mdr / m - nd - nr , which shews in what Point the Beams proceeding from D, would be collected by means of the first Refraction; but if nr cannot be subtracted from m - nd , it follows that the Beams after Refraction do still pass on diverging, and the Point φ is on the same side of the Lens beyond D. But if nr be equal to m - nd , then they proceed parallel to the Axis , and the Point φ is infinitely distant.
The Point φ being found as before, and Bφ - Bβ being given, which we will call δ, it follows by a Process like the former, that βF, or the focal Distance sought, is equal to δρ n / m - δ + m ρ = f . And in the room of δ substituting Bφ - Bβ = mdr / m - nd - nr - t , putting p for n / m - n , after due Reduction this following Equation will arise, mpdr ρ - nd ρ t + npr ρ t / mdr + md ρ - mpr ρ - m - ndt + nrt = f . Which Theorem, however it may seem operose, is not so, considering the great Number of Data that enter the Question; and that one half of the Terms arise from our taking in the thickness of the Lens , which in most Cases can produce no great Effect; however it was necessary to consider it, to make our Rule perfect. If therefore the Lens consist of Glass , whose Refraction is as 3 to 2 'twill be 6 dr ρ - 2 d ρ t + 4 r ρ t / 3 dr + 3 d ρ - 6 r ρ - dt + 2 rt = f . If of Water , whose Refraction is as 4 to 3, the Theorem will stand thus 12 dr ρ - 3 d ρ t + 9 r ρ t / 4