Laws of Molecular Force. 253 



but it is closely proportional to it. If we can find the relation 

 between e and a, then from capillary determinations we can 

 obtain relative values of the virial constant I which, as we 

 have already found some absolute values of I, can be converted 

 to absolute values ; at the same time, too, we shall be able to 

 find a value of a the mean distance apart of the molecules. 



To find the relations between e and a we can proceed thus. 

 If we have a single infinite straight row of molecules at a 

 distance a apart, the force exerted by one half of it on the 

 other is 



ra=oo p=os 3A??i 2 



^=0 Vi (p + nfa 4 ' 



which can easily be evaluated as approximately 3'6Am 2 /a 4 . 

 Two infinite continuous lines in the same line, of density m/a 

 with distance e between their contiguous ends, would exert a 

 force 



3Am 2 f ca r° dxdy 



<* J Jo 0*+3/) 4 



on one another ; this is equal to Am 2 /2a 2 e 2 , If, then, the 

 continuous distribution is to be equal to the molecular, we 

 nave 



e 2 =a 2 /7'2, e = a/2'7. 



Again, if along two infinite axes one at right angles to the 

 other and terminating in an origin at its middle point 

 molecules are arranged along each at distance a apart starting 

 from 0, then the force exerted by the unlimited row on the 

 other is 



, P =«3Am 2 



(p 2 + n 2 )*a* ' " p=1 p 4 



which can be evaluated at about 5Am 2 /a 4 . 



Replace the rows by two continuous line-distributions of 

 density m/a, the one terminating at a distance e from : it is 

 required to find e so that the force may be the same as this. 

 The force is 



6Am 2 r- r ydydx __ A 2/22 



Hence in this case 



e 2 = a 2 /5, e=a/2'2. 



From these two simple cases we get an i# dea of the relation 

 between e and a. The case of a meuiscus attracting the 

 column which it raises in a capillary tube is more analogous 

 to the second than to the first, and it is easy to see that in the 





