Page:Philosophical Transactions - Volume 001.djvu/130

 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 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, $$\mathrm B + 2\mathrm D$$, and that $$\mathrm D \ minus  \ \mathrm C.$$ be equal to $$\mathrm F$$; for, this distance will be equal to $$\mathrm B + \mathrm C + \mathrm F - r \mathrm F^2 - \mathrm C^2.$$ 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 $$\mathrm B + \mathrm C + \mathrm D.$$ the focus of the 2d Glasse will be found equal to $$\tfrac {\mathrm C \mathrm D}{\mathrm C+ \mathrm D}$$. 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 Rh