Ee 

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22, A General Theory of Osculating Conics. 
By Proressor Syamapas Muxwopapuyaya, M.A, 
INTRODUCTION. 
Differential Equations and Expressions, relating to Conics, 
have not, so as the present writer is aware, received the 
amount of attention they deserve. It is, however, worthy of note 
in this connection, that in the pages of the Asiatic Society’s 
Journal, some years ago, Dr. Asutosh Mukhopadhyaya brou 
back to light, almost from oblivion, the differential equation of the 
. 57, p. 316 ; Vol. 58, p. 181; Vol. 59, p. 61; 
Proc. Asiatic Soc. Beng. 1888, pp. 74, 165, 199). 
In the following paper, the writer ‘eas endeavoured to explain 
and establish a general theory of osculating conics, by methods 
s been first considered. The method of deducing the e equa nation 
= an osculating conic, as well as its differential « equation, from 
st principles and in general differentials, the implied indepen- 
shen variable being any quantity whatever, is a new ure. 
Two interesting theorems about the loci of centres of eons tne 
equilateral hyperbolas toa given conic have been obtained and a 
pli hey suggest an important relation among the system ot 
conics which have contact of third order with any given curve at 
a given point. These conics carry with them a system of director 
circles which are co-axial, and which have for their limiting points, 
m running into an cieaendwe length. 
