dr + 4 d ρ - 12 r ρ - dt + 3 rt = f . If it could be made of Diamant , whose Refraction is as 5 to 2, it would be 10 ⁄ 3 dr ρ - 2 d ρ t + 4 ⁄ 3 r ρ t / 5 dr + 5 d ρ - 10 ⁄ 3 r ρ - 3 dt + 2 rt = f . And this is the universal Rule for the Foci of double Convex Glasses exposed to diverging Rays. But if the thickness of the Lens be rejected, as not sensible, the Rule will be much shorter, viz. pdr ρ / dr + d ρ - prt = f , or in Glass 2 dr ρ / dr + d ρ - 2 r ρ = f , all the Terms wherein t is found being omitted, as equal to nothing. In this Case, if d be so small, as that 2 r ρ exceed dr + d ρ, then will it be - f , or the Focus will be Negative, which shews that the Beams after both Refractions still proceed diverging.
To bring this to the other Cases, as of converging Beams, or of Concave Glasses, the Rule is ever composed of the same Terms, only changing the Signs of + and -; for the distance of the Point of Concourse of converging Beams, from the Point B, or the first Surface of the Lens, I call a negative Distance or - d; and the Radius of a Concave Lens I call a negative Radius, or - r if it be the first Surface, and - ρ if it be the second Surface. Let then converging Beams fall on a double Convex of Glass, and the Theorem will stand thus
- 2drρ /
- dr - dρ - 2rt = + f, which shews that in this Case the Focus is always affirmative.
If the Lens were a Meniscus of Glass, exposed