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creases as the ellipsoid becomes more and more pointed until
finally the particles of air adjacent to the point become charged.
Having like charges, these particles repel each other and are
repelled from the point. They therefore move off, giving way for



28



ELEMENTS OF ELECTRICITY.



others which likewise become charged and move off, thus produc-
ing a continuous electric wind and rapidly discharging the body.
In consequence of the foregoing, all points, sharp corners and
angles, unless they be designedly used, are carefully avoided in
electrical apparatus.

43. Franklin's Experiment. To illustrate the effect of points
Franklin devised the following experiment. From the ceiling
there is suspended by a silk thread a pith ball as large as a marble
and upon the floor immediately beneath is placed a glass jar upon
whose mouth is balanced a metal ball (Fig. 15). The thread is of





Fig. 15.

such length that the pith ball hangs against the side of the metal
ball. A charge is communicated to the metal ball and the pith
ball is at once repelled and hangs at a distance of four or five
inches. If now a sharp-pointed wire or a needle held in the hand
be brought up to within six or eight inches of the metal ball, its
charge is instantly lost as will be shown by the pith ball falling
against it at once. In the dark a faint light, like that of a firefly,
will be seen around the point of the needle. Franklin stated that
the needle drew the electric fire from the ball. A more accurate
explanation is that the charge upon the ball induced up through
the body of the experimenter and out to the needle an opposite
charge which escaped from the point, passed over to the ball and
neutralized its charge. This experiment is noteworthy as it
suggested to Franklin the invention of the lightning-rod.

44. Other Experiments with Points. The existence of the
electric wind referred to above can be shown in several ways. If




STATIC ELECTRICITY. 29

a point attached to a charged conductor be held near the face the
wind can be distinctly felt. If such a point be held close to the
flame of a candle the flame will be blown to one side or perhaps
even extinguished.

As the charged particles of air are repelled from the point, the
point must experience an equal
repulsion in the opposite direction.
This is illustrated by tjie electric
whirl shown in Fig. 16. It consists
of a light metal hub with a set of
pointed wire spokes, the ends all
being bent at right angles and all
pointing in the same direction,
clockwise or counter-clockwise.
The hub is placed upon a pointed ^ 77"

pivot so as to turn freely like a com-
pass needle. The pivot is connected to an electric machine and
when a continuous charge is supplied the whirl rotates in the
opposite direction to that in which the ends of the wires point.

There is a final point in connection with this electric wind which
is to be noted. Just as the spray from an atomizer moistens the
surface against which it is directed, so the electrified particles of
air striking the surface of a non-conductor impart a charge to this
surface. This property is utilized in the operation of certain
electric machines described in the next chapter.

45. Division of Charge. If a charged body be brought into
contact with one not charged, both being insulated, the charge is
divided between the two in proportion to their electric capacities,
a property to be defined later (Par. 79). If both bodies be charged
they may be considered to make common stock of their charges
and to redistribute the total as stated above. This is true as well
for charges of opposite kinds; enough of the greater charge is
consumed to neutralize the lesser and the remainder, whether
positive or negative, is distributed between the two bodies.
Spheres of equal size have equal capacities, therefore, if an in-
sulated charged sphere be touched by an equal uncharged one,
likewise insulated, the original charge will be divided into halves.
This enables us to get two similar and equal charges and, as will
shortly be shown, is of very great importance in the determina-
tion of the laws of electrical attraction and of repulsion and in
the measurement of electrical charges.



30



ELEMENTS OF ELECTRICITY.



CHAPTER 6.

ELECTRICAL MACHINES.

46. Kinds of Machines. In the preceding chapters we have
seen how electric charges may be produced first by friction of dis-
similar substances and second by influence, as typically in the
case of the electrophorus. Based upon these two principles there
have been constructed two distinct classes of machines designated
respectively as frictional and influence machines. These substi-
tute for the intermittent motion of friction and for the alternate
lowering and raising of the disc of the electrophorus a motion of
rotation by which wasteful expenditure of energy is avoided, the
production of the charge becomes continuous, and a much greater
charge can be obtained than by the other means. Many kinds
have been constructed and though they are of interest the limits
of time and space restrict us to a brief description and explanation
of a typical form of each.

47. Frictional Machines. Frictional machines comprise three
parts, the material which is rubbed, the rubber and the body,
called the prime conductor, upon which the charge is accumulated.




Fig. 17.

The earliest form, invented by Von Guericke, consisted of a globe
of sulphur cast upon a wooden axis by which it was rotated. As
the globe revolved it was pressed by the bare hand and the charge
was gathered by a light chain which dangled against the globe



STATIC ELECTRICITY. 31

and hung from the prime conductor, an iron bar suspended by
silk chords. Many changes and improvements were made by
subsequent inventors. The operation of the modern machine is
best explained from the form shown in Fig. 17, the cylinder
machine.

48. Cylinder Machine. This consists of a glass cylinder A
rotating on a horizontal axis, a hair-stuffed pad B pressing
against one side of the cylinder and the prime conductor C placed
on the other side and insulated upon a glass support. This con-
ductor is of hollow brass, of the shape shown, from one end of
which projects a T-shaped rod carrying on its outer side a row of
needle-like spikes. The quantity of electricity produced depends
upon the extent of the two surfaces in contact and also upon the
material of which these consist. The farther these are apart in
the list of substances in Par. 23, the greater the electrical effect
produced by rubbing them together. The material of the cylinder,
glass, being near the top of the list, the rubber should be some
substance near the bottom. The metals come near the bottom
but their rigidity interferes with their use as rubbers. However,
certain metals dissolve readily in mercury producing a more or
less pasty amalgam which alone or mixed with grease may be
smeared upon the rubber. Zinc, tin and the sulphide of tin are
used in these amalgams.

The operation of the machine is as follows: The cylinder is
rotated in a clockwise direction, the glass becomes positively
electrified, the rubber negatively. As the positive charge on the
surface of the glass comes around opposite the prime conductor,
the points are said to collect it or take it off, but actually a nega-
tive charge is induced on the near end of this conductor, a positive
charge on the far end, the negative charge escapes from the needle
points in an electric wind, strikes against the cylinder and neutral-
izes the positive charge on its surface (Par. 43) and the conductor
acquires an increasing positive charge.

If the rubber is insulated, a negative charge may be drawn from
it but it is generally connected to the ground by means of a light
chain or otherwise.

More modern forms use rotating glass plates instead of the
cylinder but the principle of their operation is the same. It
will be noted that although designated frictional machines, in-
fluence as well as friction is involved in the production of the



32



ELEMENTS OF ELECTRICITY.



charge. ' They are very sensitive to hygroscopic moisture and
frequently fail to work on account of atmospheric conditions,
for which reason they are now superseded by the influence
machines.

49. Toepler's Influence Machine. This machine, as shown in
its simplest form in Fig. 18, consists of two plates of glass mounted




Fig. 18.

a short distance apart upon a common horizontal axis about which
one may be rotated, the other one being fastened rigidly to the
frame of the apparatus. The rotating plate is circular in form.
Fig. 19 (in which for clearness the relative proportions and posi-
tions of the parts have been greatly distorted) represents an
edgewise view of the glass plates, the eye of the observer being
supposed to travel around the circumference while being con-
tinually directed towards the axis of the machine. The letters on
these two figures correspond. A represents the fixed plate and B
the moving one, the direction of motion being indicated by the
arrow. On the outer surface of A and diametrically opposite to
each other are the two field plates C and D. These are sheets
of tin-foil glued to the glass, their thickness being greatly exagger-
ated in Fig. 19. Extending from each of these field plates there is
a conductor which passes around the outer edge of the two glass
plates to the appropriating brushes E and F on the outer side



STATIC ELECTRICITY.



33



of the revolving plate. These brushes are of fine brass wire
like a paint brush and sweep along the face of the plate B as
it revolves. On the outer surface of B there are glued six
carriers, G, H, J, K, L, M,
likewise of tin-foil. Outside
of these and opposite the
farther edge of the field plates
are the neutralizing brushes,
N and P, connected to each
other by a conductor. Mid-
way between the appropriating
and the neutralizing brushes
are the two combs, Q and R,
which connect to the two dis-
charging knobs, S and T. These
knobs are on the ends of rods
which by means of the glass
handles U and W may be slid
in or out thus adjusting the
distance between the knobs.
The operation of the machine
is as follows: From an excited
glass rod Z a small initial
charge is imparted to the plate
C. This induces a negative
charge on the inner side of the
carrier H and a positive charge
on the outer side. As the plate
B rotates H moves to the po-
sition J where it is touched
by the neutralizing brush N
which allows its free positive
charge to escape, as shown by the small arrow, and leaves it with
a negative charge. Upon reaching the position K the greater
part of this negative charge, being no longer bound, is drawn off
by the appropriating brush F and conveyed to the field plate D.
When the carrier reaches the position L the negative charge on D
induces a positive charge on the inner surface and a negative
charge on the outer. In the position M the carrier is touched by
the neutralizing brush P and the free negative charge is neutral-




U



34



ELEMENTS OF ELECTRICITY.



ized by the positive charge coming from N, M being left with a
positive charge. The carrier next reaches G, is touched by the
appropriating brush E and gives up the greater part of its charge
to the field plate C. C now has a greater positive charge than in
the beginning and its inductive action upon H is greater. In this
manner as the carriers rotate they add to the charges on the field
plates. This does not continue indefinitely. The field plate C
being much larger than the carrier G has a much greater capacity.
This property is defined later but for the present we may say (in
a figurative sense) that C requires more electricity to fill it up
than does G but once that it is filled up no more will flow into it
from G. However, induction continues to act and the unappro-
priated charges on the carriers are now taken off by the combs
Q and R as was explained in the description of the frictional
machine, and it is this surplus electricity which we draw from the
machine. In this machine, as in the frictional machine, it will be
noted that two kinds of electricity are involved in the production
of the charge, the initial charge being produced by frictional
electricity.

50. Holtz's Influence Machine. In construction this is a much
simpler machine than Toepler's. It consists (Fig. 20) of two cir-
cular glass plates face to face, one fixed, the other rotating, two
field plates and two combs with adjustable discharging knobs.

At the opposite extremities of
a diameter of the fixed plate,
window-like openings are cut
and on the corresponding side
of each of these openings are
pasted the paper field plates.
Fig. 21 represents an edgewise
view of the machine. B is the
rotating plate, the direction of
its motion being indicated by
the arrow. A is the fixed
plate with the windows and C
and D are the paper field plates. Extending from the field plates
over the edge of the openings are either tongue-like strips as
shown or else a series of sharp metal points. The operation of
the machine in detail is as follows:

The discharging knobs G and H are placed in contact.




Fig. 20.



STATIC ELECTRICITY.



35



The field plate C is given a small initial charge, say positive.
This induces a negative charge on F and repels a positive charge



B




&



toE.

An electric wind escapes from F upon B
and, as explained in Par. 43, charges the sur-
face of B negatively.

The positive charge on E induces a nega-
tive charge in D. A positive electric wind
escapes from E upon B and neutralizes the
negative charge brought along the surface
from F.

A positive wind escapes from the point of
D and charges the inner surface of B posi-
tively. As this positive charge approaches
C a negative wind escapes from C and neu-
tralizes it. The escape of this negative
electricity from C leaves C more highly
charged positively and C exerts more induc-
tion upon F.

This, as explained above, makes D more
highly charged negatively and so on, the
"building up" continuing as the plate B
rotates.

Finally, when the discharging knobs are
separated, a large positive charge is induced
in E and a corresponding negative one in
its knob G, while a large negative charge is
induced in F and a corresponding positive
one in H and the attraction between the
two in G and H is sufficient to drive sparks
across the gap between the knobs, this gap being much shorter
than the distance between C and D.

Influence machines are sensitive to atmospheric moisture but
not to the same extent as the frictional machines, one reason being
that the glass plates of the influence machines may be coated with
varnish which in a measure prevents the deposition of moisture
while in the frictional machines the plates must be kept free.

Those influence machines which employ appropriating brushes
are self-exciting, that is, the slight friction of these brushes is
enough to start the machine in operation when the plate is re-



D



D



B
Fig. 21.



36 ELEMENTS OF ELECTRICITY.

volved, but the machines of the Holtz type must be given an
initial charge.

51. Electrical Diagrams. The illustrations (Figs. 19 and 21)
in the preceding paragraphs are examples of a class of figures
termed diagrammatic which are largely used in the study of
electricity. In these the main object is to bring out clearly the
essential arrangements, connections and principles and to this end,
when necessary, details are omitted, the rules of perspective are
ignored, proportions are distorted and relative positions changed.
Conventional signs are frequently used, a simple character stand-
ing for a piece of apparatus like a cell or for a complicated machine
like a dynamo. Many examples will be noticed in the following
pages.



STATIC ELECTRICITY.



37



CHAPTER 7.

LAWS OF ELECTRIC ATTRACTION
AND REPULSION.

52. Coulomb's Torsion Balance. At various points in the
preceding pages it has been shown that charges differ from one
another in quantity and that the force of electric attraction and of
repulsion varies both with the quantity of the charges and with
the distance between the charged bodies. In the present chapter



F -




Fig. 22.



we shall see what are the laws governing this attraction and repul-
sion and also how and by what units charges may be measured.
The first exact experimental determinations of the laws of
electrical attraction and repulsion were made by Coulomb with



38 ELEMENTS OF ELECTRICITY.

an instrument called by him the torsion balance. This is shown in
Fig. 22 and consists of a vertical glass cylinder B graduated in
degrees around a belt a little below its middle and covered with a
top which is pierced with two circular openings, one in the center
and a smaller one near the edge. Around the central opening
stands a second and smaller vertical glass cylinder C (represented
in the figure as being partly cut away). This smaller cylinder
carries on its top a metal cap D graduated around its edge in
degrees and pierced in its center with a small hole in which fits
a metal spindle which may be turned by means of the milled head
E. Projecting from the shoulder below the milled head is the
pointer F which travels over the graduated edge of the cap and
thus indicates the number of degrees through which the spindle
has been turned. Hanging from the spindle is a delicate silver
wire to the lower end of which there is attached so as to swing in
the plane of the graduations a needle of shellac. At one end of
this there is a gilded pith ball G, about four-tenths of an inch in
diameter, and at the other end a sufficient counterweight to hold
the needle horizontal. In the second opening in the cover of the
larger cylinder there fits a handled stopper K from which extends
downward a needle of shellac, or of paraffine-coated glass, ter-
minating in a second gilded pith ball H of the exact size of the
first. The centers of the two balls lie in the same horizontal plane.
Finally, the instrument stands upon a bed plate A furnished with
levelling screws by means of which the silver wire can be brought
to coincide with the axis of the larger cylinder.

The operation of the instrument is as follows: It is first care-
fully levelled and then the milled head E is turned until the ball
G is just tangent to the ball H. In this position the plane through
the suspending silver wire and the center of the ball G passes
through the zero of the graduated scale on the larger cylinder. K
is now removed, a charge is imparted to H and K is then rein-
serted. As H touches G the charge on H is distributed between
the two balls. Having similar charges H and G repel each other
and G (in the case represented in the figure) swings off to the right
and as it does so twists the suspending silver wire. Now there is
a definite law that when a body such as a wire is twisted by a force,
its elastic limit not being exceeded, the resistance offered to the
twisting, or the tendency to untwist, increases directly with the
angle through which it is twisted and consequently the angle



STATIC ELECTRICITY. 39

through which it is twisted is directly proportional to the force
exerted. The force which will twist a wire through ten degrees is
exactly double that which will twist it through five degrees. As
G moves to the right the resistance of the wire to twisting increases
and as the distance between G and H increases the repelling force
grows weaker until finally a position of equilibrium is reached,
G comes to rest, and the angle through which it has turned can be
read from the scale on the surface of the cylinder.

53. The Law of Inverse Squares. By means of the torsion
balance Coulomb demonstrated that electric attraction and repul-
sion followed the law of inverse squares, or that the force exerted
between two charged bodies varies inversely as the square of the dis-
tance between these bodies. Two charged bodies which at a certain
distance repel each other with a certain force will repel each other
with only one-fourth of this force if the distance be doubled, or
one-ninth if it be trebled, etc. His experiment was conducted as
follows: The balls H and G (Fig. 22) were charged as explained in
the preceding paragraph and let us suppose that the movable ball
G was repelled until it swung through an angle of 16 degrees. By
turning the milled head E in the direction shown by the arrow an
additional twist was put upon the silver wire and the ball G was
gradually forced back towards H. When G had thus been twisted
back to within 8 degrees of H it was found that the pointer F of
the milled head had travelled over 56 degrees of the scale on the
cap D. The total angular torsion on the wire was consequently
8+56 = 64 degrees. The force exerted in the two cases was, there-
fore, as 64 is to 16, which is the same as four to one. For small
angles the chords bear to each other practically the same ratio as
their arcs, hence at sixteen degrees the balls were twice as far apart
as at eight degrees, or as the distance between the balls was divided
by two the force between them was multiplied by 2x2 and this
conforms to the law of inverse squares. These results are con-
firmed by experiments based upon other methods.

In the foregoing illustration the figures were selected to fit the
demonstration but to obtain such accurate results in practice
requires very careful manipulation and the observance of many
precautions. The most troublesome source of error is loss of a
portion of the charge during the progress of the experiment. The
shellac needles to which the balls are fastened are non-conductors
when free from hygroscopic moisture but a film soon deposits



40 ELEMENTS OF ELECTRICITY.

upon them from the air and leakage of charge results. To remedy
this there is placed in the instrument a small saucer containing
quicklime or calcium chloride or sulphuric acid which substances
have a great affinity for water and thoroughly dry the air inside
of the cylinder.

A similar experimental demonstration can be made in the case
of the attraction between unlike charges but the manipulation
is much more difficult. The two balls must separately be given
charges of the opposite kind, they attract each other and a con-
dition of unstable equilibrium exists. Should they touch, their
charges are neutralized and the process must be rebegun.

From the foregoing it will be seen that electric attraction and
repulsion follow the law of central forces. In order that the law
of inverse squares should be strictly true, the charged bodies must
be small spheres, so small as to approximate points, and should
be at such distance apart that in comparison with this distance
their own dimensions are negligible. To other bodies the law
does not apply. The force between two charged flat discs near
together does not vary with small variations in the distance.

54. Variation of Force with Charges. The force exerted between
two charged bodies varies as the product of the charges. Reflection
will show the truth of this second law. If two charged bodies
repel or attract each other and the charge of either one be doubled
or trebled, the repulsion or attraction must likewise be doubled or
trebled. If the charge of the second one be now doubled or
trebled, the existing force will be doubled or trebled, that is, the
original force will be multiplied by four or six or nine. This law
may be demonstrated by the torsion balance. It will be remem-
bered that the two balls G and H (Fig. 22) are of exactly the same
size, therefore, no matter what charge we start with, as soon as
the balls have touched they (in accordance with the principle
stated in Par. 45) divide the charge equally and we have two
similar and equal charges. We may determine the angular repul-
sion between these, then withdraw the fixed ball H, touch it to a
third and equal ball thereby halving its charge, return H to the
cylinder, determine the new angular repulsion and hence the
variation in the repulsion with the variation in the charge.

55. Variation of Force with Intervening Medium. Those non-
conducting substances which surround charged bodies and through



STATIC ELECTRICITY. 41

which electric effects are transmitted were termed by Faraday
"dielectrics." The force of attraction or of repulsion between
charged bodies varies with the nature of the dielectric. Thus two
small similarly-charged spheres which at a certain distance apart
in air repel each other with a force of so many dynes will, if kept
at the same distance and immersed in oil, repel each other with a



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