782 
Proceedings of Boyal Society of Edinburgh. [sess. 
For 
2B 1 B 2 B s B 4 - 2B 1 B 4 C S C 2 - 2 B 1 B 3 E 2 E 4 = - 2B 1 B 3 B 4 E 2 + 26^^302 - 2 B 1 B 3 E 2 E 4 
= 2 B 1 (B 3 E 2 C 4 + B 4 E 3 C 2 ); 
20^0304 - 2 CAE 3 E 4 - 262630 ^ 4 = - 2 C 1 C 2 C 4 B 3 + 2 C 1 C 2 E 3 B 4 - 26^0^4 
= 2C 1 (B 3 C 4 E 2 + C 2 E 3 B 4 ) ; 
2EjE 2 E 3 E4 - 2C3C4E4E2 - 2E 1 E 3 B 2 B 4 = - 2E4E2E3C4 + 2EJE3B4CO - 2 C.JC 4 EJE 2 
= 2 E 1 (B 3 C 4 E 2 + E 3 B 4 C 2 ) ; 
and 
<d 4 ,i >2 = 2BABI - 20^0^ - 2BJE2E4B4 - 2B 2 C 1 Bfi 4 
= - 2B 1 B 2 B 4 C 4 - 2 B 4 B 2 E 4 B 4 - 20 ^ 2^4 - 2B 1 E 2 E,B 4 - 2B 2 C 1 B,C 4 
= 2E4B2B4C4 - 20^0^4 + 2B 1 C 2 E 4 B i . 
16. So we have, 
<%.. = (BiC 5 - B/A ) 2 = (C^ - C 5 E ,) 2 = (EjB 5 - EjBj ) 2 -| 
< 0 ,., = (B,B 4 - C X C 4 ) 2 = (EjC 4 - BjE 4 ) 2 = (CjE 4 - EjB 4 ) 2 
W 4,2 = (B 2 B 4 — E 2 E 4 ) 2 
•» 4 , 3 =(c 3 c 4 -e 3 e 4 ) 2 1 - • (38) 
“> 3,1 = (B' l B 3 — EjE 3 ) 2 
“3,2 = (B 2 B 3 - C 2 C 3 ) 2 
“ 2,1 = (CA - EjEj) 2 
“ 5 = 2(BjB 2 B 3 B 4 + C 1 C 2 C 3 C 4 + EjE 2 E 3 E 4 ) ; • 
<0 4 = 2(B 1 C 2 E 3 C 5 + C 1 E 2 B 3 B 5 + EABA) ; 
<o 3 = 2(C 1 B 2 E 4 C 5 + Ep 2 B 4 B 5 + B 1 E 2 C 4 E 5 ); [ . . . (39) 
<*> 2 = 2(E 1 B 3 C 4 C 5 + CjE 3 B 4 E 5 + B,C 3 E 4 B 6 ) y 
“i = 2(E 2 C 3 B 4 C 5 + B 2 E 3 C 4 B 5 + C 2 B 3 E 4 E 5 ) ; . 
Where we observe the identity, 
“5 = 2(0,0, - EjEjXCjC* - E s E 4 ) + 2(EjE 3 - B,B 3 )(E 2 E 4 - B 2 B 4 ) 
+ 2(B,B 4 - CjC 4 )(B 2 B 3 - C 2 C 3 ) ; (40) 
&c. 
