C 967 ) 
cafe d is equal to /, and fubftituting d for f in the 
Equation, we ftiail have pd r % = d dr $4 dcl^—d p ^ r ? 
and dividing all by d. pr g = d r ~hd<? —p r p } that is 
Z ^ = d ; but if the two Convexities be of the fame 
r $ ? 
Sphere fo as /• = ^ then will the d ilia nee be = p r, that 
is, if the Lens be Glafs = 2 r, fo that if an Object be 
placed at the Diameter of the Sphere diftant, in this 
cafe the focus will be as far within as the Ofajed: is with- 
out, and the Species reprefenred thereby will be as big 
as the Life; but if it were a Piano-Convex, the fante di« 
fiance will be = z pr, or in Glafs to four times the 
Radius of the Convexity ; but of this method I may 
perhaps entertain the Curious in fome other Tranfa&i- 
on, andlhew how to magnifie or diminifli an Objeft in 
any proportion afligned, ( which yet will be obvious 
enough from what is here delivered ) as likewife how to 
ereft the Objeft which in this method is reprefented in- 
verted. 
A fecond ufe is to find what Convexity or Concavity 
is required, to make a vaftly diftant Objed be repre- 
fented at a given focus, after the one furface of the Lens 
is formed ; which is but a Corollary of our Theorem for 
findings having/, d, r and f given ; for d being in- 
r f 
finite, that Rule becomes — r = k that is in Glafs 
pr -/ * 
r f 
— — p* whence if / be greater than 2 r, ? be- 
2 r f r 
r f 
comes Negative, and 7 — - — is the Radius of the Con- 
* /- 2 r 
cave fought. 
Thofe that are wholly to begin with this Dioptrical 
Science cannot do better than to read with Attention a 
late Treatife of -Dioprricks, publifhed by W. Molineux, 
Efq; R. S. S. who hss at large (hewn the Nature of 
M m m 2 Optick 
