( 1 86 >

In cafe the Lens were Plano-Convex exposed to diverging Beams, bstead of

p dfr

* — rvimn innnirn «r hmii rtn — _ / _ *

■, r bcing infinite, it will be - f = /, or * 1 ^ ?

d—pz

d — 1 f

dr -+• df — pr Zif the Lens bs Glasi.

If the Lens be Double-Convex, and r be equal to ?, as being formed ofSegments of equal Spheres, then will P dzr

p d i

zd — p i

, , , - be reduced to

dr -r d z — pr z

:/; and in case d be infinite, then it will yet be farther con-

tracted to L. pr, and p being —-, the Focal distance in Glasi will be

m —• n

= r, in Water It r, but in Diamant f r.

This is not only ufeful to diseover the Focus from the other propofedData, but from the Focus given, we may thereby determine the Distance ofthe Object, or from the Focus and Distance giVen, we may find of whatSphere it is requisite to take another Segment, to make any given Seg-ment of another Sphere cast the Beams from the Distance d to the Fo-cus f. As. likewile from the Lens, Focus, and Distance given, to find the.Ratio of■ Refractione or of m to n, requisite to anfwer thole Data. Allwbich, it is obvious, are fully determined from- the Equation we have hithertoused, p dzr = drf dzf pr zf For to find d, the Theorem is,

p r zf

rf -+ f f —p?rdrf _

p dr “+• df ■+ p rf

— d, the Distance of the. Object ; fbr x, the, Rule is

= z ; but for pr ik will -be

d rf ~ t- d zfdzr f%r

= T

which latter determines the Ratio of Refiaction, m being to n as j -+■ p

to p.

I (hall not expatiate on these Particulars, but leave them for the exereise ofthole that are desirous to be informed in Optical Matters, which J am holdto fay are comprehended in thesi Three Rules, as fully as the moft inquifi«-tive can desire them, and in all possible Cases j regard being had to the Signs4- and —, as in the former Cales of finding the Focus. I mall only Ihewtwoconsiderable Uses of them ; the one to find the Distance whereat an Objectbeing placed {hall by a given Lens be represented in a Species as large as theObject it seif, which may be of singular use, in Drawing Faces and otherthings in their true Magnitude, by transinirting the Species by a Glasi intoa dark Room, which will not only give the true Figure and Shades, but even.the Colours themselves, almost as Vivid as the life. In this case d is equalto/, and substituting d for /in the Equation, we (hall have p dr z ddr-K,d dz — dp zr, and dividing all by d, pr z ~ dr ■+ dz.^~ prz, that is,

Z.p r z