THE LONDON, EDINBURGH, AND DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF [FIFTH SERIES.] JUNE 1895. XLVIII. On the Scale-Value of the late Dr. Joule's Thermometers. By ARTHUR SCHUSTER, F.R.S.* IN [Plates V. & VI.] N order to bring the results of Joule's researches on the mechanical equivalent of heat into relation with more modern experiments on the same subject, it is necessary to determine the scale-value of Joule's thermometers in terms of some easily reproducible standard. We possess already a comparison by Joule himself of his thermometer with one used by Rowland, who has corrected Joule's result to the scale of his own air-thermometer. Some doubt may still exist, however, as to the true scalevalue of these instruments, partly owing to the fact that we have no information how the comparison between Joule's and Rowland's thermometers was conducted, and partly because we do not know to what degree of accuracy Rowland's airthermometer would agree with that of the Bureau International des Poids et Mesures, which for the present must be considered as the standard. The historical importance of the instruments used by Joule seemed to make it desirable therefore to subject them to a more extended investigation. The request which I made to Mr. B. A. Joule to allow me the use for a short time of his late father's thermometers was met by a most ready compliance, *Communicated by the Author. Phil. Mag. S. 5. Vol. 39. No. 241. June 1895. 2 K a shape as that shown in fig. 1. But I find that, assuming the bulb to be cylindrical, the pressure-coefficient gives a thickness of 0.09*, while on the assumption that it is spherical the calculated thickness of glass is 0.076, so that the result is almost the same, and we are not probably far wrong in taking 08 as the approximate thickness. Taking account of this value and the external volume, I find the volume of mercury to be about 4 cub. centim., and from the length of one degree of the stem obtain the radius of the bore approximately as 009. These numbers do not lay claim to any accuracy, but they are sufficient to give us an idea of the principal quantities involved in the construction of this thermometer. As the thermometer was calibrated before graduation, the distance between the divisions will give us some idea as to the regularity of the bore. In Table I. the first column gives the division of the thermometer, and the second, in millimetres, the corresponding distance from the centre of the reservoir, the third column gives the differences between the numbers of the second, and the numbers of this column are therefore inversely proportional to the mean area of the bore at different points of the thermometer. * All results, unless otherwise stated, are given in centims. To calculate the pressure correction we require the distances from the centre of the bulb, but there must of course be some uncertainty as to the point which is chosen as centre. The figures in the third column were obtained by direct measurement and are not affected by the same uncertainty. It will be seen that the bore is conical, gradually diminishing in diameter. The mean cross-sections near the two ends of the tube differ by about 20 per cent. In addition to the differences in the length of division intended to correct for the changes in the bore, there are also not inconsiderable inequalities which are evidently due to faults of graduation. These irregularities are quite visible with the naked eye, two successive intervals differing occasionally by as much as the tenth part of their own length. Owing to this fact the error of a single reading of this thermometer A may amount to 0°-004 C. quite independently of the general errors of calibration. It must be remembered of course that at the time the thermometers were made such a quantity was not considered to be of any importance, so that the divisions were sufficiently accurate for the purposes for which they were originally intended, The Fundamental Points. As regards the thermometer D, Joule has supplied us with the following information : "The freezing-point of the standard D had risen from 13.3 divisions of its scale in 1844 to 15-14 in 1877. I think it probable that the boiling-point of this thermometer, if kept constantly at this temperature, would in the course of time fall as much. The five careful determinations of this boilingpoint referred to 30 bar, and 60° are respectively 706, 706-4, 706, 7059, and 706-15-mean 706-09. Subtracting 1.84, 704-25 will be the probable ultimate reading, from which if we take 15.14 we shall have 689.11 as the range between the fixed points cleared from the effects of imperfect elasticity of the glass. Mr. E. Hodgkinson has pointed out (Brit. Assoc. Report, 1843, p. 23) that the 'set' of imperfectly elastic bodies is proportional to the square of the force applied, therefore the effect of imperfect elasticity in the glass of the thermometers will be insensible for the small ranges used in the experiments, and the factor 3.3822 for reducing the indications of D to those of A may be confidently relied on. "We have therefore as the most probable value of one division of A. In my former papers the number was taken as 0°077214, which is so near that I shall continue to use it, trusting by longcontinued observations of the fixed points to give it ultimately greater accuracy, and also, by experiments above indicated, to state it in terms of the absolute interval between these points." (Phil. Trans. 1878, part ii.; Collected Works, vol. i. p. 636.) It will be noticed that the actually observed difference between the freezing- and boiling-point is 690.95 divisions, but that Joule somewhat arbitrarily reduced this by 184 divisions, thus altering the fundamental interval by over a quarter per cent. It seems curious that no one should have directed his attention to this point, which to all appearance causes an error in the scale-value of his thermometer, and would make his equivalent come out too low by 0027 of its own value. If we collect together the scale-values of the thermometer A, given by Joule in different places, we find : |