STUDIES ox MAGNETIC DISTRIBUTION 95 



where D is the diameter of the envelope, d of the rod, and /JL } the permea- 

 bility of the medium. But we are not able to estimate D. If, however, 

 we have two magnetic systems similar in all their parts, it is evident 

 that beyond a certain point similarly situated in each system we may 



neglect the resistance of the medium, and -r will be the same for the 



two systems. Hence R' is approximately constant for rods of all diam- 

 eters in the same medium, and r takes the form 



r = ^ 



It is evident that the reasoning would apply to rods of any section as 

 well as circular. 



In Green's splendid essay (Eeprint, p. Ill, or Maxwell's ' Treatise 

 on Electricity and Magnetism,' art. 439) we find a formula similar to 

 equation (5), but obtained in an entirely different manner, and applying 

 only to rods not extending beyond the helix. In the ' Keprint,' ft 

 corresponds to my r; and its value, using my notation, is obtained from 

 the equation 



231863 2 hyp. log p + 2p = _ 4 , , .... (8) 



rd 

 where p = -=-. 



rd 

 If we make p a constant in this formula, we must have p == -^ = 



constant; hence 



which is the same result for this case as from equation (7). 



When fj. in the two formula is made to vary, the results are not 

 exactly the same; but still they give approximately the same results for 

 the cases we shall consider; and since the formula is at the best only 

 approximate, we shall not spend time in discussing the merits of the 

 two. 



III. 



Among the various methods of measuring linear magnetic distribu- 

 tion, we find few up to the present time that are satisfactory. Coulomb 

 used the method of counting the number of vibrations made by a 

 magnetic needle when near various points of the magnet. Thus, in 



