306 Journal of the Asiatic Society of Bengal. [N.S., XV, 
(where By), B,, .....: B,-, are rational functions of p, A, 
Catia Gat aac ms © alee Sse x 
fT gee 3 hoe ee oo Oe ae wee te Le ey oe 
Cr ana ea n—1) 
1 n=l 
fa, + W, p” eS ts we asaiys Wa-\p” 
iin iratignd ebook ec, is (n) 
PRP yp Oss P,-, being as yet undetermined. 
Adding the above equations we get 
ts FO a. +Pyy 
MW resi) tise... + PB, (A) 
if Wat Pil Re eee + P,B,+ P,A,=9 (1) 
ee gees Oo" Se eer a + P,B,+P,A,=90 (2) 
PORES PG PE ee + P,B,-,+P\Ae- Cy (n—1) 
which equations are sufficient for the unique determination of 
the values of RE ras P,-,. Substituting these values 
in (A) and remembering y=x—A,, we get the rationalised 
equation in x, which is of the n degree only. 
II. Let the equation be: 
1 
1 
x= f (p™ ’ q”); 
which can ah be raga una the sip : 
% = y+ (Ap + Ag r+ (B, pi +B,p” fr +B,0") 
— 
8 
! 
= 
“SW 
the right-hand side containing m? terms. Be following the 
same method as before we get the rationalised algebraic equa- 
tion of the m*th degree 
III. Let the a amapac en 
t= t(p', ¢ maf 5 ore )e 
Every integrai function of p', q” A ei: ..-, where l, m, * ant 
3 
are ac a can be eee as a linear function of p, py, p' , 
2 a-1 
ie cee po! A : Pw ha 9? 5 ete, 
