![[IMAGE]](contacts/fig59-5.gif)
Let the horizontal line N P' (see Fig. 59) represent the axis, or line of resistances, the latter being represented in their respective order, beginning at the point of contact, N, between the extreme zinc plate of the battery and the liquid of the cell. N B, B C, and C P represent the respective internal resistances of the three battery cells, and N P that of the entire battery. Let P H N' represent the resistance of the line wire, and N' P' that of the battery at the opposite end of the line. Erect a perpendicular, N E, at the point N, and divide it into three portions, N F, F G, and G E, which shall be to each other as the electro-motive forces at N, B, and C. The other battery, N', P', having its negative pole, N', to the line, will give a negative tension ; therefore a perpendicular P' E' let fall below the axis from the point P, and divided in the same manner, will represent the electro-motive forces of the battery N' P'. Therefore the line N P' represents the sum of all the resistances, and N E + P' E' the sum of the electro- motive forces. It necessarily follows that the line of tension, M H M', which we get by joining E and E', varies in the angle of its inclination to the axis according to the proportion between the sum of the electro-motive forces, N E and P' E', and the sum of the resistances, N P' ; and the degree of its inclination will therefore accurately represent the effective working strength of the current in all parts of the circuit.
The varying tensions within the battery may be correctly represented as follows : Having joined E and E', erect perpendiculars at B and C and P. Now as the effective strength of current, represented by the inclination of the line E E', is the same at every point throughout the whole circuit, draw F I parallel to E E'. Then F I will be the line of tension in the first cell, falling regularly through the resistance of the liquid to the surface of generation, B, of the second zinc, where it rises suddenly to the extent of the electro-motive force there situated. Draw G K parallel to E E', intersecting B O at J. I J will then be equal to F G, which represents the electro-motive force at B, and J K will be the line of tension in the second cell. Now as G K is parallel to E E', K L will be equal to G E, the electro-motive force at C, and L M will be the line of tension in the third cell. In the same manner the line of tension within the other battery N P'.
The terminal points of the line N and P', being connected directly with the earth, their tension will be equal, and the same as that of the earth, which is assumed to be zero ; that is, neither positive nor negative. It is manifest that at the point H, midway of the circuit where the line of tension crosses the axis, the tension is the same as that of the earth, or zero.
In the illustration given, the line is supposed to be in a condition of perfect insulation. In actual practice there is a leakage at every support throughout the whole length of the circuit. The line of tension in this case would form a double catenary curve, its angle of inclination to the axis constantly increasing from H to M and M', because in an imperfectly insulated or leaky line the current continually increases in strength in each direction from the neutral point to the battery poles at P and N'.
Mr. Webb has demonstrated the correctness of the above method of geometrical projection by applying Ohm's formula for obtaining the tension at any point of the circuit. The results are found to correspond in every case. This formula may be stated as follows :
Let T = the tension at any given point of the circuit _x_.
Y = the abscissa of that point _x_, taking as origin
the point of least tension.
A = the sum of the electro-motive forces.
L = the reduced length or resistance of the entire circuit.
O = the sum of the electro-motive forces included in Y.
C = the tension of the whole circuit to external objects.
That is to say, the tension of the circuit, if it be
an insulated circuit, and electrified by a source
not contained within it.
A
Then T = --- Y - O + C
L
As in the case under consideration, the earth forms part of the
circuit, the constant C disappears and the formula becomes
A
T = --- Y - O
L
Now take a point x in the diagram, and the tension x
x' will be found to agree with the formula.The quantities in the formula are thus represented geometrically in the figure :
A = N E
L = N H
O = _x_' _x_''
Y = _x_ H
T = _x_ _x_'
Now since the triangles H N E and H x x'' are similar, we
have
N H : N E :: H _x_ : _x_ _x_''
N E
Consequently _x_ _x_'' = ----- H _x_,
N H
and J K being parallel to O L, we have
_x_' _x_'' = K L.
But _x_ _x_' = _x_ _x_'' - _x_' _x_'' ;
N E
Therefore _x_ _x_' = ----- H X - _x_' _x_'',
N H
A
Or, T = --- Y - O.
L
An experimental proof of the above theory of tension may be
obtained by connecting a wire from the neutral point in the
middle of the closed circuit of a telegraph line, and inserting
a galvanometer or relay. It will be found that no current passes
between the line and the earth, which proves that the electric
tension or potential at that point is zero, or the same as that
of the earth itself.170. Double Transmission.--- One of the most interesting problems in practical telegraphy is that of double transmission, or working in opposite directions at the same time over a single wire. This apparently paradoxical result may be accomplished in several different ways, the principles involved being very simple and easily understood. The method shown in the accompanying diagram is that of Siemens & Halske, of Berlin, Prussia ; the apparatus now used in this country differing slightly from it in some of its minor details.
A and B (Fig. 60), are the two terminal stations of the line.
The main battery E, at station A, is placed with its +, and the
battery E' at station B with its -pole to the line, as
represented. M and M' are the receiving magnets or relays,
which are wound throughout with two similar wires of equal
length, as shown in the figure, whose connections will hereafter
be explained. The rheostat or resistance, X, must be adjusted so
as to be exactly equal to that of the line A, B, added to that
of the relay wire 7, 5, at the other station. Similarly X' is
also made equal to the line including the relay wire 3, 1.
If, now, the key K at station A be depressed, the current from
the battery E will divide at the point 1, one portion going
through the relay coils to 3, over the line A, B to 7, and
thence through the relay M' to 5, key lever 6', and contact C'
to the earth at G', and the other portion in an opposite
direction through the relay coils from 2 to 4, and thence
through the resistance X to the negative pole of the battery.
These two currents will be equal to each other, the resistance
being the same by each of the two routes, as before explained,
but as they pass in opposite directions through the two wires
surrounding the relay M, they produce no magnetic effect upon
it. The relay at B, however, will be affected by the current
coming from A through the wire 7, 5, and will give signals
corresponding to the movements of the key at that station.
If, now, the key at B be also depressed, the same action takes
place ; one half the current passes over the line, combining
with the current from A, and the other half returns to the
battery through the other wire of the relay and the rheostat.
The relay wires 1, 3 and 7, 5 are now traversed by the double
current, equal to A/2 + B/2, but the wires 2, 4 and 6, 8 are
traversed only by the current of a single battery, having at A
the force of A/2 and at B the force of B/2. The latter current
being in the opposite direction to the former, the relays at
both stations are affected by the difference in the forces of
these currents, the relay at A by (A/2 + B/2) A/2, and the relay
at B by (A/2 + B/2) B/2. Thus each station receives its signal
through the action of the distant battery only.
In the arrangement shown in figure 60 a third position occurs,
where one of the keys, at B for instance, is in the act of
changing from the front contact A' to the rear contact C', or
vice versa, in which case the current from A is
interrupted at B', and therefore passes through the second wire
of the relay 6, 8, but this time in the same direction, and
thence through the rheostat X' to the ground. The current
arriving at B is considerably weakened in consequence of the
additional resistance encountered at X', but this is compensated
for by its passing through both wires of the relay M in
the same direction, and its action upon the relay, therefore,
remains about the same as before.
One slight difficulty, however, arises in this connection. It
will be seen that when the current at the receiving station is
thus momentarily thrown through both relay wires and the
rheostat, it must necessarily cause an unequal division of the
current between the two opposing relay wires at the sending
station, as the resistance of the long circuit becomes about
double that of the short one. This effect is avoided in the
American system by a modification of the transmitting apparatus,
which is operated by the lever of a sounder placed in a local
circuit in connection with the key. When the local circuit is
closed the downward movement of the sounder lever makes the
battery connection upon a flat spring, and the movements thus
imparted to the spring breaks the earth contact. The spring
being attached to the line wire the connection is necessarily
always complete, either direct or through the battery, and it is
not obliged to pass through the rheostat when the transmitter is
changing from the battery to the earth contact, or vice
versa. The disadvantage in this case arises from the fact
that the main battery is thrown on short circuit at each
movement of the transmitter, rendering it necessary to interpose
a considerable additional resistance between the back contact
and the battery, to prevent the rapid consumption of the latter
which would otherwise ensue. These improvements were devised by
Mr. J. B. Stearns.
In working this system, it is necessary to keep the rheostat so
adjusted that its resistance will correspond exactly with that
of the line, as above shown. If the relay works too feebly the
counter current must be weakened by increasing the resistance of
the rheostat. If the magnetism is too strong the resistance
should be diminished. A careful study of the diagram will show
that this system operates equally well, whether similar or
opposite poles of the two batteries are placed towards the line.
With like poles the action will be as follows :
If the key at A be depressed, the current on the line will be
A/2 and through the rheostat A/2, neutralizing each other upon
the relay of A, but giving a current of A/2 in the relay at B.
Now, if the key at B be also depressed, a current equal to B/2
is thrown through each wire of his relay, but the current A/2
being equal and opposite to B/2 the current of the main line
will = 0.
The current through the second wire of the relays being still
unaffected, each relay will give a signal corresponding to the
time the key at the other station is depressed.
171. Edison's Button Repeater.---
This is a very simple and ingenious arrangement of
connections for a button repeater, which has been found to work
well in cases where it is required to fit up a repeater in an
emergency, with the ordinary instruments used in every office.
Fig. 61 is a plan of the apparatus.
M is the western and M' the eastern relay. E is the main
battery, which, with its ground connection G, is common to both
lines. E' is the local battery, and L the sounder. S is a
common ``ground switch,'' turning on two points, 2 and 3. In
the diagram the switch is turned to 2, and the eastern relay,
therefore, repeats into the western circuit, while the western
relay operates the sounder, the circuit between 1 and 2 through
the sounder and local battery being common to both the main and
local currents. If the western operator breaks the relay M
opens, and consequently the sounder, L, ceases to work. The
operator in charge then turns the switch to 3, and the reverse
operation takes place ; the western relay repeats into the
eastern circuit, and the eastern relay operates the sounder.
The sounder being of coarse wire, offers but a slight resistance
to the passage of the main current.
172. Bradley's Tangent Galvanometer.---
The common galvanometer used for the measurement of
electric currents consists of a magnetized steel needle,
suspended in the centre of a hollow frame covered with insulated
copper wire. The degree of deflection of this needle from its
normal position in the magnetic meridian, when a current is
passing, indicates the strength of the current. In the ordinary
galvanometer, however, the angle through which the needle is
moved, or in other words, the number of degrees over which it
passes, is not an accurate measure of the strength of the
current when the deflection exceeds 15°, for the further
the needle moves from a position parallel to the wires of the
coil the more nearly does it approach a right angle, in which
position the effect is null, so that the action of the current
upon it becomes less and less powerful as the deviation
increases. Several arrangements have been tried in order to
obviate this objection, the most common being that of a ring
having a groove on its edge filled with wire. The needle is
hung precisely in the centre of the ring, and must not be longer
than one sixth of its diameter---a half inch needle requiring a
three inch ring. The needle is then deflected with a force
varying as the tangent of the number of degrees through which
the needle moves. Owing to the great distance of the coil from
the needle, this arrangement has very little sensitiveness
compared with the common galvanometer.
In Bradley's Galvanometer a compound needle is employed,
composed of several needles of thin, flat steel, fixed
horizontally upon a light flat ring of metal, forming a complete
circular disc of needles, having an agate cup in the centre, to
rest upon the pivot upon which it moves. At each extremity of
the meridian light points project, to indicate the degrees of
deflection. The compound needle, after having been magnetized,
is placed within or over a coil whose breadth is exactly equal
to the diameter of the disc. This compound circular needle,
being under the influence of the same number of convolutions of
the coil in all its deflections, fulfils the required conditions
for a true tangent galvanometer.
The theorem, ``The intensity of currents, as measured by the
tangent galvanometer, is proportional to the tangents of the
angles of deflection,'' may be verified in the following
manner :
Call the terrestrial magnetism, whose tendency is to direct the
galvanometer needle to the magnetic meridian, the unit of
directive force, and let this unit be represented geometrically
by the line A M (Fig. 62), which is the radius of the circle M B
M---the line M A M representing the meridian. When there is no
other force acting on the needle its direction is with the
meridian. Now let an electric current be sent through the
galvanometer coil, whose directive force is precisely equal to
the terrestrial force, and whose tendency is to direct the
needle in a line perpendicular to the meridian, and let this
force be represented by the line A B.
If the terrestrial force could now, for a moment, be suspended,
the needle would point due east and west ; but the combined
action of the two equal forces will direct the needle toward the
point of intersection of the line drawn perpendicularly from M,
and that drawn horizontally from B, at 1, which direction cuts
the quadrant at 45°, the line M 1 being the tangent of
45°, which is 1.
Now, if we augment the intensity of the current through the coil
to twice its present force, which will be 2, and will be
represented by the line A C, the combined forces A M and A C
will direct the needle toward the point 2. If we now lay a
protractor on the circle, we find that the line A 2 cuts it
about 63° 30', of which the tangent is 2.
We may increase the parallelogram erected upon A M at pleasure,
and the two forces combined will always so balance the needle
between them as to make it point from A, diagonally, across the
parallelogram to its opposite angle, the height of which is the
tangent of the angle of deflection.
By inspection of the diagram it is seen that the law holds good
in the subdivisions of the force A B, as at .5 .25 and .125, a
truth admitted by all experimenters, as to the relations, up to
14°.
173. Thompson's Reflecting
Galvanometer.--- This is the most delicate apparatus of
this kind which has yet been devised, and is for this reason
employed in operating the Atlantic Cables.
The special feature which distinguishes this galvanometer from
an ordinary one, is the extreme lightness of the magnet or
needle, and the delicacy with which it is suspended in a
horizontal position. Instead of an index needle, to render the
motions of the magnet visible to the eye, a reflected ray of
light is made use of, which, of course, can be made of any
required length. This arrangement is of great practical value in
measuring faint electrical currents, too feeble to be indicated
by any other apparatus. It is especially valuable in submarine
telegraphing, because it permits the use of such extremely low
battery power.
When the insulation of a cable is in the slightest degree
defective at any point, a current of intensity has a tendency to
aggravate the fault, and to corrode and eat away the conductor
by chemical decomposition, at the point where the escape occurs,
finally destroying the communication altogether.
Fig. 63 is a side elevation of this instrument, showing a
section through the galvanometer coils and the outer case
containing them. Fig 64 is a cross section through the coils,
showing the magnet, technically termed the needle. Similar
letters refer to like parts in both figures. The magnet A is a
small bar of steel, one half inch in length and one tenth of an
inch square, cemented to the back of a very thin circular glass
mirror, a. The mirror is suspended in a brass frame, B
(Fig. 64), by an exceedingly delicate silk fibre, and is
adjusted in height by the screw b. This frame slides
into a vertical groove left in the centre of the coil, dividing
it into two parts. The coil and mirror are enclosed in the
brass case D, this case having pieces of glass let in wherever
necessary, to permit the passage of light. The object of this
arrangement is to prevent the mirror and its attached needle
from being disturbed by currents of air.
A narrow pencil of luminous rays from the lamp, E, passes
through the opening, F, which is capable of adjustment by the
slide G. This pencil of light, passing through the lens, is
reflected by the mirror back through the lens upon an ivory
scale at I, as shown by the dotted lines. The scale is
horizontal, extending to the right and left of the centre of the
instrument, the zero point being exactly opposite the lens. The
luminous pencil is brought to a sharp focus upon the scale by a
sliding adjustment of the lens M, in the tube N. When the
needle is at rest in its normal position, and no current is
passing, the spot of light which serves as an index will remain
at zero on the scale.
The operator reads the signals from a point just in the rear of
the magnet and coils, the light of the lamp being cut off by the
screen Y, so that he only sees the small luminous slit through
which the light enters the instrument, and a brilliantly defined
image of the slit upon the white ivory scale just above, which
is kept in deep shadow by the screen Y. A very minute
displacement of the magnet gives a very large movement of the
ray of light on the scale I, the angular displacement of the ray
of light being double that of the needle.
It is obvious that the ray of light from the needle will be
reflected to the right or left of zero on the scale, according
as the deflection is produced by a positive or negative current.
The Morse alphabet is used for signaling through the Atlantic
cable, deflections on one side of zero indicating dots, and on
the other side dashes.
It will be observed that the end, and not the broad part of the
flame of the lamp, is presented to the slit F, which is also
arranged to receive the brightest part of the vertical section
of the flame.
The galvanometer coils, R, consist of many thousand convolutions
of fine insulated copper wire, and they are insulated from the
case, D, by a disc of hard rubber, T, to which they are
fastened.
The instrument is usually provided with a directing magnet, by
which its sensitiveness may be varied to a great extent. This
magnet is in the form of a bar, slightly curved, and is of
considerable power. It is placed upon a vertical rod passing
through its centre, which is fixed above the coil immediately
over the needle, in such a manner that it can be turned
horizontally so as to follow the movements of the needle, or be
removed nearer to or further from it vertically. If it is
placed with its south pole over the north pole of the needle, it
will add its directive force to that of the earth, and by
holding the needle more powerfully in its position, will lessen
its sensitiveness. The nearer the magnet approaches the needle
the greater will be its power over it, and it can be arranged so
as to hold the needle in any desired position. If it is placed
in a reverse direction, so as to repel the needle instead of
attracting it, it will lessen the attractive force of the earth
so as to increase its sensitiveness, and in a certain position
will render the galvanometer astatic. When the magnet is too
near the needle it repels to the full extent of the scale. If
it is raised upon the supporting rod the repelling effect will
decrease, until, at a certain distance from the magnet, the spot
of light on the scale can be held at zero. The greatest
sensibility is obtained at the point at which the slightest
lowering of the magnet upon the rod will again repel the needle
to the full extent of its swing.
An improvement in this instrument, made by Mr. C. F. Varley,
consists in giving the mirror a concave form, silvered upon the
back and thus dispensing with the use of the lens above
described.
174. Mode of Working the Atlantic
Cables.--- Very little has been made public in regard to
the precise method employed in signaling through the Atlantic
cables. As before remarked, the reflecting galvanometer is
employed as a receiving instrument, and by employing deflections
on one side of zero to represent dashes, and those on the other
side dots, the Morse alphabet is found to answer the purpose
admirably. It is said that the two cables have been looped in a
metallic circuit without ground connection, and that they have
also been worked separately with and without condensers. The
latter method is made use of in order to avoid the disturbances
generated by what are known as ``earth currents.''
Different parts of the earth and sea are found to be at
different electric potentials. One part is electro-positive or
electro-negative to another. That is to say, there is the same
difference between the two parts of the earth that exists
between the two poles of a battery. If, therefore, these two
points are joined by a wire, a current will flow through that
wire as if from a battery, and this current is termed an earth
current, to distinguish it from the current generated by an
ordinary voltaic battery. This difference of potential between
two given points, such as Newfoundland and Valencia, is not
constant but continually varies, causing a corresponding
variation in the current it produces. This current and its
fluctuations interfere with the signals. When very rapid
changes take place in the electric condition of the earth, it is
known as a magnetic storm, and this occasionally interferes with
the working of all telegraph lines.
By the method of working with condensers the disturbances from
this cause are avoided. The condenser is constructed of
alternate layers of tin foil and thin plates of mica, gutta-
percha or paper, saturated with paraffine, arranged like leaves
of an interleaved book. Each alternate metal plate is
connected so as to form two distinct series, insulated from each
other, one of which is connected with the line and the other
with the earth. By an inductive action, similar to that of the
well known Leyden jar, a quantity of electricity, in proportion
to the amount of surface exposed, may be accumulated or stored
up upon the metallic plates. If, therefore, one series of
plates be charged with positive electricity the other series
will become negative by induction, and by means of this
induction a much larger quantity of electricity may be
accumulated than would otherwise be the case.
The manner in which the condenser is made use of in working a
cable is as follows :
The sending apparatus consists of a battery, B (Fig. 65), which
is permanently connected with the cable through the back contact
of a Morse key, K, and the cable is therefore kept constantly
charged from this battery. When the key is depressed the cable
is placed in connection with the earth at E. The receiving
apparatus consists of the reflecting galvanometer G
(163), one terminal of which is
attached to the cable and the other to one series of plates in
the condenser C---the other series being connected with the
earth, as shown in the figure. R is a very high resistance,
inserted in a wire leading from the point O, between the cable
and the galvanometer, so as to allow a very slight but constant
leakage from the cable to the earth. The cable is, therefore,
charged to the tension of the battery B, and the condenser to a
tension equal to that of the point O---but owing to the high
resistance at R the tensions are nearly the same. Upon charging
the cable with the battery at K a charge of electricity enters
the cable, and a quantity sufficient to charge the condenser
passes through the galvanometer, deflecting the mirror until the
condenser is charged equal to the tension of the point O---when
the mirror will return to zero. By putting the cable to earth
at K a portion of the charge will be withdrawn, and the tension
of the point O lowered below that of the condenser. A portion
of the charge of the latter, therefore, flows into the cable,
deflecting the galvanometer in the opposite direction. The
right and left hand deflections necessary for signaling are
therefore produced without reversing the currents, or rendering
it necessary to entirely discharge the cable after each signal.
This mode of signaling possesses many important advantages over
the old method, in point of rapidity of action and freedom from
interference by earth currents. The rate of working through the
cable by expert operators is said to average from fifteen to
twenty words per minute.
175. Velocity of Electric Signals.---
For many years the velocity of electric signals in
passing through a conductor was supposed to be infinitely great,
or at least so great as to be incapable of measurement. In
1849, Professor Sears C Walker, of the United States Coast
Survey service, while engaged in measuring longitude by means of
the electric telegraph, discovered a perceptible retardation.
Experiments between Washington and St. Louis indicated a
velocity not far from 16,000 miles per second. Some of the
measurements were as low as 11,000 miles per second. On the
evening of the 28th of February, 1868, a number of experiments
were made by the officers of the Coast Survey, for the purpose
of determining accurately the difference in longitude between
Cambridge, Mass., and San Francisco, Cal. A wire was connected
from Cambridge to San Francisco and back, embracing thirteen
repeaters---the whole distance thus traversed by the signals
being about 7,000 miles.
The following table shows the time, in hundredths of a second,
occupied by a signal in passing from Cambridge to each of the
repeating stations and back. The number of repeaters in circuit
is also given :
In submarine cables the velocity of signals is considerably less
than upon air lines. Prof. Gould, in his experiments upon the
Atlantic Cable, found it to be between 7,000 and 8,000 miles per
second---being greater when the circuit was composed of the two
cables, and less when the earth formed a part of the circuit.
His experiments seemed to show that, instead of travelling
around the entire circuit in one direction, the electric wave,
or polar influence, travelled both ways from the battery, and
the signal was received when the two influences met.
Experiments made on air lines indicate that an instrument placed
at the central point of resistance between the two poles of the
battery will record the signal sooner than when placed in any
other part of the circuit, it being understood that the two
terminal batteries of a telegraph line are in effect but one,
being connected by the earth, which is a conductor of infinitely
small resistance.
176. Speed of Transmission.---
The average rate of transmission, by the most skilful
operators upon the Morse apparatus, is about 1,800 words per
hour. This has been considerably exceeded, however, by many
operators within the past two or three years. On the evening of
January 28th, 1868, 2,520 words of Press news were sent from New
York to Philadelphia in one hour, and legibly copied by the
receiving operator, without a stop or break---the average rate
being forty-two, and the maximum rate forty-six words per
minute.
On the 7th of February following 2,630 words of Press news were
sent from Milwaukee, Wis., to St. Paul, Minn., in one hour, the
distance being about 400 miles. On the 19th of the same month
1,352 words of Press news were sent from New York to
Philadelphia in thirty minutes, the average rate being over
forty-five words per minute.
This is believed to be the quickest time on record which has
been made in the transmission of regular business by the Morse
system. The receiving operator, in all the above cases, copied
entirely from the sound of the instrument.
The speed of the printing instrument exceeds that of the Morse
under favorable circumstances. On the 24th of September, 1867,
the Combination instrument transmitted from Albany to New York
1,453 words of Press news in thirty-three minutes. It is
claimed that, on some occasions, as many as 2,900 words per hour
have been transmitted by the House instrument.
177. Comparison of Wire Gauges.---
The different sizes of wire employed for telegraphic and
other purposes are designated by a series of arbitrary numbers.
The system known as the Birmingham gauge is the one in most
general use at the present time, but is objectionable, both on
account of the irregularity of its gradations and the absence of
any authorized standard---wire of the same number from different
makers often varying considerably in its size. The American
gauge is formed upon a geometrical progression, and it is to be
hoped will eventually supersede the old gauge : it is already
employed to a considerable extent.* The following table gives
the diameter, in thousandths of an inch, of each number in the
American and Birmingham gauges :
// footnote
* This gauge is manufactured by Darling, Brown & Sharpe, of
Providence, R. I.
// end footnote
The weight of any iron wire, per statute mile of 5280
The resistance per statute mile of a galvanized iron
The conductivity of any copper wire is obtained by multiplying
its calculated resistance by 100, and dividing the product by
its actual resistance. Pure copper is taken as 100.
179. Conducting Powers of
Materials.--- According to the experiments of Mr. M. G.
Farmer, made some years since, the relative electrical
resistance of different metals and fluids at ordinary
temperatures is as follows, pure copper being taken as 100 :
180. Internal resistance of
Batteries.--- This may be measured by the sine or
tangent galvanometer. Place the battery to be measured in
circuit with a sine galvanometer giving a certain deflection.
Insert resistance till the sine of the deflection becomes half
what it originally was. The total resistance of the circuit is
now doubled, and the resistance added is, therefore, equal the
the original resistance. Deduct the resistance of the
galvanometer and connections from the resistance added, and the
remainder is the resistance of the battery.
Second Method.*--- Let D = the deflection obtained with
the battery in circuit with a galvanometer whose deflections are
proportional, and some resistance r; and d the
deflection with some larger resistance R (the resistance of the
galvanometer being included in R and r), and let x
= the resistance of the battery.
// footnote
* Clark, Electrical Measurement, p. 100.
// end footnote
The approximate resistance of the batteries in common use is as
follows, according to Mr. Farmer :
// footnote
¹ Electrical Measurement, p. 108.
// end footnote
182. Measurement of Electro-motive
Force.*--- When a number of cells are joined up in
circuit with, but in opposition to, a number of other cells with
a galvanometer inserted, by adjusting the number of cells so
that no current passes, the relative electromotive force of the
two batteries may be determined.
// footnote
* Clark, Electrical Measurement, p. 103.
// end footnote
Second Method.--- Call the electro-motive forces of the
two batteries E and E'; join them up successively in circuit
with the same galvanometer, and by varying the resistance, cause
them both to give the same deflection ; their forces will then
be in direct proportion to the total resistances in
circuit in each case, or
183. Forces of Electro-magnets.---
The laws which govern the forces of electro-magnets
have been investigated by Lenz, Jacobe and Muller.
It will be noticed, in the above formulæ, that M increases
directly as Q and as n, but Q decreases as n
increases, supposing the electric force to remain constant.
Hence it is evident that a certain proportion between the
resistance of the wire and that of the remaining portions of the
circuit must be preserved to obtain the maximum magnetic force.
This relation is found to be the following :
When the resistance of the coils of the electro-magnet is
equal to the resistance of the rest of the circuit, i. e., the
conducting wire and battery, the magnetic force is a maxi-
mum.*
// footnote
* Noad's Students' Text-book of Electricity, p. 277.
// end footnote
The application of this law to a telegraphic circuit would be to
make the sum of the resistances of all the magnet coils in
circuit equal to the resistance of the line and batteries, but
as in practice the resistance of a telegraphic circuit varies,
being considerably reduced by defective insulation, the total
resistance of the instruments should be less than that of the
line when in good condition, to attain the best results during
unfavorable weather.
![[IMAGE]](contacts/fig60-5.gif)
![[IMAGE]](contacts/fig61-5.gif)
![[IMAGE]](contacts/fig62-5.gif)
![[IMAGE]](contacts/fig63-43.gif)
![[IMAGE]](contacts/fig65-5.gif)
TIME OF TRANSMISSION FROM CAMBRIDGE.
_Seconds._
To Buffalo and Return....................... 0.10 1 Repeater
`` Chicago `` ....................... 0.20 3 ``
`` Omaha `` ....................... 0.33 5 ``
`` Salt Lake `` ....................... 0.54 9 ``
`` Virginia City `` ....................... 0.70 11 ``
`` San Francisco `` ....................... 0.74 13 ``
The actual time of transmission from Cambridge to San Francisco
and back was estimated not to exceed three tenths of a second,
the ``armature times'' of the thirteen repeaters probably
amounting to four or five tenths of a second.
TABLE OF DIAMETERS OF WIRES.
=======================================================================
| American | Birmingham || | American | Birmingham
Number.| Gauge. | Gauge. || Number.| Gauge. | Gauge.
--------|------------|------------||--------|------------|-------------
0000 | .460 | .454 || 19 | .03589 | .042
000 | .40964 | .425 || 20 | .03196 | .035
00 | .36480 | .380 || 21 | .02846 | .032
0 | .32495 | .340 || 22 | .02535 | .028
1 | .28930 | .300 || 23 | .02257 | .025
2 | .25763 | .284 || 24 | .0201 | .022
3 | .22942 | .259 || 25 | .0179 | .020
4 | .20431 | .238 || 26 | .01594 | .018
5 | .18194 | .220 || 27 | .01419 | .016
6 | .16202 | .203 || 28 | .01264 | .014
7 | .14428 | .180 || 29 | .01126 | .013
8 | .12849 | .165 || 30 | .01002 | .012
9 | .11443 | .148 || 31 | .00893 | .010
10 | .10189 | .134 || 32 | .00795 | .009
11 | .09074 | .120 || 33 | .00708 | .008
12 | .08081 | .109 || 34 | .0063 | .007
13 | .07196 | .095 || 35 | .00561 | .005
14 | .06408 | .083 || 36 | .005 | .004
15 | .05707 | .072 || 37 | .00445 | ....
16 | .05082 | .065 || 38 | .00396 | ....
17 | .04526 | .058 || 39 | .00353 | ....
18 | .0403 | .049 || 40 | .00314 | ....
-----------------------------------------------------------------------
178. Useful Formulæ for Weight and
Resistance of Wires.--- The following formulæ, from
Clark's tables, will be found convenient in telegraphic
work :
_d_(squared)
feet, is -------------- lbs.; _d_(squared) denoting the square of the diame-
72 X 15
ter of the wire in ``mils'' or thousandths of an inch.
The conductivity of ordinary galvanized iron wire,
compared with pure copper 100, averages about 14, or about one
seventh that of pure copper.
395000
wire is about -------------- ohms at 60° Fahr.
_d_(squared)
The resistance of iron wire increases about .35 per cent. for
each degree, Fahr.
The _weight_ per statute mile of 5280 feet, of any cop-
_d_(squared)
per wire, is -------------- lbs. A mile of No. 16 wire weighs
3613
in practice from 63 to 66 lbs.
The resistance per statute mile of any _pure_ copper
54892
wire is -------------- ohms at 60° Fahr. No. 16 copper wire
_d_(squared)
of good quality has a resistance of about 19 ohms.
The resistance of any pure copper wire _l_ inches in
.001516 x _l_(squared)
length, weighing _n_ grains, = ------------------------ ohms.
_n_
The resistance of copper increases as the temperature rises, .21
per cent. for each degree, Fahr.
Copper Wire.......... 1.00 | Tin wire............. 6.80
Silver `` .......... .98 | Zinc `` ............. 3.70
Gold `` .......... 1.13 | Brass `` ............. 3.88
Iron `` .......... 5.63 | German Silver Wire.... 11.30
Lead `` .......... 10.76 | Nickel ``..... 7.70
Mercury `` .......... 50.00 | Cadmium ``..... 2.61
Palladium Wire....... 5.50 | Aluminum ``..... 1.75
Platinum `` ....... 6.78 |
His experiments with fluids gave the following results :
Pure Rain Water................................. 40,653,723,00
Water, 12 parts ; Sulphuric Acid, 1 part........ 1,305,467,00
Sulphate Copper, 1 pound per gallon............. 18,450,000,00
Saturated solution of common salt............... 3,173,000,00
`` `` of sulphate of zinc.......... 17,330,000,00
Nitric Acid, 30 B............................... 1,606,000,00
The following table gives the specific resistance in ohms of
various metals and alloys, at 32° Fahr., according to the
most recent determinations of Dr. Matthiessen :
============================================================================
| Resistance | Resistance | Approximate
| of wire 1 | of wire 1 | per cent.
| foot long, | foot long, | variation in
Name of Metals. | weighing | 1-1000th | resistance
| 1 grain. | inch in | per degree
| | diameter. | temperature
| | | at 20 degrees.
-----------------------------------|------------|------------|---------------
Silver annealed................... | 0.2214 | 9.936 | 0.337
`` hard drawn................. | 0.2421 | 9.151 | .....
Copper annealed................... | 0.2064 | 9.718 | 0.338
`` hard drawn................. | 0.2106 | 9.940 | .....
Gold annealed..................... | 0.5849 | 12.52 | 0.365
`` hard drawn................... | 0.5950 | 12.74 | .....
Aluminum annealed................. | 0.06822 | 17.72 | .....
Zinc pressed...................... | 0.5710 | 32.22 | 0.365
Platinum annealed................. | 3.536 | 55.09 | .....
Iron annealed..................... | 1.2425 | 59.10 | .....
Nickel annealed................... | 1.0785 | 75.78 | .....
Tin pressed....................... | 1.317 | 80.36 | 0.365
Lead pressed...................... | 3.236 | 119.39 | 0.387
Mercury liquid.................... | 18.746 | 600.00 | 0.072
Platinum silver alloy, hard or an- | | |
nealed, used for standard resis- | | |
tance coils..................... | 4.243 | 148.35 | 0.031
German silver, hard or annealed, | | |
commonly used for resistance | | |
coils........................... | 2.652 | 127.32 | 0.044
Gold silver alloy, 2 parts gold, | | |
1 part silver, hard or annealed. | 2.391 | 66.10 | 0.065
-----------------------------------------------------------------------------
The use of this table is as follows : Suppose it is required to
find the resistance at 32° Fahr. of a conductor of pure
hard copper, weighing 400 lbs. per knot. This is equivalent to
460 grains per foot. The resistance of a wire weighing one
grain is found by the table to be 0.2106, therefore the
resistance of a foot of wire weighing 460 grains will be 0.2106
/ 460, but the resistance of one knot will be 6087 times that of
one foot, therefore
6087 x 0.2106
the resistance required will be --------------- = 2.79 ohms.
460
If the diameter of the wire be given instead of its
weight per knot, the constant is taken from the second
column. Thus the resistance at 32° Fahr. of a knot of
pure hard drawn copper wire 0.1 inch in diameter
6087 x 9.94
would be ------------- = 6.05. The resistance of wires is
10000
materially altered by annealing them, and a rise in
temperature increases the resistance of all metals. Dr.
Matthiessen found that for all pure metals the increase
of resistance between 32° and 212° Fahr. is sensibly
the same. The resistance of alloys is much greater
than the mean of the metals composing them. They
are very useful in the construction of resistance coils.
The highest value which has probably been found for the
conducting power of pure copper is sixty times that of pure
mercury, according to Sabine. Commercial copper may be
considered of good quality when its conducting power is over
fifty. Different samples of copper vary greatly in their
specific conductivity, as may be seen by the following table,
which gives the result of careful determinations by Dr.
Matthiessen, the conducting power of pure copper at 59.9°
Fahr. being taken as 100.
Lake Superior, native, not fused ................. 98.8 at 59.9°
`` `` fused (commercial) ............... 92.6 at 59.0°
Burra Burra ...................................... 88.7 at 57.2°
Best selected .................................... 81.3 at 57.5°
Bright copper wire ............................... 72.2 at 60.2°
Tough copper ..................................... 71.0 at 63.1°
Demidoff ......................................... 59.3 at 54.8°
Rio Tinto ........................................ 14.2 at 58.6°
Thus Rio Tinto copper possesses no better conducting power than
iron. This shows the great importance of testing the
conductivity of the wire used in the manufacture of electro-
magnets, cables, etc.
Then D : _d_ :: R + _x_ : _r_ + _x_
(d x r) - (D x r)
and _x_ = -------------------
D - d
and by deducting x we get the value of y, or if
y be large in comparison with x, the latter may be
neglected. By this method one resistance r may be
compared with another.
Grove.................................... 0.41 ohms
Carbon................................... 0.63 ``
Daniell.................................. 1.70 ``
181. Electro-motive Force of Different
Batteries.--- The following table gives approximately
the electro-motive force of various batteries, being the mean
of numerous observations taken on a sine galvanometer by Mr.
Latimer Clark.¹ The electro-motive force of batteries is
within certain limits very variable depending on a variety of
undetermined causes. It is not much affected by temperature.
Grove's........................................ 100
Carbon with bi-chromate solution............... 107
Daniell's...................................... 56
Smee's (when not in action).................... 57
`` (when in action) about.................. 25
Copper and zinc in acid (Wollaston)............ 46
Sulphate mercury and graphite (Marie Davy)..... 76
Chloride silver................................ 62
Chloride lead.................................. 30
When connected on short circuit, the electro-motive force of
several of the batteries, especially Smee's and Wollaston's,
will fall off 50 per cent. or more, owing to the formation of
hydrogen on the negative plate. Grove's and Daniell's do not so
fall off, because the hydrogen is reduced by the nitric acid in
one case and by the oxygen in the other.
R'
E' = E X -----
R
where R represents the resistance with E (including that of
battery, galvanometer, and the adjustable resistance) and R'
with E'.
Let M = the magnetic force of the electro-magnet.
_n_ = the number of convolutions of wire.
_d_ = the diameter of the soft iron core.
Q = the quantity of electricity in circulation.
and _c_ a constant multiplier.
_____
Then M = _c_ _n_ Q \/ _d_
This law only holds good for bars of iron whose length is
considerably greater than their diameter, for feeble currents of
electricity, and under the supposition that the number of
convolutions of wire is not so great as materially to diminish
the influence exerted by the outer coils upon the bar of iron.
These conditions are fulfilled in the electro-magnets used for
telegraphic purposes.
ELECTRICAL FORMULÆ
184. Ohm's Law.--- Let C = the
quantity, or strength, or force, or intensity of the current, as
it is variously called.
Let _n_ = the number of cells.
`` E = the electro-motive force in each cell.
`` R = the internal resistance of each cell.
`` _r_ = the resistances exterior to the battery.
Then _n_ E
C = --------------
_n_ R + _r_.
185. Parallel or Derived Circuits.---
1. The joint resistance of any two parallel or derived
circuits, whose resistances = a and b, is equal to
their product divided by their sum, or
_ab_
R = -----------
_a_ + _b_
2. The joint resistance of any
three circuits, a, b and c, is
_abc_
R = --------------------
_ab_ + _bc_ + _ac_
3. The joint resistance of any
number of circuits is obtained by adding their reciprocals
together, thus :
1
R = -------------------
1 1 1
--- + --- + ---
_a_ _b_ _c_
186 Galvanometers and Shunts.--- 1. The joint resistance of a
galvanometer and shunt is as follows :
Let _g_ = resistance of galvanometer.
_s_ = resistance of shunt.
_gs_
Then R = -----------
_g_ + _s_
2. The multiplying power of any shunt is equal to
_g_ + _s_ _g_
-----------, or ----- + 1
_s_ _s_
3. To prepare a shunt having
some definite multiplying power, for example 10 100 or 1,000,
Let _n_ = the multiplying power required,
_g_
Then _s_ = ---------
_n_ - 1
187. Formula for the Loop Test
(127).---
Let x = resistance of shortest part of the
loop.
_y_ = resistance of longest part.
L = total resistance of both.
R = resistance added to shortest part, to make it equal to the longer.
Then _x_ + _y_ = L.
_y_ = _x_ + R.
L - R
and X = -------
2
188. Blavier's Formula for Locating a
Fault (128).---
Let R =
resistance of line when in good order, S = resistance of
defective line when distant end is to ground, and T the
resistance when it is disconnected or open at distant end.