354 Prof. J. A. Ewing. Contributions to the [June 19, 



If a, the half distance between neighbouring poles in the undeflected 

 position, be small compared with r, there is but little deflection before 

 instability occurs, and in that case, provided be not small nor nearly 

 equal to TT, the occurrence of instability is defined by the condition 



do pp 



which is satisfied when tan = ; being the inclination of PP' 



\/2 



to the line of centres. Hence, with the same proviso (a. not nearly 

 equal to or to TT, and a small compared with r), the value of > which 

 causes instability is 



3 .a 2 sin a 



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

 members of a long row. This is, of coarse, least for magnets which 

 lie normal to >. 



In the special case when = TT instability occurs when 



8a 2 



with the single pair, or m/4a 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 < has reached a value sufficient 

 to make the most susceptible members 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 magnetisation is included within narrow limits of magnet- 

 ising force. We accordingly obtain curves like AA (fig. 8). 



When the metal is strained sufficiently to receive permanent set 

 the curves take more rounded outlines (such as BB), showing less 

 susceptibility throughout, less residual magnetism, and more coercive 

 force. The most natural explanation of this, on the basis of the mole- 

 cular theory, appears to be that mechanical set produces on the whole 

 a shortening of the distances between molecular centres, hence greater 

 stability and more coercive force ; but this is associated with hetero- 



