264 MAGNETISM 



Similarl 



T = iL cos 6, sin 1 + sin ^ cos O l 



07T 



sin 



The resultant of N and T is a tension on unit area of the 

 surface in a direction making an angle W l with the normal. Tin- 

 resultant of the system N and T over the bodv >hould gi\i- tin- 

 actual force. 



But we may add to this system the system due to the internal 

 stresses, for these form a system in equilibrium. \Ve may take 



these internal stresses either of their actual value, , or, as N 



oTT 

 tt II 2 



more convenient, of value g-*~* '< Ut> >ii|><-r|><>^- on the actua 



. - // 2 H 2 2 II 



system -g-- a system (MI-MJ)^-' 



When the internal system i^ superposed \\ 



N = ^i- 2 (cos 2 1 - sin* 0,) - &&L(c**t 0, - sin 2 f) t ) 



O7T O7T 



, 2 COS 2 0* - MlH.* COS 1 S t . 



* - * ^ l * - ", since IIj sin H 1 = !! sin v n 



OTT 

 _ H t cos e i + H t cos 0, H t cos Q l - H, cos 8 t 



2 '^ " 47T 



H -4- 1*1 



= Normal component of - i-^ * X surface density <r, 

 where the accents are put to denote the vector values. 



' s ' n e cos * 



T = ii sin 6l cos e, - 



4-7T 4-7T 



= Hl sin e r / 



since H! sin 4 = H, sin O t 



_ H 1 sin Q t + H a sin 2 H t cos t - H, cos t 

 "^~ ~* Ml ~ ~4^~ 



V V 



IJ I TJ 



= Tangential component of ^-^ * X surface density <r. 



