166 A. Mukliopadhyay — On Mongers Differential Equation. [July, 



which is a geometrical relation, being an equation between the volumes 

 contained by certain lines belonging to the curve. 

 For the parabola, the equation becomes 



and this can be written 



9p2 + W - 3p/)2 = 

 which is again a geometrical relation involving the rectangles contained 

 by certain lines belonging to the figure. 



These are probably the best geometrical interpretations that can be 

 given. 



The above equation to parabolas can be written 



which leads at once to the ordinary formula 



2a 

 P = 



sin^;|; 

 Similarly the general equation to the conic can be written 



( 





which leads to the ordinary value for p, viz., 



1__ (a^ co&^ -f b^ sin^^|/)3 



pa"" ' M^ ' 



a%^ 

 or, ^ = ■^' 



if the constants of integration be suitably determined." 



Babu Asutosh Mukhopadhyay then made the following remarks : 

 " I have thought it proper to lay before the Society Prof. Stuart's 

 interesting remarks on the Mongian Equation, as I believe they are 

 valuable and ought to be preserved : it is rather unfortunate that he 

 cannot give the name of the author of the paper to which he refers, nor 

 that of the Journal in which it appeared. The only paper on the sub- 

 ject which I can find has anything to do with Prof. Stuart's remarks is 

 Transon's Becherches sur la Gourhure des Lignes et des Surfaces ( Liou- 

 mlle, Journal de Mathematiques, Ser. I, t. VI, 1841, pp. 191 — 208) ; the 

 equation to all parabolas 



9p^ + W - ^PP2 = 

 which Prof. Stuart gives, is on page 197 ; but I am not quite sure that 

 Transon's paper is the one to which Prof. Stuart refers ; his remarks 

 refer to my first paper on the Mongian Equation (Joiirnal, A. S. B. 1887, 

 YgI. LVI, Part II, pp. 134 — 145), and, when he wrote his letter, he was, 



