16. On the Rationalisation of Algebraic Equations. 
By Nrivenpra Nata CHATTERJEE. 
In continuation of a paper read on the same subject before 
the Asiatic Society of Bengal on the 3rd September, 1919!, 
a new method is proposed for rationalising algebraic equations. 
Let the equation to be oe sed 
be eee eee (nm an integer) 
which can be put under the form 
pw 
z 
1 n—1 
oA oe +s cib Age; p*)=0,; 
Ao, A,,...An-1 being rational. 
If we put y= —x + A,, the equation becomes 
n—1 
.+4,1p " =0 (1) 
2 
2 
Pee ee + Ap" + 
—) 
2 n= 
multiplying both sides by P, LP tw 5 Oe 
1 2 n—-1 
PB + PB, p" + P,Bp" +...+ Pi Bap ” = ven k2) 
1 2 
PC) + P,C, p? + P,O,p" +...+POr1p" =0 ...(3) 
; oe : “ 
P1V 9+ yal S + P,_-1V gp" cee ete Py Vegi? ge! Bee (n) 
where By, B, B gee C); Crs oe + Sas sve Vi; ee ee 
are rational functions of y, p, A,, Ay... 4n-1; and P,, P,,. 
-; being as yet undetermined coefficient 8. 
| Midge the above equations, we get 
y+P,B,+P,C, +---+Pa-1V,=9 (A) 
if A,+ PB +P, «4 Poli =0 (1’) 
A, + P,B, + PsC.+- +++ Pa-1V_=0 (2’) 
Agi +P.B ~1+P,C Bee sha oF. .V,-1=0 Gi 

1 Cf. Journ, Asiat. Soc. Beng. (n. 8.) XV, pp. 305-307, 191°. 
