﻿520 Mr. S. B. McLaren on Emission and Absorption 

 §3. The Modified Lagraxgian Function. 



The equations of motion can be deduced from a modified 

 Lagrangian Function derived by substituting the value of 

 F given by (17). From (26) and (24) we have directly 



( v2 4S F ^S F °-« 2F °- • • • («»> 



The variation of F and </> in (14) leads to (11) and (12) 

 which are now replaced by (28). Varying p and U 



s[L^vdt+((FS&-<l>8p\dvdt = . . (29) 



4 4 



Use (17) 



4 *4 



= -(l\h^dvdt . (30) 



4 



The action may always be modified by omitting any term 

 which is merely a perfect differential 



4 4 



And (30) becomes 



8 fi m dv dt + |Yf S £5 _ ^fy) c / r ^ = _ j FiS p ~ dv dt. (31) 



4 *4 *4 



By (24) 



(V 8 -K 2 )8F +4^^=v(5j^) . . (32) 

 So that 

 F (VW)SF -SF (V W;F U + u (f„S ^- l - ^gF ) 



-F.v-(«^)- W .yI(*). (aa) 



Now the function F as defined by (24) is such that 



DivF =0 and F normal at S. 

 Thus we have also 



Div 8F C = and 5F normal at S. 



