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tricity of contrary kinds, on the opposite faces of glass or other
non-conductor, by means of metal maintained in contact with
the glass, it is evident that the form of the glass and of the
metal in contact with it have no influence on the effects.
Neither has the thickness or volume of the metal any relation
to the results. Thus the glass, whose opposite faces are charged,
may have the form of a hollow cylinder or sphere, or of a
common flask or bottle, and the metal in contact with it need
not be massive or solid plates, but merely a coating of metallic
foil.

1760. The Leyden jar. In experimental researches, there-
fore, the form which is commonly given to the glass, with a
view to develope the above effects, is that of a cylinder or jar,
A u, fig. 500., having a wide mouth and a flat bottom. The
shaded part terminating at C is a coating of tinfoil placed on
the bottom and sides of the jar, a similar coating
being attached to the corresponding parts of the
interior surface. To improve the insulating power
of the glass it is coated above the edge of the tin-
foil with a varnish of gum-lac, which also renders
it more proof against the deposition of moisture.
A metallic rod, terminated in a ball D, descends into
the jar, and is jointed in contact with the inner
coating.

This apparatus is generally known by the name
of the Leyden phial, the experiments produced with
it having been first exhibited at the city of Leyden,
in Holland.

To understand the action of this apparatus it is only
necessary to consider the inner coating and the metallic rod as
L 6




228 ELECTRICITY.

representing the metallic surface A B, Jig. 499., and the outer
surface A' B', the jar itself playing the part of the inter-
vening non-conducting medium. If the ball D be put in com-
munication by a metallic chain with the conductor of the
electric machine, and the external coating c B with the ground,
the jar will become charged with electricity, in the same manner
and on the same principles exactly as has been explained in
the case of the metallic surfaces A' B' and A B, Jig. 499.

If, when a charge of electricity is thus communicated to the
jar, the communication between D and the conductor be removed,
the charge will remain accumulated on the inner coating of the
jar. If in this case a metallic communication be made between
the ball D and the outer coating, the two opposite electri-
cities on the inside and outside of the jar will rush towards
each other and will suddenly combine. In this case there is no
essential distinction between the functions of the outer and
inner coating of the jar, as may be shown by connecting the
inner coating with the ground and the outer coating with the
conductor. For this purpose, it is only necessary to place the
jar upon an insulating stool, surrounding it by a metallic chain
in contact with its outer coating, which should be carried to
the conductor of the machine; while the ball r>, which com-
municates with the inner coating, is connected by another chain
to the ground. In this case the electricity will flow from the
conductor to the outer coating, and will be accumulated there
by the inductive action of the inner coating, and all the effects
will take place as before.

If, after the jar is thus charged, the communication between
the outer coating and the conductor be removed, and a metallic
communication be made between the inner and outer coating,
the electricities will, as before, rush towards each other and
combine, and the jar will be restored to its natural state.

To charge the jar internally, it will be sufficient to hold it
with the hand in contact with the external coating, presenting
the ball D to the conductor of the machine. The electricity
will flow from the conductor to the inner coating, and the
external coating will act inductively, being connected through
the hand and body of the operator with the earth.

1761. Effect of the metallic coating. The metallic coatings
of the jar have no other effect than to conduct the electricity
to the surface of the glass, and when there, to afford it a free



THE LEYDEN JAR. 229

passage from point to point. Any other conductor would,
abstractedly considered, serve the same purpose ; and metallic
foil is selected only for the facility and convenience with which
it may be adapted to the form of the glass, and permanently
attached to it. That like effects would attend the use of any
other conductor may be easily shown.

1762. Water may be substituted for the metallic coating.
Let a glass jar be partially filled with water, and hold it in the
hand by its external surface. Let a chain or rod connected
with the conductor of an electric machine be immersed in
the water. A stream of electricity will flow from the machine
to the water, exactly as it did from the machine to the inner
coating of the jar ; and the inductive action of the hand
communicating through the body of the operator with the
ground, will produce a charge of electricity in the water upon
exactly the same principle as the inductive action of the
external coating of the jar communicated the charge of electri-
city on the internal coating. If, after the charge has been
communicated in the water, the operator plunge his other
hand in the water, so as to form a communication between the
water within the jar and the hand applied to its external
surface, the opposite electricities will rush towards each other
through the hand of the operator, and their motion will be
rendered sensible by a strong nervous convulsion.

1763. Experimental proof that the charge adheres to the
glass and not to the coating. The electricity with which the
jar is charged in this case resides, therefore, on the glass, or on
the conductor by which it passes to the glass, or is shared by
these.

To determine where it resides, it is only necessary to provide
means of separating the jar from the coating after it has been
charged, and examining the electrical state of the one and the
other. For this purpose let a glass jar be provided, having a
loose cylinder of metal fitted to its interior, which can be.
placed in it or withdrawn from it at pleasure, and a similar loose
cylinder fitted to its exterior. The jar being placed in the
external cylinder, and the internal cylinder being inserted in it,
let it be charged with electricity by the machine in the manner
already described. Let the internal cylinder be then removed,
and let the jar be raised out of the external cylinder. The two
cylinders being then tested by an electroscopic apparatus, will



230



ELECTRICITY.



be found to be in their natural state. But if an electroscope
be brought within the influence of the internal or external
surface of the glass jar, it will betray the presence of the one
or the other species of electricity. If the glass jar be then in-
serted in another metallic cylinder made to fit it externally,
and a similar metallic cylinder made to fit it internally be
inserted in it, it will be found to be charged as if no change had
taken place. On connecting by metallic communication the
interior with the exterior, the opposite electricities will rush
towards each other and combine. It is evident, therefore, that
the seat of the electricity, when a jar is charged, is not the
metallic coating, but the surface of the glass under it.

1764. Improved form of Ley den jar. An improved form
of the Leyden jar is represented mjfig. 501. Besides the pro-
visions which have been already explained,
there is attached to this jar a hollow brass cup
C cemented into a glass tube. This tube passes
through the wooden disk which forms the cone
of the jar, and is fastened to it. It reaches to
the bottom of the jar. A communication is
formed between c and the internal coating by
a brass wire terminating in the knob D. This
wire, passing loosely through a small hole in
the top, may be removed at pleasure for the
purpose of cutting off the communication
between the cup and the interior coating. This
wire does not extend quite to the bottom of the
jar, but the lower part of the tube is coated
with tinfoil, which is in contact with the wire,
and extends to the inner coating of the jar.

At the bottom of the jar a hook is provided,
by which a chain may be suspended so as to form a communi-
cation between the external coating and other bodies. When
ajar of this kind is once charged, the wire may be removed or
allowed to fall out by inverting the jar, in which case the jar
will remain charged, since no communication exists between
its internal and external coating ; and as the internal coating is
protected from the contact of the external air, the absorption of
electricity in this case is prevented. An electric charge may
thus be transferred from place to place, and preserved for any
length of time.




Fig. 501.



THE LEYDEN JAR. 231

In the construction of cylindrical jars it is not always possible
to obtain glass of uniform thickness, for which reason jars are
sometimes provided of a spherical form.

1765. Charging a series of jars by cascade. In charging a
single jar, an unlimited number of jars, connected together by
conductors, may be charged with very nearly the same quantity
of electricity. For this purpose let the series of jars be placed
on insulating stools, as represented in fig. 502., and let c be




Fig. 502.

metallic chains connecting the external coating of each jar with
the internal coating of the succeeding one. Let D be a chain
connecting the first jar with the conductor of the chain, and D'
another chain connecting the last jar with the ground. The
electricity conveyed to the inner coating of the first jar A acts
by induction on the external coating of the first jar, attracting
the negative electricity to the surface, and repelling the
positive electricity through the chain c to the inner coating
of the second jar. This charge of positive electricity in the
second jar acts in like manner inductively on the external coat-
ing of this jar, attracting the negative electricity there, and
repelling the positive electricity through the chain c to the
internal coating of the third jar ; and in the same manner the
internal coating of every succeeding jar in the series will be
charged with positive electricity, and its internal coating with
negative electricity. If, while the series is insulated, a dis-
charger be made to connect the inner coating of the first with
the outer coating of the last jar, the opposite electricities will
rush towards each other, and the series of jars will be restored
to their natural state.

1766. Electric battery When several jars are thus com-
bined to obtain a more energetic discharge than could be formed
by a single jar, the system is called an electric battery, and
the method of charging it, explained above, is called charging
by cascade.



232 ELECTRICITY.

After the jars have been thus charged, the chains connecting
the outer coating of each jar with the inner coating of the suc-
ceeding one are removed, and the knobs are all connected one
with another by chains or metallic rods, so as to place all the
internal coatings in electric connection, and the outer coatings
are similarly connected. By this expedient the system of jars
is rendered equivalent to a single jar, the magnitude of whose
coated surface would be equal to the sum of all the surfaces of
the series of jars. The battery would then be discharged by
placing a conductor between the outer coating of any of the
jars and one of the knobs.

If s express the total magnitude of the coating of the series
of jars, the total charge of the battery will be expressed ap-
proximately by



1767. Common electric battery. It is not always convenient,
however, to practise this method. The jars composing the bat-
tery are commonly placed in a box, as represented \\ijig. 503.,
coated on the inside with tinfoil, so as to form a metallic commu-
nication between the external coating of all the jars. The knobs,
which communicate with their internal coating, are connected
by a series of metallic rods in the manner represented in the

figure ; so that there is a con-
tinuous metallic communica-
tion between all the internal
coatings. If the metallic rods
which thus communicate with
the inner coating be placed
in communication with the
Fig. 5C3. conductor of a machine, while

the box containing the jars

is placed in metallic communication with the earth, the battery
will be charged according to the principles already explained
in the case of a single jar, and the force of its charge will be
equal to the force of the charge of a single jar, the magnitude
of whose external and internal coating would be equal to the
sum of the internal and external coating of all the jars com-
posing the battery.

1768. Method of indicating and estimating the amount of




THE LEYDEX JAR. 233

the charge. In charging a jar or a battery there is no ob-
vious means by which the amount of the charge imparted
to the jar can be indicated. It is to be considered that the
internal coating is, in effect, a continuation of the conductor ;
and if the jars had no external coating, the communication of
the internal coating with the conductor would be attended
with no other effect than the distribution of the electricity over
the conductor and the internal coating, according to the laws of
electrical equilibrium ; but the effect of the external coating is
to dissimulate or render latent the electricity as it flows from
the conductor, so that the repulsion of the part of it which
remains free is less than the expansive force of the electricity
of the conductor, and a stream of the fluid continues to flow
accordingly from the conductor to the internal coating; and
this process continues until the increasing force of the free
electricity on the internal coating of the jars becomes so great,
that the force of the fluid on the condenser can no longer over-
come it, and thus the flow of electricity to the jars from the
conductor will cease.

It follows, therefore, that during the process of charging the
jars, the depth or tension of the electricity on the conductor is
just so much greater than that of the free electricity on the in-
terior of the jars, as is sufficient to sustain the flow of electricity
from the one to the other ; and as this is necessarily so extremely
minute an excess as to be insensible to any measure which
could be applied to it, it may be assumed that the depth of
electricity on the conductor is always equal to that of the free
electricity on the interior of the jars. If e therefore express
the actual depth of the electric fluid at any time on the interior
coating, (1 m 2 ) x e will express the depth of the free electricity;
and since, throughout the process, m does not change its value,
it follows that the actual depth of electricity, and therefore the
actual magnitude of the charge, is proportionate to the depth of
free electricity on the interior of the jar, which is sensibly the
same as the depth of free electricity on the conductor. It follows,
therefore, that the magnitude of the charge, whether of a single
jar or several, will always be proportionate to the depth of
electricity on the conductor of the machine from which the charge
is derived. If, therefore, during the process of charging a jar
or battery, an electrometer be attached to the conductor, this
instrument will at first give indications of a very feeble elec-



234 ELECTRICITY.

tricity, the chief part of the fluid evolved being dissimulated on
the inside of the jars; but as the charge increases, the indications
of an increased depth of fluid on the conductor become apparent ;
and at length, when no more fluid can pass from the conductor
to the jars, the electrometer becomes stationary, and the fluid
evolved by the machine escapes from the points or into the
circumjacent air.

The quadrant electrometer, described in (1757), is the indi-
cator commonly used for this purpose, and is inserted in a hole
on the conductor. When the pith ball attains its maximum
elevation, the charge of the jars may be considered as complete.
The charge which a jar is capable of receiving, besides being
limited by the strength of the glass to resist the mutual attrac-
tion of the opposite fluids, and the imperfect insulating force of
that part of the jar which is not coated, is also limited by the
imperfect insulating force of the air itself. If other causes,
therefore, allowed an unlimited flow of electricity to the jar,
its discharge would at length take place by the elasticity of
the free electricity within it surmounting the confining pres-
sure of the air, and accordingly the fluid of the interior would
pass over the mouth of the jar, and unite with the opposite
fluid of the exterior surface.



CHAP. VIII.

LAWS OF ELECTRICAL FORCES.

1769. Electric forces investigated by Coulomb. It is not
enough to ascertain the priciples which govern the decomposition
of the natural electricity of bodies, and the reciprocal attraction
and repulsion of the constituent fluids. It is also necessary to
determine the actual amount of force exerted by each fluid in
repelling fluid of the like or attracting fluid of the opposite
kind, and how the intensity of this attraction is varied by vary-
ing the distance between the bodies which are invested by the
attracting or repelling fluids.

By a series of experimental researches, which rendered his
name for ever memorable, COULOMB solved this difficult and



LAWS OF ELECTRICAL FORCES. 235

delicate problem, measuring with admirable adroitness and pre-
cision these minute forces by means of his electroscope or
balance of torsion, already described (1756).

1770. Proof-plane. The electricity of which the force was
to be estimated was taken up from the surface of the electrified
c body upon a small circular disk c, fig. 504., coated
with metallic foil, and attached to the extremity of a
delicate rod or handle A B of gum-lac. This disk,
called a PROOF-PLANE, was presented to the ball sus-
pended in the electrometer of torsion (1756), and the
intensity of its attraction or repulsion was measured
by the number of degrees through which the suspend-



A



ing fibre or wire was twisted by it.



Fig. 504. The extreme degree of sensibility of this apparatus
may be conceived, when it is stated that a force equal to the 340th
part of a grain was sufficient to turn it through 360 degrees ;
and since the reaction of torsion is proportional to the angle
of torsion, the force necessary to make the needle move through
one degree would be only the 122,400th part of a grain. Thus
this balance was capable of dividing a force equal to a single
grain weight into 122,400 parts, and rendering the effect of
each part distinctly observable and measurable.

1771. Law of electrical force similar to that of gravitation.
By these researches it was established, that the attraction
and repulsion of the electric fluids, like the force of gravitation,
and other physical influences which radiate from a centre, vary
according to the common law of the inverse square of the dis-
tance ; that is to say, the attraction or repulsion exerted by a
body charged with electricity, or, to speak more correctly, by
the electricity with which such a body is charged, increases in
the same proportion as the square of the distance from the body
on which it acts is diminished, and diminishes as the square of
that distance is increased.

In general, if f express the force exerted by any quantity of
electric fluid, positive or negative, at the unit of distance,

^ will express the force which the same quantity of the same

fluid will exert at the distance D.

In like manner, if the quantity of fluid taken as the unL

f
exercise at the distance Dthe force expressed by-^j, the quantity



236



ELECTRICITY



expressed by E, will exert at the same distance D the force
expressed by

fXE
V*s-'

D 2

These formulae have been tested by numerous experiments
made under every possible variety of conditions, and have
been found to represent the phenomena with the greatest
precision.

1772. Distribution of the electric fluid on conductors. The
distribution of electricity upon conductors can be deduced as
a mathematical consequence of the laws of attraction and re-
pulsion which have been explained above, combined with the
property in virtue of which conductors give free play to these
forces. The conclusions thus deduced may further be verified
by the proof plane and electrometer of torsion, by means of
which the fluid diffused upon a conductor may be gauged, so
that its depth or intensity at every point may be exactly ascer-
tained ; and such depths and intensities have accordingly been
found to accord perfectly with the results of theory.

1773. It is confined to their surfaces. Numerous facts
suggest the conclusion that the electricity with which a con-
ductor is charged is either superficial, or very nearly so.

If an electrified conductor be pierced with holes a little
greater than the proof plane (Jig. 504.) to different depths,
that plane, inserted so as to touch the bottom of these holes,
will take up no electricity.

If a spheroidal metallic body
A, Jig. 505., suspended by a silken
thread, be electrified, and two
thin hollow caps BB and B'B'
made to fit it, coated on their
inside surface with metallic foil,
and having insulating handles
cc' of gum-lac, be applied to it,
on withdrawing them the sphe-
roid will be deprived of its elec-
tricity, the fluid being taken off by the caps.

Although it follows, from these and other experimental tests,
as well as from theory, that the diffusion of electricity on con-




Fig. 505.



LAWS OF ELECTRICAL FORCES. 237

ductors is nearly superficial, it is not absolutely so. If one
end of a metallic rod, coated with sealing-wax, be presented to
any source of electricity, the fluid will be received as freely
from the other end, as if its surface were not coated with a
non-conductor. It follows from this that the electricity must
pass along the rod sufficiently within the surface of the metal
which is in contact with the wax to be out of contact with the
wax, which, by its insulating virtue, would arrest the progress
of the fluid.

1774. How the distribution varies. It remains, however, to
ascertain how the intensity of the fluid, or its depth on different
parts of a conductor, varies.

There are some bodies whose form so strongly suggests the
inevitable uniformity of distribution as to render demonstration
needless. In the case of a sphere, the symmetry of form alone
indicates the necessity of an uniform distribution. If, then,
the fluid be regarded as having an uniform depth on every
part of a conducting sphere, exactly as a liquid might be uni-
formly diffused over the surface of the globe, the total quantity
of fluid will be expressed by multiplying its depth by the super-
ficial area of the globe.

1775. Distribution on an ellipsoid. If the electrified con-
ductor be not a globe, but an elliptical spheroid, such as A A',
fig. 506., the fluid will be found to be accumulated in greater

quantity at the small ends A and A' than at
the sides BB', where there is less curvature.
} This unequal distribution of the fluid is re-

presented by the dotted line in the figure.
Fig. 506. It follows from theory, and it is confirmed

by observation, that the depth of the fluid at A and A' is greater
than at BB' in the ratio of the longer axis A A' of the ellipse to
the shorter axis BB'.

If, therefore, the ellipsoid be very elongated, as in fig. 506.,
the depth of the fluid at the ends A and A'
will be proportionally greater.

1776. Effects of edges and points

Fig. 507. ^ tne conductor be a flat disk, the

depth of the fluid will increase from its

centre towards its edges. The depth will, however, not vary

sensibly near the centre, but will augment rapidly in ap-



238 ELECTRICITY.

preaching the edge, as represented \i\fig. 508., where A and B
are the edges, and c the centre of the disk, the depth of the
fluid being indicated by the dotted line.




Fig. 508.

It is found in general that the depth of the fluid increases in
a rapid proportion in approaching the edges, corners, and ex-
tremities, whatever be the shape of the conductor. Thus,
when a circular disk or rectangular plate has any considerable
magnitude, the depth of the electricity is sensibly uniform at
all parts not contiguous to the borders ; and whatever be the
form, whether round or square, if only it be terminated by
sharp angular edges, the depth will increase rapidly in approach-



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