292 PROCEEDINGS OF THE AMERICAN ACADEMY. 



This formula has the disadvantage, as compared with Griessmann's, 

 of involving the derivative of the inaccurately known function p. 

 This prohibits its use at the low temperatures close to saturation where 

 P is scarcely known at all, but makes much less difference at very high 

 temperatures where the C0 2 points of Figure 5 of the preceding paper 

 help to place the p =f(t) curve with great definiteness. This method 

 of computation is therefore at its best where many others fail completely. 



The use of the new equation at ordinary temperatures is a matter 

 requiring patience and much labor. First one computes and plots 

 against t the derivative of the p =/(t) curve of the preceding paper. 

 Next one computes from the curve of p itself the progress of some 

 curve of constant ff across the p t plane ; this is necessary so as to be 

 able to express dp/dt as a function of p in the integral. Then the 

 integral has to be evaluated, either by replotting dp/dt against p for 

 the particular ff curve in question and using an integraph, or by a 

 step by step numerical process. The results are the Naperian loga- 

 rithms of the desired ratios. 



This process has been carried through for four curves in the region 

 of moderate superheats. The results, which are presented in the first 

 part of Table V., are in general in substantial agreement with the corre- 

 sponding ratios computed from Knoblauch's curves, which are given in 



* (2). -(£).♦ '($),- « 



Now from the definition of Cp 



/dCA = /}\ (dH\ = *H_ () 



\ dp ft \dpft \dt)p dpdt' K ' 



and from (1) 



(dCA _ 1 d*H (dH\ 1 (djA 



\dt f p m dtdp \dpf t m 2 \Ot)p' y ' 



Substituting (3) and (4) in (2) and using (1) gives the desired equation. 

 Neither of the laws of thermodynamics has been used. 



The differential form of the equation can also be deduced immediately 

 from the equation 



(dCp\ ( dfaCp) \ 



\dp) t \ dt fp 



which Grindley proves on pages 31 and 32 of his paper in the Philosophical 

 Transactions. His proof depends twice over on each of the two laws of 

 thermodynamics, but it need not have, as the above derivations show. The 

 use which he makes of his form of the equation is quite different from that 

 here proposed. 



