§ 4 OF ARTS AND SCIENCES. 367 



spheres must attract or repel exactly as two small mag- 

 nets of respectively equal moments would do, if placed at 

 their centres. 



Since the field due to a small magnet is shown to vary 

 in any direction inversely as the cube of the distance,'^* the 

 attraction for a second small magnet, measured by the dif- 

 ference of the action upon the nearer and farther pole, will 

 vary as the rate of change of a force, itself var3ing inverse- 

 ly as the cube of the distance, which rate of change is 

 seen at once, by the principles of the calculus, to vary 

 inversely as the fourth power of the distance.f 



So long, therefore, as the atomic arrangement is not 

 disturbed, whether a substance be elementary or com- 

 pound, the attraction between any two atoms according to 

 the analogy will vary, as we have supposed, inversely as 

 the fourth power of the distance, and therefore, in the per- 

 fectly homogeneous expansion described in the last sec- 

 tion, the value of x will be constant and equal to 4, so 

 that we shall have 



JLD = — P". I. 



If, however, the substance be not elementary, we must 

 remember that, in the state of vapor, the spheres (or 

 atoms), which we have supposed to be completely sepa- 

 rated, must afterward be reunited in clusters, so that a part 

 of the energy required to separate them completely will 

 not be needed. An approximation to the relative amounts 

 of energ}^ required to volatilize an element and a com- 

 pound, respectively, will be found by considering from 

 how many atoms a given atom is separated in each case, 

 and what attraction is exerted by each atom from which it 

 is separated. 



It is of course impossible to obtain an exact solution 

 without knowing the atomic grouping, both in the solid 



• Gumming, ibid, 

 t See Maxwell, § 388. 



