I nowdefign to give a notable fnflance in the Dodrinc 
of Dioptricks. 
This Dioptrick Problem is that of finding the Focus of 
any fort of Lens, expofed either to Converging, Diverg. 
ing or parallel Rays of Light, proceeding from, or 
tending to a given Point in the Axis of the Lens, be the 
ratio of Refrattion what it will, according to the nature 
of the Tranfparent Material whereof the Lens is formed, 
and alfo with allowance for the thicknefs of the Lens be- 
tween the Vertices of the two Spherical Segments. This 
Problem being foived in one Cafe, mutatis mutandis will 
exhibit Theorems for all the portable Cafes, whether the 
Lens be Double-Convex or Double-Concave \ Piano-Convex 
or Piano-Concave, or Convexo Concave t which fort arc 
ufually called Menifcl ^But this is only to be underftood 
of thofe Beams which are neareft to the Axis of the Lens, 
fo as tooccafion no fenfible difference by their Inclinati- 
on thereto and the Focus here formed is by Dioptrick 
Writers commonly called the principal Focus , being that 
of ufe in Tele/copes and Micro/copes. 
Let then (in Fig. i BE/3 be a double Convex Lens 9 
C the Center of the Segment EB, and K the Center of 
the Segment E/S, B/3 the thicknefs of the Lens y D a point 
in the Axis of the Lens ; and it is required to find the 
point F } at which the Beams proceeding from the point 
D, are collected therein, the ratio of Refraction being as m 
to n. Let the diftance of the objed; DB = DA~d (the 
point A being fuppofed the fame with B, but taken at a 
diftance therefrom, to prevent the coincidence of fo ma- 
ny Lines) the Radius of the Segment towards the Ob- 
jed CBor CA=r, and the Radius of the Segment from 
the Object K/8 or Ka==j>, and let B/3 the thicknefs of the 
Lens be and then let the Sine of the Angle of inci- 
dence DAG be to the fine of the refra&ed Angle HAC/or 
CAp as m to n ; And in very (mail Angles the Angles 
them- 
