Vol. 8, 1922 MATHEMATICS: J. L. SYNGE 205 
Hence we have 
\0 {m n). 
Observing that 
^ = = 0 
we find that any three index symbol, ^ , is zero if just one of the indices 
is either* 3 or 4. Turning to the general expression 
- k [:] -s [:'] {[:iT] - [:][:]} 
we find 
='"'{[:][:] -[:][:]}■ 
Now I^^^J vanishes unless a = 4, j^^^J vanishes if 6 = 4, while g^^ vanishes 
unless a = b. Therefore 
applying similar reasoning to the second part of the expression, we find 
Thus any tensor-component with just one index equal to 4 vanishes. 
Similarly any tensor-component with just one index equal to 3 vanishes. 
From (2) we find 
and hence 
1 bgu bgii 
The surviving members of the class given in (3) are 
