distance d to the Focus f . As likewise from the Lens , Focus , and Distance given, to find the Ratio of Refraction, or of m to n , requisite to answer those Data . All which it is obvious, are fully determined from the Equation we have hitherto used, viz. pd ρ r = drf + d ρ f - pr ρ f , for to find d the Theorem is pr ρ f / rf + ρ f - p ρ r = d , the distance of the Object.
For ρ the Rule is
drf / pdr + df + prf = ρ.
But for p will be
drf + dρf / dρr + fρr = p, which latter determines the Ratio of Refraction, m being to n, as 1 + p to p.
I shall not expatiate on these Particulars, but leave them for the Exercise of those that are desirous to be informed in Optical Matters, which I am bold to say are comprehended in these three Rules, as fully as the most Inquisitive can desire them, and in all possible Cases; regard being had to the Signs + and -, as in the former Cases of finding the Focus . I shall only shew two considerable Uses of them; the one to find the distance whereat an Object being plac'd, shall by a given Lens be represented in a Species as large as the Object it self, which may be of singular Use in drawing Faces and other things in their true Magnitude, by transmitting the Species by a Glass into a dark Room, which will not only give the true Figure and Shades, but even the Colours themselves, almost as vivid as the Life. In this Case d is equal to f , and substituting d for f in the Equation, we shall have pdr ρ = ddr + dd ρ - dp ρ r , and dividing all by dpr ρ = dr