PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 39 



2irl 2 hA / . — — .dd = Q, 



* \/a* + P- 2al cosd 



h sin 0<7fl r/jg 



vV + P - 2al cos " al ' 



„ ■• 2irlhA r e- aR dR{a 2 + l*- R 2 ) 

 - 1*^ /(«* + U - R 2 ) e-« R dR, 



the limits being R = a — I, and R = a + I; 



The attraction of the caloric is (16 and 17) very nearly, 

 4,ttMPA fl ni I al 1 aa a \ 4tt o/WP 



« la 2 a a 2 a J 3 a'' 



whilst the mutual repulsion of the two particles is —j-; 



hence, the expression for the whole force of mutual attraction of the 

 particles towards each other, is 



4>ttMPA [e~ al 1,1 a ] M 2 4>tt qPMP 



&m — — s ) +- e -«i -~e-" a --e~ aa ) - — - — ^ — -, — 



a \ a 2 a a a ) OT 3 a 2 



- *-¥ ft.^4) «-t - (- 7 + ^4)--i- 



20. Here we have not taken into consideration the circumstance 

 that the mass of the particle will not be acted on exactly as if collected 

 at its centre of gravity. It has been supposed that it is so collected, 

 and that the caloric then extends to infinity, so that the attraction is 

 due to a quantity of caloric lying in a sphere about the attracting 

 particle at the distance of the attracted one. Now, in fact, nearly one 

 half the attracted particle will not be acted on so much by the laminse 

 beyond its surface, whilst the other portion is actually acted on by 

 particles beyond the laminae at the centre; but as the density of the 



