VI.-Note on the Relation of the Electrical and Mechanical Units.

By HOWARD T. BARNES, M.A.Sc., D.Sc.

(Communicated by Prof. John Cox and read May 29, 1900.)

In view of the immense amount of labour expended in establishing the international electrical units, volt, ohm and ampere, in absolute measure, it is a matter of some interest to compare a determination of some physical constant made in terms of these units with a determination of the same constant in terms of the mechanical units. Such a comparison has already been made between the value of the mechanical equivalent of heat as determined by Rowland, with that measured in terms of the electrical units by Griffiths, and independently by Schuster and Gannon. The values obtained by both these latter investigators both show as a result of the comparison with Rowland's measurements an error in one of the electrical constants.

Quite recently I have been enabled to complete an extensive investigation into the value of the mechanical equivalent of heat in terms. of the electrical units which it has been possible, through the superior equipment of the Macdonald Physical Laboratory of McGill University, to extend over the entire range of temperature between the freezing and boiling points for water, obtaining exceedingly accurate measurements of the thermal capacity at different temperatures. The method which I have used, due to Prof. Callendar, differs essentially from that used by both Griffiths and Schuster and Gannon. However, a comparison of my absolute value with that of Rowland has shown a similar error in one of the electrical units. In addition to a comparison of the mechanical equivalent at one temperature with that of Rowland, it is possible, owing to the great range of my experiments, to compare the value of the mean mechanical equivalent between 0° and 100° C., with the value obtained recently by Reynolds and Moorby by a direct mechanical method. This comparison also shows that the value which has been hitherto assumed for one of the electrical units is in error. The amount of the error from the comparison with the experiments of Rowland is :04 per cent, and from the experiments of Reynolds and Moorby is 066 per cent, both in the same direction as regards the unit in question. Of the three electrical units the ohm has attracted the largest amount of attention, not only in England, but also amongst physicists in Germany and America. The first and most important step towards the establishment of this unit was made in England in 1861, when a Sec. III., 1900. 5.

committee appointed by the British Association undertook to fix the standard of electrical resistance. They decided that the practical unit should be defined as 10° C. G. S. units in Weber's absolute system. Various coils of wire were constructed and determined in absolute measure. Copies of these coils were made and distributed and became known as the B. A. unit of resistance. Although this unit was adopted in England, on the continent another unit was in vogue which was established by Werner von Siemens, and known as the Siemens unit. This was equal to the resistance of a column of mercury one metre long and one square millimetre in cross section.

In 1878, Rowland redetermined the value of the B. A. unit by an absolute method proposed by Kirchoff, and showed that it was apparently in error by as much as 1 per cent.

In 1883, and then a few years later, Glazebrook made some determinations by the same method used by Rowland and verified his results. The mean of his measurements gave a value of the B. A. unit equal to 98665 X 10° C. G. S. units.

This has been subsequently verified, both in Germany and elsewhere, and the unit so defined has been universally adopted as the true or international ohm.

The ampere, equal to 10-1 C. G. S. units, was determined in absolute measure by Lord Rayleigh and Mrs. Sedgwick in 1888, who expressed it for practical purposes in terms of the electro-chemical equivalent of silver. Shortly after, the British Association entrusted Glazebrook and Skinner to establish the volt, 188 C. G. S. units, in terms of the E. M. F. of the Clark cell. They determined this in terms of the true ohm and ampere as defined by Lord Rayleigh and Mrs. Sedgwick's value of the electro-chemical equivalent of silver, and it was found that the international volt could be expressed as equal to 1994 of the E. M. F. of the Clark cell.

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In measuring the quantity of energy which was required to warm the water in my determinations of the mechanical equivalent of heat, it was necessary to measure the difference of potential across the terminals of a platinum wire immersed in the water, and to measure the current of electricity flowing through this wire. Instead of measuring the latter by the electro-chemical equivalent of silver, I included a specially constructed wire resistance coil in the electrical circuit which I could standardize by direct comparisons with a large number of certified resistances from the electrical standards committee of the British Association. A measure of the difference of potential across this resistance gave at once the value of the current flowing in the circuit. The difference of potential on this as well as that on the electric heating

wire was reduced to volts by comparison on an accurate potentiometer with the E. M. F. of a Clark cell, the value of which being taken as 1-4342 volts. There can be very little hesitation as to which of the units, ohm or Clark cell, to refer the error between the two values of the mechanical equivalent. As against a large number of exceedingly consistent measurements of the ohm we have only the one determination of the Clark cell, which was made only indirectly. Moreover, there have been fairly recently two determinations of the value of the Clark cell, which were made by comparing the E. M. F. with that across a standardized resistance through which an electric current was flowing, the current being at the same time measured on an absolute electrodynamometer. One determination was made by Kahle at the Reichsanstalt, who obtained the value 1.4329 int. volts at 15° C., and the other was made by Carhart and Guthe at Michigan University which came 1-4333 int. volts. Although not agreeing particularly well they both show that the older value of the Clark cell obtained by Glazebrook and Skinner is too high.

In view of this uncertainty and of the discrepancy in the values of the mechanical equivalent of heat it is interesting to calculate back in the equation of the electrical method for the value of the Clark cell by assuming the mean value of the equivalent as obtained in Reynolds and Moorby's experiments. The value so obtained comes 1.43325 int. volts at 15° C., which is identical to the value obtained by Carhart and Guthe. A similar calculation by assuming Rowland's value of the equivalent over the range of his experiments, i.e., 6° and 36° C., with the value from the present experiments over the same range gives a value for the Clark cell equal to 1.4336 int. volts at 15°. This agrees to 3 parts in 10,000 with the value in terms of Reynolds and Moorby's experiments. The agreement of the value obtained by meaning these two last determinations, which comes 1.4334, with the value obtained by meaning the two entirely independent absolute determinations which is seen to be 1.4331 int. volts, is so close as to be quite within the limits of error of the several experimental determinations upon which they depend, and gives a more satisfactory verification of the absolute values assumed for the international ohm, volt and by implication the ampere.