/ dr + d ρ - pr ρ the Term pr ρ vanishes, as being finite, which is no part of the other infinite Terms; and dividing the Remainder by the infinite Part d , the Theorem will stand thus p ρ r / r + ρ = f , or in Glass, 2 r ρ / r + ρ = f .
In case the Lens were Plano-Convex exposed to diverging Beams, instead of
pdρr / dr + dρ - prρ, r being infinite, it will be
pdρ / d - pρ = f, or
2dρ / d - 2ρ if the Lens be Glass.
If the Lens be Double-Convex, and r be equal to ρ, as being formed of Segments of equal Spheres, then will pd ρ r / dr + d ρ - pr ρ be reduced to pdr / 2 d - pr f ; and in case d be infinite, then it will yet be farther contracted