370 Mr. Megh Nad Saba on the 



After partial integration, the second term equals 



1 final J \ B^* 0,1/ J QZ 01 J 



Hence o^Xdx +Ydy + Zdz + Ldl 



=X8* + Y8y+Z&+Lfl 



anal ' J \cU' d,y / 

 (8xdy — dx8y) + 5 other similar terms. 



Now for (X, Y, Z, L) substitute m c 2 (w u iu 2 , io 3 , iv±) and 

 let us denote 



(om ow h \ , n 



Then we have 



5 \ m c 2 ds = 8 \ m c 2 (iVidx + t« 2 rf/y 4- w 3 ffe + w±dl) 



initial 

 = /h c 2 (iv 8x + it* 2 S?/ + w 3 8z + ltf 4 8/) 



final 



+ \[Q l2 (8xdy-dx8y) + £l 23 (8y dz — dy8z) + & n {8zdx — dz8x) 

 + a u (8xdl-dx8l) + VL H (8ydl-dy8l) f £l M (8zdl- dz8l)]. 



Putting the first term =0 as usual, we have from 

 equation (18'j 



f[(m c 2 n i2 + ^/i2) (8xdy —dx8y) + 5 other similar terms] =0. 



The six-components oE the six-vector (8s x ds) are not 

 independent, hence we cannot put their coefficients indi- 

 vidually = 0. If this were possible we would have obtained 

 the system of equations 



m Q c 2 



. /iS _ fsS _ fsi _ fu _ ./*24 _ fu 



e 



n i2 H23 ^31 ^14 ^24 ^34 



since (dx, dy, dz, dl) represent the actual displacement, 

 (8x, 8y } 8z, 81) the variational displacements. 



We shall have to collect the coefficients of (8x, %, 8z, 81) 

 separately and put them individually equal to zero. In this 

 way we obtain the four equations 



_ WlpC 2 _ fi 2 W 2 +/13W3 +,fu w 4 __ /21 w l +/23^3 + /24W4 "] 



e fli 2 -l0 2 + ^13^3 +^14^4 H21W1 + O23W3 ■ + H24W4 ! , 17 ,, 



_ /31^H-,/32^02+./34^4 _ . /^i +/ 4 lW 2 +/43W3 j 



~ ci 3 iiv l + n 3 2t0 2 -+- ^34^4 n 4 i^i + n 42 w 2 + £t 43 W 3 



