Determining "a" of van der Waals' Equation 155 



of b c is required. The calculation of "a" from the latent 

 heat of vapor/i&on by the formula (L - - E)/^ - - DJ 

 a/Mol.wt, where L is the total latent heat and E the part 

 consumed in doing external work, is rendered uncertain by 

 the fact that there is still another part of the heat consumed 

 by the expansion of the molecules from the size they are in 

 the liquid to the size they are in the vapor, and this correc- 

 tion is unknown. 



The following method of the comffumption of "a" from 

 the surface tension is new, so far as I can find, although it is 

 an application of the very first method used to obtain some 

 idea of the amount of the cohesive pressure of a liquid; it 

 does not involve the value "6;" and it is of interest that the 

 results obtained from it are, on the whole, closely similar to 

 those given by the usual formula. It is, I believe, more 

 trustworthy than the formula usually employed. It is a 

 method proposed by the great English philosopher, Thomas 

 Young, in his epoch-making work on Cohesion. In that 

 work, by an insight little short of marvelous, he came to the 

 conclusion that S, the surface tension, was equated to one- 

 third the total cohesive pressure, multiplied into the radius 

 of action of the cohesive attraction, or S == rK/$. 



Since "a" varies with the volume of the gas taken under 

 standard conditions of temperature and pressure, it would be, 

 in many ways, convenient to have a value which was character- 

 istic of the molecules of each substance and which would be 

 independent of the volume of gas or liquid, or the tempera- 

 ture f- pressure to which it was subjected. Such a value is 

 very easily obtained by putting "a" equal to N 2 M 2 K, where 

 N is the number of molecules in the volume V; and writing 

 V 2 as NiT 3 ; where small v is the volume at the disposal of a 

 single molecule. By dividing by N 2 we have then a/V 2 = 

 M 2 K/i> 2 . We may call M the mass of cohesion of a molecule, 

 and K is a constant of proportion. This same value may be 

 obtained directly by supposing that molecules attract each 

 other inversely as the fourth power of the distance between 

 their centers, directly as the product of their cohesive masses 



