OF MOLECULAR FORCES. Ill 



This formula contains every possible law of force : the first term 

 shews the propriety of what we have done in the last article, and further 

 proves, that an attractive molecular force varying inversely as the square 

 of the distance is the only force which possesses the properties requisite 

 for removing the difficulty there stated; or that at any rate it is the 

 simplest and best adapted for that purpose. 



Further; for a reason analogous to that assigned in (18), 



r 2 1 — — + <j)'r) , or r^-^r 



^ ............ . ■ 



must be a function of r, which decreases as r increases, and vanishes 



when r is infinite. Hence, if %(r) be any function of r which is 



positive between the least and greatest limits of r for the whole medium, 



and which decreases as r increases and vanishes when r is infinite, then 



C 1 



<t>(r) = ^ + ^f rX (r). 



Every possible law of force is included in this formula; but the 

 converse is not necessarily true, viz. that every law of force included in 

 this formula is possible. 



There may be other conditions to be satisfied, either as to the form 

 of the arrangement of the particles, or as to their distance from each 

 other, or as to the possibility of the medium existing in a state of 

 finite extension, or as to other circumstances unknown to us at present 

 which may perhaps exclude all the forms but one; which one would 

 in that case be the actual law in the luminiferous ether. Or there may 

 be peculiarities in the vibrations which constitute the waves of light 

 (such as their transversality) which will hereafter enable us to determine 

 the required law of mutual action of the particles. 



22. Whatever be the law of molecular force of the luminiferous 

 ether, each particle is placed in such a position when in equilibrium, 

 that the value of V for that particle is a maximum. 



Let us employ the notation of (21): then V=- 2(mf t <pr), and 



