THEIR APPLICATION TO THE SOLUTION OF EQUATIONS. 209 
+ 10(64253) + 18(64235) + 56(63542) + 10(63524,) 
+ 18(63452) + 12(63425) + 48(63254) + 28(63245) 
+ 18(6254.3) + 28(62534) + 56(62453) + 48(62435) 
+ 12(62354) + 10(62345)? + 465 (65333) + (68533) 
+ (63353) + (63335)} + 20§ (64442) + (64424) 
+ (64244) + (62444) } + {32(64433) + 32(64343) 
+ 48 (64334) + 48(63443) + 32(63434) + 32(63344)? 
+184 (55541) + (55514) + (55451) + (65154)? 
+58} (55532) + (55523) + (55352) + (55253)? 
+ $26(55442) + 40(55424) + 26(55244) + 26(54542) 
+ 26(54.524) + 40(52544)? + §14(55433) + 24(55343) 
+ 14(55334) + 24(54533) + 14(54543) + 14(53534)? 
+24} (54443) + (54434) + (54344) + (538444)? ] 
+26-5°Q°E?U — 8-5QEU*. 
The bar placed over the number 10 indicates that it is a 
single exponent, so that }’(105005) represents 3’2 v3 z°, 
3’(104114) represents 3'2 wtx,a,a!, &c. Whence by 
the theorem in Art. 29, 
YU=23(1055) +65(104411) + 4.3 (103322) + 53 (9641) 
+52(9542) + 145(95321) + 282(94331) 
+822 (94322) + 102(8782) +52(8651) 
+ 445 (86321) + 362 (85511) + 802(8543) 
+392 (85421) + 962(85322) + 96(84431) 
+ 962 (84422) + 202(84332) + 8605 (83333) 
+ 72=(77411) + 1803(77222) + 802(7652) 
+ 502(7643) + 545(76421) + 1362(7633 1) 
+ 482 (76322) + 1862(75521) + 605(7544) 
+1182(75431) + 76575422) + 1643(75332) 
+ 862(74441) + 2325(74432) + 485 (74333) 
+1202(66611) + 605(6653) + 965(66521) 
+922(66431) + 83365 (66422) + 1325(66332) 
+722(6554) + 1645(65531) + 1285(65522) 
+1882 (65441) + 1725(65482) + 2763(65333) 
+ 1205(64442) + 2243 (64433) + 1082(55541) 
+ 3482 (55532) + 1842(55442) + 1043 (55433) 
