42 MAJOR P. A. MxcMAHON: MEMOIR ON THE 



From the first fraction eliminate C, from the second C, and from the third B, 



obtaining 



1 



I 



(l-D/iX 7 )(l- 



l - 



l - - X 3 X 4 X 8 X 10 ) ( 1 - 1 X 2 X 4 XX 10 

 9 / \ " 



+ fl 



T A1 



'j X^jA^XgXnj 



-<7%X 6 X 9 X 1U ) 1 - X 3 X 4 



X 2 A ( jX ]u 



1 Y ^ 



/I " 



(1 (r/XiX 3 X 4 X 5 X 8 X 9 Ajo ) 



-D/.X 7 ) 1 - -2 X 1 X 4 X 8 X 9 X 1 



X 2 X 6 X, 



i 



1 - 1 X 3 X 4 X 8 X 10 ) ( 1 - 1 



L (l-^X 3 X 6 X 10 j(l- 



Eliminating D from each of the three fractions, we obtain 



1 



(1 -/ 



1 - 



1^ 

 9* 



I' 



-X S X 4 X 8 X 1 



1 \ / 1 



1 -A^-X^Ay-X^o 1(1 -A. 3 X4-X 8 X 10 

 tj ' i/ 



1 ^ / 1 * 



1 j X 2 X 4 X 9 Xi ) ( 1 ^- 2 X ] X 2 X 4 X 6 X 8 X 9 X 10 ) 



fl I \ II / 



T-Xj 



(1 X 1 X 2 X 3 X 4 X 5 X fi X 7 X 8 X 9 X lu ) 



(i -f/^x. 



(1-A 2 X 3 X 8 X 7 X 10 ) fl-ix i 



i - Ix 2 x 6 x 7 x 10 ) (i - Ix 3 x 4 x 8 x 



ts * \ y 



111 



