The Hartlib Papers

Title:Copy Extract On Smethwick'S Tube In Hand K
Ref:8/57/1A-2B: 2A BLANK
Notes:Another copy at 7/125.

                Mr Smethwicks Tube.
There are two kinds or formes of Glasses used in Perspective; the Conicall & Sphæricall. The Conicall is either Elipticall or Hyperbolicall. The Sphæricall likewise is either double Convexe, Plano-convex, or Concave & Convex; againe in respect of their certainty & correspondency with truth. The Conicall is demonstrable without any errour Mathematicall or Imaginable. The Sphæricall not so exact, according to the strict rules of art: yet in respect of the paucity of degrees used therein will be found agreeable to truth, & void of any errour Physicall or sensible. As concerning the first, it is allready sufficiently handled & clearly demonstrated by that famous & learned Ren. Des Chartes, & other learned both Philosophers & Mathematicians. And for the Sphæricall we have omitted the 2 first sorts thereof, & upon the last onely in a word or two made some little reflection. Of this sort according to any Radius proposed, there may be found infinite variety, notwithstanding every one, answering unto the same Focus or center. Amonst which there will happen out but one onely, capable of a single Refraction, their convex arches, being supposed to stand (as is requisite) towards the eye inclining. And this is that Convex & concave or [Greek: meniskos]. And

whose concavity is in such manner proportioned to the convexity, that the refracted rayes having passed the convexe side, thereof, falls upon the concave at right angles, and makes their passage through direct without a second refraction. Now if any glasse thus framed, be constituted the object glasse of a Perspective, and to this there be rightly prepared & adæquated an eye glasse, which may receive all such rayes at right angles, & transmitt them to the eye neerely parallel, then shall each of those two glasses so proportioned have but one single refraction, whereas in all others (whose arches incline) (the Conciall excepted) their converging rayes shall be twice in either glass refracted. According to this Methode & forme of a single refraction, is this Perspective fabricated, which if that Axiome in the Dioptricks be true, as undoubtedly it is, That refraction followes the Nature of Sines, then shall all converging Rayes for 15. degrees on each side the Axis be physically united into one point or focus. And (seing that not above the 1/5 of those degrees are here needfull) to all imaginable sense & purpose, shall this projection be nothing different from the Elipsis itself in the convexity, as it is the same, & doth most exactly agree in the concavity. But how farre this is or may be promoted for the better discovery of all visible & luminous bodies, & how farre it differs from all other heretofore practised, is submissively lefft to the determination of a future and indifferent examination.

[another hand:]     Inventions