146 Dr. F. Auerbach on the Passage of 



in case D is very small in comparison with M ; for the longi- 

 tudinally magnetizing force is of the same nature as the direc- 

 tion-force. This is one reason why the work of the current 

 for longitudinally magnetized is greater than for unmagnetic 

 iron. But even when the force to be overcome is the same, 

 the work is greater as soon as the angle between the direction 

 of the force which does the work and the direction of the mo- 

 lecule at the commencement of the performance of work is 

 greater. I will calculate at least the upper limit of this varia- 

 tion. Thus, let the molecule form with the axis the angle <f> ; 

 the first time let H act immediately and magnetize completely 



(that is, let the angle of rotation i/rbe = ^ — (/>) ; let this work 



£4 



be Ax. The next time let M act first and magnetize com- 

 pletely, and consequently rotate through cf> ; then let H act 



rrr 



and on its part magnetize completely, rotating through ~ ; let 



A A 



this work be -A The ratio -i~ can, evidently, never become 



greater than in this case, in which M is of a higher order than 

 D, H of a higher order than M. Now 



A 1 =D(l-sin^>), A 2 = D; 



therefore the mean values 



IT 



[A>] = ~^{1 - Bin fW = ^ D, 

 [A 2 ]= D; 



that is, 



[A 2 ]_ 7T 



[AJ 7T-2 



2-752 



Therefore, if M increases, A increases more rapidly than 

 M : — first, because, with continually greater accuracy, D can 

 be neglected in comparison with M, and hence the above for- 

 mula for srp: becomes continually more strictly applicable ; 



and, secondly, because the longitudinally magnetic state itself 

 exerts a reaction, which, in rough approximation, can be taken 

 into account by adding to A a factor constantly increasing in 



value with M from 1 to 2*752 Whoever, up to these 



data, examines the observations that have been made on the 

 extra currents, will find them qualitatively (and, as far as this 



