172 Professor Baker, On the transformation of the equations of 



^ + ^'=8 + S'. 



so that. 



Then the last square is 



8, y, 



— y, S', 



0, 0, 



0, 0, 



0, 

 0, 



a, iS' 



and the equations of electrodynamics are expressed by the vanish- 

 ing of the product 



0, 0, -Tj, fi 



0, 0, -^1, -7^1 

 ^1, li, 0, 



- ^1, Ti, 0, 



this is equivalent to the vanishing of the two products 



(-^1, - fi\ ( ^, cc'\ ( vi, ii] ( S, y' 



and the equations are therefore 



^ + 3^ = ^-^ + ^-^=0 ^^ 



?^_^:^0 — -?^'-0 1^- — -0 ^ 



These results are easily shown directly to be the same as the 

 ordinary forms (putting Tf = 0, j8'= — ^, S'= — S). They involve 

 that each of the functions a, ^, a, ^', y, S, y, S' satisfies the equa- 

 tion 



oxj^ 9^1 9zi 9^1 9^1 9zi 9?/i 9a;i 



(I). 



= 



or 



dxjjdz-^ dy-^t^ ' 



dw 927 927 927 



9^ "^ 9^ ^ 9^2^ + W 



0; 



and they are equivalent also to 



dt ^^1 + 9z ^^1) + ^ ^^1' ^1^' 



^ ^ i (~ 92i ^^'- + 9^1 "^"^i) + ^ ^^1' ^1^' 

 r'= I (- g^ <^^i + ^ ^% ) + C" (a^i, ^i), 



+ 9^^^^ 



