ON THE TIME-LAG IN THE MAGNETISATION OF IRON. 



317 



Since k is small and t is supposed to be not very large, kt may be 

 taken as a small quantity. Hence, expanding, we have 



T = e i a-ht) + c 2 (l-ht) + c 3 (l-ht)+ 



= C! + c, + c 3 + — (c l ki+c % 1e a + c 9 k t + )t. 



Hence we may put 



where 



G = ti + c 2 + c 3 + 



^ + 00 + ^3 + 



Thus, C is equal to the sum of all the c's, and K is the mean (in a 

 certain sense) of all the k's of the terms to be replaced. 



In my actual formula, p stands for C and n for K, and the fact 

 that the p's are generally greater and the ~'s generally less than they 

 ought to be, is in accordance with their nature, above explained. 



Again, if we take one or two of the terms preceding le~ ? -\ this 

 formula can even express the whole curve in which the entire 

 process of magnetisation is considered as a time effect, the magneti- 

 sation at t = o being zero. The growth in magnetisation immediately 

 after the field is created will then be enormous. J. Hopkinson's 

 experiments on a bundle of steel wires are particularly interesting in 

 this connection, inasmuch as he showed that the curve for the 

 frequency 72 per second was different from that for the^ frequency 5 

 per second, while the latter was almost identical with the statical 

 one. 1 



Next, on examining the curves actually drawn from the observa- 

 tions (PL XL, XII.) we find some irregularities, which though they 

 are of the order of a tench of 1 mm. on the scale, must not, I think, be 



1 Loc. cit. p. 358. 



