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SrSir
Havinge perused Mr Gregories candid reply, I have thought good to send you
these further considerations upon yethe differences ytthat still are between us. And
first ytthat a well polished plate reflects at yethe obliquity of degrees more truly then direct ones seems to me very certaine. For yethe flat tuberculæ or shallow valleys, such as may be yethe remains of scratches almost worne out will cause yethe least errors in yethe obliquest rays wchwhich fall on all sides the hill, excepting on yethe middle of yethe foreside & bacside of it, ytthat is where yethe hill inclines directly towards or directly from yethe ray: For if yethe ray fall on ytthat section of yethe hill, it's error is in all obliquities just double to yethe hill's declivity: but if it fall on any other part of yethe hill its error is less then double, if it be an oblique ray. & ytthat so much yethe lesse, by how much yethe ray is obliquer; but if it be a direct ray its error is just double to yethe 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 yethe charge may be varied at pleasure in my Telescope will appeare by this figure, where represents yethe great concave, yethe eye-glass, & a Prism of glass or Crystall whose sides & are not flat but spherically convex, so ytthat yethe rays wchwhich come from yethe focus of yethe great concave , may by yethe refraction of yethe first side be reduced into parallelism, & after reflexction from yethe base be made by yethe refraction of yethe next side to converge to yethe focus of yethe eyeglass . The Telescope being thus formed it appears how yethe charge may be altered by varying yethe distances of yethe glasses & speculum.
As for yethe objection ytthat Mr Gregorie's Telescope will be either overcharged or have too small an vision angle of vision &c; I apprehend ytthat yethe difference betweene us lies in limiting yethe aperture of yethe eye-glass. Mr Gregory puts it equall to ytthat of yethe little concave, but I should rather determin it by this proportion: That if a middle point be taken between yethe eye-glass & its focus, yethe apertures of yethe eye-glasse & concave be proportionall to their distances from ytthat point. That is suppose yethe little concave, yethe eye-glass, their common focus or image, & yethe meane distance between & , from yethe extremities of draw & butting on yethe eye-glass at & , & shall be its aperture. The reason of this limitation is ytthat yethe superfluous light wchwhich comes on all sides of yethe speculum to yethe space in wchwhich yethe picture of yethe object is made, may fall besides the eye-glass. For if it should passe through it to yethe eye, it would exceedingly blend those parts of yethe picture wthwith wchwhich tis mixed, and such are those parts of it wchwhich extend themselves beyond yethe lines , . As I remember I said in my former letter ytthat yethe scattering light wchwhich falls on yethe eye-glasse will disturb yethe vision & this is to be understood of any straggling light which comes not from yethe picture, but if it come from yethe picture to yethe eye-glasse yethe disturbance will be much greater so as not to be allowed of. Against yethe first I see no very convenient remedy & against yethe last none but assigning a small aperture to yethe eye-glasse; supposing yethe Telescope is used in yethe day-time or in twy-light or to view yethe Moon or any Starr very neare her or near yethe brighter planets. And if for this reason yethe aperture be be limitted by my rule, the angle of vision will become very small as I affirmed; For instance in ytthat case where Mr Gregory in his Postscript puts it above degrees it will be reduced to lesse then halfe a degree. Yet I confesse there is a way by wchwhich yethe angle of vision may be somthing inlarged but it will not be very considerably unless yethe eye-glass be also deeper charged.
Why I assign a concave wthwith an eye-glasse to magnifie small objects (in Transact:Transactions pag. 3080) & yet an eye-glass without such a concave to magnify yethe image of yethe great concave wchwhich is equivalent to a small object, is because ytthat image doth not require to be magnified so much as an object by a Microscope, & further because yethe angle of yethe penicill of rays wchwhich flow from any point of yethe small object, ytthat yethe object may appear sufficiently luminous, ought to be as great as possible; and a Concave will with equall distinctness reflect yethe rays at a greater angle of yethe penicill then a lens: but in yethe Telescope yethe angles of those penicills are not so great as to transcend yethe limits at wchwhich an eye-glass may wthwith sufficient distinctness refract them, and therefore in these instruments I chose to lay all yethe stress of magnifying upon yethe eye-glasses. In Microscopes also I would lay as much stress of magnifying upon yethe eye-glass as it is well capable of, and yethe excesse only upon yethe concave.
ConcerningeConcering my citation of Mr Gregory against MonsrMonsieur Cassegrain yethe force of it lies onely in yethe inference ytthat Optiq instruments most probably accordingeaccording to M. Cassegrains design have been tryed by reflexion; which I think I might well infer, without having regard to yethe specified figure of yethe speculum wchwhich Mr Gregory there spake of. And therefore I think it cannot be said that I magdet made him speake of Spherick figures where his meaning was of Hyperbolick & Elliptick ones. But if I should be so understood because I put yethe figure of yethe great concave to be sphericall wherever I specify it, I know not why I might not by way of consequence make ytthat interpretation. For it is not probable ytthat any man would attempt HyperbolickeHyperbolick & Elliptick figures of speculums untill yethe event of Sphericall ones had beene first tryed.
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And accordingly yethe tryall of Mr Gregory wthwith Mr Reive was by a sphericall figure. Which tryall although I am now satisfyed that it was made very rudely yet by yethe information wchwhich I had of it when I wrote yethe letter about M. Cassegrains design, I apprehended it to have beene made wthwith 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 yethe Transactions as if it had beene tryed wthwith more accuracy then really it was. And thus much concerning yethe Telescope.
The design of yethe burningeburning speculum appears to me very plausible & worthy of beinge put in practise: What Artists may think of it I know not but yethe greatest difficultie in yethe practise that occurrs to me is to proportion yethe two surfaces so, ytthat yethe force of both may be in yethe same point accordingeaccording to yethe Theory. But perhaps it is not necessary to be so curious, for it seems to me ytthat yethe effect would scarce be sensibly less if both sides should be ground to yethe concave & gage of yethe same tool. I suppose you have receiv'd a letter from me sent last weeke to signify my receipt of yethe books you sent in Queeres &c. It comes now into my mind ytthat 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 wthwith some copies. I must joyn wthwith Mr Gregory in admiring Mr Horrox. And this all at prsentpresent from SrSir
YorYour humble Servant
I. Newton.
Cambridge Apr 9. 1673.
SrSir a Friend here desires to have your judgment in the price of Francis Niceron his Thaumaturgus Opticus printed in Latitn at Paris A.D. 1646.