# Letter from Newton to Henry Oldenburg, dated 8 July 1672

Stoake: July {illeg}|8|^{th} 1672.

S^{r}

I am glad to find by y^{e} abstract of Mon^{sr} Hugenis Letter w^{ch} you transmitted to me, that he who hath done so much in Dioptricks hath been pleased to undertake the improvement of Telescopes by reflexions also, though without the desired success. For I hope the event of his next essay, if he shall think fit to attempt any thing further, will prove more happy by a little altering the manner of his proceeding. I should be glad to heare whether M^{r} Cock hath finished the four foot Telescope, & w^{t} its effects are, as also what are the best effects of those of 6 or 8 inches in length w^{ch} he hath made at any time. But I know not whether I shall make any further tryalls my selfe, being desirous to prosecute \some/ another subjects.

Touching the Theory of Colours I am apt to beleive that some of the experiments may seem obscure by reason of the brevity wherewith I writ them w^{ch} should have been described more largely & explained with schemes if they had been then intended for the publick. But I see not why the aberration of the rays from the transvers of the object-glass of a Telescope should be more then about $\frac{1}{50}$ of the Glasses aperture. For suppose DF be y^{e} Lens; CD & EF two lines parallel to its axis in or \indefinitely/ neare to w^{ch} all variety of difform rays are successively incident on two opposite parts of its Perimeter. And of those rays let DH & FG be the most refracted & DG & FH the least refracted intersecting the former in G & H. Draw GH & pr{illeg}|o|duce it both ways till at M & N it occur with CD & EF {illeg} also produced. Now since by my Principles the difference of refraction of the most difform rays is about the 24^{th} or 25^{t} part of their whole refraction, the angle GDH will be about a 25^{t} part of the angle MDH & consequently the subtense GH (w^{ch} is the diameter of the least space into w^{ch} the refracted rays converge) will be about a 25^{t} part of the subtens MH & therefore about a 49^{th} part of y^{e} whole line MN the diameter of the lens; or in round numbers about a fiftith part as I asserted.

This in hast S^{r} from

Yo^{r} Servant

I. Newton.

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