338 



DR THOMAS MUTR ON THE 



and thus obtained the eliminant in the form 



C 

 B 

 A' 



C 



B' 



B 

 A 



C 



-2 A' 



A 

 -C 

 -B' 



which, it was afterwards shown, 



= 2 



A 

 C 

 B' 



C 



B 



A' 



-2B' 



-C 

 B 



-A' 



B' 



A' 

 C 



-20' 

 -B' 



-A' 

 C 



Now the given equations may be written 



xJB 



yj± , 



xJB "*" 



zJB 



yjc 



xJC 



2C 1 



+ 



+ 



y_J2 



zJB 

 zJA 



* J a x jc 



consequently it is seen that there exists the relation 



, A'. , B' 



JAB 



_2A/ 



VBC 



2B' 



VGA j 



^ 



COS" 



and therefore 



7BC 



+ COS' 



1 



A' 



yCA 

 A' C 



+ COS" 



JBC 

 C 



VBC 

 1 

 B' 



Similarly the resultant of 



JAB JCA 



Bz 2 - 



VAB 

 B / 



VCA 



1 



c 



JAB 



= 0. 



= o, 



Dxy + Ay* = 

 Cy 2 - Eyz + Bz 2 = 

 Ls 2 -Ksw+Ch; 2 = 



Aw 2 — Gwx + Lx 2 = 



is 



COS" 



D 



+ COS" 



E 



2 JAB 2JBG 



and therefore from section 16 is 



+ COS" 



K 



2yCA 



+ COS" 



G 



2yLA 



0, 



D 



E 



K 



G 



2 JAB 



E 

 2JBC 



K 

 2JCL 



G 



2JBC 



D 

 2VAB 



G 

 2VLA 



K 



2JCL 



G 

 2 JLA 



D 

 2 JAB 



E 



+ 



DEK 



2 JLA 4BC VLA 

 K EDG 



2 N /CL + 4AB /S /CL 

 E , KGD 



2JBC 4LAJW 

 D GKE 



2 JLA 2JCL 2JBC 2 N /AB + 4CL N /AB 



= 0. 



