98 
Mr. Woobhouse on the Independence of the 
2,72 2 f PzV—1 - 4 ~ C— zV—l 
a -\-b —m , a—m\ - 
r pzV — i — p — iV — i 
, b=ZM< L 
. L zV-i 
-'.{szV-.+i-.V-, )=—?—, and (2^/-i.) l {e^ : 
or 2 
£— z VCTi \ == 
1= - ; but, from what has been premised, these 
j -vV-f 
equations . are true, when instead of % is put or zQ-fczf.or- 
4,0+3, or generally n§-\-%, (47r=0). 
Hence, — i)-| -*</{a—by/ — l) is j £ f -j- } 
f S+z-v/ZTi v — S-f^V^T 1 f w8-f-£-\/ _ i 
or generally w*1 
+ 
or mi | f 3 
— (wQ-f#)V— .r 
^ - I : there are, however, only 3 different values of x } , 
0 / — 39+2V — 1 
• 30 + 2V — I ■> — 
for the index of e in the fourth value is — , and £ 
«v/zt t v: 
£ *£ 
■ 1. 
; 
1 x .£ 3 ” 1 the fourth value is the same as 
the first. Again, the index of s in the fifth value is V 
■ i ? 
( 4 S-f z) 
but* 3 V -'=: V ~\e 1 ■’-Wif — . The 5th 
value is the same as 2d, and so on..; and, consequently, the 
indices of £ in the 3 different values of x are -=±= y v — 1, =£= 
1+2 v/=T, =* v/“. 
3 
— v^— 1 be 
+5: 
"T~ V — X 
+ 2 
3 ' 3 
If, instead of the index of s in the 3d value, 
put, the value of the root remains the same ; for, since H _i 
.gV—i 
20-f £ 
= 1 X X 1 
mi 
x £ 
V_ i — GV— x , 
X £ *r f 
— 2 0-f 2 
«1/T7 
x £ 
}■ 
ml 
e — z , - 6— z , — 
1 — ■ V_x V_i 
“T f 
This mode of representing the roots is not, as has been 
