}. . . (52c) 



200 Mr. 0. Heaviside on the 



becomes. Then 



B' 1 R f j=L' 1 LV- 



I did not give any separate development of the I/j of the core, 

 corresponding to (48c) and (49c) above for R/, but merged 

 it in the expression for the tangent of the difference in phase 

 between the impressed force and the current in the coil-circuit. 

 The full development of L^ is 



L^_ 1+ 6U6V 1+ 2 3 . 10.16 ( 1+ 3 3 . 14.16( 1+ 4 3 .13.16 ( 1 + ' 

 Li" 



the denominator being the same as in (49c) . 

 The high-speed formulae for R\ and 1/j are 



E' 1= L>= M, 



if y=16^ 2 . When z is as large as 10, this gives 



R' 1 = L> = -2234L 1 n, 

 whereas the correct values by the complete formulae are 

 R'^-198 Li*, I/i=-225 I*. 



It is therefore clear that we may advantageously use the 

 high-speed formulae when z is over 10, which is easily reached 

 with iron cores at moderate speeds. 



The corresponding fully developed formulae for R/ 2 and L/ 2 , 

 when the current is longitudinal, are 



R^ = 1+ 6T6V 1+ ^.10.16( 1+ 3 3 . J4.1h( 1+ '" 



U * 1 1 y (l 1 y (l\ y (\ I ' 



^ 2.6.16V 3.2 a .10.16\ 4.3 2 .14.16V 



showing the laws of formation of the terms, and 



1 1 y d i y d i y (\ . 



L 2 ^ 2 2 .6.16V 2.3 2 .10.16V 3.# 14.16 V" 



*/* 



the denominator being as in the preceding formula. At 

 z = 10, or y = 1600, these give 



R' 2 = 2-507 R 2 , I/ 2 =J fix '442 ; 



