116 HENKY A. ROWLAND 



iron, especially when it is very long and the iron soft, 9 we can apply 

 these to the cases we consider. 



Transforming Green's formula into my notation, it gives 



(13) 



in which < is Neumann's coefficient of magnetization by induction, and 

 is equal to 



This equation then gives 



c f 



r(/;.-i) ~- , .... (U) 



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 



2 / 1 

 Now we have found (equation 7) that r -=- J nearly; and 



this in Green's formula (equation 14) gives 



which is identical with my own when JJL is large, as it always is in the 

 case of iron, nickel, or cobalt at ordinary temperatures. 



When x is measured from the centre of the bar, my equation becomes 



(17) 



The constant part of Biot's formula is not the same as this; but for any 

 given case it will give the same distribution. 



Both Biot and Green have compared their formulae with Coulomb's 

 experiments, and found them to represent the distribution quite well. 

 Hence it will not be necessary to consider the case of steel magnets very 

 extensively, though I will give a few results for these further on. 



9 I take this occasion to correct an error in Jenkin's 'Textbook of Electricity,' 

 where it is stated that by the introduction of the iron bar into the helix, the num- 

 ber 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. 



