the quantity of electricity that passes through any section of the conductor in unit time, measured either by a galvanometer or by a voltameter, be C, then, according to Ohm's law, is directly proportional to the length of the conductor, and inversely proportional to the area of its section.

E
C

E

The coefficient of proportionality for a definite+ substance depends merely on the temperature of the substance; for unit length and unit section of a given substance the value of the ratio for a given temperature is called the specific resistance of the substance for that temperature, and is one of the most important of its physical constants.

C

This law has been directly verified by its discoverer, and by Becquerel, Davy, Fechner, Kohlrausch, and others; and indirectly it has been verified for a great variety of substances with a degree of accuracy approached in few physical measurements.

Lately, in discussing some experiments of his own, Dr. Schuster has raised the question whether after all Ohm's law is only an approximation, the limit of whose accuracy lies within the region of experiment. We might suppose

E
C

that the ratio was some function of C2, say

E

where R is a constant very nearly equal to what has hitherto been called the specific resistance, and S is a small constant which, according to Dr. Schuster's suggestion, would be positive. It is clear that can only be an even function of C, unless we admit unilateral conductivity, for which there is no experimental evidence in a purely metallic circuit.

A Committee of the British Association, appointed to consider the subject, were of opinion that it was of importance to attempt a further experimental verification of Ohm's law.

At the suggestion of Professor Maxwell, the experimental details of two methods of verification proposed by him were undertaken by the writer of this Report. Of the two experiments representing these methods the second is by far the most conclusive. It not only avoids the difficulty of eliminating temperature effects, which to a certain extent interfere with the first experiment, but it pushes the verification of Ohm's law very near the natural limit of all such verifications, viz. the limit of the solid continuity of the conductor. It has thus been rendered probable that experiment cannot detect any deviation from Ohm's law, either in the direction indicated by Dr. Schuster, or in the opposite direction as suggested by Weber, even in wires that have been brought by the electric current to a temperature beyond red heat.

A third experiment was also tried by the writer of this Report; its result agreed with the others, but, owing to certain peculiarities, it is less conclusive than they are. It led, however, to interesting results of another kind, which

*The current is supposed to be steady.

+By definite is meant in a given physical condition, except as regards E.M.F. and flow of E, and temperature. The last is excepted because we are brought face to face with possible temperature variations in the first experiment.

We suppose the conductor to be of unit length and unit section. It is of course the specific resistance which is in question; and this, if variable, will depend on the current per unit of section.

seem to show, among other things, that conclusions respecting the accuracy of Ohm's law cannot safely be drawn from experiments of the nature of those made by Dr. Schuster.

FIRST EXPERIMENT.

Suppose that we had five resistance-coils, which, when compared with each other by means of the same current, were cqual, say each = R. That is to say, if any two of the resistance-coils were inserted in the branches A B and BD of a Wheatstone's bridge, the other two arms, A C and CD, being two other equal resistances, then the galvanometer G inserted between B and C would indicate no current.

Suppose now that we replace the coil R in BD by four of the equal coils arranged in multiple arc, as in fig. 2. Then, if Ohm's law be true (i. e. if resistance be independent of current), if p be the resistance between B and D, 1 1 R'

1

1
= + =
Ρ 2R 2R

i.e. p=R, and there will still be no deflection in the galvanometer. But if Ohm's law be not true, and the resistance be a function of the current, then, since the current through A B is nearly the same as in the first experiment, while that through BED and BFD is half, the resistances in BE, ED, BF, FD will be no longer equal to R, but either greater or less, and the galvanometer will be deflected.

Under the direction of Professor Maxwell, part of the funds at the disposal of the Committee were devoted to providing two sets of coils specially adapted for the above experiment. One set consisted of five coils of silkcovered German silver wire (diameter 6 millim.), each of resistance as nearly as possible equal to 30 B.A. units. These were all wound together in the usual way round one bobbin; the terminals consisted of ten pieces of stout copper wire, insulated from each other by a ring-shaped piece of ebonite, through which all of them passed. These stout wires were bent over, and

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 ebonite 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 tho 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. I 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 9 and 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 are 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 x 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 r 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, r+Y, T+8, T+E.

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

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

a−ß={D—a−b+2(x − 5000)} {

all other terms being negligible.

This gives
10000-x

1

T

"},

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.

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¬{(B+y+d+e)=D−a−b+2(x−5000). .

(3)

(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