Mr Searle, The Expansion of a Gas, etc. 249 



Hence 



H-j C p >dt=p'v'-pv+Q-(e + g + h) 



= (f+9 + h)-(d+f) + Q-(e + g + h) 

 = Q-(d + e) 



-JTHSJ* (13) * 



the temperature having the constant value t on the right side. 

 From the modified Van der Waals' equation (12) we have 



, dv Rt + pb — a/v Rt 



v - t jT = n • 



alp p p — a/it 



Expanding the second denominator by the binomial theorem, 

 we obtain, to the order of accuracy which we have adopted, 



, dv 7 a aRt 

 dt p pv p-w 



To the same order of accuracy we may replace pv by Rt, 

 and thus 



dv _ . 2a 

 dtp~ Rt 



Hence 



H'-\y v: dt=-(p-p){b^ 



If p —p' be the difference of pressure due to a height of h cm. 

 of water, we have p—p' = 981 h, and thus we find that, when C0 2 

 enters the spiral at 873° on the absolute scale, 



= 5150/i 



8-4 x 10 6 . 

 = — -tfloft — "> er g s P er gramme. 



Taking C p > as 02 x 4'2 x 10 7 or 8*4 x 10 6 ergs per gramme 

 per degree, we see that the correction arising from a difference 

 of pressure of h cm. of water amounts to only A/1630. Thus when 

 h — 10, the correction amounts to 1/163 of a degree. Though 

 this is about four times as great as the correction we found was 

 necessary in the case of air, it is still practically negligible. 



Thanks are due to Prof. J. H. Poynting, F.R.S., for his criticism 

 and assistance in connexion with this paper. 



