18. On the Rationalisation of Algebraic Equations. 
By NrRiPpENDRA NATH CHATTERJER. - 
(Read on 3rd September, 1919.) 
Before 1908 I had contributed a few papers on more than 
one method of rationalising algebraic equations. In 1908 a 
paper on the same subject by the late Prof. Mahendranath De 
appeared in the Journal of this Society for the month of July, 
I must take this opportunity of expressing my indebtedness pA 
Rai Abinashchandra Bose Bahadur, Controller of Examinations, 
Calcutta University, for his kindness in drawing my attention 
to this pa age 
la m glad to find that Prof. bree having compared the 
different methods of renowned athematicians e.g. Prof. 
Sylvester, Prof Cayley, Capt. Man Mixhicel an others, was good 
enough to pronounce my method as the cnt general one for 
the rationalisation of algebraic equations. But he took ex- 
ception to my method, as not leading to the y teeta in the 
lowest degree. I am afraid he missed one of my other methods 
in which it was shown that the equation obtained was always 
in the abn degree. 
This evening I intend to present the Society with a novel 
method—which might with propriety be termed the “ method 
problems, it is believed that this method has not as yet found 
any sptloaim to the fatlonatiestion of algebraic equations. 
I. Let the equation be : 
1 1 
a=} (p"), (p” not rational) 
which can always be put under the form 
: : oe 
caA,t Ap" + Ap” #. 2.22 ieee t+Ae 9" , 
where Ay, A,, A,,...... are rational. 
If y=a- Ae ih ont 
Py= pao ioe a ge OE ee +P,A,_,p” > (i) 
P.y* - PB, — P.Bapr ee a Se ee + fe. } p* ’ (ii) 
