260 Proceedings of Royal Society of Edinburgh. [sess. 
which must he the same equation as that of the preceding para- 
graph. The symmetry with regard to g 2 and x 2 , and with regard 
to g x and g 3 , is apparent ; and the partition of the determinant 
into two gives immediately the value of x 2i and equally readily 
the value of g 2i if the element in the place 2,3 be written g 2 + x 2 
instead of x 2 + g 2 .* 
* The peculiar set of equations dealt with in this short paper can scarcely 
have escaped notice until now. They were suggested to me while examining 
a problem set by Professor Nanson in the Educational Times for Septem- 
ber 1900, viz., u If i a=[x 2 - y)/(l -xy), and b = (y 2 - x)/(l - xy) , prove that 
(a 2 -b)/(l -ab) = x and (b 2 - a)/(l - ab) = y.” 
