on the Mechanism of the Eye. 
2 9 
Corollary 3. For parallel rays, d = 00 , and e = 
Scholium 1. It may be observed, that the caustic by refraction 
stops short at its cusp, not geometrically, but physically, the 
total reflection interfering. 
Corollary 4. Call 6, and — ” * * — , r ; then e = - 4 —, 
and 0 — 6 = or, in words, the rectangle contained by the 
focal lengths of parallel rays, passing and repassing any surface 
in the same lines, is equal to the rectangle contained by the 
differences between these lengths and the distances of any con- 
jugate foci. 
Corollary 5. For perpendicular rays, e == = m -f j — ; 
or, if the radius be a, e = l and if d and e be given to find 
the radius, a = — 7— — • 
m d -f n e 
Corollary 6 . For rays perpendicular and parallel, e = m, or 
e = m a. 
Corollary 7. Fora double convex lens, neglecting the thicks 
ness, call the first radius^, the second h, and e == 
Hence n = ~~ e . ; and, for parallel rays, e = and 
n — e. g ~fT ’ = h = a,e = ; and for parallel rays 
€ =~ : calling this principal focal length b, e =y^- b> as in 
Cor. 4 ; whence we have the joint focus of two lenses ; also, 
Corollary 8. In a sphere, ez=m a . — ^ 1 2 ) distance 
from the centre, and b = — . 
2 
