Magnetic Tractive Force. 157 



this region where the field was practically zero. We have, 

 therefore, at x = 0, also a = 0, and the equation becomes 



^=I(H + 27rI)-fW, 



or, remembering the relation B = H + 47rl, 

 Xi_ B 2 -H 2 P 1 



Rdl (2) 



This part of the integral in (1) depends only on the longi- 

 tudinal components of the field and magnetization. 



It may be shown that the part of X depending on the 



transverse components of field and magnetization vanishes if 



the value of a. is constant at the outer end of the bar, 



dec 

 i. e.ii -=- = at x = 0* ; since this was very nearly the case 



in the experiments we may neglect these terms. 



Equation (2) gives, therefore, the tractive force per unit 

 area ; calling this P grammes weight per sq. centim., we 

 have 



W_ 

 Sirg 

 or f 



— H 2 1 P 1 

 P = ^-^l - l Udl; .... (3) 



^9 9 Jo 



B 2 H 2 1 P 1 



Sirg birg g J 



so that the expression 



y/p + W/8ng + ^^Rdl,. ... (4) 



* An approximate calculation based on Laplace's equation in cylin- 

 drical coordinates gives 



16 \dx)x=o 



where r= radius of section of bar, and &=ratio of mean radial magneti- 

 zation to mean radial " external " magnetizing force. 



f In the immediately following section of his treatise (/. c. § 641), 

 Maxwell explains these forces by his well-known theory of stresses in a 

 medium, and develops the corresponding stress equations. From these 

 the equation (3) might be more shortly deduced. In somewhat different 

 ways similar expressions have been obtained by du Bois, Wied. Ann. 

 xxxv. p. 146 (1888), and by Adler, Wien. Ber. c. 2 Abth. p. 897 (1891). 



