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the movements described in the preceding paragraph take place




Fig. 163.

has been formulated by Maxwell to the effect that every electro-
magnetic system tends to change its configuration so that the exciting
circuit will embrace in a positive direction the maximum number of
lines of force. This law applies to all combinations of closed cir-
cuits and magnetic fields, whether these fields be produced by
magnets, by other circuits, or even by the circuit itself. This last
is shown by an experiment devised by Ampere. In a wooden block
(Fig. 163) there are hollowed out two parallel troughs which are



280 ELEMENTS OF ELECTRICITY.

then filled with mercury. A wire bent as shown is then placed as
a bridge with one end in each trough and floats on the surface of
the mercury. The current entering at A crosses this bridge and
leaves by B, the lines of force in this rectangular area all pointing
up as shown by the arrows. As soon as the circuit is closed, the
wire floats off towards C, thereby increasing the area ACB and
consequently the number of lines of force embraced by the circuit.
The majority of the instruments, shortly to be described,
operate in accordance with this law and it also explains the move-
ment of all motors. It has already been shown (Par. 144) that,
in a more general form, it accounts for the position assumed by
magnetic needle.

372. Galvanometers. A galvanoscope indicates by the move-
ment of its needle both that a current is flowing and the direction
of its flow. If this movement also affords a measure of the strength

of the current, the instrument is
called a galvanometer. There are
many varieties of galvanometers
but they may all be classed under
one of two heads: first, those in
which a needle moves in a field
produced by a fixed coil and,
second, those in which there is
no needle but a suspended coil
which swings in a fixed field.
Of the latter class, the field may
be produced by a permanent
magnet or by a fixed coil. We
shall now describe examples of
each of the above.

373. The Tangent Galvanom-
eter. This is an example of a
galvanometer of the first class,
that is, one with a needle mov-
ing in a field produced by a fixed
Fig 164 coil. It consists (Fig. 164) of a

vertical circular coil, more than
one foot in diameter, mounted upon a base by which it may be
accurately placed in the magnetic meridian. The coil is composed




ELECTRO-MAGNETICS. 281

of a single turn of heavy copper wire or copper ribbon. For
measuring small currents it may consist of many turns of fine
wire. Pivoted at the center of this coil is a short thick needle,
generally less than an inch in length. Since it would be very
difficult to read with any accuracy a scale engraved upon a circle
whose diameter is only one inch, the needle is usually prolonged
by light aluminum pointers. These have no magnetic effect but
permit the use of a much larger graduated scale.

374. Measurement of Current by Tangent Galvanometer. In

order to measure a current by the tangent galvanometer, the latter
is connected up in the circuit, its coil accurately placed in the mag-
netic meridian, the circuit closed and the angle of deflection of the
needle read. If it be convenient to reverse the current, this is done,
the new angle of deflection read and the mean of the two readings
is taken as the correct one.

In Par. 146 we saw that "the magnetic field which, acting at
right angles to the meridian, produces in a needle a deflection 5, is
equal to the horizontal component of the earth's magnetism at that
point multiplied by the tangent of the angle of deflection," or



Again, in Par. 354 we saw that the field produced at the
center of a circular coil of radius r by a current of / absolute
units is

r f.ftf

J ~ r

We therefore have

1 .2-JT



whence

/ = - .H. tan 6

In this r is determined by measurement of the coil, H is
obtained from observation (Par. 148), or from a table (Par. 175),
6 is read from the galvanometer scale and tan 6 is obtained from a
table.

If the galvanometer coil has n turns, the second expression for /



- . r f

becomes / = . The factor , since it depends purely



282



ELEMENTS OF ELECTRICITY.



upon the dimensions of the instrument, is called the galvanometer
constant. Calling this G, we have

/=/.G

whence, if 7 = 1, f=G, or the

galvanometer constant is equal to the strength of the field pro-
duced at the center of the coil by a current of one absolute unit.

In practice, it is more frequent to use the tangent galvanometer
to compare currents rather than to determine them absolutely.
Various currents are to each other as the tangents of the angles of
deflection which they severally produce. If the deflection pro-
duced by a known current be ascertained, the determination of
other currents is a simple matter.

375. Remarks on Principle of Tangent Galvanometer. The
deduction in the preceding paragraph is based upon two assump-
tions, neither of which is strictly accurate, although the error is






/ / v^ - ^,}X

1 ' I \ vA^/ir/"} ; i
* \ **S~?jf/ti i '

^O;;:<'''/ / ,
**. ^ / / / /



Fig. 165.



usually negligible. First, the deflecting force is supposed to be
perpendicular to the meridian. Fig. 165 represents the field along
the horizontal diameter of the coil of a tangent galvanometer,
whence it is seen that the lines of force are curves (although
slightly different from the circles shown in the figure), and there-
fore are perpendicular to this meridian only where they pierce
the plane of the coil. They have, however, less curvature near the
center of the field and this flatness increases with the diameter of
the coil, for which reason the needle is made very short and the
coil large. A still better remedy is to use two parallel coils and
place the needle midway between them. The lines of force of the
field in this case are sensibly parallel.

Second, the expression employed for the intensity of the field is
determined for the center of the coil (Par. 354). The field, as in-



ELECTRO-MAGNETICS.



283



dicated in the figure, is much stronger near the coil and diminishes
towards the center. The needle is therefore made short so that
its poles do not extend into a field much stronger than that at the
actual center.

376. The Sine Galvanometer. The sine galvanometer, shown
in its simplest form in Fig. 166, differs from the tangent gal-
vanometer only in that the coil need not be so large and that
the needle extends as nearly across the diameter of the coil as its




Fig. 166.



surrounding graduated circle will permit. The poles of the needle
therefore lie in the strong field close to the coil and the instrument
is more sensitive than the tangent galvanometer. The coil is free
to rotate about a vertical axis and in more improved forms of the
instrument there is a horizontal graduated limb from which may
be read by a vernier the exact angle through which the coil has
been turned. This limb, however, is not essential.

To use the instrument to measure a current, it is connected up
in the circuit and accurately adjusted until the coil lies in the mag-
netic meridian. The horizontal graduated limb is then read and
the circuit is closed, causing a deflection of the needle. The coil
is then turned by hand in the direction of the deflection of the



284 ELEMENTS OF ELECTRICITY.

needle until the needle is overtaken and lies once more in the plane
of the coil. The deflecting force, or the field of the coil, is now per-
pendicular to the needle. The angle through which the coil has
been turned is read from the scale on the horizontal limb. Should
there be no horizontal limb, this angle can still be determined, for
it is only necessary to take the reading of the needle, then break
the circuit and take the reading of the needle when it has swung
back into the meridian; the difference between these two readings
is the required angle.

In Par. 147 it was shown that "magnetic fields acting at a
cvastant angle with the needle are to each other as the sines of the
respective angles of deflection." It follows that the current is
proportional to the sine of the angle through which the coil has
been turned; also, that different currents are to each other as the
sines of these angles. The sine galvanometer can therefore be
used to compare currents although it can not be used, like the
tangent galvanometer, to measure currents absolutely.

Should the deflecting force be greater than the controlling force,
the coil will never overtake the needle, and in such a case the
instrument can not be used.

377. The Mirror Galvanometer. The mirror galvanometer is
an extremely sensitive form of instrument and is more frequently
used as a galvanoscope than as a galvanometer, in fact, it was
devised by Lord Kelvin to give indications of the exceedingly small
currents transmitted by submarine cables. Its principle will be
understood from Fig. 159. It consists of a vertical coil of many
thousand turns of very fine insulated wire. The opening through
the coil is barely half an inch in diameter and in the center of this
there hangs, by a silk fibre, a very light glass mirror, about the
size of a silver ten-cent piece. The mirror is slightly concave so as
to focus in a long pencil any rays of light which fall upon it. To
the back of this mirror there are glued three or four very light
magnets made of short sections of watch spring. The controlling
force of the earth's magnetism is neutralized by Haiiy's method.
The little mirror normally hangs with its plane parallel to the
face of the coil, but when a current passes through the coil the
magnets at the back of the mirror tend to turn in accordance with
Maxwell's law until their lines of force coincide with those of the
coil. A beam of light is caused to fall upon the mirror and is
reflected back, producing a bright spot upon a blank wall or upon



ELECTRO-MAGNETICS.



285



a suitably-prepared scale. The slightest angular motion of the
mirror is revealed at once by motion of the spot of light, the
angular motion of the spot being twice that of the mirror and
the radius being the distance from the mirror to the wall or scale.
Thompson states that the most improved form of this instrument
gives indications of a current as small as one fifty-four-thousand
millionth of an ampere.

378. Suspended Coil Galvanometer. In the galvanometers
described in the preceding paragraphs, the coil carrying the cur-
rent is fixed and the magnet rotates; in the form now to be de-
scribed the magnet is fixed and the coil rotates. While not having
the extreme delicacy of the mir-
ror galvanometer, the suspended
coil galvanometer is still of a high
order of sensitiveness and is used
by practical electricians where the
most refined observations are re-
quired. There are many different
forms and it is known by other
names, such as the D' Arson val
galvanometer, the reflecting gal-
vanometer, etc., but the principle
of all is the same.

A usual form consists (Fig. 167)
of a heavy rectangular frame
of magnetized steel whose poles
are N and S. This frame is
mounted upon a wooden back C
which may be fastened to a wall,
mounted upon a tripod, or other-
wise suitably supported. Through
the center of the top of the frame
is bored a hole into which is
screwed a vertical brass tube D.
In the upper end of this tube
there fits a small brass spindle
with a cross-bar handle E. This spindle may be turned about a
vertical axis and may be raised or lowered and fastened in any
desired position by the set-screw shown at the right. The mov-
able coil is suspended from the spindle by means of a very delicate




Fig. 167.



286 ELEMENTS OF ELECTRICITY.

phosphor-bronze filament. Silk or quartz fibres can not be used
since the suspension must convey current to the coil. The
coil, which swings in the space between the poles, consists of
many turns of very fine wire wrapped upon a thin, light,
elongated rectangular metal frame. Midway between the poles
N and S there is fastened to the wooden back C a vertical
soft-iron cylinder K which projects into the opening of the coil
frame, almost entirely filling this space and leaving barely room
for the coil to turn. This, as shown in Fig. 69, Par. 143, greatly
concentrates the field in which the coil moves. Above the coil
frame and supported by it is a small mirror F. Below the coil, a
coiled phosphor-bronze filament connects to a small metal bracket
G which in turn is connected from behind to the binding post B.
The other binding post A is connected direct to the steel frame.
A current entering at A travels up the steel frame to the brass
tube, thence up this tube to the spindle, thence down the suspen-
sion to the coil, around the coil, thence through the lower filament
to G and out by B. The coil hangs normally with its face to the
front, the controlling force being the torsion of the phosphor-
bronze suspension. If the coil does not hang properly, it can be
made to do so by turning the spindle E. With the poles situated
as represented in the figure, the lines of force of the field run from
right to left. When a current flows through the coil, the lines of
force of the coil are from front to rear, or the reverse; therefore,
the coil, in accordance with Maxwell's law, turns either to the
right or left. The coil, mirror and filaments are protected by a
metal plate screwed to the frame and carrying a glass window
through which the mirror may be observed.

In using the instrument, there is attached to the hooks H H an
arm (Fig. 168) which carries at its farther end a telescope and a
printed scale. The scale, which is usually divided into millimeters,
is one-half meter from the mirror. By means of the telescope the
reflection of the scale in the mirror is observed. Since the tele-
scope inverts objects and the mirror reverses them right for left,
the numbers on the scale must be engraved both upside down and
reversed. Cross hairs in the telescope allow the scale to be read
very accurately. When the coil, and consequently the mirror, is
deflected by a current, it appears to the eye of the observer as if
the scale moved across the field of the telescope. For moderate
deflections of the coil the currents producing these deflections are



ELECTRO-MAGNETICS.



287



proportional to the number of scale divisions passed over by the
vertical hair.




Fig. 168.



379. Damping. In instruments in which readings are taken of
the angular displacement of a needle, a coil, or a mirror, the mov-
ing part may oscillate for some time before coming to its final
position of rest. This causes, in taking observations, a vexatious
delay which it is very desirable to avoid. Any process by which,
while not interfering with the freedom of movement of the part,
it is made to come to rest quickly is called "damping" and an
instrument whose needle moves at once to the proper reading on
the scale is said to be "dead beat" Damping may be brought about
by (a) mechanical means or (b) electrical means. As an example
of mechanical damping, a moving coil may have suspended below
it a metal vane which is immersed in oil, the viscosity of the liquid
slowing down the movement and preventing vacillation. Sus-
pended coil galvanometers often have attached to the mirror a
thin sheet of metal or mica which turns in a little closed box which
it nearly fits. The confined air in this box acts something like the
oil in the first case.

Electrical damping can not be thoroughly explained at present
but depends upon the principle that a piece of metal moved in a
magnetic field experiences forces which tend to stop the movement
(Par. 430). This is the method employed in the suspended coil
galvanometer just described. The metal frame upon which the
coil is wrapped turns in the strong magnetic field between the poles
and the soft-iron core and is thus brought quickly to rest.



288 ELEMENTS OF ELECTRICITY.

380. Need of Galvanometer Shunts. The currents which a
reflecting galvanometer may measure are extremely small. Thus,
if a pin be connected by a wire to one terminal of the galvanometer
and a needle be connected to the other and the pin and needle be
held tightly between the fingers, the contact of the two dissimilar
metals with the slight moisture of the fingers will drive a sufficient
current through the coil to cause the mirror to run entirely off the
scale. In order therefore to measure even minute currents we must
employ a shunt by which, as explained in Par. 301, only one-tenth,
one-hundredth, or one-thousandth of the total current is permitted
to flow through the instrument. Even in this case it is usual to
insert in the circuit a resistance of 50,000 or 100,000 ohms by
which the current is reduced to measurable intensity.

381. The Universal Shunt. We saw in Par. 301 that the resist-
ance of a galvanometer shunt must bear a fixed relation to the re-
sistance of the galvanometer with which it is used and that shunts
are not interchangeable and can be used only with the galvanom-
eter for which they are constructed. The phosphor-bronze sus-
pension of a suspended coil galvanometer is frequently broken and
must be replaced by a new one, in doing which the resistance of
the galvanometer is usually considerably changed and this change
would render useless a shunt designed to accompany the original
resistance. Reflection will show, however, that if we simply wish
to compare currents relatively it is not necessary to know what
fraction of the total current flows through the galvanometer, for
if 1/xth of a current /' flowing through a galvanometer produces
a certain deflection, and if 1/xth of a different current I" produces
a deflection twice as great, then the current /" is twice as great
as the current /'.

Carrying out the idea farther, Ayrton devised a universal shunt
which may be used with any galvanometer and which can be so
varied that, irrespective of the resistance of the galvanometer, the
deflection produced is proportional to one- tenth, one-hundredth,
or one- thousandth, etc., of the total current. This shunt is shown
diagrammatically in Fig. 169. Five contacts (sometimes six) are
arranged in the arc of a circle and marked, 1, T V, T K> T<jV<j and 0.
Between these contacts are resistance coils A, B, C, D. If R be
the total resistance, A is .9 of R, A +B is .99 of R and A+B-fC
is .999 of R. A common arrangement of these resistances is to have
A = 9000, B = 900, C = 90 and D = 10 ohms, a total of 10,000 ohms.



ELECTRO-MAGNETICS.



289



The current enters by K and leaves by H. The arm attached to
K can be placed on any desired contact. The galvanometer is
connected in shunt with the total resistance as shown. Let the
resistance of the galvanometer be x. With the arm on contact 1,
let the total current be /, and the current through the galvanom-



eter be ^ The joint resistance from K to H is



( Par - 293 )-




Hence



Whence



Rx



R+x '

R+x
R



Suppose the arm to be placed on the
resistance from K to H is now



(I)
contact. The joint



R+x

If the total current be now /' and the current through the
galvanometer be I' g



.






290



ELEMENTS OF ELECTRICITY.



Hence



From (I) and (II)



/' = /'. 100.



R +x



(II)
(III)



Or if D be the deflection produced by the first current and D f
that produced by the second

/' : 7 = 100. D' :D

or the ratio of the total

current when the arm is on the T <y contact, to the total current
when the arm is on the 1 contact, is as one hundred times the de-
flection produced in the first case, is to the deflection produced in
the second case.

It will be noted that x, the resistance of the galvanometer, does
not appear in (III), hence the shunt may be used with any galva-
nometer.



B




Fig. 170.

382. Weber's Electro-Dynamometer. This instrument, an ex-
ample of a galvanometer of the second class (Par. 372), that is, one
in which a coil swings in a magnetic field produced by other coils,
is shown diagrammatically in Fig. 170. It consists of two large
parallel coils A and B mounted so that they have a common axis



ELECTRO-MAGNETICS. 291

and their planes are vertical. Midway between these there hangs
by a bifilar suspension (Par. 127) a small coil C so arranged that
its axis is in the same horizontal plane but at right angles to the
common axis of A and B. As generally used the same current
traverses all three coils. Entering at E it flows around the coil A
and out to F, thence by the wire to G, thence down the slender
wire suspension to C, around this coil, up the other suspension to
H, down to D, around the coil B and finally out by K.

If the currents in the two coils flow as indicated by the small
arrows, the field of AB will be from right to left; that of C from
rear to front and therefore C, viewed from above, takes up a clock-
wise motion, or, in accordance with Maxwell's law, tends to turn
so that its field coincides in direction with the field of AB. The
angle of deflection is read, as in the mirror galvanometer, by means
of a small mirror attached to the suspended coil. The controlling
force is gravity which tends to pull the inner coil back to its pri-
mary position; the moment of this force being directly proportional
to the sine of the angle of deflection, or

M c = a . sin 6

The deflecting force is due to the interaction of the fields of the
suspended and the fixed coils and since these fields are severally
proportional to the currents flowing in the coils (Par. 354), the
deflecting force is proportional to the square of the current. The
moment of the deflecting force is proportional to the product of
the square of the current and the cosine of the angle of deflection,
or

M d = b . I 2 . cos 6

When the coil conies to rest the two moments are equal and
opposed, hence

6. 1 2 . cos 5 =a. sin 6
whence

/ 2 =|.tan<5

or, the square of the cur-
rent is proportional to the tangent of the angle of deflection. This
fact might have been anticipated since reflection will show that
the instrument is virtually a tangent galvanometer.

In making an actual observation a number of refinements must
be observed in determining the constants a and b above, and it
may also be necessary to allow for the effects of the earth's field.



292



ELEMENTS OF ELECTRICITY.



Should the current through the instrument be reversed in direc-
tion, the fields in the coils will also be reversed but from the figure
it will be seen that the tendency will still be for the movable coil
to turn in a clockwise direction. Since this direction of deflection
does not vary with reversal of the current, instruments of this class,
that is, two-coil instruments, are employed in the measurement of
alternating currents, or those currents which reverse many times

per second.



383. Siemen's Electro-Dynamometer. Siemen's electro-dyna-
mometer, shown diagrammatically in Fig. 171, is in principle the




Fig. 171.

same as Weber's but differs in that the movable coil is external
to the fixed, and that the controlling force is the torsion of a deli-
cate coiled spring. The base and supporting upright are of wood.
There are two fixed coils, one of a few turns of heavy wire for use
with large currents, the other of many turns of a finer wire for use
with smaller currents. The short coil is wrapped upon the long



ELECTRO-MAGNETICS. 293

coil. The terminal for one of these coils is the binding post A, that
of the other coil the binding post B, and the remaining end of each
coil is connected to the metal bracket D which at one end carries
a little cup of mercury. One terminal of the movable coil dips
into this; the other terminal dips into a similar cup just below the
first, this last cup being connected by a wire to the binding post C.
The movable coil is suspended either by a silk fibre or upon a
pivot and is free to rotate about a vertical axis. It carries a needle
or pointer which is bent over the edge of an upper circular scale.
This scale may be graduated in degrees but more often in some
arbitrary number of points, such as 400. If the current in the coils
flow as indicated by the arrows, the field of the fixed coil is from
left to right, that of the movable coil from rear to front and,
viewed from above, the rotation of the movable coil is counter-
clockwise. This movement is opposed by the torsion of the spiral
spring attached to the upper part of the movable coil and by
means of a projecting pin or stop is restricted to a few divisions
of the graduated scale. At the center of this scale there is a milled
head to whose end the upper end of the coiled spring is attached.



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