Q''. = AL^= ' , .J (15) 



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



Transforming Greenes formula into my notation, it gives 



X = [—)^r l + erb , . . . . (13) 



in which k is Neumann's coefficient of magnetization by induc- 

 tion, and is equal to 



47T 



This equation then gives 



Q^AL^jftrfr-l) 1 + 6r6 .. . . (14) 



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

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

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

 A'=— 1 ; hence 



^ e r(b-x) — e rx 



Now we have found (equation 7) that r = -j\/ — ^ nearly; 

 and this in Green's formula (equation 14) gives 



^'- AL VKR> H 1 + e" ' • ' • ^ 



which is identical with my own when fi 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 



Jq e rx^ € -rx 



x= wif'^r^i (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 formulas with 

 Coulomb's experiments, and found them to represent the distri- 

 bution 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. 



At present let us take the case of electromagnets. 



For observing the effect of the permeability, I took two wires 

 12*8 inches long and *19inch in diameter, one being of ordinary 

 iron and the other of Stub's steel of the same temper as when 



the helix, the 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. 



