THEIR APPLICATION TO THE SOLUTION OF EQUATIONS. 203 
Us= 3" § (63003) + (62112) + (61221) + (60330) + 3(54102) 
+ 4(53211) + 3(53022) +-3(52320) + 8(52203) 
+4(52131) + 3(52014) + 4(51312) + 3(51240) 
+ 4(51123) +3(50421) + 8(50232) + 3(44310) 
+ 6(44121) + 3(44013) + 6(43302) + 6(48230) 
+ (43212) + 2(43122) + 4(43113) + 6(42411) 
+ 2(42321) + (42231) + 2(42215) + (42125) 
+ 6(42033) + 3(41430) + 3(41403) + 4(41331) 
+ (41322) + 2(41232) + 6(40323)} —8-5QEU. 
Multiplying by U, and proceeding as in Art. 38, we find, 
after making the necessary reductions, &c., 
Ut=5" [4 (84004) + (80440) } + 24 (83113) + (81851) t 
+ 2(82222) + 4§ (75103) + (73015) + (71350) 
+ (70531)? + 44 (74023) + (73204) + (72480) 
+ (70342)? + 84 (74212) + (72241) + (72124) 
+ (71422)? + 8§ (73321) + (73132) + (72313) 
+ (71233)t + 6§ (66202) + (60622) } + 43 (65014) 
+ (64105) + (61540) + (60451)} + 103 (65311) 
+ (63151) + (61513) + (61135)% + 12} (65122) 
+ (62521) + (62215) + (61252) } + 6{ (64420) 
+ (64042) + (62404) + (60244) } + 104 (64114) 
+ (61441)} + 12§ (64303) + (63340) + (63034) 
+ (60433) } + §20(64231) + 2(64213) + 6(64123) 
+ 20(63412) + 6(63214) + 2(63124) + 6(62431) 
+ 2(62341) + 20(62143) + 2(61452) + 6(61542) 
+ 20(61324)} + {4(63322) + 4(63232) + 18(63223) 
+ 18(62332) + 4(62323) + 4(62283)% + 124 (55402) 
+ (55204) + (50542) + (50524)? + 124 (55141) 
» + (54511)} +124 (55330) + (55033) + (53530) 
+ (53503)? + 8§ (55312) + (55213) + (51582) 
+ (51523)} + 124 (55222) + (52522)} + $16(54421) 
+ 6(54214) + 16(54142) + 6(54124) + 6(52441) 
+ 16(52414) + 6(51442) + 16(51244)? + $6(54331) 
+ 12(54313) + 16(54133) + 16(53431) + 6(53413) 
+ 12(58341) + 16(53314) + 6(53143) + 12(53134) 
VOL, XV. EE 
