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 giveing 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 (as least, where he is) to procure Great pieces of Glass without Veins, and other faults, nor to get such, as are thick enough without Blebbs; 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 Midle, 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 Engine; In the mean time, the preciseness and delicateness is
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 steddiness, that is required, especially, for any considerable length of time.
Having premised this, he discourses upon Mr. Hook his 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 meer Theory, without having made any Experiment, though that might have been made with little charge and great speed; expence 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, 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 exceedingly difficult, if not impossible, for two contrary motions, where so many pieces are, to rest for a long time steddy and firm, as is requisite for the not swarving 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 bignesses; 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 endure 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 fastned perfectly perpendicular to the Mandril, that those two Mandrils could be put in one and the same Plain, & 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
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 Glass are not equally worn away, &c. What then, saith he, would becom of a Glass of 10000 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 minuts, and the curvity of it would be less than the eight 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 minuts 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 minuts, 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.