- d ρ - pr ρ, that is, 2 pr ρ / r + ρ = d ; but if the two Convexities be of the same Sphere so as r = ρ, then will the distance be = pr ; that is, if the Lens be Glass = 2 r , so that if an Object be placed at the Diameter of the Sphere distant, in this Case the Focus will be as far within as the Object is without, and the Species represented thereby will be as big as the Life; but if it were a Plano-Convex , the same distance will be = 2 pr , or in Glass to four times the Radius of the Convexity; but of this Method I may entertain the Curious at some other Time, and shew how to magnifie or diminish an Object in any proportion assign'd, (which yet will be obvious enough from what is here deliver'd) as likewise how to erect the Object which in this Method is represented inverted.
A Second Use is to find what Convexity or Concavity is required, to make a vastly distant Object be represented at a given Focus, after the one Surface of the Lens is formed; which is but a Corollary of our Theorem for finding ρ, having p, d, r and f given; for d being infinite, that Rule becomes
rf / pr - f = ρ, that is in Glass
rf / 2r - f = ρ, whence if f be greater than 2r, ρ becomes Negative, and
rf / f - 2r is the Radius of the Concave sought.
Those that are wholly to begin with this Dioptrical Science, cannot do better than to read with Attention a late Treatise of Dioptricks, published by W. Molineux, Esq, R. S. S. who has at large shewn the Nature of Optick Glasses, and the Construction and Use of Microscopes and Telescopes; and though some nicely Critical have endeavour'd to spy Faults, and to traduce the