** 167. The Equipment of Telegraph
Lines.--- **The satisfactory performance of any given
telegraphic circuit depends largely upon the maintenance of a
proper relation between the respective resistances of the line,
instruments, and batteries. There is in all cases an
ascertainable definite proportion between these, which gives,
theoretically, the best result with the least expenditure ; to
which practice should always be made to approximate as nearly as
possible. The disregard of the well-established laws of
electrical and magnetic action is not only the source of grave
difficulties in the practical operation of lines, but also
entails an enormous waste of material and supplies.

It is one of the fundamental laws of the electric circuit, that
*with a given resistance of conducting wire and battery, the
maximum magnetic force is developed when the total resistance of
the coils of the electro-magnet or magnets is equal to the
resistance of the other portions of the circuit, i. e., the
batteries and conducting wires.* (173.)

The resistance of the conductor, which must of necessity, always form a large proportion of the total resistance in every main circuit, is in practice determined within certain well-defined limits, by considerations of distance, mechanical construction, and first cost. It therefore becomes necessary to adjust the resistance of the remaining parts of the circuit with reference to that of the conductor, which in practice usually ranges from 10 to 20 units per mile. With the No. 9 galvanized iron wire generally used, it approximates closely to the latter figure.

The resistance of the batteries forms but a very small portion of the total resistance in an ordinary main circuit, and admits of comparatively little variation, so that the actual problem which presents itself, is to determine the proper resistance of the relays when the resistance of the conductor is given, and the form of battery which will supply the necessary electrical power for operating the line with the least expenditure of materials and labor.

The size of the conductor having been fixed upon, this taken in connection with the length will determine its total resistance. The combined resistance of the relays should be made to equal this amount as nearly as possible. It is hardly necessary to add that the resistance of the different relays should be uniform in respect to each other. With good relays the amount of battery required to operate the main circuit should not exceed 1 cell of Grove or Carbon battery for each 150 units resistance, and will generally be less than this. About double this number of the Daniell, Hill, or Callaud battery will be needed.

For example, suppose it is required to construct a telegraph line 300 miles in length, with 15 stations. If No. 9 wire is used as a conductor its resistance will be say 300 x 20 = 6000 units. The resistance of all the relays being made equal to that of the line, we have as the proper resistance for each relay 6000/15 = 400 units. The amount of battery required will be 12000/150 = 80 cups of Grove or Carbon, or about 160 cups of Daniell, Hill, or Callaud.

The approximate average resistance, and comparative electro- motive force of the different batteries in use is as follows, the Grove battery being taken as the standard at 100 :

Electromotive Resistance. force. Grove....................... .5 units 100 Bi-Chromate or Carbon....... 1.0 `` 107 Daniell..................... 2.0 `` 56 Callaud..................... 3.0 `` 56

These figures refer to the ordinary sizes of the Grove and Carbon battery, and to the Daniell and Callaud when adapted to a jar eight inches high and six inches inside diameter. Although the resistance of the battery when included in a single main circuit of the usual length, has but little influence upon the effective strength of the current as a whole, yet in local circuits, and in main batteries from which a number of lines are worked at the same time (110), it becomes an essentially important element in the calculation.

Another important law of electrical action, which applies especially to instruments which are to be worked by a local circuit, is the following :

*The greatest effective force of any given battery is
developed when the sum of all the external resistances in the
circuit is equal to the internal resistance of the
battery*.

In a local circuit there are practically no resistances except those of the battery and magnet, and it is therefore obvious that these should be so adjusted as to equal each other as nearly as possible. Tested by this rule, a great portion of the sounders, registers, and repeaters, in use in this country, will be found to have magnets of too low resistance, most of them being adapted to the use of a local of one Grove cell, although nearly all the local batteries in use are composed of 2 or 3 cells of Daniell. Such a magnet will only partially develop the effective force of a Daniell battery, and still less that of a Callaud or Hill.

The sizes of copper wire generally used in local helices vary from No. 19 to 22, American gauge, and the resistance from 0.5 units to 4 units. The most usual resistance is about 1 unit. If we take a sounder of this resistance and apply a cell of Grove battery, we have the following result :

Resistance of magnet............... 1 unit. `` `` battery.............. 1 `` ---- Total.............. 2 ``

Calling the electro-motive force 100, and dividing this by the resistance, we get 50 as the effective strength. If we take the same sounder and apply a Daniell element with 2 units resistance the total resistance will be 3, the electro-motive force 56, and the quotient or effective force 18.6, but little more than one-third that of the Grove. With 2 Daniell cells we have---

Resistance of magnet............... 1 unit. `` `` battery.............. 4 `` ---- Total.............. 5 ``

The electro-motive force of 2 cells will be 56 x 2 = 112, and dividing this by the resistance, 5, we have 22.4. With 2 Callaud cells the effect would be still less, in fact only 16.

Now let us take the same sounder, and remove the helices of No. 19 wire, which give a resistance of 1 unit, and rewind them with No. 23 wire, and observe the effect. With a given strength of current, the magnetic effect is proportional to the number of convolutions, and the latter increase inversely as the square of the diameter of the wire. The resistance of the wire also increases as its length, and inversely as the square of its diameter. The squares of the respective diameters would be as follows :

No. 19................ .00128881 `` 23................ .00051076

The average length of each convolution in a helix of a given size will be the same with any sized wire. The length being in inverse proportion to the square of the diameter, the resistance due to the increased length will be

.00051076 : .00128881 :: 1 unit : 2.52 units.

But the resistance is further increased in inverse proportion to
the *square of the diameter* of the wire, therefore

.00051076 : .00128881 :: 2.52 : 6.3

6.3 units would, therefore, be the resistance of the new helices. This is not strictly accurate, as no allowance has been made for the spaces between the convolutions, which occupy more room in the coil when finer wire is used, and somewhat reduce the number of convolutions as well as the length and resistance of the wire. We will, therefore, call the resistance of the new helices 6 units. This resistance will give the greatest possible effect obtainable with 2 Callaud cells, which will be as follows :

Resistance of magnet............... 6 units. `` `` battery.............. 6 `` ---- Total resistance............. 12 `` Divide the electro-motive force 112 ----- = 9.3 By the total resistance........ 12

But the magnetic effect is increased by the greater number of convolutions in the proportion of the squares of the diameters, or as 2.52 to 1. Therefore 9.3 x 2.52 = 23.43. This is greater than the magnetic effect of 2 Daniell cells upon the sounder of 1 unit resistance, which we before found to be 22.4. Making some deduction for the slight decrease in the number of convolutions, owing to the greater number of spaces, we may consider the actual magnetic effect to be the same in both cases. Experience has shown that this is amply sufficient to operate a well-constructed sounder or register.

In the above calculations the resistance of the Daniell is given as 2 units. It is actually over 3, except when the porous cell is defective, or so excessively porous as not to separate the liquids properly. The Callaud is also given as 3 units, but in point of fact does not exceed 2 after it has been 2 weeks in use. The resistance of the different Callaud cells is very uniform, while cells of the ordinary form of Daniell will often vary widely under precisely similar conditions. Sometimes one cell will measure 10 units, and another only 2, owing principally to difference in the quality of the porous cups. A cell of high resistance will diminish instead of increasing the effect in a local circuit.

The obvious advantage of using the Callaud battery for local circuits in connection with a magnet whose resistance is properly adjusted to it, consists in its great economy, the expense of maintenance not being more than one-fifth as great as when the ordinary Daniell is employed. The above calculations show that a great saving can be made when the Daniell itself is used, by regulating the resistance of the magnets to correspond with that of the battery.

** 168. The Working Capacity of Telegraph
Lines.--- **In order to secure the best possible result in
the working of telegraph lines we must keep down the resistance
of the conductors in the circuit
(42), and increase the
resistance of the insulation
(90) to the greatest
practicable extent. In other words, the resistance must be as
small as possible in the route we wish the electric current to
travel, and as great as possible in every other direction.
*The practical working value of a telegraph line is the
margin between the joint resistance of the conductor and the
insulation, and that of the insulation alone*. The tension
of the retracting spring of the relay armature, when upon a
``working adjustment,'' is the measure of this margin or
difference. It is evident that this margin may be increased in
two ways, viz. :

1. By increasing the insulation resistance.

2. By decreasing the resistance of the conductor.

For example, suppose a line of telegraph 100 miles in
length---the weather being rainy. Suppose that the conductor
has a resistance of 20 units per mile, while the resistance of
the insulators is 1,000,000 units per mile. Let the receiving
magnet and battery be situated at one extremity of the line and
the key at the other. When the key is closed, the force acting
upon the armature of the magnet is in proportion to the quantity
of electricity leaving the battery and passing through the
magnet to the line, and this quantity is made up of that
escaping through the insulation along the line, in addition to
that going through the conductor to the other end of the route.
When the key is open, the force exerted upon the armature is due
to the current passing through the insulation alone. The
effective working strength is therefore the difference between
the attractive forces acting upon the armature, when the key is
opened, and when it is closed at the other end of the line---or,
in other words, *the working margin is the difference between
the sum of the forces due to the joint conductivity of the wire
and insulators and that of the insulators alone*
(104).

Thus, in the case cited : The total resistance of the wire is........... 2,000 units. `` `` insulation........... 10,000 `` The joint resistance of wire and insulators is 1,666 `` The strength of current being inversely proportional to the resistance, it will be as follows : When key at other end is closed............... 100.00 `` `` `` open................ 16.66 ------ Difference, or effective working margin....... 83.33

It is not the *absolute* resistance of the conductor or of
the insulators that determines the value of a line. It is
operated by the *margin or difference* between these two
values (101). It is important
that this should not be lost sight of.

Now let us observe the effect of substituting a wire of twice the weight, having a resistance of only 10 units per mile. We now have :

Total resistance of wire...................... 1,000 units. `` `` insulation (as before)....... 10,000 `` Joint resistance.............................. 909 `` The proportionate strength of current will become : When key is closed............................ 100.00 `` `` open............................. 9.09 Difference.................................... 90.91

We have given the strength of current with key closed as 100 in
both the above cases, in order to show the proportionate
increase of margin. The *absolute* strength of current in
the two cases, is as 100 to 183, an increase of 83 per cent.,
while the increase of working margin is only 9 per cent.

We will now take the result of an actual measurement. A new No. 9 galvanized wire, 115 miles in length, on a clear and fine day, gave a resistance of 2,400 units, or about 21 units per mile. On the same poles was a No. 10 plain wire, which had been in use nineteen years. This wire, including eight instruments in circuit, gave a resistance of 13,300 units. In a rain the insulation resistance of the good wire measured 15,300 units, and the bad wire 19,650.

The joint resistance of the good wire and its insulators was 2,077. The proportion of current escaping by the insulators was to the whole current as 13.51 to 100, giving a margin to work on of 86.49.

The joint resistance of the bad wire and its insulators was 7,982. The proportion of escape to the whole current was as 40 to 100, giving but 60 per cent. as an available working margin. This wire could not be worked except when the other circuits on the same poles remained idle, either closed or open. The good wire was worked without difficulty. The escape was apparent, but was not sufficiently great to cause any serious inconvenience. The relative working margins were in the proportion of 86.49 to 60.

On a clear and cold day the insulation of the good wire showed a resistance of 2,400,000 units, the working margin being 99.99. The bad wire showed an insulation resistance of 1,700,000 units, the working margin being 99.93. The difference in this case between the two wires was only 00.06, an amount not appreciable in practice. The poor wire worked as well as the good one, but the current was not so strong. This difference could be compensated for by increasing the battery on the former.

In the above instance we have two wires on the same poles. One is new and a good conductor, the other old and a poor conductor. In fine weather the insulation of the new wire is the most perfect, but the difference in their working is inappreciable. In rain, although the insulation of the old wire is actually the best, yet it does not work nearly so well as the new wire, and this is attributable solely to the fact that the new wire has a much greater conductive capacity.

Take another example, also from actual measurement : A new wire, 150 miles in length, on a clear day gave a resistance of 2,200 units. On the same poles was an old rusty No. 11 wire, which gave a resistance of 23,500 units. On an very wet day the insulation resistance of the new wire was 4,800 units, and of the old wire 32,000 units. The working margin of the new wire was 78, and that of the old wire 60. In this case the amount of current escaping over the insulators of the new wire was 2.7 times that passing through the old wire and its insulators combined ! In other words, the current with key open on the new wire was nearly three times as strong as on the old wire when the key was closed.

In these examples the resistance of the batteries and instruments has not been taken into account, as they do not materially affect the results.

** 169. The Electrical Tension of
Telegraphic Batteries and Lines.--- **In another part of
this work (8) it was briefly
stated that the electrical tension of a battery, or its power of
overcoming resistance, is increased in direct proportion to the
number of elements of which the battery consists. Suppose we
have a battery of 100 cells, and the electro-motive force of
each element of the battery be such as to produce a difference
in tension between its plates equal to 1, the difference between
its poles or end plates will be equal to 100. But it must be
understood that degrees of tension are only relative or
comparative. The earth being our great reservoir of
electricity, its tension is called zero, and it affords us a
convenient standard of reference in comparing other tensions,
but even the absolute tension of the earth sometimes varies in
different times and places.

Suppose we take the battery of 100 cells above referred to, place it upon a well-insulated stand, and connect one pole of it, say the zinc or negative pole, to earth, and leave the other pole disconnected, and therefore insulated by the air. The end which is connected with the earth being in free communication with it, will now have a tension of zero, and the opposite end of the battery will give a tension of 100 positive or above that of the earth, and if a wire were connected from it to the earth a powerful current of electricity will pass between them.

If now the copper or positive pole be placed to the earth, and
the zinc pole insulated, the tension of the former will now be
zero, and that of the latter 100 negative, or *below* that
of the earth. In each of these cases the degree of tension is
the same, but in one case it is above that of the earth, or
positive, and in the other case below that of the earth, or
negative.

If the zinc or negative pole of the same battery be now connected to the earth, and the positive pole, instead of being left free, is connected by a short and thick wire, of no appreciable resistance, to the negative pole, the tensions throughout the circuit will be materially changed, although the electro-motive force will remain unaltered. The tension at the copper pole of the battery, which was 1,000 when the pole was entirely disconnected, now becomes the same as that of the earth, or at least but very little above it. If a wire offering considerable resistance be substituted for the short and thick wire which connects C and Z, the tension at C will be raised, although that of Z will still be kept at zero by its connection with the earth at that point. In proportion as the resistance of this connecting wire is increased, the tension at C rises until, when the resistance becomes infinite, the tension will again reach 100, for infinite resistance is absolute insulation. The tension is now equal to the electro-motive force, but it is obvious that it can never exceed it under any circumstances.

If a battery of 100 cells is connected to a telegraph line of 100 miles in length, whose insulation is perfect, and which is not connected to the earth at the remote end, the line will instantly acquire a tension of 100 throughout its whole length (this being equal to the electro-motive force of the battery), and this would occur if the wire were a thousand or a million times that length. After the line has acquired the same tension as the pole of the battery to which it is attached, no current will flow from the battery.

If the distant end of the line is connected to the earth, the battery will come into action, and a current of electricity will pass through it. This will at once change the tensions throughout the whole line. The distant end of the line, which originally had a tension of 100, will now have a tension of zero, being connected directly to the earth, and from this point the tension will rise gradually and regularly along the whole length of the line to the pole of the battery. So also the tensions within the cells of the battery itself follow the same law.

The relation existing in a voltaic circuit between the resistances, electro-motive forces, and tension, may be graphically and accurately represented to the eye by a geometrical projection based upon mathematical reasoning, a method first suggested by Ohm, and more recently elaborated by Mr. F. C. Webb, and which he explains as follows :

Let all the parts of a circuit, whether liquid of solid, be expressed in their successive order by portions of a continuous horizontal line, which shall be to one another as the reduced lengths or resistances of those parts. Let the tension at any given point in the circuit be represented by the perpendicular height of a point above, or depth below, the horizontal line representing the resistances. This when above the line will indicate a positive, and when below, a negative tension. The horizontal line of resistances may be termed the axis.

In order to represent the tension at every point in the circuit,
we must construct a line termed the *line of tension*. The
perpendicular height of this line above the axis at any point,
indicates a corresponding positive tension at that point, and
its depth below in the same manner indicates a negative tension.
When this line crosses the axis the point of intersection has no
tension.

Electro-motive force consists in a sudden and constant difference in the tension of the points situated immediately upon opposite sides of the surface of junction between the zinc element and the liquid of the battery. The electro-motive forces in the circuit must, therefore, be represented by a sudden rise in the line of tension at the points along the axis at which they occur, thus forming lines perpendicular to the axis. The magnitude of these lines must be proportional to the electro-motive force they represent. Moreover, as the electro- motive force is a quantity depending solely upon the nature of the elements at the surface of junction at which it occurs, and not at all on any change in the resistance or electrical state of the circuit, these perpendicular lines constantly maintain the same magnitude, although their position as regards the axis may be altered in various ways.

Now let us construct a diagram which shall correctly represent the electro-motive forces, tensions, resistances, and strength of current, as a telegraph line with a closed circuit, having a battery of three cells at each end of the line, which will be a sufficient number to correctly represent the arrangement of the circuit ordinarily used on American telegraph lines.

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.

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 :

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.

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

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 :

The *weight* of any iron wire, per statute mile of 5280

_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.

The *resistance* per statute mile of a galvanized iron

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.

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 :

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.

** 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

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.

The approximate resistance of the batteries in common use is as follows, according to Mr. Farmer :

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.

// footnote

¹ *Electrical Measurement*, p. 108.

// end footnote

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.

** 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

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'.

** 183. Forces of Electro-magnets.---
**The laws which govern the forces of electro-magnets
have been investigated by Lenz, Jacobe and Muller.

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.

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.

** 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.

The distance (*x*) of the fault from the testing station
will be

______________________________ _x_ = S - \/ S(squared) + T R - T S - R S ___________________ or _x_ = S - \/ (R - S) x (T - S), and the resistance of the fault (_z_) will be ______________________________ _z_ = T - S + \/ S(squared) + T R - T S - R S ___________________ or _z_ = T - S + \/ (R - S) x (T - S)

** 189. Measures of Resistance.---
**1.0456 Siemen's units = 1 ohm. To convert Siemen's
units into ohms, multiply by .9564.

1 Varley's unit = 25 ohms. 1 Megohm = 1,000,000 ohms. 1 Microhm = 1/1,000,000 ohms.

** 190. Strain of Suspended Wires.*---
**The ordinary dip of line wires, for a span of 80 yards,
is about 18 inches in mild weather ; this gives with No. 8 wire
a strain of 420 lbs., its breaking weight being about 1,300
lbs.---(*Culley*.)

// footnote

* Clark. *Resistance Measurement*. p. 154

// end footnote

The strain varies directly as the weight of the wire, and inversely as the dip or versine ; it increases as the square of the span if the dip be constant ; but to preserve a given strain the dip or versine must increase as the square of the span, or,

L(squared) : _l_(squared) :: V : _v_.

The strain is greater at the point of suspension than at the
lowest point of the span, by a quantity (equal to the weight of
a length of wire of the same height as the versine) which may be
neglected in practice. Calling *l* the length of the span
in feet, *w* the weight in cwts. of one statute mile,
*v* the versine in inches, and *s* the strain in
lbs.,

_l_(squared) x _w_ Strain = -------------------- lbs. approximately. 31.43 x _v_ _l_(squared) x _w_ and dip = -------------------- inches. 31.43 x _s_

When both supports are of the same height the lowest point in the curve will be in the centre of the span ; but if one support be higher than the other the lowest point will be near the lower support, so that the greater portion of the weight is borne by the higher pole. In calculating the strain the wire should be considered as if prolonged beyond the lower end to a point equal in height to the upper one, and the strain will be proportional to the length thus increased, or to twice the distance from the top to the bottom of the dip.

The weight of a wire increases with its strength, the quality being the same. The advantage of using thin wire for long spans is only in diminishing the weight upon the supports.

Iron expands 1/14616 of its length, or about 4 1/10 inches per
mile for every ten degrees of heat.---(*Culley*.)

THE END.