106 TREATISE ON ALTERNATING CURRENTS. 



exactly equal to the primary counter E.M.F., but opposite iii phase ; 

 we may therefore write 



w = + ~* x (mean square RTX) (34) 



If, then, the P.D. between the primary terminals, as measured by 

 a hot wire or electrostatic voltmeter, is kept constant, the total 

 iron loss is given by equation (34), whatever be the shape of the 

 wave. 



The problem of finding the area of the wave which makes the 

 iron losses a minimum is the same as that of making the area of 

 the P.D. wave as small as possible while the RM.S. potential dif- 

 ference, V, remains constant. We have, therefore, to make 



/ Vdt = a minimum 

 while 



fV 2 dt = a constant ..... (35) 



From this we deduce that / Vdt has no absolute minimum, but 

 may be made as small as we please by making the maximum value 

 of V correspondingly large and the P.D. curve narrow and peaky. 



It is to be noticed that the hysteresis losses only are affected by 

 the wave form of the primary P.D. as the eddy current losses are 

 constant when the P.D. is constant. 



It is not advisable to attempt to reduce the hysteresis loss too 

 much in the manner here indicated, as, by so doing, the maximum 

 P.D. becomes very great, and the insulation of the transformer 

 must be correspondingly increased, a course which would produce 

 a very costly appliance. 



These theoretical results have been amply proved by experi- 

 mental investigation, and we would draw the attention of our 

 readers to the writings of Mr. Steinmetz, 1 Dr. Fleming, 2 Messrs. 

 Beeton, Taylor, and Barr, 3 Dr. Eoessler, 4 Mr. Evershed, 5 and Mr. 

 Feldman, 6 on the subject. 



1 Electrician, August 24, 1894, vol. xxxiii. p. 498. 



2 Ibid., June 28, 1895, vol. xxxv. p. 304 ; January 10, 1896, vol. xxxvi. 



3 Ibid., June 21, 1895, vol. xxxv. p. 257; June 28, 1895, vol. xxxv. p. 286; 

 November 8, 1895, vol. xxxvi. p. 61. 



* Ibid., November 22, 1895, vol. xxxvi. p. 124 ; December 6, 1895, vol. xxxvi. 

 p. 222. 



5 Ibid., March 27, 1891, vol. xxvi. p. 635. 



6 Ibid., October 18, 1895, vol. xxxv. p. 809. 



