Did Newton write down his process of building a reflector telescope? Even with modern knowledge and technology, building one is no easy task so I'm curious of exactly what Newton did.
We know relatively little about Newton's original model from 1668, modern versions draw lineage from the improved 1671 version. There is a record with its detailed description, with some comments on construction, although not the entire "process of building". Here is from Newton's telescope by Mills and Turvey.
"The prime source of information on this improved instrument must be the formal description drawn up by Oldenburg (19), sent to Newton (20), and carefully checked by him (21) before its dispatch to Huygens (22). The Latin text is accompanied by the illustration shown here as Plate lJ. The most obvious refinement is the use of a substantial wooden ball to provide universal adjustment. This telescope is stated to contain a 2 in. diameter primary speculum (18, 23) with a focal length quoted as 6 1/3 in. in the original correspondence and as about 6 1/4 in. in the Opticks. It seems likely that Newton made a new, thicker, speculum - probably as the best of a pair - rather than attempt to repolish the defective mirror(s) made for his first telescope. A description based on Oldenburg (19) appeared in the Philosophical Transactions for 25 March 1672 (24), but is accompanied by an engraving differing in a number of respects from the drawing with the above manuscript. However, engravings of this period are notoriously inexact. A version obviously redrawn from the Phil. Trans. (24) appears in Hutton's abridgment of 1809 (25).
Mills and Turvey have photographs of the model, and facsimile of drawings from the original sources. They also review the description and Newton's remarks on construction in detail. For example, Newton remarked that in the second model "In that metall which I sent to London (i.e. the second telescope) there was noe Arsenick, but a small proportion of silver: as I remember is in 3 ounces of metall". Much later, in Opticks, he also revealed his method for polishing the lenses:
"I had two round Copper Plates, each six Inches in Diameter, the one convex, the other concave, ground very true to one another. On the convex I ground the Object-Metal or Concave which was to be polish'd, 'till it had taken the Figure of the Convex and was ready for a Polish. Then I pitched over the convex very thinly, by dropping melted Pitch upon it, and warming it to keep the Pitch soft, whilst I ground it with the concave Copper wetted to make it spread eavenly all over the convex. Thus by working it well I made it as thin as a Groat, and after the convex was cold I ground it again to give it as true a Figure as I could. Then I took Putty which I had made very fine by washing it from all its grosser Particles, and laying a little of this upon the Pitch, I ground it upon the Pitch with the concave Copper, till it had done making a Noise; and then upon the Pitch I ground the Object-Metal with a brisk motion, for about two or three Minutes of time, leaning hard upon it. Then I put fresh Putty upon the Pitch, and ground it again till it had done making a noise, and afterwards ground the ObjectMetal upon it as before. And this Work I repeated till the Metal was polished, grinding it the last time with all my strength for a good while together, and frequently breathing upon the Pitch, to keep it moist without laying on any more fresh Putty."