1888.] Library, 1^7 



of course, not aware of my second paper wliicli was read at the last 

 meeting of tlie Society ; I need not, however, refer further to the re- 

 sults of Transon's paper, as by analysing and extending them, I have 

 already given the geometric interpretation of the differential equations 

 of all parabolas and conies. (See pp. 156 — 158 ante.) 



" Since Prof. Stuart attempts to give a new geometrical interpreta- 

 tion of the Mongian Equation, he appears to accept implicitly my view 

 that Prof. Sylvester's interpretation is out of mark as failing to give 

 a property true of all conies. Prof. Stuart's interpretation certainly 

 satisfies the tests which every true geometrical interpretation ought to 

 satisfy, viz., it gives a property which is adequately represented by the 

 differential equation to be interpreted, and it leads to a geometrical 

 quantity which vanishes at every point of every conic ; and, the only 

 objection which can possibly be taken to this interpretation is, that the 

 quantity which is analytically represented by 



40 



PVs - ^Pl P2 P3 + Y Pl^ + ^P^Pl = ^ 



and which involves the radius of curvature at any point of a conic and 

 the radii of curvature at the corresponding points of its first, second 

 and third evolutes, does not admit of being expressed in language ; in 

 fact, we do not know how to construct geometrically the solid, the 

 vanishing of the volume of which is the geometrical meaning of the 

 equation given above; the interpretation, in fact, is only semi-geo- 

 metrical." 



The following paper was read : 



Muins and Antiquities of Udmjpdl. — By Asutosh Gupta, Esq., C. S. 



The paper will be published in the Journal, Part I. 



y 



IBRARY. 



The following additions have been made to the Library since the 

 meeting held in Jane last. 



Transactions, Proceedings and Journals, 



presented hy the respective Societies and Editors. 



Baltimore. American Chemical Journal, — Vol. X, No. 3, May, 1888. 

 Berlin. Der Koniglichen Akademie der Wissenschaften zu Berlin,— 



Sitzungsberichte, 40—54, 1887 und Inhalt, 1887. 

 Bombay. Bombay Natural History Society, — Journal, Vol. Ill, No. 2. 

 — — — . Indian Antiquary, Vol. XVII, Part 207, April, 1888. 



