Mr. H. A. Rowland on Magnetic Distribution. 263 



It is almost impossible to estimate R' theoretically, seeing 

 that it will vary with the circumstances. We can get some idea 

 of its nature, however, by considering that the principal part of 

 it is due to the cylindric envelope of medium immediately sur- 

 rounding the rod. The resistance of such an envelope per unit 

 of length of rod is 



1 D 



hyp. log 



where D is the diameter of the envelope, d of the rod, and f*' 

 the permeability 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 simi- 

 larly situated in each system we may neglect the resistance of 



the medium, and -j will be the same for the two systems. Hence 



R/ is approximately constant for rods of all diameters in the same 

 medium, and r takes the form 



- /-* 



^w < 7 > 



It is evident that the reasoning would apply to rods of any sec- 

 tion as well as circular. 



In Green's splendid essay (Reprint, 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 dif- 

 ferent manner, and applying only to rods not extending beyond 

 the helix. In the ' Reprint/ /3 corresponds to my r ; and its value, 

 using my notation, is obtained from the equation 



-231863-2hyp.lo g j> + 3p= fr-ifr* • ■ ( 8 ) 



. rd 



where p= ^-. 



If we make f* a constant in this formula, we must have 



p = — = constant ; hence 



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



When f* in the two formulas 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 for- 

 mula is at the best only approximate, we shall not spend time in 

 discussing the merits of the two. 



