( -«4 )

will follow, that as the Angle AfD, is to the Angle ADp, so i s

the Side A D, or B D, to A ?, or B ?: That is, B p will be —- ,

7H — n d — n r

vhich Ihews in what Point the Beams proceeding from D would be collectedby means of the Erst Refraction ; but if n r cannot be fubstracted fromm — n d, it follows, that the Beams after Refraction do still paß on Diverg-ing, and the Point p is on the sime side of the Lens beyond D. But if nrbe equal to m — n d, then they proceed Parallel to the Axis, and the Point- is infinitcly distant.

The Point p being found as before, and B ? — B .3 being given, whichwe wist call <h, it follows by a Proceß like the former, that ß F, or the Focal

* • eA J K

DIstance soughc, is equal to- - — ; -— /. And in the room of / sob*

stituting B - — B3 —

m — n -b in imdr

t, putting f for-

duction this Equation will arife.

7» — nd — 7t r

Tttpdrs

-,afterdueRc-

711 ■

■ 7td $ e -b nprft

mdr-bmd% — mpr? — m — ndt-bnrt

-f-

Which Theorem, however it may seem Operose, isnotso, considerlng the greattjumber of Data that entcr the Question, and that one half of theTerms arisefrom our taking in the thickneß of the Lens, which in most Cases can pro-duce no great Effect; however, it was necestäry to confider it, to make ourRule perfect. If therefore the Lens consist of Glaß, whose Refraction is as

, 6 .drx — zd?t -+ 4 r%t , f , IT

a to z, twill be---— fi It Of W ater,

Sdr-b-^ds — 6rf —dt-bzrt

whose Refraction is as 4 to 3 , the Theorem will stand thus.;

- ndr,~ld„ + 9’Jl -,f k couU ^ of

^.dr ~b d\.df — llr{ — dt -b %rtDiamant, whose Refraction is as 5 to z, it would beA f dr f — zdit -b f rft _

y dr ~b yd? — A fr? — %dt -b ZrtAnd this is the Universal Rule for the Foci of Double Convex Glastes ex-posed to Diverging Rays. But if the thickneß of the Lens be rcjected as

p dr f

not sensible, the Rule will be much Ihorter, —--—

dr ~b d f — r x

— f. All the Terms wherein t is found be-

= /•

z dr q

or in Glaß, -

dr -4* — Zr%

ing omitted, as equal to nothing. In this Gase, if d be so sinall, as thatzr ? exceed dr ~b d?, then will it be —or the Focus will be Ne-

". gativej

G