Prof. Norton on Molecular Physics, 201 



The preceding Table contains the results of numerous calcula- 



n 



2* 



7TI 



tions made after this manner, in which k stands for 



r 



71 



From these results it appears that for values of — greater than 



4*938, or thereabouts, there are two alternations of the effective 

 force f as the distance between the molecular atmospheres increases 

 indefinitely from zero. The first is from a repulsion to an attrac- 

 tion ; the second is from an attraction to a repulsion. The re- 

 pulsion which becomes effective beyond the limit of the attrac- 

 tion at first increases, and then decreases, extending to an inde- 



n 

 finite distance. If the ratio — be less than about 4*938, the 



m 



effective action of the two molecules upon each other will be 



repulsive at all distances. It will be observed also that the 



range of distance within which an attractive force takes effect is 



n 

 greater in proportion as the value of — is greater, and that this 



becomes reduced nearly to zero when this ratio is equal to 4*938 ; 

 also that in all cases in which an effective attraction manifests 

 itself at any distance whatever between the molecules (that is, in 

 the case of every known solid and liquid), the effective repulsion 

 within the limit of the attraction obtains at less distances between 

 the electric atmospheres of the molecules than about 3r, — that is, 

 than once and a half the diameter of either atmosphere. 



For the more accurate determination of the least value of the 



ratio — , we have the following results of computation : — 



n 

 For /=0 when a?=3r, - =4*93827; for /=0 when x=2'9r, 



- =4*93449; for /=0 when x = 2'8r, - =4*934409; for /=0 



m n m . n 



when x = 2'7r, — =4*93847. If then the ratio— be greater than 

 m m ° 



4*9344, the two alternations of effective molecular force above 

 mentioned will have place; if the ratio be less than 4*9344, the 

 effective action of the one molecule upon the other will be repul- 

 sive at all distances. 



It is assumed in the foregoing calculations that the surface of 

 each molecular atmosphere which receives the impulses, whether 

 attractive or repulsive, propagated from the other through the 

 intervening electric aether, may be regarded as the same as that 

 from which the electric repulsion proceeds outward ; but it will 

 be readily seen that they may be supposed to differ within cer- 

 tain limits, without vitiating the result that for certain values of 



Phil. Mag. S. 4. Vol. 28. No. 188. 'Sept. 1864. P 



