Dr. C. Fromme on the Magnetism of Steel Bar. 



301 



pulse by the number of the impulses, the saturation-moment 

 A, and the increment B of the moment from the first to the 

 last impulse. 



The magnetization by induction-currents, on the other hand, 

 is very well represented, he says, by the formula 



y = A + B(l — e-"*), 



(2) 



where A, B, and a are constants, A the moment originally 

 present, B the total increment produced by the action of the 

 force, and e the base of the natural system of logarithms. 

 This formula corresponds to a much quicker increase of the 

 residual magnetism than the first. 



While M. Bouty is inclined to deduce the difference of the 

 formulae from the difference of the methods of magnetization, 

 I should rather, judging from the examples he adduces, seek 

 them in the different initial magnetic states of the steel needles. 

 Two of his examples may serve as evidence : — 



For(l). 



For (2). 



Number of pas- 

 sages to the 

 spiral. 



Magnetic 

 moment. 



Number of di- 

 rect in- 

 duced currents. 



Magnetic 

 moment. 



1 



2 



3 



4 



5 



10 



20 



30 



50 



51-46 

 5455 

 55-43 

 5610 

 55-95 

 56-48 

 57-68 

 5792 

 5775 





 1 

 2 

 3 

 4 

 8 

 16 



71-55 

 75-30 



78-55 

 8050 

 80-80 

 8105 

 81-05 



While, then, in the first instance the little bar had no initial 

 magnetism (was " innocent of any previous magnetization "), 

 and at the conclusion possessed the residual magnetism 57'75, 

 in the second the initial magnetism was 71*55, which was 

 raised by the action of the magnetizing force to 81*05 only. 

 But then, according to the proposition previously advanced, 

 the number of the requisite impulses must be less, and the 

 augmentation of the residual magnetism follow more rapidly. 



§ 13. Frankenheim's investigation had arrived at the re- 

 markable result that, with freshly annealed bars, the residual 

 moment B^ attained by an impulse x stands in an invariable 

 ratio to the moment of saturation R, independent of the dimen- 

 sions of the bars, their hardness, and the strength of the force 

 acting upon them. Now my experiments seem to prove that 

 this holds good also for bars not freshly annealed, but having 



