Proof of the Generality of certain Formula'. 357 



of the dynamometer having one coil in the primary and the 

 other coil in the secondary circuit. 



The following is another general proof of the same for- 

 mula : — 



The watts given to the primary coil of a transformer are 

 spent partly in heating the primary coil, and partly in doing- 

 work against the back electromotive force set up by the 

 varying magnetism of the core. 



The watts spent in heating the primary coil are of course 

 pD 2 ; while the watts spent in doing work against the back 

 electromotive force are at any moment A x the back E.M.F. 



The E.M.F. generated in the secondary circuit by the 

 same variation of magnetism of iron is at any moment .sA e ; 

 therefore the back E.M.F. in the primary coil at the same 



P 



moment must be^ sA s . 



Consequently the total watts given to the primary coil are 



P v p +l^\& 



p 



/>Dp + -o s D p8 , as before. 



Ill 



This expression, as Mr. Blakesley points out, may be 

 written as follows : — 



and since pD^ + s~Di are the watts employed in heating the 

 primary coil and the whole of the secondary circuit, it follows 

 that 



are the watts employed in heating the core on account of 

 hysteresis or magnetic lag ; a result now proved true inde- 

 pendently of all assumptions as regards the sine law, or the 

 magnetic stress being directly proportional to the ampere- 

 turns, &c. 



IV. 



Since the portion of the secondary circuit outside the trans- 

 former is non-inductive and has a resistance s' say, the watts 

 Phil Mag. 8. 5. Vol. 31. No. 191. April 18*91. 2 C 



