1889.] A. Mukliopadliyay— il/oHgre's Differential Equation. 185 

 Tins result may also be obtained without calculating the value of 



— . Tor, a, /3 being the coordinates of the centre of aberrancy, we have 



dfi^ 



and 



da _da dx _X 

 d^~dx 'd^~f-' 



dl3^~dfS dx\dl3) /xT dx\ix./ 

 __L i. / ^ \ L - 5)-g 



__ £ / 3r/s-5r« y 

 Substituting, we get, as above, 



This, therefore, is the naost general expression for the radius of cur- 

 vature of the "aberrancy curve " of any given curve. Now, when 

 T = 0 



we have p = 0. 



But T = 0 



is known to be the differential equation to all conies ; hence, obviously, 

 the geometric interpretation of Monge's differential equation to all 

 conies is as follows : — 



The radius of curvature of the alerrancy curve vanishes at every point 

 of every conic. 



This geometrical interpretation will be found to satisfy all the tests 

 which every true geometrical interpretation ought to satisfy, and I 

 believe that we have at length got here the interpretation which has 

 been sought for by mathematicians during the last thirty years, ever 

 since Boole wrote his now famous lines.* 



19th May, 1888. 



* For some remarks (whicli, howevor, seem to me to be very weak) on this 

 interpretation by U. B, n, (Hayward p), see Nature, vol. xxxviii, pp, 197, 564, 

 G19. 



