The action of PQ is obvious. When the prongs approach cach other the upper dipper is depressed into the mercury in S, while the lower dipper is raised out of the mercury in T, so that the current of the larger battery passes, and vice versa when the prongs separate; and it is easy enough by throwing a galvanometer in instead of one of the batteries, and then setting the fork going with the other on, to adjust the break in such a way that there is perfect independence between the two currents. This test was in fact actually applied either at the beginning or end of each set of experiments. We have thus alternately sent through the bridge certain definite fractions of the whole current due to the large and small batteries. What fractions these are will depend on the nicety with which the break is adjusted (with perfect adjustment it would be one half of each), and also on the state of the mercury surfaces and of the dippers. As may be imagined, the main difficulty of the experiment lay in getting the dippers to work properly. Several sorts were tried; plain copper amalgamated was found to act fairly well, but broad spade-shaped pieces of platinum-foil answered on the whole best. The surface of the mercury was covered with spirit, which is effectual so far in preventing the spoiling of the surface; but ultimately the cups get clogged with finely divided mercury, and then all regular action is at an end. It was

found, however, that with some care the break could be got to work long enough to allow of good results being obtained.

On account of this gradual alteration of the break, and for other reasons as well, it was of vital importance to be able during the experiment to obtain some measure of the amount of current that passed as representative of the large and small current respectively; for the experiment would obviously be nugatory if, instead of the smaller current being nearly half the larger, it became, owing to deterioration of contact in the cup S, equal to what ought to be the larger current. To provide for this the experiments were conducted as follows:-The balance was found, whether for larger currents alone or smaller alone (acting directly or with the fork going), or for both together in the same or in opposite directions; then the block was moved as quickly as possible 6 centims. from the position of balance, and the deflection which then appeared was read off; this deflection is approximately proportional to the current. Knowing then the electromotive force of either battery and its internal resistance, one could not only tell whether the currents were passing nearly in the right proportion, but also estimate roughly how much current absolutely passed in each case. In some of the best experiments a more accurate method was adopted :-The point D was "put to earth," and the point E connected by means of a long insulated wire with one pair of the quadrants of a Thomson's electrometer in the flat of the laboratory below the room where the experiment was carried on; the other pair of quadrants being "put to earth," the deflection observed on the electrometer-scale was a direct measure of the electromotive force between D and E—that is, of the quantity denoted

above by

PE.

B+p

Before giving the quantitative results obtained from the most satisfactory experiments, it may be well to explain the principle on which these have been selected from the others. In all the experiments quoted there was either something remarkable, such as a high battery power, &c., or else the balances were obtained under very favourable circumstances, the spot of light being very steady, and the proportions of current passing, as indicated by the sensibilities* or electrometer measurements, being near the theoretically best amounts. Often where the breaks were not working satisfactorily, by working quickly a qualitative experiment could be made, the behaviour of the galvanometer indicating to an observer practised in the experiment that the proportions of current passing were not far wrong; and often part of an experiment could be made perfectly satisfactorily, and then the apparatus would go out of order. But in all the experiments, whenever the results were at all intelligible (regular), the conclusion pointed to never differed from that given by the best experiments, viz. either the balance for the currents in opposite direction lay more to the left than that for the currents in the same direction, or the two coincided. Of this the observer spared no trouble in assuring himself even in experiments that were quantitatively utterly valueless.

The first set of experiments quoted, which are not of much value quantitatively, may serve to illustrate what has just been said. In this set the time is given because the experiments were made during the slow heatingeffect already alluded to. The spot of light was not perfectly steady, though much steadier for the +- balances than for the others; the bridge-reading is given to tenths of a millimetre, though of course in the present case for

* The deflection due to six centimetres deviation from balance is called the sensibility.

the balances accuracy to less than a millimetre was not attained. The alternator was the rotating piece made by Mr. Garnett, driven by the governor, which, judging by the regularity and smallness of the oscillations. of its brake-wheel, went very uniformly during the whole experiment. The rate of revolution was about three turns (causing as many alternations) per second. The sensibilities for++and+ were respectively about 150 and 45 during the experiment, so that the large and small currents would be proportional to about 97 and 52 respectively. The fine wire was a small length of German-silver wire in. in diameter, whose resistance was about 7.3 ohms; and the counter-balancing resistance was 7.3 ohms, taken entirely from the small resistance-box. The governor being started, the batteries were set on at 4.6.

It will be seen that with some little irregularity the balance on the whole went steadily to the right during some three quarters of an hour. In one point all the observations agree, viz. that the + balance is more to the left by 1 to 3 centimetres than the++ for the corresponding time. If AR be the amount by which the average resistance is less for the smaller than for the larger current, then taking 250 as the difference between the balances, we get easily, from the formulæ given above (our unit of resistance being the resistance of millim. of the bridge-wire, i. e. 1978 ohm),

Now the variation in resistance of German silver being about 044 per cent. per deg. Cent., we get for 1° C. on 7-3 ohms a variation of about 430 in our present units. Hence the average temperature of the thin wire was something over 1° C. less during the smaller than during the larger current. Neither the magnitude of the cooling effect nor the irregularities in the progression of the balance in this experiment is to be wondered at, since we know that air-currents have a very powerful effect in cooling the thin wire; and here the wire was merely enclosed in a box to protect it from airgusts, but was otherwise unprotected. We ought therefore to expect very little of this effect in most of the following experiments, where the alternations were 20 times as fast, and where the wire was enclosed in a narrow tube protected from temperature variations.

In the experiment next quoted, the alternations were made by means of

the tuning-forks, and were at the rate of 60 per second. The resistance of the thin wire was very nearly the same, and it was enclosed in a narrow tube. The four Daniells had run down a good deal, being not quite equivalent to three, and the two had varied in proportion. The resistance which balanced the wire was, exclusive of the bridge-wire, 7.25 ohms.

It will be seen that the effect that was so conspicuous in the first experiment scarcely appears here at all. It was in fact so small that its appearance might be due to progress of the balance in the interval between the five observations.

In the next experiment the wire had a resistance of about 4-4 ohms; the material was German silver, and the diameter the same as before. The resistance against which it was balanced was a German-silver wire of about 12 centim. diameter, wound on a bobbin, the resistance of which was 4.45 ohms. The Daniells had been fresh charged, and were arranged in piles of four and two as usual, the respective internal resistances being about 5 and 3. The small resistance-box was on the left with the thin wire.

The experiment is marked in the laboratory book as very steady. It will be remarked that the sensibilities are large and well proportioned; for if we had theoretically perfect adjustment, the sum would have been 156 and the difference 54, as against 170 and 53. The + + balance is of course much more delicate than the + ; but even for the latter (6 centimetres giving, say, 54) we have 8 scale-divisions to a centimetre, so that we may rely on our + balances to about a millimetre. This experiment therefore indicates a coincidence of the two balances within 0016 per cent.

A good many experiments were tried with higher electromotive forces; but though qualitative results of some interest were got, sufficient steadiness could not be obtained to make the results of use quantitatively. In most of these the thin wire was over a red heat; in fact in many of them the experiment ended with the melting of the wire. In general there appeared to be a good

deal of the effect due to temperature oscillations already referred to. In one experiment in particular in which a Grove's battery was used, with alternations at the rate of only thirty per second, this effect came out very strong, the spot swinging off the scale when the smaller battery was reversed.

Without dwelling on these, I proceed to give the results of the final set of experiments, which were in every way by far the most satisfactory.

In the three following experiments the Daniells were used as before; the alternations were made by means of the tuning-forks at the rate of 60 per second. Three wires were experimented on, a platinum, a German-silver, and an iron wire. The balancing resistance was the German-silver bobbin with small resistance-box, which was on the left, except in the second experiment, where it was on the right. The electromotive force between D and F was now found directly by the electrometer; as a control the sensibilities are given as well. New spade-pointed platinum dippers were used, and answered admirably during the whole time the experiments were going on.

In the last set of experiments a higher electromotive force was used, viz. four cells of Grove and two, every thing else being as before. The same three wires were experimented upon, but with perfect success in the case of the iron wire only. In the experiments on the other two, although the electrometer readings were very steady and satisfactory, yet a steady balance could not be obtained; still it could be seen that the + + and + balances did not differ by much; it seemed that there was, in the case of the German-silver wire, a tending towards the effect so often alluded to. The following is the experiment with the iron wire:

:

Using the additional data that the resistance of the metre of platinumiridium wire on the bridge is 075 ohm, and that Latimer Clark's Standard Cell (1.457 volt) produces a deflection on the electrometer used of about 320 divisions, we get roughly the following results (e denotes the electromotive *Electrometer deflection for Latimer Clark's Standard = 320.