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 x'.

Assuming that the resistances of the movable cups and bows at the two ends are equal, =k in one case, l' 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 26. 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 26+4r. Hence a-(6+y+d+e) is too great owing

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 2

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

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

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 Obз. R.M.C. R.C. L.C. x. D.

1221d

3 2

4914

These experiments were done as quickly 5137 223 as possible; the balance, already approxi5226 mately known, was found by three or four 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.

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

difference between 2 and 3, by heating 2 and comparing it with 3 scarcely heated, if at all, was 16.

The above peculiarities suggested to me to make a set of experiments on the plan of keeping the current going as much as possible. It was hoped that thus a certain limiting state, as regards temperature, would be arrived at, which from the construction of the coils would in a great measure be independent of small variations of temperature in the experimenting-room *.

This method of proceeding would not introduce any error in the comparison of single coil with single, and the error introduced into multiple-arc experiments would be regular and could be allowed for. The last of the sets of experiments given below was conducted on this plan with satisfactory results.

* No special means of keeping the double and quintuple coils at a constant temperature was resorted to. The object was not to find the resistances of the coils at any definite temperature, but to compare them under the same circumstances as regards temperature. It was therefore thought that any attempt to surround the coils with water, &c. would introduce greater errors than would arise from small variations of temperature in the room during the experiment.

N.B.-In the last set of experiments 52 was used instead of 58 as the bridge correction.

The first thing to remark is the smallness of the sums of a-ß, ß-y, y —¿, d — e, e — a, as found from single-coil experiments; the sum is theoretically zero, and the largest deviation is about 20, which divided by 5 gives only 4 for the average error of a determination. Here no error from want of symmetry comes in, and errors from irregular temperature effects very nearly balance each other.

In the next place, taking the multiple-arc experiments of series No. 2, we see that there is a deviation of the observed from the calculated values of a−{(B+y+d+e) which averages 26; and here, from the way the experiments were conducted, the temperature disturbances are probably very small. Again, take the multiple-arc experiments of series No. 3. Here, from the manner of experimenting, the temperature effects will appear. We found that the greatest effect we could produce on one of the coils in a reasonable time was about 15; supposing that the whole of this was manifested in the single coil, we should get a quarter as much in each of the coils in the multiple arc (because the current is halved), that is, we have of 15 altogether in a-(ẞ+y+d+e); this necessitates a correction of about 10 to be subtracted from the observed values. This is clearly the maximum. correction, for after the first experiment we turn into the multiple-arc coils that have already been fully heated. Supposing, however, that we apply the full correction in each case, we get for the average difference -18.

This deviation is in the direction indicated by Schuster's experiments, but

it is excessively small: suppose we call it -20 for convenience of calculation; this corresponds to the fraction of 30 ohms.

20
1
4,000,000 200,000

But the whole deviation is probably introduced by some slight defect in the apparatus, and part at least can be accounted for; for it occurred to me, in looking over the results quoted above, that a defect in the insulation at the divided cup would partly account for such a deviation. Suppose that the divided cup offered a very large, but not infinite, resistance f to the passage of the current, then the single coil in multiple-are experiments would 1 1 1 be replaced by a multiple arc of resistance R', where

R=30+

Now let us find what ƒ must be to give a decrease of 20 in our observed value of a-(B+y+d+e):

that is, f=6 megohms. Curiously enough, when I proceeded to measure the insulation resistance of the divided cup it came out very nearly 6 megohms; but the insulation resistance between any two of the remaining cups was found to be about 12 megohms, which reduces the correction somewhat. The complete solution of the problem would be complicated; but we may approximate by considering each of the coils in the multiple are replaced by a multiple are whose arms are 30 ohms and 12 meghoms respectively; this requires that 3, y, d, e should each be reduced by 10. Hence the whole reduction in a-(3+y+d+e) would be on this supposition 10. It would really be somewhat less; however, this would almost bring the deviation between observation and calculation within the limits of experimental error. Any remaining difference is probably due to a defect in some mercury-cup in the multiple arc, for there being more there than on the other side of the balance the chance of a defect is greater.

It ought to be mentioned that the insulation of the quintuple coil was tested, and found in every case to be of a higher order of magnitude than a megohm.

Some time after the series of experiments just described, I dismounted the mercury-cups from the stand, which had meantime been carefully dried on the hot-water pipes in the laboratory. Each cup was remounted with a piece of gutta percha between it and the board; and the divided cup, which was found radically defective, was replaced by two mercury-cups on separate pieces of insulating material. The insulation between every pair of cups was then tested afresh and found in every case of a higher order than a megohm.

The experiments were then repeated with the altered stand. The sensibility of the arrangement was about the same as before, although a less electromotive force was used (10 cells). The results were much the same as before, except that the sum of the values of a-3+y+d+e), &c. was now much smaller, two experiments giving -31 and -34. Dividing this by 5, we get −6 for the average deviation, which is very small. The fact that we still get a result in the same direction shows that this is not an accidental error; bat it might very well be accounted for by some of the suppositions mentioned already. It might also arise from over-correction for symmetry.