Mr. Hook's Answer to Monsieur Auzout's Considerations, in a Letter to the Publisher of These Transactions

Mr. Hook's Answer to Monsieur Auzout's Considerations, in a Letter to the Publisher of these Transactions. SIR, Together with my most hearty thanks for the favour you were pleased to do me, in sending me an Epitome of what had been by the ingenious Monsieur Auzout animadverted on a description, I had made of an Engine for grinding spherical Glasses, I thought myself obliged, both for your satisfaction, and my own Vindication, to return you my present thoughts upon those Objections. The chief of which seems to be against the very Proposition itself: For it appears, that the Objector is somewhat unsatisfied, that I should propound a thing in Theory, without having first tried the Practicableness of it. But first, I could wish that this worthy Person had rectified my mistakes, not by speculation, but by experiments. Next, I have this to answer, that (though I did not tell the Reader so much, to the end that he might have the more freedom to examine and judge of the contrivance, yet) it was not meer Theory I propounded, but somewhat of History and matter of Fact: For, I had made trials, as many as my leisure would permit, not without some good success; but not having time and opportunity enough to prosecute them, I thought it would not be unacceptable to such, as enjoyed both, to have a description of a way altogether New, and Geometrically true, and seemingly, not unpracticable, whereof they might make use, or nor, as they should see reason. But nothing surprised me so much, as, that he is pleaded (after he had declared it a fault, to write this Theory, without having reduced it to practice) to lay it, as he seems to do, in one place of his book, p. 22 upon the Royal Society. Truly, Sir, I should think myself most injurious to that Noble Company, had I not endeavoured, even in the beginning of my Book, to prevent such a misconstruction. And therefore I cannot but make this interpretation of what Monsieur Auzout saith in this particular, that either he had not so much much of the Language wherein I have written, as to understand all what was said by me, or, that he had not read my Dedication to the Royal Society, which if he had done, he would have found, how careful I was, that that Illustrious Society should not be prejudiced by my Errors, that could be so little advantaged by my Actions. And indeed, for any man to look upon the matters published by their Order or Licence, as if they were Their Sense, and had Their Approbation, as certain and true, 'tis extremely wide of their intentions, seeing they, in giving way to, or encouraging such publications, aim chiefly at this, that ingenious conceptions, and important philosophical matter of Fact may be communicated to the learned and enquiring World, thereby to excite the minds of men to the examination and improvement thereof. But, to return; As to his Objections against the Matter, I do find that they are no more against mine, than any other way of Grinding Glasses; nor is it more than I have taken notice of myself in this Passage of the same Paragraph, of which sort are also those difficulties he raises about Long Glasses, which are commonly known to such; as are conversant in making them. It would be convenient also (these are my words) and not very chargeable, to have four or five several Tools: One, &c. And, if curiosity shall ever proceed so far, one for all lengths, between 1000. and 10000. foot long; for indeed, the Principle is such, that supposing the Mandrils well made, and of a good length, and supposing great care be used in working and polishing them, I see no reason, but that a Glass of 1000. nay, 10000. foot long may be made, as well as one of 10. For, the reason is the same, supposing the Mandrils and Tools be made sufficiently strong, so that they cannot bend; and supposing also, that the Glass out of which they are wrought, be capable of so great a regularity in its parts, as to its Refraction. But next, I must say that his Objections to me, seem not so considerable, as perhaps he imagines them. For; as to the possibility of getting Plates of Glass thick and broad enough without veins, I think that not now so difficult here in England, where I believe is made as good, if not much better Glass for Optical Experiments, than ever I saw come from Venice. Next, though it were better, that the thickest part of a long Object-Glass were exactly in the middle, yet I can assure Monsieur Aubert, that it may be a very good. good one, when it is an Inch or two out of it. And I have a good one by me at present, of 36. foot, that will bear an Aperture, if Saturn or the Moon in the twilight, be look'd on with it, of 3½ Inches over, and yet the thickest part of the Glass is a great way out of the middle. And I must take the liberty to doubt, whether ever my Animadverfer saw a long Glass, that was otherwise; as he might presently satisfy himself by a way I could shew him (if he did not know it) whereby the difference of the thicknesses of the sides might be found to the hundredth part of a Line. As to the exceeding exactness of the Figure of Long Object-Glasses, 'tis not doubted, but that it is a matter difficult enough to be attained any way: but yet, I think, much easier by Engine, than by Hand; and of all Engines, I conceive, none more plain and simple, than that of a Mandril. And for making Spherical Glasses by an Engine, I am apt to think, there hardly can be any way more plain, and more exact, than that which I have described; wherein there is no other motion, than that of two such Mandrils, which may be made of sufficient strength, length, and exactness, to perform abundantly much more, than I can believe possible to be done otherwise than by chance, by a man's hands or strength unassisted by an Engine, the motion and strength being much more certain and regular. I know very well, that in making a 60. foot Glass by the strength of the hand, in the common way, not one of ten that are wrought, will happen to be good, as I have been assured by Mr. Reeves; who, I am apt to think, was the first that made any good of that length. For the Figure of the Tool in that way is presently vitiated by the working of the Glass, and without much gaging will not do anything considerable. Besides, the strength of a man's hands, applied to it for the working and polishing of it, is very unequal, and the motions made, are very irregular; but in the way, I have ventured to propose, by Mandrils, the longer the Glass and Tool are wrought together, the more exact they seem to be, and if all things be ordered, as they should be, the very polishing of the Glass, does seem most of all to rectifie the Figure. As to what he objects, that the Tool does only touch the Glass in a Mathematical Circle; that is true, perhaps, at first, but before the Glass is wrought down to its true Figure, the Edge of the Tool will will be worn or grownd away, so as that a Ring of an inch broad may be made to touch the Spherical Surface of the Glass; nay, if it be necessary (without much trouble, especially in the grinding of longer Glasses) the whole Concave Surface of the Tool may be made to touch a Glass. Besides, that as to the keeping a quantity of the same Sand and Powders of several finesses, according as the glass wears, the same is possible to be done, as with the same Sand wrought finer by working in the Ordinary way. The giving the Inclination to the Mandrills, is not at all difficult; though perhaps to determine the length exactly which the Glass so made shall draw, is not so easy. But 'tis no matter, what length the Glass be of, so it be made good, whether 60 or 80 foot, or the like. Nor is it so very difficult, to lay them both in the same Plain. And to keep them steady, when once fix'd, is most easy. As to the Calculation of the propriety of a Glass of a thousand foot, perhaps for that particular Length, I had not, nor have as yet calculated, that the Convexity of one of eighteen inches broad, will not be above a seventh part of a Line. But it does not thence follow, that I had not considered the difficulties, that would be in making of it. For, I must tell him, that I can make a Plano convex Glass, though its convexity be of a smaller sphere than is usual for such a length, to be an Object-Glass of about 150 foot in Length, nay of 300 foot, and either longer or shorter, without at all altering the convexity. So that, if he will by any Contrivance he hath, give me a Plano-convex Glass of 20, or 40 foot Diameter, without Veins, and truly wrought of that Figure, I will presently make a Telescope with it, that with a single Eyeglass shall draw a thousand foot: Which Invention, I shall shortly discover, there being, I think, nothing more easy and certain. And if a Plano-convex Glass can be made of any Sphere between twenty and forty foot radius, so as that both the Convex and Plain side of the Glass be exactly polish'd of a true Figure, I will shortly shew, how therewith may be made a Telescope of any Length, supposing the Glass free from all kind of Veins, or inequality of Refraction. As for the sliding of the Glass upon the Cement, I see no reason at all for it, at least in the Cement, I make use of, having never observed any such accident in hard Cement. And for the Bearing of the Ring against one side of the Glass only at a time, I cannot see, why that should produce any inequality, since all the sides of the Glass have successively the same pressure. His ratiocination concerning a Glass of 300 foot, is much the same with the former, about the difficulty of working a true surface of a convenient figure; which how considerable both that and his Conclusion thereupon (videl. That we are not to expect Glasses of above 300 or 400 foot long at most, and that neither Matter nor Art will go so far) is, may be judged from what I have newly told you of making any Object-Glass of any Length. And for his good wishes, that those, who promise to make him see Plants or Animals in the Moon (of which I know not any, that has done so, though perhaps there may be some, notwithstanding his Objections, that do not yet think it impossible to be done) had considered; what a Man is able to see with his bare Eye at 60 Leagues distance: I cannot but return him my wishes, that he would consider the difference between seeing a thing through the Grass and Vaporous Air near the Earth, and through the Air over our heads: Which, if he observe the Moon in the Horizon, and near the Zenith with a Telescope, he will experimentally find; and, having done so, he will perhaps not be so dissident in this matter. Concerning his Advertisement to such, as publish Theories, I find not, that he hath made use of it in his own case. For, in his Theory about Apertures he seems to be very positive, not at all doubting to rely upon it, vid. that the Apertures must be thus and thus in great Glasses, because he had found them so or so in some small ones. For his Proposal of amendments of some inconveniencies in this way, I return him my thanks; but as to his first I believe, that the matter may be contained as well in the Concave Tool, as on the convex Glass. And as to that of 2 Poppet-heads, I do not well understand it, if differing from mine; and the keeping of the Tool upon the Glass with a spring or weight, must quickly spoil the whole; since, if either of the Mandrils will easily yield backwards, the regularity of all will be spoiled: and as to the wriggling and playing of the Mandril, I do not at all apprehend it. His Theory of Apertures, though he seems to think it very authentick, yet to me it seems not so cleer. For, the same Glass will endure greater or lesser Apertures, according to the lesser or greater Light of the Object: If it be for the looking on the Sun or Venus, or for seeing the Diameters of the Fix'd Stars, then smaller Apertures do better; if for the Moon in the daylight, or on Saturn, or Jupiter, or Mars, then the largest. Thus I have often made use of a 12 foot-Glass to look on Saturn with an Aperture of almost 3 inches, and with a single Eye-glass of 2 inches double convex: but, when with the same Glass I looked on the Sun or Venus, I used both a smaller Aperture, and shallower Charge. And though M. Auxout seems to find fault with the English Glasses of 36 foot, that had an Aperture of but 2½ inches French, as also, with a 60 foot Tube, used but with an Aperture of 3 inches yet I do not find, that he hath seen Glasses of that length, that would bear greater Apertures, and 'tis not impossible, but his Theory of Apertures may fail in longer Glasses. Of a means to illuminate an Object in what proportion one pleaseth; and of the Distances requisite to burn Bodies by the Sun. One of the means used by M. Auxout to enlighten an Object, in what proportion one pleaseth, is by some great Object-Glasses, by him called a Planetary one, because that by it he shews the difference of Light, which all the Planets receive from the Sun, by making use of several Apertures, proportionate to their distance from the Sun, provided that for every 9 foot draught, or thereabout, one inch of Aperture be given for the Earth. Doing this, one sees (faith he) that the Light which Mercury receives, is far enough from being able to burn Bodies, and yet that the same Light is great enough in Saturn to see clear there, seeing that (to him) it appears greater in Saturn, than it doth upon our Earth, when it is overcast with Clouds: Which (he adds) would scarce be believed, if by means of this Glass it did not sensibly appear so: Whereof he promises to discourse more fully in his Treatise.