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

should not appear in the like manner. But, I will determine nothing of any of these things. When I shall hereafter have made more frequent Observations of the Moon with my great Telescopes, in convenient time, I shall then perhaps learn more of it, than I know at present, at least it will excite the Curious to endeavor to make the like Observations; and it may be, others, that I have not thought of. 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 Plano-convex Glass of a Sphere 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 I wish, 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 Practice 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 ways, 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 may 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 Focus's are known, the distance of them will be known. If it be supposed, that the Focus of the first be B, and that of the second C, and the distance given, B + 2D, and that D minus C be equal to F; for, this distance will be equal to $B + C + F - rF = C^2$. And if you have the Focus of the first Object-glass, equal to B, the distance, where you will put the second Glass equal to $B + G + D$, the focus of the 2d Glass will be found equal to $\frac{CD}{C+D}$. And if you will that the Object shall be magnified as much with these two Glasses, as it would be with a single one, whereof the Focus should should be of the distance given, having the Focus of the Object-glass given equal to B, and the distance given to B†D; the distance between the first and the second Glass will be equal to \( \frac{2B^*+2BD}{2B†D} \), whence subducting B (the Focus of the Object-glass given) there remains \( \frac{BD}{2B†D} \); and if this sum be supposed equal to G, we shall easily know, by the precedent Rule, the Focus of the second Glass. So far M. Auzout, who, I trust, will receive due satisfaction to his desire, as soon as the happy end of the present Contagion shall give a beginning and life again to the Studies and Actions of our retired Philosophers. I shall onely here adde, That the Secret he mentions [Of measuring the distance of Places by a Telescope (fitted for that purpose) and from one station] is a thing already known (if I am not mis-informed) to some Members of our Society; who have been a good while since considering of it, and have contrived ways for the doing of it: Whether the same with those of Mr. Auzout, I know not. Nor have I (at the distance that I am now from them) opportunity of particular Information. An Experiment of a way of preparing a Liquor, that shall sink into, and colour the whole Body of Marble, causing a Picture, drawn on a surface, to appear also in the inmost parts of the Stone. This Experiment, having been hinted at in the next foregoing Papers, out of the Mundus Subterraneus of Athanasius Kircher, and several Curious Persons, who either have not the leisure to read Voluminous Authors, or are not readily skilled in that Learned Tongue wherein the said Book is written, being very desirous to have it transferred hither, it was thought fit to comply with their desire herein. The Author therefore of the Mundus, &c, having seen some