33 
on the Mechanism of the Eye. 
centre and at the surface; and the focal distance, thus determined, 
must be diminished according to the refraction at the surface. 
To find the nearer focus of parallel rays falling obliquely on 
a sphere of variable density. 
Solution. Let r be as in the last proposition, s the sine of in- 
cidence, t the cosine, and e the distance of the focus from the 
(aA-f-&B-}-cC4----)+ 2 ^A-l-66Bs , -[-iocC.? 4 -fi..., 
D = £ C. But, when s is large, the latter part of the series con- 
verges somewhat slowly. The former part might be abridged 
if it were necessary : but, since the focus in this case is always 
very imperfect, it is of the less consequence to provide an easy 
calculation. 
General Scholium. The two first propositions relate to well 
known phenomena ; the third, can hardly be new ; the fourth 
approaches the nearest to Maclaurin’s construction, but is far 
more simple and convenient ; the fifth and sixth have no diffi- 
culty ; but the two last require a long demonstration. The one 
is abridged by a property of logarithms ; the other is derived from 
the laws of centripetal forces, on the supposition of velocities 
directly as the refractive densities, correcting the series for the 
place of the apsis, and making the sine of incidence variable, 
to determine the fluxion of the angle of deviation. 
V. Dr. Porterfield has employed an experiment, first 
made by Scheiner, to the determination of the focal distance 
Proposition VIII. Problem. 
2 
point of emersion. Then e — w being = 
(r — i )s 
where a =— 1— , b 
r+ i* 
F 
MDCCCI. 
