( >- 8 ? ;

gative, which stiews that the Beams aster both Refractions stili proceed Di-verging. _ _ ,

To bring this to the other Cases, as of Converging Beams, or of Con-cave Glaffes, the Rule is ever composed of the sime Terms, only changingthe Signs of -4- and — ; for the Distance of the Point of Concourle of Con-verging Beams, from the Point B, or the first Surface of> the Lens, I call aNegative Distance, or — d ; and the Radius of a Concave Lens I call aNegative Radius, or — r if it be the first Surface, and — ? if it be thelccond Surface. Let then Converging Beams Fall on a double Convex of

Glast , and the Theorem will stand thus---= -4- /,

— dr — d ? — Ir;

which stiews, that in this Case the Focus is always Affirmative.

If the Lens were a Meniscus of Glast, cxposcd to Diverging Beams, the— z dr f

Rule

is,

= /. Which is Affirmative, when z r f is

■ dr + (/{ + 1 r j

lest then dr — dx , otherwise Negative: But in the Case of Converging

Beams falling on the fame Meniscus, ’twill be--- —f.

■4 ' dr — d f ■+■ Z r f

And it will be -+/ whilst d f — dr is lest than irf, but if it be greater thanzr f, it will always be found Negative or — /. If the Lens be double Concave,the Focus of Converging Beams is Negative, where it was Affirmative in the

Cale of Diverging Beams on a double Convex, vix. ---= /;

■+■ dr ■+■ df — 2 . rx

which is Affirmative only when irf exceeds dr -+• d ?: But DivergingBeams palling a double Concave, have always a Negative Focus, t ■;%,

— T-d rq _ —~s

-t- dr -4- df ■+ irj if '

The Theorems for Converging Beams are principali y of use to determiaethe Focus refulting from any sere of Lens placed in a Teleseope, .betwcen theFocus of the Object Glast and the Glast it self; the distance between thelaid Focus of the Object Glast and the interposed Lens being made — — d.

In case the Beams are Parallel, as coming from an infinite distance, (whichis fupposed in the case of Teleseopes) then will d be fuppoled infinite, and inp dr f

the Theorem -the Term fr ? vanilhes, as being finite,

dr ~i~ d $ — p r $

which is no part of the other infinite Terms, and dividing the remainder by

p f r , ,

the infinite part d, the Theorem will stand thus —-— ~f, or in Glast

z r e

7^r, =fi

f

VoL I.

B b

In