electrodynamics in the Maxwell and in the Einstein forms 171 



where is the zero of ordinary analysis. The above operational 

 equations may then be obtained by multiplications of such squares 

 of four rows. 



But when ^, 77, t,, t stand for 



^ 8_ a a 



dx' dij' dz' dt' 

 if we take Xj, y-^^, z-^, t^ so that 



x = Xi + Zj_, ez = x^- Zi, t = ti + y^, ey = t^ - y^, 

 we have 



and, denoting these by ^j, t^^, ^j, t^, the above square is 

 0, 0, 

 0, 0, 



^1> 



Asain 



^1, 



0, 







uW + jkL + MM + ijN + eiX + ejY + ekZ 



is 



W fE, 

 .0, E 



L (I, 0\ + M /J, 0\ + N ,K, 0\ 



[0, II [o,jJ [0, k) 



+ X f-I, 0\+Y (-J, 0\ + Z 



0, I J [ 0, J, 



K, 

 0,K 



or 



{EW + {L- X)I + {31 - Y)J +{N -Z) K, 0, 



\ 0, WE + {L + X)I + {M+ Y)J + {N+Z)K 



which, if we take E, I, J, K as above, is the same as 



W +{M~ Y)€, L - X - {N ~ Z) e, 0, 

 -{L- X)- {N - Z)e, W -{M - Y) 6, 0, 



0, 0, W +{M+ Y)€, L + X-iN + Z)€ 



0, 0, -{L + X)-{N + Z) 6, w -{M+Y)e 



Now put 



a = L+ X + €{N + Z), y ^ L - X + e {N - Z), 

 a = L + X - e (N + Z), y' = L - X - e {N - Z), 

 ^=W + €{M+ Y), 8 = W + e {M - Y), 



j8' - PF - e (M + Y), b' =W -e{M- Y), 



