218 Prof. J. A. Ewing on the Molecular 



which is satisfied when tan</> = — -~ ; (f> being the inclination 



of PP' to the line of centres. Hence, with the same proviso 

 (a not nearly equal to or to 7r, and a small compared with 

 r), the value of «£) which causes the instability is 



^ m 



12v / 3.« 2 sina 



for a single pair of magnets, and twice this quantity for the 

 middle members of a long row. This is of course least for 

 magnets which lie normal to Jq. 



In the special case when a = 7r, instability occurs when 



$= 



7n 



8^2 



with the single pair, or mjka 2 with the row. 



Applied to the case of a group of rows, uniform in distance 

 between the centres, but various as regards their direction 

 with respect to «£), these considerations show that after <£j has 

 reached a value sufficient to make the most susceptible mem- 

 bers unstable, no very great increase is required to bring 

 about instability in by far the greater number of the other 

 rows. One general effect of increasing the distance between 

 all the centres is to reduce the range of variation of <£) within 

 which most of the different rows become unstable as the force 

 is progressively increased. 



In annealed metal, where we may expect considerable 

 general homogeneity, as regards distance between the centres 

 of the molecular magnets, we find that practically the whole 

 of the abrupt stage in the process of magnetization is included 

 within narrow limits of magnetizing force. We accordingly 

 obtain curves like A A (fig. 8). 



When the metal is strained sufficiently to receive permanent 

 set the curves take more rounded outlines (such as B JB), 

 showing less susceptibility throughout, less residual mag- 

 netism, and more coercive force. The most natural explana- 

 tion of this, on the basis of the molecular theory, appears to 

 be that set produces on the whole a shortening of the dis- 

 tances between molecular centres, hence greater stability and 

 more coercive force ; but this is associated with heterogeneity, 

 that is variety in the distances, hence the rounded outlines of 

 the curves. We know that set tends to develop, or at least to 

 emphasize, heterogeneity ; for instance, a bar of iron or steel 

 pulled in the testing-machine stretches irregularly after the 

 elastic limit is passed. 



