374 
Mr. Wood on the 
v im ± 2mzv Zm ~ I -i- zm . z z v %m ~' a ± zm — - 2W g z 3 v Z!n ~ 3 4- &c 
2 2 ’ 3 * r 
ilm — » i 
/> a- 
qx zm - z 
rx vn - 3 
pv %m 1 _j_ 2 m — i . pzv Zm ~~ 7 ' ± zm — i . — — - . p z z v z:n 3 - f ^ 
q v z:n ~ z : 
and consequently, 
2 m — 2 . qzv Zm — 3 -j- &c. 
r v %m ” 3 -f Csfff. J 
v zm -\- 2 m . 
2 m - — l 
-f 2 m — i . p z j 
+ q J 
I 77 
.zm — 2 
-P e?c. -j- 2 a -' 1 
and also. 
2)H2 1 17 
+ /» 
y 
%m —i 
-f 2 m 
am — l 2 m — a 
2TO — 1 
2 3 
2 m — 2 
pz~ 
+ P z Zm - 1 
+ q z Zm — z > 
-f rz lm ~ 3 
-f Cs?c. 
v * m ~ 3 -f &C. ~\~ z mz Lm ~~ x 
> 
VZZ 9 
+ 
+ 
zm — 2 .qz 
rj 
-f zm — - 1 . pz %m ~ z 
I 
+ 2IK — 2. qz zm ~ 3 ' 
-f 2 m — 3. rz zm ~* 
+ &c. 
Assume y = p* ; and let the coefficients of the terms of the for- 
mer equation be 1, b, c , J, &c . and of the latter. A, B, C, D, 
&c. and the equations become 
y m 4- by m ~ x -J- cy m ~ 2 -f dy m -3 -f = o 
A y m ~ 1 + By m ~ 2 4- Cy”*-3 4- = o. 
These equations have a common measure of the formy =*= Z, 
where Z is expressed in terms of % and known quantities ; and 
this common measure may be found, by dividing, as in Prop. r. 
till y is exterminated, and making the last remainder equal to 
nothing. 
Now, the first remainder is (cA — bB . A 4 - B* — CA) y m ~ e 
4- {d~K^~bC . A4-BC-DA) y-“3 4- ( 7 A- 6D.A4- BD -EA) 
y«—4 4- &c.; or, by substitution, ay ra ~ 2 4" fiy m ~ 3 + yy m '~‘ iJ r 
1 
