752 ANNUAL EEPOET SMITHSONIAN INSTITUTION, 1908. 



metric scale can be founded? He arrived at the answer that such a 

 scale is obtained in terms of Carnot's theory, each degree being de- 

 termined by the performance of equal quantities of work in letting 

 one unit of heat be transformed in being let down through that 

 difference of temperature. This indicates as the absolute zero of 

 temperature the point which would be marked as — 273° on the air- 

 thermometer scale. In 1849 he elaborated this matter in a further 

 paper on " Carnot's theory," and tabulated the values of " Carnot's 

 function " from 1° C. to 231° C. Joule, writing to Thomson in De- 

 cember, 1848, suggested that probably the values of " Carnot's func- 

 tion " would turn out to be the reciprocal of the absolute tempera- 

 tures as measured on a perfect gas thermometer, a conclusion inde- 

 pendently enunciated by Clausius in February, 1850. Independently 

 of Joule, Mayer and Helmholtz had been considering the same prob- 

 lems from a more general standpoint. Helmholtz's famous publica- 

 tion of 1847, Die Erhaltung der Kraft — On the Conservation of 

 Force (meaning what we now term " energy ") was chiefly concerned 

 with the proposition, based on the denial of the possibility of per- 

 petual motion, that in all the transformations of energy the sum total 

 of the energies in the universe remains constant. 



Thomson continued to work at the subject. He experimented on 

 the heat developed by compression of air. He verified the singular 

 prediction of his brother, Prof. James Thomson, of the lowering by 

 pressure of the melting-point of ice. He gave a thermodynamic ex- 

 planation of the nonscalding property of steam issuing from a high- 

 pressure boiler. He formulated, in the years 1851 to 1854, with scien- 

 tific precision, in a long communication to the Royal Society of Edin- 

 burgh, the two great laws of thermodynamics — (1) the law of equiva- 

 lence discovered by Joule, and (2) the law of transformation, which 

 he generously attributed to Carnot and Clausius. Clausius, indeed, 

 had done little more than put into mathematical language the equa- 

 tion of the Carnot cycle, corrected by the arbitrary substitution of 

 the reciprocal of the absolute temperature; but Thomson never was 

 grudging of the fame of independent discoverers. " Questions of 

 personal priority," he wrote, " however interesting they may be to 

 the persons concerned, sink into insignificance in the prospect of any 

 gain of deeper insight into the secrets of nature." " He gave a demon- 

 stration of the second law, founding it upon the axiom that it is im- 

 possible, by means of inanimate material agency, to derive mechanical 

 effect from any portion of matter by cooling it below the temperature 

 of the coldest of the surrounding objects. Further, by a most ingen- 

 ious use of the integrating factor to solve the differential equation 

 for the quantity of heat needed to alter the volume and temperature 



« Presidential address, Brit. Ass., 1871, and Popular Lectures, Vol. II, p. 166. 



