THEIR APPLICATION TO THE SOLUTION OF EQUATIONS. 211 
¥(75332)=2-5E*, &'$(74441) + (74414) + (74144) 
+ 7444 t an 74441) =—! SE‘, 3 { (74432) + (74423) 
+ (74342) + (74324) + (74243) + (74234) + (73442) 
+ (73424) + (73244) + (72443) + (72434) + (72344) t 
=(74432)=2-5E', 2'4(74333) + (73433) + (73343) 
+ (73334)? =¥(74833)=— 5E‘, >'{(66611) + (66161) 
(66611) =-5°Q°H+2-5E*, 3° (66422) + (66242). 
+ (66224) + (64622) + (62642) + (62624)} = 2 (66422) 
=5E*, &$66332) + (66323) + (66233) + (63632) + (63623) 
+ (62633)? = 3(66332)=5E*, 3'§(65531) + (65513) 
+ (65351) + (65315) + (65153) + (65135) + (63551) 
+ (63515) + (63155) + (61553) + (61535) + (61355) t 
=>(65531)=2-5E', 3” § (65522) + (65252) + (65225) 
+ (62552) + (62525) + (62255)? = 3 (65522) = 5B, 
2’ $ (65441) + (65414) + (65144) + (64541) + (64514) 
+ (64451) + (64415) + (64154) + (64145) + (61544) 
+ (61454) + (61445)? =>(65441)=2-.5E*, 34 (65432) 
+ (65423) + (65342) + (65324) + (65243) + (65234) 
+ (64532) + (64523) + (64352) + (64325) + (64253) 
+ (64235) + (63542) + (63524) + (63452) + (63425) 
+ (63254) + (63245) + (62543) + (62534) + (624538) 
+ (62435) + (62354) + (62345)? = >(65432) =— 5Et, 
'§ (65333) + (63533) + (63353) + (63335) } = = (65333) 
=- 5, 35 (64442) + (64424) + (64244) + (62444)? 
= >(64442)=-—5E*, 5’§ (64433) + (64343) + (64334) 
+ (63443) + (63434) + (63344)? = >(64433)=5E*, 
'$(55541) + (55514) + (55451) + (55154)? = >(55541) 
=-5E*, 37$(55532) + (55523) + (55352) + (55253)? 
=>(55532)=- 5E*, 3'$ (554.42) + (55424) + (55244) 
+ (54542) + (54524) + (52544)} = 2 (55442) =5 Et, 
3 § (5543) + (55343) + (55334) + (54533) + (53543) 
+ (53534)} =>(55433)=5E*, and 3’ § (54443) + (54434) 
+ (54344) + (53444) =>(54443)=-5E*. Hence, by sub- 
stitution in the value of U® given in the last article, we 
have 
VOL. XV. ry 
