455 
1910-11.] Dr Muir on Boole’s Unisignant. 
character. Indeed there are cases where the signs of the terms in the 
final development are all negative. Thus, when 
Y = ax 2 + 2 bxy + cy 2 , 
the determinant is equal to 
and when 
— 4 xy(a 2 bx* + a 2 cx 3 y + ac 2 xy 3 + bc 2 y 4 ) ; 
Y = ax 2 + by 2 + ez 2 + *ldyz + 2 ezx + 2 fxy , 
the determinant is equal to 
- Sxyz -j ^ a 2 efx b + ^ a 2 (be + df)x^y + ^ a 2 (cf + de)xh + ^ a 2 bdx z y 2 
4- 2 + 2 def)x 3 yz + ^ ^edxh 2 + 2 abdex 2 yh | (XYI.) 
where the symbol of summation implies the performance of the cyclic 
substitutions 
^ 5 2/ 3 2 = 2 /,z,a, a,b,c = b,c,a, d,e,f=e,f,d. 
(. Issued separately May 17, 1911.) 
