Prof. Thomson on the Dynamical Theory of Heat. 117 



as the temperatures from zero*;" and values for various tempe- 

 ratures calculated by means of the formula, 



were given for comparison with those which I had calculated 

 from data regarding steam. This formula is also adopted by 

 Clausius, who uses it fundamentally in his mathematical investi- 

 gations. If fx were correctly expressed by it, we should have 



/•s ,, ,, 1+ES 



and therefore equations (1) and (2) would become 



S-T 



(12) 



(13) 



43. The reasons upon which Mr. Joule's o])inion is founded, 

 that the preceding equation (11) may be the correct expression for 

 Carnot's function, although the values calculated by means of it 

 differ considerably from those shown in Table I. of my former 

 paper, form the subject of a communication which I hope to have 

 an opportunity of laying before the Royal Society previously to 

 the close of the present session. 



[To be continued.] 



* If we take y.-=.k - — — — where k may be any constant, wq.find 



1 -\-Ejt 



which is the formula I gave when tliis ])ai)er was communicated. I have 

 since remarked, thfit Mr. Joule's hypothesis implies essentially that the 

 coefficient k must be iis it is taken in the text, the mechanical equivalent of 

 a thermal unit. Mr. Raukine, in a letter dated March 27, 1851, informs me 

 that lie has deduced, from the jninciples laid down in his paper communi- 

 cated last year to this Society, an approximate formula for the ratio of the 

 maximum (piaiitity of heat converted into mechanical effect to the whole 

 quantity expended, in an expansive engine of any substance, which, on 

 comparison, I find agrees exactly with the expression (12) given in the text 

 as a consequence of the hypothesis suggcste(l bv Mr. Joule regarding the 

 value of /i at any temperature. — [April 4, 1851.] 



