24 H. A. Rowland— Studies on Magyietic Distribution. 



of the rod. As any case of magnetism can be represented by 

 a proper combination of these rods, we see that all cases of this 

 sort can be calculated on the supposition of there being two 

 magnetic fluids distributed over the surfaces of the bodies, a 

 unit quantity of which will repel another unit of like nature 

 at a unit's distance with a unit of force. The surface-density 

 at any point will then be the quantity of this fluid on a unit- 

 surface at the given point, and the linear density along a rod 

 will be the quantity along a unit of length, supposing tbe 

 density the same as at the given point 



Where we use induced currents to measure magnetism we 

 measure the number of lines of force, or rather induction, cut 

 by the wire, and the natural unit used is the number of lines 

 of a unit-field which will pass through a unit-surface placed 

 perpendicular to the lines of force. The unit-pole produces a 

 unit-field at a unit's distance ; hence the number of lines of 

 force coming from the unit-pole is 4;r, and the linear density is 



and the surface-density 



4:7l^d^Jj 



These really apply only to steel magnets ; but as in the case ( 

 electro- magnets the action of the helix is very small compare 

 with that of the iron, especially when it is very long and tt 

 iron soft,* we can apply these to the cases we consider. 

 Transforming Green's into my notation, it gives 



^)^''''^' ■ • ■ "^ 



in which n is Neumann's coefficient of magnetization by indui 



This equation then gives 



Q-. = .L(!f)^(.-l)'-:^'. . . (H) 



Equation (5) can be approximately adapted to this case by 

 making s'=oo , which is equivalent to neglecting those lines of 

 force which pass out of the end section of the bar. This gives 

 A'= — 1, hence 



* I take this occasion to correct an error in Jenkin's " Textbook of Electricity." 



number of lines of force is increased 32 times. The number should have been 

 from a quite small number for a short thick bar and hard iron to nearly 6000 for 

 a long thin bar and softest iron. 



