156 Albert P. Mathews 



and that each molecule attracts only the six surrounding 

 molecules. In another paper I shall show that the value 

 M 2 K is proportional to the two- thirds power of the product 

 of the molecular weight and the number of valences in the 

 molecule. In this paper I wish to show how M 2 K may be 

 derived from the surface tension. The computations are 

 made in absolute units. 



The formula, S == fK/3, states that the surface tension 

 of a liquid is a function of the cohesive pressure of the liquid 

 alone. It is clear, then, that this formula can hold only at 

 very low temperatures, since only at such temperatures can 

 the cohesive pressure in the vapor be neglected. The surface 

 tension, strictly speaking, can not represent the cohesive 

 pressure of the liquid alone, since it is in the very nature of 

 things an expression of the difference in cohesive energy of 

 the liquid and vapor. I shall, then, take the formula as 

 holding at absolute zero, since, if we are going to a tempera- 

 ture in which the vapor may be entirely neglected, it is more 

 convenient to go to the end. 



The radius of action of the cohesive attraction, or r, has 

 been found, both by calculation and by direct measurement, 

 to be, at higher temperatures, very nearly equal to the 

 distance between the molecular centers; and at absolute zero, 

 with the molecules in contact, we may safely assume that 

 "r" is equal to v l/ '\ K is Laplace's constant and is equal to 

 a/V 2 , or M 2 K/i; 2 . The formula becomes then: S = 

 D Q 1/3 M 2 K/> 2 = M 2 K/ 3 i; 5/3 . By multiplying both sides of the 

 equation by v 2/3 we have, $v 2/3 == M 2 K/3?; ; v , the volume 

 at the disposal of one molecule at absolute zero, is, for sub- 

 stances of medium complexity such as ether, very nearly 

 equal to TJ C , the volume of a molecule at the critical tempera- 

 ture, divided by 4. For simpler substances, such as O 2 or 

 CO 2 , the volume v is equal to V c /3.63; and for more complex 

 substances, such as octane, it is 1^/4.04, or for some even 

 i; c /4.io. The volume of a molecule is obtained by dividing 

 the volume of a gram mol by 6.21 X io 23 , which is the most 

 probable number of molecules in a gram mol. There is a 



