lo2 Mr. J. Rose-Innes on the Practical Attainment of 



Integrate with respect to t along an isopiestic, and we 

 obtain 



t ~ (n + l)t n+v 



where P is a function of p only. Multiply by pt, and we 

 have 



Denote pv by the single symbol t/t and differentiate with 

 regard to p, keeping t constant, 



(?).-{' + '*}-*pSip 



or 



The quantity / ~-\ is found by experiment to be a function 



of t only to the degree of accuracy to which we are at present 

 working. Hence the right-hand side o£ the last equation is 

 a function of t only ; while we readily see that the left-hand 

 side of the equation is a function of p only. We infer that 

 both sides must be equal to a constant quantity, say e; thus 



P+p j-=e. 



1 dp 



The integral of this equation is 



where R is an arbitrary constant introduced by the integration, 

 Employing this value of P, we obtain 



pv^m + eptr-pt^j^ 



If v is kept constant while p and t are both made to increase 

 together, the term ept will ultimately become more important 

 than Jit. As it seems improbable that this can represent the 

 true state of things at high temperatures, we ought to try to 

 make e vanish. We can secure this result if for a single 

 isothermal we can put 



/oty\ _ . a n 



\dp)~ (n +.!)«*" 



