FOR EQUATION OF ANY ORDER. 
107 
0=( 1)‘®=0, viz. the function in 9^ is 
8^ 
A 
3^ 
A . 
0. 
0“. 
r \ 
1250 X 
' 62500 X 
62500 X 
3125 X 
— 3 a^ef ' 
— 4 a'^cef^ 
- 1 a*dy^ 
+ 1 ay^ 
+ 12 a^hdf- 
+ 3 a^dy- 
+ 2 aV/2 
— 20 a^ey* 
+ 30 a^be^f 
+ 4 a^de^f 
+ 3 a^bcf^ 
— 120 a^cdf '^ 
+ 40 a*(rf^ 
+ 4 a*e* 
— 1 a^bdef^ 
+ 160 dcdf- 
— 172 a*cdef 
+ 4 a^b-ef^ 
— 20 a^bey 
+ 360 a^d^ef^ 
— 16 a^ce^ 
— 2 a^bcdf '^ 
— 30 a^c^ef^ 
— 640 (ddey 
-t- 112 a*dy 
+ 28 a^bcerf 
+ 48 a^cdy- 
+ 256 d^e' 
+ 228 
— 62 a^bd^ef 
+ 8 a^cd^f 
+ 160 d^b-df ^ 
— 8 a^b^def 
- 84 a^bde^ 
+ 32 a^ce* 
— 10 cdb^ey- 
- 98 a^b‘cf ^ 
+ 28 a^cy- 
— 36 a^d^ef 
+ 360 o?b(?f^ 
— 39 a®6'e* 
— 132 a^c‘def 
- 8 a^d^e^ 
— 1640 cdbcdey^ 
+ 116 o?b(ref 
- 72 aVe^ 
- 2 aWy^ 
+ 320 dbcey 
— 320 cdbcd-f 
+ 96 awy 
+ 39 a-Wcef- 
- 1440 a-bdy^ 
— 31 6 cdbcd^ 
+ 384 a3^^2gs 
- 46 a^V^dy- 
+ 
0 
00 
0 
- 2384 d'bd^e 
- 216 a’^d^e 
+ 117 aWdey 
— 1920 a-bde^ 
+ 128 aW/ 
- 1232 aW 
- 4 
+ 18 a-b^e* 
— 1440 d^d^ef- 
- 32 aW^f 
- 168 d^b<?df- 
+ 2640 a-ddy- 
+ 4896 aVrf-e 
- 81 aW(ry^ 
+ 276 od’bc^ey 
+ 4480 a^dddf 
- 1632 a^cd^ 
+ 348 a^b^cdef 
— 220 crbcdref 
— 2560 cddd’ 
+ 49 aWf- 
+ 20 0 a^b'ce^ 
— 504 a^bcde^ 
— 10080 a^cd^ef 
+ 180 cdb^cef 
+ 28 aW-dy 
+ 144 a^dy 
+ 5760 dhdh^ 
+ 224 flWy 
+ 275 a2J2^2g2 
+ 276 a^d^e^ 
+ 3456 aHy 
- 2160 d-d^d 
+ 460 a-b^d^ 
+ 116 a‘b(?ef 
+ 108 a‘cy^ 
+ 344 (db'(?df 
— 336 a^bedy 
— 264 cd'c^def 
- 640 ab^cf^ 
+ 3880 
— 780 d‘bc‘de~ 
— 448 aW 
+ 320 abHef^ 
+ 3000 a'b^cd^e 
— 960 a'bcd^e 
+ 96 d^c^dy 
— 180 ab^ey 
-(- 6400 aW-d^ 
+ 864 aHd'^ 
+ 1736 aWV 
+ 4080 ab“def - 
- 384 a^hcy 
+ 64 a^ddf 
— 1584 cdcd^e 
+ 4480 ab-cdy- 
-20160 cdbc^de 
— 60 
+ 432 
-14920 ab-cdey 
+ 8480 a~d’e 
+ 1120 ahWe 
- 12 ab^ef- 
+ 7200 ab-ed 
- 1120 a-c*d^ 
- 720 a^c-d^ 
+ 264 ab^cdy"^ 
+ 960 ab^d^ey 
— 170 a¥ef 
+ 84 ab^cf^ 
- 615 aWcey 
- 600 a5W 
— 860 ab'cdf 
- 100 ab^def 
- 12 ab^d^ef 
-10080 abc^dy^ 
- 4450 ab*ce^ 
- 60 ab^e^ 
+ 45 aWdd' 
+ 960 abdey 
- 2700 a¥d^e 
- 310 ab'^c^ey 
- 180 ab-cy^ 
+ 28480 abdd-ef 
+ 23400 alMe 
— 100 ab^cdy 
+ 1188 ab-c‘def 
— 16000 abddd 
+ 680 aPc^f 
— 890 aPcde' 
+ 1410 ab^ee^ 
-11520 abcdy 
-29600 ab^cd^ 
- 140 ab^d^e 
- 616 ab^ccPy 
+ 7200 abcd'^e- 
-11200 ah-c*e 
+ 520 a¥c^df 
— 1140 ab-cd‘‘e- 
+ 3456 adf^ 
+ 44800 
+ 1120 a6W 
+ 120 ab‘^d*e 
-11520 addef 
-27200 abed 
+ 4920 aiWe 
— 288 abdef 
+ 6400 add 
+ 6400 ac^ 
-3120 ab^cd* 
+ 192 abc^dy 
+ 5120 addy 
+ 400 b'^df 
- 192 abcy 
-3720 a5cW 
- 3200 acW 
1625 b^e- 
-6560 abdde 
+ 4640 abc^d^e 
+ 256 by^ 
- 300 5V/ 
+ 4160 abdd^ 
— 1440 abcd^ 
- 1920 b^cef- 
— 7500 b^c.de 
+ 1920 ac^e 
+ 1440 ade- 
— ddy^ 
+ 14000 55^3 
-1280 aed- 
— 1920 add'-e 
+ 7200 b*ddf 
+ 4000 5Ve 
— 28 by- 
+ 640 add^ 
- 3375 5V 
-24000 
+ 140 b^cey 
- 96 b^df^ 
+ 5760 b^ddf- 
+ 16000 Wc^d 
+ 120 b^fT-f 
+ 270 5V/ 
— 600 Idddy 
- 4000 6V 
+ 600 6W 
- 320 b^ddf 
— 625 iVe" 
-2700 f/cdh 
+ 1700 b^d* 
+ 120 5V/ 
+ 3800 5Vrfe 
-2400 Pc^d^ 
-1200 5Ve 
+ 800 I/dd^ 
+ 72 b^cy^ 
- 600 b^cdef 
- 675 Idcd 
+ 320 b^dy 
+ 450 b^d'^d 
+ 180 6Ve/ 
- 120 5Vf/y 
+ 2100 }Mdd 
-2600 b^cd:^e 
+ 800 Vd^ 
- 900 5Ve= 
+ 1200 Iddd^e 
- 400 Iddd^ 
- I6OOO d'cd'^ef 
+ 9000 b^cdd 
+ 6400 svy 
- 4000 bWd 
- 2160 5V/' 
+ 7200 5 We/ 
- 4000 bVd 
- 3200 5wy 
+ 2000 b^dd'^e^ 
i«. 1)” 
