Laws of Molecular Force. 257 



molecules at a distance of one centim. apart ; that is, to 

 calculate Am 2 and Gm 2 , where m is the actual mass of the 

 molecule, and G the constant in the expression Gm 2 /r 2 for 

 gravitation. 



In the expression 



*=7rj5 2 Atf/2'2(2+x/2), 



using the value 10 micromms. for x and the values previously 

 given for the other quantities, we can find A, and then using 

 the value 3'5/10 19 for the mass of a molecule of ethyl oxide we 

 find Am 2 =9/10 30 in terms of the dyne. To calculate Gr we 

 have 981 as the acceleration of gravitation ; the mass of the 

 earth is 6 x 10 9 grm. and its radius is 6*37 x 10 7 cm., so that 

 Gm 2 = 2'l/10 29 in terms of the dyne. Hence at a distance of 



( 1 centim. the gravitation of two ethyl-oxide molecules is 

 about double their molecular attraction, or, allowing for un- 

 certainties in our calculation, we may say that at about 

 1 centim. apart two molecules exert the same gravitational as 



I molecular force on one another. 



We now return to the main business of this section, which 

 is the Fifth Method of finding the virial constant I. This 

 consists in using the equation already used for calculating 

 molecular distances in the form 



1 = 7*5A(4 log 2L/-9#-16/3)/ff. 



Now a, the molecular distance for different liquids, varies as 

 mi v*, and the expression in brackets may be assumed to be the 

 same for all bodies ; hence l-=cotv*/niv, where c is a constant 

 whose value can be obtained on substituting in the case of 

 ethyl oxide the known values of I, a, v, and m, or, more 

 safely, by taking a mean value from several substances. 



But we must remember that we are using v the volume in 

 the body of the liquid, instead of v that in the surface- film ; a 

 replacement which is not justified by experiment, seeing that 

 for a given liquid otv% measured at different temperatures is 

 not constant, the reason being that v varies much more rapidly 

 with temperature than v. But, in our ignorance of the rela- 

 tion between surface and body-density, all that we seek for 

 from the above equation for /, is true values for I from mea- 

 sured values for a. Accordingly the question arises, Can Ave 

 choose temperatures at which to measure a for different sub- 

 stances, so as to get true relative values of I irrespective of 

 our ignorance of v ? 



As we have seen (Section 6) that at equal fractions of their 

 critical temperatures, and under equal fractions of their critical 

 pressures, one liquid is approximately a model of another on 



