Forces of Attraction between Atoms and Molecules. 791 



But the assumption that the matter is evenly distributed 

 in space is not true, and zero cannot therefore be a limit in 

 the above integrals ; moreover, the use of integrals is then 

 not generally admissible. We will, therefore, develop a 

 formula which takes into account the fact that the matter of 

 a substance is not evenly distributed in space. 



Suppose the liquid cut up into squares by three systems 

 of parallel equidistant planes one of which is parallel to the 

 plane AB, fig. 2, and suppose a molecule is situated at each 



Fisr. 2. 













Qa 



c 













/ 









A 









/ 



/ 



/■s 







B 



O 



o 



•fj ■ 



o 4 







■6 o 



OqO 



o 



O 



o 



&b 



o 



o 



o o 



O 







point of intersection of three planes. Let x a denote the 

 distance between two molecules situated at the two corners 

 of the edge of a square. 



Consider two molecules a and b, a being situated in the 

 slab C and b in the slab D. Let the coordinates of the 

 molecule a be (nx ai 0, 0), using the same system of coordi- 

 nates as before, and those of b be (icx a , ux a , vx a ). The com- 

 ponent of attraction of the molecule a by b along a line at 

 right angles to the plane AB is 



csow 



(nx a + wx a ) 



where 



z= ^\(nx a + wx a )* + u 2 x 2 a + v 2 xl} = x a \Z{(n + w) 2 + u 2 + v 2 }. 



The attraction produced by the whole slab of liquid I) on a 

 is therefore 



V = 00 !( = I 



(tc a y 2 2 2 ^(^)- a (n+ W ) = (2c a ) 2 Fsay. 



v= — oo «-= — ao tv—O £ 



The work done in moving the molecule a to infinity is 



(Zc a y I" F.dn.v a ={%c„)-.i'A 



J nx a •A 



F.rffl. 



• (?) 



