<33r>

Sr

Havinge perused Mr Gregories candid reply, I have thought good to send you these further considerations upon ye differences yt still are between us. And first yt a well polished plate reflects at ye obliquity of 45 degrees more truly then direct ones seems to me very certaine. For ye flat tuberculæ or shallow valleys, such as may be ye remains of scratches almost worne out will cause ye least errors in ye obliquest rays wch fall on all sides the hill, excepting on ye middle of ye foreside & bacside of it, yt is where ye hill inclines directly towards or \directly/ from ye ray: For if ye ray fall on yt section of ye hill, it's error is in all obliquities just double to ye hill's declivity: but if it fall on any other part of ye hill its error is less then double, if it be an oblique ray. & yt so much ye lesse, by how much ye ray is obliquer; but if it be a direct ray its error is just double to ye declivity & therefore greater in that case. I presume Mr Gregory, if you think it convenient to transmit this to him, will easily apprehend me.

How ye charge may be varied at pleasure in my Telescope will appeare by this figure, where A represents ye great concave, E ye eye-glass, & BCD a Prism of glass or Crystall whose sides BC & BD are not flat but spherically convex, so yt ye rays wch come from G ye focus of ye great concave A, may by ye refraction of ye first side BC be reduced into parallelism, & after reflex|ct|ion from ye base CD be made by ye refraction of ye next side BD to converge to ye focus of ye eyeglass H. The Telescope being thus formed it appears how ye charge may be altered by varying ye distances of ye glasses & speculum.

As for ye objection yt Mr Gregorie's \Telescope/ will be either overcharged or have too small a|n| vision angle of vision &c; I apprehend yt ye difference betweene us lies in limiting ye aperture of ye eye-glass. Mr Gregory puts it equall to yt of ye little concave, but I should rather determin it by this proportion: That if a middle point be taken between ye eye-glass & its focus, ye apertures of ye eye-glasse & concave be proportionall to their distances from yt point. That is suppose AB ye little concave, EF ye eye-glass, GH their common focus or image, & K ye meane distance between GH & EF, from ye extremities of AB draw AK & BK butting on ye eye-glass at F & E, & EF shall be its aperture. The reaso{n} of this limitation is yt ye superfluous light wch comes on all sides of ye speculum AB to ye space GH in wch ye picture of ye object is made, may fall besides {illeg}the eye-glass. For if it should passe through it to ye eye, it would exceedingly blend those parts of ye picture wth wch tis mixed, and such are those parts of it wch extend themselves beyond ye lines AK, BK. As I remember <33v> I said in my former letter yt |ye| scattering light wch falls on ye eye-glasse will disturb ye vision & this is to be understood of any straggling{illeg} light which comes not from ye picture, but if it come from ye picture to ye eye-glasse ye disturbance will be much greater so as not to be allowed of. Against ye first I see no very convenient remedy & against ye last none but assigning{illeg} a small aperture to ye eye-glasse; supposing{illeg} ye Telescope is used in ye day-time or in twy-light or to view ye Moon or any Starr very neare her or near ye brighter planets. And if for this reason ye aperture be be {sic} limitted by my rule, the angle of vision will become very small as I affirmed; For instance in yt {illeg} \case/ where Mr Gregory in his Postscript puts it above 20 degrees it will be reduced to lesse then halfe a degree. Yet I confesse there is a way by wch ye angle of vision may be somthing inlarged but it will not be very considerably unless ye eye-glass be also deeper charged{.}

Why I assign a concave wth an eye-glasse to magnifie small objects (in Transact: pag. 3080) & yet an eye-glass without such a concave to magnify ye image of ye great concave wch is equivalent to a small object, is because yt image doth not require to be magnified so much as an object by a Microscope, & further because ye angle of ye penicill of rays wch flow from any point of ye small object, yt ye object may appear sufficiently luminous, ought to be as great as possible; and a Concave will with equall distinctness reflect ye rays at a greater angle of ye penicill then a lens: but in ye Telescope ye angles of those penicills are not so great as \to/ t{illeg}|r|anscend ye limits at wch an eye-glass may wth sufficient distinctness refract them, and therefore in these instruments I chose to lay all ye str{e}ss of magnifying{illeg} upon ye eye-glasses. In Microscopes also I would lay as much stress of magnifying upon ye eye-glass as it is well capable of, and ye excesse only upon ye concave.

Concerninge {sic} my citation of Mr Gregory against Monsr Cassegrain ye force of it lies onely in ye inference yt Optiq instruments most probably accordinge {sic} to M. Cassegrains design have been tryed by reflexion; which I think I might well infer, without having regard to ye specified figure of ye speculum wch Mr Gregory there spake of. And therefore I think it cannot be said that I mag|d|{illeg}|e|t made him speake of Spherick figures where his meaning was of Hyperbolick & Elliptick ones. But if I should be so understood because I put ye figure of ye great concave to be sphericall wherever I specify it, I know not why I might not by way of consequence make yt interpretation. For it is not probable yt any man would attempt Hyperbolicke {sic} & Elliptick figures of speculums untill ye event of Sphericall ones had beene first tryed.

<34r>

And accordingly ye tryall of Mr Gregory wth Mr Reive was by a sphericall figure. Which tryall although I am now satisfyed {illeg} that it was made very rudely yet by ye information wch I had of it when I wrote ye letter about M. Cassegrains design, I apprehended it to have beene made wth very great diligence & curiosity as I signified in my former letter at large. And this I hope may excuse me for speaking of it in ye Transactions as if it had beene tryed wth more accuracy then really it was. And thus much concerning ye Telescope.

The design of ye burninge {sic} speculum appears to me very plausible & worthy of be{illeg}|in|ge put in practise: What Artists may think of it I know not but ye greatest \difficultie/ in ye practise that occurrs to me is to proportion ye two surfaces so, yt ye force of both may be in ye same point accordinge {sic} to ye Theory. But perhaps it is not necessary to be so curious, for it seems to me yt ye effect would scarce be sensibly less if both sides should be ground to ye concave & gage of ye same tool. I suppose you have {illeg}|r|eceiv'd a letter from me sent last weeke to signify my receipt of ye books you sent in Queeres &c. It comes now into my mind yt when I sent Mr Pitts 4łł for Kinkhuysen he further urged a promise of some copies. When you have opportunity you will oblige me to remember him that his proposall was either 4łł absolutely or 3łł wth some copies. I must joyn wth Mr Gregory in admiring Mr Horrox. And this all at prsent from Sr

Yor humble Servant

I. Newton.

Cambridge Apr 9. 1673.

< insertion from lower down >

Sr a Friend here desires to have your
judgment in the price of Francis Niceron
his Thaumaturgus Opticus printed in Latit|n|
at Paris A.D. 1646.

< text from f 34r resumes >
<34v>

These

For Mr John Collins at
Mr William Austins house, at the
Adam & Eve in Petty France
Westminster
London
2

|Mr Newton of Tellescopes|