Magnetic Circuit of Dynamo Machines. 509 



rounding off the straight line into the Frohlich by hand. In 

 applying our rule to the Manchester dynamo we employed 

 neither of these methods, as one's judgment is vitiated when 

 one has seen the actual observations ; and we have assumed 

 that the very roughly correct rule, 



N=p tan- 1 (A . S 2 A 2 ), 



may be applied, making its slope the same as that of the 

 straight line at the origin, and making it pass through the 

 point whose position we have calculated. In this case 



ph = 660; 

 and it will be found that 



^ = 34-65 xlO 5 , 

 and 



/i = 19-03xl0 -5 

 for this case. 



As Dr. Hopkinson has given his characteristics, not in 

 terms of ampere-turns S 2 A 2 , but in absolute units, calling 



— Y S 2 A 2 by the letter F to denote the magneto-motive force in 



absolute units, the above formula becomes for this comparison, 



N=34-65 x 10 5 tan" 1 (15-15 x 1(T 5 F). 



In the figure we have plotted the curve obtained by calcu- 

 lation as A ; B shows Dr. Hopkinson's calculated curves ; 

 the dotted line passes as nearly as possible through the points 

 determined by experiment. It will be observed that the 

 Drs. Hopkinson have only ventured to calculate the chai-ac- 

 teristic up to F = 12,000 on the ascending, and 9500 on 

 the descending part ; whereas the observations extend to 

 F = 29,500. As the very straight part near the origin pre- 

 sents no difficulty, it may be said that all their elaborate 

 calculation represents only the characteristic from about 

 F = 6000 to F = 12,000, and that part very indifferently. It 

 is, besides, to be observed that in an actual dynamo there are 

 no such differences between observations made with steadily 

 increasing and with steadily diminishing magneto-motive forces, 

 as the theory requires. 



In the above calculation we have neglected the clearance d, 

 as we did not know it. It would have been easy to calculate 

 a value of d, possibly not very different from the real value, to 

 make our curve agree more closely with the observations. In 

 conclusion we would say that, in our opinion, it is impossible, 

 until a machine is constructed, to compute its characteristic 



