
38, On Rationalization of Algebraical Equations. 
By ManenpranaTa De. 
The subject ot vig dpaemmny is discussed i - all the text- 
books of Algebra known to me a most perfunctory manner. 
Even Chrystal’s well-known tr oats ada the diediiaion to. a 
few gle cases. 
2. In aper on the subjert (‘On the Rationalization ‘of 
certain Algebraica equations —Cambridge and Dublin Mathemati- 
eal Journal, Vol. viii), Professor, Cayley gives a general methed 
for the rationalization of equations of the form 
eee tga m 
Following up a suggestion of Professor Sylvester he show 
that a. similar proegs would suffice’ for the. rationalization ‘of 
equations of the 
Sar Vbt Yer: .X0 
His results, however, appear in hike form of determinants of 
rk 
very high orders, the calculation of which is, in general, a wor 
of. tremendous labour. Thus, for instance, the result of rationaliz- 
1 le 1 ; 4 - 
ing the equation a*+b6*+c*=0.comes out in the form of a deter- 
minant of the 9th order. Strangely enough, Professor Cayley 
does not observe that a slight extension and a slight modification 
of his method would suffice for the solution ‘of-the ‘problem of 
a in its most general form, 
3. . xv, of the ‘‘ Messenger of Mathematics,” there are 
two mane on i Saticunlianbion over the names.of Captain Macmahon 
and Mr. P. C. Ward. be ace Mariette pei not attempt the 
4 ba +¢ #26: 
He does not, however, even so much as a to, pdihipuditz 
the equation a ee " =0, exes contents himself with two or three 
oR cases, €.9., a Bebo. > 
I have lately come across:a short, paper by Nripendra 
Nath Chattopadhyaya, in hich: the robles 3 is treated in ts most 
