16i M. R. Clausius on the Moving Force of Heat, 



as correct, the equation (IV.) will thereby be rendered unneces- 

 sary for the nearer determination of (Ila.), inasmuch as the same 

 object is anived at in a much more complete manner by equa- 

 tion (9.), which flowed immediately from the combination of the 

 said assumption with the original maxim. The equation (IV.), 

 however, furnishes us with a means of submitting both princi- 

 ples to a reciprocal trial. The equation (9.) was thus expressed, 



c?Q\_R.A(a4-0 



(S) 



V 



and when we compare this with equation (IV.), we find that 

 both of them express the same thing ; with this difference only, 

 that one of them expresses it more definitely than the other. In 

 (IV.) the function of the temperature is expressed in a general 

 manner merely, whereas in (9.) we have instead of C the more 

 definite expression A{a-{-t). 



To this surprising coincidence the equation (V.) adds its testi- 

 mony, and confirms the result that R(fl + 1) is the true expres- 

 sion for the function C. This equation is used by Clapeyron 

 and Thomson in determining the values of C for single tempe- 

 ratures. The temperatures chosen by Clapeyi-on were the boiling- 

 points of sether, of alcohol, of water, and of oil of turpentine. He 



determined by experiment the values of ~, 5 and r, for these 



fluids at their boiling-points ; and setting these values in equa- 

 tion (V.), he obtained for C the numbers contained in the second 

 column of the following table. Thomson, on the contrary, 

 limited himself to the vapour of ivater ; but has observed it at 

 various temperatures, and in this way calculated the value of 

 C for every single degree from 0° to 230*^ Cent. The observa- 

 tions of Regnault had furnished him with a secure basis as 



regards the quantities -^ and r ; but for other temperatures than 



the boiling-point, the value of s is known with less certainty. 

 In this case, therefore, he felt compelled to make an assumption 

 which he himself regarded as only approximately correct, using 

 it merely as a preliminary help until the discoveiy of more exact 

 data. The assumption was, that the vapour of water at its 

 maximum density follows the law of M. and G. The numbers 

 thus found for the temperatm'cs used by Clapeyron, as reduced 

 to the French standard, are exhibited in the third column of the 

 foUoTving table : — 



