Part 6

Lengths of |For excellent| For good |For ordinary | Glasses. | ones. | ones. | ones. | Feet, Inches.|Inch, Lines.|Inch, Lines.|Inch, Lines.| | | | | 4| 4.| 4| 3| 6| 5.| 5| 4| 9| 7| 6| 5| 1 0| 8.| 7| 6| -------------|-------------|-------------|-------------| 1 6| 9| 8.| 7| 2 0| 11| 10| 8| 2 6|1 0| 11| 9| 3 0|1 1|1 0| 10| -------------|-------------|-------------|-------------| 3 6|1 2.|1 1| 11| 4 0|1 4|1 2|1 0| 4 6|1 5|1 3|1 .| 5 0|1 6|1 4|1 1.| -------------|-------------|-------------|-------------| 6 |1 7.|1 5|1 2| 7 |1 9|1 6|1 3| 8 |1 10|1 8|1 4| 9 |1 11.|1 9|1 5| -------------|-------------|-------------|-------------| 10 |2 1|1 10|1 6| 12 |2 4|2 0|1 8| 14 |2 6|2 2|1 9.| 16 |2 8|2 4|1 11.| 18 |2 10|2 6|2 1| 20 |3 0|2 7|2 2.| -------------|-------------|-------------|-------------| 25 |3 4|2 10|2 4.| 30 |3 8|3 2|2 7| 35 |4 0|3 4.|2 10| 40 |4 3|3 7|3 .| -------------|-------------|-------------|-------------| 45 |4 6|3 10|3 2.| 50 |4 9|4 0|3 4.| 55 |5 0|4 3|3 6.| 60 |5 2|4 6|3 8.| -------------|-------------|-------------|-------------| 65 |5 4|4 8|3 10| 70 |5 7|4 10|4 .| 75 |5 9|5 0|4 2.| 80 |5 11|5 2|4 5| -------------|-------------|-------------|-------------| 90 |6 4|5 6|4 7.| 100 |6 8|5 9|4 10| 120 |7 5|6 5|5 3| 150 |8 0|7 0|5 11| -------------|-------------|-------------|-------------| 200 |9 6|8 0|6 9| 250 |10 6|9 2|7 8.| 300 |11 6|10 0|8 5| 350 |12 *6.|10 9|9 0| 400 |13 4|11 6|9 8| -------------+-------------+-------------+-------------+

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_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 {58} 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 {59} _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 {60} 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.

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 smalness 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 {61} 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 (_saith he_) 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, wherewith 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 my self (_saith he_) have by tryal found, when we endeavoured to make _Moulds_ by their means, & 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 inconveniencies 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, {62} 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 _Scrue_ be made firm.

But he doubts, whether all can be remedied, which he leavs 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 {63} accompanying 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 18432^{th} 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 _hundreth_, and _twohundreth_ Magnitude, as they do, and as they would shew yet much lesser ones, if they did magnifie more? {64}

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__M^r. Hook_'s Answer to Monsieur _Auzout_'s Considerations, in a Letter to the Publisher of these _Transactions_._

_SIR_,