Considerations of Monsieur Auzout upon Mr. Hook's New Instrument for Grinding of Optick-Glasses

Considerations of Monsieur Auzout upon Mr. Hook's New Instrument for Grinding of Optick-Glasses. In the above-mentioned French Tract, there are, besides several other particulars, to be represented in due place, contained some Considerations of Monsieur Auzout upon Mr. Hook's New Engine for grinding Optick-Glasses. Where he premises in General his thoughts touching the working of Great Optick-Glasses, and that by the help of a Turn lathe; affirming first of all, that not only the Engin is to be considered for giving the Figure, but the Matter also, which ought to be brought to greater perfection, than it hath been hitherto. For, he finds it not so easie (at least, where he is) to procure Great pieces of Glass without Veins, and other faults, nor to get such, as are thick enough without Blebs; which, if they be not, they will yield to the pressure and weight, either when they are fitted to the Cement, or wrought. Secondly, He finds it difficult to work these Great Glasses of the same thickness, which yet is very necessary, because, that the least difference in Figures so little convex, can put the Center out of the Middle, 2 or 3 Inches; and if they be wrought in Moulds, the length of time, which is required to wear and to smooth them, may spoil the best Mould, before they be finished. Besides, that the strength of Man is so limited, that he is unable to work Glasses beyond a certain bigness, so as to finish and polish them all over so well, as Small Glasses; whereas yet, the bigger they are, the more compleat they ought to be: And if any weight or Engine be used to supply strength, there is then danger of an unequal pressure, and of wearing away the Engines; In the mean time, the preciseness and delicateness is greater, greater than can easily be imagined. Wherefore he could never, having some experience of this preciseness, conceive, that a Turn-lathe, wherein must be two different, and in some manner contrary motions, can move with that exactness and steadiness, that is required, especially, for any considerable length of time. Having premised this, he discourses upon Mr. Hook's Turne, intimating first of all, that he was impatient to know what kind of Turne this was, imagining, that it had been tried, and had succeeded, as coming from a Society that professeth, they publish nothing but what hath been maturely examin'd. But that he was much surprised when he saw the Micrography of Mr. Hook, and found there, that his Engine was published upon a new Theory, without having made any Experiment, though that might have been made with little charge and great speed; expense of Money and Time being the onely thing, that can excuse those who in matter of Engines impart their inventions to the publick, without having tried them, to excite others to make trial thereof. Whereupon he proposes some difficulties, to give the Inventor occasion to find a way to remove them. He affirms therefore, that though it be true in the Theory, that a Circle, whose Plain is inclined to the Axis of the Sphere by an Angle, whereof half the Diameter is the Sine, and which touches the Sphere in its Pole, will touch in all its parts a spherical Surface, that shall turn upon that Axe. But that it is true also, that that must be but a Mathematical Circle, and without Breadth, and which precisely touches the Body in its middle: Whereas in the practice, a Circle capable to keep Sand and Putty, must be of some breadth; and he knows not whether we can find such a dexterity of keeping so much of it, and for so long a time, as needs, upon the Brim of a Ring that is half an Inch broad. He adds, that it is very difficult to contrive, that the middle of the Glass do always precisely answer to the Brim of this Ring, seeing that the position of the Glass does always change a little in respect of the Ring, in proportion as 'tis worn, and as it must be pressed because of its inclination. He believes it also very hard, to give to the Axis or to the Mandril, which holds the Glass, that little Inclination, Inclination, that would be necessary for great Glasses, and to make the two Mandrils to have one and the same Plain, as is necessary. And, having done all this, he persuades himself, that it is exceeding difficult, if not impossible, for two contrary motions, where so many pieces are, to rest for a long time steady and firm, as is requisite for the not swerving from it a hair's thickness, since less than that can change all. He goes on, and, seeing that this Inventor speaks of Glasses of a thousand, & ten thousand foot, which he supposed not impossible to be made by this Engine, discourses of what is necessary for the making Glasses of such bigness; which he believes this Inventor may perhaps not have thought of. Wherefore he affirms, that if the Table, made by himself for the Apertures of Glasses (which is that, that is above delivered) be continued unto a thousand feet, by taking always the Subduplicate proportion of Lengths, it will be found, that for pretty good ones, the Aperture must be of 15. Inches; for good ones, more than 18. and for such as are excellent, more than 21. Inches: whence it may be judged, what piece of Glass, and of what thickness it must be, to resist the working. But he proceeds to speak of the Inclination, which the Mandril must have upon the Plain of the Ring, when the Ring should have 10. or 12 Inches; and finds, that it would make but 6. or 7. minutes of inclination, and that a Glass would have less Convexity, and consequently, less difference from a Glass perfectly plain, than the 7. or 8. part of a Line. And then he leaveth it to be judged, whether a Glass of such a Length being found, we ought to hope, that a Turn can be firm enough to keep such a piece of Glass in the same Inclination, so that a Mandril do not recede some Minutes from it: and, though even the Glass could be fastened perfectly perpendicular to the Mandril, that these two Mandrils could be put in one and the same place, & that that little Inclination, which is requisite, could be given, and the Mandril be continued to be pressed in that same Inclination, according as the Glass is worn. All which particulars, he conceives to be very hard in the practice; not to mention, that the weight of the Glass, that should be inclined to the Horizon, as 'tis represented by Mr. Hook, would make it slide upon the Cement, and so chance change the Center; and that the Glass is not pressed at the same time by the Ring but in one part on the side, vid. about a fourth; and that the parts of the Glasses are not equally worn away, &c. What then, saith he, would become of a Glass of 1000 feet, which, according to the said Table, would have more than four feet, or four feet and nine inches, or five feet, seven inches Aperture, and of which the Ring, though it were two feet nine inches, would have but one minut of Inclination, and the Glass of 5 feet Aperture would have but 4 minutes, and the curvity of it would be less than the hundredth part of a Line. But, saith he, let us consider, only a Glass of 300 foot, to see what is to be hoped of that, and to know at least the difficulty, to be met with in making a Glass only of that Length. A Glass then of 300 foot, according to his Table, must have more than 8 inches Aperture, which maketh but 16 minutes of its Circle, and it should have more than 11 inches, if it be an excellent one. If Mr. Hook (adds he) did use but his Ring of 6 inches, which he would use from twelve to an hundred foot Glass, the Inclination, which the Axis, or Mandril, that bears his Glass, should have, should be but 16 minutes, and the Curvity of the Glass would be less than the eighth part of a Line, and if he should use a bigger; the Inclination would be proportionable. Whence it may be judged (continues he) that we are yet very far from seeing Animals &c. in the Moon, as Monsieur Des Cartes gave hope, and Mr. Hook despairs not of. For, he believes by what he knows of Telescopes, that we are not to look for any above 300 or 400 foot at most; and he fears, that neither Matter nor Art will go even so far. When therefore (saith he) a Glass of 300 foot should bear an Eye-glass of 6 inches (which would appear wonderful) it would magnifie but 600 times in Diameter, that is, 360000 times in Surface: but suppose, that such could be made, as would magnifie a 1000 times in Diameter, and 1000000 of times in Surface, admitting there were but 60000 leagues from the Earth to the Moon, and that the smallness of the Aperture of the Glasses (which yet would diminish the Light more than 36 times), and the obstacle of the Air were not considered, we should not see. See the Moon, but as if we were a 100, or at least, 60 leagues distant from her without a Glass. He here wishes, that those that promise to make us see Animals and Plants in the Moon, had thought on what our naked Eyes can make us discern of such Objects, only at 10 or 12 leagues distance. But this he would not have understood as a discouragement from searching with all care and earnestness after the means of making long Telescopes, or of facilitating the working thereof; but only as an Advertisement to those, who light upon the Theory of any Engine, not to expose it presently as possible and useful, before they have tried it, or if it have succeeded in small, not to endeavour to persuade, that it will also succeed in great. As it may happen (faith be) that the Engin of Mr. Hook may, by using all necessary precautions, succeed in the making of Eye-Glasses, or small Optick-Glasses, but not in making great ones; as we see, that an instrument composed of two Rulers, where-with are traced Portions of Circles, succeeds well enough in small, but when there is no more than half a Line, a quarter of a Line, or less convexity, it will be no longer just at all, as he tells us to have made the proof of it in Circles drawn by the means of one of these Instruments, made by one of the best Workmen in his time, who, whilst he lived, esteemed them above price, although they be not just; as others and myself (faith be) have by tryal found, when we endeavoured to make Moulds by their means, &c., as those, who by the like Instrument laboured to trace portions of Circles of 80 or 100 foot, &c. Diameter, can attest. But, notwithstanding all this, he hath thought upon two or three things, which he thinks may remedy some inconveniences of Mr. Hook his Turn. The first is, to invert the Glass, and to put it under the Ring, that so not only the Glass may be placed more Horizontally, and not slide upon the Cement, but that the Sand also, and the Putty may stay upon the Glass. The other is, that there must be two Poppetheads, into which the Mandril must pass, where the Ring is to be fastned; and the Mandril must be perfectly Cylindrical, that so it may advance upon the Glass as it wears away by the means of its weight; or by the means of a spring, pressing it, without wrigling from one place to another, as it would presently happen in the fashion, as the Turn is composed. For, when the Glasses do wear, especially when they are very convex, it cannot be otherwise, but the Mandril will play and wrigle, before the Sorue be made firm. But he doubts, whether all can be remedied, which he leaves to the industry of Mr. Hook, considering what he saith in the Preface of his Micrography, touching a Method, he knows, of finding out as much in Mechanicks, as can be found in Geometry by Algebra. Besides this, he taketh notice, that most of those that medle with Optick-Glasses, give them not as much Aperture, nor charge them so deep as they ought. And he instances in the Telescope, which His Majesty of Great Britain presented the Duke of Orleans with, videl. that it did bear but 2 inches, and 9 lines French, for its greatest Aperture, though there be 5 or 6 lesser Apertures, of which it seems (saith he) the Artificer would have those, that use it, serve themselves more ordinarily, than of the greatest; which conveys but almost half as many Rays as it should do, according to his Calculation, which is, as 9 to 16; Whereas, according to his Table of Apertures, an excellent 35 foot Telescope should bear 4 inches Aperture in proportion to excellent small ones. He notes also, that the Eye-glass of the said Telescope, composed of 2 Glasses, hath no more effect, when it is most charged, than a Glass of 4½ inches; which makes it magnifie not a 100 times. And he finds by Mr. Hook, that he esteems a Telescope made in London of 60 feet, (which amount to about 57 feet of France, the foot of France being to that of England as about 15 to 16) because it can bear at least 3 English inches Aperture, and that there are few of 30 feet, that can bear more than 2 inches, (which is but 22½ Lines French) although he (M. Auzout) gives no less Aperture, than so, to a 15 foot-Telescope, and his of 21 feet hath ordinarily 2 Inches, 4 Lines, or 2 inches, 6 Lines Aperture. This Discourse he Concludeth with exhorting those, that work Optick-Glasses, to endeavor to make them such, that they may bear great Apertures and deep Eye-glasses; seeing it is not the length that gives esteem to Telescopes; but on the contrary renders them less estimable, by reason of the trouble accompanying panying them, if they perform no more, than shorter ones. Where, by the by, he takes notice, that he knows not yet, what Aperture Signor Campani gives to his Glasses, seeing he hath as yet signified nothing of it; but that the small one, sent by him to Cardinal Antonio, hath no more Aperture, than ordinary ones ought to have. He promises withall, that he will explicate this way in his Treatise of the usefulness of Telescopes, where he intends to assign the Bigness of the Diameter of all the Planets, and their proportion to that of the Sun; as also, that of the Stars, which he esteems yet much less, than all those have done, that have written of it hitherto; not believing, that the Great Dog, which appears to be the fairest Star of the Firmament, hath 2 Seconds in Diameter, nor that those, which are counted of the sixth Magnitude, have 20 thirds; nor thinking, that all the Stars, that are in the Firmament, do enlighten the Earth as much as a Luminous Body of 20 seconds in Diameter would do, or, because there is but one half of them at the same time above our Horizon, as a Body of 14 seconds in Diameter; and as the 18432th part of the Sun would enlighten us, or as the Sun would do, if we were 14 times more distant from it, than Saturn, and 137 times further, than the Earth: Which, he saith, would not be credible, if he did not endeavor to evince it both by Experience and Reason. And he doubts not, but that Venus, although she sends us no Light but what is reflected, does sometimes enlighten the Earth more, than all the Stars together. Yet he would not have us imagine, from what he hath spoken of the smallness of the Stars, that Telescopes do not magnifie them by reason of their great distance, as they do Planets; for this he judgeth a Vulgar Error, to be renounced. Telescopes magnifie the Stars (saith he) as much in proportion, as they do all other Bodies, seeing that the demonstration of their magnifying is made even upon Parallel rays, which do suppose an infinite distance; though the Stars have none such: And if the Telescopes did not magnifie the Stars, how could they make us see some of the fiftieth, and it may be some of the hundredth, and two hundredth Magnitude, as they do, and as they would shew yet much lesser ones, if they did magnifie more?