Sir W. Thomson on the Dissipation of Energy. 347 



communicated to the Royal Society of Edinburgh in April 

 1852, and published in the c Proceedings ' of the Society for 

 that date, and republished in the Philosophical Magazine for 



1852, second half year, is a sufficient answer to the challenge 

 referred to in the opening sentence of Professor Tait's letter. 



I think Professor Tait quite right in referring also to that 



paper for the formula t 1 — . The whole matter is contained 



in the formula it , e~JJT M , which is given explicitly in that 

 paper. At the top of the next page in the Philosophical Ma- 

 gazine reprint the following passage occurs : — " If the system 



of thermometry adopted be such that [i = , that is, if we 



agree to call a the temperature of a body, for which /ul is. 



the value of Carnot's function (a and J being constants), &c.;" 

 and on the word " adopted " the following footnote is given : 

 "According to Mayer's i hypothesis ' this system coincides 

 " with that in which equal differences of temperature are defined 

 " as those with which the same mass of air under constant 

 " pressure has equal differences of volume, provided J be the 



et mechanical equivalent of the thermal unit, and - the coeffi- 



" cient of expansion of air." Here the true foundation of the 

 absolute thermodynamic scale now universally adopted was, I 

 believe, for the first time given. I had previously, in Part III. 

 of my " Dynamical Theory of Heat," published in the Transac- 

 tions of the Royal Society of Edinburgh, and in the Philoso- 

 phical Magazine for 1852, second half-year, taking advantage 

 of a suggestion made to me by Joule, in a letter of date De- 

 cember 9, 1848, shown that the assumption u= reduces 



Lips a + T u + t 



the formula we~JJ T tow — — „: and I used this transforma- 



tion in the concluding formulas of the article referred to by 

 Professor Tait (corrected in the errata of Phil. Mag. 1853, 

 first half-year). It was not, however, until the experiments 

 by Joule and myself, made in the course of the years 1852, 



1853, and the early part of 1854, on the thermal effects of 

 forcing air and other gases through porous plugs, had proved 

 that my proposed thermodynamic scale agreed as nearly with 

 the scale of an air-thermometer as different air-thermometers 

 agreed with one another, that I definitively adopted it in fun- 

 damental formulas of thermodynamics. Thus, for example, 

 in Part VI. ("Thermo-electric Currents ") of my "Dynamical 



