Preliminary experiments. The preliminary experiments gave the differences between the coils and the variation-coefficients approximately.

The results appeared in some cases different from former measurements, so that it was thought better not to rely on these, but to make a more careful set of experiments on which to found the final comparison.

Approximate coefficient of " Flat Coil" and Middle Coils.-The variationcoefficient of the "Flat Coil" was taken from the preliminary experiments. This was given by a fairly good series of experiments; and a first approximation was considered sufficient, since the coil during the final experiments never varied in temperature more than two degrees, being always bathed in the tap-water. A similar remark applies to the middle coils. The coils used for middle coils were 29 and 43 (F and G) when neither of these was being measured, in which case 2 and 3 (A and B) were used. The coefficients of these coils, so far as required for small temperature-corrections, were taken from the preliminary experiments.

Method of experimenting.—The method used in the final experiments was as follows:

First. All the coils (the flat coil, the two middle coils, and the coil to be compared with the flat coil) were bathed in a stream of tap-water, the temperature of which was carefully taken by means of a Casella's thermometer (lent us by Mr. Gordon), reading to tenths of a degree Centigrade and easily estimable to hundredths. After the temperature of the stream had been constant for twenty minutes or so, the difference between the coil to be compared and the flat coil was found.

Secondly. Another series of experiments was made in which the flat coil and the middle coils were kept at the temperature of the tap as before; but the remaining coil was raised by careful nursing, which lasted two hours or more, to the temperature (or to one of the temperatures) at which, according to the B.A. Report, it is correct.

Lastly. The coils were compared with each other at the standard temperatures, the middle coils being kept at the temperature of the tap-water.

Variation-coefficients, how found.-The first two sets were used to give the variation-coefficients, being peculiarly fitted to do so, because in them the temperature of the flat coil did not alter much in comparison with the alteration in the coil compared with it.

Differences between the coils, how found.-Then using the low-temperature experiments the differences of resistance between the respective coils and the flat coil (all at 10° C.) were found.

This was

Control experiments, how used.-From this, of course, the difference between any two coils at any temperatures could be calculated. done for the old standard temperatures, and the results compared with the results of direct experiment obtained from our third set of experiments. This gave a test of the accuracy of our work; and it is on this mainly that we rely in claiming to have stated the temperatures at which the coils are equal within 0°.1 C. in all cases.

Degree of accuracy.-The degree of accuracy of resistance varies, of course, for the different coils. For the platinum units 0°-1 C. corresponds to a variation of 03 per cent. resistance, for the platinum-silver to about 002 per cent.

In the B.A. Report, 1865 (p. 303)*, all the coils are stated to be accurate at the temperatures indicated within '01 per cent. This corresponds to about one thirtieth of a degree Centigrade for the platinum units. It is not stated

* Reprint, p. 137

how this degree of accuracy was attained. Some such statement was perhaps necessary, considering the difficulty of controlling the temperature of an inaccessible wire, even within 1° Centigrade.

Arrangement &c. of apparatus.-The instruments used in these experiments for resistance measurements were the Wheatstone's bridge and Thomson's galvanometer belonging to the Association. The arrangements in the low-temperature experiments were as in the annexed figure. At one corner of a large

table is the bridge A B (see B.A. Report, 1864, p. 353*); by means of mercurycups at D and G, are inserted the flat coil and the coil being compared with it; at E and F are similarly inserted the middle coils, which were always two of the units, as small and as nearly equal in temperature-variation as possible. X, Y, Z are three earthenware jars in which the coils are placed; these stand in a trough, V W, provided with a waste-pipe going to the sink. The jars were kept constantly overflowing by means of a feed-pipe fitted with an offset for each. The temperature in all three jars was carefully observed, and it was found that after the tap had been turned on for fifteen minutes or so the temperature in all three in general became constant, and remained so within a tenth of a degree for a long time. Now and then irregularities occurred, which caused the rejection of the results concerned. Thin wires go from E and from the contact-block C to the galvanometer at the other end of the table. The last adjustments of the balance were made by observing the spot on the galvanometer-scale with the telescope from where the observer sits. The battery-circuit terminates at H and J, and is made and broken by means of a treadle worked by the observer's foot. A small Leclanche's cell was found sufficient to indicate a deviation from balance of a tenth of a millimetre on the bridge-scale. Since the contact of the block-piece could not be relied on within less than this, no higher batterypower was ever used.

Thermoelectric disturbances.-To avoid thermoelectric currents, owing to the junction of copper with brass at the block, the button of the block-piece was never touched by the fingers, but always by means of two pieces of wood, which were exchanged now and again to prevent heating. It was

* Reprint. p. 119.

found impossible to avoid this disturbance altogether; and accordingly the following mode of procedure was adopted :

Direct magnetic disturbances.-We first carefully investigated whether there was any direct magnetic effect on the galvanometer owing to the currents in the apparatus; this was done by simply short-circuiting the galvanometer. No such effect could be detected. Being assured of this, we always operated as follows:-Threw in the galvanometer by pressing down the button, then allowed the needle to come to rest with the small permanent deflection due to the thermoelectric current. If now, on pressing down the treadle for an instant, there was no motion of the spot, we concluded that there was a balance. It is to be noticed that since we are near balance the battery-circuit is conjugate to the galvanometer-circuit, and that, therefore, making or breaking the battery-circuit does not alter the effective resistance opposed to any electromotive force, thermoelectric or other, in the galvanometer-circuit. (Of this we also assured ourselves by direct experiment.) Another advantage of this method is that it ensures the least possible use of the battery, and thus avoids disturbances from heating. During our final experiments both of us had acquired by considerable practice an acquaintance with the indications of the galvanometer, which enabled us to adjust the balance quickly, and thus secure in greater measure the advantage above mentioned.

Self- and mutual induction.—It is also worth remarking that from the way the B.A. unit coils are wound, and from the general arrangement of the apparatus, neither self- nor mutual induction could have any sensible disturbing effects in our experiments

幣

Method of using bridge for finding coefficients of variation &c.-In finding the variation-coefficients of the coils the bridge arrangement was used in the way described in the Report on Electrical Standards, 1864 (p. 353, &c.); but in finding the difference between the resistances of two coils, the method described by Prof. Foster (in the Journal of the Society of Telegraph Engineers, October 1874) was used. In this method the bridge is first read with the normal coil and the coil to be compared with it in one position, and then the coils are interchanged; the difference of the bridge-readings gives the required difference of resistance in units of the bridge.

Bridge-units.-The unit in which we shall state our results further on is the resistance of a tenth of a millimetre of the bridge-wire, which is a metre long and has a resistance of about 075 ohm.

Calibration of bridge and thermometer.--The wire was carefully calibrated, but no errors were found large enough to affect our results.

The thermometer used was also compared with a standard thermometer belonging to the laboratory, and the corrected temperatures are in every case given. The degree of accuracy attained in this last comparison was probably about 05 Centigrade.

Description of coils in the case.-In the case containing the coils there are altogether fourteen coils. Five of these are multiples of the unit, viz. 2, 3, 5, 8, and 10, and have brass labels on them; but the inscriptions have never been completed by filling in the last two figures of the temperature at which they are equal to the standard. We have not been able to get any description of these whatever, and have therefore not measured them. Besides these there accompany the box two coils marked A and B, which are not units, and a flat coil described as a normal coil, besides a set of

Another precaution of less importance was to cover the platinum-iridium wire of the bridge with pieces of wood to screen it from dust and radiation from the body of the

observer.

tubes for mercury units. The flat coil we used and found very convenient, both from its shape and on account of its small variation-coefficient, which was only 34 per deg. Cent. in the above-mentioned units. The case contains altogether nine unit coils, viz. :—

Of the first six, all except 57, which we have not measured, are mentioned at p. 146 of the Reports, but none of them have proper labels. All, however, were marked in some way or other so as to be identifiable. Of the last three all have labels, which are complete in 6 and 43. Nos. 6 and 29 do not appear in the Reports. The temperature on 43, which does appear, agrees with that given on p. 146. We used 29 as a companion middle coil to 43, because its variation-coefficient was small and nearly equal to that of 43; but otherwise we have not bestowed much care on it.

Coils measured.-The coils which we have measured are, therefore, 2, 3, 58, 35, 36, 29, 43. These we call for convenience A, B, C, D, E, F, G. The normal coil is the flat coil at 10° Centigrade. This temperature is chosen because it was the lower limit of the temperature of the tap-water, which varied on different days from 10° to 12°, though it was very constant during a good part of any one day. As far as our experience went, the use of a stream of tap-water was the best as well as most convenient way of reducing the coils to a known temperature *.

Results of comparison: the first statement.-The following Table exhibits our results in the way which lies nearest the method by which they were obtained :

R stands for resistance of flat coil at 10° C.

of the respective coils A, B, &c. at 10° C. variation-coefficients.

Second statement.-The above is the most convenient form of representing our results; but for the sake of comparison we give also the following (Y now stands for the resistance of the coils A, B, C, &c., at the temperatures, or at some one of them, given at p. 483, B.A. Report, 1867 †) :

* One of us, in endeavouring to find the conductivity of paraffin, has since found that the temperature of a wire imbedded in a much greater thickness of paraffin than there is in the B.A. coils, reaches the temperature of the tap-water in considerably less than an hour, the paraffin-jacket having been at a temperature of about 30° throughout to start Reprint, p. 146.

with.

1876.

с

It will thus be seen that B and C are practically equal at the temperatures given, while A does not differ very much from these. D and E are not very different inter se, but differ somewhat from the first three; while G, considering its small coefficient, is considerably out.

Statement of standard temperatures.-If we consider B and C to be right at the temperatures given above and reduce the others so as to be equal to them, we should get the following Table of standard temperatures :—

Results of control experiments.-In the next place we give the results of our control experiments, in which the several coils were nursed to temperatures very near those given in the Report, and then compared with each other. The small deviations from the temperatures in the Report arise from thermometer corrections. The differences thus found are given side by side with those calculated from the data given above; the differences are given in the next column, and in the last the greatest possible difference, owing to an error of 0°.1 C. in temperature determination.

It appears, therefore, that the differences between the observed and calculated values are always less than what would arise in the most unfavourable case, owing to an error of 0°-1 C. in the temperature determinations.