Philosophical Transactions of the Royal Society Part 6

__Monsieur Auzout_'s Judgment touching the Apertures of _Object-Gla.s.ses_, and their _Proportions_, in respect of the several _Lengths_ of _Telescopes_._

This Author, observing in a small _French Tract_ lately written by him to a Countryman of his, Monsieur _L' Abbe Charles_; That great _Optick Gla.s.ses_ have almost never as great an _Aperture_ as the small ones, in proportion to what they Magnifie, and that therefore they must be more dim; takes occasion to inform {56} the _Reader_, that he hath found, that the _Apertures_, which _Optick-Gla.s.ses_ can bear with distinctness, are in about a _subduplicate proportion_ to their _Lengths_; whereof he tells us he intends to give the reason and demonstration in his _Diopticks_, which he is now writing, and intends to finish, as soon as his Health will permit. In the mean time, he presents the _Reader_ with a _Table_ of such _Apertures_; which is here exhibited to the Consideration of the Ingenious, there being of this _French_ Book but one Copy, that is known, in _England_.

A _TABLE_ of the _Apertures_ of _Object-Gla.s.ses_.

_The Points put to some of these Numbers denote Fractions._

Lengths of |For excellent| For good |For ordinary | Gla.s.ses. | 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| -------------+-------------+-------------+-------------+

{57}

_Considerations of Monsieur _Auzout_ upon Mr. _Hook_'s New Instrument for Grinding of _Optick-Gla.s.ses_._

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-Gla.s.ses_. Where he premises in _General_ his thoughts touching the working of _Great_ Optick-Gla.s.ses, 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 Gla.s.s 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_ Gla.s.ses 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 Gla.s.ses beyond a certain bigness, so as to finish and polish them all over so well, as _small_ Gla.s.ses; 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 Gla.s.s do always precisely answer to the Brim of this _Ring_, seeing that the position of the Gla.s.s 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 Gla.s.s, that little {59} _Inclination_, that would be necessary for great Gla.s.ses, 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 Gla.s.ses 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 Gla.s.ses 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 Gla.s.ses (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 Gla.s.s, 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 Gla.s.s would have less _Convexity_, and consequently, less difference from a Gla.s.s perfectly plain, than the 7. or 8. part of a Line. And then he leaveth it to be judged, whether a Gla.s.s of such a Length being found, we ought to hope, that a _Turn_ can be firm enough to keep such a piece of Gla.s.s in the same Inclination, so that a _Mandril_ do not recede some Minutes from it: and, though even the Gla.s.s 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 Gla.s.s is worn. All which particulars, he conceives to be very hard in the practice; not to mention, that the weight of the Gla.s.s, 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 Gla.s.s 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 Gla.s.s are not equally worn away, &c. What then, _saith he_, would becom of a Gla.s.s 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 Gla.s.s 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 Gla.s.s 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 Gla.s.s only of that Length. A Gla.s.s 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 Gla.s.s, the _Inclination_, which the _Axis_, or _Mandril_, that bears his Gla.s.s, should have, should be but 16 minuts, and the _Curvity_ of the Gla.s.s 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 Gla.s.s of 300 foot should bear an Eye-gla.s.s 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 Gla.s.ses (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 Gla.s.s. 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 Advertis.e.m.e.nt 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-Gla.s.ses_, or _small_ Optick-Gla.s.ses, 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 Gla.s.s, and to put it under the _Ring_, that so not only the Gla.s.s may be placed more _Horizontally_, and not slide upon the _Cement_, but that the _Sand_ also, and the _Putty_ may stay upon the Gla.s.s.

The _other_ is, that there must be two _Poppetheads_, into which the _Mandril_ must pa.s.s, where the _Ring_ is to be fastned; and the _Mandril_ must be perfectly _Cylindrical_, that so it may advance upon the Gla.s.s 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 Gla.s.ses 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-Gla.s.ses_, 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-gla.s.s of the said _Telescope_, composed of 2 Gla.s.ses, hath no more effect, when it is most charged, than a Gla.s.s of 4 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 22 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-Gla.s.ses_, to endeavor to make them such, that they may bear great _Apertures_ and deep Eye-gla.s.ses; 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 Gla.s.ses, 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 a.s.sign 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}

__M^r. 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 Gla.s.ses_, I thought my self 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_ it self: 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 judg 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 not, as they should see reason. But nothing surprised me so much, as, that he is pleased (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 my self most injurious to that _n.o.ble 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 {65} 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 _Ill.u.s.trious 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 Gla.s.ses_; nor is it more than I have taken notice of my self in this Pa.s.sage of the same _Paragraph_, of which sort are also those difficulties he raises about _Long Gla.s.ses_, 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 farr, 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 Gla.s.s 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 Gla.s.s 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 Gla.s.s 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 Gla.s.s for _Optical Experiments_, than ever I saw come from _Venice_. Next, though it were better, that the thickest part of a long _Object-Gla.s.s_ were exactly in the middle, yet I can a.s.sure Monsieur _Auzout_, that it may be a very {66} 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 bare an _Aperture_, if _Saturn_ or the _Moon_ in the _twilight_, be look'd on with it, of 3 Inches over, and yet the thickest part of the Gla.s.s is a great way out of the middle. And I must take the liberty to doubt, whether ever my _Animadversor_ saw a long Gla.s.s, that was otherwise; as he might presently satisfie himself by a way I could shew him (if he did not know it) whereby the difference of the thickness of the sides might be found to the hundreth part of a Line.

As to the exceeding exactness of the _Figure_ of Long _Object-Gla.s.ses_, '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 Gla.s.ses_ 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 una.s.sisted by an _Engine_, the motion and strength being much more certain and regular. I know very well, that in making a 60. foot Gla.s.s 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 a.s.sured 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 Gla.s.s, and without much _gaging_ will not do any thing 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 _Gla.s.s_ 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 Gla.s.s, does seem most of all rectifie the _Figure_.

As to what he objects, that the Tool does only touch the Gla.s.s in a _Mathematical Circle_; that is true, perhaps, at first, but before the Gla.s.s is wrought down to its true _Figure_, the _Edge_ of the _Tool_ {67} 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 Gla.s.s; nay, if it be necessary (without much trouble, especially in the grinding of longer Gla.s.ses) the whole _Concave Surface_ of the _Tool_ may be made to touch a Gla.s.s.

Besides, that as to the keeping a quant.i.ty of the same sand and Powders of several finesses, according as the gla.s.s wears, the same is possible to be don, as with the same Sand wrought finer by working in the Ordinary way.

The giving the _Inclination_ to the _Mandrils_, is not at all difficult; though perhaps to determine the length exactly which the Gla.s.s so made shall draw, is not so easie: But 'tis no matter, what length the Gla.s.s be off, 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 _steddy_, when once fix'd, is most easie.

As to the Calculation of the propriety of a Gla.s.s 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_ Gla.s.s though its convexity be a smaler sphere than is usual for such a length to be an _Object-Gla.s.s_ 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_ Gla.s.s 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 Ey-gla.s.s shall draw a thousand foot: Which _Invention_, I shall shortly discover, there being, I think, nothing more easie and certain. And if a _Plano-convex_ Gla.s.s can be made of any _Sphere_ between twenty and fourty foot _radius_, so as that both the _Convex_ and _Plain_ side of the Gla.s.s be exactly polish'd of a true _Figure_, I will shortly shew, how therewith may be made a _Telescope_ of any Length, supposing the Gla.s.s free from all kind of _Veins_, or inequality of _Refraction_.

As for the sliding of the Gla.s.s 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_. {68}

And for the Bearing of the _Ring_ against one side of the Gla.s.s only at a time, I cannot see, why _that_ should produce any inequality, since all the sides of the Gla.s.s have successively the same pressure.

His ratiocination concerning a Gla.s.s 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 Gla.s.ses 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-Gla.s.s_ 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 _Gross_ and _Vaporous_ Air neer the Earth, and through the Air over our heads: Which, if he observe the Moon in the _Horizon_, and neer 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 Advertis.e.m.e.nt 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_ Gla.s.ses, 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 conteined as wel in the _Concave_ Tool, as on the _convex_ Gla.s.s. 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 Gla.s.s with a spring or weight, must quickly spoyl the whole; since, if either of the _Mandrils_ will easily yield backwards, the _regularity_ of _all_ will be spoiled: and as to the wrigling and playing of the _Mandril_, I do not at all apprehend it.

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His _Theory_ of _Apertures_, though he seems to think it very authentick, yet to me it seems not so cleer. For, the same Gla.s.s 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-Gla.s.s to look on _Saturn_ with an _Aperture_ of almost 3 inches, and with a single Eye-gla.s.s of 2 inches _double convex_: but, when with the same Gla.s.s I looked on the _Sun_ or _Venus_, I used both a smaller _Aperture_, and shallower _Charge_. And though M. _Auzout_ seems to find fault with the _English_ Gla.s.s of 36 foot, that had an _Aperture_ of but 2 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 Gla.s.ses of that length, that would bear greater _Apertures_, and 'tis not impossible, but his _Theory_ of _Apertures_ may fail in longer Gla.s.ses.

_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. _Auzout_ to enlighten an Object, in what proportion one pleaseth, is by some great _Object-Gla.s.s_, 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 (_saith 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 cleer 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 Gla.s.s it did not sensibly appear so; Whereof he promises to discourse more fully in his {70} _Treatise of the usefulness of great Optick-Gla.s.ses_, where he also intends to deliver several Experiments, by him made, 1. Touching the quant.i.ty of Light, which a Body, that is 10, 15 and 20 times, &c. remoter than _Saturn_, would yet receive from the _Sun_. 2. Touching the quant.i.ty of Light, by which the _Earth_ is illuminated even in the _Eclipses_ of the _Sun_, in proportion of their bigness. 3. Touching the quant.i.ty of Light, which is necessary to burn Bodies: he having found, that not abating the Light, which is reflected by the Surfaces of the Gla.s.s (whereof he confesseth, he doth not yet exactly know the quant.i.ty) there would be necessary about 50 times as much Light, as we have here, for the burning of _Black_ Bodies; and neer 9 times more for the burning of _White_ Bodies, than for the burning of _Black_ ones: and so observing the immediate proportions between these two, for burning bodies of _other_ Colors. Whence (he tells us) he hath drawn some consequences, touching the distance, at which we may hope, to burn Bodies here, by the means of _great Gla.s.ses_ and great _Looking-gla.s.ses_. So that (_saith he_) we must yet be seven times neerer the _Sun_, than we are, to be in danger of being burned by it. Where he mentions, that having given _Instructions_ to certain persons, gon to travel in _Hot Countries_, he hath among other particulars recommended to them, to try by means of great _Burning-gla.s.ses_, with how much less _Aperture_ they will burn _there_, than _here_, to know from thence, whether there by more Light _there_ than _here_, and how much; since this perhaps may be the only means of trying it, supposing, the same matters be used: although the difference of the Air already heated, both in _hot Countries_, and in the _Planets_, that are neerer than we, may alter, if not the quant.i.ty of Light, at least that of the Heat, found there.

_A further Account, touching Signor _Campani_'s Book and Performances about _Optick-gla.s.ses_._

In the above-mentioned _French_ Tract there is also conteined M. _Auzout's_ Opinion of what he had found New in the _Treatise_ of Signor _Campani_, which was spoken of in the first _Papers_ of these _Transactions_, concerning both the Effect of the _Telescopes_, contrived after a peculiar way by the said _Campani_ at _Rome_, and {71} his New Observations of _Saturn_ and _Jupiter_, made by means thereof.