cut as nearly as possible of the same length, so that their amalgamated ends might go in pairs into mercury-cups. The wire and bobbin were enclosed between two coaxial cylinders of sheet brass, which were fastened to the cbonito piece above, and connected by a ring of sheet brass below. The whole had a rough resemblance to a large spider. The other set consisted of two coils made of the same wire, and having each as nearly as possible the same resistance. They were arranged in the same way, except that the terminals of the same coil were adjacent.

As the adjustment of the coils was necessarily not perfect, the experiment could not be tried exactly as described in the above scheme. I decided, therefore, to operate as follows:-First, to compare each coil of the five with the coil next in order; the differences between any two coils could then be found in terms of an arbitrary unit (the resistance of a tenth of a millimetre of the platinum-iridium bridge wire at the temperature of the room during the experiment); second, to compare each coil with the four others arranged in multiple arc, as before described. The results thus obtained were compared, as will be described further on.

To facilitate these comparisons, the following arrangement of mercury-cup connexions was made for me by Mr. Garnett, of St. John's College, the Demonstrator at the Cavendish Laboratory :

To a massive board are glued five large mercury-cups, made of boxwood, with a piece of amalgamated sheet copper at the bottom. Into these go the ten terminals of the five coils, so that there would be metallic connexion round all the five coils in series were it not that the cup A is divided by a piece of vulcanite, which insulates the two terminals in that cup. 7 is a stout copper bow connecting B and the lower division of A; to this bow is soldered one of the galvanometer terminals. Into the cups u and v dip the two terminals of one of the two coils. m is a stout bow of copper connecting the upper half of A with u. Another bow goes from v to F, one end of the bridge, which is the instrument used by the British-Association Committee of 1863, and will be found described at p. 353 of the Report (1864) of the Com

mittee on Electrical Standards. To m is soldered one of the battery terminals. The connexions on the right are similar to those on the left, and may be understood from the diagram. The other galvanometer terminal goes to the contact-block L. The battery used consisted of twelve Leclanché's cells, the whole internal resistance of which was about 13 B.A. units, its E.M.F. being about 16 times that of a Daniell. The whole resistance of the bridge from F to G was about 075. The galvanometer is an instrument made by Elliott Brothers, belonging to the British Association; its resistance is about half a B.A. unit.

Good contact between the feet of the copper terminals of the quintuple coil and the bottom of the mercury-cups was secured by placing a weight on the top of the coil; the spring in the terminals was then sufficient to ensure contact everywhere.

In the arrangement figured in the diagram the coil p is balanced against a multiple arc, containing q and r in one branch, and s and t in the other. To compare one single coil with the next single coil, 7 is removed, and one end of the galvanometer wire connected instead with the cup E, while m is made to connect the lower instead of the upper half of A with u; with this arrangement the coil t is balanced against the coil s.

The coils in the quintuple coil are numbered 1, 2, 3, 4, 5; and in experiments with multiple arc the coil between A and B is referred to as the "single coil;" in experiments with single coils those between D and E and E and A are called right coil (R.C.) and left coil (L.C.); the coils between w and a and u and v are called right and left middle coils (R.M.C. and L.M.C.), and are numbered 1 and 2. The bridge is read from left to right.

Some preliminary experiments were made with the apparatus, which showed that the coils had been very well adjusted by the makers, Messrs. Warden, Muirhead, and Clark. It was found that with the arrangement described (the best at our command in the Cavendish Laboratory), the bridge could be read to a quarter, if not to an eighth of a millimetre. A small correction was found necessary for the magnetic field, due to the current in the bridge connexions; this was allowed for by adjusting a loop of the battery-wire till the galvanometer showed no effect when the battery was turned on. Thermoelectric currents in the galvanometer circuit, owing to heating from the hand at the contact-block, were avoided almost entirely by using two pieces of wood, which were interposed between the fingers and the block, and were continually changed so as not to get hot.

The order of experiment was generally as follows:-The weight was adjusted on the quintuple coil, the battery was thrown in for a moment by means of a treadle which closed the battery circuit; if there was no direct effect on the galvanometer, the battery was thrown out, and contact made at the block; the spot of light on the scale was watched through a readingtelescope, and if it was at rest the battery was thrown in: the deviation indicated which way the block had to be moved to get a balance. Two or three trials in general sufficed to get the balance. The bridge was then read; the middle coils were then reversed, the balance found, and the bridge read again. The difference of the readings gives the difference of the resistances of the middle coils, as may easily be shown (see Journal of Society of Telegraph Engineers,' Oct. 1872). The middle coils being replaced as before, the quintuple coil was moved round one step, and the same process repeated. * On the avoidance of small thermoelectric effects, see below in the discussion of the second experiment.

Formula of Reduction.

T

Let the right-hand middle coil (No. 1) be taken to be 30 ohms, the bridgewire being 075 of the same units. Let denote the resistance of this coil, the unit being the resistance of a tenth of a millimetre of the bridge-wire, therefore

Let the resistances of 1, 2, 3, 4, 5 of the quintuple coil, measured in the same units, be r+a, r+ß, T+Y, 7+d, 7+e.

Hence, comparing middle coil 1 with 2, 1 being on the right,

τ+α

=

+b+D+x

T+T+10000+a-x'

(1)

where +D=resistance of middle coil 2, x the bridge-reading, a and b the resistances of the connexions at its two ends. This gives

a− ß= {D — a − b + 2(x − 5000)} {

all other terms being negligible.

Now the greatest possible value of 10000-x is 6000, since the readings never went below 4000, and D+2(x-5000) was never greater than 400.

Hence the term involving

1000-x

is less than

and is therefore negligible, since we do not read beyond tenths of a millimetre. Hence we may use the formula.

Similarly, in comparing one coil against four, we get the formula.

a−1(3+y+d+e)=D−a−b+2(x−5000). . (4)

To find a-b, the "bridge correction," a reading is taken with the coils.

arranged as usual either for a single experiment or for a multiple-arc experiment: let this reading be x. Then the connexions are crossed, as in the

figure, by introducing two new pieces of copper and two more mercury-cups, the arrangement independently of the bridge being very nearly symmetrical: let the reading now be a'.

Assuming that the resistances of the movable cups and bows at the two ends are equal, k in one case, k' in the other, then

A variety of experiments were made with the coils arranged sometimes in one way, sometimes in the other, and closely agreeing values of a-b were found varying from 52 to 58.

Correction for want of Symmetry.

Referring back to fig. 4, we see that in the arrangement for multiplearc experiments the connexions are not quite symmetrical. The copper bows were all nearly of the same length and thickness: let the resistance of one of them be 20. Let also the average resistance of a mercury-cup be 2r. Then we get for the addition to †(ẞ+y+d+e),

(2b+10r)+b+r,

for the addition to a 2b+4r. Hence a-(B+y+d+e) is too great owing

to the connexions by +
2 2

Various experiments were made to find the value of b+r, and all gave very nearly the same result. The following is a specimen :--A copper bow very slightly longer than those in the connexions was inserted by means of an additional mercury-cup, first on the right then on the left of the bridge; the readings were 5032 and 4982, the difference being 50;

.•.2(b+r)=50,
b 7.
2+2=12.

The correction was actually taken to be 10.

Limits of Temperature Effects.

The coils were arranged for a multiple-arc experiment; the balance was

ON OHM'S LAW,

taken at 3.25; the battery was then thrown in and kept in for about a quarter of an hour with the following results :

:

X.

h m

3 25

5007

3 35

5020

3 42

5022

The reading therefore increased by 15, the greater part of increase taking place in the first 10 minutes. Another series of experiments were made with single coils against single, as follows:

Time of Obs. R.M.C. R.C. L.C.

1221

3

x.

4914

D.

These experiments were done as quickly
5137 223 as possible; the balance, already approxi-
mately known, was found by three or four
5226
5008 218 instantaneous contacts, so that the coils
were as little heated as possible.

The battery was thrown in at 12.36 and kept in, the coils being as in last experiment.

Crossed connexions

4818

Bridge correction 52.

Reducing these experiments by the formula given above we get

Several important inferences may be drawn from these experiments.

1. The difference of resistance between the middle coils decreases as the temperature increases, and that so regularly, that the value of D may be used as a sort of thermometer, indicating how nearly these coils are kept at the same temperature during any series of experiments. This fact shows the propriety of using the appropriate value of D for each case in our reducing formula instead of the average value.

2. The coils 4 and 5 possess the same property, though in a less degree. 3. The coils 1 and 2 possess this property to a very slight extent.

4. The greatest effect that could be produced in a reasonable time on the