118 Mr. R. L. Wills on the Effect of 



the fixed coil of the electrodynamometer being connected in 

 series with the magnetizing coil. 



The complete theory of the method will be found in the 

 Trans. Roy. Soc. * and thus it will be sufficient to give here 

 a brief outline of the theory applicable to the present 

 experiments ; for convenience in reference the notation 

 employed by Searle and Bedford will be used here. 



If the primary and secondary coils are wound closely upon 

 the specimen and if E be the voltage between the ends of 

 the primary coil, then 



E = KC + NAZ~, (1) 



where C is the primary current, R the resistance of the 

 primary coil, A the sectional area and I the mean circum- 

 ference of the ring, and N the number of turns per unit of 

 length in the primary coil. 



If c be the secondary current we may write 



= Sc + nA^, (2) 



where S is the resistance of the secondary circuit and n is the 

 total number of turns in the secondary coil. 



Now of the work done by E in any time, part is spent in 

 increasing the magnetic energy of the system, and the rest is 

 dissipated in hysteresis and eddy-currents in the specimen 

 and in heating the wires of the primary coil and of the 

 secondary circuit. 



When the specimen is subjected to a complete cycle of 

 magnetic changes, the magnetic energy on the whole is 

 unchanged and we have 



fiCdt = Al(W + X) +jRC 2 ^+jSc 2 ^, 



where W and X represent the space-averages of the energy 

 dissipated per cub. cent, per cycle by hysteresis and eddy- 

 currents respectively. But from equation (1) 



jEOft= inc 2 dt + NAZ fc ^-dt, 



hence 



AZ(W + X)=NAz(c^^- fec 2 dt 



* G. F. C. Searle and T. G. Bedford, Phil. Trans. A, vol. 198, pp. 40-52 

 (1902). '** 



