Addition to Nore, p. 96. 
Tue different conclusions in this note for the grinding surface 
necessary to obtain the different conic sections, are reducible to the 
simple condition of the absolute value of the ordinate in the curve 
(sec y*) traced upon the pitch tool: or what is the same thing, to 
the time of grinding, the absolute value of the ordinate being given. 
It will be most convenient to assume the ordinate so as to make the 
grinding surface continuous at the circumference of the pitch tool, 
(see Fig. 5.) The figure of the mirror, which is at first truly spherical, 
will migrate successively into an elliptical spheroid, a paraboloid, a hyper- 
boloid, according to the time of grinding. ‘The times of producing these 
effects will be respectively proportional to v* — 6°, v*, v> + b*. 
WAC: 
ERRATA. 
Page 96, Line 9. For Fig. 6. read Fig. 5. 
—— — Note. Line 5 from the bottom, for ax + ma‘? read aa’ + nx’. 
—— 98, Note. Lines 7, 8, 13, 14 from the bottom, 
»  v*-+ 5? ah ihe 
for = rea 
va 
