;^66 PROCEEDINGS OF THE AMERICAN ACADEMY § 4 



interest to inquire whether there are any known forces, simi- 

 lar to those of electric or magnetic action, which may be 

 adequate to this task; and the following sections arc ac- 

 cordingly devoted, for the most part, to the analytical inves- 

 tigation of the consequences of various suppositions. 



The solution of problems in the theory of cohesion can 

 only be obtained through some simple hypothesis; and the 

 first which we shall examine is that the normal attraction 

 of two particles is inversely as the fourth power of the dis- 

 tance. The investigation of the theory of cohesion from 

 this point of view will be greatly facilitated by the study of 

 the attraction and repulsion of small magnets, the laws 

 for which are apparently identical with those which we 

 have supposed. 



Since any distribution of magnetism may be represent- 

 ed as the resultant of an indefinite number of very small 

 magnetized particles, arbitrarily arranged, no matter what 

 the shape of these particles may be,* I shall assume for 

 convenience, in this investigation, that the ultimate par- 

 ticles of matter which need be considered are analogous 

 to small uniformly magnetized spheres, which may or 

 ma}' not correspond to the chemical atoms. The corres- 

 pondence, if any exist, will appear in this and in the next 

 section. 



The strength of field at any point, due to a uniformly 

 magnetized sphere, may be represented by that due to a 

 small magnet of equal moment at its centre ;f hence the 

 action of one magnetized sphere on another may be repre- 

 sented by that of a small magnet at the centre of the first 

 upon the whole mass of the second sphere; but the action 

 of the second sphere upon this small magnet would by the 

 same proposition be equal to that of a second small mag- 

 net at its own centre; and therefore, since action and reac- 

 tion are equal and opposite, two uniforml}' magnetized 



* See Gumming, Theory of Electricity, Prop. I., page 225, et seq. 

 t See Gumming, Theory of Electricity, Prop. IX., page 276. 



