244 THE MAGNETIC CIRCUIT [ART. 70 



energy. The physical dimensions of F' and W are also the 

 same. 



If F{ is in kg. per sq.cm., B in kilolines per sq.cm., and 

 H in kiloampere-turns per cm., the preceding formula becomes, 

 when applied to air, 



F/ = 2/24.7= 



These formulae apply directly to the lifting magnet (Fig. 

 58), and give the carrying weight per unit area of the contact 

 between the core and its armature. The total weight which 

 the magnet is able to support is 



F,=A 2 /24.7 = A# 2 /15.6kg., . . . (171) 



where A is the sum of the areas denoted by S\ and S 2 . Of course, 

 H is taken for the air-gap, which is the only part of the circuit 

 that is changing its dimensions when the armature is moved. 



(6) The Lateral Compression. Let now the simple magnetic 

 circuit be allowed to expand laterally by a small length Js in 

 directions perpendicular to the surface of the toroid. Let F e ' 

 be the pressure (compression) exerted by the lines of force upon 

 the winding, per sq. cm. of the surface of the toroid. Then 

 the mechanical work done by the magnetic forces in expanding 

 the ring against the external forces which hold the winding, 

 is SF C 'JS, where S is the surface of the toroid. Let again the 

 current be slightly decreased during the deformation, so as to 

 keep the flux constant. No voltage is induced in the winding, 

 and hence there is no interchange of energy between the electric 

 and the magnetic circuit. Thus we can find F c ', as we found 

 the stress in the case of the tension, by equating the work done 

 to the decrease in the stored energy. The stored energy is 

 expressed by eq. (162), in which A is the only variable; hence 

 by differentiating W with respect to A we get : 



This is a negative quantity, because the stored energy decreases. 

 But UA represents the increase in the volume of the ring, so 

 that I A A = SJs, and consequently 



F c ' = lB 2 /fjL=1tiJLH 2 =W' = F t ' ..... (172) 

 In other words, the lateral compression is nummerically equal to 



