Temperature on the Hysteresis Loss in Iron. 119 



When the whole change is completed in a short time \Ccdt is 



proportional to the angular momentum gained by the coil of 

 the dynamometer and this again to the "throw" 0. 



By means of an earth-inductor placed in the secondary 

 circuit a known change P in the number of lines of magnetic 

 force passing through that circuit can be suddenly produced 

 while a constant current (7 is flowing through the primary. 

 If — <j> be the (C throw " of the movable coil and S' the 

 secondary resistance, then 



-fccdt*. C'P/S'=0:0. 

 Hence 



,,__. „ NC'PS/0 n'A*C/dB\*, 



When the rate of variation of B is so small that dB/dt may 

 be taken as uniform over the section we may write 



dt ~ a \ dt) 



where Q is a numerical constant depending on the geometrical 

 form of the section and a the specific resistance of the 

 material. Searle and Bedford shew that for a circular 

 section Q = l/87r = 0*03979, and for a square section 

 Q = 0'03512. 



Thus, finally we have 



w NCTS0 A /Q, * a \(7dB\* 



»"• (2 + f;)^-N.Af(gy*,c, 



(3) 



■nAS' (/> 



if c be neglected in comparison with C in the integral, then 

 dB/dii is a function of C but not of dC/dt. Hence for any 

 given value of 0, the contribution to the integral due to the 

 increment dO is proportional to dG/dt. 



Using a suitable reversing key we can, as Searle and 

 Bedford show, increase dC/dt in any ratio by increasing the 

 resistance of each of the two parts into which the primary 

 circuit is divided by the key in the same ratio, the battery 

 power being at the same time increased in the same ratio so 

 as to keep the maximum current constant. 



Writing U for NCTSfl/ziASV-f), we then have 



W = U-(a+|)R (4) 



where a and b are constants. 



