7 68 Proceedings of Royal Society of Edinburgh. [sess. 
and observing the equations 
x q V2 x + y 6 U y + z 6 12 z = 6l2 , 112 = 0, <fcc. 
this becomes 
612 
• 
. 
• 
645 
145 
245 
. 
. 
623 
123 
. 
423 
523 
156 
256 
356 
456 
. 
. 
. 
534 
361 
461 
561 
reducible to 
145 
245 
123 
. 
423 
156 
256 
356 
456 
.. 
361 
461 
or, omitting the factor 612 . 534, and expanding 
i 45 . 256 . 423 . 361 + 245.123.456.361 
- 245 . 123 . 356 . 461 - 245 . 156 . 423 . 361 = 0.” 
The purely algebraical identity involved in this is in later notation 
i«l 1 2/4% I 1 2/2% I I %% I • 
l%* 2 l l%* 6 l l%* 3 l I %*6 1 • 
1*i2/ 2 I \ x tVb\ l^l 1*524,1 • 
• ! 2/2*3 I I 2/5% I 12/3% I I 2/6% I 
• • 1 %*3 1 I %*6 I 1 %*4 I I %*1 I 
• • ! *2^3! 1*52/6 1 ! *3^4! 1*62% 
I*i2/ 2 %I • • 1 * 42 / 2 %! 
I *12/4% 1 1*22/4%! 
I *12/5% I I *22/5% 1 1 *32/5% 1 1 *42/5% I 
• 1 * 32 / 6 %! 1 * 42 / 6 %! 
