MR. TALBOT’S RESEARCHES IN THE INTEGRAL CALCULUS. 
215 
/ p d x 
have been called ultra- 
elliptic by Legendre. I think I have sufficiently shown that no line of distinction can 
be drawn between them and integrals in general ; all of which, that are functions of 
a given polynomial, possess the property which was supposed to characterize the 
ultra-elliptic class. 
