Laws of Molecular Force. 245 



We can now remove ft and greatly simplify this equation, if 

 we apply it to latent heats near the ordinary boiling-point 

 T5. The last term taken in its entirety has a small numerical 

 value compared to the rest, so that in it we can make approxi- 

 mations without any sacrifice of accuracy worth considering : 

 we have seen that {3 is approximately proportional to k (see 

 Table XXI.) and v v the volume of the liquid at the boiling- 

 point, may be assumed to be approximately proportional to k! 

 the volume at the critical temperature, and k' = 7k/6: hence 

 the coefficient of (l/2v 1 — H'T) in the last term is approxi- 

 mately the same for all bodies and we can evaluate it for 

 ethyl oxide ; call it 0. Again, in P(v 3 — 1^) neglect v l and 

 assume the gaseous law Pv 3 = RT 6 . And further, k is small 

 compared to u 3 , so that 2v 3 /{v B + k) is nearly 2, and its value 

 for ethyl oxide can be applied to all bodies. R' = 25R/13. 

 Hence multiplying by M the molecular weight we can write 



¥{Hs-') +1 *& + S0" n * + »(S<'- 1 )* 



MR is the same for all bodies, and T b is the absolute boiling- 

 point. This equation still involves k as well as I ; when k is 

 not known we must eliminate it by means of our previous 

 assumption, namely, that k is proportional to v u which we 

 know to be approximately true ; in so far as it is inexact it 

 will introduce inexactness into our calculation of I. Accord- 

 ingly in symbols k/v 1 = r J where r is the same for all bodies, 

 and can be found for ethyl oxide. Making the numerical 

 reductions we get 



MZ/ Vl =66-5M\-101T ft 



as the equation which gives I in terms of the megadyne as 

 unit of force, when X is the latent heat of a gramme in 

 calories and v 1 its volume in cubic centimetres at the absolute 

 boiling-point T b . This equation will be abundantly verified 

 afterwards in Table XXIV. ; but meanwhile, if to test it we 

 apply it to calculate the latent heat of ethyl oxide, we find 

 \ = 83'4, whereas several experimenters have agreed in an 

 estimate of about 90 ; but, on the other hand, Ramsay and 

 Young (Phil. Trans. 1887) have made a special study of the 

 terms in the thermodynamic relation J\=(r 3 —v l )TdP/dT, 

 and have so calculated values of X almost up to the critical 

 temperatures, their value at the boiling-point is 81*4, and 

 there is the same amount of discrepancy between their values 

 at higher temperatures and Regnault's experimental deter- 

 minations. Yet Perot, who has made an elaborate study 

 (Ann. de Ch. et de Ph. ser. 6, t. xiii.) both of \ experimentally 



