572 Dr. S. P. Thompson and Miles Walker on the 



to leakage and ensure the field being nearly uniform in the 

 gap-spaces, the pull should be also very nearly constant 

 throughout a range equal to at least one third of the breadth 

 of the pole-face. 



7. [Added April 10th, 1894.]— It is useful also to know 

 the ratio between the different voltages that are needed, for 

 a given electromagnet, to produce an equal number of ampere- 

 turns with alternating and continuous electromotive forces. 

 i Let V a stand for the alternating volts and V e for the con- 

 tinuous volts which must be applied to the terminals of the 

 coil in order to produce equal virtual amperes. Then 



Y c R iL ~ < 6 > 



When, as is generally the case, It is small compared with jt?L, 

 we may take as a sufficient approximation 



-=^ . . (7) 



The alternate voltage ratio is proportional to the frequency 

 and to the time-constant of the electromagnet.- — F or this ratio 

 we may, on certain assumptions, find an expression in terms 

 of the dimensions of the core and coil. Confining ourselves 

 to the case where the magnetic circuit is closed we may find 

 the value of L as follows : — 



Let l x be the length (in centimetres) of the iron magnetic 

 circuit, A x its cross section, v x its volume, m x its mass in 

 grammes, fx its permeability, and S the number of windings 

 in the coil. Now m 1 = 7*79« 1 . Then L (in henries) will be 



L = 47rA 1 ^S 2 /10 9 / 1 = 47ri^S 2 /10 9 / 1 2 = 4:7rm 1 ^S 2 /7-79 x 10V- 

 Assuming that B does not exceed 6000 lines per square 

 centimetre, we may take for ordinary wrought-iron sheet 

 /Lt = 2000, and inserting this we obtain 



1^ = ^^/310,000 I, 2 . 

 Further, let l 2 be the mean length of one turn of the copper 

 winding, A 2 the cross section of the copper wire, k its con- 

 ductivity (mhos per centimetre cube = 10 6 -Hl'6o), v 2 the 

 volume of copper (=SA 2 / 2 ), and m 2 the mass of copper 

 ( = 8*8v 2 ). Then we have for the resistance of the coil 



R = l 2 S/A 2 k = Z 2 2 S 2 2 /V = 8-8Z 2 2 S 2 7m 2 &. 



Inserting these values for L and S we obtain : — 



V« _ plu _ 27mS 2 m 1 7?? 2 .10 6 



V c = ~R ~ 3100001? X 8-8Z 2 2 S 2 * 



V a . 1 m x m 2 



— L'Atln-r^pi (b) 



Ye" "*"(!*/. 



