
498 Journal of the Asiatic Society of Bengal. [November, 1908. 
tan d was beautiful, and he rightly thought he had obtained 
the third affection of curvature when he had determined the value 
of R, which enabled him to construct the panes! conic. 
rofessors M. and R. Roberts and J. Wolstenholme have, as 
isolated Se a set in University Papers or published in Collec- 
tions of Problems, made a number of useful determinations about 
osculating conics. They have not done, however, any systematic 
work, and it is not apparent what methods they may have fol- 
lowed in deducing the results. There is eh trecd presumption that 
they have mainly relied on Transon’s researc 
D opadhyaya, in his admirable ener ore to the 
Journal of fh Asiatic Society of Bengal, more specially in his 
paper ‘On the differential equation of all parabolas,’ has treated 
the subject more methodically, and has deduced and interpreted 
several important weg 
This second paper is based entirely on certain transforma- 
tions of analytical siakibnts, deduced in nee nant forms, in 
the first paper. The results have been invariably per ae in 
general differentials. The use made of the fuatbiines $Q Ba, 
etc., will, it is hoped, be found interesting. 
14, The a equation of the osculating conic, obtained as 
equation (41), namely— 
(X—a)* (Y—y)? 
vile 2 ay 
dee 
sda) + 8dzd*z a. on as + 8dyd>y 
= SP ale (¥~y)de-(X-2)dy 
2dad: d?yda — d’ady 
Sdadty + Byde — Bxdy 
6d?2axdty + ite + dyd8z) d*ydx — d*ady 
is capable of a simple transformation. 
If we write— 
(Y—y)da —(X—2)dy= 
(Y—y)die — (X—- eydhy I 
d*ydx — d*ady = (51) 
dbyro— diy a = 9’ 
+dy?=P 
ne Q; 
then, equation (41) easily transforms into— 
L : Me LM 
. 20)? O 
Be io i ah ae ee 
Of... SOR... -. :—40R 


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