468 MOSSOTTI ON THE FORCES WHICH REGULATE 



tion of this equation, that the molecules attract each other most 

 forcibly. 



Recapitulating these results, we shall say then, that the action of two 

 spherical molecules on each other is repulsive, from their point of con- 

 tact to a distance given by the equation {b). At this distance the two 

 molecules are in a state of fixed equilibrium, and as it were linked 

 together ; at a greater distance their action is attractive, and the 

 attraction continues to increase until they are at the distance T^ fur- 

 nished by the equation (c), which distance is still very inconsiderable 



because of the magnitude of a in the exponential term e \ From 

 this point the force remains always attractive, and, when the distance 

 has acquired a sensible value, follows the inverse ratio of the square of 

 the distance. All these properties of molecular action flow as neces- 

 sary consequences from Franklin's hypothesis respecting statical elec- 

 tricity, and appear perfectly conformable to those indicated by the 

 phaenomena. 



Let us suppose four homogeneous and equal molecules placed at the 

 points of a regular tetrahedron. If we assume as the origin of the co- 

 ordinates the place occupied by the molecule whose equilibrium it is 

 proposed to consider, and as the plane of the x y, & plane parallel to 

 that in which the three others are found, the coordinates of these 

 molecules will be given by the formulae 



x=o y=o z=o 



X. = — =^ cos i3 y, = — ^- sin /3 z.=r* /_ 



.. = -^cos(..-) , = -^sin(,.-) ,=ryi 



x, = -^cos(/3-h^) y3=-^sin (/3 + ^) ^^='\/l 



V3 ' V 3 / --^ V3 V 3 / " V 3 



where r denotes the mutual distance of the molecules, which is the same 

 for all ; /3 the angle which is formed in the plane oi x y with the axis 

 of the X, by the projection of the straight line drawn from the molecule 

 placed at the origin of the coordinates to the first of the three others ; 

 and TC the semicircumference. 



If these values be substituted in the three equations (A), and it is 

 observed that we always have, whatever may be the value of /3, 



cos/3 -I- cos U + ^.^+ cos (q + ^\= o, sin/3 + sin^/3 + |:) 



+ sin ^/3 + -^ j =o, 

 it will be seen that the two first are verified by themselves, and that 



