1904 - 5 .] Three-line Determinants of a Six-by -Three Array. 371 
(10) The relations between products of three factors it is less 
necessar} 7- to study, the foundation of them being laid in what 
precedes. For example, there are numerous results like 
1(01'+ 59) | 2(02'+ 67) = 3(03'+ 48) 
which is clearly obtainable from the first triad of § 8. Less 
easily verifiable from the foregoing are the pair 
1 8 6 
r 8' 6' 
4 2 9 
= 000', 
4' 2' 9' 
7 5 3 
7' 5' 3 
the process being — 
1 8 6 
4 2 9 
7 5 3 
= 1(23-59) + 4(56-38) + 7(89-26) 
= 1 Or + 4 04' + 7 07', 
= 0(11'+ 44'+ 77') 
= 000 '. 
(. Issued separately January 20 , 1905 .) 
