§ 4 OF ARTS AND SCIENCES. 365 



cal shells whose mean radii are proportional to the num- 

 bers I, 2, 3, 4, etc., into which all the particles of a body 

 may be considered as distributed in numbers proportional 

 nearly to the squares of the radii, will be a constant multi- 

 plied by the series, 



■+(i)-"'+(i)'""+(i)'"'+«- 



or its equivalent as far as convergence is concerned. Now 

 it is well known that, unless the exponent in this series 

 were greater than unity, the series would not converge; 

 accordingly the potential at any point would depend upon 

 the whole quantity of surrounding matter, and not merely 

 upon the nature and distribution of the substance in the 

 immediate neighborhood; hence the latent heat would be 

 governed, not only by the amount vaporized, but also by 

 that which remained in the liquid or solid state. That is, 

 a definite latent heat for a given substance would be im- 

 possible unless X — 3 > i. We conclude that it is abso- 

 lutel}^ necessary that the attraction between different 

 particles of a body, upon which latent heat depends, 

 should vary, on the whole, inversely as some power of the 

 distance greater than the fourth, so that this application of 

 the law of universal gravitation must finally be abandoned. 

 A number of facts, based upon the variations of spe- 

 cific heat in the liquid state and the departures in gases 

 from the Law of Boyle and Mariotte, might be brought 

 forward to support the evidence already adduced; enough 

 has probably been said to prove that if the phenomena are 

 to be solved at all, it must be by some force which varies, 

 for the most part, inversely as the fourth or filth power of 

 the distance. 



§ 4. Having proved that a force of no other type can 

 explain the phenomena arising from cohesion, it is now of 



