Electromagnet and the Equations of the Dynamo. 289 



out that Lamont had in 1867 published a rational theory of 

 the electromagnet, based upon the assumption that the per- 

 meability of the iron was at every stage of the magnetization 

 proportional to the deficit of saturation, leading him to an 

 exponential expression, 



m=M(l— €-**), 



where m is the magnetism present at any stage, M its maxi- 

 mum value, k the ratio of the permeability to the deficit of 

 saturation, and x the magnetizing force proportional (approxi- 

 mately) to the number of ampere-turns of the magnetizing 

 current. This formula more correctly expressed the facts than 

 either of the commoner formulae of Lenz and Jacobi and of 

 Miiller. 



I further pointed out that Lamont had himself* given, as a 

 sufficient approximation to the formula, the simpler expression, 



aKx 



m- 



M + ax 



which formula is mathematically identical with that now 

 commonly attributed to Dr. Frolich. For, writing a=kM, 

 we get at once 



which is the formula claimed by Frolich. 



Lamont having developed his exponential expression in a 

 series of ascending powers of kx, I did the same for the 

 simpler formula for the purpose of comparison, and showed 

 that, neglecting the fourth and higher terms of each series, the 

 expansions are very nearly equal for all values of kx except 

 for very large ones, and are identical for the value kx — f. 

 Dr. Frolich, overlooking the words I have above italicized, 

 commits the mistake of supposing that I had said that La- 

 mont' s exponential expression is identical in value with the 

 simpler formula when Jcx = ^. I have said nothing of the 

 kind. 



Further, when Dr. Frolich says, " Hiernach ist die Aussicht 

 vorhanden dass nicht die Lamontsche sondern die von mir 

 benutzte Formel die wahre Gesetz der Elektromagnete ent- 

 h'alt," he is forgetting that the formula used by him is also 

 Lamont's. He has proved, in his most recent communication, 

 that the differences between the calculated and the observed 

 values are about half as great when calculated by the simpler 

 formula. The second and simpler formula suggested by 

 Lamont appears therefore to be better than the first and more 

 * Lamont, Magnetismus, p. 41. 



