_The Instance of the _same Person_ to Mr. _Hook_, for communicating his Contrivance of making, with a Glass of a Sphere of 20 or 40 foot _diameter_, a _Telescope_ drawing several hundred foot; and his offer of recompensing that Secret with another, teaching To measure with a _Telescope_ the _Distances of Objects_ upon the Earth._ In _Numb._ 4. Of these _Papers_, pag. 67. Mr. _Hook_ had intimated, that he would shortly discover a way of his, with a _Plane-convex_ Glasse of a Sphaere of 20. or 40. feet _Diameter_, without _Veines_, and truly wrought of that _Figure_, to make a _Telescope_, that with a single _Eye-glass_ should draw 300, 400, yea 1000 feet, _without_ at all _altering the Convexity_: Monsieur _Auzout_ returns this consideration, and offer upon it, which follows: To perform (_saith he_) with a _lesser Object-glass_ the effect of a _great Telescope_, we must find out a way to make such an _Object-glass_ to receive as many Rayes as one will, without their being sensibly distant from one another; to the end, that by applying to it a _stronger Eye-glass_, there may be still Beams enough to see the Object, and to obliterate the small specks and imperfections of the _Eye-glass_. And if Mr. _Hook_ hath this Invention, I esteem it one of the greatest, that can be found in the matter of _Telescopes_. If he please to impart it to us, we shall be obliged to him; and {124} I wish, I had a secret in _Opticks_ to encourage him to that communication. If I did believe, that this would be esteemed one, To measure with a _great Telescope_ the _distance of Objects_ upon the _Earth_; which I have found long since, and proposed to some by way of Paradox; _Locorum distantias ex unica statione, absque ullo Instrumento Mathematico, metiri_; I doe here promise to discover it to him, with the necessary Tables, as soon as He shall have imparted his to me; which I will use, as he shall order me. For, although the _Practise_ doe not altogether answer the _Theory_ of my Invention, because that the length of the _Telescopes_ admits of some Latitude; yet one comes near enough, and perhaps as Just, as by most of the wayes, ordinarily used with Instruments. That, which I am proposing, I doubt not but M. _Hook_ will soon understand, and see the determination of all Cases possible. I shall only say, that if we look upon the sole _Theory_, we make use of an ordinary _Telescope_, whereof the _Eye-glass_ is to be _Convexe_: for, by putting the Glasses at a little greater distance, than they are, proportionably to the distance for which it is to serve, and by adding to it a _new Eye-glass_, the Object will be seen distinct, though obscure; and if the _Eye-glass_ be _Convexe_, the Object will appear erect. They may be done two manner of ways; either by leaving the _Telescope_ in its ordinary situation, the _Object-glass_ before the _Eye-glass_; or by inverting it, and putting _this_ before _that_. But if any will make use of two _Object-glasses_, whereof the