82G 



DR THOMAS MUIR ON THE 



h • 



• 6, 



• \ 

 d 2 . 



d a 



i.e., — ajb x = B x say, 

 i.e., — a.^ = B 2 say, 

 i.e., — a^ = B 3 say, 

 i.e., — b.f, = B 4 say, 

 i.e., — b 4 d 2 = B 5 say, 

 i.e., — c 4 d 3 = B say. 



Using the last six equations to eliminate b u c u d u c 2 , d 2 , d z — these being the elements 

 on one side of the primary diagonal of | a^biC^U | — from the preceding five equations, 

 we have 



B^+BA + BsB,- 



B b 6 ^ + Bi b;4 



2 6 a 3 c 4 W 



>> 



3 a 4 i 4 % 2 5 3 c 4 



= D, 



+ B 2 B 5 ^ + B 3 B 4 ^ 

 _ 2 °a 3 & 4 3 % 4 & 3 





- B^- 3 + B^-% 



= c 1; 



- B 3 a ^ + B x B,-%- 

 3 a 4 x 5 a 2 6 4 



= c 2 , 



- B 3 ^ + B 2 B 6 ^ 



= C 3 , 



R & 3 C 4 , r. TJ 5 4 



= c 4 .^ 



_,..... . . a<>&3 « 2 6 4 a 3 c 4 & 3 c 4 . , 



But the lour fractional quantities — , , , -j- — or say y lt y 2 , y 3 , y 4 — in the 



(^3 CI4. Ct^. O4 



last four equations are connected by the relation 



7i73 = 7 2 74> 

 and the three similar quantities in the remaining equation of the set are expressible in 

 terms of these four, viz.: — 



a Jh . . 72 



or & 



a 3 c i y s 



74 



„.. -yiy» 



or y 2 y 4 , 



-4°3 = 7i or 74 



afi. 



S & 4 72 73 



It is thus possible by the elimination of y u y 2 , y iy 74 to deduce five equations, not more 

 than two of which, however, can be independent. 



