300 Mr. W. Sutherland on the Recalculation of 



Although Hirn's formulas represent his experiments excel- 

 lently, yet they introduce in this manner a certain amount of 

 inaccuracy into his final determinations of the specific heats. 

 However, it is easy to calculate from his full published data 

 the correct values. 



The cooling of the large bulb is due to two causes — (1) ra- 

 diation, and (2) introduction of cool liquid from the stem. As 

 it is the rate of cooling due to radiation only that is required 

 in the method of cooling, we must calculate this from the 

 actual rate of cooling. 



If, in time dt, a mass dp passes from the stem where its 

 temperature is i to the bulb where it is 0, then if k is the 

 specific heat at 0, and k' is the mean specific heat between i 

 and 0, the cooling effect produced by dp on the mass p in the 



bulbis d P k\e-i)ik P . 



If, then, d6 is the actual amount of cooling, and dr the 

 amount due to radiation in time dt, we have 



dO _dr dp k f {0-i) 

 dt dt dt kp 



Now dp/dt is given by Hirn in his experiments on the rate 

 of expansion, so also is p ; k'\k can be estimated with sufficient 

 accuracy from Regnault's formula for lower temperatures ; 

 i can be taken as the temperature of the surrounding air, 

 though that is too low ; but the whole of the last term is small 

 compared to the others, so that roughness in its estimation 

 does not produce much effect in the first calculation of specific 

 heats. 



From the above equation, then, we get the required rate of 

 cooling due to radiation only. 



Let P be the water-equivalent of the bulb and stirrer ; then 

 if the rate of cooling of water at temperature 0, of specific 

 heat kij is v x , while pi is the mass of water in the bulb, then, 

 by the usual equation for the method of cooling, we have 



(^+P)i;=( j pA+PK 



where v stands for dr/dt ; v and v ± are calculated from Hirn's 

 data, as explained above ; p,fi, and P are given by Hirn ; 

 whence we can calculate k if we take the values of k' from 

 Regnault's determinations. A communication by Velten 

 (Wied. Ann. xxi. 1884) would seem to show that Regnault's 

 values for the specific heat of water at high temperatures are 

 altogether worthless ; but I shall show, in an addendum to 

 this paper, that the apparent discrepancies in Regnault's 



