity issues from a conductor into the
air through a series of points. It has
been established that ozone is an allo-
tropic modification of oxygen.
With these effects may be associated
a certain class of phenomena observed
when gases are made to act as the dielec-
tric in a charged Leyden jar. An appa-
ratus by which this is effected is repre-
sented in fig. 655 ; it is a modification
of one invented by Siemens. It con-
sists of a glass cylinder E, containing
weak sulphuric acid ; a is a glass tube
closed at the bottom, and also containing
sulphuric acid, in an enlargement of which
at the top the inner tube e c fits. There is
a tube /by which gas enters, and one dt',
by which it emerges. When the acids in
E and e are respectively connected with
the two combs of a Holtz's machine, or
with the two terminals of a Ruhmkorff s
coil, a certain condition or strain is pro-
duced in the dielectric, which is known as
the silent discharge or the electric effluvium,
What that condition is cannot be definitely stated ; but it gives rise to power-
ful and characteristic chemical actions, often differing from those produced
by the spark.
By this apparatus large quantities of ozone may be produced.
Fig. 655.
-794] Application of Electrical Discharge to Firing Mines. 695
794. Application of the electrical discharge to firing mines. By the
labours of Prof. Abel in this country, and of Baron von Ebner in Austria, the
electrical discharge has been applied to firing mines for military purposes,
and the methods have acquired a high degree of perfection. The principle
on which the method is based may be understood from the following state-
ment :
One end of an insulated wire in which is a small break is placed in con-
tact with the outside of a charged Leyden jar, the other end being placed
near the inner coating. If
now this end be brought in
contact with the inner coat-
ing the jar is discharged, and
a spark strikes across the
break ; and if there be here
some explosive compound it
is ignited, and this ignition
may of course be communi-
cated to any gunpowder in
which it is placed. If on
one side of the break, in-
stead of having an insulated
wire direct back to the outer
coating of the Leyden jar,
an uncovered wire be led
into the ground, the outside
of the jar being also con-
nected with the ground, the
result is unchanged, the
earth acting as a return wire.
Moreover, if there be several
breaks, the explosion will
still ensue at each of them,
provided the charge be suf-
ficiently powerful.
In the actual application it is of course necessary to have an arrange-
ment for generating frictional electricity which shall be simple, portable,
powerful, and capable of working in any weather. Fig. 656 represents a
view of Von Ebner's instrument as constructed by Messrs. Elliott, part of
the case being removed to show the internal construction.
It consists of two circular plates of ebonite, #, mounted on an axis so that
they are turned by a handle, , between rubbers, which are so arranged as
to be easily removed for the purposes of amalgamation, &c. Fastened to a
knob on the base of the apparatus and projecting between the plates is a
pointed brass rod, which acts as a collector of the electricity. The condenser
or Leyden jar arrangement is inside the case, part of which has been re-
moved to show the arrangement. It consists of india-rubber cloth, coated
on each side with tinfoil, and formed into a roll for the purpose of greater
compactness. By means of a metal button the knob is in contact with one
tinfoil coating, which thus receives the electricity of the machine, and cor-
Fig. 656.
Frictional Electricity.
[794-
responds to the inner coating of the Leyden jar. Another button connected
with the other tinfoil coating, rests on a brass band at the base of the appa-
ratus which is in metallic contact with the cushions, the knob d, and the
perforated knob in which slides a rod at the front of the apparatus. These
are all in connection with the earth. The knob e is in metallic connection
with a disc g provided with a light arm. By means of a flexible chain this
is so connected with a trigger on the' side of the apparatus, not represented
in the figure, that when .the trigger is depressed, the arm,
and therewith the knob e, is brought into contact with
the inner coating of the condenser.
On depressing the trigger, after a certain number of
turns, a spark passes between the knob e and the sliding
rod, and the striking distance is a measure of the work-
ing condition of the instrument.
The fuse used is known as Abel's electrical fuse, and
has the following construction : The ends of two fine
copper wires (fig. 658) are imbedded in a thin solid gutta-
percha rod, parallel to each other, but at a distance of
about 1*5 mm. At one end of the gutta-percha a small
cap of paper or tinfoil, c c, is fastened, in which is placed a
small quantity of the priming composition, which consists
of an intimate mixture of subsulphide of copper, sub-
phosphide of copper, and chlorate of potassium. The
paper is fastened down so that the exposed ends of the
wires are in close contact with the powder.
This is the actual fuse ; for service the capped end of
the fuse is placed in a perforation in the rounded head
of a wooden cylinder, so as to project slightly into the
cavity g of the cylinder. This cavity is filled with meal
powder, which is well rammed down, so that the fuse is
firmly imbedded. It is afterwards closed by a plug of
gutta-percha, and the whole is finally coated with black
varnish.
The free ends of the wire a a are pressed into small
grooves in the head of the cylinder (fig. 658), and each
end is bent into one of the small channels with which the
cylinder is provided, and which are at right angles to
the central perforation. They are wedged in here by
driving in small copper tubes, the ends of which are
then filed flush with the surface of the cylinder. The
bared ends of two insulated conducting wires are then
pressed into one of the small copper tubes or eyes, and
fixed there by bending the wire round on to the wood, as
shown at e.
The conducting wire used in firing may be thin, but it must be well insu-
lated. One end, which is bared, having been pressed into the hole d of the
fuse (fig. 657), the other is placed near the exploder. In the other hole d' of
the fuse a wire is placed which serves as earth wire, care being taken that
there is no connection between the two wires. The fuse having been intro-
Fig. 657-
Fig. 658.
-795] Duration of the Electric Spark. 697
duced into the charge, the earth wire is placed in good connection with the
ground. The knob/ of the exploder is also connected with the earth by
leading uncovered wire into water or moist earth, and the condition of the
machine tested. The end of the insulated wire is then connected with the
knob e and the rod drawn down ; at the proper signal the handle is turned
the requisite number of times, and when the signal is given the trigger is
depressed, and the explosion ensues.
When a number of charges are to be fired they are best placed in a single
circuit, care being taken that the insulation is good.
795. Duration of the electric spark. Wheatstone measured the dura-
tion 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
reflection (520) 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-
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 g^oo or
__!__ of a second. Thus the discharge is not instantaneous, but has a certain
duration, which, however, is excessively short.
Feddersen found that when greater resistances were interposed in the
circuit through which the discharge was effected, the duration of the
spark was increased. With a tube of water 9 mm. in length, the spark
lasted 0-0014 second; and with one of 180 mm. its duration was 0-0183
second. The duration increased also with the striking distance, and with
the dimensions of the battery.
To determine the duration of the electric spark Lucas and Cazin
used a most accurate method, by which it may be measured in millionths
of a second. The method is an application of the vernier. A disc of mica
1 5 centimetres in diameter is blackened on one face, and at the edge are
traced 180 equal divisions 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 100 to 300 turns
in a 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 ^\ x
transparent lines are traced, forming a Fjg 6sg
vernier with the lines on the mica. For
this, the distance between two consecutive lines on the two discs is such that
rive divisions of the mica disc DC correspond to six divisions of the glass
H H
698
Frictional Electricity.
[795-
disc AB as seen in fig. 659. Thus the vernier gives the sixths of a
division of the mica disc (10). In the apparatus the lines AB are not above
the lines CD, but are at the 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. 660), on the hinder face
of which is fixed the vernier. In the front face is a 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's
Fig. 660.
machine. The sparks strike between two metal balls a and b, 1 1 millimetres
in diameter. Their distance can be varied, and at the same time measured,
by means of a micrometric screw, r. The two opposite electricities arrive
by wires m and #, 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.
-796] Velocity of Electricity. 699
These details being premised, suppose the velocity of the disc is 400
turns in a second. In each second 400 x 180 or 72,000 lines pass before the
observer's eye in each second ; hence an interval of Y . 3 ^ of a second elapses
between two consecutive lines. But as the spark is only seen when
one of the lines of the disc coincides with one of the six lines of the vernier ;
and as this gives sixths of a division of the moveable disc, when the latter
has turned through a sixth of a division, a second coincidence is pro-
duced ; so that the interval between two successive coincidences is
? - = 0-0000023 of a second.
72000x6
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 (625) the observer will see two luminous
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 i 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 , and varying the number of the jars, MM. Lucas
and Cazin obtained the following results :
Duration in
Number of jars millionths of
a second.
2 26
4 41
6 45
8 47
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 the spark strikes.
The spark of electrical machines has so short a duration that it could not
be measured with the chronoscope.
796. Velocity of electricity. To determine the velocity of electricity
Wheatstone constructed an apparatus the principle of which will be under-
stood from fig. 66 1 ; six insulating metal knobs were
arranged in a horizontal line on a piece of wood called
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 I
was a tenth of an inch distant from the knob 2 ;
while between 2 and 3 a 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 which a wire led directly to the
outer 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 i and 2, between 3 and 4, and between
5 and 6. Thus the discharge, supposing it to proceed from the inner coat-
H H 2
70O Frictional Electricity. [796-
ing, 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 sparks would be seen as three dots j , 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 800 revolutions in a second, can be shown to correspond to a duration
of 24000 f a secon d. With a slow rotation the lines present the appearance
.ZZ= ; 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 -^^^, ; an( j 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 the others. This arc corresponds to a
duration o or VT^TTKTI of a second ; the space traversed in this
2 x 720 x 100
time being a quarter of a mile, gives for the velocity of electricity 288,000
miles in a second, which is greater than that of light. The velocity of
dynamical electricity is far less ; and, owing to induction, the transmission
of a current through submarine wires is comparatively slow.
In the above experiment the images of the two outer sparks appear
simultaneously in the mirror, from which it follows that the electric current
issues simultaneously from the two coatings of the Leyden jar.
From certain theoretical considerations based upon measurements of
constant electrical currents Kirchhoff concluded that the motion of elec-
tricity in a wire in which it meets with no resistance is like that of a wave
on a stretched string, and has the velocity of 192,924 miles in a second,
which is about that of light in vacuo (507).
According to Walker, the velocity of electricity is 18,400 miles, and ac-
cording to Fizeau and Gounelle, it is 62,100 miles in iron, and 111,780 in
copper wire. These measurements, however, were made with telegraph wires,
which induce opposite electricities in the surrounding media ; there is thus
produced a resistance which diminishes the velocity. The velocity is less
in insulated wires in water than in air. The nature of the conductor appears
to have some influence on the velocity ; but not the thickness of the wire,
nor the potential of the electricity.
For atmospheric electricity, reference must be made to the chapter on
Meteorology.
-797J
' s Experiment.
701
BOOK X.
DYNAMICAL ELECTRICITY.
CHAPTER I.
VOLTAIC PILE. ITS MODIFICATIONS.
797. Galvani' experiment and theory. The fundamental experiment
which led to the discovery of dynamical electricity is due to Galvani pro-
fessor of anatomy m Bologna. Occupied with investigations on the influence
3f electricity on the nervous excitability of animals, and especially of the frog,
he observed that
when the lumbar
nerves of a dead
frog were connected
with the crural
muscles by a me-
tallic circuit, the
1 atter 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-
posed of zinc and
copper, is then taken (fig. 662), 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
Fig. 662.
7O2 Dynamical Electricity. [797-
that this electricity, which he called vital 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.
798. 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 only officiated 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. 640), the lower plate is touched with a plate of copper, c,
soldered to a plate of zinc, 2, which is held on the other hand. On breaking
the connection and lifting the upper plate (fig. 641), 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 #, 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 two 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 in-
teresting experiments with animal tissues. In some of these he obtained
indications of contraction, even though the substances in contact were quite
homogeneous.
799. 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 (798)
Volta obtained signs of electricity. But De la Rive showed that if the zinc
be held in a wooden clamp, all signs of electricity disappear, and that the
same is the case if the zinc be placed in gases, such as hydrogen or nitrogen,
-799] Disengagement of Electricity in Chemical Action. 703
which exert upon it no chemical action. De la Rive accordingly concluded
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 (786) : 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 variety 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, con-
dition. 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 Sir W.
Thomson, afford perhaps the most conclusive arguments hitherto adduced
in favour of the latter view :
A very light metal bar was suspended by a fine wire so as to be moveable
about an axis, perpendicular to the plane of a ring made up of two halves,
one of copper and the other of zinc. When the two halves of the ring were
in contact, or were soldered together, the light bar turned from the copper
to the zinc when it was negatively electrified, and from the zinc to the copper
when it was positively electrified, thus showing that the contact of the two
metals causes them 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, were
connected by a drop of water, no change was produced in the position of the
bar by altering its electrification, provided it hung quite symmetrically re-
lative to the two halves of the ring. This result shows that, under the cir-
cumstances mentioned, no difference is produced in the electrical condition
704 Dynamical Electricity. [799-
of the two metals. Hence the conclusion has been drawn by Sir \V. Thom-
son 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 dissimilar metals. These results have been confirmed by some recent
very careful experiments by Prof. 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 all cases two different metals connected by an electrolytic
(8 1 6) liquid, assume the same electrical condition. It may, therefore, still
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.
An instructive discussion of this question, with some additional experi-
mental evidence in favour of the chemical theory, will be found in a paper by
Dr. Fleming, published in the ' Proceedings of the Physical Society ' (Taylor
and Francis).
800. 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
Fig. 66 3 7~ tne f act tnat tn ^ s 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 to understand 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
lower potential that is, from the positive along the wire to the negative
and the potentials become equal. This is, indeed, nothing more than an elec-
trical 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
place when the two spheres are respectively connected with the two con-
ductors rand r lt of a Holtz's machine (figs. 615, 616), this equalisation of
potentials, thus taking place, is virtually continuous, and the phenomena
above mentioned are also continuous.
-801] Voltaic Couple. Electromotive Series. 705
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 only
produced 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 +e 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 4 e ( and fixed to a cover,
c, which rests on the porous vessel.
The platinum is connected with a
binding screw, b, and there is a
similar binding screw on the zinc.
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
Fig. 668.
Fig. 669.
-810]
Ilnnscn's Battery.
713
of the two-fluid batteries. It is, however, expensive, owing to the high price
of platinum ; besides which the platinum is liable, after some time, to
become brittle and break very easily. But as the platinum is not consumed,
it retains most of its value, and when the plates which have been used in a
battery are heated to redness, they regain their elasticity.
8 10. Bunsen's battery. Kunserfs, also known as the zinc carbon
battery, was invented in 1843; it is m effect a Grove's battery, where
the plate of platinum is replaced by a cylinder of carbon. This is made
either of the graphitoidal carbon deposited in gas retorts, or by calcin-
ing in an iron mould an intimate mixture of coke and bituminous coal, finely
powdered and strongly compressed. Both these modifications of carbon are
good conductors. Each element consists of the following parts : i. a vessel,
F (fig. 670), 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
is ordinary nitric acid ; 4. a rod of carbon, C, prepared in the above
manner. In the vessel F the zinc is first placed, and in it the carbon C in
the porous vessel V as seen in P. To the carbon is fixed a binding screw,
;//, to which a copper wire is attached, forming the positive pole. The zinc
is provided with a similar binding screw, //, and wire, which is thus a negative
pole.
The elements are arranged to form a battery (fig. 671) by connecting each
carbon to the zinc of the following one by means of the clamps mn, and a
strip of copper, c, 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 n, which is fitted on the zinc of the following element, and so
forth. The clamp of the first carbon and that of the last zinc are alone pro-
vided with binding screws, to which are attached the wires.
The chemical action of Bunsen's battery is the same as that of Grove's,
and being equally powerful, while less costly, is almost universally used on
the Continent. But though its first cost is less than that of Grove's batter)-,
it is more expensive to work, and is not so convenient to manipulate.
Callaris battery is a modified form of Grove's. Instead of zinc and plati-
num, zinc and platinised lead are used, and instead of pure nitric acid Callan
714 Dynamical Electricity. [810-
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 has 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 electro-
negative, and does not dissolve. If, however, the nitric acid becomes too
weak, the iron is dissolved with simultaneous 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, better, 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 oxide of chromium,
Fig. 671.
which remains dissolved iii sulphuric acid. With the same view, sesqui-
chloride of iron is sometimes substituted for nitric acid ; it becomes re-
duced to protochloride. But the action of the elements thus modified is
considerably less than when nitric acid is used, owing to the increased re-
sistance.
8 1 1. Smee's battery. In this battery the polarisation of the negative
plate is prevented by mechanical means. Each element consists of a sheet of
platinum placed between two vertical plates of zinc, as in Grove's battery;
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, which
facilitates the disengagement of hydrogen to a remarkable extent, and conse-
quently diminishes the resistance of a couple. Instead of platinum, silver
covered with a deposit of finely divided platinum is frequently substituted, as
being cheaper.
Walkers battery. This resembles Smee's battery, but the electronegative
-812]
Recent Batteries.
715
plate is either gas grapnite or platinised graphite ; it is excited by dilute
sulphuric acid. This battery is used in all the stations of the South-Eastern
Railway ; it has considerable electromotive force, is convenient and econo-
mical in manipulation, and large-sized elements can be constructed at a
cheap rate.
812. Recent batteriec. The mercury sulphate battery (fig. 672) de-
vised by Marie" 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 from the pasty mass. The carbon
Fig. 672.
Fig. 673.
Fig. 674.
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 only when the cell is closed. The zinc then
decomposes the water, liberating hydrogen, which, traversing the porous
vessel, 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 DanielFs element, but it has greater resistance ; it is rapidly exhausted
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 liable to many objections,
more especially in the case of DanielPs battery, in which they gradually
become encrusted with copper, which destroys them. 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. 673 represents a form devised
by Callaud. V is a glass or earthenware vessel in which is a copper plate
soldered to a wire insulated by gutta percha. On the plate is a layer of
716 Dynamical Electricity. [812-
crystals of copper sulphate, C ; the whole is then filled with water, and the
zinc cylinder, Z, is immersed in it. The 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 rs easily manipulated, the
consumption of copper sulphate is economical, and when not agitated it
works constantly for some time, provided care be taken to replace the water
lost by evaporation.
Meidinger's element, which is much used in Germany, is essentially a
gravity battery of special construction with zinc in solution of magnesic
sulphate, and copper in solution of copper sulphate.
Minotttfs 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. 674) is placed a layer of coarsely-
powdered copper sulphate a, and on this a copper plate provided with an
insulated copper wire i. On this there is a layer of sand or of sawdust be,
and then the whole is filled with water, in which rests a zinc cylinder Z.
The action is just that of a Daniell ; the sawdust prevents the mixture of
the liquids, but it also offers great resistance, which increases with its thick-
ness. From its simplicity and economy, and the facility with which it is
constructed, this battery merits increased attention.
De la Rue and Mailer's element consists of a glass tube about 6 inches
long by 075 inch in diameter, closed by a vulcanised india-rubber stopper
through which passes a zinc rod 18 inches 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 Rue and 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 | 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 I \ inch.
The electromotive force of a silver chloride cell is 1*03 of a volt, and that
of one made with silver bromide is 0-908 ; hence a series of 4 cells, three of
the silver chloride cells with one of bromide, give an average electromotive
force of i volt -(8 1 4).
Mr. Latimer Clark has devised an element which consists of pure mer-
cury as a negative plate covered with a paste, obtained by boiling sul-
phate of mercury in a saturated solution of zinc sulphate. The positive
metal is a plate of zinc resting on this paste of sulphate. Insulated wires,
leading to the mercury and the zinc respectively, form the connections.
This battery is not well adapted for continuous work, but it furnishes
a standard of electromotive force, which is constant and can be relied
upon.
813. Leclanche's element. This consists (fig. 675) of a rod of carbon,
C, placed in a porous pot, which is then very tightly packed with a mixture
-814]
Electromotive Force of Different Elements.
717.
of pyrolusite (peroxide of manganese) and gas graphite M. This is covered
over with a layer of pitch. At the top of the carbon is soldered 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 electromotive force of the ele-
ment is said to be about one-third greater
than that of a DanielFs element ; its in-
ternal resistance varies of course with the
size, but is stated to be from two to three
times that of an ohm. The battery is not
adapted for continuous work, as in heavy
telegraphic circuits, or in electroplating,
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.
A rod of carbon 4^xi;x 3 5 - inches
should have a maximum resistance of I
ohm ; but good plates made from the
carbon of gas retorts do not average
more than 0-5, and in some cases o-i unit. If the resistance = an ohm, the
conducting 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, at the junction with the binding screw, a local cur-
rent which injures or destroys 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 rod thus prepared is not altered.
814. Electromotive force of different elements. The following numbers
represent the electromotive force of some of the elements most frequently
used, compared with that of an ordinary Daniell's cell charged as above
described ; they are the means of many careful determinations :
Daniell's element set up with water
pure zinc and pure water, with pure
copper and pure saturated solution
of copper sulphate
zinc in saturated solution of am-
monium chloride .
Fig. 675.
I -00
I'02
Leclanchd's
Marie Davy's,,
Bunsen's
55
Grove ; s
carbon in nitric acid
carbon in chromic acid
platinum in nitric acid
32
4i
77
87
7 1 8 Dynamical Electricity. [814-
The greatest electromotive force as yet observed is by Beetz in a couple
consisting of potassium amalgam in caustic potash, combined with pyro-
lusite in a solution of potassium permanganate. It is three times as much
as that of a DanielPs element.
The standard of electromotive force on C. G. S. system is the Volt.
This is equal to 1,000,000,000 or io 8 absolute electromagnetic units ; the
latter way of expressing it is convenient, as avoiding the use of long numbers.
The volt is rather less than the electromotive force of a Daniell's cell, the
mean value of which may be taken at 1-12 volt. The unit of current, which
is usually called a Weber* is the current due to an electromotive force of i
volt working through a resistance of i ohm.
815. 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 De la Rue and Muller'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 0-012 in. with the potential due to 1,200 of their cells, it was
0-049 m - w i tn 4>8oo 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 deli-
cate condensing electroscope, and by extremely careful insulation, it can be
shown that one pole possesses a positive and the other a negative charge.
For this purpose one of the plates of the electroscope is connected with
one pole, and the other with the other pole or with the ground. The
electroscope thus becomes charged, and on breaking the communication
electroscopic indications are observed.
On the other hand the strength of current which a voltaic element can
produce in a good conductor is much greater than that which can be pro-
duced by a machine. Faraday immersed two wires one of zinc, and the
other of platinum, each T \ 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 has ascertained by quantitative measurements 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 (812) ; 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.
8 1 6. 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, is rapidly dissolved by dilute acid. This,
doubtless, arises from the impurity of the zinc, which always contains traces
either of iron or lead. Being electronegative towards zinc, they tend to
produce local electrical currents, which accelerate the chemical action with-
out increasing the quantity of electricity in the connecting wire.
-818] Dry Piles. 719
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 platinum plate immersed in the same liquid. To amalgamate a zinc plate,
it is first immersed in dilute sulphuric or hydrochloric acid so as to obtain a
clean surface, and then a drop of mercury is placed on the plate and spread
over it with a brush. The amalgamation takes place immediately, and the
plate has the brilliant aspect of mercury. Zinc as well as other metals are
readily amalgamated by dipping them in an amalgam of one part sodium
and 200 parts of mercury. Zinc plates may also be amalgamated by dipping
them in a solution of mercury prepared by dissolving one pound of mercury
in rive pounds of aqua regia (one part of nitric to three of hydrochloric acid),
and then adding five parts more of hydrochloric acid.
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
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.
817. Dry piles. In dry piles the liquid is replaced by a solid hygrometric
substance, such as paper or leather. They are of various kinds : in Zamboni's,
which is most extensively used, the electromotors are tin or silver, and bin-
oxide of manganese. To construct one of these a piece of paper silvered or
tinned on one side is taken ; the other side of the paper is coated with finely-
powdered binoxide of manganese 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 i, 800 couples, they are placed in a glass tube, which is provided with a
brass cap at each end. In each cap there is a 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 permanence of their action, which
may continue for several years. Their action depends greatly on the tem-
perature 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 Zamboni's pile of 2,000 couples gives neither shock nor spark,
but can charge a Leyden jar and other condensers. A certain time is, how-
ever, necessary, for electricity only moves slowly in the interior.
8 1 8. Bohnenberger's electroscope. Bohnenberger has constructed a
dry pile electroscope of great delicacy. It is a condensing electroscope
(fig. 641), from the rod of which is suspended a single gold leaf. This is at
an equal distance from the opposite poles of two dry piles placed vertically,
inside the bell jar, on the plate of the apparatus. As soon as the gold leaf
possesses 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.
720 Dynamical Electricity. [819- .
CHAPTER II.
DETECTION AND MEASUREMENT OF VOLTAIC CURRENTS.
819. 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 effects. 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.
820. Oersted's experiment. Oersted published in 1819 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 moveable magnetic needle, as repre-
sented in fig. 676. 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 element, the needle is de-
flected, and tends to take a position
which is the more nearly at right angles
to the magnetic meridian in proportion
as the current is 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. Re-
membering our assumption as to the direction of the current in the con-
necting wire (803) the preceding experiment 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.
ii. If the current passes below the needle, also from south to north, the
north pole is deflected towards the east.
iii. When the current passes above the needle, but from north to south,
the north pole is deflected towards the east.
-821]
Galvanometer or Multiplier.
721
iv. Lastly, the deflection is towards the west when the current goes from
north to south below the needle.
Ampere has given the following memoiiatechtiica 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 : /// the directive action of currents on magnets, the north
pole is always deflected towards the left of the current.
821. 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 in Germany a short time after Oersted's dis-
covery.
In order to understand its principle, let us suppose a magnetic needle
suspended by a filament of silk (fig. 677), and surrounded in the plane of
7 p
Fig. 677.
Fig. 678.
the magnetic meridian by a copper wire, mnopq, 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 ab, 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 intensity 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
in the magnetic meridian, and thus opposes the action of the current, the
I i
722
Dynamical Electricity.
[821-
eftect of the latter is increased by using an astatic system of two needles,
as shown in fig. 678. The action of the earth on the needle is then very
feeble, and, further, the actions of the current on the two needles become
accumulated. 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 no and qp, but as the first is nearer, its action pre-
ponderates. Now this current passing below the needle, evidently tends
to turn the pole a' towards the east, and, consequently, the pole b' 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. 679 consists of a thick brass
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, / and o. Above the
frame is a graduated '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
there are two graduations on
the scale, the one on the right
and the other on the left of
zero, but they only extend to
90. By means of a very fine
filament of silk, an astatic sys-
tem is suspended ; it consists
of two needles, ab and a'b', one
above the scale, and the other
within the circuit itself. These
Fig. 6 79 . needles, which are joined to-
gether by a copper wire, like
those in fig. 577 and fig. 678 and cannot move separately, must not have
exactly the same magnetic intensity ; for if they are exactly equal, every
current, strong or weak, would always put them at right angles with itself.
In using this instrument the diameter, to which corresponds the zero of
the graduation, is brought into the magnetic meridian by turning the plate
P until the end of the needle ab 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
-822] Sir W. Thomsons Marine Galvanometer. 723
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,
which have low intensity, require a thicker and shorter wire ; for example,
thirty turns of a wire f 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 of high potential, as those of the electrical machine (791)
may be shown. One end of the galvanometer is connected with the con-
ductor, and the other with the ground, and on working the machine 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, 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 in-
strument is used as a galvanoscope or rheoscope that is, to ascertain rather
the presence and direction of currents than as a galvanometer or rheometer
in the strict sense ; that is, as a measurer of their intensity. The term
galvanometer is, however, commonly used.
The differential galvanometer consists of a needle, as in an ordinary
galvanometer, but round the frame of which are coiled two wires of the same
kind and dimensions, carefully insulated from each other, and provided 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 direc-
tions, 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.
822. Sir W. Thomson's marine galvanometer. In laying submarine
cables the want was felt of a galvanometer sufficiently sensitive to test insula-
tion, which at the same time was not affected by the pitching and rolling of
the ship. For this purpose, Sir W. Thomson invented his marine galvano-
meter. B (fig. 680) represents a coil of many thousand turns of the finest 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. The magnet itself is made of a
piece of fine watch-spring about f of an inch 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 exactly passes through the centre of gravity in every position. As the
mirror and magnet weigh only a few grains, they retain their position rela-
tively to the instrument, however the ship may pitch and roll. The slide fits in
a 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 object of
this is to counteract the influence of the terrestrial magnetism when the ship
changes its course.
I I 2
724
Dynamical Electricity.
[822-
Underneath the coil is a large curved steel magnet N, which compensates
the earth's directive action upon the magnet D ; and in the side of the case,
and on a level with D, a pair of magnets, C, are placed with opposite poles
together. By a 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 three feet, there is a scale with the zero in the
centre and the graduation extending on each side. Underneath this zero
Fig. 680.
point is a narrow slit, through which passes the light of a paraffine lamp, and
which, traversing the window, is reflected from the curved 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 terminals, the spot of light is deflected either to
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.
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 (522). It is used in observing the motion of oscillating bodies,
in measuring the variations of magnetism, in determining the expansion of
solids, &c.
It will be seen from the article on the Electric Telegraph, how alternate
- 823] Tangent Compass, or Tangent Galvanometer. 72$
deflections of the spot of light may be utilised in forming a code of
signals.
823. Tangent compass, or tangent galvanometer When a magneti
needle is suspended in the centre of a voltaic current in the plane of the
magnetic meridian, it can be proved that the intensity of a current is directly
proportional to the tangent of the
angle of deflection, provided the
dimensions of the needle are suffi-
ciently small as compared with the
diameter of the circuit. An instru-
ment based on this principle is
called the tangent galvanometer or
tangent compass. It consists of a
copper ring, 12 inches in diameter,
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 TO OI "
the diameter of the circle. Under- Fig
neath the needle there is a graduated
circle. The ends of the ring are prolonged in copper wires, fitted with
mercury cups, ab, by which it can be connected with a battery or element.
The circle is placed in the plane of the magnetic meridian, and the deflection
of the needle is directly read off on the circle, and its corresponding value
obtained from a table of tangents.
On account of its small resistance, the tangent galvanometer is well
adapted for currents of low potential, but in which a considerable quantity
of electricity is set in motion.
To prove that the intensities of various currents are proportional to the
tangents of the corresponding angles of deflection, let NS, fig. 682, represent
the wire of the galvanometer and ns the needle, and let $ be the angle of
deflection produced when a current C is passed. Two forces now act upon
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 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 corre-
sponding lines an and bn. Now the whole intensities of these forces do not
act so as to turn the point of the needle round, but only those components
which are at right angles to the needle. Resolving them, we have ng and nf
as the forces acting in opposite directions on the needle ; and since the
needle is at rest these forces must be equal.
The angle nag is equal to the angle 0, and therefore ng-=an sin < ; and
in like manner the angle bnf'is equal to < and nf=bn cos < ; and therefore
since nf=ng, bn cos
C = H tan <.
sin <, or bn = an = an tan < ; that is,
726
Dynamical Electricity.
[824-
g
Fig. 682.
If any other current be passed through the galvanometer we shall have
similarly C' = H tan <' ; and since the earth's magnetism does not appreciably
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 it is deflected. This
is only the case when the dimensions of the needle are
small compared with the diameter of the ring it should
not be more than | or ^ the diameter. In order to
measure with accuracy the deflection a light index is
placed at right angles to the needle.
Wiedemanrts tangent galvanometer consists of a
short thick copper tube, in which is suspended, instead
of a needle, a small but thick magnetised sheet iron
mirror, the position of which can be observed by a
telescope and scale (522). 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 arrangement
of the current in reference to the magnetic needle, the
error of the tangent galvanometer is diminished ; for
when the needle is deflected, one end moves away from
the current, while the other approaches it.
According to Gaugain, the tangent of the angle of deflection is most
nearly proportional to the strength of the current when the centre of the
needle is at a distance of one
quarter the diameter of the ring
from the centre of the ring.
824. Sine galvanometer.
This is another form of galvano-
meter for measuring powerful
currents. Round the circular
frame, M (fig. 683), several turns
of stout insulated copper wire
are coiled, the two ends of
which, z, terminate in the bind-
ing screws at E. On a table in
the centre of the ring there is a
magnetic needle, m ; a second
light needle, , fixed to the first,
serves as pointer along the
graduated circle, N. Two
copper wires, <2, b, from the
sources of electricity to be
F measured, are connected with
E. The circles M and N are
supported on a foot O, which
can move about a vertical axis
Fig. 683. passing through the centre of a
fixed horizontal circle H.
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 needles,
-825]
Sine Galvanometer <
727
being deflected, the circuit M is turned until it coincides with the vertical
plane passing through the magnetic needle ;. 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 proportional to the
sine of the angle of deflection : this angle is measured on the circle H by
means of a vernier on the piece C. This piece, C, fixed to the foot O, turns
it by means of a knob, A. The angle of deflection, and hence its sine, being
known, the intensity of the current may be thus
deduced : let mm' be the direction of the mag-
netic meridian, d the angle of deflection, C the
strength of the current, and H the directive action
of the earth. If the direction and intensity of this
latter force be represented by ak, it may be replaced
by two components, ah and ac (fig. 684.) Now, as
the first has no directive action on the needle, the
component ac must alone counterpoise the force C,
that is, C ae. But in the triangle, ack, ac = ak cos
cak, from which ac = H sin d, for the angle cak is the
complement of the angle d, and ak 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 d, we shall have C' = H sin d', whence C : C' = sin d : sin tf.
825. Ohm's iaw. 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 have received the fullest confirmation,
and their great theoretical and practical importance has been fully established.
i. 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 intensity
or, perhaps better, the 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 same current is passed respec-
tively 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 resist-
ance to the passage of the current than in the former ; and he proved that
' the resistance is inversely proportional to the strength of the current?
On these principle* Ohm founded the celebrated law which bears his
name, that the strength of the current is equal to the electromotive force
divided by the resistance.
This is expressed by the simple formula
C- K
L ~'
728 Dynamical Electricity. [825-
where C is the strength of the current, E the electromotive force, and R the
resistance.
ii. The resistance of a conductor depends on three elements ; its conduc-
tivity, which is a constant, determined for each conductor ; its section ; and
its length. The resistance is obviously inversely proportional to the conduc-
tivity ; that is, the less the conducting power the greater the resistance. It
has been proved that the resistance is inversely as the section and directly
as the length of a conductor. If then AC is the conductivity, o>the section, and X
the length of a conductor, we have, that is, the strength of a current is inversely
t> X , ~ E
R = and C = = .
KM XX
KO>
proportional to the length of the conductor and directly proportional to its
section and conductivity.
iii. In a voltaic batteiy 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 com-
posed of elements of the same kind, each having, in intention at least, the
same electromotive force and the same resistance,
In an ordinary element there are essentially two resistances to be con-
sidered : i. That offered by the liquid conductor between the two plates,
which is frequently called the internal or essential resistance ; and 2. That
offered by the interpolar conductor which connects the two places outside the
liquid ; this conductor may consist either wholly of metal, or may be partly of
metal and partly of liquids to be decomposed : it is the externals non-essential
resistance. Calling the former R and the latter r, Ohm's formula becomes
C- 1 U
R + r
iv. If any number, 72, of similar elements are joined together, there is n
times the electromotive force, but at the same time n times the internal
resistance, and the formula becomes -^ . If the resistance in the inter-
nR + r
polar, r, 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 re-
sistance, and then we have
r ;/ ^ ^
= nR~ ~R'
that is, a battery consisting of several elements produces in this case no
greater effect than a single element.
v. If, however, the external resistance is very great, as when the current
has to produce the electric light, or to work a long telegraphic circuit, ad-
vantage is gained by using a large number of elements ; for then we have
the formula
if r is very great as compared with ;/R, the latter may be neglected, and the
expression becomes
r n ^
-825]
Ohm's Law.
729
that is, that the strength, within certain limits, is proportional to the number
of elements.
In a thermo-electric pile, which consists of very short metallic conductors,
the internal resistance R is so small that it may be neglected, and the
strength is inversely as the length of the connecting wire.
vi. If the plates of an element be made m times as large, there is no
increase in the electromotive force, for this depends on the nature of the
metals and of the liquid (802), but the resistance is m times as small, for the
section is /// times larger ; the expression becomes then
C - = wE
R + r R + mr
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 in-
Fig. 685.
T
Fig. 688.
definite extent ; for ultimately the resistance of the element R vanishes in
comparison with the resistance r, and the strength continually approximates
to the value C = .
r
vii. 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 : I. In a single series (fig.
i i 3
73 Dynamical Electricity. [825-
685), in which the zinc Z of one element is united with the copper C of the
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. 686) ; 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. 687) ; 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. 688).
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 battery of six elements
the internal resistance R of each element is 3, and the external resistance
r= 12. Then, in the first case, where there are six elements, arranged in
series, we have the value,
C= 6E _ 6E _6E (n
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. 686), the electromotive force would then
be the electromotive force in each element ; there would also be a resistance
R in each element, but this would only be half as great, for the section of
the plate is now double ; hence the strength in this case would be
C' = 3E _. 3E _6E. ,.
3R + r 9 + 12 33 '
2 2
accordingly this change would lessen the strength.
If, with the same elements, the resistance in the connecting wire were
only r=2, we should have the values in the two cases respectively
6 x E = 6E
'
_
3R + ^ 9 + 4 13
The result in the latter case is, therefore, more favourable. If the re-
sistance r 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 r.
826. Arrangement of multiple battery for maximum current. It can
be shown that in any given combination the maximum effect is obtained when
the total resistance in the elements is equal to the resistance of the interpolar.
For let N be the total number of cells available for a given combination, and
let n be the number of cells arranged tandem, or in series ; that is, when
the zinc of one is connected with the copper of the next, and so on ; then
N
there will be elements arranged abreast. If e be the electromotive force,
n
and r the resistance of one cell, while / is the external resistance, then the
strength of the current will be
-826] Arrangement of Multiple ^Battery for Maximum Current 731
C= nr " = //V+ XV
If this combination be such that the total internal resistance- r is
to the external resistance /, we have
C= ne
~ ~2l'
For suppose that the whole number of cells is arranged so as to form
another combination of cells tandem, let n' be this number, which shall be
equal to n v \ then we have
_
tfir+vr* 2
or since ,V-N/-
Xow the value of C C l is always positive ; for reducing to a common
denominator
r _ 2 X& (n + rv) + v-rne . r 2N/o currents which are parallel, and in the same direction, attract one
another.
I 1. Two currents parallel, but in contrary direction, 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 moveable. This is effected
764
Dynamical Electricity.
[856-
713-
by the apparatus (fig. 712), which is a modified and improved form of one-
originally devised by Ampere.
It consists of two brass columns, A and D, between which is a shorter
one. The column D is provided with a multiplier (821) of 20 turns, MN (fig.,
712), which greatly increases the sensitiveness of the instrument. This can>
be adjusted at any height, and in any position, by means of a universal screw
clamp (see figs. 712, 714-718).
The short column is hollow, and in its interior slides a brass tube ter-
minating in a mercury cup,V, which can be raised or lowered. On the
column A is another mercury cup represented in
section at fig. 713 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 far as 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, suspended to the ends.
The details being known, the current of a Bunsen's battery of 4 or 5 cells
ascending by the column A (fig. 712) to the cup <2, traverses the circuit BC,
reaches the cup c, descends
the central column, and
thence passes by a wire, P,
to the multiplier MN, from
whence it returns to the bat-
tery by the wire O. 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 current
passes, the side B is repelled,
which demonstrates the se-
cond 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 figure 714
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.
857. Regret's vibrating: spiral. The attraction of parallel currents may
also be shown by an experiment known as that of Rogefs -vibrating spiral.
A copper wire about 07 mm. in diameter is coiled in a spiral of about 30
coils of 25 mm. in diameter. At one end it is hung vertically from a binding
-858]
Laws of Angular Currents.
765.
Fig. 715-
screw, while the other just dips in a mercury cup. On passing the current
of a battery of 3 to 5 Grove's cells through the spiral by means of the mer-
cury cup and the binding screw, its coils are traversed 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, con-
tact with the mer-
cury is re-estab-
lished, and the
series of pheno-
mena are indefi-
nitely produced.
The experiment is
still more striking
if a magnetised
rod the thickness
of a pencil is intro-
duced into the interior. This will be intelligible if we consider the action
between the parallel Amperian currents of the magnet and of the helix.
858. Xiaws of angular currents. I. Two rectilinear currents, the direc-
tions of which firm an angle with each oilier, attract one another when both
approach, or re-
cede from, the apex
of the angle.
II. They repel
one another, if one
approaches and the
other recedes from
the apex of the
angle.
These two laws
may be demon-
strated by means
of the apparatus
above described,
replacing the mov-
able circuit by the
circuit BC (fig. 715). If then the multiplier is placed horizontally, so that
its current is in the same direction as in the movable current, if the latter
is removed and the current passes so that the direction is the same as in the
movable part, on removing 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 directions, and then repulsion ensues (fig. 716).
Fig. 716.
766
Dynamical Electricity.
[858-
In a rectilinear current each element of the current repels the succeeding
one, and is itself repelled.
This is an important consequence of Ampere's law, and may be experi-
mentally demonstrated by the fol-
lowing arrangement, which was
devised by Faraday. A (J -shaped
piece of copper wire, whose ends
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
accordingly repelled.
The repulsion may also be shown
by means of the following experi-
ment. A rod of charcoal, C (fig.
717), drawn out to a fine point, is
fixed horizontally in a support. In
contact with it is another similar
Fig. 717.
pointed rod, C', counterpoised by the weight K at the end of a light hori-
zontal rod, A ; this rod is suspended by a wire, and is in metallic connection
with a mercury cup, M. If
now C and C' be connected
with the poles F and F' of a
battery, the movable cone
C' is repelled from C. As
the wire thereby 'experiences
some torsion, a stable equili-
brium is established, and the
point C' is kept at a fixed
distance from C. At the
same time the voltaic arc
(833) is formed between C
and C'.
859. laws of sinuous
currents. The action of a
sinuous current is equal to
that of a rectilinear ciirrent
of the same length in projection. This principle is demonstrated by ar-
ranging the multiplier vertically and placing near it a movable circuit of
insulated wire half sinuous and half rectilinear (fig. 718). It will be seen
-860]
Direction of Currents by Currents.
767
that there is neither attraction nor repulsion, showing that the action of the
sinuous portion mn is equalled by that of the rectilinear portion.
An application of this principle will presently be met with in the appa-
ratus called solenoids (872), which are formed of the combination of a sinuous
with a rectilinear current.
DIRECTION OF CURRENTS BY CURRENTS.
860. Action of an infinite current on a current perpendicular to its
direction. From the action exerted between two angular currents (869) the
action of a fixed and infinite rectilinear current, PQ (fig. 719), on a movable
>5t
.a,::'... ...:.--,
R:
o
Fig. 719.
Fig. 720.
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 PC
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 (858) the portion GO ot
the current PQ attracts the current KH, because they both flow towards the
summit of the angle formed by their direccions. 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 mq and ;;// 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
arranged in reference to the two sides of the point O, these two forces may
be resolved into a single force, mn, 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. 720), it will be readily seen from similar considerations that it moves
parallel to this current, but in the same direction.
Hence follows this general principle. A finite movable current -which
approaches a fixed infinite current is acted on so as to move in a direction
parallel and opposite to that of the fixed current; if the movable current
tends from the fixed current, it is 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,
XV, parallel to its direction (figs. 721 and 722), any horizontal current, PQ,
will have the effect of turning the movable current about its axis, until the
plane of the axis and of the current have become parallel to PQ ; the vertical
;68
Dynamical Electricity.
[860-
current stopping, in reference to its axis, on the side from which the current
PQ comes (fig. 721), or on the side towards which it is directed (fig. 722),
Fig. 721.
Fig. 722.
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. 723 and 724) is directed by a horizontal
current, PQ, in
X: a plane parallel
to this current
when one of
the vertical cur-
rents is ascend-
ing and the other
descending (fig,
723) ; but that if
Fig. 723. Fig. 724. tne y are botn as -
cending or both
descending (fig. 724), they are not directed.
861. Action of an infinite rectilinear current on a rectangular or
circular current. It is easy to see that a horizontal infinite current exercises
the same directive action on a rectangular current movable about a vertical
axis (fig. 725) as
A.] ^^o T-I sL'<
tj - J - 4a
>& n A
what has been
above stated. For,
from the direction
of the currents
indicated by the
arrows, the part
Q Y acts by at-
traction not only
on the horizontal
portion YD (law
of angular cur-
rents}, but also on
The same action
Hence,
Fig. 725.
Fig. 726.
the vertical portion AD (law of perpendicular currents}.
evidently takes place between the part PY and the parts CY and BC.
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 is the same.
-863]
Rotation of Currents by Currents.
769
This principle is readily demonstrated by placing the circuit ABCD on
the apparatus with two supports (fig. 725), so that at first it makes an angle
with the plane of the supports. On passing below the circuit, a somewhat
powerful current in the same plane as the supports, the movable part passes
into that plane. It is best to use the circuit in fig. 734, which is astatic,
while that of fig. 725 is not.
What has been said about the rectangular current in fig. 725 applies
also to the circular current of fig. 726, and is demonstrated by the same
experiments.
ROTATION OF CURRENTS BY CURRENTS.
862. Rotation of a finite horizontal current by an infinite horizontal
rectilinear current. The attractions and repulsions which rectangular
currents exert on one another :
may readily be transformed
into a continuous circular mo-
tion. Let OA (fig. 727) be a
current movable about the
point O in a horizontal plane,
and let PQ be a fixed infinite
current also horizontal. As - ^
these two currents flow in the p^ g ?27 Fig ?28
direction of the arrows, it fol-
lows that in the position OA, the moveahrfe current is attracted by the current
PQ, for they are in the same direction. Having reached the position OA',
the movable current is attracted by the part NO of the fixed current, and
repelled by the part PN. Similarly, in the position OA", it is attracted by
MO and repelled by PM, and so on ; from which follows a continuous rota-
tory' motion in the direction AA'A"A m . 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 in a direction opposite 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. 728) be a fixed circular current, and mn a rec-
tilinear current moveable about the axis //, both currents being horizontal.
These currents, flowing in the direction of the arrows, would attract one
another in the angle AC, for they both flow towards the summit (858). In
the angle ;iAB, 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 ///;/ in the same direction ACB.
863. 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 repre-
sented in fig. 729 is used.
L L
770
Dynamical Electricity.
[863-
Fig. 729
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, bb, bent at its ends in two ver-
tical branches, which are soldered to a very light copper ring immersed in
acidulated water
/(l ^^^^^ contained in the
01 _jr ]/ , A
vessel A cur -
rent entering
through the wire
/;/, reaches the
wire A, and
having made
several circuits,
terminates at B,
which is con-
nected by a wire
underneath with the lower part of the column a. Ascending in this column,
it passes by the wires bb into the copper ring, into the acidulated water, and
into the sides of the vessel, whence it returns to the battery by the strip D.
The current being thus closed, the circuit bb and the ring tend to turn in a
direction con-
trary to that of
the fixed cur-
rent, a motion
due to the action
of the circular
current on the
current in the
vertical bran-
ches bb ; for, as
follows from the
two laws of an-
Ifgular currents,
If the branch b on
the right is at-
tracted by the
portion A of the
fixed current,
and the branch b on the left is attracted in the contrary direction' by the
opposite part, and these t\vo 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 bb would tend to turn it in the same
direction ; but from its distance it may evidently be neglected.
864. Rotation of magnets by currents. Faraday proved that currents
impart the same rotatory motions to magnets which they do to currents.
This may be shown by means of the apparatus represented in fig. 730. 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
Fig. 730.
-865]
Directive Action of Magnets on Currents.
771
platinum cylinder. At the top of the magnet is a small cavity containing
mercury ; the current ascending the column m passes into this cavity by the
rod C. From the magnet it passes by the mercury to a copper ring, G, whence
it emerges by the column ;/. When this takes place 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
in fig. 731.
This rotatory motion is readily intelligible on Ampere's theory of mag-
netism, which will be subsequently explained (877), according to which,
magnets are traversed on their surface by an infinity of circular currents in
the same direction, in planes perpendicular to the axis of the magnet. At
the moment at which the current passes from the magnet into the mercury,
it is divided on the surface of the mercury into an infinity of rectilinear
currents proceeding
from the axis of the
magnet to the cir-
cumference of the
glass. Figs. 732 and
c/-^
733, which corre-
spond respectively to
figs. 73oand 731, give
on a larger scale, and
on a horizontal plane
passing through the
surface of the mer-
cury, the direction of
the currents to which the rotation is due. In figure 732 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 indicated by the arrow z (877),
while the currents which radiate from the rod C towards the metal ring GG',
have the direction CD, CE. Thus (858) any given element e of the mag-
netic current of the bar A is attracted by the 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. 733 the currents CD, CE being in the opposite direction to those
of the bar would repel the latter, which would be attracted by the currents
CE, CA. Hence the bar rotates in a circular direction, shown by the arrow
j, about the vertical axis which passes through the rod C.
If the north pole is below, or if the direction of the current be altered, the
rotation of the magnet is in the opposite direction.
Fig. 732.
Fig- 733-
ACTION OF THE EARTH AND OF MAGNETS ON CURRENTS.
865. Directive action of magnets on currents. Not only do currents
act upon magnets, but magnets also act upon currents. In Oersted's funda-
mental experiment (fig. 677), the magnet being movable while the current is
L L 2
772 Dynamical Electricity, [865-
tixed, the former is directed and sets at right angles with the current. If,
on the contrary, the magnet is fixed and the current movable, the latter is
directed and sets
across the direc-
tion of the mag-
net. This may be
illustrated by the
apparatus repre-
sented in fig. 734.
This is the origi-
nal form of Am-
pere's stand and
is frequently used
in experimental
demonstration. It
needs no explana-
tion. The circuit
which the current
traverses is mov-
able, and below
F 'g. 734-
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, and indeed for establishing the
fundamental laws of electrodynamics, a small
apparatus, known as De la Rive's floating
battery, is well adapted. It consists of a small
Daniell's element, contained in a glass tube
attached to a cork, so that it can float freely on
water. The plates are connected with minute
mercury cups on the cork float ; and with these
can be connected either circular or rectangular
wires, coils, or solenoids ; they are then tra-
versed by a current, and can be subjected to
the action either of magnets or of currents.
866. Rotation of currents by mag-nets.
Not merely can currents be directed by mag-
nets, but they may also be made to rotate, as
is seen from the following experiment, devised
by Faraday, fig. 735. 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 wire, AB,
and at the top is a 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 reservoir full of mercury.
Fig. 735-
-867] Electrodynaiuic and Electromagnetic Rotation of Liquids. 773
The apparatus being thus arranged, the current from 4 or 5 Bunsen's
elements enters at the binding screw b : it thence ascends in the rod, I),
i edescends 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 be 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
magnets ; currents which act on the vertical branches EF in the same way
as the circular current on the arm in fig. ^30.
In this experiment the magnetised bundle may be replaced by a solenoid
(872) 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 electromagnet.
867. Electrodynamic and electromagnetic rotation of liquids. In
the experiments hitherto discussed rotation is produced by causing a fixed
current to act upon a movable linear current. The condition of a linear
current is not necessary. Fig. 736 represents an apparatus devised by Bertin
to show the electrodynamic and electromagnetic rotation of liquids. This
apparatus consists of an annular earthen vessel, VV ; that is to say, it is
open in the
centre so as to
be traversed by
a coil, H. it
rests on a board
which can be
raised along two
columns, E and
I, and which
are fixed by
means of the
screws KK.
Round the ves-
sel VV is a se-
cond larger coil,
G, fixed on the
columns SS'.
The vessel VV
rests on the
lower plane. In
the centre of the coil there is a bar of soft iron, JIT, which makes an electro-
magnet.
The vessel VV contains acidulated water, and in the liquid are plunged
two cylindrical copper plates c and /, soldered to copper wires, e' and /',
which convey the current of a battery of four couples through the rods E
and I.
The whole system is arranged on a larger base, on the left of which is a
commutator represented afterwards on a larger scale (fig. 737). With the
base of the columns E, I, S and S', are connected four copper strips, three
of which lead to the commutator and the fourth to the binding screw A,
which receives the wire from the positive pole.
774 Dynamical Electricity. [867-
These details being premised, the following three effects may be obtained
with this apparatus : (i), the action of the coil G alone ; (2), the action of
the electromagnet H alone ; (3), the simultaneous action of the coil and of
the electromagnet.
I. Fig. 736 represents the apparatus arranged for the first effect. The
current coming by the binding screw A attains the column S', which leads it
to the coil G, with regard to which it is left that is, in a contrary direction
to the hands of a watch. Then descending by the column S, it reaches the
commutator, which leads it by the plate marked centripete to the column E
and to the' electrode e'. The current here traverses the liquid from the cir-
cumference to the centre, attains the electrode z, the column I, and by the
intervention of the plate centrifuge the central piece of the commutator. This
transmits it finally to the negative binding screw, which leads it to the
battery. The liquid then commences a direct rotatory motion that is to
say, in the same direction as the coil.
If the direction of the current in the liquid is centrifugal that is, proceeds
from, the centre to the circumference the rotation is inverse ; that is, is in
the opposite direction to that of the coil. In both cases the rotations may
be shown to those at a distance by means of small flags, f, f, fixed on discs
of cork which float on the liquid, and which are coated with lampblack to
prevent adherence by capillary attraction between the discs and the elec-
trodes e and z.
II. To experiment with the electromagnet alone, the positive wire of the
battery is joined with the binding screw C, and the binding screws D and B
are joined by a copper wire. The current first passes into the electromagnet
H, then, reaching the commutator by the binding screw B, passes into the
centripetal plate, whence it rises in the column E, traverses the liquid in the
same direction as at first, reascends by the column I, and from thence to the
centre of the commutator and the negative binding screw which leads it to
the battery.
If the north pole of the electromagnet is at the same height as the glass
vessel, as in the figure, the Amperian currents move in the opposite direction
to the hands of a watch, and the floats then move in the same direction as
above ; and if the electromagnet is raised until the neutral line is at the same
height as the vessel, the floats stop ; if it is above them, the floats move
again, but in the opposite direction.
III. To cause the coil and the electromagnet to act simultaneously, the
positive wire of the battery is attached at C, and the binding screws D and
A are connected by a conductor. Hence, after having traversed the coil H,
the current arrives from D, and the binding screw A, whence it traverses
exactly the same circuit as in the first experiments. The effects are the
same, though more intense ; the action of the coil and the electromagnet
being in the same direction.
868. Ber tin's commutator. Commutators are apparatus by which the
direction of currents may be changed at pleasure, or by which they may be
opened or closed. Bert-in's has the advantage of at once showing the direc-
tion of the current. It consists of a small base of hard wood on which is
an ebonite plate, which, by means of the handle in (fig. 737), is turned
about a central axis, between two stops, c and c'. On the disc are fixed two
-869] Directive Action of t fie ^Earth on Vertical Currents. 775
copper plates, one of which, o, is always positive, being connected by the
axis and by a plate, + , with the binding screw P, which receives the positive
electrode of the battery ;
the other, i e, bent in the
form of a horse-shoe, is
connected by friction be-
low the disc with a plate
which passes to the ne-
gative electrode N. On
the opposite side of the
board are two binding
screws, b and ', to which
are adapted two elastic
metal plates, r and r'.
These details being
premised, the disc being turned as shown in the figure, the current coming
by the binding screw P passes into the piece 0, the plate r and the binding
screw b, which by a second plate, or by a copper wire, leads it to the appa-
ratus of fig. 736, or any other. Then returning to the binding screw b', the
current attains the plate r\ the piece / e, and ultimately the binding screw
N, which returns it to the batten-.
If the disc is turned so that the handle is halfway between c and r', the
pieces o and / e being no longer in contact with the plates r and r 1 , the
current does not pass. If ;// is turned as far as c, the plate o touches r',
the current thus passes first to b' and returns by b ; it is therefore reversed.
869. Directive action of tlie earth on vertical currents. The earth
which exercises a directive action on magnets (690), acts also upon currents
738.
giving them, in some cases, a fixed direction, in others a continuous rotatory
motion, according as their currents are arranged in a vertical or horizontal
direction.
The first of these two actions may be thus enunciated : Every vertical
current movable about an axis parallel to itself, places itself under the direc-
tive action of the earth in a plane through this axis perpendicular to the
Dynamical Electricity.
[869-
7/6
magnetic meridian, and stops after some oscillations, on the east of its axis
of rotation when it is descending, and on the west when it is ascending,
This may be demonstrated by means of the apparatus represented in
fig. 739, 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, b, insulated from the vessel a, but
communicating with the vessel K. This column terminates in a small cup,
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 in passes to a strip of copper, which is
connected underneath the base of the apparatus with the bottom of the
column b. Ascending in this column, the current reaches the vessel K, and
the acidulated water which it contains ; it ascends from thence in the wire
c, 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 ;/.
The current being thus closed, the wire e moves round the column b, 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 n, the wire e
stops to the west of the
column //>,in a position directly
opposite to that which it as-
sumes when it is descending.
If the rod with a single
wire, in fig. 739, be replaced
by one with two wires, as in
fig- 738, the rod will not
move, for as each wire tends to place itself on the east of the column b, two
equal and contrary effects are produced, which counterbalance one another.
870. 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 gives them a contimious rotatory
motion from the east to the west wlien the hori-
zontal current moves away from the axis of
rotation and from the west to the east when it
is directed towards this axis.
This may be illustrated by means of the
apparatus represented in fig. 740, which only
differs from that of fig. 739 in having but one
vessel. The current ascending by the column
a, traverses the two wires cc, and descends by
the wires bb, from which it regains the pile ;
the circuit bccb then begins a continuous rota-
tion, either from the east to the west, or from
the west to the east, according as in the wires cc
the current goes from the centre, as is the case in the figure, or according as
it goes towards it, which is the case when the current enters by the wire m
Fig. 740.
Fig. 741.
872]
Structure of a Solenoid.
777
instead of by //. But we have seen (869) that the action of the earth on the
vertical wires bb is destroyed : hence the rotation is that produced by the
action on the horizontal branches cc. This rotatory action of the terrestrial
current on horizontal currents is a consequence of the rotation of a finite
horizontal by an infinite horizontal current (862).
871. 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 (869), in virtue of which
tlie current places itself in a plane perpendicular to the magnetic meridian,
so that, for an observer looking at the north, it is descending on the east of
its axis ofictation, and ascending on the west.
This property, which can be shown by means of the apparatus repre-
sented in fig. 741, 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 opposite directions, from the law of
horizontal currents (860) ; 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 (854).
From the directive action of the earth on currents, it is necessary, in most
experiments, to obviate 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 them in opposite
directions, and hence destroys them. This
condition is fulfilled in the circuit in fig. 734.
astatic circuits.
872. Structure of a solenoid. A solenoid 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. 742. A sole-
noid, however, is only com-
plete when part of the wire
BC passes in the direction of
the axis in the interior of the
helix. With this arrange-
ment, when the circuit is
traversed by a current, it
follows from what has been
said about sinuous currents
(859) that the action of a
solenoid in a longitudinal
direction, AB, is counter-
balanced by that of the recti-
linear current BC. This ac-
tion is accordingly null in the
direction of the length, and the action of a solenoid in a direction per-
pendicular to its axis is exactly equivalent to that of a series of equal parallel
currents.
Li-3
Fig. 742.
Such circuits are hence called
743-
778
Dynamical Electricity.
[873-
873. Action of currents on solenoids. What has been said of the
action of fixed rectilinear currents on finite rectangular, or circular currents
(862), 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 experimentally, a solenoid is constructed as shown in
fig. 743, so that it can be suspended by two pivots in the cups a and c of the
apparatus represented in fig. 734. The solenoid is then movable about a
vertical axis, and if beneath it a rectilinear current OP be passed, which at
the same time traverses the wires of the solenoid, the latter is seen to turn
and set at right angles to the lower current that is, in such a position that
its circuits are parallel to the fixed current ; and, further, in the lower part
of each of the circuits the current is in the same direction as in the recti-
linear 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 in the vertical wire, and in the nearest part of the solenoid, the two
currents are in the same or in contrary directions.
874. Directive action of the earth on solenoids. If a solenoid be
suspended in the two cups (fig. 734), not in the direction of the magnetic
meridian, and a current be 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 be removed, 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 north pole, as in magnets, is that end which points towards the
florth, and the south fiole that which points towards the south. This experi-
ment may be made by means of a solenoid fitted on a De la Rive's floating
battery.
Fig- 744
875. Mutual action of magnets and solenoids. Exactly the same
phenomena of attraction and repulsion exist between solenoids and magnets
-877] Amperes Theory of Magnetism. 779
as between magnets themselves. For if one of the poles of a magnet be pre-
sented 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. Hence the law of attractions and repulsions
applies exactly to the case of the mutual action of solenoids and of magnets.
876. 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. 744, attraction and repulsion will take place just as in the case of two
magnets. These phenomena are readily explained by reference to what has
been said about the mutual action of the currents, bearing in mind the direc-
tion of the currents in the extremities presented to each other.
877. Ampere's theory of magnetism. Ampere propounded a theory,
based on the analogy between solenoids and magnets, by which all magnetic
phenomena may be referred to electrodynamical principles.
Instead of attributing magnetic phenomena to the existence of two fluids
Ampere assumed that each individual molecule of a magnetic substance is
traversed by a closed 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 them in any position in which they happen to be.
When the magnetic substance is not magnetised, these molecular 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 limit of mag-
netisation is attained when the currents are completely parallel.
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. 745 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 abc
are infinitely near, they form a series of elements in the same direction
situated in planes perpendicular to the axis of the magnet, and which consti-
tute a true solenoid.
The direction of these currents in magnets can be ascertained by con-
sidering the suspended solenoid (fig. 743). If we supposed it traversed by a
780 Dynamical Electricity. {877-
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 east to
west. We have then the following rule. At the north pole of magnet, the
direction of the Ampeiian currents is opposite that of the hands of a 'watch,
and at the south pole the direction is the same as that of 'the hands.
878. Terrestrial current. In order to explain on this supposition
terrestrial magnetic effects, 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
traversing the magnetic equator from east to west. They are supposed by
some to be thermoelectric 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.
878^. Ball's experiment. In the actions of magnets on currents which
have been described in the foregoing, we have been concerned with the
action of the magnet on the body conveying the current.
Professor Hall of Baltimore has made the following experiment to
determine whether the path of a current 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, 9 centimetres in length by 2 centimetres broad, was
fastened on a glass plate, which was placed between the poles of an electro-
magnet in such a manner that the plane of the strip was at right angles to
the lines of force of the magnetic field. The ends of this strip were in
connection with the poles of a Bunsen's cell. Two wires leading to a
Thomson's galvanometer were connected with two isopotential points at
the opposite edges of the strip ; that is to say, in two points, found by trial,
in which there was no deflection of the galvanometer (748). When now the
electromagnet was excited by passing a current through it, a distinct deflec-
tion was produced in the galvanometer, showing that the path of the current
in the conducting strip had been deflected. This deflection was permanent,
and could not therefore be due to induction, and its direction was reversed
when the current in the magnet was reversed.
The magnetic field acts thus upon the current in the gold leaf in such
a manner as to displace it from one edge towards the other, and to cause a
small portion to pass through the circuit of the galvanometer.
This experiment has greatly interested physicists from its theoretical
bearings, as leading to a method of determining the velocity of electricity in
absolute measure.
-879]
Magnetisation by Currents.
781
CHAPTER V.
MAGNETISATION BY CURRENTS. ELECTROMAGNETS.
ELECTRIC TELEGRAPHS.
879. Magnetisation by current*. From the influence which currents
exert upon magnets, turning the north pole to the left and the south pole to
the right, it is natural to think that by acting upon magnetic substances in
the natural state the currents would tend to separate the two magnetisms.
In fact, when a wire traversed by a current is immersed in iron filings, they
adhere to it in large quantities, but become detached as soon as the current
ceases, while there is no action on any other non-magnetic metal.
The action of currents on magnetic substances is well seen in an experi-
ment due to Ampere, which consists in coiling an insulated copper wire round
a glass tube, in which there is an unmagnetised steel bar. If a current be
passed through the wire, even for a short time, the bar becomes strongly
magnetised.
If, as we have already seen, the discharge of a Leyden jar be transmitted
through the wire, by connecting one end with the outer coating, and the
Fig. 746.
other with the inner coating, the bar is also magnetised. Hence both voltaic
and frictional electricity can be used for magnetising.
If in this experiment the wire be coiled on the tube in such a manner
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 right-handed or
dextrorsal spiral or helix (fig. 746), of which the ordinary screw is an
example. In a left-handed or sinistrorsal helix the coiling is in the opposite
direction, that is from left to right (fig. 747).
747-
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
Dynamical Electricity.
[87S-
polarity is easily found by the following rule : If a person swimming in the
current look at the axis of the spiral, the north pole is always on his left.
If the wire be not coiled regularly, but
if its direction be reversed, at each
change of direction a consequent pole
(68 1) is formed in the magnet. The
simplest method of remembering the
polarity produced is as follows :
Whatever be the nature of the helix,
either 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
versa. The same polarity is produced,
whether or not there is an iron core
within the helix.
The nature of the tube on which
the helix is coiled is not without in-
fluence. Wood and glass have no
effect, but a thick cylinder of copper
may greatly affect the action of the
current unless the copper be slit longi-
tudinally. This action will, be subse-
quently explained. The same is the
case with iron, silver, and tin.
In order to magnetise a steel bar
by means of electricity, it need not be
748. placed in a tube, as shown in figs. 746
and 747. It is sufficient to coil round it a copper wire, covered with silk,
cotton, or gutta-percha in order to insulate the circuits from one another.
The action of the current is thus multiplied, and a feeble current is sufficient
to produce a powerful magnetising effect.
880. Electromagnets. Electromagnets are bars of soft iron which, under
the influence of a voltaic current, become magnets ; but this magnetism is
only temporary, for the coercive force of perfectly soft iron is null, and the
two magnetisms neutralise each other as soon as the current ceases to pass
through the wire. If, however, the iron is not quite pure, it retains more or
less traces of magnetism. Electromagnets have the horse-shoe form, as
shown in fig. 746, and a copper wire, covered with silk or cotton, is rolled
several times round them on the two branches, so as to form two bobbins,
A and B. In order that the two ends of the horse-shoe may be of opposite
polarity, the winding on the two limbs A and B must be such that if the
horse-shoe were straightened out, it would be in the same direction.
Electromagnets, instead of being made in one piece, are frequently con-
structed of two cylinders, firmly screwed to a stout piece of the same metal.
Such are the electromagnets in Morse's telegraph (886), the electromagnetic
motor (895). The helices on them must be such that the current shall flow
in the same direction as the hands of a watch as seen from the south pole,
and against the hands of a watch as seen from the north pole.
-880] Electromagnets. 783
The results at which various experimenters have arrived as regards the
force of electromagnets are often greatly divergent, which is partly due to
the different senses they have attached to the notion of electromagnetic force.
For this may mean (I.) the induction current which the development and
disappearance of the magnetism of an iron core indicate in a spiral which
surrounds it; this is the excited magnetism; or (II.) the free magnetism
measured by the action on a magnetic needle, oscillating at a distance :
(1 1 1.) the attractive force ', or the force required to hold an armature at a
distance from the electromagnet ; (IV.) the lifting power measured by the
force with which an armature is held in direct contact with the pole.
The most important results which have been arrived at are the follow-
ing :
(i.) Using the term electromagnetic force in the first two senses, it is
proportional to the strength of the current. This only applies when the cur-
rents are not very powerful, and to stout bars ; for in each bar there is, as
Muller has found, a maximum of magnetisation which cannot be exceeded.
(ii.) Taking into account the resistance,///^ electromagnetic force is in-
dependent of the nature and thickness of the 'wire. Thus, the strength of the
current, and the number of coils being the same, thick and thin wires produce
the same effect.
(iii.) With the same current the electromagnetic force is independent of
the width of the coils, provided the iron projects beyond the coils, and the
diameter of the coil is small compared with its length.
(iv.) The temporary magnetic moment of an iron bar is, within certain
limits, proportional to the number of windings. The product of the intensity
into the number of turns is usually spoken of as the magnetising power of
the spiral. The greatest magnetising power is obtained when the resistance
in the magnetising spiral is equal to the sum of 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.
(v.) The magnetism in solid and in hollow cylinders of the same dia-
meters is the same, provided in the latter case, there is sufficient thickness
of iron for the development of the magnetism.
(vi.) The attraction of an armature by an electromagnet is proportional
to the square of the intensity of the current so long as the magnetic moment
does not attain its maximum. Two unequally strong electromagnets attract
each other with a force proportional to the square of the sum of both cur-
rents.
(vii.) For powerful currents the length of the branches of an electro-
magnet is with Jl|^ influence on the weight which it can support.
Beetz observecl that, for the same strength of current, electromagnetism
is produced more rapidly in circuits with great resistance and great electro-
motive force than in circuits with small resistance and correspondingly smaller
electromotive force ; in the latter case the reverse currents which occur in
the coils of the electromagnet come into play more in the latter case than
in the former.
As regards the quality of the iron used for the electromagnet, it must be
pure, and be made as soft as possible by being reheated and cooled a great
many times ; it is polished by means of a file so as to avoid twisting. If
784 Dynamical Electricity. [880-
this is not the case, the bar retains, even after the passage of the current, a
quantity of magnetism ^vhich is called the remanent magnetism. A bundle
of soft iron wires loses its magnetism more rapidly than a massive bar of
the same size. According to Stone, iron wires may be materially improved
for electromagnetic experiments by forming them into bundles by tying
them round with wire ; these bundles are then dipped in paraffine and set
fire to.
During magnetisation the volume of a magnet does not vary. This has
been established by placing the bar to be magnetised with its helix in a sort
of water thermometer, consisting of a flask provided with a capillary tube.
On magnetising, no alteration in the position of the water is observed. But
the dimensions vary ; the diameter is somewhat lessened, and the length
increased : according to Joule to the extent of about 2?uboo ^ ^ ie bar
magnetised to saturation.
88 1. 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 closirg
or opening the current. This phenomenon, which was first observed by
Page in America, and by Delezenne in France, has been particularly inves-
tigated by De la Rive, who attributed it to a vibratory motion of the mole-
cules of iron in consequence of a rapid succession of magnetisations and
demagnetisations.
When the current is broken and closed at very short 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, is compared by De la Rive to the noise of rain falling on a
metal roof. The most marked sound, says he, is that obtained by stretch :
ing, on a sounding-board, pieces of soft iron wire, well annealed, from i to 2
mm. in diameter, and i to 2 yards long. 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.
Wertheim has obtained the same sounds by passing a discontinuous cur-
rent, not through the bobbins surrounding the iron wires, but through the
wires themselves. The musical sound is then stronger and more sonorous
in general than in the previous experiment. The hypothesis of a molecular
movement in the iron wires at the moment of their magnetisation, and of
their demagnetisation, is confirmed by the researches of Wertheim, who has
found that their elasticity is then diminished.
882. Reis's telephone. The essential features of this instrument (fig.
749) 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 (893) with one end of a coil of insulated wire surrounding an
iron wire, the other end of which is put to earth.
-883]
Electric Telegraphs.
-85
When the mouthpiece is spoken or sung into, the sounds set the mem-
brane in vibration ; this alternately opens and closes the current, and these
Litim
1
Fig. 749.
makes and breaks being transmitted through the circuit to the electro-
magnet F, produce the corresponding sounds.
ELECTRIC TELEGRAPH.
883. Electric telegraph. 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, Sremmering invented a
telegraph, in which he used the decomposition of water for giving signals.
In 1820, at a time when the electromagnet was unknown, Ampere 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,
Gausst 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 them belongs the honour of
having first demonstrated experimentally the possibility of electrical com-
munication 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 circuit
consisting of a metallic connection between two places, and an electromotor
for producing the current ; 2, a communicator for sending the signals from
the one station ; and, 3, an indicator tor 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.
One form of electromotor still sometimes used in England is a modifica-
786
Dynamical Electricity.
[883-
tion of Wollaston's battery. It consists of a trough divided into compartments
in each of which is an amalgamated zinc plate and a copper plate ; these
plates are usually about 4* inches in height by 3* in breadth. The compart-
ments are filled with sand, which is moistened with, dilute sulphuric acid.
This battery is inexpensive and easily worked, only requiring from time to
time the addition of a little acid ; but it has very low electromotive force
and considerable resistance, and when it has been at work for some time
the effects of polarisation begin to be perceived. On the telegraphs of the
South-Eastern Railway, the platinised
graphite (811) battery, invented by Mr.
C. V. Walker, is used with success.
On circuits on which there is constant
work some form of UanielPs battery is
used, and for other circuits Leclanche's
cell is coming into more extended use.
In France, Daniell's battery is used for
telegraphic purposes.
The connection between two sta-
tions is made by means of galvanised
iron wire suspended by porcelain sup-
ports (fig. 750), which insulate and pro-
tect 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 paid
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. 751, while fig. 752 represents a cross section
Fig. 751-
Fig. 752.
In the centre is the core, which is the conductor ; it consists of seven copper
wires, each one i mm. in diameter, twisted in a spiral strand and covered with
several layers of gutta-percha, between each of which is a coating of
Chattertorfs compound a mixture of tar, resin, and gutta-percha. This
forms the insulator proper, and it should have great resistance to the passage
of electricity, combined with low specific inductive capacity (748). Round
the insulator is a coating of hemp, and on the outside is wound spirally a
protecting sheath of steel wire, each of which is 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
-884] WJicatstone's and Cooke V Single Needle Telegraph. 787
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 deptlj
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 resistance of
the earth beyond a short distance is absolutely nil. The earth really dissi-
pates the electricity, and does not actually return the same current to the
battery.
884. Wheatstone's and Cooke's single needle telegraph. This con-
sists essentially of a vertical multiplier (821) with an astatic needle, the
arrangement of which is
seen in fig. 754, while fig.
753 gives a front view of
the case in which the ap-
paratus is placed. A (fig.
754) is the bobbin, con-
sisting of about 400 feet
of fine copper wire, wound
in a frame in two con-
nected coils. Instead of
an astatic needle, Mr.
Walker 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.
The signs are made
by transmitting the cur-
rent in different directions
through the multiplier, by
which the needle is deflec-
ted either to the right or
left, according to the will
of the operator. The instrument by which this is effected is a commutator
or key, G; its construction is shown in fig. 754, while fig. 755 shows on a
large scale how two stations are connected. It consists of a cylinder of
boxwood with a handle, which projects in front of the case (fig. 753). On
its circumference parallel to the axis are seven brass strips (fig. 755), 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 : a with b and c,f with
rotation takes place.
We have already seen that the two ends of the wire of the bobbin, those
in the same direction with respect to the currents passing through them .at
N N
8 1 8 Dynamical Electricity. [910-
any time, which will be found to be those farthest away from the armature
V, terminate in the metallic axis k, and therefore on the half-ferrule o' ;
while the other two ends, both in the same direction with respect to the
current, are joined to the ferrule perfectly insulated, the induced current requires such a strength as to pro-
duce very powerful effects. Frzeau increased this strength still more by
interposing a condenser in the primary circuit.
This condenser (fig. 800) consists of sheets of tinfoil placed over each
other and insulated by larger sheets of stout paper, v, soaked in paraffine or
resin. The sheets of tinfoil project at the end of the paper, one set at s s' s'',
and the other at the other end, at e e' e", so that when joined by a binding
screw the odd numbers form one coating of a condenser, and the even
numbers the other coating. In large condensers, the surface of each con-
denser is as much as 75 square yards. The whole being placed in a box
at the base of the apparatus, one of the coatings, the positive, is connected
Fig. 799.
$34
Dynamical Electricity.
[918-
Fig. 800.
with the binding screw z, which receives the current on emerging from
the bobbin ; and the other, the negative, is connected with the binding
screw ;, which communi-
cates by the plate K with
the commutator C, and with
the battery.
To understand the
effect of the condenser, it
must be observed that at
each break of the inducing
current an extra current
is produced in the same
direction, which, continuing in a certain manner, prolongs its duration. It
is this extra current which produces the spark that passes at each break
between the hammer and the anvil ; when the current is strong this spark
rapidly alters the surface of the hammer and anvil, though they are of
platinum. By interposing the condenser in the inducing circuit, the extra
current, instead of producing so strong a spark,
passes into the condenser ; the positive elec-
tricity in the coating connected with z', and the
negative in that connected with m. But the
opposite electricities combining quickly by the
thick wire of the primary coil, by the battery
and the circuit CK;/z, give rise to a current
contrary to that of the battery, which instanta-
neously demagnetises the bundle of soft iron :
the induced current is thus shorter and more
intense. The binding screws m and n on the
base of the apparatus are for receiving this
extra current.
The commutator or key serves to break contact or send the current in
either direction. The section in fig. Soi is entirely of brass, excepting the
core A, which is of ebonite : on the two sides are two brass plates CC'.
Against these press two elastic brass springs, joined to two binding screws,
a and c, with which are also connected the electrodes of the battery. The
current arriving at a ascends in C, thence by a screw y it attains the binding
screw b and the bobbin : then returning by the plate K, which is connected
with the hammer, the current goes to C' by the screw .r, descends to c, and
rejoins the battery by the wire N. If, by means of the milled head, the key
is turned 180 degrees, it is easy to see that exactly the opposite takes place :
the current reaches the hammer by the plate K and emerges at b. If, lastly,
it is only turned through 90 degrees, the elastic plates rest on the ebonite
A instead of on the plates CC', and the current is broken.
The two wires from the bobbin at o and o' (fig. 798) are the two ends of
the secondary wire. They are connected with the thicker wires PP', so that
the current can be sent in any desired direction. With large coils the
.hammer cannot be used, for the surfaces become so much heated as to melt.
But Foucault invented a mercury contact-breaker which is free from this in-
convenience, and which is an important improvement.
Fig. 801.
-919] Effects produced by Ruhmkorff's Coil. 835
919. Effects produced by Ruhmkorff's coil The high degree of poten-
tial which the electricity of induction coil machines possesses has long been
known, and many luminous and heating effects have been obtained by their
means. But it is only since the improvements which Ruhmkorff has intro-
duced into his coil, that it has been possible to utilise all the potential of
induced currents, and to show that these currents possess powerful statical
as well as dynamical properties.
Induced currents are produced in the coil at each opening and breaking
of contact. But these currents are not equal either in duration or in poten-
tial. The direct current, or that on opening, is of shorter duration, but
higher potential ; that of closing of longer duration, but lower potential.
Hence if the two ends P and P' of the fine wire (figs. 798 and 799) are con-
nected, as there are two equal and contrary quantities of electricity in the
wire the two currents neutralise each other. If a galvanometer is placed in
the circuit, only a very feeble deflection is produced in the direction of the
direct current. This is not the case if the two ends P and P' of the wire are
separated. As the resistance of the air is then opposed to the passage of the
currents, that which has highest potential that is, the direct one passes in
excess, and the more so the greater the distance of P and P' up to a certain
limit at which neither pass. There are then at P and P' nothing but poten-
tials which are alternately contrary.
The physiological effects of Ruhmkorff's coil are very powerful ; in fact,
shocks are so violent that many experimenters have been suddenly pro-
strated by them. A rabbit may be killed with two of Bunsen's elements,
and a somewhat larger number of couples w r ould kill a man.
The calorific effects are also easily observed ; it is simply necessary to
interpose a very fine iron wire between the two ends P and P' of the induced
wire ; this iron wire is immediately melted, and burns with a bright light. A
curious phenomenon may here be observed, namely, that when each of the
wires P and P' terminates in a very fine iron wire, and these two are brought
near each other, the wire corresponding to the negative pole alone melts,
indicating that the tension is greater at the negative than at the positive
pole.
The chemical effects are very varied ; thus, according to the shape and
distance of the platinum electrodes immersed in water, and to the degree
of acidulation of the water, either luminous effects may be produced in
water without decomposition, or the water may be decomposed and the
mixed gases disengaged at the two poles, or the decomposition may take
place, and the mixed gases separate either at a single pole or at both poles.
Gases may also be decomposed or combined by the continued action of
the spark from the coil. If the current of a Ruhmkorff s coil be passed
through a hermetically sealed tube containing air, as shown in fig. 802,
nitrogen and oxygen combine to form nitrous acid.
The luminous effects of Ruhmkorff's coil are also very remarkable, and
vary according as they take place in air, in vapour, or in very rarefied vapours.
In air the coil produces a very bright loud spark, which, with the largest-
sized coil hitherto made, that of Mr. Spottiswoode, has a length of 42
inches. In vacuo the effects are also remarkable. The experiment is made
by connecting the two wires of the coil P and P' with the two rods of the
836
Dynamical Electricity.
[919-
electrical egg (fig. 646) used for producing in vacuo the luminous effects of
the electrical machine. A vacuum having been produced up to I or 2 milli-
metres, a beautiful luminous trail is produced from one
knob to the other, which is virtually constant, and has the
same intensity as that obtained with a powerful electrical
machine when the plate is rapidly turned. This ex-
periment is shown in figs. 807 and 808. Fig. 806 re-
presents a remarkable deviation which light undergoes
when the hand is presented to the egg.
The positive pole of the current shows the greatest
brilliancy ; its light is of a fiery red, while that of the
negative pole is of a feeble violet colour ; moreover,
the latte'r extends along all the length of the negative
rod, which is not the case with the positive pole.
The coil also produces mechanical effects so powerful
tnat i w i tn the largest apparatus, glass plates two inches
thick have been perforated. This result, however, is
not obtained by a single charge, but by several successive charges.
The experiment is arranged as shown in fig. 803. The two poles of the
induced current correspond to the binding screws a and b ; by means of a
copper wire, the pole a is connected with the lower part of an apparatus for
piercing glass like that already described (fig. 651), the other pole is attached
to the other conductor by a wire d. The latter is insulated in a large
Fig, 802.
Fig. 803.
glass tube r, filled with shellac, which is run in while in a state of fusion.
Between the two conductors is the glass to be perforated, V. When this
presents too great a resistance, there is danger lest the spark pass in the coil
itself, perforating the insulating layers which separate the wires, and then the
coil is destroyed. To avoid this, two wires, e and c, connect the poles of the
coil with two metallic rods whose distance from each other can be regulated.
If then the spark cannot penetrate through the glass, it strikes across, and
the coil is not injured.
-919]
Effects .produced by Rnhmkorff's Coil.
837
The coil can also be used to charge Leyden jars. With a large coil,
giving sparks of 6 to 8 inches, and using 6 Bunsen's elements with a large
surface, Ruhmkorff charged large batteries of 6 jars each, having about 3
square yards of coated surface.
The experiment with a single Leyden jar (fig. 804) is made as follows :
The coatings of the latter are in connection with the poles of the coil by
the wires d and /, and these same poles are also connected, by means of
Fig. 804.
the wires c and = *'&/, or since
the sections are as the squares of the diameter, *^ 2 = t'df. The conductivity
of copper is unity, and that of iron 0-138 Hence we have 2'5 2 = and that of I2 = 0-504.
238 238
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 n'35 ?
The volume of the lead is 64 cubic centimetres ; its weight in air is therefore
64 x 1 1 '35, and its weight in water 64 x 11-35 64 = 662-4 gr.
If r be the radius of the sphere in centimetres, its volume in cubic centimetres will
be 4 ir _?L f and its weight in grammes is ^ ff x 2 ^. Now, as the weight of the
3 3
displaced water is obviously - w r 5 in grammes, there will be an upward buoyancy
represented by 4 ? 1 4 r 8 x 0^4 = 4 -^ x 076 wh - ch must be equal to the
weight of the lead ; that is, 4 - ? 6 = 662-5, from which r = 5 cm '925 and ,the
diameter = n'8^.
On Liquids and Gases. 933
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
\\hen 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 21-5.
The weight of the steel in grammes will be 15 * r z x 7*8 and of the platinum
A r* x 21-5.
These are together equal to the weight of the displaced mercury, which is
w r- (14 + x) 1 3 '6, from which x = 9*29 cm.
32. A cylindrical silver wire o m *ooi5 in diameter weighs 3*2875 grammes ; it is to
be covered with a layer of gold o ra *ooo2 in thickness. Required the weight of the gold ;
the specific gravity of silver being 10*47 an d that of gold 19*26.
If r is the radius of- the silver wire and R its radius wfien covered with gold, then
r = o c 'O75 and R = cfog^. The volume of the silver wire will be T r'- 1 and its
\\vight n- r 2 / io'47, from which / = 1^-768.
The volume of the layer of gold is
* (R* - r*) 17768,
and its weight
IT (o*095 2 o'075 7 ) x 17768 x 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 / cm. in length, the weight of which is
/- /8'88, and this is equal to 1000 grammes. Hence / = 56 m *oo85.
3i. 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
drawn into wire? Ans.
86617
35. Determine the volumes of two liquids, the densities of which are respectively
I -3 and 07, and which produce a mixture of three volumes having the density 0*9.
If x and y be the volumes, then from P = VD, 1*3* + 077 = 3 x 0*9 and
x + y = 3, from which .r = i and y = 2.
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 8 2, 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
7}
from the formula P = VD, which gives V = , the volumes of the two metals and of
the alloy are respectively X - + ^ = ^ . From these two equations we get x = 17*07
andjy = 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*5. 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 the density of water.
770
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 P = 2?
D D x 770 8-3 x 770'
By similar considerations, if x is the weight of platinum in vacuo, its weight in air
934 Problems and Examples in Physics.
will be x minus the weight of air displaced, that is x and this weight
21-5 x 770'
is equal to that of the true weight of the brass ; and we have
= 27 ; from which x = 26 '996.
21-5 x 770 8-3 x 770
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 i 293 gramme, the same volume of
carbonic acid weighs 1*293 x 1*524 = 1*97 gramme. 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 = 7547 grammes,
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 5 _ 250 square metres. This surface being that of
0*25
a sphere, is equal 104*- R~, whence 4 n-^ 3 = 250 and R = 4*459 ; therefore V 4- 7r -_
= 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 - (3 6-88 + 62< 5) = 3 8 '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 ^ n R z = 33*51 cubic metres, and the surface 4 * R' 2 = 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 kil.
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 26'324gr. ; and the other
is 5 centimetres in the side, and weighs 26*2597 grammes. When a partial vacuum is
made these cubes just balance each other. What is the pressure? Ans. o m *374.
43. A soap bubble 8 centimetres in diameter was filled with a mixture of one
volume of hydrogen gas and 15 volumes air. The bubble just floated in the air ; re-
quired the thickness of the film.
The weight of the volume of air displaced is ^ r 5 x 0*001293 gramme, and that
of the' mixture of gases 4 r 5 x 0*001293 x *-$ ?__93 . an( j tne difference of
3 16
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 n r 2 1 s in grammes, where s is the specific gravity
==i*t. Hence
4 TT r 5 ( '001293 '001293 x I^ 93 s ) _ 4 n r i t j.j
3 \ io /
Dividing each side by 4 r-, and putting r = 4, we get
4 x -001293 ( i - I5 -
On Liquids and Gases. 935
001293 x '9W = 3-3 / :
whence/ = '000091166290111.
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 i-^, that of the nitro-
gen will remain unchanged, and that of the carbonic acid will be . Hence the
total pressure will be
+ - + = 9^ atmospheres.
323
45. A vessel containing 10 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 100 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 0*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
78 x * 2 = '326 cm.
IOO-42
Similarly the 10 litres of water will dissolve 10 litres of carbonic acid gas, the total
volume of which w'll be no, of which 100 are in the gaseous state and 10 are dissolved.
Its pressure is therefore 72 x KO = 65-454 cm.
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 6578 is
o llt> 42 x = o llt '00208, and that of the carbonic acid 10 x ^ ^^ = 9-95.
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 701
mm. Required the atmospheric pressure at the time of observation. Ans. = 764 mm .
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. ^0385.85 kilos.
48. What is the pressure of the atmosphere at that height at which an ascent of 21
metres corresponds to a diminution of i mnj in the barometric height? Ans. 378'9 mm .
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 i 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 i^fi, and this, together with the height of the mercurial
column 302, will be the pressure exerted in the interior of the tube on the level of the
Problems and Examples in Physics.
mercury in the bath, which is equal to the. atmospheric pressure ; that is T ~ * + 302
= 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 ob above
the surface of the mercury (fig. i) 18 centimetres, and the pressure of the atmosphere
077 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
ir R- x 077 x 13 '6.
The pressure on the inside is that of the atmosphere less the weight of a column
of mercury whose base is cd and height ob. This is equal ton- J? 1 * x (077 o'i8) x 13-6;
and the effort necessary is the difference of these two pres-
sures. Making R = 3 cm., this is found to be 69-216 kilo-
grammes.
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 i
+ -3
5550
to i +
5550
, and the height h would therefore be
75
3:
5550,
5550
and since in the closed space, the elastic force o f the air increases in the ratio
i + 30 a : i + 15 a we shall have finally h = 301*74 mm.
54. The heights of two barometers A and B have been observed at 10 and
+ 15, respectively, to be A = 737 and B = 763. Required their corrected heights
at o. 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
T 5'S- Compare the quantities of gas given by the two currents. Ans. i : 1-129.
56. The volume of air in the pressure gauge of an
apparatus for com pressing gases is equal to 152 parts.
By the working of the machine this is reduced to
7 parts, and the mercury is raised through 0-48
metre. What is the pressure of the gas ?
Here AB = 152, AC = 37 parts, and BC = o m- 48.
The pressure of air therefore in AC is, from Boyle's
law,
37
The pressure in the receiver is therefore
3-122 + 0-48 = 3 m '6o2,
which is equal to 474 atmospheres.
57. An air-tight bladder holding two litres of
air at the standard pressure and temperature is
immersed in sea water to a depth of 100 metres
where the temperature is 4. Required the volume
Fig. 2. of the gas.
Air pump. 937
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
= I02 : 6 ! = 9-94 atm.
10-33
Hence, adding the atmospheric pressure, the bladder is now under a pressure of 10-94
atmospheres, and its volume being inversely as the pressure will be +-'- = 0-183 litre,
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
0*183 x 277 = 0-18568 litre.
58. To what height will water be raised in the tube of a pump by the first stroke of the
piston, the length of stroke of which is 0-5111. , the height of the tube 6 metres, and its section
r x o that of the piston ? At starting the air in the tube is under a pressure of 10 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 5. 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 pump are 6 at the pressure 10, and 5 + 6 - x
at the pressure 10 x.
Forming an equation from these terms, and solving, we have two values, x' = i8 m 26
and x" = 274. 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 10 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 -i- that of water. The coefficient of the expansion of gases is 0-00366.
Required the weight 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
admitted, x * I 3_ will represent in kilogrammes its pressure on a square centi-
IOOO
metre ; and therefore the internal pressure on the valve, and which is equal to the ex-
ternal pressure of 25 kilogrammes, is x x ' ^-2? = 25 k. From which x = 57-44.
IOOO
For the weight we shall have
p _ 10 x 0-001293 x 57-44 = 8-8055 grammes,
i + 0-00366 x 30 76*00
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.
At o and 76 cm. the weight of air in the bell-jar is
1-293 x 3 -I 7 = 4'0988i.
At o and under the pressure 76 65 the weight
of the residual air is
IH^JL". 0-393..
and therefore the weight of that which is withdrawn is
4-0988 - 0-5932 = 3-5056 gr.
61. The capacity of the receiver of an air-pump
938 Problems and Examples in Physics.
is 7 '53 I it i s ^ u ^ f a i r under the ordinary atmospheric pressure and at o. Re-
quired the weight of air when the pressure is reduced to o'2i ; 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 9736 grammes.
Under a pressure of o'2i it will be 2*69 grammes, and at the temperature 15 it will
be 5 = 0-255 gramme.
i + '00366 x i 5
62. In a theoretically perfect air-pump, how great is the rarefaction after 10 strokes,
if the volumes of the barrel and the receiver are respectively 2 and 3 ?
Ans. = 4'59 mm ; or about x of an atmosphere.
1 66
63. What must be the capacity of the barrel of an air-pump if the air in a re-
ceiver of 4 litres is to be reduced to J the density in two strokes ? Ans. 2-9.
64. The reservoir of an air-gun, the capacity of which is 40 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? Ans. 6 '05 atmospheres.
65. Suppose that at the limit of the atmosphere the pressure of the attenuated
air is the I of a millimetre of mercury and the temperature 135, and that in a
1000
place at the sea level, in latitude 45, the pressure of the atmosphere is 76o mm and its
temperature 15 C. Determine from these data the height of the atmosphere.
From the formula 18400 { i + o'oo2 { T + /} j- log --, we get for the height in metres
82237, which is equal to 51 'i 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 ? Ans. 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. 30 feet.
68. What is the ratio of the pressure in the above two cases? Ans. i : 9.
69. What is the theoretical velocity of water from an aperture which is 9 feet
below, the surface of water ? Ans. 24 feet.
70. In a 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 '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 = Sigh, it will readily be seen that the weight in grammes of water
which flows in a given time, t, will be given by the formula w = a a t\/ zgh, where a is
the area in square centimetres, o the coefficient of efflux, t the time in seconds, and h
the height in centimetres. Hence in this case a = 0*699.
73. Similarly through a square 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 a = 0-78.
Sound. 939
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 io'74.
From the formula v = 333 \f \ + at 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 \gfl = x will represent
the depth of the well ; on the other hand, the time occupied by the report will be 4 /,
and the distance will be (4 t] v = x (i) ; thus (4 t) v = \gfl (ii), from which,
substituting the values,
(4 - t} 339-5 = 4-9 fl
1 ~ 3793 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.
_* + * = 4; x = 738-2.
4H 333
76. At what distance is an observer from an echo which repeats a sound after 3
seconds, the temperature of the air being io?
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
*7- = 5o8 . 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 between 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? Ans. 454*1 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 no metres.
79. What is the velocity of sound in coal gas at o, the density being 0-5 ?
Ans. 470-9 metres.
80. What must be the temperature of air in order that sound may travel in
the same velocity as in hydrogen at o ? 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 o ? Ans. io55 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 o ? 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
X 5 x 333 -s/i + 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.
S S 2
940 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 i6'5. Ans. 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 n -- / -- As in the present case, the tensions, the length of the
strings, and the number of vibrations are the same, we have
1 fL. = -1 /Z", from which Z A = * / 7 ;
rl V ir d r,l V * d, r V d r t V d t
** d ' j
d 7-8
.whence - = = ; hence r = / 8 ^ = 1-062.
r, \/ 7 -8
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.
"9O. The diameters of two wires of the same length and material are 0-0015 and
0-0038. ;- and their stretching weights 400 and 1600 grammes respectively. Required
the ratio of the numbers of their vibrations. Ans. n : n, = 1-266 : i.
91. A brass wire i 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 /-*V
rl\/ ntt rl, V n 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 o ; at what temperature
will it yield the major third of this note? Ans. 153 C.
95. A brass wire a metre in length, and stretched by a weight of a kilogramme,
yields, the same note as a 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. io'o68.
96. How many beats are produced in a second by two notes, whose rates of vibra-
tion are respectively 340 and 354 ? Ans. 14.
Heat. 941
V. ON HEAT.
97. Two mercurial thermometers are constructed of the same glass ; the internal
diameter of one of the bulbs is 7 IDn>> 5 and of its tube 2-5 ; the bulb of the other i*
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 A and B be the two thermometers, D and D the diameters of the bulbs, .and
d and *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"o625 and 99 0- 8i25.
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 phosphorus 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 x ; this is expended in raising the whole weight of the phos-
phorus from 30 to 44 '2. Hence we have 5*4 x = i x (44*2 30) 0*2, from which
x 2 4 = 0*526, so that 0-474 f phosphorus will remain liquid.
5 '4
112. A pound of ice at o is placed in two pounds of water at o ; required the
weight of steam at 100 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 3-3, the final temperature is found to be 3-1. The specific heat of
turpentine is 0*4, and it is contained in a vessel weighing 25 grammes, whose specific
heat is o'i. The specific heat of ice is 0*5. Required the value of x.
Ans. x = 382*0 grammes.
114. In what proportion must water at a temperature of 30 and linseed oil
(sp. heat = 0-5) 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.
943
115. 3y how much will mercury at o be raised by an equal volume of water at
ioo j ? Ans. 68'9 C.
116. The specific heat of gold being 0-03244, what weight of it at 45 will raise a
kilogramme of water from i2'3 to 15 -7?
Let x be the weight sought ; then x kilogrammes of gold in sinking from 45 to
i57 will give out a quantity of heat represented by x (45 i57) 0-0324, and this is
rqual to the heat gained by the water, that is to i (15-7 12*3) = 3-4, that is x = 3-58.
117. The specific heat .of sulphide of copper is 0-1212, and that of sulphide of.silver
0-0746. 5 kilos, of a mixture of these two bodies at 40, when immersed in 6 kilos, of
water at 7-669 degrees, raises its temperature to 10. How much of each sulphuret did
the mixture contain ?
The weight of the copper sulphuret = 2, and that of the silver sulphuret 3.
118. Into a mass of water at o, 100 grammes of ice at 12 are introduced ; a
weight of 7 '2 grammes of water at o 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, c, of
copper? Ans. c = 0-0926.
120. Two pieces of metal weighing 300 and 350 grammes, heated to a temperature
x, have been immersed, the former in 940-8 grammes of water at 10, and the latter in
546 grammes at the same temperature. The temperature in the first case rises to 20,
and in the second to 30. Required the original tempferature and the specific heat of
the metal. Ans. x the temperature = 1980; c the specific heat = '1038.
121. In what proportions must a kilogramme of \vater at 50 be divided in order that
th3 heat which one portion gives out in cooling to ice at zero may be sufficient to change
the other into steam at 100 ? Ans. x = 0-830.
122. Three mixtures are formed by mixing two and two together, equal quantities
of ice, salt, and water at o. Which of these mixtures will have the highest and which
the lowest temperature ? Ans. 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 i2 0- 5 are placed 6*17 kilos, of a body at a
temperature of 80 ; the mixture acquires the temperature 14-!. Required the specific
heat of the body.
If c is the specific heat required, then me (f 0) represents the heat lost by the body
in cooling from 80 to 14 'i ; and that absorbed by the water in rising from 12 -5 to
14-! is m' (0 t). These two values are equal. Substituting the numbers, we have
C = O'lOII.
124. Equal lengths of the same thin wire traversed by the same electrical current are
placed respectively in i 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 i C.
by one thermal unit ? Ans. 5105 cubic feet.
126. Given two pieces of metal, one x weighing 2 kilos, 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 26'3.
The experiment is repeated, the two metals being at the temperature 100 and 40
respectively, and, as before, they are placed in a kilogramme of water at 10, which
this time is raised to 28 4. Required the specific heats of the two metals.
Ans. x = 0-115 5 y = 0-0555.
127. For high temperatures the specific heat of iron is 0-1053 * '000071 /. What
is the temperature of a red-hot iron ball weighing a kilogramme, which, plunged in 16
944 Problems and Examples in Physics.
kilogrammes of water, raises its temperature from 12 to 24? What was the tempe-
rature of the iron ?
(o'io53 4- o*ooooi7/) (/ 24) = 16 (24 12),
r '000017 ft + "1048892 t 2*5272 = 192 ;
transposing and dividing by the coefficient of / 2 , we get
/* + 6176 / = 11442776,
/ 8 + 6170 / + (3085)2 = 20960001 ;
hence t + 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. Ans. 23877.
129. Determine the temperature of combustion of charcoal in burning to form car-
bonic acid.
We know from chemistry that one part by weight of carbon in burning unites
with 2 parts by weight of oxygen to form 3! parts by weight of carbonic acid.
Again the number of thermal units produced by the combustion of a pound of charcoal
is 8080 ; the whole of this heat is contained in the 3$ parts of carbonic acid produced,
and if its specific heat were the same as that of water, its temperature would be
o = 2204 C. ; but since the specific heat of carbonic acid is 0*2163 that of an equal
weight of water, the temperature will be .- 20 4 = IOI 89 C.
0-2163
ISO. A glass globe measuring 60 cubic centimetres is found to weigh 19 -515
grammes when filled with air under a pressure of 752-3'" m and at a temperature of 10 C.
Some ether is introduced and vaporised at a temperature of 60, whereupon the flask
is sealed while quite full of vapour, the pressure being 753 "4 mm . Its weight is now
found to be 19-6786 grammes. Required the density of the ether vapour compared
with that of hydrogen. Ans. 54-4.
131. Calculate the density of alcohol vapour as compared with air by Gay-Lussac's
method from the following data :
Weight of alcohol o - 1047 grm.; vol. of vapour at 110 C. =82*55 c.c. '< height of
mercury above the level in the bath, 98 mm. ; barometric height, 752-3 mm. ; tempera-
ture of the room, 15 C. Ans. 1*6.
132. In a determination of the vapour density by Gay-Lussac's method, 0*1163
gramme of substance was employed. The volume observed was 5079 cc, the height
of the mercury above the level of that in the bath was 8o'o mm , the height of the oil
column reduced to millimetres of mercury 16-9; the temperature 215 C., and the
height of the barometer at the time of observation 755 -5 mm . Required the specific
gravity of the vapour as compared with that of hydrogen. Ans. 50' i.
133. Through a U-tube containing pumice saturated with sulphuric acid a cubic
metre of air at 15 is passed, and the tube is found to weigh 3-95 grammes more.
Required the hygrometric state of the air.
The pressure of aqueous vapour at 15 is 12*699; hence the weight of a cubic
metre of aqueous vapour saturated at 15 is I2 93 x I2 ' 6 99J^_5 _ I2 - 79 g rammes
O 3 ) 76ox 8
and the hygrometric state is JL$ = 0*309.
12-79
134. The quantity of water given out by the lungs and skin may be taken at
30 ounces in 24 hours. How many cubic inches of air already half saturated at 10 will
be fully saturated by the moisture exhaled from the above two sources by one man ?
Tension of aqueous vapour in inches = 0-532. Pressure of the atmosphere = 30 inches.
Ans. 328782*5 c.i. = a cube 5*752 feet in the side.
Heat. 945
135. A mass of air extending over an area of 60,000 square metres to a height of
300 metres has the dew point at 15, its temperature being 20. How much rain will
fall if the temperature sinks to io?
The weight of vapour condensed from one cubic metre under these circumstances
will be 3*1435 grammes, and therefore from 18,000,000 cubic metres it will be 56,583
kilogrammes, which is equal to a rainfall 0-0943 mm. in depth.
136. When 3 cubic metres of air at 10 and 5 cubic metres at 18, each saturated
with aqueous vapour at those temperatures, are mixed together, is any water precipi-
tated ? And if so, how much ?
The weight of water contained in the two masses under the given conditions are
respectively 28 -i8ad 76 -59 grammes ; the weight required to saturate the mixture at the
temperature of 15 is 102-39 grammes, and therefore 2-38 grammes will be precipitated.
137. The temperature of the air at sunset being 10, what must be the lowest hygro-
metric state, in order that dew may be deposited, it being assumed that in conse-
quence of nocturnal radiation the temperature of the ground is 7 below that of the air ?
Ans. The hygrometric state must be at least 0-608 of total saturation.
138. It is stated as a practical rule that when the tension of aqueous vapour present
in the atmosphere, as indicated by the dew point, is equal to x mm. of mercury, the
weight of water present in a cubic metre of that air is x grammes. What is the error
in this statement for a pressure of 10 mm. and the temperature 15 C. ?
Ans. '172 gr.
139. A raindrop falls to the ground from a height of a mile ; by how much would
its temperature be raised, assuming that it imparts no heat to the air or to the
ground? Ans. 3 -8 C.
140. A lead bullet falls through a height of 10 metres ; by what amount will its
temperature have been raised. when it reaches the ground, if all the heat is expended in
raising the temperature of the bullet? Ans. o'75i5 C.
141. From what height must a lead bullet fall in order that its temperature may
be raised n degrees ? and what velocity will it have acquired'? ft is assumed that all the
heat is expended in raising the temperature of the bullet, the specific heat of lead is
taken at 0-0314, and Joule's equivalent in metres at 424.
Ans. 13-31- x n metre ; v = 28-8 Vn.
142. How much heat is disengaged if a bullet weighing 50 grammes and having
a velocity of 50 metres strikes a target ?
Ans. Sufficient to raise one gramme of water through 15 C.
143. How much heat is produced in the room of a manufactory in which 1*2 horse-
power of the motor is consumed each second in overcoming the resistance of friction ?
Ans. A quantity sufficient to raise 41024 pounds of water one degree Centigrade.
144. What is the ratio between the quantities of heat which are respectively pro-
duced, when a bullet weighing 50 grammes and having a velocity of 500 metres,
and a cannon-ball weighing 40 kilogrammes with a velocity of 400 metres, strike a
target? Ans. i : 512.
145. The specific heat of lead is 0-031, and its latent heat 5*37. What is the
mechanical equivalent of the heat necessary to raise 5 pounds of lead from a tempera-
ture of 270 C. to its melting-point 335 C., and then to melt it ?
Ans. 51326 foot-pounds.
146. Assuming that the temperature at which heat leaves a perfect engine is 16 C.,
at what temperature must it be taken in in order to obtain a theoretical useful effect of J ?
A MS. 160-5 C.
147. Assuming that in a perfect engine heat is taken in at a temperature of 144,
and is given out at a temperature of 36^ : what is the greatest theoretical useful effect ?
Ans. o'26i.
553
946 Problems and Examples in Physics.
VI. LIGHT.
148. How many candles are required to produce at a distance of 2-5 metres, the
same illuminating effect as one candle at a distance of 0-45 m. ? Ans. 31.
149. Two sources of light whose intensities are as i : 2 are two metres apart. At
what position is a space between them equally illuminated ?
Ans. 0-828 metre from the less intense light.
150. A candle sends its rays vertically against a plane surface. When the candle is
removed to thrice the distance and the surface makes an angle of 60 with the original
position, what is the ratio of the illuminations in the two cases ? Ans. i : -
151. An observer, whose eye is 6 feet above the ground, stands at a distance of 18
feet from the near edge of a still pond, and sees there the image of the top of a tree,
the base of which is at a distance of 100 yards from the place at which the image is
formed. Required the height of the tree. Ans. 100 feet.
152. What is the height of a tower, which casts a shadow 56-4 m. in length when a
vertical rod 0*95 m. in height produces a shadow 1-38 m. in length? Ans. 38-8.
153. A minute hole is made in the shutter of a dark room, and at a distance of
2 '5 metres a screen is held. What is the size of the image of a tree which is 15*3
metres high and is at a distance of 40 metres? Ans. 0*95625 metre.
154. What is the length of the shadow of a tree 50 feet high when the sun is 30
above the horizon? What when it is 45, and 60 ? Ans. 86'6 ; 50, and 28-867 f eet -
155. Under what visual angle does a line of 30 feet appear at a distance of 18 feet ?
Ans. 79 '36.
156. The apparent diameter of the moon amounts to 31' 3". What is its real dia-
meter if its distance from the earth is taken at 239000 geographical miles ?
Ans. 2166 geographical miles.
157. For an ordinary eye an object is visible with a moderate illumination and pure
air under a visual angle of 40 seconds. At what distance, therefore, can a black circle
(6 inches in diameter) be seen on a white ground ? Ans. 2578 feet.
158. At what distance from a circle with a diameter of one foot is the visual angle a
second? Ans. 206265 feet.
159. At what distance would a circular disc i inch in diameter, of the same bright-
ness as the sun's surface, illuminate a given object to the same extent as a vertical sun
in the tropics, the light absorbed by the air being neglected ?
Ans. Taking the sun's angular diameter at 30', x = 38 inches.
160. What is the minimum deviation for a glass prism (n = i -53), whose refracting
angle is 60 ? Ans. 39 50'.
161. What is the minimum deviation for a prism of the same substance when the
refracting angle is 45 ? Ans. 63 38'.
162. The refracting angle of a prism of silicate of lead has been found by measure-
ment to be 2i'i2, and the minimum deviation to be 240-46. Required the refractive
index of the substance. Ans. 2-122.
163. Construct the path of a ray which falls on an equiangular crown-glass prism
at an angle of 30 ; and find its deviation. Ans. 70 -45.
164. W T hat are the angles of refraction upon a ray which passes from air into glass
at an angle of 40 ; from air into water at an angle of 65 ; and from air into diamond
at an angle. of 80 ? Ans. 250-20 ; 44 -5 ; 23 -12.
165. The focal distance of a concave mirror is 8 metres. What is the distance of
the image from the mirror when the object is at a distance of 12, 5, and 7 metres
respectively? Ans. 24; 13-3 and 56.
Light. 947
166. An object at a distance of 10 feet produces a distinct image at a distance of 3
feet. What is the focal distance of the mirror? Ans. 2^3077 feet.
167. Required the focal distance of a crown-glass meniscus, the radius of curvature
of the concave face being 45 mm., and that of the convex face 30 mm. ; the index of
refraction being 1-5. Ans. f = 180 mm.
168. What is the principal focal distance of a double-convex lens of diamond, the
radius of curvature of each of whose faces is 4 mm., and the refractive index of dia-
mond 2^487? Ans. 1*34 mm.
169. A watch-glass with ground edges, the curvature of which was 4*5 cm., was
filled with water and a glass plate slid over it. The focus of the plano-convex lens
thus formed was found to be 13-5 cm. Required the refractive index of the water.
Ans. n = 1-33.
170. What is the focal distance of a double-convex lens when the distances of the
image and object are respectively 5 and 36 centimetres? Ans. 4-4 centimetres.
171. The radii of curvature of a double-convex lens of crown glass are six and
eight inches. What is the focal distance? A ns. 6-85 inches.
172. The focal distance of a double-convex lens is 4 inches ; the radius of cur-
vature of one of its faces is 3 inches. What is that of the second? Ans. 6 inches.
173. The radius of curvature of a plano-convex lens is 12 inches. Required its
focal distance. Ans. 24 inches.
174. If the focal distance of a double-convex lens is i centimetre, at what distance
must a luminous object be placed so that its image is formed at 2 centimetres dis-
tance from the lens ? Ans. 2 centimetres.
175. A candle at a distance of 120 centimetres from a lens forms an image on the
other side of the lens at a distance of 200 feet. Required the nature of the lens and
its focal distance. Ans. It is a convex lens, and its focal distance is 75 cm.
176. A plano-convex lens was found to produce at a distance of 62 cm. a sharp
image of an infinitely distant object. In front of the same lens, at a distance of 84 cm.,
a millimetre scale was placed, and a sharp image was formed at a distance of 250 cm.
It was thus found that 10 millimetres in the object corresponded to 29 in the image.
From these observations determine the focal distance of the lens. Ans. The mean
of the results is 62-4.
177. The image of a distant tree was sharply formed at a distance of 31 cm. from
the centre of a concave mirror.
In another case the image of an object 18 mm. in length at a distance of 405 mm.
from the mirror was formed at 1350 mm. from the mirror and had a length of 61 mm.
In another experiment the distances of object and image and the size of the image were
respectively 2200, 355, and 3 mm.
Deduce from these several data the focal distance of the mirror. Ans. 31*2 ; 3o'5.
178. What must be the radii of curvature of the faces of a lens of best form made
of glass (// = 1*5) if its focal distance is to be 6 inches? Ans. 3^5 inches and 21 inches.
179. A diffraction grating, with lines 0-05 mm. apart, is held in front of a Bunsen's
burner in which common salt is volatilised, and when viewed through a telescope it is
found that the angular distances of the first, second, fourth, and sixth bright bands from
the central one are respectively o 41', i 21', 2 42', and 4 3'. Required the wave-
length of sodium light.
The formula \ = _ S1 _" ', where K is the wave-length, the angular distance of
n
any bright line of order n from the central one, gives as the mean of the 4 observa-
tions : Ans. o'ooo59o88 mm.
948 Problems and Examples in Physics.
VII. MAGNETISM AND FRICTIONAL ELECTRICITY.
ISO. A compass needle at the magnetic equator makes 15 oscillations in a minute ;
how many will it make in a place where the horizontal force of the earth's magnetism is
~ as great? Ans. 12.
25
181. A compass needle makes 9 oscillations a minute under the influence of the
earth's magnetism alone ; how many will it make when re-magnetised so as to be
half as strong again as before? Ans. n.
182. A small magnetic needle makes loo oscillations in 7 min. 42 sees, under the
influence of the earth's force only ; when the south pole of a long bar magnet A is
placed 10 inches north of it, it makes too oscillations in 4 min. 3 sees. ; and with the
south pole of another magnet B in the same place, it makes 100 oscillations in 4 min.
48 sees. What are the relative strengths of the magnets A and B ?
Ans. A = 1*404 B.
183. On a table where the earth's magnetism is counteracted, the north pole of a
compass needle makes 20 oscillations in a minute under the attraction of a south pole
4 inches distant ; how many will it make when the south pole is 3 inches distant ?
Ans. 26 '6.
184. If the oscillating magnet be re-magnetised so as to be twice as strong as
before, how many oscillations in a minute will it make in the two positions respectively ?
Ans. 28-28 and 50-27.
185. At one end of a light glass thread, carefully balanced so as to oscillate in a
vertical plane, is a pith ball. Over this and in contact with it is a fixed pith ball of the
same dimensions. Both balls being charged with the same electricity it is found that
to keep them i -4 inch apart, a weight of -9 mgr. must be placed at the free end of the
glass thread. What weight must be placed there to keep the balls 1-05 inch apart ?
Ans. i '6 mgr.
186. A small insulated sphere A charged with the quantity of + electricity 2 is
at a distance of 25 mm. from a second similar sphere B charged with the quantity 5 ;
the latter is momentarily touched with an unelectrified sphere B, of the same size, and
the distance altered to 20 mm. What is the ratio of the repulsive forces in the two
cases? Ans. 32 : 25.
187. Two insulated spheres A and B, whose diameters are respectively as 7 : 10,
have equal quantities of electricity imparted to them. In what ratio are their electrical
densities? Ans. 100 : 49.
188. Two such spheres whose diameters are as 3 : 5 contain respectively the
quantities of electricity 7 and 10. In what ratio are their densities ? Ans. 35 : 18.
189. Three insulated conducting spheres, A, B, and C, whose radii are respectively
i, 2, and 3, are charged with electricity, so that their respective potentials are as 3 : 2 : i,
and are then connected by wires, whose capacity may be neglected. What is the total
quantity and potential of the system ? Ans. Q = io ; V = r66.
190. Supposing each of the spheres discharged separately, what would be the total
work they would produce, as compared with that produced by the discharge of the
whole system? Ans. 30 : 25.
Voltaic Electricity. 949
VIII. VOLTAIC ELECTRICITY.
191. A galvanometer offering no appreciable resistance is connected by short thick
wires with the poles of a cell, and deflects 20. By how much will it be deflected if two
exactly similar cells are connected with the first side by side ? Ans. 47'3o.
192. By how much if the three cells are connected in series ? Ans. 20.
193. Two cells each of i ohm resistance are connected in series by a wire the
resistance of which is also i ohm. If each of these when connected singly by short
thick wires to a galvanometer of no appreciable resistance deflects it 25, how much
will the combination deflect it, the connections being made by short thick wires?
Ans. I7'i6.
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; or a BA unit equals 1*0485 Siemens unit, or equals a column of mercury i'O485
metre in length and a square mm. in cross section.
194. A single thermo-electric couple deflects a galvanometer of 100 ohms resist-
ance o 30'; how much will a series of 30 such couples deflect it, the connections being
made by short thick wires? Ans. i4'4o.
195. Suppose a sine galvanometer had been used in the last question, and the
first reading had been 6'3o', what would the second be? Ans. i5'io.
196. The internal resistance of a cell is half an ohm ; when a tangent galvano-
meter of i 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 i ohm
resistance is substituted ? Ans. 7'37.
197. \Vhat will be the deflection if each of the wires is replaced by a thin wire of
\\ ohm resistance ? Ans. 6 10'.
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? Ans. 375 ohms.
199. What would be the deflection if for the cell in the last question three exactly
similar cells in series were substituted (a) when the galvanometer alone is in circuit ;
(b] when both the galvanometer and the thin wire are in circuit?
Ans. a 67 -48. b = 57 '41.
200. A galvanometer offering no sensible resistance is deflected 50 by a cell
connected with it by short thick wires. If a 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. o'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
16
diameter is an ohm, express in that unit the resistance of 8242 yards of copper wire
of an inch in diameter. Ans. 35-66.
204. One form of fuse for firing mines by voltaic electricity consists of a platinum
wire | 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
1 1 "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.
9 SO 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. o'O738.
207. What length of platinum wire 0*05 of an inch in diameter must be taken to
get a resistance equal to i ohm, the specific resistance of platinum being taken at 5-55
that of copper ? Ans. 14-25 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 0-0416 of an inch in diameter. Find the specific
resistance of iron, that of copper being unity. Ans. 6-15.
209. Ten exactly similar cells in series produce a deflection of 45 in a tangent
galvanometer, the external resistance of the circuit being 10 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. % 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. Ans. 46.
211. Ten exactly similar cells each of f of an ohm resistance give, when arranged
in five series of 2 each, a deflection of 23'S7 '< but when arranged in 2 series of 5 each
a deflection of 33 '42. Required the external resistance of the circuit including that
of the galvanometer. A us. 3*,.
212. A cell in a 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 i ohm deflect it 29 '2. Find the internal resistance of one cell '
and that of the circuit. Ans. R = r = i'66.
213. What is the best arrangement of 6 cells, each of f of an ohm resistance,
against an external resistance of 2 ohms ?
Ans, Indifferent whether in 6 cells of i each or in 3 cells of 2 each.
214. What is the best arrangement of 20 cells, each of o"8 ohm resistance, against
an external resistance of 4 ohms ? Ans. 10 cells of 2 each.
215. In a 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. 0-01895.
217. A knot of nearly pure copper wire weighing one pound has a resistance of
1200 ohms at i5'5 C. ; what is the resistance at the same temperature of a knot of the
same quality of wire weighing 125 pounds? Ans. 9-6 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^
9
as great. What length of platinum wire weighing 100 grains has the same resistance
as zoo inches of copper wire also weighing 100 grains? Ans. 27.
221. A cell 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 i ohm resistance, find the deflection. Ans. 36 52'.
222. The resistance of a galvanometer is half an ohm, and the deflection when
Voltaic Electricity. 951
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.
Ans. 1-23.
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 i
the deflection is 33'42. Find the resistance of the galvanometer. Ans. 2.
224. A cell whose internal resistance is 2 ohms has its copper pole connected with
the binding screw A of a galvanometer formed of a thick band of copper. From
the other screw B a wire of 20 ohms resistance passes to the zinc pole, and the deflection
read off is 7'8. Find the deflection when B is at the same time connected with the
zinc pole by a second wire of 30 ohms resistance. Ans. n-&'.
225. What would be the deflection in 212 if the second wire instead of passing
from B to the zinc pole passed directly from the zinc pole to the copper pole ?
Ans. 2-437.
226. A Leclanche* 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 Leclanche" 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 io'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? Ans. The resistance of the iron
wire will be i'i8 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 diameter
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 2o'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 i, a current 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. =% - = 176.
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 () 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 A was found to be 2'8i ohms. A being insulated, a test from B showed the
resistance to be 2*76. Required the distance from A to the injured spot.
Ans. 867 yards.
INDEX.
(THE NUMBERS REFER TO THE ARTICLES.)
ABE
\ BEL'S electric fuse, 794
Aberration, chromatic, 583 ;
spherical, 533
Absolute expansion of mercury, 322
Absolute measure of electrical resistance,
947
Absorbent power of aqueous vapour, 973
Absorbing power, 424
Absorption, of gases, 144 ; of gases by
liquids, 184; of heat by liquids, 434;
,' vapours, 435 ; heat produced by,
2
Acceleration of a force, 27, 78
Accidental haloes, 627 ; images, 626 ;
magnetic variations, 694
Accommodation (of the eye), 620
Achromatism, 584 ; of the microscope,
592
Achromatopsy, 632
Acidometer, 127
Acierage, 855
Aclinic 1 nes, 698
Acoustic foci, 237 ; attraction and repul-
sion, 290
Acoustics, 220-287
Actinic rays, 436, 573
Action and reaction, 39
Adhesion, 87
Aerial meteors, 964
Aerolite?, 480
yEsculine, 582
Affinity, 86
Agents, 6
Agonic line, 692
Air, aspirating action of currents of, 197 ;
causes which modify temperature of,
963, 994 ; heating by, 491 ; ther-
mometer, 334 ; resistance of, 48
Air-balloons, 186; chamber, 207
Air-pump, 467 ; Bianchi's, 193 ; con-
densing, 190; Deleuil's, 194; gauges,
AQU
191 ; rarefaction in, 190 j receiver of,
IQO ; Sprengel's, 195 ; uses of, 200
Ajutage, 214
Alarum, electric, 894
Alcarrazas, 373
Alcoholic value of wines, 378
Alcoholometer, 129 ; Gay-Lussac's, 129 ;
centesimal, 129
Alcohol thermometer, 306
Alloys, 340
Amalgam, 754
Amalgamated zinc, 816
Amber, 723
Amici's microscope, 591 ; camera lucida,
603
Ampere's memoria tcchnica, 820 ; theory
of magnetism, 877
Amplitude of vibration, 55
Analogous pole, 732
Analyser, 656
Analysis, spectral, 575 ; of solar light, 430
Anelectrics, 724, 748
Anelectrotonus, 828
Anemometer, 963, 964
Aneroid barometer, 182
Angle of deviation, 544, 990; optic, 617 ;
of polarisation, 654 ; of reflection and
incidence, 511, 536; of repose, 39;
of refraction, 536 ; visual, 617
Angular currents, laws of, 858 ; velocity,
53
Animal heat, 485
Anione, 841
Annealing, 91
Annual variations, 693
Anode, 841
Antilogous pole, 732
Anvil, 918
Aqueous humour, 612
Aqueous vapour, its influence on climate,
973; tension of, 355, 356, 357
954
Index.
ARA
Arago's experiment, 175
Arbor Dianre, 851 ; Saturni, 851
Arc of vibration, 55 ; voltaic, 833
Archimedes' principle, 114; applied to
gases, 185
Area, unit of, 22
Armatures, 718 ; Siemens', 912
Arms of levers, 40
Armstrong's hydro-electric machine, 758
Artesian wells, 112
Artificial magnets, 680
Ascent of liquids in capillary tubes, 133 ;
between surfaces, 134
Aspirating ac.tion of air currents, 197
Astatic currents, 871 ; needle and system,
700 ; circuits, 871
Astronomical telescope, 595
Athermancy, 434
Atmosphere, its composition, 151 ; crush-
ing force of, 153 ; amount of, determi-
nation of, 157 ; electricity in the, 981,
982 ; moisture of, 400
Atmospheric electricity, causes of, 980,
983; pressure, 152, 961
Atomic heat, 458 ; weight deduced from
specific heat, 458
Atoms, 3
Attraction, capillary, 135 ; and repulsion
produced by capillarity, 135 ; mole-
cular, 84 ; universal, 67
Attractions, magnetic laws of, 703 ;
electrical, laws of, 734
Atwood's machine, 78
Aura, 764
Aurora borealis, 694, 991
Aurum musivum, 754
Austral pole, 689
Avoirdupois, 23
Axis of crystal, 640 ; electric, 732 ;
lenses, 551 ; optic, 617 ; of a magnet,
68 1 ; of oscillation, 80
Azimuthal circle, 695
BABINET'S stopcock, 192
Bad conductors. 404
Bain's electro-chemical telegraph, 892
Balance, 72 ; beam of, 73 ; compensat-
ing, 320 ; delicacy of, 74 ; hydrostatic,
121 ; knife-edge of, 72 ; physical and
chemical, 75 ; torsion, 90, 704, 733
Ballistic pendulum, 82
Balloons, 186-189; construction and
management of, 187 ; Mongolfier, 186;
weight raised by, 189
Bands of spectrum, 576
Barker's mill, 217
BOI
Barometers, 158 ; aneroid, 182 ; Bun-
ten's, 161 ; cistern, 159; corrections
in, 164 ; determination of heights by,
172; fixed, 169; Fortin's, 160; Gay-
Lussac's, 161 ; glycerine, 170 ; pre-
cautions with, 162 ; wheel, 168 ; va-
riations of height of, 165
Barometric formula, Laplace's, 172 ;
gradients, 9670; height of, corrected
for heat, 327 ; manometer, 180 ; va-
riations, 1 66
Baroscope, 185
Battery, Bunsen's, 810 ; Callan's, 810 ;
chemical effects of, 840 ; Daniel's,
808 ; electric, 774 ; gas, 848 ; gravity,
8 12 ; Grove's, 809 ; Leclanche's, 843 ;
Leyden, constant, 807 ; charged by
coil, 919 ; local, 875 ; luminous ef-
fects, 833; magnetic, 717; measure-
ment of charge, 777 ; mechanical
effects of, 838; Menotti's, 812; Marie
Davy's, 812; postal, 875; Smee's,
811 ; sulphate of mercury, 812; ten-
sion of, 815; thermo-electric, 938;
voltaic, 804, 805; Walker's, 811 ;
Wollaston's, 805
Beam of a balance, 73 ; of a steam-en-
gine, 467
Beats, 262
Beaume's hydrometer, 128
Becquerel's pyrometer, 943 ; thermo-
electric battery, 938 ; electrical ther-
mometer, 942
Bell of a trumpet, 237
Bell's telephone, 924 ; photophone, 930
Bellows, 243 ; hydrostatic, 102
Bennett's electroscope, 751
Berthollet's experiment, 183
Bertin's commutator, 868
Bianchi's air-pump, 193
Biaxial crystals, double refraction in,
644 ; optic axis of, 644 ; rings in, 667
Bifurcation, 639
Binnacle, 697
Binocular vision, 621
Biot's apparatus, 676
Black's experiments on latent heat, 461
Bladder, swimming, 119
Block and tackle, 45
Blood-globules, 15
Blue cloud. 974
Bodies, properties of, 7> I2 3
Bohnenberger's electroscope, 818
Boiler, 466
Boiling, 350 ; by cooling, 367 ; laws of,
363
Boiling-point, influence of dissolved sub-
Index.
955
BOR
stances on, 365 ; of nature of vessel,
366 ; of pressure on, 367 ; in a ther-
mometer, 302 ; measure of heights by,
. 369
Boreal pole, 689
Boutigny's experiments, 385
Boyle's law, 174-176
Bramah's hydraulic press, 109
Branch currents, 954
Breaking weight, 92
Breezes, land and sea, 966
Breguet's thermometer, 309
Bridge, \Vheatstone's, 949
British imperial yard, 22 ; and French
system of weights and measures, 126
Browning's regulator, 836
Brush discharge, 787
Bull's eye, 591
Bunsen's filter pump, 196 ; battery, 811 ;
burner, 576 ; ice calorimeter, 452 ;
photometer, 509
Bunsen and KirchhofTs researches, 578
Bunten's barometer, 161
Buoyancy of liquids, 101
Burning mirrors, 420
CJ-.SIUM, 578
Cagniard-Latour's syren, 242 ; ex-
periments on formation of vapour,
370
Cailletet's and Pictet's researches, 382
Cnllan's batter)-, 811
Calorescence, 433
Caloric, 448
Calorific effects of electrical discharge,
790 ; of current electricity, 829, 830 ;
of Ruhmkorft's coil, 919 ; of the spec-
trum, 573
Calorimeter, 450; Bunsen's ice, 451;
Black's, 451 ; Favreand Silbermann's,
463; Lavoisier and Laplace's, 451
Calorimetry, 447
Camera lucida, 594; Amici's, 603; ob-
scura, 602; Porta's obscura, 514
Campani's eyepiece, 592
Capacity, electrical, 739; specific induc-
tive, 748
Capillarity, 132 ; attraction and repul-
sion produced by, 135; correction for,
163
Capillary phenomena, 132-139 ; electro-
meter, 839; tubes, 133; ascent and
depression in, 133 ; between parallel or
inclined surfaces, 134
Capsule of the eye, 612
Cardan's suspension, 160
COA
Carre's mode of freezing, 374; dielectri-
cal machine, 760
Carriage lamps, 535
Cartesian diver, 117
Cascade, charging by, 776
Cathetometer, 89
Catoptric telescopes, 598
Caustics, 533, 534
Celsius' scale, 303
Centesimal alcoholometer, 129
Centigrade scale, 303
Centimetre, 126
Centre, optical, 555; of gravity, 69; ol
parallel forces, 37 ; of pressure, 103
Charge of a Leyden jar, penetration of,
773 ; measurement of, 787 ; laws of,
778; residual, 773
Charging by cascade, 776
Chatterton's compound, 883
Chemical affinity, 86; combination, 483 ;
effects of the battery, 793 ; of electrical
discharge, 793 ; of voltaic currents,
821; of Ruhmkorffs coil, 919; har-
monicon, 278; hygrometer, 394; pro-
perties of the spectrum, 573
Chemistry, I
Chevallier's microscope, 591
Cheval-vapeur, 473
Chimes, electrical, 763
Chimney, 487
Chladni's experiments, 284
Chlorophylle, 580
Chords, major and minor, 247 ; physical
constitution of, 264; tones dominant
and subdominant, 248 ; vocal, 259
Choroid, 612
Chromatic scale. 250 ; aberration, 583
Chromium, magnetic limit of, 720
Ciliary processes, 612
Circle, azirnuthal, 685
Circular polarisation, 669
Cirrocumulus, 969
Cirrostratus, 969
Cirrus, 969
Cistern barometer, 159
Cfamond's thermo-electric battery, 939
Clarke's magneto-electrical machine, 909
Cleavage, electricity produced by, 731
Clement and Desorme's experiment, 197
Climate, 996 ; constant, 996 ; influence
of aqueous vapour on, 973
Climatology, 992-999
Clocks, 82 ; electrical, 895
Clouds, 969; electricity of, 984; forma-
tion of, 970
Coatings, 769 ; Leyden jar with movable,
771
956
Index.
COB
Cobalt, 720
T Coefficients of linear expansion, 313,
3!5, 3i6
Coercive force, 687
Cohesion, 85
Coil, primary, 877; RuhmkorfPs, 912;
effects produced by, 912; secondary,
877
Cold, apparent reflection of, 422; pro-
duced by evaporation, 373 ; expansion
of gases, 494; by nocturnal radiation,
495 ; sources of, 493
Colladon and Sturm's experiments, 234
Collecting plate, 779
Collimation, 595
Collision of bodies, 59
Colloids, 141
Coloration produced by rotatory polari-
sation, 675
Colour, 7 ; of bodies, 592 ; of heat, 436 ;
of thin plates, 650
Colour disease, 632
Colours, contrast of, 627; mixed, 570;
simple, 566; comp ementary, 570;
produced by polarised light, 662-668 ;
by compressed glass, 668
Combustion, 483 ; heat disengaged dur-
ing, 484
Comma, musical, 248
Common reservoir, 726
Communicator, 883
Commutator, 884, 886, 910, 918; Ber-
lin's, 868
Compass, correction of errors, 696 ; de-
clination, 695 ; manner's, 697 ; incli-
nation, 698 ; sine, 824 ; tangent, 823
Compensating cube, 438
Compensation pendulum, 320 ; balance,
320; gridiron, 320; strips, 320
Complementary colours, 570
Component forces, 32
Composition of velocities, 52
Compound microscope, 56
< "Compressed glass, colours produced by,
668
Compressibility, 7, 16; of gases, 174;
of liquids, 96
Concave mirrors, 419, 5 2 ^
Concert pitch, 251
Concordant tones, 247
Condensation of vapours, 375
Condensed gas, 145 ; wave, 225
Condenser, 467, 759, 765 ; limits to
charge of, 768 ; of Ruhmkorff's coil,
918; Liebig's, 377
Condensing engine, 472; air-pump, 199;
force, calculation of. 767 ; electro-
CUR
scope, 779> plate, 779; hygrometers,
395
^Conduction of heat, 403 ; of electricity,
725 ; lightning, 989
Conductivity of bodies for heat, 404 ; co-
efficient of, 404, 405 ; of gases, 409 ;
of liquids, 407; for electricity, 948,
951
Conductors, 725 ; equivalent, 949 ; good
and bad, 404; lightning, 989; prime,
753 ; resistance of, 946
Congelation, 343
Conical pendulum, 57
Conjugate mirrors, 420; focus, 525, 552
Connecting rod, 467
Conservation of energy, 66
Constant currents, 807
Contact theory of electricity, 799
Contractile force, 319
Convection, 408
""Con-vex meniscus, 132 ; mirrors, 526,
529
Cooling, method of, 455 ; Newton's law
of, 417
Cornea, 612
Corpuscular theory, 499
Corti's fibres, 260
Cosine, law of the, 414, 508
Coulomb's law, 703
Couple, 36; terrestrial magnetic, 690;
voltaic, 801 ; thermo-electric, 936
\ Couronne des tasses, 805
I Cowper's writing telegraph, 887
Cox well's balloon, 186
Crab, 42
Critical angle, 540 ; temperature, 370
Crookes's radiometer, 445 ; vacuum, 446;
experiments, 921
Cross-wire, 595
Crutch of a clock, 82
Cryohydrate, 348
Cryophorus, 373
Crystal, hemihedral, 732
! Crystalline, 612
I Crystallisation, 344
i Crystalloids, 141
_ Crystals, 343; expansion of, 315; doubly
refracting, 639, 652, 663; uniaxial,
642 ; positive and negative, 643
Cube, Leslie's, 423
Cumulostratus, 968
Cumulus, 968
Current electricity, 800
-Currents, action on currents, 860, 86 1 ;
action of magnets, 864 ; action of
earth on, 870, 871 ; action on sole-
noids, 872, 877 ; constant, 807 ; di-
Index.
957
CUR
vided, 954 ; detection and measurement
of voltaic, 819 ; diaphragm, 838 ;
direct and inverse, 897, 898, 905 ;
effects of enfeeblement of, 806 ; extra,
904, 905 ; of inclination, 956 ; inten-
sity of, 825 ; induction by, 897 ; laws
of angular, 858 ; laws of sinuous, 859 ;
local, 816 ; magnetisation by, 869 ;
motion and sounds produced by, 88 1 ;
muscular, 955 ; in active muscle, 958 ;
in nerve, 959 ; rotation of magnets by,
854 ; secondary, 806 ; terrestrial, 878 ;
thermal effects of, 830, 831 ; transmis-
sions by, 843
Curvature of liquid surfaces, 136; in-
fluence of, on capillary phenomena,
137
Curves, magnetic, 704
Cushions, 753
Cyanogen gas, 380
Cyclones, 967^
Cylinder, 467 ; electrical machine, 757
-pvAGUERREOTYPE, 608
L/ Daltonism, 632
Dalton's laws on gases and vapours, 383 ;
method of determining the tension of
aqueous vapour, 356
Damper, 279, 902
Danielt's batter)', 808 ; hygrometer, 396 ;
pyrdmeter, 311
Dark lines of the spectrum, 574 ; of
solar spectrum, 579
Davy's battery, 812
Davy's experiment, 421
Day, apparent, 21
Decimetre, 24, 126
Declination compass, 695 ; errors of,
696 ; magnetic, 691 ; of needle, 691 ;
variations in, 692 ; of a star, 600
Decomposition, chemical, 840 ; of white
light, 564 ; of salts, 842
Deflagrator, Hare's, 805, 829
Degrees of a thermometer, 303
De la Rive's floating battery, 865 ; ex-
periments, 922
De la Rue and M tiller's experiments,
9220
Deleuil's air-pump, 194
Delezenne's circle, 903
Delicacy of balance, 74 ; of thermometer,
307
Densimeter, 131
Density, 24 ; of the earth, 68 ; electric,
736 ; of gases, 335-337 ; maximum of
water, 330 ; of vapours, Gay-Lussac's
DIV
method, 386 ; Dumas', 388 ; Deville
and Troost's, 389 ; Hofmann's, 387
Depolarisation, 665
Depolarising plate, 663
Depression of liquids in capillary tube,
133 ; between surfaces, 134
Derived currents, 954
Descartes' laws of refraction, 537
Despretz's experiment, 404
Developer, 609
Deviation, angle of, 544
1 Deville and Troot's method, 389
Dew, 975 ; point, 395
Diabetic urine, analysis of, 678
Dial telegraphs, 885
Dialyser, 141
Dialysis, 141
Diamagnetism, 932
Diapason, 257
Diaphanous bodies, 500
Diaphragm, 591 ; currents, 838
Diathermancy, 434
Diatonic scale, 248
Dielectrical machine, Carre's, 760
Dielectrics, 748
Differential barometer, 180
Differential galvanometer, 821 ; thermo-
meter, Leslie's, 308 ; Matthiessen's,
308 ; tone, 263
Diffraction, 503 ; spectra, 648 ; fringes,
646
Diffusion of heat, 437 ; of liquids, 141
Digester, Papin's, 371
Dionoea muscipula, 827
Dioptric telescopes, 598
Diplopy, 631
Dip, magnetic. 698
Dipping needle, 698
Disc, Newton's, 567
Discharge, electrical. 766 ; effects of the,
783 ; lateral, 989 ; slow and instanta-
neous, 766 ; universal, 775
Discharging rod, 766
Dispersion, 544 ; abnormal, 581
' Dispersive power, 564
Displacement, 46
Dissipation of energy, 498
Distance, estimation of, 618 ; adaptation
of eye to, 620
Distillation, 376
Distribution of free electricity, 735 ; of
magnetism, 722 ; of temperature, 997 ;
of land and water, 999
Diurnal variations, 693
; Diver, Cartesian, 117
Divided currents, 954
| Dividing machine, 1 1
953
Index.
DIV
Divisibility, 7, 12
Dobereiner's lamp, 482
Dominant chords, 248
Doppler's principle, 233
Double-action steam-engine, 467, 468
Double refraction, 652
Doublet, Wollaston, 586
Dove's law of storms, 967
Draught of fire-places, 488
Driving wheels, 470
Drummond's light, 606
Dry piles; 817
Duboscq's microscope, 606 ; regulator,
835
Ductility, 7, 93
Duhamel's graphic method, 245
Dulong and Arago's experiments on
Boyle's law, 1 75 ; method of deter-
mining the tension of aqueous vapour,
Dulong and Petit's determination of ab-
solute expansion of mercury, 322 ;
method of cooling, 455 ; law, 458
Dumas' method for vapour density, 388
Duplex telegraphy, 890
Duration of electric spark, 795
Dutroche's endosmometer, 140
Dynamical theory of heat, 429
Dynamic radiation and absorption, 442
Dynamo-magnetic machine, 914
T? AR, the, 7
L_^ Earnshaw on velocity of sound. 230
Earth, its action on currents, 869-871 ;
action of solenoids, 876 ; current, 891 ;
flattening of, by rotation, 83 ; magnetic
poles of the, 698 ; magnetisation by, 714
Earth's magnetism, 701
Ear trumpet, 239
Ebullition, 350 ; laws of, 363
Eccentric, 467, 468
Echelon lenses, 607
Echoes, 237 ; monosyllabic, trisyllabic,
multiple, 237
Edison's phonograph, 291 ; tasimeter,
927 ; telephone, 928
Efflux, velocity of, 21 1 ; quantity of,
213 ; influence of tubes on, 214
Effusion of gases, 143
Elastic bodies, 59
Elastic force, 146; of vapours, 351
Elasticity, 7, 17 ; limit of, 17, 89; of
traction, 89 ; modulus of, 89 ; of tor-
sion, 90; of flexure, 91
Electric alarum, 894; axis, 73 2 > bat-
teries, bottle, 774. 789 ; charge, 778 ;
EME
chimes, 763 ; clocks, 895 ; density,
736 ; discharge, 783 ; egg, 788 ; fish,
960 ; fuse, 794 ; glow, 787 ; light,
831-833; stratification of the, 920
pendulum, 724 ; pistol, 793 ; poles,
732 ; residue, 773 ; shock, 77> 785 ;
spark, 762 ; telegraphs, 883-896 ; ten-
sion, 736 ; tube, 789 ; whirl, 764
Electrical attractions and repulsions,
734; potential, 738; capacity, 739;
measurement of, 740 ; resistance, unit
of, 947 ; conductivity, 951 ; quantity,
733.
Electrical machines, 752-761 ; precau-
tions in, 754
Electricity, 6, 723 ; application of, to
medicine, 961 ; atmospheric, 980-
989 ; current, 800 ; communication of,
749 ; development of, by friction, 724 ;
by pressure and cleavage, 731 ; dis-
tribution of, 735 ; dynamical, 797-
954 ; disengagement of, in chemical
actions, 793, 799 ; factional, 730 ;
loss of, 743 ; mechanical effects, 792 ;
power of points, 742 ; produced by
induction, 744 ; velocity of, 796 ;
theories of, 728 ; work required for
production of, 761
Electrified bodies, motion of, 729, 750
Electro-capillary phenomena, 839
Electrochemical telegraph, 892 ; series,
841
Electrodes, 803 ; polarisation of, 806
Electrodynamics, 856
Electrogilding, 853
Electrolysis, 841 ; laws of, 845
Electrolyte, 841
Electromagnetic force, 880 ; machines,
896
Electromagnets, 88 1
Electrometallurgy, 852-854
Electrometer, 751 ; Lane's, 777; quad-
rant, 756 ; Thomson's, 780
Electromotive series, 801 ; force, 802,
814, 825, 952 ; determination of, 952 ;
force of elements, 814
Electromotor, 883
Electrophorus, 752
Electropyrometer, 943
Electroscope, 724 ; Bohnenberger's, 818;
Volta's condensing, 779 ; gold leaf, 751
Electrosilvering, 854
Electrotonus, 828
Elements, electronegative and electro-
positive, 841
Elliptical polarisation, 672
Emergent rays, 542
Index.
959
EMI
Emission theory, 499
Emissive power, 425
Endosmometer, 136
Endosmose, 140 ; electrical, 838 ; of
gases, 142
Endosmotic equivalent, 140 .
Energy', 63 ; conservation of, 66 ; dissi-
pation of, 498 ; transformations of, 65 ;
varieties of, 64
Engines, gas, 475 ; steam, 465 ; double-
action, 467 ; low and high pressure,
472; single action, 469; locomotive,
454 ; fire, 209 ; transformation of, 65
Eolipyle, 471
Equator, 68 1 ; magnetic, 698
Equilibrium of forces, 35 ; of floating
bodies, 116; of heavy bodies, 70; of
liquids, 107, 108 ; mobile of tempera-
ture, 414; neutral, 71; stable, 71;
unstable, 71
Equivalent, endosmotic, 140 ; conduc-
tors, 948
Escapement, 82 ; wheel, 82
Ether, 429 ; luminiferous, 499
Eustachian tube, 260
Evaporation, 350 ; causes which accele-
rate it, 362 ; cold due to, 373 ; latent
heat of, 372
Evaporation and ebullition, 364
Exchanges, theory of, 415
Exhaustion, produced by air-pump, 193;
by Sprengel's pump, 195
Exosmose, 140
Expanded wave, 225
Expansibility of gases, 146
Expansion, 296; apparent and real, 321 ;
absolute, of mercury, 322 ; apparent,
of mercury, 323 ; of liquids, 326 ; of
solids, 313 ; of gases, 331-333 ; linear
and cubical, coefficients of, 313 ;
measurement of linear, 314 ; of crystals,
318 ; applications of, 319 ; force of, 329
Expansion of gases, cold produced by,
494 ; problems on, 332
Expansive force of ice, 346
Experiment, Berthollet's, 183 ; Frank-
lin's, 368 ; Florentine, 98 ; Pascal's,
156 ; Torricellian, 155
Extension, 7, 9
Extra current, 904, 905 ; direct, 905 ;
' inverse, 905
Eye, 612 ; accommodation of, 620 ; not
achromatic, 628 ; refractive indices of
media of, 613 ; path of rays in, 615 j
dimensions of various parts of, 614
Eye-glass, 544, 630 ; lens, 592 ; piece,
5 8 3> 590, 592 5 Campani's, 592
FOR
TTAHRENHEIT'S hydrometer, 124
r scale, 303
Falling bodies, laws of, 77
Faraday's experiments, 745 ; wheel, 625 ;
theory of induction, 747; voltameter,
845
Favre and Silbermann's calorimeter, 463;
determination of heat of combustion,
483
Field lens and glass, 592
Field of a microscope, 591 ; of view, 593;
magnetic, 707
Figures, Lichtenberg's, 772
Filter pump, 196
Finder, 595
Fire engine, 209 ; places, 487 ; works,
217
Fish, electrical, 960
Fishes, swimming bladder of, 118
Fizeau's experiments, 316, 507
Flame, 483
Flask, specific gravity, 122
Flattening of the earth. 83
Flexure, elasticity of, 91
Float, 466
Floating bodies, 1 1 6
Florentine experiment, 13, 98
Fluid, 4; imponderable, 6; elastic, 149;
magnetic, 683
Fluidity, 7
Fluorescence, 582
Flute, 280
Fluxes, 340
Fly-wheel, 467
Focal distance, 419
Foci, acoustic, 237; of convex mirrors,
526; in double convex lenses, 552
Focus, 419, 525 ; conjugate, determina-
tion of the principal, 527 ; of a sphe-
rical concave mirror, 525
Focussing the microscope, 587
i Fogs, 968
\ Foot, 22
( Foot-pound, 60, 473
j Force, 26; conservation of, 66; coer-
cive, 687 ; direction of, 30; elastic, of
gases, 146 ; lines of magnetic, 707 ;
of expansion and contraction, 319;
electromotive, 802, 814 ; representa-
tion of, 30; parallelogram of, 33; of
liquids, 529 ; portative, 719
Forces, 6; along the same line, 31;
equilibrium of, 38 ; impulsive, 6 1 ;
magnetic, 708 ; molecular, 84 ; mo-
ments of, 38 ; polygon of, 35 ; triangle
of, 35
Formulae for expansion, 318; barome-
960
Index.
FOR
trie, 168; for sound, 231; for spheri-
cal mirrors, 530, 531 ; for lenses, 559
Fortin's barometer, 1 60
Foucault's determination of velocity of
light, 506; experiment, 834, 923
Fountain in vacuo, 200 ; at Giggleswick,
204 ; intermittent, 202 ; Hero's, 201
Franklin's experiment, 368, 980; plate,
769 ; theory of electricity, 728
Fraunhofer's lines, 574, 575
Freezing, apparatus for, 374
Freezing mixtures, 347, 348 ; point in a
thermometer, 302
French weights and measures, 1 24 ;
boiler, 466
Fresnel's experimentum crucis, 645;
rhomb, 671
Friction, 26, 47; heat of, 477 ; hydrau-
lic, 214 ; internal, of gases, 446 ; deve-
lopment of electricity by, 720
Friction wheels, 78
Frigorific rays, 422
Fringes, 646
Frog, rheoscopic, 957
Frost, 975
Frozen mercury, 373, 380, 384
Fulcrum, 44
Fulgurites, 987
Fulminating pane, 769
Fuse, Abel's, 794 ; Chatham, 829, 830
Fusing point, 338
Fusion, laws of, 338 ; vitreous, 338 ;
latent heat of, 461 ; of ice, 450
ALILEAN telescope, 597
Galleries, whispering, 237
Gallon, 126
Galvani's experiment, 797
Galvanometer, 821 ; differential, 821 ;
Sir W. Thompson's, 822
Galvanoscope, 821
Galvano-thermometer, 830
Gas battery, 848 ; engines, 475
Gaseous state, 4
Gases, absorption of, by liquids, 184 ;
application of Archimedes' principle
to, 185 ; cold produced by expansion
of, 494 ; compressibility of, 148, 174 ;
conductivity of, 409; diamagnetism
of, 931 ; density of, 335, 337 ; dyna-
mical theory of, 293 ; expansion of,
147, 331-334 ; endosmose of, 142 ;
effusion and transpiration of, 143 ;
Gay-Lussac's method, 331 ; index of
refraction of, 550 ; law? of mixture of,
183 ; and vapours, mixtures of, 383 ;
HAI
permanent, 380 ; problems in, 332,
383; liquefaction of, 380; physical
properties of, 146 ; pressure exerted
by, 150; radiation of, 441; Regnault's
method, 336 ; specific heat of, 460 ;
velocity of sound in, 230, 231, 232 ;
viscosity of, 446 ; weight of, 149
Gassiott's battery, 815
Gauge, air-pump, 191 ; rain, 971
Gay-Lussac's alcoholometer, 129 ; baro-j
meter, 161 ; determination and expan-;
sion of gases, 331 ; of vapour-density, ]
385 ; stopcock, 382
Geissler's tubes, 195, 578, 921
Generating plate, 80 1
Geographical meridian, 691
Geometrical shadows, 503
Giffard's injector, 197
Gilding metal, 853
Gimbals, 697
Glacial pole, 997
Glaciers, 979
Glashier's balloon ascents, 1 86 ; factors,;
398
Glass, expansion of, 325 ; magnifying,]
583 ; object, 588 ; opera, 397 ; un-
annealed, 668
Glasses, periscopic, 629; weather, 168
Globe lightning, 985
Glow, electrical, 787
Glycerine barometer, 1 70
Gold-leaf electroscope, 75 1
Goniometers, 534
Good conductors, 404
Gramme, 24, 126
Gramme's magneto-electrical machine, 9 1
Graphic method, Duhamel's, 245 ; Fos
ter's, 831
Gratings, 647
Gravesand's ring, 295
Gravitation, 6, 83 ; terrestrial, 68 ; ac
celerative effect of, 27
Gravity, battery, 812
Gravity, centre of, 69
Gregorian telescope, 599
Gridiron pendulum, 320
Grimaldi's experiment, 645
Grotthiiss' hypothesis, 844
Grove's battery, 809 ; gas, 848
Guericke's air-pump, 190
Gulf Stream, 994
Guthrie's researches, 348
HADLEY'S reflecting sextant, 521
Hail, 977
Hair hygrometer, 399
hidex.
96 1
HAL
HaMat's apparatus, 102
Hall's experiment, 878
Hallstronvs experiments, 329
Haloes, 627
Hammer, 279, 918
Hardening, 91
Hardness, 7 ; scale of, 94
I Lire's deflagrator, 805, 829, 830
Harmonicon, chemical, 278
Harmonics, 254, 273
Harmonic triad, 247; grave, 263
Harp, 281
I [arris's unit jar, 778
Heat, 292 ; animal, 485 ; absorption of,
by vapours, &c., 435, 439 ; diffusion
of, 437 ; developed by induction, 923;
dynamical theory of, 429 ; hypothesis
on, 292 ; influence of the nature of,
435 ; latent, 341 ; mechanical equi-
valent of, 497 ; polarisation of, 679 ;
produced by absorption and imbibi-
tion, 482 ; radiated, 403 ; radiant,
411; reflection of, 418 ; scattered, 424 ;
sources of, 477-496 ; specific, 448 ;
transmission of, 403; terrestrial, 481
Heaters, 466
I 1 eating, 486 ; by steam, 490 ; by hot
air, 491 ; by hot water, 492
Height of barometer, 159, 165 ; varia-
tions in, 165
Heights of places, determination of, by
barometer, 172, 173 ; by boiling point,
369
Heliograph, 523
Heliostat, 534
Helix, 45, 879
Helmholtz's analysis of sound, 255 ; re-
searches, 258
Hemihedral crystal, 732
Hemispheres, Magdeburg, 154
Henley's electrometer, 756; discharger,
792
Henry's experiment, 906
Herepath's salt, 656
Hero's fountain, 201
Herschelian rays, 430 ; telescope, 601
Hirn's experiments, 474
Hoar frost, 975
Hofmann's density of vapours, 387
Holmes's magneto-electrical machine, 91 1
Holtz's electrical machine, 759
Homogeneous light, 572 ; medium, 502
Hope's experiments, 330
Horizontal line, 68 ; plane, 68
Horse power, 473
Hotness, 297
Hour, 21
IND
Howard's nomenclature of clouds, 969
Hughes's microphone, 925 ; induction
balance, 926
Humour, aqueous, 612
Huyghens' barometer, 171
Hyaloid membrane, 612
Hydraulic press, 109 ; friction, 214 ;
tourniquet, 217
Hydraulics, 96
Hydrodynamics, 96
Hydro-electric machine, 758
Hydrometers, 120 ; Nicholson's 121 ;
Fahrenheit's, 124; with variable
volume, 127; Beaume's 128; of con-
stant volume, 127 ; specific gravities,
1 20 ; uses of tables of, 1 26
Hydrostatic bellows, 102; paradox, 104;
balance, 121
Hydrostatics, 96-99
Hygrometers, 393 ; of absorption, 399 ;
chemical, 394 ; condensing, 395 ; wet-
bulb, 398; Mason's, 398; Regnault's,
397
Hygrometric state, 392 ; substances, 39 1
Hygrometry, 391 ; problem on, 401
Hygroscope, 399
Hypothesis, 5
Hypsometer, 369
ICE, 978 ; method of fusion of, 450
Ice calorimeter, 450 ; Bunsen's,
451; expansive force of, 346; ma-
chine, 494
Iceland spar, 659
Idio-electrics, 724
Image and object, magnitudes of, 561
Images, accidental, 626 ; condition of
distinctness of, 587 ; formation of, in
concave mirrors, 528; in convex mir-
rors, 529; in plane mirrors, 513; of
multiple, 516; magnitude of, 532;
produced by small apertures, 504 ;
virtual and real, 514; inversion of, 616
Imbibition, 144; heat produced by, 482
Impenetrability, 7
Imperial British yard, 22
Imponderable matter,
Impulsive forces, 58
Inch, 126
Incident ray, 536
Inclination, 708 ; compass, 699
Inclined plane, 43 ; motion on, 50
Index of refraction, 538 ; measurement
of, in solids, 548 ; in liquids, 549 ; in
gases, 550
Indicator, 883, 885, 886
XT
962
Index.
IND
Indices, refractive, table of, 550
Indium, 578
Induced currents, 897-909
Induction, apparatus founded on, 909 ;
by the earth, 903 ; by currents, 897 ;
of a current on itself, 904 ; electrical,
744 ; in telegraph cables, 888 ; limit
to, 746 ; Faraday's theory of, 747 ;
heat developed by, 923 ; by magnets,
901 ; magnetic, 686 ; vertical, 715
Inductive capacity, specific, 748
Inductorium, 917
Inelastic bodies, 59
Inertia, 19 ; applications of, 20
Influence, magnetic, 686 ; electrical, 744.
Ingenhaus's experiment, 404
Injector, 197
Insects, sounds produced by, 242
Insolation, 635, 636
Instruments, optical, 585 ; polarising,
656 ; mouth, 270 ; reed, 272 ;
stringed, 279 ; wind, 271, 280
Insulating bodies, 726 ; stool, 762
Insulators, 725
Intensity of the current, 825 ; of the
electric light, 837 ; illumination, 508 ;
of reflected light, 519 ; of a musical
tone, 246 ; of radiant heat. 414 ; of
sound, causes which influence, 226;
of terrestrial magnetism, 7 O1 j f ter-
restrial gravity, 83
Interference of light, 645 ; of sound, 261 \
Intermittent fountain, 202 ; springs, 204 ;
syphon, 204
Interpolar, 825
Intervals, musical, 247
Intrapolar region, 828
Inversion of images, 616
lones, 841
Iris, 612
Iron, passive state of, 849 ; electrical \
deposition of, 855
Iron ships, magnetism of, 715
Irradiation, 627
Irregular reflection, 518
Isobars, 967^
Isochimenal line, 905
Isoclinic lines, 698
Isodynamic lines, 701
Isogeothermic lines, 995
Isogonic lines, 692
Isotheral lines, 995
Isothermal lines, 995 ; zone, 995
J
ACOBl'S unit, 947
Jar, Leyden, 770-780
LEN
Jar, luminous, 785 ; Harris's unit, 777
Jet, lateral, 211; height of, 212; form
of, 216
Jordan's barometer, 170
Joule's experiment on heat and work,
497 ; equivalent, 497
Jupiter, 505
Jurin's laws of capillarity, 133
TV^ALEIDOPHONE, 625
iS^ Kaleidoscope, 516
Kamsin, 966
Kathelectrotonus, 828
Kathode, 841
Katione, 841
Keepers, 718
Kerr's electro -optical experiments, 931
Key, 884, 903, 910, 918; note, 249
Kienmayer's amalgam, 754
Kilogramme, 24, 126
Kilogrammetre, 473
Kinetic energy, 63
Kinnersley's thermometer, 792
Kirk's ice machine, 494
Knife edge, 72
Konig's apparatus, 256 ; manometric
flames, 288
Kravogl's machine, 896
Kiilp's method of compensation, 719
Kundt's velocity of sound, 277
LABYRINTH of the ear, 260
Lactometer, 130
Ladd's dynamomagnetic machine, 914
Land and water, 999
Lane's electrometer, 777
Lantern, magic, 604
Laplace's barometric formula, 172
Laryngoscope, 563
Larynx, 259
Latent heat, 341 ; of fusion, 461 ; of
vapours, 372, 462
Latitude, influence on the air, 993 ;
parallel of. 83
Lavoisier and Laplace's calorimeter, 450 ;
method of determining linear expan-
sion, 314
Law, 5
Lead tree, 851
Leclanche's elements, 813, 814
Ledger lines, 252
Leidenfrost's phenomenon, 385
Lemniscate, 667
Length, unit of, 22 ; of undulation, 225
Lenses, 551-559; achromatic, 582;
aplanatic, 558; centres of curvature
Index.
963
LEN
551 ; combination of, 560 ; foci in
double convex, 552 ; in double con-
cave, 553 ; formation of images in
double convex, 556; in double con-
cave, 557-; formula? relating to, 559 ;
lighthouse, 607; optical centre, secon-
dary axis of, 555
Lenz's law, 898
Leslie's cube, 423 ; experiment, 373,
thermometer, 308
Level, water, no; spirit, in
Level surface, 68
Levelling staff, no
Lever, 40
Leyden discharge, inductive action of, 900
Leyden jars, 770 -780 ; charged by
RuhmkorfFs coil, 919 ; potential of,
782 ; work by, 784
Lichtenberg's figures, 772
Liebig's condenser, 377
Ligament, saspensory, 612
Light, 499 ; diffraction of, 646 ; homo-
geneous, 569, 572 ; intensity of, 508 ;
interference of, 645 ; laws of reflection
of, 511 ; medium, 502 ; oxyhydrogen,
606 ; polarisation of, 652 ; relative
intensities of, 510; sources of, 634;
theory of polarised light, 661 ; un-
dulatory theory of, 499, 637 ; velocity
of, 505-507
Lighthouse lenses, 607
Lightning, 987 ; ascending, 985 ; effects
of, 985 ; conductor, 989 ; globe, 987 ;
heat, 985; brush, 985; flashes, 985;
zigzag, 985
Limit, magnetic, 720; to induction, 746;
of perceptible sounds, 244
Line, aclinic, 698 ; of collimation, 595 ;
isoclinic, 698 ; agonic, 692 ; isogonic,
692 ; isodynamic, 701 ; of sight, 595
Linear expansion, coefficients of, 313, 315
Lippmann's capillary electrometer, 839
Liquefaction of gases, 380, 381 ; of
vapours, 375
Liquids, ioo; active and inactive, 667 ;
buoyancy of, IOI ; compressibility of,
98 ; conductivity of, 407 ; calculation
of density of, 108 ; diffusion of, 141 ;
diamagnetism of, 932 ; expansion of,
321 ; equilibrium of, 105 ; manner in
which they are heated, 408 ; pressure
on sides of vessel, 103 ; refraction of,
549 ; rotatory power of, 676 ; sphe-
roidal form ot", 85 ; spheroidal state of,
385 ; specific heat of, 456 ; volatile
and fixed, 349 : tensions of vapours of,
359 ; of mixed liquids, 360
T
MAG
Lissajous's experiments, 284 286
Lithium, 578
i Litre, 24, 126
i Local action, 806; attraction, 715; bat-
tery, 886 ; currents, 816
Locatelli's lamp, 428
Locomotives, 470, 471
Lodestone, 680
Long sight, 629
Loops and nodes, 269
Loss of electricity, 743 ; of weight in air,
correction for, 402
Loudness of a musical tone, 246
Luminiferous ether, 499
Luminous bodies, 500 ; effects of the
electric discharge, 773, 833 ; of the
electric current, 919 ; of RuhmkorflPs
coil, 919; jar, 789; meteors, 981 ;
pane, 789 ; pencil, 501 ; ray, 501 ;
tube, 789 ; square, and bottle, 789
Luminous radiation, 432 ; heat, 434
MACHINE, Atwood's, 78; elec-
trical, 752-760 ; Von Ebner's,
794; electromagnetic, 883
Mackerel-sky, 969
! Magazine, 717
Magdeburg hemispheres, 154
Magic lantern, 604
Magnetic attractions and repulsions, 702 ;
battery, 717 ; couple, 690 ; curves,
706; declination, 695; dip, 698;
effects of the electrical discharge, 791 ;
equator, 698 ; field, 707 ; fluids, 683 ;
induction, 686; influence, 686; limit,
720; meridian, 691 ; needle, 691, 692;
oscillations of, 705 ; observatories,
702; poles, 698; saturation, 716;
storms, 694
Magnetisation, 710; by the action of the
earth, 714; by currents, 879; single
touch, 711
I Magnetism, 6, 700 ; determination of,
in absolute pressure, 709; earth's, 701 ;
of iron ships, 715; Ampere's theory of,
877; remanent, 880; theory of, 683;
terrestrial distribution of free, 721
Magneto-electrical apparatus, 909 ;
Gramme's, 915; machines, 911-914
I Magneto and dynamo- electrical machines,
916
! Magnets, artificial and natural, 680;
broken, 685 ; action of earth on, 689 ;
equator of, 68 1 ; floating, 722 ; north
and south poles of, 682 ; portative force
of, 719; saturation of, 716; influence
T 2
964
Index.
MAG
of heat, 720; induction by, 901; in-
ductive action on moving bodies, 902 ;
action on currents, 865 ; on solenoids,
875 ; rotation of induced currents by,
922 ; optical effects of, 926 ; total action
of two, 708
Magnification, linear and superficial, 89;
measure of, 589; of a telescope, 55, 65
Magnifying power, 594
Magnitude, 9; apparent, of an object,
588 ; of images in mirrors, 587
Major chord, 247 ; triads, 248
Malleability, 857
Mance's heliograph, 523
Manganese, magnetic limit of, 720
Manhole, 466
Manipulator, 885
Manometer, 98, 177; open-air, 178;
with compressed air, 179; Regnault's
barometric, 181
Manometric flames, 288
Mares' tails, 969
Marie Davy battery, 812
Marine galvanometer, 822
Mariner's card, 964 ; compass, 697
Mariotte and Boyle's law, 174
Mariotte's tube, 174; bottle, 219
Marloye's harp, 281
Maskelyne's experiment, 68
Mason's hygrometer, 398
Mass, measure of, 23 ; unit of, 23
Matter, 2
Matteucci's experiment, 900
Matthiessen's thermometer, 308; table of
electromotive forces, 934; electrical
conductivity, 951
Maximum current, conditions of, 826
Maximum and minimum thermometers,
310; of tension, 755
Mayer's floating magnets, 722
Mean temperature, 992
Measure of force, 29; of work, 61
Measure of magnification, 589, 594; of
mass, 23; of space, 22 ; of time, 21 ;
of velocity, 25
Measurement of small angles by reflec-
tion, 522
Mechanical equivalent of heat, 497 ;
effects of electrical discharge, 792
Melloni's researches, 429; thermomul-
tiplier, 412, 940
Melting point, influence of pressure on,
339
Membranes, vibrations of, 283
Memoria technica, 820
Meniscus, 133; in barometer, 163;
Sagitta of, 163
MOR
Menotti's battery, 812
Mercury, frozen, 373, 381, 384; pendu-
lum, 320; coefficient of expansion,
323; expansion of, 322; pump, 198
Meridian, 21 ; geographical and mag-
netic, 691
Metacentre, 116
Metal, Rose's and Wood's fusible, 340
Metals, conductivity of, 951
Meteoric stones, 480
Meteorograph, 963
Meteorology, 962
Metre, 22, 126
Mica, 664
Micrometer lines, 594; screw, II
Microphone, 925
Microscope, 12 ; achromatism of, 592 ;
Amici's, 591 ; compound, 590 ; focus-
sing, 587 ; magnifying powers of, 5945
photo-electric, 606 ; simple, 586 ;
solar, 605
Microspectroscope, 580
Mill, Barker's, 217
Millimetre, 126
Mineral waters, 988
Mines, firing by electricity, 795, 829
Minimum thermometer, 310; deviation,
547
Minor chord, 247
Minute, 21
Mirage, 541
Mirrors, 512; applications of, 534; bum-
ing, 420 ; concave, 419 ; conjugate,
420; glass, 515; parabolic, 535; ro-
tating, 520, 795 ; spherical, 524
Mists, 968
Mixture of gases, 183; of gases and
liquids, 184
Mixtures, freezing, 347 ; method of, 452
Mobile equilibrium, 415
Mobility, 7, 18
Modulus of elasticity, 89
i Moisture of the atmosphere, 400
Molecular forces, 3 ; attraction, 84 ;
state of bodies, 4 ; velocity, 294
Molecular state, relation of absorption to,
443
Molecules, 3
Moments offerees, 38
Momentum, 28
| Mongolfier's balloon, 186
Monochord, 266
Monochromatic light, 569
Monosyllabic echo, 237
Moon, 510
Morgagni's humour, 610
Morin s apparatus, 79
Index.
965
MOR
Morren's mercury pump, 198
Morse's telegraph, 886
Moser's images, 144.
Motion, 1 8 ; on an inclined plane, 50 ;
curvilinear, 25 ; in a circle, 53, 54 ;
rectilinear, 25 ; resistance to, in a
fluid, 48 ; uniformly accelerated rec-
tilinear, 48 ; quantity of, 29 ; of a
pendulum, 55 ; of projectile, 51
Mouth instrument, 271
Multiple battery, 826
Multiple echoes, 237 ; images formed by
mirrors, 515, 516, 517
Multiplier, 821
Muscular currents, 955, 956, 957
Music, 217 ; physical theory of, 246-
264
Musical boxes, 279 ; intervals, 247 ;
scale, 248 ; temperament, 250 ; tones,
properties of, 246 ; intensity, notation,
252 ; pitch and timbre, 246 ; sound,
223 ; range, 252
Myopy, 619, 629
NAIRNE'S electrical machine, 757
Nascent state, 86
Natterer's apparatus, 381
Nauman's law, 458
Needle, dipping, 698 ; astatic, 700 ;
magnetic, 691
Negative plate, 801
Negatives on glass, 609
Nerve currents, 959
Neutral line, 744; equilibrium, 71;
point, 744
Newtonian telescope, 600
Newton's disc, 568 : law of cooling, 416 ;
rings, 650, 651 ; theory of light, 568
Nicholson's hydrometer, 121
Nickel, electrical deposition of, 855 ;
magnetic limit of, 720
Nicol's prism, 660
Nimbus, 969
Nobili's battery, 937 ; rings, 850 ; ther-
momultipliers, 939; thermo-electiic
pile, 428, 431, 937
Nocturnal radiation, 495
Nodal points, 271, 645
Nodes and loops, 269 ; of an organ pipe,
274 ; explanation of, 276
Noises, 221
Nonconductors, 725
Norremberg's apparatus, 657
Northern light, 991
Norwegian stove, 410
Notation, musical, 252
PEN
Notes in music, 247 ; musical, of women
and boys. 259 ; wave-length of, 253
Nut of a screw, 45
OBJECT glass, 590
Objective, 590
Obscure radiation, 432 ; rays, 433 ;
transmutation of, 433
Observatories, magnetic, 702
Occlusion of gases, 145
Octave, 249
Oersted's experiment, 820
Ohm's law, 825
Opaque bodies, 500
Opera-glasses, 597
Ophthalmoscope, 633
Optic axis, 607 ; axis of biaxial crystals,
644 ; angle, 607 ; nerve, 612
Optical centre, 555 ; effects of magnets,
929 ; instruments, 585
Optics, 499
Optometer, 619
Organ pipes, 274 ; nodes and loops of, 274
Orrery, electrical, 764
Oscillations, 55 ; axis of, 80 ; method of,
70S
Otto von Guericke's air-pump, 190
Outcrop, 112
Overshot wheels, 218
Oxyhydrogen light, 606
Ozone, 793, 987
PALLET, 82
Pane, fulminating, 769 ; luminous ;
790
Papin's digester, 371
Parabolic mirrors, 535; curve, 61, 211
Parachute, 188
Paradox, hydrostatic, 104
Parallel of latitude, 83 ; forces, 36 ;
centre of, 27
Parallel rays, 501
Parallelogram offerees, 33
Paramagnetic bodies, 932
Partial current, 954
Pascal's law of equality of pressures, 99
experiments, 156
Passage tint, 677
Passive state of iron, 849
Pedal, 279
Peltier's cros?, 944
Pendulum, 55; application to clocks,
82 ; ballistic, 82 ; corrcal, 57 ; com-
pensation, 320 ; electrical, 698 ; grid-
iron, 320; mercurial, 320; length of
966
Index.
PEN
compound, 80 ; reversible, 80 ; verifi-
cation of laws of, 8 1
Penumbra, 503
Percussion, heat due to, 479
Periscopic glasses, 629
Permanent gases, 380
Persistence of impression on the retina,
625
Perturbations, magnetic, 692, 693
Phenakistoscope, 625
Phenomenon, 5
Phial of four elements, 107
Phonautograph, 287
Phonograph, Edison's, 291
Phosphorescence, 635, 636
Phosphorogenic rays, 573
Phosphoroscope, 636
Photo-electric microscope, 606
Photogenic apparatus, 606
Photographs on paper, 609 ; on albu-
menised paper and glass, 611
Photography, 608-61 1
Photometers, 509, 511
Photophone, 930
Physical phenomena, 5 ; agents, 6 ;
shadows, 503
Physics, object of, I
Physiological effects of the electric dis-
charge, 785; of the current, 827; of
Ruhmkorffs coil, 919
Piezometer, 98
Pigment colours, 570
Pile, voltaic, 804-818
Pipes, organ, 274
Pisa, tower of, 70
Pistol, electric. 793
Piston of air-pump, 190; rod, 467
Pitch, concert, 251 ; of a note, 246 ;
a screw, 45
Plane, 45 ; electrical inclined, 764 ;
wave, 642
Plante's secondary battery, 847
Plants, absorption in, 144
Plate electrical machine, 753
Plates, colours of thin, 650 ; vibrations
of, 282
Plumb line, 68
Pluviometer, 971
Pneumatic syringe, 148, 479
Poggendorffs law, 793
Point, boiling, 366, 367
Points, power of, 742
Poiseuille's apparatus, 215
Polar aurora, 991
Polarisation, 847 ; angle of, 654 ; cur-
rent, 847 ; of electrodes, 806 , by
double refraction, 652 ; by reflection,
PRO
653 ; by single refraction, 655 ; ellip-
tical and circular, 669, 670, 672 ; of
heat, 679 ; galvanic, 806, 847 ; of the
medium, 747 ; plane of, 654 ; plate,
804 ; rotatory, 674
Polarised light, theory of, 66 1 ; colours
produced by the interference of, 662,
668 ; rays, 662
Polariser, 656
Polarising instruments, 656
Polarity, 806 ; boreal, austral, 689
Poles, 803 ; analogous and antilogous,
841 ; of the earth, 698 ; of a magnet,
68 1 ; mutual action of, 682 ; precise
definition of, 684 ; austral and boreal,
689
Polygon of forces, 35
Polyprism, 544
Ponderable matter, 6
Pores, 13
Porosity, 7, 13 ; application of, 15
Portative force, 719
Positive plate, 80 1
Positives on glass, 610
Postal battery, 886
Potential energy, 63 ; of electricity, 738 ;
of a Leyden jar, 782; of a sphere, 741
Pound, 126 ; avoirdupois, 23, 29 ; foot,
60
Powders, radiation from, 443
Power of a lever, 40 ; of a microscope,
594
Presbytism, 619, 629
Press, hydraulic, 109
Pressure, centre of, 103 ; on a body in a
liquid, 113 ; atmospheric, 152 ; amount
of, on human body. 157 ; experiment
illustrating, 200 ; influence on melting
point, 339 ; heat produced by, 479 ;
electricity produced by, 731
Pressures, equality of, 99 ; vertical down-
ward, IOO ; vertical upward, 101 ; in-
dependent of form of vessel, 102 ; on
the sides of vessels, 103
Prevost's theory, 415
Primary coil, 890
Primitive current, 954
Principal current, 954
Principle of Archimedes, 114
Prisms, 543-547 ; double refracting, 659;
Nicol's, 660 ; with variable angle, 544
Problems on expansion of gases, 332 ;
on mixtures of gases and vapours, 384 ;
on hygrometry, 401
Projectile, motion of, 51
Proof plane, 735
Propagation of light, 502
Index.
967
PRO
Protoplasm, 827
Protuberances, 579
Pulley, 41
Pump ,air, 190 ; condensing, 199 ; filter,
196
Pumps, different kinds of, 205 ; suction,
206 ; suction and force, 207
Pupil, 612
Psychrometer, 398, 963
Pyroelectricity, 732
Pyroheliometer, 480
Pyrometers, 311 ; electric, 943
^vUADRANTAL deviation, 715
Quadrant electrometer, 756
RADIANT heat, 515 ; detection and
measurement of, 412 ; causes
which modify the intensity of, 414 ;
Melloni's researches on, 428 ; relation
of gases and vapours to, 438
Radiated heat, .403, 411
Radiating power, 425 ; identity of ab-
sorbing and radiating, 426 ; causes
which modify, &c., 427 ; of gases, 441
Radiation, cold produced by, 495 ; from
powders, 443 ; of gases, luminous, and
obscure, 432 ; laws of, 413 ; solar,
480
Radiative power, 973
Radiometer, 445
Rain, 971 ; clouds, 971 ; bow, 990; fall,
963> 971 J gauge, 971 ; drop, velocity
of, 48
Ramsden's electrical machine, 753
Rarefaction in air-pump, 190 ; by Spren-
gel's pump, 195
Ray. incident, 536 ; luminous, 501 ;
ordinary and extraordinary, 641
Rays, actinic, or Ritteric. 433 ; diver-
gent and convergent, 501 ; frigorific,
422; of heat, 411, 429; invisible,
429 ; obscure. 433 ; path of, in eye,
615 ; polarised, 662 ; transmutation of
thermal, 434
Reaction and action, 39
Reaction machines, 471
Real volume, 14 ; foci, 552 ; focus, 525;
image, 528, 556
Reaumur scale, 303
Receiver of air-pump, 190
Recomposition of white light, 567
Reed instruments, 272
Reeds, free and beating, 272
Reflected light, intensity of, 519
RIN
Reflecting power, 423 ; goniometer,
534; sextant, 521 ; stereoscope, 623 ;
telescope, 598
Reflection, apparent, of cold, 422 ; of
heat, 418 ; from concave mirrors, 419;
irregular, 518; laws of, 417; verifi-
cation of laws of, 420 ; in a vacuum,
421 ; of light, 511-541 ; of sound, 236
Refracting stereoscope, 624 ; telescope,
598
Refraction, 536-545 ; double, 639 ; po-
larisation by, 652 ; explanation of
single, 638 ; of sound, 238
Refractive index, 538 ; determination of,
562 ; of gases, 550 ; of liquids, 549 ;
of solids, 548 ; table of, 550 ; indices
of media of eye, 613
Refractory substances, 338
Refrangibility of light, alteration of, 582
Regelation, 978
Regnault's experiments, 229 ; determi-
nation of density of gases, 336; mano-
meter, 181 ; methods of determining
the expansion of gases, 333 ; of specific
heat, 454 ; of tension of aqueous va-
pour, 356, 358 ; hygrometer, 397
Regulator of the electric light, 835, 836
Reis's telephone, 882
Relay, 886
Remanent magnetism, 880
Repulsions, magnetic, 705 ; electrical
laws of, 731
Reservoir, common, 726
Residual charge, 773
Residue, electric, 773
Resinous electricity, 727, 728
Resistance of a conductor, 825 ; of an
element, 950
Resonance, 237 ; box, 251 ; globe, 255
Rest, 1 8
Resultant of forces, 32-34
Retina, 612; persistence of impression
on, 625
Return shock, 988
Reversible pendulum, 80
Reversion, method of, 696
Rheometer, 821
Rheoscope, 821
Rheoscopic frog, 957
Rheostat, 945
Rhomb, Fresnel's, 671
Rhumbs, 697, 964
Right ascension, 600
Rime, 975
Rings, coloured, 666 ; in biaxial crys-
tals, 667; Newton's, 650, 651; No-
bili's, 850
968
Index.
KIT
Ritchie's experiment, 426
Ritteric rays, 433
Robinson's anemometer, 963
Rock salt, heat transmitted through, 437
Rods, vibrations of, 281
Roget's vibrating spiral, 857
Rose's fusible metal, 340
Rotating mirror, 795
Rotation, electrodynamic and electro-
magnetic, of liquids. 867
Rotation of the earth, 81 ; of magnets
by currents, 910 ; of currents by mag-
nets, 866 ; of induced currents by
magnets, 922
Rotatory power of liquids, 676 ; polari-
sation, 673, 674 ; coloration produced
by, 675
Rousseau's densimeter, 131
Roy and Ramsden's measurement of
linear expansion, 316
Rubbers, 753
Rubidium, 578
Ruhlmann's barometric and thermome-
tric observations, 173
Ruhmkorff's coil, 917 ; effects produced
by, 919
Rumford's photometer, 509
Rutherford's thermometers, 310
QACCHARIMETER, 677
^^ Saccharometer, 127
Safety-valve, 109, 371 ; tube, 379 ;
whistle, 466
Sagitta of meniscus, 163
Salimeters, 130
Salts, decomposition of, 842
Saturation, degree of, 392 ; magnetic,
716 ; of colours, 570
Saussure's hygrometer, 399
Savart's toothed wheel, 241
Scale of hardness, 94
Scales in music, 248 ; chromatic, 250 ;
of a thermometer, 303 ; conversion of,
into one another, 303
Scattered heat, 424; light, 518
Schehallien experiment, 68
Sclerotica, 612
Scott's phonautograph, 287
Screw, ii, 45
Secchi's meteorograph, 963
Secondary axis, 555 ; batteries, 847 ;
currents, 806 ; coil, 890
Second of time, 21, 25
Seconds pendulum, 80
Secular magnetic variations, 692
Segments, ventral and nodal, 216
SOU
Segner's water-wheel, 218
Selenite, 664
Semicircular deviation, 715
Semi-conductors, 725
Semiprism, 526
Semitones, 249
Senarmont's experiment, 406
Sensitive membrane, 229
Serein, 973
Series, thermo-electric, 934
Serum, 12
Sextant, 521
Shadow, 503
Shaft, 467
Shock, electric, 770-780 ; return, 988
Shooting stars, 480
Short sight, 629
Siemens's armature, 912 ; unit, 946 ;
electrical thermometer, 953-
Sight, line of, 595
Silver, voltameter, 845
Simoom, 966
Sine compass, 824
Singing of liquids, 363
Sinuous currents, 859
Sirocco, 966
Size, estimation of, 618
Sleet, 976
Slide valve, 467
Smee's battery, 8il
Snow, 976 ; line, 979
Soap-bubble, colours of, 650
Solar microscope, 605 ; light, thermal
analysis of, 430 ; radiation, 480 ;
spectrum, 564; properties of the, 573;
dark lines of, 574, 579; time, 21 ;
day, 21
SoleiPs saccharimeter, 677
Solenoids, 872-876 ; action of currents
on, 873 ; of magnets and of earth on,
874, 875 ; on solenoids, 876
Solidification, 343 ; change of volume
on, 343, 346 ; retardation of, 345
Solidity, 4, 7
Solids, conductivity of, 404 ; index of
refraction in, 548 ; diamagnetism of,
932 ; linear and cubical expansion of,
3H, 319
Solids, formulae of expansion, 318
Solution, 342
Sondhauss's experiments, 238
Sonometer, 266
Sonorous body, 222
Sound, 221 ; cause of, 223 ; not propa-
gated in vacuo, 222 ; propagated in all
elastic bodies, 224 ; propagation of, in
air, 225 ; causes which influence in-
Index,
969
sou
nsity of, 226 ; apparatus to streng
en 227 ; interference of, 261 ; velocity
of, in gases, 230-232; in liqui ds,2
solids, 235 ; reflection of, 236 ; refrac-
tion of, 237 ; transmission of, 228 ;
waves, 229
Sound, Helmholtz's analysis of, 255
Sound, Konig's apparatus, 255; Kundt's,
277
Sounder, 893
Sounds, intensity of, 289 ; limit of, per-
ceptible, 244 ; synthesis of, 257 ; per-
ceptions of, 260 ; produced by currents,
863
Space, measure of, 22
Spar, Iceland, 659
Spark and brush discharge, 787 ; elec-
trical, 762, 787 ; duration and velocity
of, 795
Speaking trumpet, 239 ; tubes, 228
Specific .gravity, 24, 120, 125 ; bottle,
122; of solids, 121 ; of gases, 335 ;
of liquids, 124; tables of, 125, 126
Specific heat, 448-461 ; compound bo-
dies, 564 ; determination of, by fusion
of ice, 450 ; by method of mixtures,
452 ; by Regnault's apparatus, 454 ;
of solids and liquids, 456, 457 ; of
gases, 460
Specific inductive capacity, 748
Spectacles, 630
Spectra, 648
Spectral analysis, 575 ; colours and pig-
ment, 571
Spectroscope, 576 ; direct vision, 577 ;
experiments with, 578 ; uses of the, 580
Spectrum, calorific, 573 ; chemical, 573
Spectrum, 430; colours of, 566; pure,
565 ; solar, 564, 577
Spectrum, dark lines of, 574
Spectrum, diffraction, 648
Spectrum, luminous properties of, 573 "
Spectrum of aurora borealis, 991 ; pro-
perties of, 573
Specular reflection, 518
Spherical aberration, 533, 558 ; mirrors,
524 ; focus of, 525 ; formulae for, 530
Spheroidal form of liquids, 85 ; state,
o
Spherometer, n
Spiral, 879 ; Roget's vibrating, 857
Spirit-level, in
Sprengel's air-pump, 195
Springs, 998
Stable equilibrium, 71
Stars, spectral analysis of, 582
Staubbach, 77
TEM
Steam-engines, 465 ; boiler, 468 ; double
action, or Watt's, 467; pipe, 197;
various kinds of, 472 ; work of, 473 ;
heating by, 490
Steeling, 855
Stereoscopes, 622-624
Stethoscope, 240
Stills, 376
Stool, insulating, 762
Stopcock, doubly exhausting, 192 ; Gay-
Lussac's, 382
Storms, magnetic, 694
Stoves, 489 ; Norwegian, 410
Stratification of electric light, 920
Stratus, 969
Stringed instruments, 279
Strings, 265 ; transverse vibration of, 265
Subdominant chords, 248
Suction pump, 206 ; and force pump,
207 ; load which piston supports, 208
Sulphate of mercury battery, 812
Sun, 510; analysis of, 579; constitution
of, 579
Sun-spots, 701
Surface level, 68 ; tension, 138
Suspension, axis of, 72 ; Cardan's, 1 60
Suspensory ligament, 612
Swimming, 1 1 9 ; bladder of fishes, 118
Symmer's theory of electricity, 728
Synthesis of sounds, 257
Syphon, 203 ; barometer, 161 ; inter-
mittent, 204 ; recorder, 889
Syren, 242
Syringe, pneumatic, 148, 479
*~pAMTAM metal, 95
J_ Tangent compass, or galvanome-
ter, 823, 846
Tasimeter, 927
Telegraph, cables, Cowper's writing,
887 ; induction in, 888 ; electric, 883 ;
dial, 885 ; Morse's, 886
Telegraphy, duplex, 890
Telephone, 882, 924
Telescopes, 595-601 ; astronomical, 595 ;
Galilean, 597 ; Gregorian, 599 ; Her-
schelian, 60 1 ; Newtonian, 600 ; re-
flecting, Rosse's, 601
Telluric lines, 573
Temper, 95
Temperature, 297, 448 ; correction for,
in barometer, 164 ; critical, 370 ; of a
body, 297 ; determined by specific
heat, 457
Temperature, absolute zero of, 496 ; in-
fluence of, on specific gravity, 124 ;
U U
9/0
I tide. v.
TEM
mean, 992 ; how modified, 993 ; dis-
tribution of, 997 ; of lakes, seas, and
springs, 998
Temperatures, different remarkable, 312 ;
influence on expansion, 318
Tempering, 91, 95
Tenacity, 7, 92
Tension, 118, 736, 918 ; maximum of,
electrical machine, 755 ; maximum of,
vapours, 353 ; of aqueous vapour at
various temperatures, 357-361 ; of
vapours of different liquids, 359 ; of
mixed liquids in two communicating
vessels, 361 ; free surface, 138
Terquem's experiment, 735
Terrestrial currents, 898 ; heat, 481 ;
magnetic couple, 690 ; telescope, 596
Terrestrial gravitation, 68, 83
Terrestrial magnetic couple, 690
Tetanus, 827
Thallium, 578
Thaumatrope, 625
Theodolite, 10
Theory, 5 ; of induction, 747
Thermal analysis, 430 ; unit, 447, 484 ;
springs, 998
Thermal effects of the current, 829, 830
Thermal rays, transmutation of, 434 ;
unit, 447
Thermo-barometer, 369
Thermocrose, 436
Thermo-electric battery, 412, 938 ;
couples, 936 ; currents, 935, 937, 941 ;
pile, 412, 431, 937 ; series, 934
Thermo-electricity, 933
Thermo-element, 934
Thermometer, electric, 792
Thermometers, 298 ; Becquerel's elec-
trical, 942 ; correction of readings, 328 ;
division of tubes in, 299 ; filling, 300 ;
graduation of, 301 ; determination of
fixed points of, 302 ; scale of, 303 ;
displacement of zero, 304 ; limits to
use of, 305 ; alcohol, 306 ; conditions
of delicacy of, 307 ; Kinnersley's, 779 ;
Leslie's, 308 ; Matthiessen's, 308 ;
Breguet's, 309 ; maximum and mini-
mum, 310; Siemens' electrical, 953 ;
weight, 323 ; air, 331, 332
Thermometry, 297-300
Thermo-multiplier, Melloni's, 940
Thermoinotive wheel, 476
Thermoscope, 308
Thomson's electrometers, 780, 781 ; gal-
vanometer, 822 ; apparatus for atmo-
spheric electricity, 981
Thread of a screw, 45
VAC
Thunder, 986
Timbre, 246
Time, measure of, 21 ; mean solar, 21
Tint, 570 ; transition, 677
Tones, combinational, 263 ; differential,
263
Tonic, 248
Torricelli's experiment, 155; theorem,
210 ; vacuum, 162
Torsion, angle of, 90 ; balance, 90, 704,
734 ; force of, 90
Total reflection, 540
Tourmaline, 658, 732 j pincette, 666
Tourniquet, hydraulic, 217
Traction, elasticity of, 89
Trajectory, 25
Transformation of energy, 65
Transition tint, 677
Translucent bodies, 500
Transmission of heat, 403 ; of light, 499,
542 ; by the current, 843
Transmission of sound, 228
Transparency, 7, 500
Transparent media, 542-549
Transpiration of gases, 143
Triad, harmonic, 247
Triangle, 281
Triangle of forces, 35
Trumpet, speaking, ear, 239
Tubes, Geissler's, 195, 921 ; luminous,
789 ; safety, 379 ; speaking, 228
Tuning-fork, 251, 281, 290
Turbines, 218
Twilight, 518
Tympanum, 260
Tyridall's researches, 431, 974, 979
UNANNEALED glass, colours pro-
duced by, 668
Undershot wheels, 218
Undulation, length of, 225, 637
Undulatory theory, 499
Uniaxial crystals, 640 ; double refraction
in, 642 ; positive and negative, 643
Unit jar, Harris's, 778 ; Siemens's, 946 ;
thermal, 447
Unit of length, area and volume, 22 ;
heat, 447 ; of work, 62
Unstable equilibrium, 71
Urinometer, 130
VACUUM, application of, to con-
struction of air-pump, 190; extent
of, produced by air-pump, 191 ; fall of
bodies in a, 77 > formation of vapour
Index.
971
YAL
in, 352; heat radiated in, 413; re-
flection in a, 421 ; Torricellian, 162
Valve, safety, 109, 371 ; chest, 466
Vane, electrical, 764
Vaporisation, 350 ; latent heat of, 372,
462
Vapour, aqueous, tension of, at various
temperatures, 357-361 ; formation of,
in closed tube, 370 ; latent heat of, 372
Vapours, 349 ; absorption of heat by.
435 ; absorptive powers of, 440 ;
density of, Gay-Lussac's method, 380 ;
Ilofmann's, 387; determination of
latent heat of, 461 ; Dumas 's method,
388; elastic force of, 351; formation
of, in vacuo, 352 ; saturated, 353 ;
unsaturated, 354 ; tension of different
liquids, 359 ; of mixed liquids, 360 ;
in communicating vessels, 361
Variations, annual, 693 ; accidental,
694 ; barometric, 165 ; causes of,
1 66; diurnal, 693; relation of, to
weather, 166 ; in magnetic declination,
691, 695
Varley unit, 946
Velocity, 25 ; direction of, 56 ; of efflux,
210 ; of electricity, 795 ; of light,
505-507 ; graphic representation of
changes of, 56 ; molecular, 294 ; of
sound in gases, 230, 231 ; formula for
calculating, 231; of winds, 964
Velocities, composition of, 52 ; examples
of, 25
Vena contracta, 213
Ventral and nodal segment, 216, 269,
274
\ ernier, 10
Vertical line, 68
Vestibule of the ear, 260
Vibrating spiral, Roget's, 857
Vibration, 222 ; arc of, 55 ; produced by
currents, 881 ; of tuning-forks, 290
Vibrations, 262 ; formulae, 275 ; of
membranes, 283 ; laws of, 267 ; mea-
surement of number of, 241 ; number
of, producing each note, 251 ; of mu-
sical pipe, 275 ; of rods, 281 ; of
plates, 282; of strings, 265, 267, 270
Victoria Regia, 485
View, field of, 593
Vinometers, 130
Virtual and real images, 514 ; focus,
525 ; velocity, 46
Viscosity, 97 ; of gases, 246
Vision, distance of distinct, 619 ; bino-
cular, 621
Visual angle, 617
WHI
Vis viva, 60, 448, 477
Vital fluid, 797
Vitreous body, 612 ; electricity, 727 ;
fusion, 338 ; humour, 612
Vocal chords, 259
Volatile liquids, 349
Volta's condensing electroscope, 779 ;
electrophorus, 752; fundamental ex-
periment, 798
Voltaic arc, 833 ; couple, 801 ; currents,
819 ; induction, 897 ; pile and battery,
804,805,815,832
Voltameter, silver, 845 ; Faraday's, 845
Volume, 22 ; unit of, 22, 24 ; determi-
nation of, 115; change of, on solidi-
fication, 346 ; of a liquid and that of
its vapour, relation between, 390
Volumometer, 180
Von Ebner's electrical machine, 794
WALKER'S battery, 811, 883
Water bellows, 197 ; decompo-
sition of, 124 ; hammer, 77 ; hot, heat-
ing by, 492 ; level, no
Water, maximum density of, 330 ; spouts,
972 ; wheels, 218
Watt's engine, 467
Wave, condensed, 225 ; expanded, 225 ;
lengths, 637, 649 ; plane, 642
Weather, its influence on barometric va-
riations, 165, 1 66; glasses, 168; charts,
9670; forecasts, 9670:
Wedge, 44
Wedgewood's pyrometer, 311
Weighing, method of double, 76
Weight, 23, 83 ; relative, 43 ; of bodies
weighed in air, correction for loss of,
402; of gases, 150; thermometer, 324
Weights and measures, 126
Wells, artesian, 112
Wells's theory of dew, 975
Wet bulb hygrometer, 398
Wheatstone's bridge, 948 ; photometer,
509 ; rheostat, 945 ; rotating mirror,
795 ; and Cooke's telegraph, 884
Wheel and axle, 42
Wheel barometer, 168; thermomotive,
476
Wheels, friction, 78; escapement, 82 ;
water, 218
Whirl, electrical, 764
Whispering galleries, 237
Whistle, safety, 466
White light, decomposition of, 564 ; re-
composition of, 567
White's pulley, 41
972
Index,
WIE
Wiedemann and Franz's tables of con-
ductivity, 404
Wiedemann's determination of electro-
motive force, 952
Wild's magneto-electrical machine, 913
Winckler's cushions, 753
Wind chest, 272 ; instruments, 270, 280
Winds, causes of, 965 ; direction and
velocity of, 963, 964, 993 ; law of ro-
tation of, 967 ; periodical, regular, and
variable, 966
Wines, alcoholic value of, 378
Wollaston's battery, 805 ; cryophorus,
373 ; doublet, 585
W T ood, conductivity of, 404
Wood's fusible metal, 340
Work, 34, 60 ; measure of, 61 ; of an
engine, 472 ; rate of, 473 ; unit of, 62 ;
ZON
internal and external, of bodies, 295 ;
of a voltaic battery, 832 ; required for
the production of electricity, 761
Writing telegraphs, 886, 887
YARD, British, 22, 126
Young and Fresnel's experiment,
645
yAMBONFS pile, 817
/^ Zero, absolute, 496 ; aqueous va-
pours below, 355 ; displacement of,
304
Zinc, amalgamated, 816 ; carbon battery,
810
Zone, isothermal, 995
LONDON : PRINTED BY
SPOTTISWOODE AND CO., NEW-STREET SQUARE
AND PARLIAMENT STREET
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