114 Mr. W. Sutherland on the 



lates for the unknown law of molecular force in order that it 

 may account for capillary action, that the potential energy of 

 a number of molecules must be inversely proportional to the 

 volume occupied by them ; but my attention was first drawn 

 to the form A/r 4 as that expressing the law of molecular 

 force by the fact that it is the only particular case of the 

 general form A/r m (m having any value fractional or integral) 

 which satisfies Laplace's conditions when they are established 

 on a satisfactory physical basis. The fact (which I will after- 

 wards show) that Laplace^s conditions tacitly exclude the 

 possibility of expressing the law of molecular force by a finite 

 series of inverse powers of r fractional or integral, unless the 

 series reduces to A/r 4 , gives the law of the inverse fourth 

 power a special claim to investigation, and also calls for an 

 inquiry into the physical soundness of the conditions ; for 

 while to the mathematician the conception of a function of r, 

 which increases rapidly as r diminishes, but which cannot be 

 expressed as a finite series of inverse powers of r, is easy enough, 

 the physicist, who naturally looks on the law of gravitation as a 

 first approximation to the complete law of the action of matter 

 on matter (for which I would propose the name molic force, 

 including gravitation, molecular and chemic force), must find 

 the exclusion of a law expressible by a series of inverse powers 

 of r highly arbitrary, and suggestive rather of the domination 

 of nature by formulae, than of her expression, which is the 

 object of the physicist. 



Laplace's expression for the resultant attraction of a mass 

 of liquid of density p with a plane surface on a column of the 

 same liquid of section &>, terminating at the plane surface and 

 normal to it, is 



o\ dz\ ldl\ 



Jo Jo Jl 



2tt P 2 (o] dz\ ldl\ (r)dr, 



Jo Jo Jl 



mm'f(r) representing the attraction between two molecules of 

 masses m and m' . The only express stipulation made at first 

 about r is that its value is to be insensible at sensible distances. 

 To remove the vagueness inherent in this general expression 

 of this condition, Gauss (Werke, V., Principia generalia 

 theorise figurse fluidorum in statu equilibrii) casts it into the 

 following definite form : — 



Let M be a mass such as we have to deal with in ordinary 

 experiments, and which is therefore negligible in comparison 

 with the mass of the earth, then Mf(r) being of the same 

 dimensions as g is comparable with it, and the definite expres- 

 sion of the above condition is that Mf(r) is to be negligible in 

 comparison with g when r has a sensible value, but that it may 

 have a very large value in comparison with g for insensible 

 values of r. Even yet there is a vagueness in the use of the 



