358 Proof of the Generality of certain Form idee. 



developed in it are of course s'D 2 s . Consequently the efficiency 

 of the transformer is 



pvi+l*>r 



V. 



Using the various assumptions already referred to, Mr. 

 Blakesley arrived, by means of a geometrical proof, at a formula 

 for measuring the mean square of the P.D. at the terminals 

 of the primary coil by means of the two ammeters and the 

 dynamometer. 



The following general proof of this formula is very much 

 simpler than the proof for only a special case which Mr. 

 Blakesley gives, and furnishes a very good example of the 

 fact that sometimes it is more easy to give an analytical proof 

 which is true independently of any assumptions about the 

 harmonic law, &c. than to give a geometrical proof which is 

 only true when these suppositions hold. 



Y p =pA p + the back E.M.F. at the moment 

 P 



=P A P + $ sA s> 

 1 f* T 2 C* T T32 2 C* T "P C* T 



•'• TJo V ^ = T 1 A ** + B»y„ K < dt + 2 S T J V-* ; 



that is, the mean square of the P.D. at the terminals of the 

 primary coil equals 



which is the formula given by Mr. Blakesley. 



From the preceding it follows that Mr. Blakesley's ex- 

 pressions for the watts given to the primary coil of a trans- 

 former, for the efficiency of the transformer, and for the mean 

 square of the P.D. at the terminals of the primary coil, are 

 true irrespectively of any assumptions as to the functions the 

 E.M.F.s, the currents, or the magnetic flux are of the time as 

 well as of any assumptions as to the presence or absence of 

 hysteresis or magnetic lag. 



This being the case, the application of this two ammeters 

 and dynamometer method for measuring power in other 

 cases than those already treated of is worthy of careful 

 consideration. 



