Dr. Young's Lecture 
at each point be called y ; then y — sx T , jr= 1 s x r x, and the fluxion 
of the area =: - - r — y . i — yy| 2 , of which the fluent is 2 ~^ Y, y being the sine 
of the arc Y ; and the angle corresponding is ~~i ^ • The va l ue of that angle being 
found for any two values of x or y, the difference is the intervening angle described 
by the radius. This angle is therefore always to the difference of the inclinations as 
r to r — 1 , and the deviation is to that difference as i to r — i . 
Corollary. Hence, in the passage to the apsis, and the return to the surface, the 
deviation is always proportionate to the arc cut off by the incident ray produced : 
therefore such a sphere could never collect parallel rays to any focus, the lateral den- 
sity being too small towards the surface. 
Page 33, line 20, for but the two last &c. read the seventh may either be de- 
duced from the eighth, or may be demonstrated independently of it. 
Page 42, line 18, after internally, insert Or, if a lens of equal mean dimen- 
sions, and equal focal length, with the crystalline, be supposed to consist of two 
segments of the external portion of such a sphere, the refractive density at the centre 
of this lens must be as 18 to 17. 
Page 47, line 12, for calculated & c. read estimated by means of the eighth 
proposition ; and probably. 
Page 53, line 24, for 24, read 21 ; line 25, for 17, read 15. 
Page 61, line 21, for sixtieth, read fortieth. 
