CONSTITUTION AND TEMPERATURE ON MAGNETIC SUSCEPTIBILITY. 91 



gramme of a diamagnetic liquid the molecules of which have a small mutual influence. 

 If k t be the susceptibility per unit volume, this energy is shown to be 



(15) 



where X is a constant approximately equal to iy (our ,). In accordance with our 

 notation we have Tc L . H = n . AM ; , where n is the number of molecules per cubic 

 centimetre, and AM the diamagnetic moment induced in each by H. Therefore, 

 instead of (15), we may write 



] ......... (16) 



Comparing (14) with (16) we may identify a' c with X and I with n. AM ; . Further, 

 the applied field H is associated with the moment n . AM, which it produces, in the 

 same manner as the molecular field H c is associated witli the aggregate of the local 

 intensity of magnetization per unit volume, I, which it produces. The analogy is 

 complete. In (14) we are concerned with the local forces of the crystalline structure 

 which, on account of the relative fixity of the molecules,' do not average out ; whereas 

 in (16) we are concerned with the average forces within the fluid, the large local forces 

 having become averaged out on account of the motions of the molecules round any point. 



Prof. LAEMOE has pointed out an interesting case in which the term in X 

 predominates.* If we suspend a bunch of iron nails from the pole of a magnet, we 

 find that they adhere to each other endwise and repel one another sideways, while 

 non-adjacent nails have no action on one another. This is analogous to the result 

 disclosed by (14) for a diamagnetic crystalline substance. Each molecule may be 

 considered as possessing two little magnets opposing one another, and these molecules 

 fit together in such a way that the magnets nearest to one another in adjacent 

 molecules help one another. 



In the case of a fluid X and k t 2 are small, so that the predominant term in the 



expression for the energy is - . k t . H 2 , as is ordinarily assumed. For a crystalline 



2ft 



medium taken as a whole the corresponding energy term is - . k c . H 2 , the expression 



*Pc 



usually taken in measuring k c .1[ It is only when we are inquiring into the local 

 forces binding the molecules together into a crystalline lattice, the energy term of 



which is . a' c . I 2 , that we get the true diamagnetic analogy with the bunch of 



2/Jc 



iron nails. The molecules of the diamagnetic structure are held together endwise, so 

 to speak, but we may have attractive forces in a perpendicular direction depending 



* Loc. cit., p. 64. 



t Strictly speaking, to each of these expressions for the energy should be added a term proportional 

 to 2 , which is very small. 



N 2 



