ENTROPY 71 



the same amount, that I venture to say that few will be found who are critical 

 enough to insist on the doubt. 



This concordance might be shown by giving actual values of the right- 

 hand member of (15), for actual gases at one or more points adjoining the 

 curve which divides solid from gas on the phase-diagram. The usage is, 

 however, different, and it is of some value to abide by the usage, even 

 though I am now required to make one more transformation of (15) which 

 I have hitherto avoided. This involves the auxiliary equation, 



dL/dT - Cr - Cf (32) 



which makes it possible to calculate L for any temperature, provided it be 

 measured at any other temperature and the specific heats be known at all 

 the temperatures in between. We may thus start from any measured value 

 of L, calculate a value Lo appropriate to the absolute zero, and thereafter 

 we may write the integrals, as always heretofore, extending from zero to T. 



L = Lo + j cr dT - j c dT m 



The first of these two integrals is equal for a monatomic gas to (5/2)RT 

 per mole. Since it is L/T which appears in (15), this entails a term (5/2)i? 

 on the right of that equation. This term neatly blots out the term R In e^'^ 

 which is a portion of our statistical value of I as given in (31), so that after 

 all the equation is not much worsened in appearance. It has in fact assumed 

 the form 



RlnP = -Lo/T -f- (5/2)i? In T 



- I {C;'/T) dT + (l/D J C;' dT + J (34) 



and here / is yet another additive constant — the additive constant of the 

 vapor-pressure equation in its commonest form — of which this may be said, 



(r, ^\3/2 ,5/2 



J = Rln ^^"^ , ^ (35) 



if the statistical theory is sound and if in addition the entropy of a crystalline 

 solid of a single kind at the absolute zero is zero. 



It is evident that if the two presumptions are true, then the remainder 

 left behind when (3/2) In m is subtracted from the experimental value of / 

 will have a definite value, the same for all gases. This indicates how the test 

 is made, or rather how it is set forth in the literature. The remainder, 

 expressed in units which need not concern us, should be —1.589. Now, 



